West High School has a math building in the shape of a regular octagon. When Mrs. Woods measures an interior angle of the octagon (which is inside her classroom), she gets 135°.
Mrs. Wood’s ceiling is 10.0 feet high and the length of one side of the building is 25.0 feet. What is the volume of West High School’s math building?

ANSWERS

A. AB ≅ FG

B. ∡C≅ ∡H

EXPLANATION

A. To use SAS theorem, we have to know if one more side is congruent to the corresponding side of the other triangle. SAS is side-angle-side. The angle must be included between the two sides. Therefore the missing side is AB congruent to FG:

B. To use ASA Theorem we have to know one more angle. Since ASA is angle-side-angle, the side must be between two angles. Therefore, the missing angle is angle C congruent to angle H:

Answer:B and D

Step-by-step explanation:big brain

The (f + g)(x) = 15x - 2 is represent the total round trip time.

According to the statement

we have given that the f(x) represents the time it takes a boat to travel upstream and g(x) represents the time it takes a boat to travel downstream.

And we have to find the total round trip time.

So, For this purpose, the given information is:

f(x) = 3x − 10 and g(x) = 12x + 8

And

The total round trip time is represented by the term (f + g)(x)

We know that the

(f + g)(x) = f(x) + g(x)

Substitute the given values in it

So, (f + g)(x) = f(x) + g(x)

(f + g)(x) = (3x - 10) + (12x + 8)

(f + g)(x) = 15x - 2

Hence, The (f + g)(x) = 15x - 2 is represent the total round trip time.

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The mean absolute percentage error is 33.3%

The mean absolute percentage error measures the forecast accuracy by determining how well a particular forecasting method is able to reproduce the time series data that are already available.

This method is referred to as the forecasts of accuracy, which help to measure the number of errors that are in a former forecast.

Then this would factor these errors into a new forecast while making adjustments to the new forecast.

Forecasted sales were $4,000

Actual sales were $3,000

Absolute error = |Actual sales - Forecasted sales|

                        = |3,000-4,000|

                        = 1000

Mean Absolute error percentage = (Absolute error / Actual sales) *100%

                                                       =(1000/3000)*100

                                                       = 33.33%

Hence, The Mean Absolute error percentage is 33.3%

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Answer:

x = -5/2  + root(33)/2   or   x = -5/2 - root(33)/2

Step-by-step explanation:

ok so your computer is

saying:

x^2  + 5x = 2

and takes the 5 divides it by 2  and squares the result

x^2  + 5x  +  25/4    =   2 + 25 /4   but then   replaces a trinomial with a binomial

(x + 5/2)^2  =  2 + 25/4 =  33/4

solving

x = -5/2  + root(33/4)   or   x = -5/2 - root(33/4)

or

x = -5/2  + root(33)/2   or   x = -5/2 - root(33)/2

Answer:

C and D

Step-by-step explanation:

correct on edge

The perimeter of Rebekah's new mural is 9 meters.

The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

A rectangular mural measures 1 meter by 3 meters.

Rebekah creates a new mural that is 0.5 meters longer.

The perimeter of Rebekah's new mural,

= 2 (1.5 + 3)

= 9 meters.

Therefore, the perimeter is 9 meters.

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Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

we have to know what the numbers are

The indefinite integral of cos14 x sin x dx= -cos 14x cos x + 14 sin x + C, Where C is the constant of integration.

We can solve the given problem by using the substitution method.

Using the formula:

∫u'v = uv - ∫uv' dx

Consider,

cos 14x as u' and sin x dx as v

Now we find v' as derivative of

v.∫ cos14 x sin x dx = ∫ u'v

Now,

v' = sin x

Therefore, v = -cos x

Now we have:

∫ cos 14x sin x dx

= ∫ u'v∫ cos 14x sin x dx

= -cos 14x cos x + ∫ cos x * 14 * sin x dx

Now we apply the formula again. We get:

∫ cos14 x sin x dx = -cos 14x cos x + 14 ∫ cos x sin x dx

Now we apply the same substitution again. We get:

∫ cos14 x sin x dx = -cos 14x cos x + 14 ∫ cos x sin x dx

u' = cos xv = sin x dxv' = cos x

Therefore, the solution is:

∫ cos14 x sin x dx

= -cos 14x cos x + 14 ∫ cos x sin x dx

= -cos 14x cos x + 14 sin x + C, Where C is the constant of integration.

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The average total cost can be found by dividing the total cost by the quantity produced. In this case, the total cost function is given as C = 90 + 35Q + 25Q^2 + 10Q^3, and we want to find the average total cost when Q = 2.

To find the average total cost, we need to calculate the total cost when Q = 2. Plugging Q = 2 into the cost function, we get:
C = 90 + 35(2) + 25(2^2) + 10(2^3)
C = 90 + 70 + 100 + 80
C = 340

Next, we divide the total cost by the quantity produced:
Average Total Cost = Total Cost / Quantity
Average Total Cost = 340 / 2
Average Total Cost = 170

Therefore, the value of average total cost when Q = 2 is $170.

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The largest area that can be enclose in straight wall is 2450 m².

Let 'x' be the length of rectangle.

Let 'y' be the width rectangle.

Perimeter =  140 meters

2x + y = 140      

y = 140 - 2x

Area = xy

Put the value of y in area.

Area = x(-2x + 140)

Area = -2x² + 140x

Differentiating the area with respect to x.

dA/dx = -4x + 140

Put dA/dx = 0 to get the critical point.

-4x + 140 = 0

x = 140/4

x = 35

Largest area at x = 35.

y = 140 - 2x

y = 140 - 2×35

y = 70

Area = xy

Area = 70×35

Area = 2450 m²

Thus, the largest area that can be enclose in straight wall is 2450 m².

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x - 12 = 18 is the the equation that represents ."Twelve less than a number, ×, is 18."

given the number is x

the equation of the given statement

x - 12 = 18

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The study described is a retrospective study.

A retrospective study, also known as a historical study, involves the collection and analysis of data from past events or behaviors. In this case, the study involves collecting and analyzing data on the different types of shoe designs by the designer Calvin Klein over the years from 1987 to 2014. The data has already been collected in the past, and the researcher is analyzing it to draw conclusions or make inferences about the shoe designs.

In contrast, a cross-sectional study involves the collection of data from a population at a specific point in time, while a prospective study (also known as a longitudinal study) involves the collection of data over a period of time to observe changes or trends in a population. An experiment involves the manipulation of one or more variables to observe their effect on a dependent variable, with the aim of establishing cause-and-effect relationships.

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Confounding may invalidate the conclusions of the study as it can cause a bias that can make the effect of the explanatory variable look larger or smaller than it actually is.

This means that the relationship between alcohol drinking status and incidence of lung cancer is influenced by  After the classification of smokers and non-smokers, a separate analysis can be done to find the effect of alcohol drinking on lung cancer in both groups.

Explanatory and Confounding Variable in the study :In the given study, the explanatory variable is obesity and the response variable is coronary disease. Whereas, the confounding variable is hypertension and diabetes because these diseases are associated with obesity. The confounding variable can invalidate the conclusions of the study as it can affect the relationship between obesity and coronary disease .To eliminate the effect of the confounding variable, the study can be changed in the following ways.

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a. The radius for the first circle is r = 17cm

b. The radius for the second circle is r = 13.2cm

A. To find the radius of the circle, we say XY = 16cm and OM = 15cm

XM = 1/2XY

The length of half the chord (MX or MY) is 16cm / 2 = 8cm.

Thus, the triangle OMX is right triangle

OMX = 90°

Using Pythagoras Theorem

r² = OM² + MX²

r² = 15cm² + 8cm²

r² = 225cm² + 64cm²

r² = 289cm²

r = √289cm²

r = 17cm

B. We follow the same process XY = 11cm and OM = 12cm

The length of half the chord (MX or MY) is 11cm / 2 = 5.5cm.

r² = OM² + MX²

r² = 12cm² + 5.5cm²

r² = 144cm² + 30.25cm²

r² = 174.25cm²

r = √174.25cm²

r = 13.2cm

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Answer: 9/11 diveded by 3/4

Step-by-step explanation: divde to get middle answer

The height of the pyramid can be represented ,as per the given details as 3x.

The volume is 3/2 times 3 x 3, and the hexagon base's area is six times greater than the equilateral triangle's.

A pyramid's base edge's length is equal to x units.

In other words, the pyramid's height is three times as long as its base edge.

The pyramid's height is equal to 3x

A three-dimensional structure with a polygon at its base is referred to as a pyramid. You must be familiar with The Great Pyramid of Giza, which was built using a similar framework. This structure has a distinct shape because each corner is connected to a single apex.

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Th given number " six hundred thousand eight" can be written in the standard form as 600,008.

To write "six hundred thousand eight" in standard form, we need to write the number using digits in the appropriate place value positions.

The digit "8" is in the "ones" position, the digit "0" is in the "tens" position, the digit "0" is in the "hundreds" position, the digit "0" is in the "thousands" position, the digit "0" is in the "ten thousands" position, and the digit "6" is in the "hundred thousands" position.

Therefore, it can be concluded that we can write the given number in standard form as 600,008.

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Answer:

70t = 60t + 10

10t = 10

t = 1 hour

----------

1 hour  70 mi/hr = 70 miles

Step-by-step explanation:

Answer: For number 8 it is 2  For number 9 it is confusing

Step-by-step explanation:

The Wald test is a statistical test that can be used to test the significance of a group of coefficients in a multiple regression model.

The test statistic is calculated as the ratio of the estimated coefficient to its standard error. If the test statistic is significant, then the null hypothesis that the coefficient is equal to zero can be rejected.

Suppose we have a multiple regression model with three independent variables: age, gender, and education. We want to test the hypothesis that the coefficients for age and education are both equal to zero. The Wald test statistic would be calculated as follows:

Test statistic = (Estimated coefficient for age) / (Standard error of estimated coefficient for age) + (Estimated coefficient for education) / (Standard error of estimated coefficient for education)

If the test statistic is significant, then we can reject the null hypothesis that the coefficients for age and education are both equal to zero. This would mean that there is evidence that age and education are both associated with the dependent variable.

The Wald test is a powerful tool that can be used to test the significance of a group of coefficients in a multiple regression model. However, it is important to note that the test statistic is only valid if the assumptions of the multiple regression model are met. If the assumptions are not met, then the p-value of the Wald test may be inaccurate.

Here are some of the assumptions of the multiple regression model:

* The independent variables are independent of each other.

* The dependent variable is normally distributed.

* The errors are normally distributed.

* The errors have constant variance.

If any of these assumptions are not met, then the Wald test may not be accurate.

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The function with y and x, representing cost and shipping charges will be y = 3.50x + 9.50.

The express that can be used to write the function is as follows-

Total amount = number of shirts × cost of shirts + shipping fee

Write the function based on the formula -

y = 3.50×x + 9.50

As stated x represents the number of shirts bought online. We know that shipping charges will be calculated once while cost of shirt will vary according to the number of shirts.

Hence the function will be -

y = 3.50x + 9.50

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The value of 1/\((e^(^1^/^1^0^))\) correct to five decimal places is approximately 0.90484.

The Maclaurin series expansion for the exponential function \(e^x\) is a mathematical approximation that allows us to calculate the value of e raised to a given exponent x. By substituting x = 1/10 into the Maclaurin series for e^x, we can obtain an approximation for 1/\((e^(^1^/^1^0^))\).

By including a sufficient number of terms in the series and summing them, we arrive at the result of approximately 0.90484.

This approximation provides a reasonably accurate value for 1/\((e^(^1^/^1^0^))\) to five decimal places, allowing us to estimate the reciprocal of the exponential function at a specific point.

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The area of the region bounded by the given curves. y = 6x2 ln(x), y = 24 ln(x) is 2.85 sq.units.

In this question we need to find the area of the region bounded by the given curves. y = 6x^2 ln(x), y = 24 ln(x)

Equating both the equations of the curve,

6x^2 ln(x) = 24 ln(x)

24 ln(x) - 6x^2 ln(x) = 0

x = 1, 2

This means,  the curves intersect at x = 1 and x = 2.

So, the required area would be,

A = ∫[1 to 2] [24 ln(x) - 6x^2 ln(x)] dx

First we find the indefinite integral ∫[24 ln(x) - 6x^2 ln(x)] dx

= -6  ∫[-4 ln(x) + x^2 ln(x)] dx

= -6 ∫ln(x) (x^2 - 4) dx

= -6 ln(x) (1/3 x^3 - 4x) + 2/3 x^3 - 24x

So,  ∫[1 to 2] [24 ln(x) - 6x^2 ln(x)] dx

= [-6 ln(x) (1/3 x^3 - 4x) + 2/3 x^3 - 24x] _(x = 1 to x = 2)

= 32 ln(2) - 58/3

= 22.18 - 19.33

= 2.85 sq.units.

Therefore, the area of the region is 2.85 sq.units.

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Answer:

No

Step-by-step explanation:

irrational numbers have nonrepeating and non terminating decimals

This decimal stops at one digit so this is a rational number

Answer:

I would say no

Step-by-step explanation:

An irrational number can't be written as a simple fraction.  

Answer:

x(x + 3)(x + 1)(x - 1)

Step-by-step explanation:

f(-3) = 0 ⇒  (x + 3) is a factor

f(-1)= 0 ⇒     (x + 1) is a factor

f(0) = 0 ⇒       (x + 0) is a factor

f(1) = 0 ⇒       (x -1) is a factor

f(x) as a product of linear factors

x(x + 3)(x + 1)(x - 1)

Answer

equation of L₁ is y = 2x - 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given L₂

x + 2y = 3 ( subtract x from both sides )

2y = - x + 3 ( divide through by 2 )

y = - \(\frac{1}{2}\) x + \(\frac{3}{2}\) ← in slope- intercept form

with slope m = - \(\frac{1}{2}\)

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{2} }\) = 2

slope of L₁ = 2 and passes through (3, - 1 ) , then

y = 2x + c ← is the partial equation of L₁

to find c substitute (3, - 1 ) into the partial equation

- 1 = 6 + c ⇒ c = - 1 - 6 = - 7

y = 2x - 7 ← equation of L₁

The value of s for the given value is 24.05.

Given is an equation v² = u²+2gs, we need to find the value of s if v = 25, u = 12 and g = 10,

So,

25² = 12² + 2(10)s

625 = 144 + 20s

20s = 481

s = 24.05

Hence the value of s for the given value is 24.05.

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