Answer:
{3, 5}.
Step-by-step explanation:
y = x^2 - 8x + 15
(x - 5)(x - 3) = 0
x - 5 = 0 or x - 3 = 0
So the roots are {3, 5}.
Miss Silverstein bought three cakes for her birthday party she cut each cake in 2/4 and plans to serve each guest a quarter of a cake how many gas can she serve with all her cakes
Answer:
Miss Silver stein can serve for 12 guests with amount of cake that she has bought.
Step-by-step explanation:
Given:
Number of cakes she bought = 3
Amount of cakes given to each guest = [tex]\frac{1}{4}[/tex]
We need to find the number of guest cakes can be served.
Solution:
Now we can say that;
the number of guest can have the cake to can be calculated by dividing the Number of cakes she bought from Amount of cakes given to each guest
framing in equation form we get;
Number of guest can have cake = [tex]\frac{3}{\frac{1}{4}} = 3\times\frac{4}{1} =12[/tex]
Hence Miss Silver stein can serve for 12 guests with amount of cake that she has bought.
A race car travels with a constant tangential speed of 82.6 m/s around a circular track of radius 667 m. Find the magnitude of the total acceleration.
Answer:
TOTAL ACCELERATION =10.229m/s²
Step-by-step explanation:
total acceleration = [tex]\sqrt{centripetal accleration^{2} +tagential acceleration^{2} }[/tex]
since tangential speed is constant , tangential acceleration =0
Thus total acceleration = centripetal acceleration.
centripetal acceleration = v²/r
v=82.6m/s , r= 667m
centripetal acceleration = 82.6²/667
centripetal acceleration = 10.229m/s²
TOTAL ACCELERATION =10.229m/s²
Final answer:
The magnitude of the total acceleration of a race car traveling with a constant tangential speed of 82.6 m/s around a circular track of radius 667 m is 10.20 m/s², which is the centripetal acceleration.
Explanation:
The question asks to find the magnitude of the total acceleration of a race car traveling with a constant tangential speed of 82.6 m/s around a circular track of radius 667 m. In circular motion, the total acceleration is the centripetal acceleration, since the tangential speed (speed along the arc of the circle) is constant and there is no tangential acceleration. The formula for centripetal acceleration (ac) is ac = v2 / r, where v is the tangential speed and r is the radius of the circular path.
Using the given values:
ac = (82.6 m/s)2 / 667 m = 10.20 m/s2
Therefore, the magnitude of the centripetal acceleration of the race car is 10.20 m/s2.
I will give brainilest please help!!! ASAP.
PLEASE MARK BRAINLIEST!
Answer:
Life hack in this answer!
Step-by-step explanation:
The correct table is the second one, or the table on the bottom right. (Picture included).
Life hack --> To find the relative percentage/frequency of something, all you have to do is take the frequency you are trying to find, and divide it with the total.
Example: You are trying to find the frequency of REGULAR MALE jeans. What is its frequency? To find, all you have to do is divide 120 from 28. Like this:
28 = male regular jeans
120 = total
28 ÷ 120 = ?
28 ÷ 120 = 0.23333333...
Final answer: 0.23
In this scenario, we must round. But remember that you might not always need or have to round.
And, as predicted, the answer of 0.23 is in the second table under REGULAR MALE jeans.
If you have any questions, let me know!
I hope this helps!
- sincerelynini
Sam has a total of 40 dvds, movies and tv shows. The number of movies is 4 less then 3 times the number of tv shows. Write and solove a system of equations to find the number of movies and tv shows.
Answer:Sam has 29 movies.
Sam has 11 TV shows.
Step-by-step explanation:
Let x represent the number of movies that Sam has.
Let y represent the number of TV shows that Sam has.
Sam has a total of 40 dvds, movies and tv shows. This means that
x + y = 40 - - - - - - - - - - -1
The number of movies is 4 less then 3 times the number of tv shows. This means that
x = 3y - 4 - - - - - - - - - - -2
Substituting equation 2 into equation 1, it becomes
3y - 4 + y = 40
4y - 4 = 40
4y = 40 + 4 = 44
y = 44/4 = 11
x = 3y - 4 = 3 × 11 - 4
x = 33 - 4
x = 29
By creating a system of equations from the given problem, m + t = 40 and m = 3t - 4, and solving it through substitution, it was determined that Sam has 29 movies and 11 TV shows in his DVD collection.
Explanation:To solve the given problem, we need to use a system of linear equations. The two variables we need to find are the number of movies (m) and the number of TV shows (t).
According to the problem, the total number of DVDs, which includes both movies and TV shows, is 40. This can be written as an equation: m + t = 40. Additionally, we are told that the number of movies is 4 less than three times the number of TV shows. This gives us a second equation: m = 3t - 4.
Now we have the following system of equations:
m + t = 40m = 3t - 4We can solve this system by substitution. First, substitute the second equation into the first equation:
(3t - 4) + t = 404t - 4 = 404t = 44t = 11Now that we have found the number of TV shows (t), we can calculate the number of movies (m):
m = 3t - 4m = 3(11) - 4m = 33 - 4m = 29Therefore, Sam has 29 movies and 11 TV shows in his collection of 40 DVDs.
A cone has a diameter of 8 centimeters and a height that is 4 times the diameter. Using 3.14 for pl, which of the following can be used to calculate
volume of the cone?
Answer:
Volume of cone is [tex]539.89 \ cm^3[/tex].
Step-by-step explanation:
Given:
Diameter of Cone = 8 cm
Now we know that radius is half of diameter.
radius = [tex]\frac{1}{2}\times8 =4\ cm[/tex]
Also Given:
height that is 4 times the diameter.
So we can say that;
Height = [tex]4\times8 =32\ cm[/tex]
We need to find the volume of the cone.
Solution:
Now we know that Volume of the cone is given by one third times π times square of radius times height.
framing in equation form we get;
Volume of the cone = [tex]\frac{1}{3}\pi r^2h= \frac{1}{3} \pi \times (4)^2\times 32 =539.89 \ cm^3[/tex]
Hence Volume of cone is [tex]539.89 \ cm^3[/tex].
this my last question and don't know it
Answer:
i am 70% sure its a
Step-by-step explanation:
If a ball is thrown in the air with a velocity 44 ft/s, its height in feet t seconds lateris given by y = 44t -16t2. (a) Find the average velocity for thetime period beginning when t = 2 and lasting 0.5second. ft/s(b) Find the average velocity for the time period beginning whent = 2 and lasting 0.1 second. ft/s(c) Find the average velocity for the time period beginning whent = 2 and lasting 0.05 second. ft/s(d) Find the average velocity for the time period beginning whent = 2 and lasting 0.01 second. ft/s(e) Estimate the instantaneous velocity when t = 2.
Answer: a. 28ft/s. b. 40.08ft/s. c. 42.4ft/s. d. 43.68ft/s. e. - 20ft/s
Step-by-step explanation: Since your displacement was given that is (y) , we just have to differentiate y with respect to time t. That is the first derivative only.
I have worked it out and here is the attachment.
Final answer:
To find the average velocity during different time periods, we can calculate the changes in height and time. By substituting the given values of t into the height equation, we can determine the heights at different times. We can then calculate the average velocities by taking the change in height divided by the change in time. Additionally, to estimate the instantaneous velocity when t = 2, we can differentiate the height equation and substitute t = 2 into the derivative.
Explanation:
To find the average velocity for a given time period, we need to calculate the change in height and the change in time. Using the equation y = 44t - 16t^2, we can substitute the values of t = 2 and t = 2.5 to find the heights at these times. Then, we can find the average velocities.
(a) For the time period of 0.5 seconds starting at t = 2, we calculate the heights at t = 2 and t = 2.5: y(2) = 44(2) - 16(2^2) = 36 ft and y(2.5) = 44(2.5) - 16(2.5^2) = 35 ft. The average velocity is the change in height divided by the change in time: (35 - 36) ft / 0.5 s = -2 ft/s.
(b) For the time period of 0.1 second starting at t = 2, we calculate the heights at t = 2 and t = 2.1: y(2) = 36 ft and y(2.1) = 44(2.1) - 16(2.1^2) = 37.644 ft. The average velocity is the change in height divided by the change in time: (37.644 - 36) ft / 0.1 s = 16.44 ft/s.
(c) For the time period of 0.05 second starting at t = 2, we calculate the heights at t = 2 and t = 2.05: y(2) = 36 ft and y(2.05) = 44(2.05) - 16(2.05^2) = 37.079 ft. The average velocity is the change in height divided by the change in time: (37.079 - 36) ft / 0.05 s = 21.58 ft/s.
(d) For the time period of 0.01 second starting at t = 2, we calculate the heights at t = 2 and t = 2.01: y(2) = 36 ft and y(2.01) = 44(2.01) - 16(2.01^2) = 36.764 ft. The average velocity is the change in height divided by the change in time: (36.764 - 36) ft / 0.01 s = 76.4 ft/s.
(e) To estimate the instantaneous velocity when t = 2, we can calculate the derivative of the height function. The derivative of y(t) = 44t - 16t^2 with respect to t is dy/dt = 44 - 32t. Substituting t = 2 into this equation, we get dy/dt = 44 - 32(2) = -20 ft/s.
Match the vocabulary word with the correct definition. 1. an angle in the plane of a circle with the vertex at the center of the circle central angle 2. the union of the endpoints of a diameter and all points of the circle lying on one side of the diameter. minor arc 3. the union of two points of a circle, not the end points of a diameter; and all points of the circle that are in the exterior of the central angle whose sides contain the two points. major arc 4. the union of two points of a circle, not endpoints of a diameter, and all points of the circle that are in the interior of the central angle whose sides contain the two points semicircle
Answer:
1. central angle
2. semicircle
3. major arc
4. minor arc
Step-by-step explanation:
1. central angle is an angle whose vertex rest on the center of a circle, with its sides containing two radii of the same circle.
2. semicircle is simply a half circle which is formed by cutting a full circle along a diameter (that is union of the endpoints of a diameter).
3. major arc is an arc that is larger than a semicircle and is bounded by a central angle whose angle is lesser than 180°.
4. minor arc is an arc that is smaller than a semicircle and is bounded by a central angle whose angle is greater than 180°.
Answer:
major arc
1
the union of two points of a circle, not the end points of a diameter; and all points of the circle that are in the exterior of the central angle whose sides contain the two points.
2. central angle
the union of two points of a circle, not endpoints of a diameter, and all points of the circle that are in the interior of the central angle whose sides contain the two points
3. semicircle
the union of the endpoints of a diameter and all points of the circle lying on one side of the diameter.
4. minor arc
an angle in the plane of a circle with the vertex at the center of the circle
Step-by-step explanation:
A researcher wants to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). The researcher measures the amount of soil washed away for various flow rates, and from these data calculates the least-squares regression line to be: amount of eroded sol = 0.4 + 1.3x (wbere x is flow rate). The correlation between amount of eroded soil and flow rate would be:________
a) 1.3.
b) positive, but we canno say what the exact value is.
c) either positive or negative, but it is impossible to say anything about the correlation from the information given.
d) 11.3,
Answer:
b)
Step-by-step explanation:
The correlation between amount of eroded soil and flow rate would be positive because the slope is positive. The correlation coefficient cannot be determine using the given information as the information is not enough.
If we have data value or standard deviation for y and standard deviation x then the correlation coefficient can be calculated. From the given regression equation amount of eroded sol = 0.4 + 1.3x (where x is flow rate), the intercept=0.4 and slope=1.3.
We can only tell the sign of correlation coefficient by considering the sign of slope which is positive in the given scenario.
Hence, the correlation is positive but exact value cannot be determine.
What is the domain of the function f (x) = StartFraction x + 1 Over x squared minus 6 x + 8 EndFraction? all real numbers all real numbers except –1 all real numbers except –4 and –2 all real numbers except 2 and 4
Answer:
all real numbers except 2 and 4
Step-by-step explanation:
The exceptions in the domain are the values that make the denominator zero. For a denominator of x² -6x +8 = (x -4)(x -2), the values that make it zero are x=4 and x=2.
The domain is all real numbers except 2 and 4.
Answer:
Option D is correct.
The domain of the function f(x) is all real numbers except 2 and 4.
Step-by-step explanation:
f(x) = (x+1)/(x²-6x+8)
The domain of a function expresses the region of values of x, where the function exists.
And logically, a function exists where ever f(x) has a finite value. That is, the only point where A function does not exist is when f(x) gives infinity.
For a rational function, the point where a function doesn't exist is when the denominator of the rational function is equal to 0. Because (numerator/0) --> ∞
So, the denominator in this question is
x²-6x+8
The function doesn't exist when
x²-6x+8 = 0
So, we solve the quadratic equation that ensues to get the values of x where the function doesn't exist.
x²-6x+8 = 0
x² - 4x - 2x + 8 = 0
x(x-4) - 2(x-4) = 0
(x-2)(x-4) = 0
(x-2) = 0 or (x-4) = 0
x = 2 or x = 4
This means that the function doesnt exist at x = 2 and x = 4
Indicating further that the function exists everywhere except at x = 2 and x = 4.
Hence, from the definition of domain given above, it is clear that the domain of the given function is all real numbers except 2 and 4.
Hope this Helps!!!
Constant of 15-8y
a.15
b.8
c. -8
d. -15
The constant of the expression 15-8y is 15
Constants are values that are not attached to any variable. For example:
The constant of x + 5 is 5Now given the expression 15 - 8y
First, we can re-arrange to have:
-8y + 15
From the expression, we can see that 15 is not attached to any variable. Hence the constant of the expression is 15
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A high positive correlation is found between college students' age and their GPA. However, if one student aged 44 with a high GPA is omitted from the study, the correlation all but disappears. This is an example of:
Answer:
Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.
Step-by-step explanation:
Previous concepts
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
By definition an outlier is a point "that diverges from an overall pattern in a sample". The residual for this outiler is usually high and when we have presence of outliers our model probably would be not significant since the tendency is not satisfied.
By definition and influential point is a point that has "a large effect on the slope of a regression line fitting the data:. And usually represent values that are too high or low respect to the others.
Solution to the problem
For this case we assume that we have a high positive correlation between college student's age and the GPA.
So we assume that [tex] 0.7 \leq r \leq 1[/tex]
And We see that after introduce the value of 44 for the age the correlation disappears, that means decrease significantly.
Then we can conclude that this value is an influential point since is affecting probably the significance of the model and for this reason is that we see that the correlation disapear.
One inch of rain on a square foot of land weights 5.2 pounds. About how many ghallons of rain are there? round your answer to the nearest tenth
Answer: 0.60 gallon
Step-by-step explanation:
There are 12pounds in a standard US gallon.
12pounds= 1 gallon
5.2 pounds=?
5.2/12 × 1 gallon
0.624 gallon
Rounding to the nearest tenth =0.60
PLEASE PLEASE PLEASE HELP ME!! WILL GIVE BRAINLIEST!!!
Simplify the radical expression. √32x^2y^5
Answer:
The answer is 4xy^2√2y
Step-by-step explanation:
Carlos plans to build a grain bin with a radius of 15 ft. The recommended slant of the roof is 25 degrees. He wants the roof to overhang the edge of the bin by 1 ft. What should the length x be?
Answer: The length x =17.64ft
Step-by-step explanation:
Looking at the diagram,to find x,we ues adj/hyp = cos 25°
16/x=cos25°
Cross multiply
X=16/cos25°
X=17.64ft
Answer:
17 feet 8 in
Step-by-step explanation:
im doing it in class imao
A window-washer is climbing a 37-foot ladder leaning against a building. The ladder touches the building 35 feet above the ground. What is the distance from the bottom of the ladder to the base of the building?
Answer: the distance from the bottom of the ladder to the base of the building is 12 feet.
Step-by-step explanation:
The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.
The length of the ladder represents the hypotenuse of the right angle triangle.
The distance from the ground to the point where the ladder touches the wall of the building represents the opposite side
Therefore, to determine the distance from the bottom of the ladder to the base of the building, x, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
37² = 35² + x²
1369 = x² + 1225
x² = 1369 - 1225 = 144
x = √144 = 12 feet
Final answer:
To find the distance from the bottom of the ladder to the base of the building, use the Pythagorean theorem with the given ladder height and building contact point. Calculate the distance as 12 feet.
Explanation:
A window-washer is climbing a ladder leaning against a building. In this scenario, the ladder is 37 feet long and touches the building 35 feet above the ground. To find the distance from the bottom of the ladder to the base of the building, we can use the Pythagorean theorem.
By applying the Pythagorean theorem: a² + b² = c², where a and b are the distances from the bottom of the ladder to the building and from the base to the building, respectively, and c is the length of the ladder, we can calculate the distance to be 12 feet.
Therefore, the distance from the bottom of the ladder to the base of the building is 12 feet.
Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?I. At least one of the homes was sold for more than $165,000.II. At least one of the homes was sold for more than $130,0000 and less than $150,000.III. At least one of the homes was sold for less than $130,000.A. I onlyB. II onlyC. III onlyD. I and IIE. I and III
Answer:
A. 1 only.
Step-by-step explanation:
A college bookstore marks up the price that it pays the publisher for a book by 40 %. If the selling price of a book is $ 81.00 comma how much did the bookstore pay for this book?
Answer:
32.40
Step-by-step explanation:
81 x 40% =48.60
81. -48.60 = 32.40
Answer:the college bookstore paid
$57.86 for the book.
Step-by-step explanation:
Let x represent the price that the college bookstore paid the publisher to get the book.
The college bookstore marks up the price by 40%. It means that the value of the mark up would be .40/100 × x = 0.4 × x = 0.4x
Therefore, the selling price of the book at the college bookstore would be
x + 0.4x = 1.4x
If the selling price of a book is $ 81.00, it means that
1.4x = 81
x = 81/1.4 = $57.86
Tara is leaving home to attend college the drive covers a total distance of 1100 mi terrace car can travel 400 miles on a full tank of gas how many tanks of gas will Terry car need for the entire trip
Answer:
Terry car will need 3 full tanks to complete the total distance.
Step-by-step explanation:
Given:
Total distance to be covered = 1100 miles
distance travel in full tank =400 miles.
We need to find the number of tanks Terry car needs.
Solution:
Now we can say that;
the number of tanks Terry car needs can be calculated by dividing Total distance to be covered by distance travel in full tank.
framing in equation form we get;
number of tanks Terry car needs = [tex]\frac{1100}{400}= 2.75\ tanks[/tex]
number of tanks cannot be decimal value.
Hence Terry car will need 3 full tanks to complete the total distance.
A two-dimensional array can be viewed as ________ and ________. rows, columns arguments, parameters increments, decrements All of these None of these
Answer:
rows, columns
Step-by-step explanation:
Two dimensional array can be viewed as rows and columns.
It is viewed as matrix or grid as well therefore we can conclude that it can be viewed in terms of rows and columns.
The correct option is the first one, A two-dimensional array can be viewed as rows and columns.
How to complete the statement?A two-dimensional array is a data structure that stores elements in a grid-like format with rows and columns. It can be visualized as a table or matrix.
In this context, "rows" refer to the horizontal dimension of the array. Each row consists of a series of elements that are stored sequentially from left to right. The number of rows in the array represents the height or the total count of rows.
"Columns" refer to the vertical dimension of the array. Each column consists of a series of elements that are stored sequentially from top to bottom. The number of columns in the array represents the width or the total count of columns.
By organizing data in rows and columns, a two-dimensional array allows for efficient storage and retrieval of elements. The elements within the array can be accessed by specifying both the row and column indices.
Learn more about arrays:
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x²-2x+1 let a, b, c be positive integers such that the quadratic equation ax² - bx + c = 0 has two distinct roots in the interval (0,1). Find the smallest possible value of a.
Answer:
The least value of a = 1
Step-by-step explanation:
As it has two distinct roots . According to roll's theorem there should be a point where f'(x)=0
In a quadratic equation ax² + bx + c = 0 the point of maxima or minima is
x = - b/2a
We can find by differentiating it
2ax - b= 0
x = b/2a
So 0 < b/2a < 1
0 < b/a < 2
0 < b < 2a
a > b/2
then, the least value of b = 2 and the least value of a = 1
Frank made a New Years resolution to get into better shape. He decides to join LA fitness. He has to pay a one-time enrollment fee of $50 and then membership costs $25 per month. Write an equation that represents the total costs of the gym membership based on the number of months
Answer: an equation that represents the total costs of the gym membership based on the number of months is
y = 25x + 50
Step-by-step explanation:
Let x represent the number of months that Frank makes use of the gym at LA fitness in order to get better in shape.
Let y represent the total cost of using the gym for x months.
He has to pay a one-time enrollment fee of $50 and then membership costs $25 per month. This means that the total cist for x month would be
y = 25x + 50
Oil Tankers The mean number of oil tankers at a port city is eight per day. Find the probability that the number of oil tankers on any given day is (a) exactly eight, (b) at most three, and (c) more than eight.
Answer:
a) P(8) = 0.1395
b) P(at most three) = 0.0423684
c) P(X > 8) = 0.41
Step-by-step explanation:
Data provided in the question:
Mean, μ = 8
Now,
Probability that the number of oil tankers on any given day is
a) exactly eight
using Poisson distribution
we have
P(x) = [tex]\frac{\mu^xe^{-\mu}}{x!}[/tex]
for x = 8
P(8) = [tex]\frac{8^8e^{-8}}{8!}[/tex]
or
P(8) = [tex]\frac{16777216\times e^{-8}}{40320}[/tex]
or
P(8) = 0.1395
b) at most three
i.e P(0) + P(1) + P(2) + P(3)
thus,
P(0) = [tex]\frac{8^0e^{-8}}{0!}[/tex] = 0.0003354
P(1) = [tex]\frac{8^1e^{-8}}{1!}[/tex] = 0.002683
P(2) = [tex]\frac{8^2e^{-8}}{2!}[/tex] = 0.01073
P(3) = [tex]\frac{8^3e^{-8}}{3!}[/tex] = 0.02862
⇒ P(at most three) = 0.0003354 + 0.002683 + 0.01073 + 0.02862
= 0.0423684
c) more than eight.
P(X > 8) = 1 - P(X ≤ 8)
Now,
P(0) = [tex]\frac{8^0e^{-8}}{0!}[/tex] = 0.0003354
P(1) = [tex]\frac{8^1e^{-8}}{1!}[/tex] = 0.002683
P(2) = [tex]\frac{8^2e^{-8}}{2!}[/tex] = 0.01073
P(3) = [tex]\frac{8^3e^{-8}}{3!}[/tex] = 0.02862
P(4) = [tex]\frac{8^4e^{-8}}{4!}[/tex] = 0.05725
P(5) = [tex]\frac{8^5e^{-8}}{5!}[/tex] = 0.091603
P(6) = [tex]\frac{8^6e^{-8}}{6!}[/tex] = 0.1221
P(7) = [tex]\frac{8^7e^{-8}}{7!}[/tex] = 0.13958
P(8) = [tex]\frac{8^8e^{-8}}{8!}[/tex] = 0.13758
Thus,
P(X > 8) = 1 - [ 0.0003354 + 0.002683 + 0.01073 + 0.02862 + 0.05725 + 0.091603 + 0.1221 + 0.13958 + 0.13758 ]
P(X > 8) = 1 - 0.5904814
or
P(X > 8) = 0.41
Final answer:
Explains the probability of different scenarios for the number of oil tankers at a port city per day.(a) The probability of exactly eight oil tankers is 0, as it matches the mean.
(b) The probability of at most three tankers is 0.1724.
(c) The probability of more than eight tankers is 0.
Explanation:
Oil Tankers Probability:
(a) The probability of exactly eight oil tankers is 0, as it matches the mean.
(b) The probability of at most three tankers is 0.1724.
(c) The probability of more than eight tankers is 0.
A twelve-hour clock is set at the correct time on the afternoon of May 17th. Somebody knocked the clock off the wall and now it loses 6 minutes per day. How much time will the clock be behind 3 weeks later?
1 hour and 42 minutes
2 hours and 6 minutes
3 hours and 12 minutes
2 hours and 36 minutes
Answer:
2 hours and 6 minutes. Second option
Step-by-step explanation:
Proportions
If two variables are proportional, it's easy to find the value of one of them knowing the value of the other and the proportion ratio. We know that each day our clock loses 6 minutes per day. It gives us the ratio between time lost vs days passed.
Three weeks (21 days) from now, from now, the clock will be behind a total time of 6 * 21 = 126 minutes.
Two hours are 120 minutes, thus the time behind is 2 hours and 6 minutes. Second option
The clock will be behind 3 weeks later by 2 hours and 6 minutes.
Explanation:To find out how much time the clock will be behind 3 weeks later, we first need to calculate the total amount of time the clock will lose in 3 weeks. Since the clock loses 6 minutes per day, we can multiply this by the number of days in 3 weeks (21 days). 6 minutes per day x 21 days = 126 minutes.
Next, we convert the minutes into hours and minutes. There are 60 minutes in an hour, so we divide the 126 minutes by 60 to get 2 hours and a remainder of 6 minutes.
Therefore, the clock will be behind 3 weeks later by 2 hours and 6 minutes.
Suppose that the scores on a test have a normal distribution with mean 24 and standard deviation 4. What is the proportion of scores less than 28?
Answer: 0.8413
Step-by-step explanation:
Given : The scores on a test have a normal distribution with mean 24 and standard deviation 4.
i.e. [tex]\mu= 24[/tex] and [tex]\sigma= 4[/tex]
Let x denotes the scores on the test.
Then, the probability that a student score less than 28 will be :-
[tex]P(x<28)=P(\dfrac{x-\mu}{\sigma}<\dfrac{28-24}{4})\\\\=P(z<1)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=0.8413 \ \ [\text{By z-table}][/tex]
Hence, the the proportion of scores less than 28 is 0.8413 .
At 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal. About how high is the building?
Answer:
203 feet.
Step-by-step explanation:
Please find the attachment.
Let h represent the height of the building.
We have been given that at 3:30 in the afternoon in mid-September the Kimball Tower casts a shadow about 290 feet long when the sun's rays come down at an angle about 35 degrees above the horizontal.
We know that tangent relates opposite side of a right triangle to its adjacent side.
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\text{tan}(35^{\circ})=\frac{h}{290}[/tex]
[tex]290*\text{tan}(35^{\circ})=\frac{h}{290}*290[/tex]
[tex]290*0.70020753821=h[/tex]
[tex]h=290*0.70020753821[/tex]
[tex]h=203.0601860809[/tex]
[tex]h\approx 203[/tex]
Therefore, the building is approximately 203 feet high.
Solve the system of equations by the addition method. If a system contains decimals, you may want to first clear the equation of decimals.
1.3x + 0.5y = 17
-0.7 - 2.5y = -73.4
Answer:
(x, y) = (2, 28.8)
Step-by-step explanation:
Your ability to do arithmetic should not be limited to integers. Here we see the coefficients of y are related by a factor of -5, so multiplying the first equation by 5 can make the y-terms cancel when that is added to the second equation.
5(1.3x +0.5y) +(-0.7x -2.5y) = 5(17) +(-73.4)
6.5x +2.5y -0.7x -2.5y = 85 -73.4 . . . . . eliminate parentheses
5.8x = 11.6 . . . . . . collect terms
x = 11.6/5.8 = 2 . . . . . . . divide by the coefficient of x
1.3(2) +0.5y = 17 . . . . . . substitute for x in the first equation
0.5y = 14.4 . . . . . . subtract 2.6
y = 28.8 . . . . . . . . multiply by 2
The solution is (x, y) = (2, 28.8).
Answer:x = 2
y = 28.8
Step-by-step explanation:
The given system of simultaneous equations is expressed as
1.3x + 0.5y = 17 - - - - - - - - - - - - 1
-0.7 - 2.5y = -73.4 - - - - - - - - - - - - - 2
The first step multiply all the terms by 10 in order to eliminate the decimal points. The equations become
13x + 5y = 170 - - - - - - - - - - - - 1
-7 - 25y = -734 - - - - - - - - - - - - - 2
Then we would multiply both rows by numbers which would make the coefficients of x to be equal in both rows.
Multiplying equation 1 by 7 and equation 2 by 13, it becomes
91x + 35y = - 1190
91x + 325y = 9542
Subtracting, it becomes
- 290y = - 8352
y = - 8352/- 290 = 28.8
Substituting y = 28.8 into equation 1, it becomes
13x + 5 × 28.8 = 170
13x + 144 = 170
13x = 170 - 144 = 26
x = 26/13 = 2
Solve 2r – 15 = -9r + 18.
Answer:
The answer to your question is r = 3
Step-by-step explanation:
2r - 15 = - 9r + 18
Process
1.- Add 9r in both sides
2r + 9r - 15 = - 9r + 18 + 9r
2.- Simplify
11r -15 = 18
3.- Add 15 to both sides
11r - 15 + 15 = 18 + 15
4.- Simplify
11r = 33
5.- Divide both sides by 11
11/11 r = 33/11
6.- Simplify and result
r = 3
Answer:
what ur insta?
Step-by-step explanation:
At the city Museum child omission is $5.70 and adult admission is $9.80. On Tuesday 124 tickets were sold for a total sales of $936. How many child tickets were sold that day
Answer: 68 child tickets were sold
Step-by-step explanation:
Let x represent the number of child tickets that were sold that day.
Let y represent the number of adult tickets that were sold that day.
A total of 124 tickets were sold on Tuesday. This means that
x + y = 124
At the city Museum child admission is $5.70 and adult admission is $9.80. The total sales from tickets was $936. This means that
5.7x + 9.8y = 936 - - - - - - - - -1
Substituting x = 124 - y into equation 1, it becomes
5.7(124 - y) + 9.8y = 936
706.8 - 5.7y + 9.8y = 936
- 5.7y + 9.8y = 936 - 706.8
4.1y = 229.2
y = 229.2/4.1
y = 55.9
y = 56
x = 124 - y = 124 - 56
x = 68
Ros is trying to find the solution(s) to the system {f(x)=−x3+2x2+x−2g(x)=x2−x−2.
Roz wants to find the solution(s) to this system. After analyzing the graph of the functions, Roz comes up with the following list ordered pairs as possible solutions: (0,−2), (2,0), and (−1,0).
Which work correctly verifies whether each of Roz’s ordered pairs is a solution?
A. A solution to the system will be the intersection of f(x) and g(x) such that f(x)=g(y). Roz must verify one of the following: f(0)=g(−2) and f(−2)=g(0); f(2)=g(0) and f(0)=g(2), or f(−1)=g(0) and f(0)=g(−1).
1. f(0)=−03+2(02)+0−2=−2; g(−2)=(−2)2−2−2=0 Thus, (0,−2) is a solution.
2. f(2)=−23+2(22)+2−2=0; g(0)=02−0−2=2 Thus, (2,0) is a solution.
3. f(−1)=−(−1)3+2(−1)2+(−1)−2=0; g(0)=02−0−2=2 Thus, (−1,0) is not a solution.
B.A solution to the system will be the intersection of f(x) and g(x) such that f(x)=g(x). Roz must verify that f(0)=g(0)=−2, f(2)=g(2)=0, and f(−1)=g(−1)=0 as follows:
1. f(0)=−03+2(02)+0−2=−2; g(0)=02−0−2=−2 Thus, (0,−2) is a solution.
2. f(2)=−23+2(22)+2−2=0; g(2)=22−2−2=0 Thus, (2,0) is a solution.
3. f(−1)=−(−1)3+2(−1)2+(−1)−2=0; g(−1)=(−1)2−(−1)−2=0 Thus, (−1,0) is a solution.
C. A solution to the system will be the intersection of f(x) and g(x) such that f(x)=g(x). Roz must verify that f(−2)=g(−2)=0, and f(0)=g(0)=2 or f(0)=g(0)=−1 as follows:
1. f(−2)=−23+2(22)+2−2=0; g(−2)=(−2)2−2−2=0 Thus, (0,−2) is a solution.
2. f(0)=−03+2(02)−0+2=2; g(0)=02−0−2=2 Thus, (2,0) is a solution.
3. Since f(0)=g(0)=2, f(0) and g(0) cannot equal −1. Thus, (−1,0) is not a solution.
D.A solution to the system will be the intersection of f(x) and g(x) such that f(x)=g(x). Roz must verify that f(−2)=g(−2)=0, and f(0)=g(0)=2 or f(0)=g(0)=−1 as follows:
1. f(−2)=−23+2(22)+2−2=0; g(−2)=(−2)2−2−2=0 Thus, (0,−2) is a solution.
2. f(0)=−03+2(02)−0+2=2; g(0)=02−0−2=2 Thus, (2,0) is a solution.
Since f(0)=g(0)=2, f(0) and g(0) cannot equal −1. Thus, (−1,0) is not a solution.
Answer:
B. A solution to the system will be the intersection of f(x) and g(x) such that f(x)=g(x). Roz must verify that f(0)=g(0)=−2, f(2)=g(2)=0, and f(−1)=g(−1)=0.
Step-by-step explanation:
In order for f(x) = g(x) to have a solution the same values of x and y must satisfy both ...
y = f(x)y = g(x)This will be the case for (x, y) = (-1, 0) or (0, -2) or (2, 0).
Ros can show this using the steps offered in answer choice B:
1. f(0)=−0^3+2(0^2)+0−2=−2; g(0)=0^2−0−2=−2. Thus, (0,−2) is a solution.
2. f(2)=−2^3+2(2^2)+2−2=0; g(2)=2^2−2−2=0. Thus, (2,0) is a solution.
3. f(−1)=−(−1)^3+2(−1)^2+(−1)−2=0; g(−1)=(−1)^2−(−1)−2=0. Thus, (−1,0) is a solution.