5000e^72

and

5000e^0.72

By DeMoivre's theorem,

(3 (cos(5π/6) + i sin(5π/6)))⁴ = 3⁴ (cos(4×5π/6) + i sin(4×5π/6))

… = 81 (cos(20π/6) + i sin(20π/6))

… = 81 (cos(10π/3) + i sin(10π/3))

… = 81 (cos(-2π/3) + i sin(-2π/3))

… = 81 (cos(2π/3) - i sin(2π/3))

… = 81 (-1/2 + √3/2 i )

… = -81/2 + 81√3/2 i

Answer:

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Step-by-step explanation:

Answer:

1,590.02

just round it to the nearest centimeter

Step-by-step explanation:

Answer:

60cm

Step-by-step explanation:

given:

focal length (f) = 20cm

image height (v) = ½u

object height (u) = ?

(1÷v) + (1÷u) = (1÷20)

(1÷(½u)) + (1÷u) = (1÷20)

(2÷u) + (1÷u) = (1÷20)

(3÷u) = (1÷20)

u = 20 × 3

u = 60cm

The values of the [tex]\bar x[/tex] (x-bar) (the mean) and the median of the dataset in the question are;

[tex]\bar {x}[/tex] ≈ 13.05

Median = 13.60

The mean and the median are descriptive statistical values that provides a description of the data that can be found in the dataset.

The mean is the average value of the data in the dataset, and the median is the middle value of the set of data arranged in an order of increasing values.

The mean is the average value of the set of data which is obtained by dividing the sum of the data points by the number of the datapoints, we get;

The number of data points = 28

The sum of the data is;  (4.7 + 12.6 + 3.6 + 16.1 + 2.3 + 28.2 + 2.2 + 16.9 + 10.7 + 19.5 + 11.4 + 27.9 + 11 + 15 + 4.2 + 15.8 + 15.9 + 17.3 + 24.9 + 10.8 + 16.4 + 7.3 + 3.2 + 14.6 + 2.6 + 8.4 + 21.2 + 20.8) = 365.5

The average is the mean is therefore; [tex]\bar x[/tex] = 365.5 ÷ 28 ≈ 13.05

The median is the value of the number in the middle when the numbers are arranged in increasing order as follows;

2.2, 2.3, 2.6, 3.2, 3.6, 4.2, 4.7, 7.3, 8.4, 10.7, 10.8, 11, 11.4, 12.6, 14.6, 15, 15.8, 15.9, 16.1, 16.4, 16.9, 17.3, 19.5, 20.8, 21.2, 24.9, 27.9, 28.2

The numbers at the middle of the set of numbers are 14th and 15th numbers, which are 12.6 and 14.6, which indicates that the median is the average of the two numbers, which is therefore;

Median = (12.6 + 14.6)/2 = 13.60

The median is 13.60

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The dimensions of the rectangle are 40 and 18 units respectively

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: The length of a rectangle is 4 feet more than twice the width.

Then let the width be x then length is equal to 2x+4 and therefore the perimeter is 2(2x+4+x)=116

                       3x+4      = 58

                             3x    = 54

                               x     = 18

Hence, the dimensions of the rectangle are 40 and 18 units respectively.

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[tex]6(2b - 4)[/tex]

Expanding the terms,

[tex](6 \times 2b) - (6 \times 4) \\ = 12b - 24[/tex]

Plugging in our value b,

[tex]b = 5 \\ 12b - 24 = 12(5) - 24 = 36[/tex]

So the answer is,

[tex]36[/tex]

Answer:

Given expression:  6(2b - 4)

To find the value of 6(2b - 4) at b= 5, we need to substitute the b=5 in the expression, we get

6(2(5) - 4)

= 6(10 - 4)…[solve parentheses]

= 6(6)

6 * 6 = 36

=> 6(2(5) - 4) = 36

Therefore, the value of 6(2b - 4) is 36, when b=5.

The relative frequency table that summarizes the data is given by the image at the end of the answer.

The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.

Given:

The percentage of people interested in waterskiing

= 90/250 x 100

= 36%.

Thus, the percentage of people that was not interested in waterskiing is

=100-36

= 64%

Now, the percentages related to paddle boarding are :

Yes: 72/250 = 28.8%.

No: 18/250 = 7.2%.

Of those not interested in waterskiing, the percentages related to paddle boarding are

Yes: 112/250 = 44.8%.

No: (120 - 72)/250 = 19.2%.

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Answer: 178.31

Step-by-step explanation: subtract 574.54 by 396.23

Answer:

8835.73ft^3

Step-by-step explanation:

First:

Find area of the base circle.

Diameter is 15, so radius is 7.5

Area of the base circle is 56.25pi (use formula: A=pi(r)^2 ) (also ill convert pi into decimals only later)

next find the volume of the cylinder

height is 40 so volume = 56.25pi*40 = 2250pi

next find the volume of the dome at the top.

you know the radius is 7.5

Use volume of sphere formula below :

4 /3πr^3

=1767.15

alright now add the two bolded values

1767.15+2250pi

= 8835.73

hope this helps

Answer:

where is the circle graph

Answer:Y, R, B, G

Step-by-step explanation:

Order matters since the ball is being replaced each time. This is all the possible combinations to take 2 balls with replacement, so you can look at the list and see that RR, RB, and RG are listed. The only other combination when choosing a red first would be to pick a yellow, so RY. This is the same pattern for the others also. Look at the list and see what combinations are already listed.

This is the correct answer;

Please leave a Thanks!

It helps!

The correct factorization of 33³ × 39 × 4¹¹ = 2²² × 3⁴ × 11³ × 13

Factorization is the collecting together of the common terms of an expression so as to have it in simpler form.

To find  the correct factorization of 33³ × 39 × 4¹¹, we write out each term in terms of its common factors.

so, we have that the factorization of the first term is 33³ = (3 × 11)³ = 3³ × 11³

Also, we have that the factorization of the second term is 39 = 3 × 13

Finally, we have that the factorization of the last term is 4¹¹ = (2²)¹¹ = 2²²

So, we have that 33³ × 39 × 4¹¹ = 3³ × 11³ × 3 × 13 × 2²²

= 3³ × 3 × 13 × 11³  × 2²²

= 2²² × 3⁴ × 11³ × 13  

So, the correct factorization is 2²² × 3⁴ × 11³ × 13

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The right triangles are congruent by HL theorem.

The triangles having congruent corresponding parts are called congruent triangles.

Given are two right triangles, with equal hypotenuse and one of the bases.

The question is by which theorem do they are congruent,

HL theorem :-

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

Since, we know that, when two right triangles have congruent hypotenuse and one of their legs are also congruent, then both are congruent by HL theorem of congruence.

Here, both the right triangles are following the condition of the HL theorem.

Hence, the correct option is HL.

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Answer:

Step-by-step explanation:

$4.50 + $4.50(0.15) = $5.18

$2.25 + $2.25(0.15) = $2.59

$3.00 + $3.00(0.15) = $3.45

Answer:

[tex]\frac{27}{8}[/tex]

Step-by-step explanation:

using the rules of  exponents/ radicals

• [tex](\frac{a}{b}) ^{-m}[/tex] = [tex](\frac{b}{a}) ^{m}[/tex]

• [tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a}) ^{n}[/tex]

then

[tex](\frac{16}{81}) ^{-\frac{3}{4} }[/tex]

= [tex](\frac{81}{16}) ^{\frac{3}{4} }[/tex]

= [tex]\frac{(\sqrt[4]{81})^3 }{(\sqrt[4]{16})^3 }[/tex]

= [tex]\frac{3^3}{2^3}[/tex]

= [tex]\frac{27}{8}[/tex]

Answer:

8×5= 40 is the answer .......

One pitcher serves 8 people, so to figure out how many 5 pitchers would serve you would do 8×5 which is 40. 5 pitchers would serve 40 people. I hope this helps!

If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.

Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.

given

Table 1:  

x 0 -4 3 -2 9 3

y 5 8 7 8 5 -2

No, Table 1 is not a function.

Since there are two images of element '3'.

i.e. 3 is mapped to 7 and -2.

Table 2:

x 2 -7 5 1 -6 3

y 5 8 -6 8 5 7

Yes, this relation is a function.

Because corresponding to each x there is a single image.

If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.

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We add  (x +7 ) (x - 10) up to -3 and multiply to -70.

What is a quadratic equation?

Any equation in algebra that can be written in the standard form where x denotes an unknown value and a, b, and c denote known numbers, where a 0 is a quadratic equation.

Here,

We illustrate and prove that -9 and 10 multiply to -90 and add up to 1:

7 × -10 = -70

-10 + 7 = -3

We are trying to determine how to factor the following quadratic equation.

x²  -3 x - 70 = 0

If so, the solution to factor the quadratic equation above is:

(x +7 ) (x - 10)

To summarize, -10 and 7 multiplied by -70 and add up to -3, you know that the following is true:

x² -3x - 70

= (x +7 ) (x - 10)

Hence, we add  (x +7 ) (x - 10) up to -3 and multiply by -70.

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957÷3=319 this divide answer i hope help you

Answer:

a. x^4 - 12x^3 + 2x^2 - 2x + 4

Degree: 4

b. x^4 - 2x^2 - 2x - 4

Degree: 4

Step-by-step explanation:

For part a, all you are doing is adding the polynomials together. They already set up the boxes in standard form, so all you need to do is add each like term as I wrote out in the answer. The degree is then going to be the first exponent that you see once the polynomial is in standard form, which is 4.

For part b, you are now subtracting the polynomials. Again, it is set up for you in standard form. There is no x^3 terms because they cancel out, but you basically subtract each like term from another, and remember to distribute the subtraction sign (it acts as a -1) across the parenthesis. The degree is the first exponent you see, and that is 4.

An area surrounding a measurement that indicates how accurate it is called a confidence interval.

Let X = The proportion of n randomly selected consumers who receive the discount. So, X = B(n, p), where p is the likelihood that a consumer will receive the discount.

Back-up Theory 100(1 - α) % Confidence Interval for the population proportion, p is:

p ± Zα/2[√{P(1 –p)/n}] ……(1)

where

Zα/2 is the upper (α/2)% point of N(0, 1),

pcap = sample proportion, and

n = sample size.

One can conclude with 100(1 - )% confidence that the population proportion, p, is p if a 100(1 - )% Confidence Interval for p holds a specific hypothesized value of p…………. (2)

Now to work out the solution,

The given confidence interval is: 0.12 ± 0.05 i.e., [0.07, 0.17] or [7%, 17%]……………………. (3)

for Part (a)

equation (2) and (3), [7%, 17%] holds 15%. Hence the statement is NOT valid.

for Part (b)

equation(2) and (3), [7%, 17%] holds 15%. Hence the statement is valid.

For Part (c)

Margin of error is: Zα/2[√{P(1 –P)/n}]

If the sample sizes under Part (c) and (a) are respectively, n2 and n1, the ratio of respective margin of errors would be

[Zα/2.√t{P(1 –P)/n2}]/[Zα/2√{P(1 –P)/n1}]

= √(n1/n2)

= 1/√6 [given the second sample size is 6 times the first sample size]

= 0.4082

= > the margin of error under Part (c) = the margin of error under Part (c) x 0.4082

= 0.05 x 0.4082

= 0.020.

Thus, the margin of error when the sample size if 6-fold is 0.020.

For Part (d)

The revised Confidence Interval from Part (c) is 0.12 ± 0.02 or [0.10, 0.14], which does not hold 0.15 as a result, according to (2), the program is NOT operating as anticipated.

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Answer: It's not possible to accurately describe the function g(x) without more information about the equation or the graph. The equation provided is g(x)=√x + , which is incomplete, it does not have a value assigned for the "+" operator, it could be added to any number, for example, g(x)= √x + 1, or g(x)= √x+5, and so on.

Additionally, the statement that the function g(x) has a domain x² and range y ≥ , is not a valid mathematical notation or statement. The domain of a function is the set of all input values (x-values) for which the function is defined, it's usually a set of real numbers or interval, like [-∞,+∞], (a,b) or [a,b], for example.

And range is the set of all output values (y-values) of a function, it's also usually a set of real numbers or interval.

I would suggest if you can provide me with the complete function of g(x) and more detailed information about the graph. I can help you better understand its features and properties.

Step-by-step explanation:

Answer:

C. 2^8p=2^5p+15

:D

Answer:

Step-by-step explanation:

w≥-2

or -2 ≤w≤5

Step-by-step explanation:

lcm = hcf × remaining expressions

7xy= 7 × x × y

6y² = 6 × y × y

here only y is common in both. so y is the hcf. now, without hcf, the remaining expressions are : 7x and 6y.

so LCM = hcf × remaining expressions

= y × 7x × 6y

= 42xy²

Answer:

1,440 inches^3

Step-by-step explanation:

First, remember the formula for volume is v = l x w x h

Next, sub in your values for your prism 6 x 15 x 16 = 1,440in^3

So, the final answer is 1,440 inches^3

Answer:

Yes

Step-by-step explanation: