What is the length of PR ?

A. 36 units
B. 48 units
C. 42 units
D. 24 units

11 x 7 + 11 x 4 is the expression of the total area as the sum of the areas of

each room.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

11 (7 + 4)

Using the property of multiplication over addition.

11 x 7 + 11 x 4

Thus,

11 x 7 + 11 x 4.

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Jordan spend 25 minutes writing each dayNoHow much time does Jordan spend writing each dayFrom the question, we have the following parameters that can be used in our computation:D + W = 75W + 25 = DSo, we haveW + W + 25 = 75EvaluateW = 25This means that Jordan spends 25 minutes on writing is it possible?Based on the answer in (a), the truth statement is No

Answer: Reference angle= 40 degrees

Step-by-step explanation: Here we want to find the Reference angle for -230 degrees,

 Step 1: Draw the angle in the standard position i.e. drawing the angle with its initial side on the positive x-axis and its vertex at the origin.

 Step 2: By this, we get that -230 degrees lies in the third quadrant. (The quadrant is determined by the location of the terminal side of the angle.)

 Step 3: To find the Reference angle we have to determine the absolute value of -230 degrees and which is 230 degrees.

 Step 4: We have the formula to determine as the angle is in the 3rd quadrant we use 270-(given angle)=270-230=40

Step 5: 40 degrees is the reference angle for -230 degrees.

Answer:

-1/2

Step-by-step explanation:

take the change in y and divide by the change in x: (4 / -2)

Answer: Ig

Step-by-step explanation:

To write a linear expression in standard form, rearrange the terms in alphabetical order.

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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By de Moivre's theorem,

\(\left(\cos\left(\dfrac\pi6\right) + i \sin\left(\dfrac\pi6\right)\right)^{18} = \cos\left(\dfrac{18\pi}6\right) + i \sin\left(\dfrac{18\pi}6\right) \\\\ ~~~~~~~~ = \cos(3\pi) + i \sin(3\pi) = \boxed{-1}\)

The value of the given complex number is -1

Given the polar form of a complex number expressed as:

\((cos\theta + isin\theta)^n\\\)

This can also be expressed according to the de moivre's theorem as;

\(=(cos\theta + isin\theta)^n\\\\=(cosn\theta+isinn\theta)\)

Given the expression below;

\((cos\frac{\pi}{6} + isin\frac{\pi}{6} )^{18}\\(cos18\cdot\frac{\pi}{6} + isin18\cdot\frac{\pi}{6} )\\(cos3\pi + isin3\pi)\\=-1\)

Hence the value of the given complex number is -1

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The biconditional statement is: A rectangle is a parallelogram with four right angles if and only if a parallelogram has four right angles.

The term "if and only if" or biconditional statement refers to a compound statement composed of two conditional statements connected by a logical operator.

This definition is commonly utilized to describe the characteristics of a rectangle when it comes  to its correlation with a parallelogram. The opening section of the biconditional statement is comprised of a conditional statement indicating that a rectangle is defined as a parallelogram featuring four right angles.

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Write this definition as a biconditional statement.

A rectangle is a parallelogram with four right angles.

Answer:

4

Step-by-step explanation:

4 is the only whole number between 5 and 3.

Answer:

n(B) = 1350

Step-by-step explanation:

Using Venn sets, we have that:

\(n(A \cup B) = n(A) + n(B) - n(A \cap B)\)

Three values are given in the exercise.

The other is n(B), which we have to find. So

\(n(A \cup B) = n(A) + n(B) - n(A \cap B)\)

\(2290 = 1300 + n(B) - 360\)

\(940 + n(B) = 2290\)

\(n(B) = 2290 - 940 = 1350\)

So

n(B) = 1350

The length of e is 29.53 inches.

In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".

Given:

f= 33 inches

<F= 140, <D = 5

Now,

<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35

Using Sine law

sin F / f = sin E/ e

sin 140 / 33 = sin 35 / e

0.642/ 33 = 0.573 / e

0.0194 e= 0.573

e= 29.53 inches

Hence, the length of e is 29.53 inches.

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Answer:

F(x) = -1/3 x^2 - 7x + C

The horizontal shift is to the right.

The exact period is 8/7.

In a trigonometric function, written of the form

y = A csc (Bx - C)

the parameters are interpreted as follows

A is the amplitude

B is period / 2π

C is the horizontal shift

comparing with the equation y = 2 csc (7π/4x - 21π/2). we have that

horizontal shift = -21π/2 since it is positive it is to the right

The exact period is

Period = 2π / (7π/4)

= 8/7

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Answer:

The answer is 3380

Step-by-step explanation:

i took the test

Answer:

719.4244604

Step-by-step explanation:

100/0.139=719.4244604

Question Completion

PIE CHART NUMBERS:

Answer:

0.000063

Step-by-step explanation:

Number of Respondents, n=1400

Probability that they would rate their financial shape as​ excellent = 0.09

Number of Those who would rate their financial shape as excellent

=0.09 X 1400

=126

Therefore:

The probability that 4 people chosen at random would rate their financial shape as​ excellent

\(=\dfrac{^{126}C_4 \times ^{1400-126}C_0}{^{1400}C_4} \\=\dfrac{^{126}C_4 \times ^{1274}C_0}{^{1400}C_4}\\=0.000063 $(correct to 6 decimal places)\)

Answer:

  x = (1 +i√83)/6  or  x = (1 -i√83)/6

Step-by-step explanation:

You want the solutions to the quadratic equation 3x² -x +7 = 0.

The solutions to the equation ax² +bx +c = 0 are given by the formula ...

  \(x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

The given equation has a=3, b=-1, c=7, so the solutions are ...

  \(x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(3)(7)}}{2(3)}=\dfrac{1\pm\sqrt{-83}}{6}\\\\\\\boxed{x=\dfrac{1+i\sqrt{83}}{6}\quad\text{or}\quad x=\dfrac{1-i\sqrt{83}}{6}}\)

<95141404393>

Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

We can see that Natalie is reducing the amount she owes by $18 every two weeks.

Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.

This means that after n weeks, the amount she still owes is:

$180 - $18n

Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:

$180 - P

After two weeks, she will owe:

($180 - P) - P = $180 - 2P

After four weeks, she will owe:

($180 - 2P) - P - P = $180 - 4P

After six weeks, she will owe:

($180 - 4P) - P - P = $180 - 6P

And after eight weeks, she will owe:

($180 - 6P) - P - P = $180 - 8P

We can set up an equation using the information we have:

$180 - 8P = $108

Solving for P, we get:

P = $9

Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.

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The complete question:

Natalie borrowed money from her parents to pay for a trip. ​Natalie will ​pay her parents in equal amounts every week until she pays back the ​entire amount she borrowed. ​ ​The table below shows the amount of ​money Natalie still owes her parents at the end of every two weeks for ​the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?

Week 0 = $180

Week 2 = $162

Weeks 4 = $144

Week 6 = $126

Week 8 = $108

The height of the hexagonal-based pyramid is approximately 101.61 inches.

To find the height of the hexagonal-based pyramid, we can use the formula for the volume of a pyramid:

Volume = (1/3) × Base Area × Height

In this case, the base of the pyramid is a regular hexagon, and we have the side length (s) and apothem (a) given.

The base area of a regular hexagon can be calculated using the formula:

Base Area = (3√3/2) × s²

Let's calculate the base area first:

Base Area = (3√3/2) × (6 in)²

Base Area = (3√3/2) × 36 in²

Base Area ≈ 93.53 in²

Now, we can rearrange the volume formula to solve for the height:

Height = Volume / ((1/3) × Base Area)

Height = 3168 in³ / ((1/3) × 93.53 in²)

Height = 3168 in³ / (31.177 in²)

Height ≈ 101.61 in

Therefore, the height of the hexagonal-based pyramid is approximately 101.61 inches.

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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1. The finance charge on the loan is $9,920.

2. The total deferred payment price of the airplane is $39,120.

To find the finance charge on the loan, we need to first determine the amount financed. George Bell made a 15% down payment on the airplane, so the amount financed is:

= $29,200 - (0.15)($29,200)

= $29,200 - $4,380

= $24,820

The total amount of payments made over the life of the loan is:

= $579/month x 60 months

= $34,740

The finance charge on the loan is:

= $34,740 - $24,820

= $9,920.

The total deferred payment price of the airplane is the sum of the down payment and the total amount of payments made over the life of the loan. The down payment is 15% of the purchase price which is:

= 0.15 * $29,200

= $4,380

The total amount of payments made over the life of the loan is:

= $579/month * 60 months

= $34,740

The total deferred payment price of the airplane is:

= $4,380 + $34,740

= $39,120.

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Answer:

a)

b)-4

Step-by-step explanation:

a) f(13) = 13-7=

b) f(3)= 3-7= -4

Answer:

let the three consecutive Integers be

x , x+1 , x+2

their sum is 60,

so,

x + x + 1 + x + 2 = 60

→ 3x + 3 = 60

→ 3x = 60 - 3 = 57

→ x = 57/3 = 19

therefore, 1st integer = 19

2nd integer = x + 1 = 19 + 1 = 20

3rd integer = x + 2 = 19 + 2 = 21

so,

the three consecutive Integers are 19 , 20 and 21.

hope this answer helps you dear... take care and may u have a great day ahead!

Answer:

y=6x-4

Step-by-step explanation:

What we know

-9 is x and -58 is y so we have to find the y-intercept y=mx+b is also the formula for this

-58=6(-9)+b

-58=-54+b

-58=54+b        - we changed -54 to a positive 54

54-58=-4

y=6x-4

Answer:

3/4

Step-by-step explanation:

4/8 can be simplified by dividing 2 from the numerator and denominator, which equals 2/4.

This turns the equation into 2/4 + 1/4, giving you a common denominator.

Answer:

Both B & C answers are correct

Step-by-step explanation:

To solve these two fractions, 1st you have to make both the numerator and the denominator the same.

For that, you can multiply both the numerator and the denominator of 1/4 by 2.

\(\sf\frac{4}{8} +\sf\frac{1}{4} \\\\\sf\frac{4}{8} +\sf\frac{1*2}{4*2}\\\\\sf\frac{4}{8} +\sf\frac{2}{8}\\\\\sf\frac{6}{8}\)

To write the fraction in its simplest form, divide both sides by 2.

\(\sf\frac{3}{4}\)

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

No,the ray AB and BA are not same because the ray AB denotes the ray(light) is coming from the direction through A while the ray BA denotes the ray is coming from the direction through B.

Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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