The square cake can be distributed in such a way that each person out of 15 guest may get 8 , with the least amount left over .
The Correct option is (1).
What is Volume of any shape?
The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms ofof cubic units.
First find the volume of square cake,
Volume = l x b x h
= 8 x 8 x 2
=128
Now there are total 15 guests, Each of get
=
= 8.533
2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)
Volume=
=
=
=28.26
Now there are total 15 guests, Each of get
=
= 1.884
3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)
Volume=
=
=
=50.24
Now there are total 15 guests, Each of get
=
= 3.349
4. Volume = l x b x h
= 6 x 9 x 2
=108
Now there are total 15 guests, Each of get
=
= 7.2
According to question each person may get 8 .
Only the square cake can be distributed in such a way that each person may get 8 , with the least amount left over .
What’s x+2(7-x)=12 but like this ( , )
The solution to the equation x + 2(7 - x) = 12 is x = 2.
What is the solution to the given equation?Given the equation in the question:
x + 2(7 - x ) = 12
To solve the equation, you need to use algebraic techniques to isolate the variable x on one side of the equation.
x + 2(7 - x) = 12
Apply distributive property
x + 2×7 + 2×-x = 12
x + 14 - 2x = 12
Combine like terms by subtracting 14 from both sides:
x - 2x = 12 - 14
-x = -2
Solve for x by dividing both sides by -1:
-x/-1 = -2/-1
x = 2
Therefore, the value of x is 2.
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A researcher claims that the proportion of smokers in a certain city is less than 20%. To test this claim, a random sample of 700 people is taken in the city and 150 people indicate they are smokers.
The following is the setup for this hypothesis test:
H0:p=0.20
Ha:p<0.20
In this example, the p-value was determined to be 0.828.
Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%)
Answer:
Based on the hypothesis test conducted with a significance level of 5%, we fail to reject the null hypothesis that the proportion of smokers in the city is 20%. This means that we do not have sufficient evidence to conclude that the proportion of smokers is less than 20%. The p-value of 0.828 suggests that there is a high probability that the observed proportion of smokers in the sample is due to chance and not a true difference in the proportion of smokers in the population. Therefore, we cannot conclude that the city has a lower proportion of smokers than 20%.
In this hypothesis test set up by the researcher, the p-value is 0.828, which is greater than the significance level (0.05). Therefore, we do not reject the null hypothesis, meaning there is not enough statistical evidence to validate the researcher's claim that the proportion of smokers is less than 20%
Explanation:A hypothesis test in statistics uses test statistics based on sample data to accept or reject a null hypothesis. In this scenario, the null hypothesis (H0) states that the proportion of smokers (p) is 20%. The alternative hypothesis (Ha) claims that the proportion of smokers is less than 20%. The p-value is a measure of the probability that the observed data could occur under the null hypothesis. In our case, a p-value of 0.828 means that there is an 82.8% chance of observing the data if the true proportion of smokers is 20%, or higher.
Usually a threshold known as the significance level (in this case 5% or 0.05) is used to determine whether the null hypothesis should be rejected or not. If the p-value is less than or equal to the significance level, it suggests that the observed data is inconsistent with the null hypothesis, and the null is usually rejected. However, since our p-value is greater (0.828 > 0.05), we would not reject the null hypothesis, suggesting that there is not enough evidence to support the researcher's claim that the proportion of smokers is less than 20%.
Therefore, the conclusion is that the researcher's claim cannot be validated using the provided data.
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A group of 7 friends is planning a hike. Each friend will need of a gallon of water to drink during the hike. How many gallons of water will the group need for the hike?
Question 10 of 10
A minor arc will have a measure that is
O A. less than 180°
B. equal to 180°
OC. more than 180°
Answer:
Less than 180
Step-by-step explanation:
Minor: Less than 180
Major: More than 180
compute (x^2 + 3x - 10) / (x + 5)
Step-by-step explanation:
[tex] \frac{ {x}^{2} + 3x - 10 }{x + 5} \\ = \frac{(x + 5)(x - 2)}{(x + 5)} \\ = (x - 2)[/tex]
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Which expression is equivalent to 5(6x + 3y)?
A 11x+3y
B 11x+8y
C 30x+3y
D 30x+15y
Answer:
The answer is **D. 30x+15y**.
```
5(6x + 3y) = 5*6x + 5*3y = 30x + 15y
```
Step-by-step explanation:
1. Distribute the 5:
```
5(6x + 3y) = (5 * 6x) + (5 * 3y)
```
2. Simplify:
```
5(6x + 3y) = 30x + 15y
```
Therefore, 5(6x + 3y) is equivalent to 30x + 15y.
Use the even and odd properties of the following functions to answer the questions:
a) If secθ=-3.1,then sec(-θ)=?
b)If sinθ=0.62,then sin(-θ)=?
Answer:
[tex]sec(-\theta)=-3.1[/tex]
[tex]sin(-\theta)=-0.62[/tex]
Step-by-step explanation:
Part a.
[tex]sec(\theta)[/tex] is related to [tex]cos(\theta)[/tex] through a reciprocal relationship [tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex].
Since [tex]cos(\theta)[/tex] is an even function (reflecting left-right across the y-axis doesn't change the graph), then [tex]sec(\theta)[/tex] is also an even function.
For any input in the domain, even functions produce the same output if the opposite of the input is used. In other words, if "f" is an even function, for all x in the domain of f, [tex]f(x)=f(-x)[/tex].
Thus, for the secant function, if a mystery value "x" is used as an input, and -3.1 is obtained as an output, then if the opposite of x, or -x, is input into the secant function, the output will also be -3.1.
[tex]sec(-\theta)=-3.1[/tex]
Part b.
The [tex]sin(\theta)[/tex] function does not reflect left-right across the y-axis to produce the same graph, so the sine function is not even.
However, the sine function can be rotated 180 degree about the origin, sometimes thought of as reflecting through the origin, to produce the same graph. Visually, this is an "odd" function.
For any input in the domain, if the opposite of the input is used, odd functions produce the opposite of the original output. In other words, if "g" is an odd function, for all x in the domain of g, [tex]-g(x)=g(-x)[/tex].
Thus, for the sine function, if a mystery value "x" is used as an input, and 0.62 is obtained as an output, then if the opposite of x, or -x, is input into the sine function, the output will be the opposite of 0.62, meaning -0.62.
[tex]sin(-\theta)=-0.62[/tex]
Assistance needed pls and thanks
By using the parallelogram method, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, 1).
How to add vectors by using the head to tail method or parallelogram method?In Mathematics, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."
Furthermore, the head to tail method of adding two (2) vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).
By adding the given vectors algebraically, we have the following:
[tex]\vec a + \vec b[/tex] = (2, -3) + (1, 4)
[tex]\vec a + \vec b[/tex] = [(2 + 1), (-3 + 4)
[tex]\vec a + \vec b[/tex] = (3, 1).
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Please help me out it’s a new topic and I don’t know how to do it
Answer:
=x2-100
Step-by-step explanation:
When I said x2 I mean (x*x)
If tanθ=-5/2 and sinθ>0, find the exact values of sinθ,cosθ,secθ,cscθ,cotθ.
The exact values are;
sinθ = -5/√29
cosθ = 2/√29
secθ =√29/2
cscθ = -√29/5
cotθ = -2/5
We are given that
tanθ=-5/2 and sinθ>0
First quadrant: I, 0°<θ<90°
We can find the first quadrant between 0° and 90° , the values from 0 to the positive numbers for the x-axis and the y-axis, the functions sine, cosine and tangent will always have positive values.
sinθ = -5/√29
cosθ = 2/√29
secθ =√29/2
cscθ = -√29/5
cotθ = -2/5
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Assume that women's heights are normally distributed with a mean given by μ = 63.6 in, and a standard deviation given by a = 2.5 in. Complete parts a and b.
a. If 1 woman is randomly selected, find the probability that her height is between 62.9 in and 63.9 in.
The probability is approximately
(Round to four decimal places as needed.)
The probability that the woman's height is between 62.9 in and 63.9 in is 0.1580
Calculating the probability of values from the the z-scoresFrom the question, we have the following parameters that can be used in our computation:
Mean = 63.6Standard deviation = 2.5Age = between 62.9 and 63.9So, the z-scores are
z = (62.9 - 63.6)/2.5 = -0.28
z = (63.9 - 63.6)/2.5 = 0.12
i.e. between a z-score of -0.28 and a z-score of 0.12
This is represented as
Probability = (-0.28 < z < 0.12)
Using a graphing calculator, we have
Probability = 0.1580
Hence, the probability is 0.1580
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Find m so that x + 5 is a factor of - 3x^4 - 10x^3 + 20x^2 - 22x + m.
If x + 5 is a factor of the given polynomial, then (x + 5) must divide the polynomial evenly, meaning that the remainder is 0 when the polynomial is divided by x + 5.
We can use polynomial long division or synthetic division to find the quotient and remainder, but it's easier to use the fact that if x + 5 is a factor, then (-5) must be a root of the polynomial.
So, we can substitute x = -5 into the polynomial and set it equal to 0 to find m:
-3(-5)^4 - 10(-5)^3 + 20(-5)^2 - 22(-5) + m = 0
Simplifying and solving for m:
-3(625) + 10(125) + 20(25) + 110 + m = 0
-1875 + 1250 + 500 + 110 + m = 0
m = 1015
Therefore, m = 1015 so that x + 5 is a factor of - 3x^4 - 10x^3 + 20x^2 - 22x + m.
Element X is a radi
an experiment starts out with 490 grams of Element X, write a function to represent
the mass of the sample after t years, where the monthly rate of change can be found
from a constant in the function. Round all coefficients in the function to four decimal
places. Also, determine the percentage rate of change per month, to the nearest
hundredth of a percent.
In a survey, 54.5% of respondents have portable earbuds and 30% of the respondents who have portable earbuds also have a smart speaker. What is the probability that a respondent has both portable earbuds and a smart speaker? If necessary, round to the nearest hundredth of a percent.
The probability that a respondent has both portable earbuds and a smart speaker is 0.16
What is the probability that a respondent has both portable earbuds and a smart speaker?From the question, we have the following parameters that can be used in our computation:
54.5% of respondents have portable earbuds 30% of the respondents who have smart speaker.This means that
P(earbuds) = 54.5%
P(smart speaker) = 30%
Using the above as a guide, we have the following:
P = P(earbuds) * P(smart speaker)
Substitute the known values in the above equation, so, we have the following representation
P = 54.5% * 30%
Evaluate
P = 0.16
Hence, the probability is 0.16
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50 Points! Multiple choice algebra question. Which function represents exponential growth? Photo attached. Thank you!
The exponential growth model is represented by the function y = 10 · 3ˣ. (Correct choice: D)
What function is an exponential growth function?
In this problem we must determine what function does represent an exponential growth model. With this purpose, we must define and understand the following functions:
Exponential growth model
y = a · rˣ, for r > 1.
Exponential decay model
y = a · rˣ, for 0 < r < 1.
Polynomic model
y = ∑ cₙ · xⁿ
The function y = 10 · 3ˣ represents an exponential growth model.
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College Level Trig Question Any help will do!!
The value of x in the equation y = 9 sec(2x) at [0, π/4) ∪ (π/4, π/2] is x = 1/2[sec₋¹(y/9)]
Calculating the values of xFrom the question, we have the following parameters that can be used in our computation:
y = 9 sec(2x)
The interval of x is also given as
[0, π/4) ∪ (π/4, π/2]
This means that the values of x is from 0 to π/2, however, the function is undefined at x = π/4 i.e. there is a hole at x = π/4
Next, we set the equation to y
So, we have
9 sec(2x) = y
Divide both sides by 9
sec(2x) = y/9
Take the arc sec of both sides of the equation
2x = sec₋¹(y/9)
Divide both sides by 9
x = 1/2[sec₋¹(y/9)]
Hence, the value of x is x = 1/2[sec₋¹(y/9)]
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Yogi is installing carpet in the hotel lobby. He Charges 4.30$ per square foot for the carpet plus $75 installation fee what is the total cost
If Yogi Charges 4.30$ per square foot for the carpet plus $75 installation fee, the total cost of installing carpet in the hotel lobby with Yogi is $2,225.
To determine the total cost of installing carpet in the hotel lobby with Yogi, we need to know the area of the lobby in square feet. Once we have the area, we can use Yogi's pricing scheme to calculate the total cost.
Assuming that we have measured the area of the lobby to be 500 square feet, we can calculate the total cost as follows:
Cost of carpet = area × price per square foot
= 500 × $4.30
= $2,150
Cost of installation = $75
Total cost = cost of carpet + cost of installation
= $2,150 + $75
= $2,225
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find two numbers who’s product is -9 and who’s sum is -8
Answer:
1, -9
Step-by-step explanation:
xy = -9
x + y = -8 solve this for x and substitute into the 1st equation
x = -8 - y
(-8 - y)y = -9
-y² - 8y + 9 = 0
y² + 8y -9 = 0
Solve for y by factoring:
(y - 1)(y + 9) = 0
y = 1, -9
x(1) = -9
x = -9
x(-9) = -9
x = -9/-9 = 1
what is the mode of 14, 17, 21, 28, 40
Answer:
24
Step-by-step explanation:
14 + 17 + 21 + 28 +40 / 5
120 / 5
24
PLEASE HELP ME WITH THE WHOLE PROBLEM PLEASEEEE
The probability of getting blue or green is 1/3, the probability of getting blue is 3/4 and there are 8 blue marbles.
What is the probability in each case?a) If the probability of getting a yellow marble is 2/3, then the probability of getting a blue or green marble is:
P(blue or green) = 1 - P(yellow) = 1 - 2/3 = 1/3
b) If the probability of getting a green marble is 1/4, then the probability of getting a blue marble is:
P(blue) = 1 - P(green) = 1 - 1/4 = 3/4
c) The total number of marbles in the bag is 24. Let x be the number of blue marbles. Then the number of yellow marbles is 2x, and the number of green marbles is 24 - x - 2x = 24 - 3x. We know that:
2x/24 = 2/3 (probability of getting a yellow marble is 2/3)
=> x = 8
Therefore, there are 8 blue marbles in the bag.
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A red marble is drawn from a bag containing 3 red and 3 blue marbles. If the red marble is not replaced, find the probability of drawing a second marble that is blue.
The probability of drawing a second marble that is blue is 3/5
Finding the probability of drawing a second marble that is blue.From the question, we have the following parameters that can be used in our computation:
A red marble is drawn from a bag containing 3 red and 3 blue marbles.
If the marbles were not replaced, then we have
P(Red) = 3/6
Now there are
3 blue marbles and 2 red marbles left
So, we have
The probability of choosing a blue marble, after a red marble is
P(Blue) = 3/5
Evaluate
P(Blue) = 3/5
Hence, the probability of choosing a blue marble, after a red marble is 3/5
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2. How does making tables help you
identify relationships between terms in
patterns?
Answer:
Step-by-step explanation:
well if you know the term than you know the pattern
Solve and check: 3/4h+11=20 helpp!
Answer: 12
Step-by-step explanation:
We have to find h so the first step is to subtract the 11 from the 20
3/4h=9
Then to move the 3/4 over to the other side, you must multiply it by it's reciprocal, 4/3.
h= 4/3 x 9
This equals 12.
The function f(x) = 2-5* can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function? 0 2 05 10 • 32
The given function does not represent the curve passing through the given points. The multiplicative rate of change of the function is 5.
What is Curve Line ?A curve is a continuous, smooth line that gradually alters direction. Rather than being straight line that follows a curve may be referred to as a curve line. A curve line can be made by connecting a number of non-straight-line-lying sites. In mathematics, a curve is a geometrical object that can be described by equations, such as parametric or function equations.
The rate of change of a function is the ratio of the change in the output (y) to the change in the input (x). In this case, we can calculate the rate of change between the first two points:
Changing at what rate between (1, 10) and (2, 50)?
Y change = 50 – 10 = 40
Variation in x = 2 - 1 = 1
Rate of change equals change in y/change in x, or 40/1, or 40.
In a similar manner, we can determine how quickly the second and third points will change:
The change between (2, 50) and (3, 250) is as follows:
Changing y by 250 - 50 equals 200
Variation in x = 3 - 2 = 1
Rate of change equals change in y/change in x, which is 200/1, or 200.
Now that we have the second rate of change, we can compute the multiplicative rate of change by dividing it by the first:
Multiplicative rate of change is equal to 200/40, or 5.
The function's multiplicative rate of change is thus 5.
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what is the area of a circle with the diameter of 22 in
Answer:380.1 square inches
Step-by-step explanation:Area of a circle in terms of diameter: Area = π· (d2) 2 = 3.14· (222) 2 = 3.14· (11) 2 = 380.1 square inches (*)
If g(x) = 3x -2 and (gof)(x) = 15x + 10, find f(x).
Answer:
the function f(x) is f(x) = 5x + 4.
Step-by-step explanation:
To find f(x), we need to use the formula:
(gof)(x) = g(f(x)) = 3f(x) - 2
We are given that (gof)(x) = 15x + 10, so we can substitute this expression into the formula to get:
3f(x) - 2 = 15x + 10
Simplifying this equation, we get:
3f(x) = 15x + 12
Dividing both sides by 3, we get:
f(x) = 5x + 4
Therefore, the function f(x) is f(x) = 5x + 4.
22. The expression 3(-4b) - 2(a - b - c) is equal to which of the following expressions?
(1) -2a - 10b - 2c
(2) -2a - 10b + 2c
(3) -2a -5b + 2c
(4) -2a -4b - 2c
(5) 2a-4b - 2c
Answer:
We can simplify the expression as follows:
3(-4b) - 2(a - b - c) = -12b - 2a + 2b + 2c
Combining like terms, we get:
= -2a - 10b + 2c
Therefore, the expression 3(-4b) - 2(a - b - c) is equal to option (2), -2a - 10b + 2c.
Step-by-step explanation:
Im smart
esson Quiz
The ages, in years, of 6 volunteers at the local food pantry are listed below. If a 7th volunteer joins them, what would their age be so that the range of their ages will be 557
(56, 81, 54, 47, 45, 94)
O
S
8
18
10
The age of the 7th volunteer has to be 602 years so that the range of the all volunteer ages will be 557.
Given ages of 6 volunteers = (56, 81, 54, 47, 45, 94)
The range = maximum value - minimum value.
So, range of the given list = 94 - 45 = 49.
To increase, the range to 557, we have to add an age that is greater than 94, To obtain that age we have to solve 557 - 45 = 508. [here 557 is the maximum value]
Now, by adding the obtained range to the 94 we can get the required age of 7th volunteer. So 508 + 94 = 602.
From the above explanation, we can conclude that the age of the 7th volunteer has to be 602 years which is unrealistic so that the range becomes 557.
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what are the answers to these questions?
If the line passes through the point (2,8) that cuts off the least area from the first quadrant, the slope is 8/3 and the y-intercept is 0.
To find the equation of the line that passes through the point (2, 8) and cuts off the least area from the first quadrant, we need to first determine the slope of the line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
We can use the point-slope form of the equation of a line to find the slope. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line. Plugging in (2, 8) as the point, we get:
y - 8 = m(x - 2)
Next, we want to minimize the area that the line cuts off in the first quadrant. Since the line passes through the origin (0, 0), the area cut off by the line in the first quadrant is equal to the product of the x- and y-intercepts of the line.
We can express the x-intercept in terms of y by setting y = 0 in the equation of the line and solving for x:
0 - 8 = m(x - 2)
x = 2 + 8/m
The y-intercept is simply the y-coordinate of the point where the line intersects the y-axis, which is given by:
y = mx + b
8 = 2m + b
b = 8 - 2m
We can now express the area cut off by the line as:
A = x*y
A = (2 + 8/m)*8 - (8 - 2m)*2/m
A = (16 + 64/m) - (16 - 4m)/m
A = 64/m + 4m/m
To minimize the area, we can take the derivative of A with respect to m and set it equal to zero:
dA/dm = -64/m² + 4/m² = 0
64 = 4
m = 8
Plugging m = 8 into the equation for the x-intercept, we get:
x = 2 + 8/8 = 3
So the equation of the line is y = 8x/3.
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The line plot shows the number of televisions
owned by the families in a neighborhood. Use
clusters, gaps, peaks, outliers, symmetry,
skewness, and spread to describe the shape of
the distribution and summarize the data. (Example 1)
●●●+o
...
Number of Televisions
.....
N.
2
.....
●
4
6
8
10
The correct statements are as follows:-
There is a cluster from 3 to 4.
There is a gap between 1 and 3.
There is a peak at 4.
The data is skewed left.
We have,
Scatter plots are graphs that show how two variables in a data collection relate to one another. On a two-dimensional plane or in a Cartesian system, it represents data points.
The right statements for the dot plots are as follows:-
There is a cluster from 3 to 4.
There is a gap between 1 and 3.
There is a peak at 4.
The data is skewed left.
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