Researchers have determined that a hip roof offers the most protection to a
house during a hurricane.
a. The house has a square base with a side length of 50 feet. The house has
a variation of a hip roof in the shape of a regular pyramid with a square
base. The roof extends 1 foot beyond the walls of the house on all sides.
What is the length of each side of the base of the roof?
b. The slant height of the roof is 35 feet. Find the sum of the areas of the
lateral faces of the pyramid.
c. A metal roof covering offers the most protection to a house during a
hurricane. The cost of installing metal roof covering is $350 for every
100 square feet of roof. What is the cost of installing a metal roof
covering on the house?

45 points to first answer (actually)

Answer:

A. x/3 + 10

Explanation:

According to the question, we are to choose the equation that will result in 15 if x = 15

Looking at the first option, we are given;

f(x) = x/3 + 10

if x = 15

f(15) = 15/3 + 10

f(15) = 5 + 10

f(15) = 15

Since the result is 15, hence option A is correct.

The other functions are incorrect because they will give a value that is not 15 when 15 is substituted as x.

Answer:

Domain: [1, 7]

Range: [-4, 2]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The ordered pairs that represent points on the graph of y = 2x - 3 are (0,-3), (5,7), (-2,-7), (2,1), and (4,5).

An ordered pair is a pair of numbers written in a specific order (x,y) that represents a point in the coordinate plane.

A graph is a visual representation of data or a mathematical function that is plotted on a coordinate plane, usually with an x and y-axis. It is used to analyze trends and relationships between variables.

According to the given information:

To determine whether a given ordered pair represents a point on the graph of the equation y = 2x - 3, we need to substitute the values of x and y into the equation and see if the equation is true.

a) (3,-3):

y = 2x - 3

-3 = 2(3) - 3

-3 = 3

This is not true, so (3,-3) is not on the graph.

b) (0,-3):

y = 2x - 3

-3 = 2(0) - 3

-3 = -3

This is true, so (0,-3) is on the graph.

c) (5,7):

y = 2x - 3

7 = 2(5) - 3

7 = 7

This is true, so (5,7) is on the graph.

d) (-2,-7):

y = 2x - 3

-7 = 2(-2) - 3

-7 = -7

This is true, so (-2,-7) is on the graph.

e) (2,1):

y = 2x - 3

1 = 2(2) - 3

1 = 1

This is true, so (2,1) is on the graph.

f) (4,5):

y = 2x - 3

5 = 2(4) - 3

5 = 5

This is true, so (4,5) is on the graph.

Therefore, the ordered pairs that represent points on the graph of the equation y = 2x - 3 are: (0,-3), (5,7), (-2,-7), (2,1), and (4,5). Answer: b), c), d), e) and f).

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Red, orange, yellow, Green, Blue,indigo and violet

To evaluate whether x or o won the tic tac toe game, we need to check for the three possible winning conditions:
- A horizontal row of three x's or o's
- A vertical column of three x's or o's
- A diagonal of three x's or o's

Here's the step-by-step process:

1. Read in the first number from the file, which represents the number of data sets to follow.
2. For each data set, read in the 9 letter string representing the tic tac toe game.
3. Check for the three winning conditions by comparing the values in the string.
4. If any of the winning conditions are met, return the winning player (x or o).
5. If none of the winning conditions are met, return "No winner".

Here's the code in Python:

```
# Read in the first number from the file
num_data_sets = int(input())

# Loop through each data set
for i in range(num_data_sets):
 # Read in the 9 letter string
 game = input()

 # Check for the three winning conditions
 if (game[0] == game[1] == game[2]) or (game[3] == game[4] == game[5]) or (game[6] == game[7] == game[8]) or (game[0] == game[3] == game[6]) or (game[1] == game[4] == game[7]) or (game[2] == game[5] == game[8]) or (game[0] == game[4] == game[8]) or (game[2] == game[4] == game[6]):
   # If any of the winning conditions are met, return the winning player
   print(game[0])
 else:
   # If none of the winning conditions are met, return "No winner"
   print("No winner")
```

This code will read in the values for a tic tac toe game and evaluate whether x or o won the game.

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When Henry ran 1 5/8 miles in the morning and 9/10 miles in the afternoon, In all he a total of 2 21/40 miles

The number of miles Henry ran is calculated by addition operation

The sum of the miles Henry ran in the morning plus the number of miles he ran in the afternoon gives the what Henry ran in all

The procedure involves addition of tractions and done as follows

= 1 5/8 + 9/10

= 13/8 + 9/10

adding both fractions will result to

= 101/40 miles

= 2 21/40 miles (as a mixed number)

Henry ran a sum of 2 21/40 miles

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The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Answer:

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sofiapenaloza

05/31/2023

Mathematics

College

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The equation for the line of best fit for change in temperature, y, to amount of rain, r, is given by ŷ = − 1.4r + 0.2. On Monday, the observed amount of rain was 0.4 inches and the temperature change was 2.3 degrees. Find and interpret the residual.

2.66; The line of best fit overpredicts the temperature change.

2.66; The line of best fit underpredicts the temperature change.

1.94; The line of best fit underpredicts the temperature change.

−1.94; The line of best fit overpredicts the temperature change.

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joaobezerra

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31.3K answers

261.9M people helped

The correct statement regarding the residual in this problem is given as follows:

2.66; The line of best fit underpredicts the temperature change.

What are residuals?

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a rain amount of 0.4 inches, the predicted temperature change is given as follows:

y = -1.4 x 0.4 + 0.2

y = -0.36.

Then the residual is given as follows:

R = 2.3 - (-0.36)

R = 2.66 -> underpredicts the change.

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Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The mean is the average of a data set. It can be found by adding up all of the values in a data set and then dividing it by the number of values in the data set.

The values in this data set;

\(7,5,5,3,2,2\)

The number of values in this data set,

\(6\)

Find the mean;

\(\frac{sum\ of\ vlaues}{number\ of\ values}\)

\(=\frac{7+5+5+3+2+2}{6}\\\\=\frac{24}{6}\\\\=4\)

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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The interest that Harold pay is $768.75 and his maturity value is $17168.75.

Harold Hill borrowed $16,400

Harold must repay the loan at the end of 15 months in one payment with 3 3/4 % of interest

First we need to calculate the interest amount

=  loan amount x rate of interest x number of months

interest = (16400 x 3 3/4 x 15/12)/100

interest = $768.75

The maturity value = loan amount + interest

= 16400 + 768.75

= 17168.75

Therefore, the interest that Harold pay is $768.75 and his maturity value is $17168.75.

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Answer:

\(x+8=7*10\)

Step-by-step explanation:

Sum of X and 8: \(x+8\)

Product of seven and 10: \(7*10\)

Put them together:

\(x+8=7*10\)

Answer:

Step-by-step explanation:

y=mx+b

m= slope and b= y intercept

you'll start with a point on the y axis on -1

and the slope will go up so towards the right corner up but 2/1 points

Answer:

T = 2 pi sqrt (L/g)

g = 32 ft/s2

here

2 = 2 (22/7) sqrt (L/32)

sqrt (L/32) = 7/22

L/32 = 49/484

L = 3.24 ft

check by hanging a weight from a 3' 3" string

Step-by-step explanation:

The correlation coefficient for the data is given as follows:

r = 0.53.

Hence there is an association between the variables that is positive and not strong.

The correlation coefficient is an index between -1 and 1 that measures the relationship between two variables, as follows:

The correlation coefficient is obtained inserting the points of a data-set into a correlation coefficient calculator.

From the table given at the end of the answer, the points are given as follows:

(43, 99), (21,65), (25, 79), (42, 75), (57, 87), (59, 81).

Inserting these points into a calculator, the equation is given as follows:

r = 0.53.

Meaning that the relationship between the variables is positive and not strong.

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Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

\(\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10\)

\(\qquad\displaystyle \tt \dashrightarrow \: 5x = 100\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5\)

\(\qquad\displaystyle \tt \dashrightarrow \: x = 20\)

Value of x = 20°

Hey! there . Thanks for your question :)

Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

\( \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }\)

Solving :

\( \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }\)

Step 2: Subtracting 10 on both sides :

\( \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }\)

We get ,

\( \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }\)

Step 3: Dividing both sides by 5 :

\( \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }\)

On cancelling , we get :

\( \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar\)

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

Answer:

(4,0)

Step-by-step explanation:

You basically are plotting a point on the positive number 4 on the x line. Since they're only asking for an X and not a Y, you'd leave it as (4,0). Hope this helps!

Answer:

x = ±3

Step-by-step explanation:

(3x² + 27)(x² - 9) = 0

(3x² + 27)(x + 3)(x - 3) = 0

3x² = -27

x² = -9  

x = √-9  (this will result in an imaginary number)

x + 3 = 0

x = -3

x - 3 = 0

x = 3

Answer:

The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

In a random sample of 250 students, we found that 75 work out 4 or more times a week.

This means that \(n = 250, \pi = \frac{75}{250} = 0.3\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a p-value of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.2432\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.3568\)

The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).

Answer:

-3 and 4

Step-by-step explanation:

since they aren't multiplied a variable

Answer:

A would be your answer if I'm not mistaken

Answer:

x=4.875

Step-by-step explanation:

19.5=4x

19.5/4=4.875

x=4.875

Check:

4.875×4=19.5

Answer: $35x 12= $420 so that's for the remaining 12 months. $420+ 75=$495. The next step is to multiply $25 and 6. $25x6= $150.

$495+$150= $645 per month.

Step-by-step explanation:

The answer is when x = 1.75, y is approximately 5.69.

What is the equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

To evaluate y = 1.4 (2.3)^x when x = 1.75, we substitute x = 1.75 into the expression and simplify:

y = 1.4 (2.3)ˣ

\(y = 1.4 (2.3)^{(1.75)}\)

y ≈ 5.69

Therefore, The answer is when x = 1.75, y is approximately 5.69.

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Equivalence means to be same, whether it be value, temperature, size, etc.

First, let's convert \(\frac{3}{4}\) into a different fraction.

We know this because each side of the fraction \(\frac{3}{4}\) can be multiplied by 25 to get \(\frac{75}{100}\).

Now that we know this, we can convert the fraction \(\frac{75}{100}\) into a percentage.

A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

if we know that percentages are expressed as a fraction of 100, we know that \(\frac{75}{100}\) is equal to %75.

To convert percentages into decimals, we can just take the percentage (%75) and fit it into 0.00, making it 0.75.

Therefore, the fraction \(\frac{3}{4}\) as a percentage is %75, and as a decimal it is 0.75.

Answer:

The model that has 2 blue slices filled.

Explanation:

In the first circle, there are 4/10 blue slices filled. In the second circle, there are 2/10 purple slices filled.

4/10 - 2/10 = 2/10

Therefore, your answer is 2/10 shaded blue.

the 2nd one (right of the one that is full)

Answer:

95

Step-by-step explanation:

Because I did the math, and it answered 95.

Answer: x=−94/5

Step-by-step explanation:

Answer:

x= -94/5 Decimal: -18.8 Mixed Number: -18 4/5

Step-by-step explanation: