(Q3) Apply the 45º-45º-90º Triangle Theorem to find the length of the hypotenuse of a right triangle if the length of a leg is 7 in. Round to the nearest inch.

the present value of the payments is £386.40 at time 0.To calculate the present value of the payments, we can use the formula for the present value of an annuity:

PV = C * (1 - (1 + r)^(-n)) / r

Where PV is the present value, C is the payment amount, r is the annual effective interest rate, and n is the number of payment periods.

Using this formula, we can calculate the present value of the payments:

PV = £50 * (1 - (1 + 0.042)^(-10)) / 0.042
  = £50 * (1 - 0.67704) / 0.042
  = £50 * 0.32296 / 0.042
  = £386.40

Therefore, the present value of the payments is £386.40 at time 0.

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The population mean is 15.6 if A population consists of the following five values: 11, 13, 15, 17, and 22.

What is Mean ?

In statistics, the mean is a measure of central tendency of a set of numerical data. It is commonly referred to as the average, and is calculated by adding up all the values in the data set and dividing the sum by the total number of values.

a. To list all samples of size 3, we can take all possible combinations of 3 values from the population:

{11, 13, 15}: mean = 13

{11, 13, 17}: mean = 13.67

{11, 13, 22}: mean = 15.33

{11, 15, 17}: mean = 14.33

{11, 15, 22}: mean = 16

{11, 17, 22}: mean = 16.67

{13, 15, 17}: mean = 15

{13, 15, 22}: mean = 16.67

{13, 17, 22}: mean = 17.33

{15, 17, 22}: mean = 18

b. To compute the mean of the distribution of sample means, we need to find the mean of all the sample means computed in part (a). There are 10 sample means, so we add them up and divide by 10:

(13 + 13.67 + 15.33 + 14.33 + 16 + 16.67 + 15 + 16.67 + 17.33 + 18)  ÷10 = 15.4

To compute the population mean, we simply take the average of the population values:

(11 + 13 + 15 + 17 + 22) ÷ 5 = 15.6

Therefore, the population mean is 15.6

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it displays the computed sum and product of the diagonal elements.

Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:

```matlab

% Define the matrix A

A = ones(5);

% Get the size of the matrix

[n, ~] = size(A);

% Initialize variables for sum and product

diagonal_sum = 0;

diagonal_product = 1;

% Calculate the sum and product of diagonal elements

for i = 1:n

   diagonal_sum = diagonal_sum + A(i, i);

   diagonal_product = diagonal_product * A(i, i);

end

% Display the results

disp("Sum of diagonal elements: " + diagonal_sum);

disp("Product of diagonal elements: " + diagonal_product);

```

Example execution for `A = ones(5)`:

```

Sum of diagonal elements: 5

Product of diagonal elements: 1

```

In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.

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First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

The boys in the class that wear glae are 6 people.

The boys in the class that wear glae can be calculated as follows:

First we should calculate how many boys there are in the class. We can calculate it by multiplying the percent of the boys to the total students.

Boys in the class = \(\frac{20}{100} X 50\) = 10 people.

Thus, we can calculate the boys who wear the glae by multiplying the percent of the boys wearing glae of the boys in the class.

Boys wear glae = \(\frac{60}{100} X 10\) = 6 people.

Hence, The boys in the class that wear glae are 6 people.

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Answer (first one):

\({x|-2\leq x\leq 8}\)

Step-by-step explanation:

think of f(x) as y.

\(y>-2\)

Now find the parts on the x axis that correspond with parts on the y value that are greater than -2.

\(x\geq -2 \\x \leq 8\)

This would be all of the numbers between -2 and 8 (inclusive).

The reason it is inclusive is because the arrow ends are shaded in.

Answer:

CAN YOU HEAR THE SILIECE

Step-by-step explanation:

Answer:

I'm not sure if you're asking for this answer...

Step-by-step explanation:

In-plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length

The inverse function of a function is one that undoes the operation of the former expression.

It should be noted that the information is incomplete. Therefore, an overview will be given.

It should be noted that an inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

A function that has an inverse is called invertible and the inverse is denoted by f−1.

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Yes, the expressions with predicates P, T and E are propositions.

For the expression P(x): x is even, it is a proposition and its truth value is True, since any even number x is true.

For the expression T(x,y): 2x=y, it is a proposition and its truth value depends on the numbers x and y. If 2x=y is true, then the truth value of this expression is True. If 2x≠y is false, then the truth value of this expression is False.

For the expression E(x,y,z):xy=z, it is a proposition and its truth value depends on the numbers x, y, and z. If xy=z is true, then the truth value of this expression is True. If xy≠z is false, then the truth value of this expression is False.

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Answer:

Multiply each side by −8, subtract 35 from each side

Step-by-step explanation:

8*1/8 (x + 35) = −7*8

x+35=-56

subtract 35 on each side

x=21

When the scale factor is greater than one, then the dilation is not a reduction.

What is a dilation?

Dilation is a process of changing a thing. It is a process of transformation that to make the objects smaller or larger, with the use of specific scale factor.

The new figure that is the result of dilation is known as the image. Initial figure is referred to as the pre-image.

What is a center of dilation?  

Center of dilation is the resizing that happens from a point. The objects/figures are expanded or contracted from the center of dilation.

Scale factor is a figure by which the size of any geometrical figure can be resized, with respect to its original size. The scale factor is multiplied to get image.

Figure size increased, when the scale factor is greater than 1.

Thus, the dilation will be a expansion, when the scale factor is a greater than one.

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After combining like terms to create equivalent expression we get (-1.9 + 1.2) + (5.1 - 3.6)t. Simplifying further, we get: -0.7 + 1.5t.

To combine like terms, we add or subtract the coefficients of the same variables. In this case, the variables are t and the constant terms (without variables) are -3.6, -1.9, and 1.2.

So the equivalent expression after combining like terms is:

(-1.9 + 1.2) + (5.1 - 3.6)t

Simplifying further, we get:

-0.7 + 1.5t

A coefficient is a numerical factor that is multiplied by a variable in an algebraic expression. It tells you how many times the variable appears in the expression. For example, in the expression 3x + 2, the coefficient of x is 3. Variables are symbols used to represent unknown quantities in mathematical equations or expressions. They can take on different values, and their value can be solved for using algebraic techniques. Equivalent expressions are expressions that have the same value for all possible values of the variables involved. For example, 2x + 4 and 4 + 2x are equivalent expressions since they simplify to the same value. Equivalent expressions can be useful in simplifying and solving algebraic equations.

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Complete Question

Combine like terms to create an equivalent expression. −

3. 6−1. 9+1. 2+5. 1 −3. 6−1. 9t+1. 2+5.

The 99% confidence interval for the true population proportion of people with kids is approximately 0.188 to 0.272.

To construct a 99% confidence interval for the true population proportion of people with kids, we can use the formula:

CI = p ± z * √(p(1-p)/n)

where p is the sample proportion, z is the z-score corresponding to the desired confidence level, and n is the sample size.

Firstly, we calculate the sample proportion by dividing the number of people with kids (138) by the sample size (600), resulting in a sample proportion of 0.23.
p = 138/600

= 0.23

Next, find the z-score for a 99% confidence level. The z-score for a 99% confidence level is approximately 2.576.

Then, we calculate the margin of error by multiplying the z-score by the square root of the product of the sample proportion and the complement of the sample proportion, divided by the sample size.

ME = z * √(p(1-p)/n)

= 2.576 * √(0.23(1-0.23)/600)

≈ 0.042

Finally, we construct the confidence interval by adding and subtracting the margin of error from the sample proportion, resulting in a range of approximately 0.188 to 0.272.

CI = p ± ME = 0.23 ± 0.042

Therefore, with 99% confidence, we can conclude that the true population proportion of people with kids lies within the interval of 0.188 to 0.272.

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Answer:

  m = 39°

Step-by-step explanation:

The useful relations here are ...

__

Angle ACB subtends the same arc (AB) as angle ADB, so has the same measure, 36°. Then the sum of angles in triangle ACB is ...

  33° +36° +72° +m = 180°

  m = 180° -141° = 39°

Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer 2x-3y+3=0

The problem focuses on the simplification of the function

y-3=2/3(x-2)

Y-3=2/3-2

3y-9=2x-6

2x-3y+3=0

Answer:

I believe its 11 so sorry if wrong

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Answer:

A function is a set of ordered pairs where there is exactly one y value for each x value.

This is the case with this graph, so this graph IS a function.

Let me know if this helps!

A 6-ounce serving of salmon has 2 grams of saturated fat. To determine the percentage of saturated fat in the serving of salmon, we divide the amount of saturated fat by the total amount of fat and multiply by 100.

The total amount of fat in the serving is 7 grams. So:2g / 7g × 100% = 28.57%Therefore, 28.57% of the 6-ounce serving of salmon is saturated fat. This information can be helpful for individuals who are monitoring their saturated fat intake due to health concerns such as high cholesterol or heart disease.

Saturated fat is a type of fat that is solid at room temperature and is typically found in animal products such as meat and dairy. Consuming too much saturated fat can contribute to high cholesterol levels and increase the risk of heart disease. It is important to consume a balanced diet and limit intake of saturated and trans fats.

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Answer:

c. 122.1 cm

Step-by-step explanation:

so l * w + \(\frac{\pi r^2}{2}\)

since 6 cm is the diameter

6/2 = 3

the radius (or r) is 3

so 18 * 6 + \(\frac{3.14 * 3*3}{y}\)

108 + \(\frac{3.14*9}{y}\)

108 + \(\frac{28.26}{2}\)

108 + 14.13 = 122.13

simplified: 122.1 cm

hope this helps:)

Answer:

C. 122.1

Step-by-step explanation:

The area of a semicircle is HALF of the area of the circle. As the area of a circle is \(\pi r^2\). So, the area of a semicircle is \(\frac{1}{2}(\pi r^2)\), where r is the radius.

18 × 6

= 108

108 \(cm^2\) is the area of the rectangle,

For the semicircle, we know the diameter is equal to 6 cm,

(Remember that Diameter is equal to the radius times 2 (r × 2)),

To find the radius, divide the diameter by 2,

6 ÷ 2

= 3

The radius of the semicircle is 3 cm

Now use the equation \(\frac{1}{2}(\pi r^2)\) to find the area of the semicircle,

\(\frac{1}{2} (\pi 3^2)\)

(Remember pie is 3.14...)

Slove:

\(\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\)

\(=\frac{1}{2}\pi 3^2\)

\(\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}\)

\(=\frac{1\pi 3^2}{2}\)

\(\mathrm{Multiply:}\:1\pi =\pi\)

\(=\frac{3^2\pi }{2}\)

\(3^2=9\)

\(=\frac{9\pi }{2}\)

\(\frac{9\pi }{2} =\left(\mathrm{Decimal:\quad }\:14.13716\dots \right)\)

Now take the decimal 14.13716.... and round to the nearest tenth,

14.13

(Remember 4 or less keep it the same, 5 or more bring the value up one more)

3 less than 5 so keep the 1 the same,

14.1

Now add 108 and 14.1,

108 + 14.1

= 122.1

Therefore the total area of the shape is 122.1 \(cm^2\). Answer ⇒ C.

After answering the given query, we can state that As a result, the quadratic equation formula for x2+8x+7=-8 is \(x^2 + 8x + 15 = 0\)

A mathematical equation is a process that links two statements and indicates equality with the equals sign (=). A mathematical assertion that proves the equality of two mathematical statements is known as an equation in algebra. For instance, the equal symbol separates the numbers 3x plus 5 and 14 in the equation 3x + 5 = 14. A mathematical formula can be used to understand the connection between the two lines that are written on opposite sides of a letter. Frequently, the emblem and the particular program are identical. as in 2x - 4 = 2, for example.

the quadratic equation for x^2+8x+7=-8, we first need to change the equation to normal quadratic form, which is ax^2+bx+c=0.

With 8 added to both edges, we obtain:

\(x^2 + 8x + 15 = 0\)

The factors a, b, and c are now clear:

a = 1

b = 8

c = 15

These numbers are substituted into the quadratic formula:

\(x=(-b sqrt(b2 - 4ac)) / 2a\\x = (-8 + \sqrt(8^2 - 4(1)(15))) / 2(1)\\x = (-8 +/- \sqrt(64 - 60)) / 2\\x = (-8 +/- \sqrt(4)) / 2\\x = (-8 + 2) / 2\)

Therefore, the options are:

x = -4 or x = -3

As a result, the quadratic formula for x2+8x+7=-8 is

\(x^2 + 8x + 15 = 0\)

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To answer your question, I would need more information about the terminal point and its relationship to the circle.

If you have a point on the circumference of a circle and you draw a line from the center of the circle to that point, the measure of the terminal point's vertical distance above the center of the circle in units of the radius of the circle can be found using trigonometry. Specifically, if the angle between the line and the horizontal axis is theta (in radians), then the vertical distance is given by:

vertical distance = sin(theta)

In this case, the vertical distance is measured in units of the radius of the circle.

55 adult tickets were sold that day.

Let us assume the number of adult tickets sold is x.

Given that the child admission is $5.50 and adult admission is $9.80.

We will set up the following equations:

Simplifying the equations:

x + 131 - x = 131

9.80x + 720.50 - 5.50x = 957.00

Combining like terms:

131 = 131

4.30x = 236.50

Dividing both sides by 4.30:

x = 55.

Full question:

At the movie theatre, child admission is $5.50 and adult admission is $9.80. 131 tickets were sold for a total sales of $957.00.How many adult tickets were sold that day.

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