Answer:
15 students visited both museums.
Step-by-step explanation:
Operations With Sets
Sets are a collection of elements. Some sets have elements in common with other sets. These elements are said to be in their intersection. If we know the number of elements in the set A and in the set B, and also the total number of elements in both sets, we can say
[tex]N(A\bigcup B)=N(A)+N(B)-N(A\bigcap B)[/tex]
where [tex]N(A\bigcup B)[/tex] is the total number of elements, N(A) and N(B) are the number of elements in A and B respectively, and [tex]N(A\bigcap B)[/tex] is the number of elements in their intersection. If we wanted to know that last number, then we isolate it
[tex]N(A\bigcap B)=N(A)+N(B)-N(A\bigcup B)[/tex]
Let A= Students who visited the museum of natural history
B=Students who visited the natural air and space museum
We know [tex]N(A)=18, N(B)=22, N(A\bigcup B)=25,\ so[/tex]
[tex]N(A\bigcap B)=18+22-25=15[/tex]
Answer: 15 students visited both museums.
Note: We are assuming no students didn't visit at least one museum
The set theory in Mathematics implies that 15 out of the 25 students must have visited both the Museum of Natural History and Natural Air and Space Museum, since these students are counted twice when you add the students who visited each museum separately.
Explanation:The problem asked is: When 25 students went to Washington DC, 18 of them visited the Museum of Natural History and 22 visited the Natural Air and Space Museum. How many students visited both museums?
To answer this, we need to understand the concept of the set theory in Mathematics. It helps us know the total number of students who visited both museums: we subtract the total number of students from the sum of students who visited each museum separately.
So, if we add those who visited the Museum of Natural History (18 students) and those who went to the Natural Air and Space Museum (22 students), we get 40. But we know there were only 25 students in total, implying that 15 students must have visited both museums since these students are counted twice in our sum. Therefore, 15 students visited both museums.
Learn more about Set Theory here:https://brainly.com/question/27333813
#SPJ12
Which numerical setup can be used to calculate the heat energy required to completely melt 100 grams?
Answer:
Multiplying the mass of ice by the specific latent heat of fusion of ice
Step-by-step explanation:
The heat energy required to completely melt 100 grams can be calculated by multiplying the mass of ice (100g) by the specific latent heat of fusion of ice (336J/g)
A postal worker counts the number of complaint letters received by the United States Postal Service in a givenday. Identify the type of data collected.
A) quantitative
B) qualitative
Answer:
A) quantitative
Step-by-step explanation:
A data that can be counted or expressed numerically constitute quantitative data. Quantitative data collection method is capturing statistical data in numbers, figures, or values. Quantitative data collection usually answered the questions of “how many?”, "how much?" and “how often?” are the occurrence of a particular data. These questions are quantitative data collection methods based on numbers and mathematical calculations. Quantitative data collection methods are based on random sampling and structured data collection. Some of the quantitative data collection methods are surveys, questionnaires, quizzes, interviews and direct observation.
Robert's dog is 4 years older than Karen's cat. In 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. How old is Robert's dog right now?
Answer:
5.5 years old.
Step-by-step explanation:
Let D represent present age of Robert's dog and C represent present age of Karen's cat.
We have been given that Robert's dog is 4 years older than Karen's cat. We can represent this information in an equation as:
[tex]D=C+4...(1)[/tex]
We are also told that in 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. After 3 years age of dog and cat would be [tex]D+3[/tex] and [tex]C+3[/tex] respectively.
We can represent this information in an equation as:
[tex]D+3+C+3=13...(2)[/tex]
From equation (1), we will get:
[tex]C=D-4[/tex]
Upon substituting this value in equation (2), we will get:
[tex]D+3+D-4+3=13[/tex]
Combine like terms:
[tex]2D+2=13[/tex]
[tex]2D+2-2=13-2[/tex]
[tex]2D=11[/tex]
[tex]\frac{2D}{2}=\frac{11}{2}[/tex]
[tex]D=5.5[/tex]
Therefore, Robert's dog is 5.5 years old right now.
This activity will help you meet these educational goals:
You will create a function to model a fireworks show and examine the attributes of the function.
You’re in charge of planning a fireworks show. The company you hire proposes using fireworks called mortar fireworks. These fireworks are placed in a tube that sits on the ground or a flat surface and are shot from the tube with an initial velocity that propels them into the sky.
Mortar fireworks have two fuses that are lit at the same time. The first fuse burns fastest and causes the initial force that launches the firework into the sky. The second fuse takes longer to burn. When the second fuse reaches the middle of the firework, the firework explodes and we see the light show in the sky. This second fuse does not add any extra propulsion to the firework while it’s in the air.
You plan to have the company light the fireworks from the ground. Based on information provided by the company, you’ve determined that the fireworks will have an initial velocity of 192 feet/second.
The formula for the vertical motion of an object is h = -16t2 + v0t + h0, where h is the height of the object, h0 is the initial, or starting, height, v0 is the initial velocity, and t is the time in seconds.
Part A
Create a function to model the height of a firework when shot in the air. Explain whether the function will have a maximum or a minimum value.
Part B
Using the equation representing the height of the firework (h = -16t2 + v0t + h0), algebraically determine the extreme value of f(t) by completing the square and finding the vertex. Interpret what the value represents in this situation.
Answer:
A
[tex]h = -16t^2 + 192t[/tex]
B
Vertex=(6,576)
Step-by-step explanation:
The problem gives us the following data:
[tex]v_o=192\ ft/s,\ h_o=0[/tex]
A.
Thus the function is
[tex]h = -16t^2 + 192t[/tex]
The graph of h has the shape of an inverted parabola. Recall if the coefficient of the quadratic term is negative, the parabola is concave down, so it has a maximum value.
Part B
Let's take the function of h
[tex]h = -16t^2 + 192t[/tex]
Factoring by -16
[tex]\displaystyle h = -16(t^2 - 12t)[/tex]
Completing squares
[tex]\displaystyle h = -16(t^2 - 12t+36-36)[/tex]
[tex]\displaystyle h = -16(t^2 - 12t+36)+576[/tex]
Factoring
[tex]\displaystyle h = -16(t-6)^2+576[/tex]
Rearranging
[tex]\displaystyle h -576= -16(t-6)^2[/tex]
We can get the coordinates of the vertex from this standard form of the parabola.
Vertex=(6,576)
The maximum value means that at t=6 seconds, the firework will be 576 feet high and then it will start falling back to the ground.
Which sentence below represents the number of test questions in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. If the test has 25 questions, how many multiple choice questions are there?
A. The number of multiple-choice questions plus the number of short-answer questions is 25.
B. The number of multiple-choice questions times the number of short-answer questions is 25.
C. The number of multiple-choice questions minus the number of short-answer questions is 80.
D. The number of multiple-choice questions plus the number of short-answer questions is 80.
Answer: there are 10 multiple choice questions and 15 short-answer questions
Step-by-step explanation:
Let x represent the number of multiple choice questions in the test.
Let y represent the number of short-answer questions in the test.
If the test has 25 questions, it means that
x + y = 25
Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. The test is worth a total of 80 points. It means that
2x + 4y = 80 - - - - - - - -1
Substituting x = 25 - y into equation 1, it becomes
2(25 - y) + 4y = 80
50 - 2y + 4y = 80
- 2y + 4y = 80 - 50
2y = 30
y = 30/2 = 15
x = 25 - y = 25 - 15 = 10
A. The number of multiple-choice questions plus the number of short-answer questions is 25.
Answer:
A makes the most sense
Step-by-step explanation:
as if you don't get tricked and notice that C and D are not true but between A and B are two answers but B isn't correct if you go over what it means without getting tricked and A is to be the right answer
Which of the following is the simple interest paid on a loan of $354 at 6% for six months?
$12.74
$12.47
$10.26
$10.62
Answer:
12.47 is the correct answer
welp! help! brainly deleted my last question so here's this!
Answer:
Part 1) [tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]
Part 2) [tex]\frac{a}{b}=\frac{2}{3}[/tex]
Part 3) [tex]\frac{a^3}{b^3}=\frac{8}{27}[/tex]
Step-by-step explanation:
Part 1) Find the ratio Area I/Area II
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
The ratio of the areas is equal to divide the surface area cylinder I by the surface area cylinder II
Let
a^2 -----> the surface area cylinder I
b^2 ----> the surface area cylinder II
we have
[tex]a^2= 8\pi\ in^2[/tex]
[tex]b^2= 18\pi\ in^2[/tex]
Find the ratio
[tex]\frac{a^2}{b^2}=\frac{8\pi }{18\pi}[/tex]
Simplify
[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]
That means
[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex] --->[tex]4b^2=9a^2[/tex]
Four times area cylinder II is equal to nine times the surface area of cylinder I.
Part 2) Find the ratio a/b
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor.
In this problem
[tex]\frac{r_1}{r_2}=\frac{h_1}{h_2}=\frac{a}{b}[/tex] ----> scale factor
we have
[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]
so
square root both sides
[tex]\frac{a}{b}=\frac{2}{3}[/tex]
That means
[tex]\frac{r_1}{r_2}=\frac{2}{3}[/tex] --->[tex]2r_2=3r_1[/tex]
Two times radius cylinder II (r_2) is equal to three times radius cylinder I (r_1)
[tex]\frac{h_1}{h_2}=\frac{2}{3}[/tex] --->[tex]2h_2=3h_1[/tex]
Two times height cylinder II is equal to three times height cylinder I
Part 3) Find the ratio Volume I/Volume II
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
we have
[tex]\frac{a}{b}=\frac{2}{3}[/tex] ----> scale factor
[tex]\frac{Volume\ I}{Volume\ II}=\frac{a^3}{b^3}[/tex]
substitute the values
[tex]\frac{Volume\ I}{Volume\ II}=\frac{2^3}{3^3}[/tex]
[tex]\frac{Volume\ I}{Volume\ II}=\frac{8}{27}[/tex]
[tex]8Volume\ II=27Volume\ I[/tex]
8 times volume cylinder II is equal to 27 times volume cylinder I
Roddy Richards invested $12014.88 in Wolverine Meat Distributors (W.M.D.) five years ago. The investment had yearly arithmetic returns of minus9.7%, minus8.1%, 15%, 7.2%, and 15.4%. What is the arithmetic average return of Roddy Richard's investment?
Answer:
The arithmetic average return would be 3.96%
Step-by-step explanation:
Given,
The returns in 5 years are,
-9.7%, -8.1%, 15%, 7.2%, and 15.4%
We know that,
[tex]\text{Arithmetic average}=\frac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]
Hence,
The arithmetic average return of the investment = [tex]\frac{-9.7-8.1+15+7.2+15.4}{5}[/tex]
[tex]=\frac{19.8}{5}[/tex]
= 3.96%
Eugene had 3 pies. He gave 1 4/5 to his friend. And kept the rest for himself. Who had more pie? How much more?
Answer:
Eugene friend will have more pie than Eugene.
Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.
Step-by-step explanation:
Given:
Amount of pie Eugene has = 3
Amount of Pie given to friend = [tex]1\frac{4}{5}[/tex]
[tex]1\frac{4}{5}[/tex] can be Rewritten as [tex]\frac{9}{5}[/tex]
We need to find who has pie and how much more.
We will first find the amount of pie Eugene is left with.
The amount of pie Eugene is left with is equal to Amount of pie Eugene had minus Amount of pie given to friend.
Framing the equation we get;
The amount of pie Eugene is left = [tex]3-\frac{9}{5}[/tex]
We will take LCM to solve the same.
The amount of pie Eugene is left = [tex]3-\frac{9}{5} = \frac{3\times5}{5}-\frac{9}{5} =\frac{15}{5}-\frac{9}{5} = \frac{15-9}{5} =\frac{6}{5}[/tex]
Now [tex]\frac{9}{5} = 1.8[/tex] and [tex]\frac{6}{5} = 1.2[/tex]
Hence [tex]\frac{9}{5}[/tex] is greater than [tex]\frac{6}{5}[/tex]
Hence Eugene friend will have more pie than Eugene.
Now we will find amount more pie Eugene friend has.
Amount More Eugene friend has can be calculate by Subtracting Amount of of Eugene has with Amount of pie his friend has.
Amount More Eugene friend has =[tex]\frac{9}{5} - \frac{6}{5} =\frac{9-6}{5}= \frac{3}{5}[/tex]
Hence Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.
Lee can purchase gas for his rental car for $3.25 per gallon. It will cost him $96 to rent the car. How much will it cost Lee if he purchases 160 gallons of gas? Write your answer in proper money form.
Answer:
It will cost him $616 for 160 gallons of gas.
Step-by-step EXPLANATION FIRST YOU HAVE TO MULTIPLY 3.25 BY 160 TO GET $520, THEN JUST ADD IT BY $96 TO GET $616.
It will cost Lee $520 to purchase 160 gallons of gas.
What are arithmetic operations?
The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division. The priority of these opeartors in a given expression can be determined by PEDMAS. Each letter represents one operation as P for Parenthesis, E for exponential, D for division, M for Multiplication, A for Addition and S for Subtraction.
The price of gas per gallon is $3,25.
The cost of 160 gallons can be calculated as follows,
Number of gallons × Price per gallon
⇒ 160 × 3.25
⇒ 520
Hence, the price of 160 gallons is given as $520.
To know more about arithmetic operation click on,
https://brainly.com/question/25834626
#SPJ5
Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought?
Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.
Let x represent the number of boxes of cookies bought by Kendal.
Each box has 12 cookies, hence:
number of cookies = 12x
Kendal brings 60 cookies to the party. She keeps 2 boxes for herself. To find the number of boxes we use:
12x = 60 + 12(2)
12x = 84
x = 7
Therefore Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.
Find out more at: https://brainly.com/question/21105092
Final answer:
To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. The equation (x - 2) * 12 = 60 can be used to find the number of boxes Kendal bought.
Explanation:
To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. Kendal initially buys x boxes of cookies. Each box contains 12 cookies. She decides to keep two boxes for herself and brings 60 cookies to the party.
The number of cookies Kendal brings to the party can be calculated by multiplying the number of boxes she bought minus the number of boxes she kept for herself by the number of cookies in each box. So, the equation to find x would be:
(x - 2) * 12 = 60
Solving this equation will give us the value of x, which represents the number of boxes Kendal bought.
Water pump A, B and c could empty a pool for 6 hours, a and b pump could empty a pool for 8 hours how long (to the nearest minute) will it take to drain the pool if both pumps are used simultaneously?
Answer:
3.4286 hours or 3 hours 26 minutes
Step-by-step explanation:
Well, it is considered that there are 5 different pumps (A, B, C, a and b). Pumps A and B are not same with pumps a and b.
Let us solve it. Well, it says a and b pump could empty a pool for 8 hours. So in 1 hour, pumps a and b empty 1/8 part of the pool.
And pumps A, B and C could empty a pool for 6 hours. Then A, B and C pumps empty 1/6 part of pool in 1 hour.
5 pumps (A, B, C, a and b) altogether can empty 7/24 parts (1/6+1/8=7/24) of a pool in 1 hour.
To drain whole pool, it will take 24/7=3.4286 hours or 3 hours 26 minutes.
A circle has a radius of 5 inches (What is the measure, in radians, of this central angle?
Answer:
Step-by-step explanation:
Given
Circle has radius [tex]r=5 in.[/tex]
Area of the sector is given by
[tex]A_s=\frac{\theta }{2\pi }\times \pi r^2[/tex]
if [tex]A_s[/tex] is one-sixth of area of circle then
[tex]A_s=\frac{\pi r^2}{6}[/tex]
[tex]\frac{\pi r^2}{6}=\frac{\theta }{2\pi }\times \pi r^2[/tex]
[tex]\theta =\frac{2\pi }{6}=\frac{\pi }{3}\ radian[/tex]
If [tex]A_s[/tex] is one-fourth of area of circle then
[tex]A_s=\frac{\pi r^2}{4}[/tex]
[tex]\theta =\frac{2\pi }{4}[/tex]
[tex]\theta =\frac{\pi }{2}[/tex]
The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekendis $600 or less. Amember of the hotel’s accounting staff noticed that the total chargesfor guest bills have been increasing in recent months. The accountant will use a sample ofweekend guest bills to test the manager’s claim.a. Which form of the hypotheses should be used to test the manager’s claim? Explain.$H0:μ≥600Ha:μ<600H0:μ≤600Ha:μ>600H0:μ=600Ha:μ≠600$b. What conclusion is appropriate when H0 cannot be rejected?c. What conclusion is appropriate when H0 can be rejected?
Answer:
[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]
Step-by-step explanation:
We are given the following in the question:
Manager's claim: The mean guest bill for a weekend is $600 or less.
A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months.
A sample of weekend guest bills were collected to test the manager’s claim.
We design the null and alternate hypothesis in the following manner:
[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]
Conclusion when null hypothesis cannot be rejected:
When we fail to reject the null hypothesis and accept the null hypothesis, thus, we have enough evidence to support the manager's claim that the mean guest bill for a weekend is $600 or less.
Conclusion when null hypothesis can be rejected:
When the null hypothesis is rejected, we accept the alternate hypothesis.
Thus, there are not sufficient evidence to support the manager's claim that the mean guest bill for a weekend is $600 or less.
The manager of an industrial plant is planning to buy a new machine. For each day’s operation, the number of repairs X, that the machine needs is a Poisson random variable with mean 0.96 repairs per day. The daily cost of operating the machine is C = 160 + 40X2 . Find the expected value of the daily cost of operating the machine.
Answer: Expected value of the daily cost of operating the machine is 235.264.
Step-by-step explanation:
Since we have given that
E[x]= 0.96 repairs per day
And Var[x] = 0.96 repairs per day.
[tex]C=160+40x^2[/tex]
[tex]E[c]=160+40E[x^2]\\\\E[c]=160+40(Var[x]+(E[x])^2)\\\\E[c]=160+40(0.96+0.96^2)\\\\E[c]=235.264[/tex]
Hence, Expected value of the daily cost of operating the machine is 235.264.
The expected value of the daily cost of operating the machine is $235.264.
Explanation:To find the expected value of the daily cost of operating the machine, we need to calculate the expected value of C = 160 + 40X^2, where X is the number of repairs the machine needs per day. Since X follows a Poisson distribution with a mean of 0.96, we can use the formula for the expected value of a function of a random variable:
E(C) = E(160 + 40X^2) = 160 + 40E(X^2)
To calculate E(X^2), we need to find the variance of X first.
The variance of X is Var(X) = λ = 0.96.
Then, E(X^2) = Var(X) + [E(X)]^2 = 0.96 + (0.96)^2 = 0.96 + 0.9216 = 1.8816.
Now, we can calculate the expected value of the daily cost:
E(C) = 160 + 40E(X^2) = 160 + 40(1.8816) = 160 + 75.264 = 235.264.
Therefore, the expected value of the daily cost of operating the machine is $235.264.
Learn more about Expected Value here:https://brainly.com/question/37190983
#SPJ3
Volleyball A volleyball is hit when it is 4 ft above the ground and 12 ft from a 6-ft-high net. It leaves the point of impact with an initial velocity of 35 ft>sec at an angle of 27° and slips by the opposing team untouched.
a. Find a vector equation for the path of the volleyball.
b. How high does the volleyball go, and when does it reach maximum height?
c. Find its range and flight time.
d. When is the volleyball 7 ft above the ground? How far (ground distance) is the volleyball from where it will land?
e. Suppose that the net is raised to 8 ft. Does this change things? Explain. 38. Shot put In
Answer:
a) the vector equation is r(x,y) = (35cos27°t, 16t^2 -35sin27° - 4)
b) Maximum height = 7.945ft
c) Time of flight = 1.201 secs and range = 37.45ft
d) when t = 0.74, the distance above the ground = 14.37ft
When t = 0.254, the distance above the ground = 26.53ft
e) if the ball is raised to 8ft, the ball won't be able to reach it. This is because the maximum height is 7.954ft
Step-by-step explanation:
a) From the diagram
x0 = 0
y0= 4
V0(initial velocity) = 35
α= 27°
y = 4 + 35sin27°t - 16t^2
y = -16t^2 + 35sin27°t+ 4
y = 16t^2 - 35sin27°t - 4
x = 35cos27°t
Vector equation for the path of the volleyball = r(x,y)
r(x,y) = (35cos27°t, 16t^2 -35sin27° - 4)
b) the ball reaches maximum when dy/dt = 0
y = 16t^2 - 35sin27°t - 4
dy/dt = 32 - 35sin27°
0 = 32 - 35sin27°t
-32 = -35sin27°t
t = -32 / -35sin27°
t = 0.4966 seconds
Put t = 0.4966 into y = 16t^2 - 35sin27°t - 4
y = 16(0.4966)^2 - 35sin27°(0.4966) - 4
y = 7.945 ft
The maximum height is 7.945 ft
c) To find the range and flight time, put y= 0
0 = 16t^2 - 35sin27°t - 4
0 = 16t^2 - 15.89t - 4
Using quadratic equation general formula,
[-b +/- √b^2 -4ac] / 2a
a = 16, b = -15.89, c = -4
= [-(-15.89) +/- √ (-15.89)^2 - 4(16)(-4)] /2(16)
= [15.89 +/- √(15.89)^2 + 256] / 32
= (15.59 +/- 22.55) / 32
= (15.89 + 22.55) / 32 or (15.89 - 22.55) / 32
= 1.201 or -0.208
Time of flight = 1.201 secs
Range = x = 35cos27°t
Range = 32cos27°(1.201)
= 37.45 ft
d) when the volley is 7ft above ground, y = 7
Recall that y = 16t^2 - 35sin27°t - 4
7 = 16t^2 - 35sin27°t - 4
0 = 16t^2 - 35sin27°t - 4 +7
0 = 16t^2 - 35sin27°t + 3
0 = 16t^2 - 15.89t + 3
Using quadratic equation general formula,
[-b +/- √b^2 -4ac] / 2a
a = 16, b = -15.89, c = 3
= [-(-15.89) +/- √ (-15.89)^2 - 4(16)(3)] /2(16)
= [15.89 +/- √(15.89)^2 - 192] / 32
= (15.59 +/- 7.7778) / 32
= (15.89 + 7.7778) / 32 or (15.89 - 7.7778) / 32
= 0.74 or 0.254
When t = 0.74,
x = 35cos27°t
x = 35cos27°(0.74)
x = 23.08 ft
Therefore , R - x(0.74)
= 37.45 - 23.08
= 14.37ft
When t = 0.254,
x = 35cos27°t
x = 35cos27°(0.254)
x = 7.92 ft
Therefore R - x(0.254) =
37.45 - 7.92 = 29.53ft
e) if the ball is raised to 8ft, the ball won't be able to reach it. This is because the maximum height is 7.954ft
Sales variances may be computed in a manner similar to cost variances–that is, computing both price and volume variances.
Answer:
The answer is True.
Step-by-step explanation:
Sales variance is computed in same manner as cost variance that is computing both price and volume variance. However interpretation of end result will not be same. For example in material price variance if
A = actual purchase price = $ 4, B = standard purchase price= $ 5 and Qt= quantity purchased = 500 units then
Material price varaince = 500 (5-4) = 500,
This gives us favourable price variance of 500 dollars. However in sales price variance if
A = actual sales price = $ 4, B = standard sale price= $ 5 and Qt= quantity sold = 500 units then
Sale price varaince = 500 (5-4) = (500)
This gives us unfavourable sales price variance of 500 dollars.
This show that formulas to compute variances are same but sale price decrease give us un favorable variance and cost price decrease gives us favorable price variance and vice versa.
Triangle PQR with vertices P(3, −6), Q(6, −9), and R(−15, 3) is dilated by a scale factor of 3 to obtain triangle P′Q′R′. Which statement best describes triangle P′Q′R′?A. It is similar to triangle PQR and has coordinates P′(1, −2), Q′(2, −3), and R′(−5, 1).B. It is congruent to triangle PQR and has coordinates P′(1, −2), Q′(2, −3), and R′(−5, 1).C. It is similar to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).D. It is congruent to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).
Answer:
Option C.
Step-by-step explanation:
The vertices of triangle PQR are P(3, −6), Q(6, −9), and R(−15, 3).
It is given that triangle PQR dilated by a scale factor of 3 to obtain triangle P′Q′R′.
We know that a figure and its image after dilation are similar. It means triangle PQR and triangle P′Q′R′
If a figure dilated by factor k about the origin then
[tex](x,y)\rightarrow (kx,ky)[/tex]
PQR dilated by a scale factor of 3, so
[tex](x,y)\rightarrow (3x,3y)[/tex]
Using this rule we get
[tex]P(3,-6)\rightarrow P'(3(3),3(-6))=P'(9,-18)[/tex]
[tex]Q(6,-9)\rightarrow Q'(3(6),3(-9))=Q'(18,-27)[/tex]
[tex]R(-15,3)\rightarrow R'(3(-15),3(3))=R'(-45,9)[/tex]
The vertices of image are P'(9,-18), Q'(18,-27) and R'(-45,9).
Therefore, the correct option is C.
Answer:
C
Step-by-step explanation:
Six hundred chances are sold at $3 apiece for a raffle. There is a grand prize of $700, two second prizes of $200, and five third prizes of $50. First calculate the expected value of the lottery. Determine whether the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair.
Answer:
Expected net gain is -$0.75. Not a fair game. Appropriate price is $2.25.
Step-by-step explanation:
There is 1 in 600 chance to win the grand price (1/600)
There are 2 in 600 chance to win the 2nd price (2/600 = 1/300)
There are 5 in 600 chance to win the 3rd price (5/600 = 1/120)
We can use these probability to calculate the expected gain from this game
[tex]E_g = 700\frac{1}{600} + 200*\frac{1}{300} + 50*\frac{1}{120} = \$2.25[/tex]
Since the cost to play is $3, the expected net gain from this game is
$2.25 - $3 = -$0.75
So this game is not fair as the player is losing money. The appropriate price should instead be $2.25
The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.
Calculate the total amount collected from selling all tickets: 600 tickets × $3 = $1800.Calculate the expected value by taking into account the probabilities of winning and the respective prizes: ($700 × 1/600) + ($200 × 2/600) + ($50 × 5/600) = $1.91.Determining Fairness:
The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.
The table shows the ages and weights of babies at a hospital. A 2-row table with 10 columns. The first row is labeled age (weeks) with entries 1, 2, 3, 3, 4, 4, 6, 8, 9, 9. The second row is labeled weight (pounds) with entries 7.5, 7.25, 8.2, 7.95, 8.0, 9.75, 9.25, 8.9, 9.85, 10.0. What is the correlation between age and weight as shown in the table? none positive negative constant
Answer:
Option (b) is correct.
The correlation between age and weight shown in the table is positive.
Step-by-step explanation:
According to the given values, it is found that there is a positive correlation between age and weight.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.In this problem, when the age increases, so does the weight, hence they have positive correlation.
More can be learned about correlation coefficients at https://brainly.com/question/25815006
#SPJ2
Abigail"s parents pay her $5 an hour for weeding the yard and pay her little sister $3 an hour for raking leaves. Write and expression two different ways to represent the amount for parents will pay Abigail and her sister from work you same amount of hours
Final answer:
To represent the total amount Abigail's parents will pay both Abigail and her sister for working the same number of hours, you could use the algebraic expressions 5h + 3h or (5 + 3)h, where h is the number of hours worked.
Explanation:
Abigail's parents pay her for weeding the yard and pay her little sister for raking leaves. If both of them work for the same amount of hours, we can represent the total amount their parents will pay using algebraic expressions. Let h be the number of hours they work.
One way to write the expression is: 5h + 3h, where 5 represents the dollars per hour for Abigail and 3 represents the dollars per hour for her sister.
Another way to represent this is: (5 + 3)h, which simplifies the expression by adding the hourly wages first and then multiplying by the number of hours worked, h.
Both expressions will give us the total amount paid to Abigail and her sister for the same number of hours worked, h.
The ratio of corresponding side lengths of two similar MP3 players is 4:3. The area of the larger MP3 player is 8 square inches. What is the area of the smaller MP3 player?
The area of smaller mp3 player is 4.5 square inches
Solution:
Given that ratio of corresponding side lengths of two similar MP3 players is 4:3
The area of the larger MP3 player is 8 square inches
To find: area of the smaller MP3 player
If two MP3 players are similar, then their corresponding sides are proportional.
To find the area ratios, raise the side length ratio to the second power
[tex]\frac{\text {area of larger mp3}}{\text {area of smaller mp3}}=\left(\frac{4}{3}\right)^{2}[/tex]
From given information,
area of larger mp3 = 8 square inches
Let the area of smaller mp3 = x
So the above ratio becomes,
[tex]\frac{8}{x}=\left(\frac{4}{3}\right)^{2}\\\\\frac{8}{x} = \frac{16}{9}\\\\16x = 9 \times 8\\\\16x = 72\\\\x = 4.5[/tex]
Thus the area of smaller mp3 player is 4.5 square inches
Final answer:
The area of the smaller MP3 player is 128/9 square inches.
Explanation:
The area of the larger MP3 player is 8 square inches and the ratio of corresponding side lengths of the two MP3 players is 4:3. To find the area of the smaller MP3 player, we need to use the ratio of the side lengths squared. Since the ratio is 4:3, the area ratio will be (4/3)^2 = 16/9. Given that the area of the larger MP3 player is 8 square inches, we can find the area of the smaller MP3 player by multiplying 8 by the area ratio: (8) * (16/9) = 128/9 square inches.
question 1. Enter the ratio equivalent to sin(B)
question 2. Consider this a right triangle. enter the measure of angle CAB to the nearest hundredth degree.
question 3. Suppose angle A is an angle such that angle cosA < sinA. select ALL angle measures that are possible values for angle A. 25, 35, 45, 55, 66, 75.
Answer:
The three questions about the given triangle has been answered below.
Step-by-step explanation:
We are given a right angled triangle whose sides are of length 20, 21 and 29.
(1) sin(B) = [tex]\frac{side opposite to B}{hypotenuse}[/tex]
= [tex]\frac{21}{29}[/tex]
= 0.72
(2) sin(A) = [tex]\frac{20}{29}[/tex]
sin(A) = 0.689
∠CAB = [tex]sin^{-1}(0.689)[/tex]
∠CAB = 43.551°
(3) We suppose that cosA < sinA and we haveto find which all angles will satisfy this condition.For this the angle A should be greater than 45°.
From the given options the angles that satisfy this are 55 , 66 and 75.
45 is not included as then sinA = cosA and that condition is not there.
We can use sine and cosine trigonometric ratios to calculate the ratio and measures of angles.
A: The ratio equivalent to sin(B) is [tex]\dfrac{21}{29}[/tex]
B: The measure of angle ∠CAB is [tex]43.6^\circ[/tex]
C: The possible measures of angle A can be: 55, 66 or 75
Given that:AB = 29 unitsBC = 20 unitsCA = 21 unitsUsing definitions of specific trigonometric ratios:A: The ratio equivalent to sin(B) is:
[tex]sin(B) = \dfrac{CA}{AB} = \dfrac{21}{29}\\[/tex]
B: The measure of angle ∠CAB is calculated as:
[tex]sin(A) = \dfrac{CB}{BA} = \dfrac{20}{29} = 0.69\\\\A = arcsin(0.69) = 43.6^{\circ}\\\\\angle CAB = 43.6^{\circ}[/tex]
C: When sin A > cos A, the measures of angle A from 25,35,45,55,66,75 are:
55, 65 and 75:
The reason for the angles possible are 55, 66 ,75 is that:
[tex]\theta \leq 45\\sin(\theta) \leq cos(\theta)[/tex]
Thus, we have:
A: The ratio equivalent to sin(B) is [tex]\dfrac{21}{29}[/tex]
B: The measure of angle ∠CAB is [tex]43.6^\circ[/tex]
C: The possible measures of angle A can be: 55, 66 or 75
Learn more about trigonometric ratios here:
https://brainly.com/question/95152
The yearbook was sold for $26 at the beginning of the year.Since the price has increased to $28.What was the percent of increase in price (round to the hundredths place
Answer:the percent of increase in price is 7.69%
Step-by-step explanation:
The yearbook was sold for $26 at the beginning of the year. This means that the initial price of the year book was $26.
The price has increased to $28. The amount by which it was increased would be the current price - the initial price. It becomes
28 - 26 = $2
The percent of increase in price would be
Increase/initial price × 100
It becomes
2/26 × 100 = 7.69%
GASB requires a budget to actual comparison in the financial statements for the general fund and the ________.
Answer: Major special revenue funds with legally adopted budgets.
Step-by-step explanation: GASB ( Governmental accounting standards board) is a private organization based in Norwalk,that tries to regulates Government accounting process in the United States of America by giving specific standards to ensure proper accounting.
Governmental accounting standards board (GASB) requires a budget to actual comparison in the financial statements for the general fund and major special revenue funds with legally adopted budgets.
Property A initially sold for $412,500. The property sold a second time 12 months later for $430,500. What was A's monthly rate of change? (Round the final calculation to four decimal places.)
i got 1.0436 on my calculation hope this helps...
PLLLZ HELP HAVE A DEADLINE 30 POINTS Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cot θ= - 3/7 . Find the exact values of the five remaining trigonometric functions of θ.
Answer:
answer is the first option
Step-by-step explanation:
The function f is f of x= √4-x
What is the xcoordinate of the point on the functions graph that is closest to the origin?
Answer:
0.5
Step-by-step explanation:
We assume your function is
[tex]f(x)=\sqrt{4-x}[/tex]
The distance formula can be used to find the distance from the point on the curve (x, f(x)) to the origin:
d^2 = (x)^2 + (f(x))^2 = x^2 + (4 -x)
Written in vertex form, this is ...
d^2 = (x -1/2) + 3.75
This has a minimum at x=1/2, so that is the x-coordinate of the point closest to the origin.
In the function f(x) = √(4-x), the x-coordinate of the point on the graph that is closest to the origin is x=0 because the function exists in the first quadrant, meaning the shortest distance to the origin is along the y-axis.
Explanation:The function described is f(x) = √(4-x). We're looking for the x-coordinate of the point on the graph of this function that is closest to the origin. The distance from any point (x, y) to the origin (0, 0) is given by D=√(x²+y²). For this function, y=f(x) = √(4-x), so the distance can be written as D=√(x²+(4-x)²). To find the minimum distance, we take the derivative of this distance function with respect to x, set it equal to zero and solve for x. However, because this function lives in the first quadrant (y is always equal to or greater than 0), the shortest distance to the origin would be along the y-axis. Thus, the solution is x=0, and that is the x-coordinate of the point on the function's graph that is closest to the origin.
Learn more about Minimum Distance here:https://brainly.com/question/31871004
#SPJ11
Two trains leave a town at the same time heading in opposite directions. One train is traveling 12 mph faster than the other. After two hours, they are 232 miles apart. What is the average speed of each train?
Answer:
Step-by-step explanation:
I'm going to paint you a picture in words of what this looks like on paper. We have a train leaving from a point on your paper heading straight west. We have another train leaving from the same point on your paper heading straight east. This is the "opposite directions" that your problem gives you.
Now let's make a table:
distance = rate * time
Train 1
Train 2
We will fill in this table from the info in the problem then refer back to our drawing. It says that one train is traveling 12 mph faster than the other train. We don't know how fast "the other train" is going, so let's call that rate r. If the first train is travelin 12 mph faster, that rate is r + 12. Let's put that into the table
distance = rate * time
Train 1 r
Train 2 (r + 12)
Then it says "after 2 hours", so the time for both trains is 2 hours:
distance = rate * time
Train 1 r * 2
Train 2 (r + 12) * 2
Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r. The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24. The distance between them (which is also the length of the whole entire arrow) is 232. Thus:
2r + 2r + 24 = 232 and
4r = 208 so
r = 52
This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph
Answer: its A ^3^❤
Step-by-step explanation:
that guy above me probably got yall confused
Need some help with these problems!
Answer:
h=12, w=24, t=8
Step-by-step explanation:
System of Linear Equations
We have 3 unknown variables and 3 conditions between them. They form a set of 3 equations with 3 variables.
We have the following data, being
w = price of a sweatshirt
t = price of a T-shirt
h = price of a pair of shorts
19.
The first condition states the price of a sweatshirt is twice the price of a pair of shorts. We can write it as
[tex]\displaystyle w=2h[/tex]
The second condition states the price of a T-shirt is $4 less than the price of a pair of shorts. We can write it as
[tex]\displaystyle t=h-4[/tex]
The final condition states Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for $136, thus
[tex]\displaystyle 3w+2h+5t=136[/tex]
This is the system of equations we need to solve for w,t,h
20.
To solve the system, we replace w in terms of h and t in terms of h. Those relations have been already written, so
[tex]\displaystyle 3(2h)+2h+5(h-4)=136[/tex]
Operating
[tex]\displaystyle 6h+2h+5h-20=136[/tex]
[tex]\displaystyle 13h=156[/tex]
Solving for h
[tex]\displaystyle h=12[/tex]
The other two variables are
[tex]\displaystyle w=2h=24[/tex]
[tex]\displaystyle t=12-4=8[/tex]