#3c Part 1: What postulate did you make use of to answer parts a and b?
1 point
Segment Addition Postulate
Angle Addition Postulate
Corresponding Angles Postulate
Ruler Postulate

The present value of your winnings is $20.07 million.

Present value is the value right now of some amount of money in the future.

For example, if you are promised $110 in one year, the present value is the current value of that $110 today.

Given:

The present value of an annuity is determined by:

PV = P [ 1- \((1+ r)^{-n\) / r]

With annual payments (P) of $1.75 million, for a period (n) of 20 years at a discount rate (r) of 6 percent, the present value is:

PV = 1.75  [ 1- \((1+ 0.06)^{-20\) / 0.06]

PV = 1.75 [ 1- 0.31180472688 / 0.06]

PV = 1.75 x 11.4699

PV = $20.07 million

Hence, the present value is $20.07 million.

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Answer:

Below in bold.

Step-by-step explanation:

A = value of y when x = -1:

A = -2(-1)^2 + 4(-1) + 9

   = -2*1 - 4 + 9

   = -2 - 4 + 9

   = 3.

B = value of y when x = 2:

B = -2(2)^2 + 4(2) + 9

   = -2*4 + 8 + 9

   = - 8 + 8 + 9

    = 9.

Answer:

Area = 40

Perimeter = 26

Step-by-step explanation:

length = 8

width = 5

Area = 8 x 5 = 40

Perimeter = 2(8 + 5) = 26

Complete Question

The complete question is shown on the first uploaded image

Answer:

The value is  \(P( 1.39 < z < 1.53 ) = 0.0193\)

Step-by-step explanation:

From the question we are told to obtain the area to the of the z-score 1.39 and to the left of the z-score 1.53, this is mathematically represented as

        \(P( 1.39 < z < 1.53 ) = P( z < 1.53 ) - P( z < 1.39 )\)

From the z table on the question the area under the normal curve to the left corresponding to 1.53 and  1.39  is

       \(P( z < 1.53 ) = 0.9370\)

and

      \(P( z < 1.39 ) = 0.9177\)

So

     \(P( 1.39 < z < 1.53 ) = 0.9370 - 0.9177\)

=>  \(P( 1.39 < z < 1.53 ) = 0.0193\)

Answer:

Step-by-step explanation:

60 divided by c-n=how many you have left

Answer:C

Step-by-step explanation:

The balances for Retained Earnings and Stock Dividends Distributable may change depending on the actual closing of the dividend's accounts on December 31.

The T accounts for the stockholders' equity accounts and additional accounts are as follows:

Common Stock, $5 stated value:

Opening balance (Jan. 1): $3,100,000

Issuance of 200,000 shares (Apr. 13): +$1,000,000

Closing balance: $4,100,000 (620,000 + 200,000 shares issued)

Paid-In Capital in Excess of Stated Value—Common Stock:

Opening balance (Jan. 1): $1,240,000

Closing balance: $1,240,000 (no additional transactions affecting this account)

Retained Earnings:

Opening balance (Jan. 1): $4,875,000

Dividend declared on December 1: -$34,320

Dividend declared on June 14 (3% stock dividend): -$123,000 (200,000 shares × $7.50 per share)

Dividend declared on Dec. 30: -$49,600 (620,000 shares × $0.08 per share)

Closing balance: $4,668,080

Treasury Stock:

Opening balance (Jan. 1): -$288,000

Sale of treasury stock (Mar. 15): +$324,000 (48,000 shares × $6.75 per share)

Purchase of treasury stock (Oct. 30): -$300,000 (50,000 shares × $6 per share)

Closing balance: -$264,000

Paid-In Capital from Sale of Treasury Stock:

Opening balance (Jan. 1): $0

Sale of treasury stock (Mar. 15): +$324,000

Stock Dividends Distributable:

Opening balance (Jan. 1): $0

Declaration of stock dividend (June 14): +$123,000 (200,000 shares × $7.50 per share)

Distribution of stock dividend (July 16): -$123,000

Closing balance: $0

Stock Dividends:

Opening balance (Jan. 1): $0

Declaration of stock dividend (June 14): +$123,000

Cash Dividends:

Opening balance (Jan. 1): $0

Payment of cash dividends (Jan. 15): -$34,320

Closing balance: -$34,320

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A. The graph of the absolute value function is V-shaped, with the features given as follows:

B. The transformation is that the function was shifted right two units, hence the features are given as follows:

The absolute value function, with vertex (h,k), is defined as follows:

y = |x - h| + k.

The features of the function are given as follows:

For the first item, the function is |x + 3|, hence we just have to identify the features.

For the second function, the definition if h(x) = |x - 2|, with vertex at (2,0), meaning that the function was shifted two units right from the parent absolute value function y = |x|. The shift just changes the turning point of the graph, not altering domain and range.

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Answer:

1.8 < x

Step-by-step explanation:

you add the 1 x to the 4 x

9< 5x then u divided by 5

1.8 <x

Answer and Step-by-step explanation:

To find the length of PQ, we need to set the length of PQ equal to the length of QR (since in the question it tells us that PQ is equal to QR).

PQ = QR

x + 1 = 12

Solve for x.

Subtract 1 from both sides of the equation.

x + 1 - 1 = 12 - 1

x = 11

Now plug this number into the expression length for PQ.

11 + 1 = 12

The length of PQ is 12.

(you can also see that QR has a length of 12, so we can just say that PQ 12).

#teamtrees #PAW (Plant And Water)

I hope this helps!

Answer: 16

Step-by-step explanation:

Range is the largest number in the set minus the smalllest number in the set pf numbers or data.

9-(-7)

9+7

16

Answer:

  {-7, -1, 0, 9}

Step-by-step explanation:

The range of a function is the set of second values of the ordered pairs of the function.

  range = {-7, -1, 0, 9}

_____

It is often convenient, but not essential, to list the elements of a set in order.

SOLUTION:

The equation is;

The equation has one solution

When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)

First, we shall determine the value of A. Details below:

Quadratic equation is expressed as:

x² - (sum of root)x + product of root

Comparing the above with x² - 11x + 30, we have

x² - 11x + 30 = x² - (sumof root)x + product of root

Product of roots = 30

Thus,

A = 30

Next, we shall determine the value of B. details below:

f(x) = x² + 5

f(2) = 2² + 5

f(2) = 9

Thus,

B = 9

Next, we shall determine the value of C. Details below:

Let

x + 4 = 0

Thus,

x = -4

Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:

Remainder = x² - 2x - 24

Remainder = (-4)² - 2(-4) - 24

Remainder = 0

Thus,

C = 0

Finally, we shall determine value of A/5 + √(B - C). Details below:

A/5 + √(B - C) = 30/5 + √(9 - 0)

A/5 + √(B - C) = 6 + √(9

A/5 + √(B - C) = 6 + 3

A/5 + √(B - C) = 9

Thus, the value of A/5 + √(B - C) is 9 (option B)

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Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Answer:

Value of x = 11 ° , ∠B = 108° ,∠C = 36° ,∠D = 36°

Step-by-step explanation:

Given :

In ΔBCD , BC = BD And ∠B= (13x-35)° , ∠C= (5x-19)° ,∠D=(2x+14)°

To Find :

value of x and ∠D , ∠B and ∠C

Solution:

∵ BC=BD , So ∠C = ∠D

Therefore 5x-19 = 2x+14

3x = 33 , ∴ x=11°

So, ∠B = (13×11) - 35 = 108°

∠C = (5×11)-19 = 36°

∠D= (2×11) +14 =36°

The correct answer is D. No because 23 and 25 are not supplementary.

In the given diagram, it is stated that the measures of angles 23 and 27 are 45°, and the measure of angle 25 is 135°. To determine if lines C and D are parallel, we need to analyze the angles formed by these lines.

If the alternate interior angles or corresponding angles are congruent, then the lines are parallel. However, in this case, we don't have enough information about the angles formed by lines C and D to make that determination.

The fact that angle 23 and angle 27 are congruent (both measuring 45°) doesn't provide any information about the relationship between lines C and D. Similarly, the measure of angle 25 being 135° doesn't give us any insight into the parallelism of lines C and D. Therefore, we cannot conclude that lines C and D are parallel based on the given information, and the correct answer is D.

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Using the z-score, mean and sample mean, the standard deviation of the sample is 7.57

A z-score describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

The formula is given as;

z = x - μ / σ

Substituting the values into the formula;

-2.13 = 19.3 - 29 / σ

Cross multiply both sides;

-2.13σ = 19.3 - 29

-2.13σ = -9.7

Divide both sides by the coefficient;

-2.13σ / -2.13 = -9.7 / -2.13

σ = 7.57

The standard deviation is 7.57

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Answer:

25

Step-by-step explanation:

900/36 = 25 tables an hour

Answer:

25

Step-by-step explanation:

You divide the total tables made by the total hours to get how many is made per hour, since it's all the same per hour the answer is 25.

25x36=900
900/36=25

(Let me know if this helped c: )

In a case whereby Apollo Spas services 298 hot tubs and each hot tub needs 175 mL of muriatic acid,number of liters of acid that are needed for all of the hot tubs is 52.15 litres.

The unit conversion can be described as the changing of bone unit to another.

We can calculate the number of liters of acid that are needed as (298 * 175)= 52150ml

This can be converted to liter by dividing  52150ml by 1000 which  can be done as (52150ml/1000) = 52.15 litres of acid.

Therefore, the  liters of acid are needed for all of the hot tubs can be expressed as the 52.15 litres

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Cindy will have $42.52 after buying the shoes.

Cindy's main money is $120:

Shoe cost: $82.23

With applying the coupon shoe cost: $82.23 -$4.75 = $77.48

So Cindy's total spent was $77.48

Therefore Cindy left with: $120 - $77.48 = $42.52

A coupon is a ticket or document that can be redeemed for a cash discount or credit when purchasing a product.

Consumer package manufacturers or retailers usually issue coupons for use in retail stores as part of a sales promotion. They are often widely distributed through mail, coupon envelopes, magazines, newspapers, the Internet, directly from the retailer, and through portable devices such as cell phones.

The New York Times reported that "more than 900 producer coupons" per household were distributed and that "four out of five families use the coupons, according to the United States Department of Agriculture. "Only about 4% percent" of the coupons received were redeemed. . Coupons can be targeted selectively to regional markets where price competition is fierce.

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Answer:

D

it is D D D D D D D D D D D D D D D D D D D

Answer:

12 + 7 = 19

19 + 10 = 29

answear = 29

Step-by-step explanation:

\( \underline{ \underline{ \text{Given}}} : \)

\( \underline{ \underline{ \text{To \: find}}} : \)

\( \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : \)

\( \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}\)

⤑ \( \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }\)

⤑ \( \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }\)

⤑ \( \sf{ \sqrt{100 - 64}} \)

⤑ \( \sf{ \sqrt{36}} \)

⤑ \( \boxed{ \sf{6\: units}}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}\)

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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When y = 36 the value of x is 24.

What is Proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

As per the given data:

y and x have a proportional relationship:

Consider: y = ax ...(i) {where a is a constant}.

y = 24 when x = 16

Substituting in eq (i)

24 = a × 16

a = (24/16) = 1.5

For value of x when y = 36

y = 1.5x

36 = 1.5x

x = (36/1.5) = 24

x = 24

The value of x is 24

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Answer:

The 15th term is 160

Step-by-step explanation:

The details are not clear. So, I will make the following assumptions

\(d = 10\) ---- common difference

\(a_1 = 20\) ---- first term

Required

The 15th term

This is calculated as:

\(a_{n} = a + (n - 1) * d\)

Substitute 15 for n

\(a_{15} = a + (15 - 1) * d\)

\(a_{15} = a + 14 * d\)

Substitute values for d and a

\(a_{15} = 20 + 14 * 10\)

\(a_{15} = 20 + 140\)

\(a_{15} = 160\)

PQ/JK is congruent to PS/JL. Option D is the correct option.

What is the scalene triangle?

A scalene triangle is a triangle with three different side lengths and three different angle measurements. However, the sum of all the interior angles of the scalene triangle is unaffected by the various measurements. Scalene triangles satisfy the angle sum property of triangles because the sum of their three interior angles is always 180 degrees.

Given that △JKL and △PQS are two triangles.

Angle P is congruent to angle J.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

△JKL and △PQS are similar triangles if

1) angle K is congruent to Q

or,

2)  angle L is congruent to S

or,

3) PQ/JK = QS/KL = PS/JL

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Answer:

2.5 i think

Step-by-step explanation:

The graph of\(f(x) = (3x)^{2 - 1}\) is a stretched version of the parent function \(f(x) = x^2\), making option B (The parent function has been stretched) the correct answer.

The graph of the function \(f(x) = (3x)^{2 - 1}\)represents a transformation of the parent function \(f(x) = x^2\). Let's analyze the given options and determine how the graph of f(x) relates to its parent function:

A. The parent function has been compressed: This option implies that the graph of f(x) is narrower or more compact compared to the parent function. However, since the function  \(f(x) = (3x)^{2 - 1}\) involves multiplying the x-values by 3, it actually stretches or expands the graph horizontally rather than compressing it. Therefore, option A is not correct.

B. The parent function has been stretched: This option accurately describes the transformation in the graph. The function  \(f(x) = (3x)^{2 - 1}\)stretches the parent function  \(f(x) = x^2\). horizontally by a factor of 3. As a result, the graph becomes wider or more spread out compared to the parent function. Therefore, option B is correct.

C. The parent function has been translated down: This option refers to a vertical shift of the graph, which is not applicable in this case. The function  \(f(x) = (3x)^{2 - 1}\) does not involve any vertical translation, as the constant term (-1) affects the vertical position of the graph.

D. The parent function has been translated to the left: This option refers to a horizontal shift of the graph. The function \(f(x) = (3x)^{2 - 1}\) does not involve a horizontal shift, as there is no addition or subtraction of a constant value to the x-values. Therefore, option D is not correct.

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