What is the value of k in the product of powers below?

10 Superscript negative 3 Baseline times 10 times 10 Superscript k Baseline = 10 Superscript negative 3 Baseline = StartFraction 1 Over 10 cubed EndFraction

The proof that z lies on the x-axis is shown below

For z to lie on the x-axis, then the coordinate must be represented as (x, 0)

Given that

\(\frac{|z - 5i|}{|z + 5i|} = 1\)

We start by simplifying the given expression using the definition of the modulus of a complex number:

So, we have

\(\frac{|z - 5i|}{|z + 5i|} = \frac{\sqrt{(x - 0)^2 + (y - 5)^2}}{\sqrt{(x - 0)^2 + (y + 5)^2}} = 1\)

Where

z = x + yi or z = (x, y)

Squaring both sides of the equation above, we obtain:

\(\frac{(x - 0)^2 + (y - 5)^2}{(x - 0)^2 + (y + 5)^2} = 1\)

This gives

\(\frac{x^2 + (y - 5)^2}{x^2 + (y + 5)^2} = 1\)

By comparison, we have

\((y + 5)^2 = (y - 5)^2\)

Set y = 0 to test the equation

So, we have

\((0 + 5)^2 = (0 - 5)^2\)

25 = 25 --- true

The equation is true for y = 0

This means that

z = (x, 0)

Hence, z lies on the x-axis

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Answer: 177

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x be the random variable representing the SAT scores for the students at a local high school. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 1527

σ = 291

the probability to be determined is expressed as P(x > 1207)

P(x > 1207) = 1 - P(x ≤ 1207)

For x < 1208

z = (1207 - 1527)/291 = - 1.1

Looking at the normal distribution table, the probability corresponding to the z score is 0.16

P(x > 1207) = 1 - 0.16 = 0.84

Therefore, the percentage of students from this school earn scores that satisfy the admission requirement is

0.84 × 100 = 84%

Answer:

pizza

Step-by-step explanation:

... :D

Answer: 4ft

Step-by-step explanation: V= l * w * h

The width needed to reach the desired volume is 4 feet.

A prism is a three-dimensional object.

There are triangular prism and rectangular prism.

We have,

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.

We are given that the length is 6.8 feet, the height is 2 feet, and the volume is 54.4 ft3.

We can use these values to find the width as follows:

V = lwh

54.4 = 6.8(w)(2)

54.4 = 13.6w

w = 54.4/13.6

w = 4

Therefore,

The width needed to reach the desired volume is 4 feet.

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Answer:

https://www.sensorsone.com/length-width-and-height-to-volume-calculator/

Step-by-step explanation:

Answer:

I hope it helped U

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Answer:

Step-by-step explanation:

The measure of the length of segment AB in the triangle is 20 units.

The figure in the image is of two similar triangles:

From the image,

For the smaller triangle:

Leg 1 AP = 12

Leg 2 AQ = 8

For the larger triangle:

Leg 1 AC = 12 + 18 = 30

Leg 2 AB = 8 + QB

First, we determine length QB, we take the ratio of the sides of the two triangle since they similar:

Hence:

Leg 1 AP : Leg 2 AQ = Leg 1 AC : Leg 2 AB

12 : 8 = 30 : ( 8 + QB )

12/8 = 30/( 8 + QB )

Solve for QB:

12( 8 + QB ) = 8 × 30

96 + 12QB = 240

12QB = 240 - 96

12QB = 144

QB = 144/12

QB = 12

Now,

Leg 2 AB = 8 + QB

Plug in QB = 12:

Leg 2 AB = 8 + 12

Leg 2 AB = 20

Therefore, AB measure 20 units.

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Answer:

B) 8x + 350 ≥ 800

Step-by-step explanation:

A dance squad needs at least $800, this means the inequality sign will be greater than or equal to.

They already have $350, and each ticket is $8.

So,

8x + 350 ≥ 800

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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The hοle needs tο be 39 inches deeper.

A cοnversiοn factοr is a number used tο change οne set οf units tο anοther, by multiplying οr dividing. When a cοnversiοn is necessary, the apprοpriate cοnversiοn factοr tο an equal value must be used. Fοr example, tο cοnvert inches tο feet, the apprοpriate cοnversiοn value is 12 inches equals 1 fοοt.

The current depth οf the hοle is 2 feet 9 inches, which is the same as 2 + 9/12 = 2.75 feet (since there are 12 inches in 1 fοοt).

Tο find οut hοw much deeper the hοle needs tο be, we need tο subtract the current depth frοm the required depth:

6 feet - 2.75 feet = 3.25 feet

Hοwever, we are asked tο express the answer in inches, sο we need tο cοnvert the 3.25 feet tο inches using the given cοnversiοn factοr:

3.25 feet x 12 inches/1 fοοt = 39 inches

Therefοre, the hοle needs tο be 39 inches deeper.

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Given:

Let x percent of 160 is 32

Let 'x' be the percent

Therefore, 20% of 160 is 32.

Answer:

-7/4 = 2/5t

x5        x5

-35/4 = 2t

Divide by 2 on both sides

-4 3/8 = T

Answer:

35/8

Step-by-step explanation:

The statement that correctly compares the number of songs on Georgia and Scarlet's playlists are is  17 < 36.

Georgia has 17 songs on her playlist while Scarlet has 36 songs on her playlist.

In the number line, the number 36 comes after the number 17. This means that 36 is greater than 17.

The statement that therefore correctly compares the number of songs in the playlist is:

17 < 36

In conclusion, the statement that correctly compares the songs in the two playlists is 17 < 36.

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The correct answer for this would be: Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

According to the ASA theorem, if the included side of one triangle and its two angles are comparable to the parts of another triangle, then the triangles are said to be congruent.

Check the attached file for the image of this problem.

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E. None of the above solutions

The probability of 800 or more heads out of 1600 tosses of a fair coin falls into none of the specified ranges. To compute exact probabilities, we can use the normal distribution to approximate the binomial distribution of the numbers.

The average number of heads in 1600 flips is 800, with a standard deviation of about 25.8. Using the normal distribution, we can compute the probability of more than 800 tables as follows:

P(X > 800) = 1 - P(X <= 800)

Using a standard regular table or calculator, we find that P(X <= 800) is approximately 0.5. So the probability of getting more than 800 heads is 1 - 0.5 = 0.5 or 50%. Since this is not in any given range, the correct answer is

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The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.

Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.

Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.

The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.

The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.

Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.

The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.

The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.

However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.

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Step-by-step explanation:

\({ \purple{ \tt{(X₁ + X₂)²}}}\)

This above problem is in the form of

\({ \blue{ \tt{ {(a + b)}^{2}}}}\)

where the expanded form of

\({ \blue{ \tt {(a + b)}^{2}}} = { \green{ \bold{ {a}^{2} + {b}^{2} + 2ab}}} \)

then the (X₁ + X₂)² answer will be

\({ \purple{ \tt{(X₁ + X₂)²}}} = { \purple{ \tt{ {X₁}^{2} + {X₂}^{2} + 2X₁X₂}}}\)

The total surface area of the pyramid is 220 cm squared

The total surface area of the pyramid is the sum of the area of the four triangles and the area of the square. That is:

total surface area of the pyramid = 4*(area of triangle) + area of square

total surface area of the pyramid = 4*(30) + 10²

total surface area of the pyramid = 120 + 100

total surface area of the pyramid = 220 cm²

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1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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There are 28 units in total between the first and last clothespin.

The resulting displacement may be measured using the distance. It represents the distance between the two places. It may be measured using a variety of units, including meters and centimeters.

The specified parameter is shown as intervals in the query. The phrase can be written as follows:

There are 15 total clothespins.

The distance between clothing pegs is 2 feet.

No, the following is the distance from the initial location to the last one:

0 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 28 units

There are 28 units in total between the first and last clothespin.

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The expression is equivalent to 1/3(9x + 12) + 4x + 6 will be 7x + 10. Then the correct option is B.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 1/3(9x + 12) + 4x + 6

Simplify the expression, then we have

⇒ 1/3(9x + 12) + 4x + 6

⇒ 3x + 4 + 4x + 6

⇒ 7x + 10

The expression is equivalent to 1/3(9x + 12) + 4x + 6 will be 7x + 10. Then the correct option is B.

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Answer:

135.

Step-by-step explanation:

(21 + 3) · 6 - 9

*21 + 3 = 24

24 · 6 - 9

**24 · 6 = 144

144 - 9

***144 - 9 = 135

answer:

131.88 inches

step-by-step explanation:

2πr = circumference

2(21)(3.14)

= 131.88

The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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Answer:

\(1.25\)

Step-by-step explanation:

\(let \: a = x \: and \: b = y\)

\(36x = \frac{45}{y} \)

\(36xy = 45\)

\(xy = \frac{45}{36} \)

\(xy = 1.25\)

\(therefore \: ab \: is \: 1.25\)