Find the perimeter of WXYZ. Round to nearest tenth if necessary.​

Check the picture below.

\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x) \qquad \begin{cases} x_1=-4\\ x_2=-3 \end{cases}\implies \cfrac{f(-3)-f(-4)}{-3 - (-4)}\implies \cfrac{[-6]~~ - ~~[-4]}{-3+4} \\\\\\ \cfrac{-6~~ + ~~4}{1}\implies \text{\LARGE -2}\)

Answer:

-2

\(\hrulefill\)

Step-by-step explanation:

The average rate of change of a function f(x) on the interval a ≤ x ≤ b can be calculated using the formula:

\(\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}\)

The given interval is -4 ≤ x ≤ -3, so:

From observation of the given graph, the values of f(a) and f(b) are:

\(f(a)=f(-4)=-4\)

\(f(b)=f(-3)=-6\)

Substitute the values of a, b, f(a) and f(b) into the formula to calculate the average rate of change of the function f(x) on the interval -4 ≤ x ≤ -3:

\(\begin{aligned}\textsf{Average rate of change}&=\dfrac{f(-3)-f(-4)}{-3-(-4)}\\\\&=\dfrac{-6-(-4)}{-3-(-4)}\\\\&=\dfrac{-6+4}{-3+4}\\\\&=\dfrac{-2}{1}\\\\&=-2\end{aligned}\)

Therefore, the average rate of change of the function f(x) on the given interval is -2.

If you want to round a number within an arithmetic expression, you should use the ROUND function.

The ROUND function allows you to specify the number of decimal places to which you want to round a given number. It is commonly used in programming languages and spreadsheet software.

The syntax for the ROUND function typically involves specifying the number or expression you want to round and the number of decimal places to round to. For example, if you want to round a number, let's say 3.14159, to two decimal places, you would use the ROUND function like this: ROUND(3.14159, 2), which would result in 3.14.

Using the ROUND function ensures that the rounded number is calculated within the arithmetic expression, providing the desired level of precision in the calculation.

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Answer: 5

Step-by-step explanation: Substitute the value of the variable into the expression and simplify

15 bags are expected for the journey for 9 people to fit backpacks in the trailer.

The fundamental principle of multiplication

To calculate the sum of two or more numbers, utilize the mathematical operation of multiplication. If an event can happen in m different ways and a second event can happen in n different ways after it, then the two events that happen in succession can happen in m n distinct ways.

Given that 5 backpacks can fit in the trailer for every 3 people.

Then 3 people = 5 backpacks

1 people = \(\frac{5}{3}\) backpacks

therefore  If 9 people are going on the trip, then;

9 people = \(\frac{5}{3}*9\) backpacks

= 5 x 3

= 15 backpacks

Hence, the trailer can fit 15 backpacks if 9 people go on the trip.

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40. A vector w that is perpendicular to the plane containing the given points A,B, and C is  (9,-4,-6)

41. A vector w that is perpendicular to the plane containing the given points A,B, and C is  (1,1,3)

40. To find a vector that is perpendicular to the plane containing A, B, and C, we can find the cross product of two vectors that lie in the plane. For example, we can use the vectors AB and AC:

AB = (2-(-1), 1-1, -1-2) = (3,0,-3)

AC = (0-(-1), -2-1, 4-2) = (1,-3,2)

Taking the cross product of these vectors, we get:

AB x AC = (0-(-9), -2-(-2), -3-(-3)) = (9,-4,-6)

So the vector w = (9,-4,-6) is perpendicular to the plane containing A, B, and C.

41. Again, to find a vector that is perpendicular to the plane containing A, B, and C, we can find the cross product of two vectors that lie in the plane. For example, we can use the vectors AB and AC:

AB = (0-1, 1-0, 0-0) = (-1,1,0)

AC = (2-1, 3-0, 1-0) = (1,3,1)

Taking the cross product of these vectors, we get:

AB x AC = (1,1,3)

So the vector w = (1,1,3) is perpendicular to the plane containing A, B, and C.

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Answer:

Step-by-step explanation:

3

Answer:

\(\sf (a) \quad AC=2\sqrt{3}\:\:cm\)

\(\sf (b) \quad AB=2\sqrt{7}\:\:cm\)

\(\sf (c) \quad \angle ACB=90^{\circ}\)

Step-by-step explanation:

Cosine rule

\(\sf c^2=a^2+b^2-2ab \cos C\)

where:

Sketch the triangle using the given information (see attached).

Given:

Substitute the given values into the formula and solve for AC:

\(\implies \sf c^2=a^2+b^2-2ab \cos C\)

\(\implies \sf AC^2=2^2+4^2-2(2)(4) \cos 60^{\circ}\)

\(\implies \sf AC^2=4+16-16 \left(\dfrac{1}{2}\right)\)

\(\implies \sf AC^2=20-8\)

\(\implies \sf AC^2=12\)

\(\implies \sf AC=\sqrt{12}\)

\(\implies \sf AC=\sqrt{4 \cdot 3}\)

\(\implies \sf AC=\sqrt{4}\sqrt{3}\)

\(\implies \sf AC=2\sqrt{3}\:\:cm\)

Given:

Substitute the given values into the formula and solve for AB:

\(\implies \sf c^2=a^2+b^2-2ab \cos C\)

\(\implies \sf AB^2=2^2+4^2-2(2)(4) \cos 120^{\circ}\)

\(\implies \sf AB^2=4+16-16 \left(-\dfrac{1}{2}\right)\)

\(\implies \sf AB^2=20+8\)

\(\implies \sf AB^2=28\)

\(\implies \sf AB=\sqrt{28}\)

\(\implies \sf AB=\sqrt{4\cdot7}\)

\(\implies \sf AB=\sqrt{4}\sqrt{7}\)

\(\implies \sf AB=2\sqrt{7}\:\:cm\)

Given:

Substitute the given values into the formula and solve for ∠ACB:

\(\implies \sf c^2=a^2+b^2-2ab \cos C\)

\(\implies \sf \left(2\sqrt{7}\right)^2=\left(2\sqrt{3}\right)^2+4^2-2\left(2\sqrt{3}\right)(4) \cos ACB\)

\(\implies \sf 28=12+16-16\sqrt{3} \cos ACB\)

\(\implies \sf 28=28-16\sqrt{3} \cos ACB\)

\(\implies \sf 0=-16\sqrt{3} \cos ACB\)

\(\implies \sf \cos ACB=0\)

\(\implies \sf ACB=\cos^{-1}(0)\)

\(\implies \sf ACB=90^{\circ}\)

The inequality and the maximum possible width are 12w  ≥ 132 and 11 feet respectively

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

If the room is 12 feet long and  Tom had enough paint to cover an area of 132 square feet. This implies Tom had paint that can cover greater or equal to 132 square feet of area. Thus:

L x w ≥ A

where l = 12 feet, A = 132 square feet

12w  ≥ 132    (This is the inequality)

To solve for width:

12w  ≥ 132

w ≥ 132 /12

w ≥ 11 feet

Therefore, the inequality is 12w  ≥ 132 and the maximum possible width is  11 feet

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There are 24 students in the class. Take 2/3 of this to get (2/3)*24 = 16

A more detailed step by step would be

(2/3)*24 = (2/3)*(24/1) = (2*24)/(3*1) = 48/3 = 16

The result 16 is smaller than the original number 24. This is expected because 2/3 is smaller than 1. The key thing here is that the result 16 is a whole number.

You can think of 2/3 as the approximate percentage 66.7%, so you're applying roughly 66.7% to the entire class to get 16 people who like hip hop.

It appears you're thinking in reverse when you went from 24 to 36, because 2/3 of 36 is 24, but not the other way around. Keep in mind there are 24 students total in the class, and we can't go higher than this. We can't say there are 36 people who like hip hop.

So to answer the question, yes it is possible Gertrude's survey is correct because 2/3 of 24 is a whole number.

Answer:

Volume of the cylinder is 1521π in³

Step-by-step explanation:

Hello,

To find the volume of a cylinder, we need the know the formula used for calculating it.

Volume of cylinder = πr²h

r = radius

h = height

Data,

Radius = 13in

Height = 9in

Volume of a cylinder = πr²h

Now we need to substitute the values into the formula

Volume of a cylinder = π × 13² × 9

Volume of a cylinder = 169 × 9π

Volume of a cylinder = 1521π in³

Therefore the volume of the cylinder is 1521π in³

Answer:

1521

Step-by-step explanation:

$5744 is Ashley’s monthly payment.

The amount of the down payment made by Ashlee is 15% of $875,000, which is:

Down payment = 0.15 x $875,000 = $131,250

The amount that Ashlee took out on a mortgage is:

Mortgage amount = Purchase price - Down payment

= $875,000 - $131,250

= $743,750

The monthly payment on a mortgage:

\(M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]\)

where:

M = monthly payment

P = principal amount (mortgage amount)

i = monthly interest rate (annual interest rate / 12)

n = total number of monthly payments (amortization period x 12)

In this case, the annual interest rate is 6.95% and the term is for 5 years, so we need to first calculate the monthly interest rate and the total number of monthly payments.

Monthly interest rate = 6.95% / 12 = 0.57917%

Total number of monthly payments = 20 years x 12 = 240

Substituting these values into the formula, we get:

M = $743,750 [ 0.0057917 (1 + 0.0057917)^240 ] / [ (1 + 0.0057917)^240 - 1 ]

= $5744.002

Therefore, Ashley's monthly payment on the mortgage is $5744.

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We have to indicate the steps to follow in order to evaluate:

(12.9-3.1) x 6.2-2 + 43

So FIRST: we solve for the operation indicated inside the parenthesis

12.9 - 3.1 = 9.8 (we subtract 3.1 from 12.9)

This is the answer you need to select.

you will pay approximately $11,542 in interest over the life of the loan.

it will take approximately 82.3 months to pay off the loan.

To calculate the number of years, we divide the number of months by 12:

Years ≈ 82.3 / 12 ≈ 6.9 (rounded to one decimal place)

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future value of the annuity (total amount paid)

P = Monthly payment amount ($140)

r = Monthly interest rate (16% / 12 = 0.16 / 12 = 0.0133)

n = Number of periods (months)

We need to solve for n. Rearranging the formula, we have:

n = log((FV * r) / (P * r + P)) / log(1 + r)

Plugging in the given values:

FV = $3,400

P = $140

r = 0.0133

n = log(($3,400 * 0.0133) / ($140 * 0.0133 + $140)) / log(1 + 0.0133)

Calculating this expression:

n ≈ log(45.22) / log(1.0133)

Using a calculator, we find:

n ≈ 82.3

To calculate the number of years, we divide the number of months by 12:

Years ≈ 82.3 / 12 ≈ 6.9 (rounded to one decimal place)

So, it will take approximately 6.9 years to pay off the loan.

To calculate the total interest paid, we subtract the initial loan amount from the total amount paid:

Total interest = (P * n) - $3,400

Total interest = ($140 * 82.3) - $3,400

Total interest ≈ $11,542

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The given expression is (5 - 3)³ ÷ 2. First, we simplify the expression within the parentheses: 5 - 3 = 2. Substituting 2 for (5 - 3) in the expression, we get 2³ ÷ 2. Now, we evaluate 2³, which is 8. So, the expression simplifies to 8 ÷ 2 = 4.

To evaluate the given expression, we first need to simplify the expression within the parentheses using the order of operations or BODMAS rule (Brackets, Order, Division, Multiplication, Addition, and Subtraction).

In this case, we have only one set of parentheses, which contains a subtraction operation between 5 and 3. So, we perform the subtraction and replace (5 - 3) with 2.

Now, we have (2)³ ÷ 2.

Next, we evaluate 2³, which gives us 8.

Finally, we divide 8 by 2 to get the final answer of 4.

Therefore, the expression (5 - 3)³ ÷ 2 simplifies to 4.

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\(\huge\text{Hey there\bf!}\)

\(\mathtt{(5 - 3)^3 \div 2}\)
\(\mathtt{= (2)^3 \div 2}\)

\(\mathtt{= 2^3 \div 2}\)

\(\mathtt{= 2 \times 2 \times 2 \div 2}\)

\(\mathtt{= 2 \times 2 \times 2 \div 2}\)

\(\mathtt{= 4 \times 2 \div 2}\)

\(\mathtt{= 8 \div 2}\)

\(\mathtt{= 4}\)

\(\huge\text{Therefore your answer should be: }\)

\(\huge\boxed{\mathtt{4}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

12

Step-by-step explanation:

3*4=12

Answer: it will be 48 in 4 years.

Step-by-step explanation: If it’s triples every 6 months that mean times 3 so 2 times 3 is 6 and since there are 12 months you can also do times 6 so 2 times 6 is 12 . And it’s 4 years so 12 times 4 is 48

Answer:

height of tress is 20 feet

Step-by-step explanation:

because tan = perpendicular/ height

we see option only 20 feet satisfy it

Answer:

Option D :- 20 feet

Step-by-step explanation:

\( \sf \tan ( \theta) = \frac{height}{distance} \)

\( \rightarrow \sf \: \tan (\theta) = \frac{20}{50} \)

\( \sf \: height \: = 20 \: ft\)

Answer:

you know who else like the shape my mom

(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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Therefore, the measure of the area of rhombus EFGH is 252 square units.

A rhombus is a four-sided geometric shape that has the following properties:

All four sides are of equal length.

Opposite sides are parallel to each other.

The angles formed between adjacent sides are equal (i.e., they are all congruent).

The diagonals of a rhombus bisect each other at right angles, meaning they intersect at a 90-degree angle. Additionally, the length of one diagonal is equal to the product of the length of the other diagonal and the sine of one of the angles formed by adjacent sides.

by the question.

\(EK^2 = EG^2/4 + KH^2 (where KH is half the length of FH)EK^2 = 36^2/4 + (14/2)^2EK^2 = 324 + 49EK^2 = 373EK = sqrt(373)\)

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Answer:

\(f(t) = 4100( {2}^{ \frac{t}{2} }) \)

Answer: Option C is most Appropriate.

C) Kadesha is not correct because the number of units between points A and B is different than those between points A primeand B prime.

Step-by-step explanation:

Coordinates of vertices of ΔABC are =A(1,-1), B(1,-4),C(4,-4)

 Coordinates of vertices of ΔA'B'C' are =A'(1,5), B'(1,1),C(4,1)

Suppose, Preimage =ΔABC

Image =ΔA'B'C'

If you will find distance between two vertices of Both the triangles or length of sides of triangles

Kadesha is not correct because the number of units between points A and B is different than those between points A prime and B prime. Option (C) is the correct answer.

"A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things".

For the given situation,

The triangle ABC has points A(1,-1), B(1,-4), C(4,-4)

The triangle A'B'C' has points A'(1,5), B'(1,1), C'(4,1)

Plot these two triangles in the graph as shown below.

The graph shows the relation between the triangle ABC and A'B'C'.

Both the triangles are separated by different units and are not images of one another.

Hence we can conclude that Kadesha is not correct because the number of units between points A and B is different than those between points A prime and B prime. Option (C) is the correct answer.

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Check the picture below.

notice, the pairs in the Unit Circle are the (cosine , sine) pair, which are equivalent to (x , y) values in a cartesian plane.

Answer:

D on edg 2022

Step-by-step explanation:

Answer:

-1/4x^2 -4x - 1

The variance of  is approximately 1.6361 (rounded up to fourth decimal place).

To find the variance of , we need to first calculate its expected value or mean, E(). We can do this by using the formula:

E() = Σ xi pi

where xi is the number of courses and pi is the probability of taking xi courses.

E() = (1)(0.02) + (2)(0.01) + (3)(0.20) + (4)(0.17) + (5)(0.39) + (6)(0.20) + (7)(0.01) = 4.31

So the expected value of  is 4.31.

Next, we need to calculate the variance of . We can use the formula:

Var() = E[( - E())^2]

where E() is the expected value of , as calculated above.

Var() = (1-4.31)^2(0.02) + (2-4.31)^2(0.01) + (3-4.31)^2(0.20) + (4-4.31)^2(0.17) + (5-4.31)^2(0.39) + (6-4.31)^2(0.20) + (7-4.31)^2(0.01)

Var() = 1.6361

Therefore, the variance of  is approximately 1.6361 (rounded up to fourth decimal place).

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Answer:

ab^2-(a-c)b-c

ab^2-ab+bc-c

ab(b-1)+c(b-1)

(b-1)(ab+c)

Answer:

y - 6 = 1/4(x - 4).

Step-by-step explanation:

The slope m = (7-6)/(8-4) = 1/4

y - y1 = m(x - x1)

Using the point (4, 6)

y - 6 = 1/4(x - 4)  (answer)

The equation of line passes through the points (4, 6) and (8, 7) will be;

⇒ y = 1/4x + 5

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (4, 6) and (8, 7).

Now,

Since, The equation of line passes through the points (4, 6) and (8, 7) .

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (7 - 6) / (8 - 4)

m = 1 / 4

m = 1/4

Thus, The equation of line with slope 1/4 is,

⇒ y - 6 = 1/4 (x - 4)

⇒ 4 (y - 6) = x - 4

⇒ 4y - 24 = x - 4

⇒ 4y = x - 4 + 24

⇒ 4y = x + 20

⇒ y = 1/4x + 5

Therefore, The equation of line passes through the points (4, 6) and

(8, 7) will be;

⇒ y = 1/4x + 5

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