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Mia is building a three-sided shelter for her action figures. The shelter will resemble a rectangle with one of the long sides removed. She has boards that measure 36 inches, 39 inches, and 42 inches in length; all the boards are the same width. Mia will need to convert some of these measurements into other imperial units to build the shelter the way she wants.

Mia will use one of these boards for the length of the shelter. She knows she wants the length of the shelter to measure 3.25 feet. She will use a different board for the width of the shelter. The width of the shelter will be shorter than the length.

Which board will Mia use for the length of the shelter, given that 1 foot = 12 inches?

What is the width of the shelter, measured in feet?

Mia needs to cut the third board to match the width of the shelter. How many feet of board will she need to cut off the existing board to reach this goal?

The best estimate for the age of the sample is; 9.4 days

We are told that;

The amount of a sample remaining after t days is given by the equation; P(t) = A(¹/₂)^(t/h)

Where;

A is the initial amount of the sample.

h is the half-life, in days, of the substance

The equation is:

P(t) = A(¹/₂)^(t/h)

If a sample contains 18% of the original amount of Radon - 222 and h = 3.8, then we have;

0.18 * A = A * (0.5)^(t/3.8)  

divide both sides of the equation by A to get;

0.18 = ( 0.5 )^(t/3.8)

(t/3.8)log 0.5 = log 0.18

(t/3.8) = log 0.18/log 0.5

t/3.8 = 2.47

t = 3.8 * 2.47 ≈ 9.4 days

This is the best estimate for the age of the sample

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The complete question is;

The amount of a sample remaining after t days is given by the equation P(t)=A(1/2)^(t/h), where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?

Answer:

It's C

Step-by-step explanation:

Answer:

-2,838

Step-by-step explanation:

A good way to do this is 2,938-100 which equals 2,838. Then since you know it will be a negative number add the negative sign.

Answer:

1 liter

Step-by-step explanation:

A milliliter is 1/1000 of a meter; measuring a pool by millimeters wouldn't make sense.

Answer:

15 dimes and 6 pennies

The 5th value of the 60% percentile is 47 when for each test score in the data set is 12, 28, 35, 47, 49, 50.

Given that,

For each test score in the data set, the percentile rank is determined. 12, 28, 35, 42, 47, 49,  

We have to find what number represents the 60% of the population.

We know that,

So,

Percentile rank =[(Number of values below x)+0.5]/ total number of values × 100

For 12,

Percentile rank = [0 +0.5]/7×100

= 7th

For 28,

Percentile rank = [1 +0.5]/7×100

= 21st

For 35,

Percentile rank = [2 +0.5]/7×100

= 36th

For 42,

Percentile rank = [3 +0.5]/7×100

= 50th

For 47,

Percentile rank = [4 +0.5]/7×100

= 64th

For 49,

Percentile rank = [5 +0.5]/7×100

= 79th

For 50,

Percentile rank = [6 +0.5]/7×100

= 93rd

Now,

n = 7

60th percentile = 60% of n

So,

60% of n = 60/100×7

= 0.6×7

= 4.2

Therefore, The 5th value of the 60% percentile is 47 when for each test score in the data set is 12, 28, 35, 47, 49, 50.

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The domain of the red curve in the given graph is

x > 4

The domain is controlled by the input values. considering the graph the input values are in the x axis

The least number and the maximum number is what makes the domain as it shows the extents the input values can go

The maximum number is not showing so we assume infinity since the curve continued.

For the minimum this is the point before 5 which is 4

The domain starts from 4, with 4 not inclusive to infinity and the correct option is x > 4

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to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term then it is a true statement

we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.

So, For his purpose, we know that the

A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.

And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.

By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.

So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

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Answer: 5

Step-by-step explanation:

slope is m in the formula y=mx+b

plug in the numbers for m and that's the slope

Answer:

Step-by-step explanation:

The answer is that yes it is because a pentagon has three triangles inside it  and a triangle is equal to 180 degrees so you times 180 times three and you get 540 degrees so yes that is correct!

Answer:

[tex]f(g(16)) = 6[/tex] and [tex]f(g(x)) = \sqrt{x} + 2[/tex]

Step-by-step explanation:

Step 1 and Step 2 appear to be asking the same thing, so I will assume you meant for g(16) to be found in Step 1 and for f(g(16)) to be found in Step 2.

Step 1: Find g(16)

[tex]g(x) = \sqrt{x}[/tex], so we must plug in 16 for x to find g(16)

[tex]g(16) = \sqrt{16} = 4[/tex]

Step 2: Find f(g(16))

In order to do this, we must plug the value we found for g(16) into the equation for f(x). Thus, we must plug in 4 (the value we found in Step 1) for x in f(x).

[tex]f(x) = x + 2[/tex], so we must plug in 4 to find f(4)

[tex]f(4) = 4 + 2 = 6[/tex]

Thus, [tex]f(g(16)) = 6[/tex]

Step 3: Find f(g(x))

We must plug in the value of g(x) into f(x) to find f(g(x)).

These are the expressions for f(x) and g(x):  [tex]g(x) = \sqrt{x}[/tex], [tex]f(x) = x + 2[/tex]

We find that [tex]f(g(x)) = \sqrt{x} + 2[/tex]

The required value of the function f(g(16)) is given as f(g(16)) = 6.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
f(x) = x + 2
g(x) = √x

In order to determine f(g(16)),
g(16) = √16
g(16) = 4

Now,

f(g(16)) = 4 + 2 = 6
f(g(16)) = 6

Thus, the required value of the function f(g(16)) is given as f(g(16)) = 6.

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Shortest time taken for a is 0.666hours and for b is 0.866hours.

Take a variable x on the possible road. Evaluate an equation of time in terms of x and find the extrema of the function. To find extrema differentiate the function and equal it to zero. Then find the roots of equation to get the extreme value, which should be the minimum time path.

A is initial point

P is oasis

S is intermediate point

Let us assume he directly reaches  x km from N at S.

then AS=[tex]\sqrt{100+X^2}[/tex] and SP=20-X

Time taken:

[tex]\frac{\sqrt{100+X^2}}{30}[/tex]+[tex]\frac{20-X}{50}[/tex]

Differentiating it and putting this to zero gives extrema value

[tex]\frac{2x}{60(\sqrt{100+X^2})}[/tex]=[tex]\frac{1}{50}[/tex]

⇒[tex]\frac{50x}{30}[/tex]=[tex]\sqrt{100+X^2}[/tex]

⇒By squaring on both sides

⇒100+X^2=[tex]\frac{25x^2}{9}[/tex]

⇒x=7.5km

x is independent of PN as while differentiating PN term became 0

Now time:

a) t= [tex]\frac{\sqrt{100+7.5^2}}{30}[/tex]+[tex]\frac{20-7.5}{50}[/tex]=0.666hours

b) t=[tex]\frac{\sqrt{100+7.5^2}}{30}[/tex]+[tex]\frac{30-7.5}{50}[/tex]=0.866hours

Shortest time taken for a is 0.666hours and for b is 0.866hours.

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Answer:

22 is the third quartile for this set

Answer:

2398 cents

Step-by-step explanation:

Every dollar equals 100 cents

So 23 times 100 equals 2300, then we add the 98 cents left over from the dollar

Which would be 2398 cents

The inequality which represents the given phrase is 1/2(3x - 2/3) + 6 ≤  x+5​ and the solution are x ≤ -4/3.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

1/2(3x - 2/3) + 6 ≤  x+5​

3/2 x - 1/3 + 6 ≤  x+5​

3/2 x + 17/3 - x ≤ 5

x/2 ≤ -2/3

x ≤ -4/3

Hence "The inequality 1/2(3x - 2/3) + 6 ≤ x+5 represents the provided sentence, and the answer is x ≤  -4/3.".

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If a and b are independent events with p(a) = 0.38 and p(b) = 0.55, then p(a | b) = 0.38

In the given question, a and b are independent events with p(a) = 0.38 and p(b) = 0.55, then we have to find p(a | b).

Events classified as independent do not depend on other events for their occurrence.

The likelihood of both A and B happening is equal to the sum of the probabilities of A and B, which is how mathematics expresses the independence of events A and B.

If A and B are independent events, then

P(A and B) = P(A) * P(B)

Then P(A | B) = P(A and B) / P(B)

P(A | B) = P(A) * P(B) / P(B)

P(A | B) = P(A) = 0.38

Hence, if a and b are independent events with p(a) = 0.38 and p(b) = 0.55, then p(a | b) = 0.38.

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Six unrelated African American people in the United State are elected at random then the probability that  all three have type O+ blood would be 0.103823

The probability that a person in the United States has type O+ blood is 47%. Three unrelated people in the United States are selected at random. Find the probability that  all three have type O+ blood.

Since the probability of having a O+ blood is an independent event, so to find probability that  all three have type O+ blood we will use multiplication rule of independent events as:

0.47*0.47*0.47= 0.103823

Therefore, the probability that  all three have type O+ blood would be 0.103823

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Answer: z=10, y=7

Step-by-step explanation:

z+30=40

y+10=17

solve for z by isolating z, Subtract 30 from both sides

z+30-30=40-30

z=10

solve for y by isolating y, Subtract 10 from both sides

y+10-10=17-10

y=7

Answer:

2.15

Step-by-step explanation:

I will assume that "−1/4(−8.6)" is telling us to multiply (-8.6) times -(1/4):

(-1/4)*(-8.6)

= (8.6/4)

= 2.15

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~6 - 0~~)^2 + (~~1 - 9~~)^2} \implies d=\sqrt{(6 +0)^2 + (1 -9)^2} \\\\\\ d=\sqrt{( 6 )^2 + ( -8 )^2} \implies d=\sqrt{ 36 + 64 } \implies d=\sqrt{ 100 }\implies d=10[/tex]

The probability of washing dishes by me tonight will take between 15 and 16 minutes is 14.29%.

The term "uniform distribution" refers to a type of probability distribution in which the likelihood of each potential result is equal.

Let's consider, the lower limit for this distribution as a and the upper limit for this distribution as b.

The following formula gives the likelihood that we will discover a value for X between c and d,

[tex]P(c\leq X\leq d)=\frac{d-c}{b-a}[/tex]

Given the time it takes me to wash the dishes is 11 minutes and 18 minutes. From this, a = 11 and b = 18.

Then,

[tex]P(15\leq X\leq 16)=\frac{16-15}{18-11}=0.1429=14.29\%[/tex]

The answer is 14.29%.

The complete question is -

The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 18 minutes. What is the probability that washing dishes tonight will take me between 15 and 16 minutes?

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Answer: 1

Step-by-step explanation: -2 times x the x would just be 1 so -2 times 1 equals -2 then -2 plus 3 is 1

The value of  f(g(5)) is obtained as -2.

For two functions f(x) and g(x), a composite function is defined as f(g(x)) or g(f(x)). The properties of this function are as follows,

The inverse of a composite function is the same as the composition of the inverse of both functions.

The composition of two one to one functions is always one to one.

The value of f(g(5)) is equal to the value of the composite function f(g(x)) at x = 5.

The value of g(5) from the graph is 2.

Now, f(g(5)) = f(2)

The value of f(2) from the graph is -2.

Thus, f(g(5)) = -2

Hence, the value of the given composite function is f(g(5)) = -2.

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The total surface area of a solid quarter-cylinder is 10(13π + 32) cm².

Given:-

The radius of a solid quarter-cylinder = 10 cm.

Height of solid quarter-cylinder = 16 cm.

To calculate the surface area we have a formula:-

Total surface area of solid quarter-cylinder = (TSA of cylinder / 4) + 2(Area of rectangle)= 2πr(h + r)/4 + 2(r * h) = πr(h + r)/2 + 2rh .

Solution:-

r = 10 cm.

h = 16 cm.

So,

→ Area of rectangle so formed = r * h = 10 * 16 = 160 cm².

then,

→ Area of two rectangles so formed = 2 * 160 = 320 cm².

Therefore,

→ Total surface area of solid quarter-cylinder = πr(h + r)/2 + Area of two rectangles.

→ Total surface area of solid quarter-cylinder = π * 10 * (10 + 16) / 2 + 320

→ Total surface area of solid quarter-cylinder = 5π * 26 + 320

→ Total surface area of solid quarter-cylinder = 5(26π + 64)

→ Total surface area of solid quarter-cylinder = 5*2(13π + 32)

→ Total surface area of solid quarter-cylinder = 10(13π + 32) cm².

Hence, the Total surface area of a solid quarter-cylinder is 10(13π + 32) cm².

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To carpet the rectangular floor, it will cost $1,137.6. The result if obtained by multiplying the area of the carpet by the cost per square yard.

To calculate the cost of a product, multiply the product price for one item by the quantity.

We have a rectangular floor with a dimension of 27 feet by 24 feet. The carpet cost is $15.8 per square yard. Find the total cost to carpet it!

Let's change the unit of length.

The area of the carpet is

A = 9 yard × 8 yard

A = 72 square yard

The total cost is

C = A × price/square yard

C = 72 × $15.8

C = $1,137.6

Hence, the total cost to carpet the floor is $1,137.6.

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Answer:

Dilation

-by-step explanation:

the figure is dilated (larger than original)

Answer: see below

Step-by-step explanation:

They intersect at the point (2,6) which is the solution

The solution to the given quadratic equation by completing the square is; x = 3 ± √2

We are given the quadratic equation;

y = x² - 6x + 7

1) Set the value of y to zero to get;

x² - 6x + 7 = 0

2)  Remove the constant term from both sides using the opposite operation to get;

x² - 6x = -7

3) Take half of the x term and square it and add to both sides of the equation to get;
x² - 6x + 9 = -7 + 9

4) Rewrite the perfect square on the left to get;

(x - 3)²  = 2

5) Take the square root of both sides to get;

x - 3 = ±√2

6) The solution will be;

x = 3 ± √2

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