Answer:The percentage of bottles expected to have a volume less than 32 or is 40.13%
Step-by-step explanation: The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz
b=1.2 oz
Let S be the volume of randomly selected soda bottles
Y-score: S-a/b
For S=32 oz
Substitute the values of S,a and b into the equation
Y=32-32.3/1.2
Y=-0.25
Probability of bottles that have a volume less than 32 oz is
P(S<32)=P(Y<-025)= 0.40129
Percentage of bottles that have volume less than 32 oz will be
0.40127×100%=40.13%
There are 13 steps in the stairwell, each measuring one foot by three foot. In order to cover all the steps, how many square feet of carpet does Mr. Meglio need to purchase?
Answer:
Mr. Meglio need to purchase 39 square feet of carpet.
Step-by-step explanation:
Given:
Total number of steps = 13
Length of each step = 1 foot
Width of each step = 3 foot
We need to find the square feet of carpet does Mr. Meglio need to purchase.
Solution:
First we will find the area of each step.
area of each step is equal to length times width.
framing in equation form we get;
area of each step = [tex]1\times 3 = 3\ ft^2[/tex]
Now amount of carpet required in square feet we multiply number of step with area of each step.
framing in equation form we get;
Amount of carpet required = [tex]13\times3 =39\ ft^2[/tex]
Hence Mr. Meglio need to purchase 39 square feet of carpet.
Final answer:
Mr. Meglio needs to purchase 39 square feet of carpet to cover the 13 steps in the stairwell, as each step has an area of 3 square feet.
Explanation:
The student is asking how many square feet of carpet are needed to cover a stairwell with 13 steps, where each step is one foot by three feet.
To calculate the area of a single step, multiply the length by the width. For one step, the calculation is 1 foot × 3 feet = 3 square feet. Since there are 13 steps, multiply the area of one step by the number of steps: 3 square feet/step × 13 steps = 39 square feet. Therefore, Mr. Meglio will need to purchase 39 square feet of carpet to cover all the steps.
This type of problem is a practical application of the area calculation in real-world context, and the measurement conversion from square inches to square feet is also pertinent to understanding the measurement of areas in different units.
7x+3(-x+6)=42 Show all steps
Answer:
X=6
Step-by-step explanation:
Distributing the 3
7x-3x+18=42
Adding like terms
4x+18=42
Subtracting 18 from both sides
4x=24
Dividing both sides by 4
X=6
Christilla and her friends purchased tickets for the factory that costs $13 each and bottled water that costs $1.50 each. Write an algebraic expression for the total cost of their night out
Answer:
An algebraic expression for the total cost of their night out is [tex]T=13x+1.5y[/tex].
Step-by-step explanation:
Given:
Cost of per person ticket to factory = [tex]\$13[/tex]
Cost of each bottled water = [tex]\$1.50[/tex]
we need to write an algebraic expression for the total cost of their night out
Solution:
Let the number of persons visiting the factory be 'x'.
Also Let the number of bottled water be 'y'.
Also Let the total cost be 'T".
So we can say that;
total cost is equal to Cost of per person ticket to factory multiplied by the number of persons visiting the factory plus Cost of each bottled water multiplied number of bottled water.
framing in equation form we get;
[tex]T=13x+1.5y[/tex]
Hence an algebraic expression for the total cost of their night out is [tex]T=13x+1.5y[/tex].
Four houses in a row are each to be painted with one of the colors red, blue, green, and yellow. In how many different ways can the houses be painted so that no two adjacent houses are of the same color? There are possible ways to paint the houses.
Answer:
Possible ways to paint the house is 108
Step-by-step explanation:
Total number of houses to be painted=4
Total number of colours to b used(red,blue,green and yellow)=4
Number of ways to paint the first house=4
Number of ways to paint the second house=3
Number of ways to paint the third house=3
Number of ways to paint the fourth house=3
Total number of ways to paint the 4 houses=4×3^3=108 ways.
Final answer:
There are 24 different ways to paint the houses so that no two adjacent houses are of the same color.
Explanation:
To solve this problem, we can use the concept of permutations. Since there are 4 houses and 4 colors to choose from, we can start by selecting a color for the first house. We have 4 options for the first house. Next, we need to choose a color for the second house, but we must ensure that it is different from the color chosen for the first house. We have 3 options for the second house. For the third house, we have 2 options, and for the fourth house, we have only 1 option.
Therefore, the total number of ways to paint the houses without any two adjacent houses being the same color is calculated as:
4 x 3 x 2 x 1 = 24
If the graph f(x)= 9x^2+36x+41/3x+5 has an oblique asymptote at y=3x+k what is the value of k
Answer:
The value of k is 7.Explanation:
To find the oblique asymptote of a rational function you divide the numerator by the denominator and take the quotient (not the remainder).
Such quotient (without the remainder) is the equation of the line that is the oblique asymptote of the rational function.
The rational function is:
[tex]\frac{9x^2+36x+41}{3x+5}[/tex]
You can see the long division in the picture attached. The quotient is 3x + 7.
Hence, by comparison with y = 3x + k, k = 7.
Answer:
7
Step-by-step explanation:
Correct on EDGE
Which system is represented by the graph?
Answer:
The answer to your question is the first option
Step-by-step explanation:
Process
1.- Identify the y-intercepts of the lines
blue line y-intercept = -1
brown line y-intercept = -2
With this information, we can discard the last option because those lines don't have those y-intercepts.
2.- We observe in the graphs that the lines are increasing so the slopes are positive. From this information, we can discard the second option.
3.- Calculate the slopes of the lines of options 1 and 3
Blue line Points (0, -1) (1, 2)
m = [tex]\frac{2 + 1}{1 - 0} = \frac{3}{1} = 3[/tex]
Brown line Points (0, -2) (1, 1)
m = [tex]\frac{1 + 2}{1 - 0} = 3[/tex]
As the slopes are 3, we conclude that the answer is the first option.
A 40 question test has 132 possible points there are M 5 point questions. And N 1 point questions how many of each type of questions is on the test?
Answer:
There are 23 5-point questions and 17 1-point questions.
Step-by-step explanation:
there are M 5 point questions
And N 1 point questions
M + N = 40
A 40 question test has 132 possible points
5M + N = 132
We have a system of equations.
M + N = 40
5M + N = 132
Multiply both sides of the first equation by -1. Write the second equation below it. Add the equations.
-M - N = -40
+ 5M + N = 132
----------------------------
4M = 92
M = 23
Now substitute 23 for M in the first equation and solve for N.
M + N = 40
23 + N = 40
N = 17
There are 23 5-point questions and 17 1-point questions.
Answer:the number of 5 point questions is 23
the number of 1 point questions is 17
Step-by-step explanation:
Let M represent the number of 5 point questions.
Let N represent the number of 1 point questions.
The total number of questions in the test is 40. It means that
M + N = 40 - - - - - - - - - - - - 1
The possible total points in the test is 132 and it contains M 5 point questions and N 1 point questions. This means that
5M + N = 132 - - - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
- 4M = - 92
M = - 92/-4 = 23
Substituting M = 23 into equation 1, it becomes
23 + N = 40
N = 40 - 23 = 17
Mr.Brent uses 1/4 cup of blue paint and 1/4 cup of yellow paint to make each batch of green paint. How many batches of green can he make with the amount of paint he has left?
Answer:the common denominator is 4 so your answer is 1/4
Step-by-step explanation:
Complete the table for the following function (Image down below)
y=3^x
Graph the function and describe what the graph looks like.
a.
Increases in Quadrant III
b.
Increases from left to right
c.
Decreases from left to right
d.
Decreases in Quadrant II
Answer:
b
Step-by-step explanation:
The graph of the given function will increase from left to right.
What are the needs for graphs in mathematics?Graphs are a popular tool for visually illuminating data relationships. A graph serves the objective of presenting data that are either too many or complex to be fully expressed in the text while taking up less room.
Given, a function y = 3ˣ. graph of this function is attached below. as we can see in the attached graph that it will increase from left to right.
For x = -3
y = 3⁻³ = 1/27
For x = -2
y = 3⁻² = 1/9
for x = 2
y = 3² = 9
For x = 3
y = 3³ = 27
Therefore, The supplied function's graph will rise from left to right.
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Heights of adult males are normally distributed. If a large sample of heights of adult males is randomly selected and the heights are illustrated in a histogram, what is the shape of that histogram?
Answer:
histogram is a graphical representation of data using he concepts of statistics.
Step-by-step explanation:
your question is incomplete as ample information is not provided for solving this problem.
Fortuna worked 39.5 hours this week at $8.18 an hour.
What was her gross pay?
$327.20
$323.90
$323.11
$319.02
Answer:
c
Step-by-step explanation:
because 39.5 hours makes 8.18
Fortuna's gross pay is $323.11
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Given that, Fortuna worked 39.5 hours this week at $8.18 an hour.
Since, she is being paid $8.18 for 1 hour, that mean her unit rate is $8.18
To find total rate we will multiply her unit rate with total hours she worked.
Therefore,
The total pay = 39.5 × 8.18 = $323.11
Hence, Fortuna's gross pay is $323.11
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Ken drives a taxi cab and receives $100 a day plus $0.50 for every mile he drives. He is saving up for a new television that costs about $2500. If Ken drives an average of 400 miles per day, how many days will he have to drive to save enough money to buy the television? In a inequality statment
Answer:
i got 8.33 so I would say about 9. Im not sure about inequality statements but I know that's about how many days since he makes 300 per day, and you divide that by 2500
Step-by-step explanation:
A building 64 ft high casts a 288-ft shadow. Sarah casts a 18-ft shadow. The triangle formed by the building and its shadow is similar to the triangle formed by Sarah and her shadow. How tall is Sarah?
6 ft
5 ft
4 ft
3 ft
Answer:
The answer to your question is 4 ft
Step-by-step explanation:
Data
Building's shadow = 288 ft
Building's high = 64 ft
Sarah's shadow = 18 ft
Sarah's height = ?
Process
1.- Use proportions to solve this problem
[tex]\frac{Sarah's height}{Sarah's shadow} = \frac{building's height's}{building's shadow}[/tex]
2.- Solve for Sarah's height
[tex]Sarah's height = \frac{Sarah's shadow x building's height}{building shadow}[/tex]
3.- Substitution
[tex]Sarah's height = \frac{18 x 64}{288}[/tex]
4.- Simplification
[tex]Sarah's height = \frac{1152}{288}[/tex]
5.- Result
Sarah's height = 4 ft
Mr. Abed tries a new mathematics game to help his third grade students learn their multiplication tables and records the results. This would best be described as which of the following?
Group of answer choices
A. true experiment
B. one-shot case study
C. one-group
D. pretest–posttest design
E. correlational research
Answer: D Pretest–posttest design
Step-by-step explanation:
According to the question, Mr Abed is just designing the game and the purpose is to help the grade 3 students learn their mutiplication table, upon completion of the game design, the students are to use (play) it - all this makes up the pretest stage
The result of the game will then be evaluated by Mr Abed to Know if the game is effective or not, if the students have actually learnt their multiplication table by playing the game, if there is need for modification - all this makes the posttest stage.
Suppose that you bet $5 on each of a sequence of 50 independent fair games. Use the central limit theorem to approximate the probability that you will lose more than $75.
Answer:
chances chances of happening = 0.0119
Step-by-step explanation:
given data
bet = $5
independent fair games = 50
solution
we will think game as the normal distribution
so here mean is will be
mean = [tex]\frac{50}{2}[/tex]
mean = 25
and standard deviation will be
standard deviation = [tex]\sqrt{50*0.5*0.5}[/tex]
standard deviation = 3.536
so
we have to lose 33 out of 50 time for lose more than $75
so as chance of doing things z score is
z score = [tex]\frac{33-25}{3.536}[/tex]
z score = 2.26
so from z table
chances chances of this happening = 0.0119
Simplify the radical expression and shows steps
Answer: [tex]4\sqrt{2}+10[/tex]
=============================================
Let [tex]x = \sqrt{8}[/tex]
We can replace every square root of 8 with x, since we have that equation above. We end up with 3-x+7+3x. This simplifies to 2x+10 after combining like terms.
Now we can reintoduce the square root back in
[tex]2x+10 = 2\sqrt{8}+10[/tex]
The use of x is optional as you can combine like terms directly. However, it might help to make the temporary replacement.
-------------
Now simplify the square root
[tex]\sqrt{8} = \sqrt{4*2}[/tex]
[tex]\sqrt{8} = \sqrt{4}*\sqrt{2}[/tex]
[tex]\sqrt{8} = 2\sqrt{2}[/tex]
--------
Therefore,
[tex]2\sqrt{8}+10[/tex]
turns into
[tex]2*2\sqrt{2}+10[/tex]
[tex]4\sqrt{2}+10[/tex]
Answer:
10 + 4sqrt(2)
Step-by-step explanation:
3 - sqrt(8) + 7 + 3sqrt(8)
3 - 2sqrt(2) + 7 + 6sqrt(2)
10 + 4sqrt(2)
sqrt: square root
The least-squares regression line is ________.
a. the line that passes through the most data points.
b. the line that minimizes the vertical distances of the data points from the line.
c. the line such that half of the data points fall above the line and half fall below the line.
d. All of the choices are correct.
Answer:
a. the line that passes through the most data points.
Step-by-step explanation:
Regression analysis, is used to draw the line of‘ best fit’ through co-ordinates on a graph. The techniques used enable a mathematical equation of the straight line form y=mx+c to be deduced for a given set of co-ordinate values, the line being such that the sum of the deviations of the co-ordinate values from the line is a minimum, i.e.
The least-squares regression lines is the line of best fit
The marching band in selling poinsettias and wreaths to raise money for new uniforms. Trey sold 7 poinsettias and 3 wreaths and raised $201. Molly sold 4 poinsettias and 6 wreaths and raised $252. How much is a poinsettia
The cost of 1 poinsettia is $ 15
Solution:
Let "x" be the cost of 1 poinsettias
Let "y" be the cost of 1 wreath
Trey sold 7 poinsettias and 3 wreaths and raised $201
Therefore, we frame a equation as:
7 poinsettias x cost of 1 poinsettias + 3 wreaths x cost of 1 wreath = 201
[tex]7 \times x + 3 \times y = 201[/tex]
7x + 3y = 201 ------- eqn 1
Molly sold 4 poinsettias and 6 wreaths and raised $252
4 poinsettias x cost of 1 poinsettias + 6 wreaths x cost of 1 wreath = 252
[tex]4 \times x + 6 \times y = 252[/tex]
4x + 6y = 252 ------- eqn 2
Multiply eqn 1 by 2
14x + 6y = 402 -------- eqn 3
Subtract eqn 2 from eqn 3
14x + 6y = 402
4x + 6y = 252
( - ) -----------------------
10x = 150
x = 15
Thus cost of 1 poinsettia is $ 15
The price of a poinsettia is $15.
To determine the price of a poinsettia, we need to set up and solve a system of linear equations based on the given information.
Trey sold 7 poinsettias and 3 wreaths and raised $201. Let's denote the price of a poinsettia as 'P' and the price of a wreath as 'W'. Thus, the equation is:7P + 3W = 201
Molly sold 4 poinsettias and 6 wreaths and raised $252. Therefore, the equation is:4P + 6W = 252
To eliminate one variable, we can multiply the first equation by 2 to get:14P + 6W = 402Now, subtract the second equation from the new equation:(14P + 6W) - (4P + 6W) = 402 - 25210P = 150P = 15Therefore, the price of a poinsettia is $15.
If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
f(x) = -16x^5 - 7x^4 - 6
Degree: -16; leading coefficient: 5
Degree: 5; leading coefficient: -16
Not a polynomial function.
Degree: 9; leading coefficient: -16
Degree: 5; leading coefficient: –16
Explanation:
Given polynomial function is [tex]f(x)=-16x^5-7x^4-6[/tex]
The degree of the polynomial is a highest value of the exponent in one variable in the given polynomial.
Here, highest value of the exponent = 5
So, degree of the polynomial = 5
Leading coefficient is the value before the highest degree of the variable in the polynomial.
Here, leading coefficient = –16
Hence, the answer is Degree: 5; leading coefficient: –16.
If the businesswoman randomly selects one of the possible itineraries and Denver and San Francisco are two of the cities that she plans to visit, what is the probability that she will visit Denver before San Francisco?
Answer: The probability that she will visit Denver before San Francisco is [tex]\dfrac{1}{2}[/tex] .
Step-by-step explanation:
Given : The businesswoman randomly selects one of the possible itineraries and Denver and San Francisco are two of the cities that she plans to visit.
The possible itineraries = (First Denver and then San Francisco , First San Francisco and then Denver)
i.e. Total outcomes =2
If she visit Denver before San Francisco , then the favorable outcome = 1
Now , the probability that she will visit Denver before San Francisco = [tex]=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{1}{2}[/tex]
Hence, the probability that she will visit Denver before San Francisco is [tex]\dfrac{1}{2}[/tex] .
Descriptive statistics are useful because _____. a. you can analyze results and draw conclusions b. trends are not determined any other way c. averages can be found without completing an experiment d. you can find the causes of problems
Answer:
a. you can analyze results and draw conclusions
Step-by-step explanation:
Descriptive Statistics: It interprets results in a simple way so that you can analyze the results and draw conclusions.
Jean has a ride metro card. It costs $2.50 to get on the tram plus $0.75 for each stop. If Jeans metro card allows her 8 rides and costs $44 how many stops can she make?
Answer: she can make 32 stops
Step-by-step explanation:
Let x represent the number of stops that she can make.
Jean has a ride metro card. It costs $2.50 to get on the tram plus $0.75 for each stop.
If Jeans metro card allows her 8 rides and costs $44, it means that if she makes x stops, then
2.5 × 8 + 0.75 × x = 44
20 + 0.75x = 44
0.75x = 44 - 20 = 24
x = 24/075 = 32
plz, help me ASAP!!!!!
ALL I NEED TO KNOW IS ............. MY ANSWER IS CORRECT OR WRONG AND WHY?
Answer:
A translation right 10 and up 9.
Step-by-step explanation:
Looks like you wrote the reverse translation
M'N'P'Q'R'S' to MNPQRS
What function is represented by the graph?
F(x) = (3/4)^x + 6
F(x) = (3/4)^x + 5
F(x) = (4/3)^x + 5
F(x) = (4/3)^x + 6
Answer:
[tex]\displaystyle f(x) = [\frac{3}{4}]^x + 5[/tex]
Explanation:
All you have to do is plug in some intervals into the function based off of the graph, to make sure your function is authentic.
* Anytime that [tex]\displaystyle a < 1,[/tex]the graph will be falling from the left.
I am joyous to assist you anytime.
Trilobites to concert tickets from her friend she pays $90 for the two tickets she looks at the tickets and see that each ticket has a space value of 52. 50. How much of a markdown did her friend give Shelia. Explain how you know.
Answer:
Her friend gave Sheila a markdown of $15.
Step-by-step explanation:
Given;
Amount paid for 2 tickets = $90
Actual amount for each ticket = $52.50
we need to find the markdown value did her friend gave to Shelia.
Solution:
each ticket = $52.50
2 tickets = Cost of 2 tickets.
By using unitary method we get;
Cost of 2 tickets = [tex]52.50\times 2 =\$105.00[/tex]
Now To find the markdown we will subtract the Amount paid for 2 tickets from the actual Amount of 2 tickets.
framing in equation form we get;
Markdown [tex]105-90 =\$15[/tex]
Hence her friend gave sheila a markdown of $15.
Grace started her own landscaping business. She charges $6 an hour for mowing lawns and $11 per house pulling weeds. In September she mowed lawns for 63 hours and pulled weeds for 9 hours. How much money did she make in September?
Answer:
The total money made by Grace is $477.
Step-by-step explanation:
Given:
Charge per hour for mowing lawn = $6
Charge per hour for pulling weeds = $11
Number of hours for which lawns are mowed = 63 hours
Number of hours for which weeds are pulled = 9 hours
Now, total money made by Grace in September can be calculated by adding the total money gained in mowing lawns and pulling weeds.
Total money gained in mowing lawns is given as:
[tex]C_m=\textrm{Number of hours of mowing}\times\textrm{Charge per hour}\\\\C_m=63\times 6=\$378[/tex]
Total money gained in pulling weeds is given as:
[tex]C_w=\textrm{Number of hours of pulling weeds}\times\textrm{Charge per hour}\\\\C_w=9\times 11=\$99[/tex]
Now, total money made = [tex]C_m+C_w=378+99=\$477[/tex]
Therefore, the total money made by Grace is $477.
Find a counterexample to show that the following conjecture is false.
The quotient of any two integers is always less than 1.
Answer:
4/2 = 2 > 1
Step-by-step explanation:
The quotient of any two integers of the same sign and the dividend having the larger magnitude will be greater than 1:
-88/-11 = 8 > 1
4/2 = 2 > 1
Hence the conjecture is false.
Which of the following can be derived from other assumptions about numbers. A. Subtraction. B. Multiplication. C. Division D. All of the above. E. B and C above.
Answer: D All of the above
Step-by-step explanation:
Addition,subtraction,multiplication and division are basic mathematical operations used in the determination and assumption of numbers.
Without them,there will be no theorems .
Henry mixes 1 cup grape concentrate with 4 cups water to make his favorite drink. How much water will he need to mix if he uses 5 cups grape concentrate
Answer:he will need to mix 20 cups of water if he uses 5 cups grape concentrate.
Step-by-step explanation:
Henry mixes 1 cup grape concentrate with 4 cups water to make his favorite drink. It means that the number of cups of grape concentrate that henry requires to mix 1 cup of water would be
1/4
Therefore, the number of cups of water that he needs to mix if he uses 5 cups grape concentrate would be
5/(1/4) = 20 cups of water
Determine whether the quantitative variable is discrete or continuous. Depth of the ocean floor Is the variable discrete or continuous? A. The variable is discrete because it is countable. B. The variable is continuous because it is not countable. C. The variable is discrete because it is not countable. D. The variable is continuous because it is countable.
Answer:
B. The variable is continuous because it is not countable.
Correct, from the definition about of continuous data we see that is a random variable is continuous then it can't be countable.
Step-by-step explanation:
Previous concepts
A discrete random variable "has a countable number of possible values" in a domain defined. So then the possible values for these types of random variables are the integers.
A continuous is a random variable "where the data can take infinitely many values" that means that can take values from the rational with decimals. Ans is not countable.
Solution to the problem
Let's analyze one by one the possible options:
A. The variable is discrete because it is countable.
False, the depth of the ocean is a continuous random variable since we can have for exampe a depth of 1200.56 mi and we can't express this as a discrete random variable.
B. The variable is continuous because it is not countable.
Correct, from the definition about of continuous data we see that is a random variable is continuous then it can't be countable.
C. The variable is discrete because it is not countable.
False, the depth of the ocean is a continuous random variable since we can have for exampe a depth of 504.67 Km and we can't express this as a discrete random variable.
D. The variable is continuous because it is countable.
False the variable is continuous but cannot be countable since that's the opposite from the definition of continuous random variable.
The correct answer is option is B). The variable is continuous because it is not countable.
The depth of the ocean floor is a quantitative variable that can take on any value within a range and can be measured to any level of precision. This means that the depth can be a non-integer number and is not restricted to integer counts. Therefore, it is not countable in the sense that one can count individual, distinct units, such as the number of people in a room or the number of cars in a parking lot. Instead, the depth of the ocean floor is a continuous variable because it can vary smoothly and without gaps over a range of values.
To illustrate, consider that the depth of the ocean can be 100.5 meters, 100.52 meters, 100.526 meters, and so on, with an infinite number of possible values between any two depths. This characteristic of having an infinite number of possible values within any given interval is what defines a continuous variable.