20. MODELING REAL LIFE You are designing a box like
the one shown.
23
A
1
B
32
C
a. The measure of Z1 is 70°. Find m22 and m/3.
b. Explain why ZABC is a straight angle.
c. If m/1 is 60°, will ZABC still be a straight angle?
Will the opening of the box be more steep or less
steep? Explain.

Answer:

81 years

Step-by-step explanation:

The answer is 81 because 5% of 9100 is 455 and 36900 divided by 455 is rounded to 81.

the answer is 6 minutes and 46 seconds

The correct option is exponential

Steps

Let's check if the data is linear. Recall that the general form for a linear equation is:

Since the slope should be constant, we can check across two data points.

Using points (3, 48) and (4, 12). The slope(m) is:

Using the points (4,12) and (5, 3). The slope(m) is :

Since, the slope is inconsistent, the table is not linear

To check if it is exponential,

Recall that the general equation for an exponential function is :

Using the data points (3,48) and (4,12), we can solve for the constant a, and then check if it is the same across the table.

Check:

using points (4,12) and (5,3)

Since a is constant across data points, the table represents an exponential equation

Answer:

13

Step-by-step explanation:

The average of a group of numbers is calculated by adding all of the numbers up and then dividing by the number of numbers. Because of this, we can easily find the sum of the numbers by multiplying the average by the numbers.

1.) The average of the first 3 numbers is 15, meaning that the total of the numbers is 15*3 = 45.

2.) The average of the 6 other numbers is 12, meaning that the total of the numbers is 6*12 = 72.

3.) Since we know the totals of both groups of numbers, to find the total of all the numbers, we add these totals together. 45 + 72 = 117.

4.) Finally, we are finding the average, and since we know the total is 117 and there are 9 numbers, we just divide 117 by 9 to get 13. Therefore, the average of the numbers is 13.

Step-by-step explanation:

when means of more than two groups are to be compared, ANOVA is perferred

Start using the distributive

bring the constants and variables to contrary sides

simplify each side

solve for x

Answer:

s = 2 1/3 + 1/2

t = 2/3 + 3/2

We have to find the sum of both s and t.

2 1/3 + 1/2 = 2 2/6 + 3/6 = 2 5/6

2/3 + 3/2 = 4/6 +  9/6 = 13/6 = 2 1/6

If we look at the number lines, we can see that c matches with both points.

The number of elements in the intersection A∩B is 2.

The intersection of two sets A and B, denoted as A∩B, represents the set that contains all the elements that are common to both A and B.

A = {1, 2, 4, 5}

B = {1, 3, 5, 7}

To find the intersection A∩B, we compare the elements of set A with the elements of set B.

Any element that appears in both sets is considered to be part of the intersection.

The elements that are common to both A and B are 1 and 5.

These two elements appear in both sets, so they are included in the intersection.

Thus, the intersection A∩B = {1, 5}.

Hence, the number of elements in the intersection A∩B is 2, as there are two elements in the set {1, 5}.

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Answer:

7, 24, 26

Step-by-step explanation:

The correct triple should be 7,24,25

Answer:

=17 + 6n.

Step-by-step explanation:

\(4 \times 5 + 6n - 3 \\ = 20 + 6n - 3 \\ = 20 - 3 + 6n \\ = 17 + 6n\)

Answer:

the equation 10 = x - y

Step-by-step explanation:

Let x represent the initial value of the investment, and let y represent the amount of money that each person receives after the investment is withdrawn.

We know that the cost of withdrawing the investment is $10, so we can write the equation 10 = x - y. We also know that each person receives $40, so we can write the equation y = 40.

We can now solve for x by substituting the value of y into the first equation. Since y = 40, we can substitute 40 for y in the equation 10 = x - y to get 10 = x - 40. Solving this equation for x, we find that x = 50.

Therefore, the initial value of the investment was $50.

Answer:

1/4 yards squared

Step-by-step explanation:

Area of a rectangle equals length times width.

1/3 x 3/4 = 3/12, or 1/4

Answer:

It would be 1/4 and if not try 3/12

Step-by-step explanation:

I hope this helped

Answer:

the assistants salary before was $44,6653

The distance that Mr. Stein drove can be represented by the expression: \(140 - x\)

A mathematical phrase made up of one or more variables, constants, and arithmetic operations like addition, subtraction, multiplication, and division is known as an algebraic expression. Exponentiation and other mathematical operators could also be present.

Let's assume that Mr. Smith drove "x" miles before Mr. Stein took over the driving.

Then, the total distance they traveled is 140 miles.

So, the distance that Mr. Stein drove can be represented by the expression:

140 - x

Therefore, This is because if Mr. Smith drove "x" miles, then the remaining distance that needed to be covered by Mr. Stein would be the difference between the total distance of 140 miles and the distance already driven by Mr. Smith.

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Answer:

E110

Step-by-step explanation:

well there is E176 (sorry for bad symbol) and then he spends 1/4+1/8 or 3/8 on food  so then its 3/8*176 which is 66. 176-66 is 110

HOpe this helps plz hit the crown :D

Answer:

thanks so that will do it now I think it is the cost for me and the following sentences to make it more possible to get school.she to use it for a few hours

The measure of  ∠BDC can be found for the given case as 20°.

A circle is a geometric shape, all of which points are equidistant from a fixed point called as the Centre.

The centre of the circle does not lie on it.

The diagram for the given case can be drawn as follows,

In ΔADB, ∠ADB = 90° (angle subtended by the diameter)

∠BAD = 70°

Now, ∠ABD can be found as below,

As per the property of triangle it can be written as,

∠ADB  + ∠BAD + ∠ABD = 180°

Substitute the values to obtain,

90° + 70° + ∠ABD = 180°

⇒ ∠ABD = 20°

Since, AB ║DC, ∠ABD = ∠BDC (alternate interior angles).

Thus,  ∠BDC = 20°.

Hence, the measure of ∠BDC is given as 20°.

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Answer:

The 90% confidence interval for the mean reduction in systolic blood pressure is between 22.66 and 40.14.

Step-by-step explanation:

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

The mean and standard deviation for the before treatment were 168.6 and 9.3, respectively. The mean and standard deviation for the after treatment were 137.2 and 7.4.

This means that

\(\mu = 168.6 - 137.2 = 31.4\)

\(\sigma = \sqrt{9.3^2+7.4^2} = 11.88\)

90% confidence interval:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.9}{2} = 0.05\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.645\frac{11.88}{\sqrt{5}} = 8.74\)

The lower end of the interval is the sample mean subtracted by M. So it is 31.4 - 8.74 = 22.66

The upper end of the interval is the sample mean added to M. So it is 31.4 + 8.74 = 40.14

The 90% confidence interval for the mean reduction in systolic blood pressure is between 22.66 and 40.14.

Answer:

1) draw a line from (2,4) to (6,4)

2) 27.5

3) 16

4) 43.5

5) $97.88

Step-by-step explanation:

1) draw a line from (2,4) to (6,4)

2) (7+4)/2=5.5x5=27.5

3) 4x4=16

4) 27.5+16=43.5

5) 43.5x2.25= 97.875 = $97.88

Use the quadratic formula to find the values of x:

In this case, a is 1, b is 8 and c is -2. Replace for these values and find the values of x.

The solutions are

Answer:

c. 0.62%

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 30 - 1 = 29

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 29degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 1.6991

The margin of error is:

\(M = T\frac{s}{\sqrt{n}}\)

Sample of 30, standard deviation of 2%.

Then

\(M = T\frac{s}{\sqrt{n}} = 1.6991\frac{2}{\sqrt{30}} = 0.62\)

0.62%, so option c.

Using an exponential function, it is found that Erina will run 490.5 yards each day in the third week of her training.

An increasing exponential function is modeled by:

\(A(t) = A(0)(1 + r)^t\)

In which:

In this problem:

Then, the equation is:

\(A(t) = A(0)(1 + r)^t\)

\(A(t) = 200(1.5)^t\)

In the third week, the daily distance in meters that she runs is:

\(A(2) = 200(1.5)^2 = 450\)

Since there approximately 27.34 yards in 25 meters, we apply the proportion:

\(d = \frac{450}{25} \times 27.34 = 490.5\)

Erina will run 490.5 yards each day in the third week of her training.

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Answer:

Step-by-step explanation:

YESS

Because these are f r e e points

Answer:

n=12

Step-by-step explanation:

1/4n+7=10

n+28=40

n=12

There are 400 students in the hall.

Given,

There are 20 students kept in each row and each column of a square hall.

We need to know how many students are in total in the square hall.

In a square all four sides are equal.

If we have a square hall then the number of rows and columns must be equal.

So we have 20 rows and 20 columns in the square hall.

Total number of students in the square hall  

= Number of rows x number of columns    

= 20 x 20    

= 400 students

We can also find the total number of students by calculating the number of students in all the rows or in all the columns.

If one row = 20 students

then,

20 rows = 20 x 20 students = 400 students.

If one column = 20 students,

then,

20 columns = 20 x 20 students = 400 students.

Thus, the total number of students in the square hall is 400 students

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√(a² + b²)²  - 4a²b²cos²θ is the product of the lengths of the two diagonals is given by the expression.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.

                                An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.

we have AB as a, AD as b and the angle between them is theta.

So using the cosine rule, we have

  BD = √a² + b² - 2abcosθ

So now consider the triangle ABC

Here AB is a, BC is b and the angle is 180-theta

So using cosine rule, we get AC as

   AC = √a² + b² - 2abcosθ( 180 - θ )

    AC = √a² + b² - 2ab(-cosθ )

    AC = √a² + b² - 2abcosθ

Now we have the two diagonals AC and BD. So multiplying, we get

 AC × BD = √a² + b² + 2abcosθ × √a² + b² - 2abcosθ

Simplifying, we get

AC × BD = √(a² + b² + 2abcosθ) × (√a² + b² - 2abcosθ)

AC × BD = √(a² + b²)² - (2abcosθ)²

AC × BD = √(a² + b²)²  - 4a²b²cos²θ

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a) The estimated average yearly increase in the percentage of​ first-year college males claiming no religious affiliation is 0.5%.

b) Based on the above average, the percentage of​ first-year college males who will claim no religious affiliation in 2020 is 22.7%

Year     Male

1980     6.6%

1990    10.6%

2000   13.5%

2012    21.8%

Percentage of first-year college males claiming no religious affiliation in 2012 = 21.8%

Percentage of first-year college males claiming no religious affiliation in 1980 = 6.6%

The number of years between 2012 and 1980 = 32 years

The percentage increase from 1980 to 2012 = 15.2% (21.8% - 6.6%)

a. Average yearly increase = 0.475% (15.2% ÷ 32)

= 0.5%

b. The number of years between 2020 and 2012 = 8 years

In 2020, the percentage of first-year college males who will claim no religious affiliation based on the average yearly increase above =

Percentage in 2012 x (1 + Yearly Average)^8

21.8% = 0.218 (21.8 ÷ 100)

0.5% = 0.005 (0.5 ÷ 100)

= 0.218(1.005)⁸.

= 0.2269

= 22.69%

= 22.7%

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The probability P(X < 4) is approximately 0.2734 when X has a binomial distribution with n = 7 and p = 0.5.

When X has a binomial distribution with n = 7 and p = 0.5, we can use the cumulative distribution function (CDF) or the formula for the probability mass function (PMF) of the binomial distribution to determine the probability P(X 4) by adding the probabilities for X = 0, 1, 2, and 3.

Binomial CDF usage:

P(X 4) = P(X 3) = binom.cdf (3, n = 7, p = 0.5) 0.2734

Binomial PMF usage:

P(X 4) = P(X = 0), P(X = 1), P(X = 2), and P(X = 3) = binom.pmf(0, n=7, p=0.5), binom.pmf(1, n=7, p=0.5), binom.pmf(2, n=7, p=0.5), and binom.pmf(3, n=7, p=0.5), and binom.pmf(3, n=7, p=0.5) = 0.2734.

Since X has a binomial distribution with n = 7 and p = 0.5, the chance P(X 4) is roughly equal to 0.2734.

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