Question 15 please and i will mark the brainliest!!! And thank you to whoever answers

Answer:

Standard Complex Form  : [tex]-\frac{25\sqrt{3}}{2}+\frac{25}{2}i[/tex]

Step-by-step explanation:

We want to rewrite this expression in standard complex form. Let's first evaluate cos(5π / 6). Remember that cos(x) = sin(π / 2 - x). Therefore,

cos(5π / 6) = sin(π / 2 - 5π / 6),

π / 2 - 5π / 6 = - π / 3,

sin(- π / 3) = - sin(π / 3)

And we also know that sin(π / 3) = √3 / 2. So - sin(π / 3) = - √3 / 2 = cos(5π / 6).

Now let's evaluate the sin(5π / 6). Similar to cos(x) = sin(π / 2 - x), sin(x) = cos(π / 2 - x). So, sin(5π / 6) = cos(- π / 3). Now let's further simplify from here,

cos(- π / 3) = cos(π / 3)

We know that cos(π / 3) = 1 / 2. So, sin(5π / 6) = 1 / 2

Through substitution we receive the expression 25( - √3 / 2 + i(1 / 2) ). Further simplification results in the following expression. As you can see your solution is option a.

[tex]-\frac{25\sqrt{3}}{2}+\frac{25}{2}i[/tex]

Answer:

The score is  [tex]x = 1884[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 1500[/tex]

     The standard deviation is  [tex]\sigma = 300[/tex]

From the question we are told that the score follow a normal distribution

i.e     [tex]X \~ \ N( 1500 , 300)[/tex]

The proportion of score in the top 10% is mathematically

           [tex]P(X > x ) = P( \frac{X - \mu}{\sigma } > \frac{x - \mu}{\sigma } ) = 0.10[/tex]

Where x is the minimum score required to be in the top 10%

Now the [tex]\frac{X - \mu}{\sigma } = Z (The \ Standardized \ value \ of \ X)[/tex]

  So

            [tex]P(X > x ) = P( Z > \frac{x - \mu}{\sigma } ) = 0.10[/tex]

So

            [tex]P(X > x ) = P( Z > \frac{x - 1500}{300} ) = 0.10[/tex]

So the critical value of  0.10  from the normal distribution table is  [tex]Z_{0.10} = 1.28[/tex]

So

               [tex]\frac{x - 1500}{300} = 1.28[/tex]

              [tex]x = 1884[/tex]

Answer:

3800 meters

Step-by-step explanation:

Answer:

The  90% confidence interval is  [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  64

     The sample  mean is  [tex]\= x = \$ 32, 000[/tex]

     The  standard deviation is  [tex]\sigma= \$ 8, 200[/tex]

Given that the confidence interval is  90% then the level of significance is mathematically evaluated as

             [tex]\alpha = 100 - 90[/tex]

             [tex]\alpha = 10 \%[/tex]

            [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table , the value is  

       [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

  Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{ \sqrt{n} }[/tex]

  =>   [tex]E = 1.645 * \frac{ 8200 }{ \sqrt{64} }[/tex]

  =>   [tex]E = 1686.13[/tex]

The 90% confidence interval is mathematically represented as

      [tex]\= x - E < \mu < \= x + E[/tex]

 =>    [tex]32000 - 1689.13 < \mu < 32000 + 1689.13[/tex]

=>    [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]

Answer: 2/7 of a gallon (in decimal it’s 0.286)

Step-by-step explanation: This one’s really easy.

2/7 of 1 gallon. Checking: so that if you multiply it by 7 it equals to 2

The gallon he used each hour he works is 2/7.

What is unit rate?

A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity.

The common examples used are:

Distance per second

Kilometer per hour

Meter per second

Earning per month

Given,

he used 2 gallons liquid for every 7 hours he works.

gallons used for per hour = 2/7

Hence, He used 2/7 gallons per hour.

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Answer:

(a) 1155.84

(b) 48.2%

(c) D

Step-by-step explanation:

The number of total responses is, N = 38,528.

(a)

It is provided that 3% answered with "a lot".

Compute the actual number of responses consisting of "a lot" as follows:

n (a lot) = N × P (a lot)

            = 38528 × 0.03

            = 1155.84

Thus, the actual number of responses consisting of "a lot" is 1155.84.

(b)

The number of responses consisting of "very little or none" is,

n (very little or none) = 18,566

Compute the percentage of responses consisted of "very little or none" as follows:

[tex]P(\text{very little or none})=\frac{n(\text{very little or none})}{N}[/tex]

                                  [tex]=\frac{18566}{38528}\\\\=0.481883\\\\\approx 0.482[/tex]

The percentage is: 0.482 × 100% = 48.2%.

Thus, the percentage of responses consisted of "very little or none" is 48.2%.

(c)

As the sample size increases the sample statistic value gets closer and closer to the actual population parameter value.

Thus, making the sample statistic an unbiased estimator of the population parameter.

And proving that the sample is a true representative of the population.

Thus, the correct option is (D).

Answer:

0.572

Step-by-step explanation:

From the question,

We have

n = 1090 of US adults

x = 623 selected from this population at random who consider the occupation to be one of great prestige

So we have that

The probability of X = x/n

= 623/1090

= 0.572

We conclude that 0.572 is the probability that a US adult selected at random thinks the occupation has great prestige.

Answer:

9 m

Step-by-step explanation:

Given that

Width of rectangular flower garden, w = 4 m

Perimeter of rectangular flower garden, p = 26 m

To find:

Length of Lisa's flower garden = ?

Solution:

First of all, let us understand perimeter, length and width of a rectangle.

Let ABCD be a rectangle. Please refer to the attached image.

Opposite sides of a rectangle are equal to each other.

AB = CD = Length  

Let the length be [tex]l[/tex] m.

BC = DA = Width = 4 m

Perimeter of a closed image is equal to the sum of all the sides of the image.

So, perimeter of ABCD:

[tex]p = AB + BC + CD + DA \\\Rightarrow \bold{ p = 2 \times (Length +Width)}[/tex]

[tex]26 = 2 \times (l +4)\\\Rightarrow 2l =26-8\\\Rightarrow \bold{l = 9 m}[/tex]

Answer:

[tex]\boxed{\sqrt{65}}[/tex]

Step-by-step explanation:

Magnitude is solved with the following equation: [tex]\sqrt{x^{2}+y^{2}}[/tex]

Therefore, just plug in your x and y-values and solve.

[tex]\sqrt{4^{2}+7{^{2}}[/tex]

[tex]\sqrt{16 + 49}[/tex]

[tex]\sqrt{65}[/tex]

Because [tex]\bold{\sqrt{65}}[/tex] cannot be simplified further, this is the magnitude of the vector.

Answer:

When all possible differences between pairs of population means are evaluated not with an F test, but with a series of regular t tests, the probability of at least one:

A. type I error is larger than the specified level of significance.

B. type II error is larger than the specified level of significance.

C. type I error is smaller than the specified level of significance.

D. type II error is smaller than the specified level of significance.

Answer :  Type I error is larger than the specified level of significance.( A )

Step-by-step explanation:

An F test is a test that is used to test whether the variances between pairs of populations are equal while a T test is a test used to check if a pair of population are equal not considering the fact that the variances of the population are different .

When a T test is used to evaluate all possible differences between pairs of population instead of F test there is a probability of atleast one type 1 error larger than the specified level of significance.

Answer:

The circumference is 50.24 in. and the area is 200.96 in².

Step-by-step explanation:

The circumference formula is C = 2πr where C = Circumference, π = pi and r = radius. We know that r = 8 and π = 3.14 and that we're solving for C, so we can substitute those values into the equation to get C = 2 * 3.14 * 8 = 50.24 in.

The area formula is A = πr² where A = Area, π = pi and r = radius. Again, we're solving for A and we know that r = 8 and π = 3.14 so A = 3.14 * 8² = 3.14 * 64 = 200.96 in².

Answer:

The circumference is 50.24 in. and the area is 200.96 in².

Step-by-step explanation:

MARK SNOG AS BRAINLIEST

Answer:

3 each

Step-by-step explanation:

The answer is already on this site

Answer:

0

Step-by-step explanation:

0 because there is a $100 duty free exemption.

answer:

For this problem, use the tables and charts shown in this section.  

A United States Citizen returning to the States declares the following items at the customs office:

3 shirts at $8.50 each

2 dresses at $27.50 each

1 pair of gold cuff links at $17.50 per pair

If he has not used his duty free exemption yet, how much duty should he pay?

$0.00 !

$5.00

$10.00

$300

Answer:

volume of  redwood tree is 6400 π ft^3(option 4)

Step-by-step explanation:

concept =

volume of cylinder = πr^2l

where r is the radius and l is the length of cylinder

circumference of cylinder = 2πr

_____________________________________

shape of  redwood tree can be taken as cylindrical

given

circumference of a redwood tree trunk is 16π ft

2πr = 16π

=> r = 16π/2π = 8

Thus, radius is 8 feet

Therefore volume of  redwood tree = πr^2l = π8^2*100 = π*64*100

volume of  redwood tree =6400 π ft^3

Answer:

6,400π ft3

Step-by-step explanation:

took test and got it right

Answer:15x^2-3x

Step-by-step explanation:

Answer:

x = -6,3,15,-12; y = 11,5,-3,15

Step-by-step explanation:

Domain is the x value, so plugged in the x values into the equation and got the y values or range.

Answer:

 x:  y:

-6  11

3       5

15 -3

-12    15

Answer:

see below (I hope this helps!)

Step-by-step explanation:

9) We know that the perimeters of the square and triangle are equal so to find x, we can write:

4(x - 5) = x + x + 12

4x - 20 = 2x + 12

2x = 32

x = 16

10) To find the perimeter, we can substitute x = 16 into 4(x - 5) which would be 4(16 - 5) = 4 * 11 = 44.

Answer:

  C.  70°

Step-by-step explanation:

The inscribed angle marked 15° intercepts an arc that is double that measure, so the intercepted arc on the right is 2×15° = 30°.

The external angle marked 20° is half the difference of the intercepted arcs, so is ...

  20° = (1/2)(x - 30°)

  40° = x - 30° . . . . . . multiply by 2

  70° = x . . . . . . . . . . . add 30°

The value of x is 70°.

Answer:

See below.

Step-by-step explanation:

1 gal = 4 qt

With a full gallon oil tank, you can fill 4 1-qt bottles.

The problem does not mention the number of quarts that go in a case, so there is not enough information to answer the question.

Also, is the full tank really only 1 gallon, or is there a number missing there too?

Answer:

(B) [tex]\sqrt{221}[/tex] yards

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem to find the length of x.

The Pythagorean Theorem states that [tex]a^2 + b^2 = c^2[/tex], where a and b are our legs and c is the hypotenuse.

We need to find c, and we already know a and b, so let's substitute.

[tex]10^2 + 11^2 = c^2\\\\100+121=c^2\\\\221=c^2\\\\c=\sqrt{221}[/tex]

Hope this helped!

Answer: [tex]\dfrac{x^2}{81}+\dfrac{y^2}{32}=1[/tex]

Step-by-step explanation:

The standard form of equation of ellipse with foci (±c,0) as:

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

, where major axis = 2a and minor axis = 2b

Given: Foci: (±7, 0); major axis of length 18

i.e. c= 7 and 2a =18 ⇒a= 9

Also,

[tex]c^2=a^2-b^2\Rightarrow\ b^2= a^2-c^2\\\\\Rightarrow\ b^2={9^2-7^2}={81-49}\\\\\Rightarrow\ b^2=32[/tex]

Put value of [tex]a^2[/tex] and [tex]b^2[/tex] , we get the required equation :

[tex]\dfrac{x^2}{81}+\dfrac{y^2}{32}=1[/tex]

Answer:

B. y = –2.9x + 13.5

Step-by-step explanation:

You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is

y = a + bx, where a is the y intercept and b is the slope.

To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.

x    y    xy    x²  

1  .  11 = 11 → x² = 1² = 1

2 .  8 = 16 → x² = 2² = 4

3 .  4 = 12 → x² = 3² = 9

4 .  1 = 4 → x² = 4² = 16

5 .  0 = 0 → x² = 5² = 25

Total x = 1 + 2 + 3 + 4 + 5 = 15

Total y = 11 + 8 + 4+ 1 + 0 = 24

Sum of xy = 11 + 16 + 12 + 4 + 0 = 43

Sum of x² =  1 + 4 + 9 + 16 + 25 = 55

n = 5

So b =  5 (43) - (15) . (24) / 5 (55) - 15² = -2.9

a =  y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5

Answer:

Below

Step-by-step explanation:

The quadratic equations form is:

● ax^2+bx+c

Using the zeroes, we can write a factored form.

● a (x-x') (x-x")

x and x' are the zeroes

■■■■■■■■■■■■■■■■■■■■■■■■■■

●y = a (x-x') (x-x")

x' and x" are khown but a is not.

We are given a point so replace x and y with its coordinates to find a.

So the steps are:

● 1) Write the factored form of the quadratic equation

● 2) replace x' and x" with their values.

● 3) replace x and y with the coordinates of a khwon point.

● 4) solve the equation for a.

The steps are write the factored form of the quadratic equation then, replace x' and x" with their values. To replace x and y with the coordinates of a known point. To solve the equation for a.

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Using the zeroes, we can write a factored form;

a (x-x') (x-x")

x and x' are the zeroes

y = a (x-x') (x-x")

x' and x" are known but a is not.

We are given a point so replace x and y with their coordinates to find a.

So the steps are:

1) Write the factored form of the quadratic equation

2) To replace x' and x" with their values.

3) To replace x and y with the coordinates of a known point.

4) To solve the equation for a.

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Answer:

155.00-65.50-23.25-26.45+165.30

Step-by-step explanation:

Answer:

155 + 165.3 - 65.5 - 23.25 - 26.45

Step-by-step explanation:

She had $155 dollars in the starting = +155

She withdrew $65.5 = -65.5

She withdrew another $23.25 = -23.25

She withdrew another $26.45 = -26.45

She deposited $165.3 = +165.3

The expression looks like:

155 + 165.3 - 65.5 - 23.25 - 26.45

We could solve the expression:

155 + 165.3 - 65.5 - 23.25 - 26.45

=> 320.3 - 88.75 - 26.45

=> 320.3 -115.2

=> 205.1

At the end of the week, she had a total of $205.10.

Answer:

8×8×8×8×8

= 8^5

because there are five 8 number

I hope this helps

if u have question let me know in comments ^_^

[tex]8\cdot8\cdot8\cdot8\cdot8=8^5[/tex]

Answer:

d

Step-by-step explanation:

(-7 + 3i) + (2-6i)

=-7 + 3i + 2 -6i

=(-7+2) + (3i -6i)

=-5 -3i

Answer:

(-7+3I)+(2-6I)

= -7+3i+2-6i

= -5-3I

so answer is d ie -5-3i

Answer:

16 x 16 = 256

Step-by-step explanation:

So 256 might be the answer? this is confusing but are you on IXL?

Answer:

Option D - Because the Z* was only a little bigger than the Zc, the test supports the null hypothesis and we conclude μ = 10

Step-by-step explanation:

In z-value problems, the normal practice is that If the calculated z-value is less than the critical z-value, we will reject the null hypothesis and accept the alternative hypothesis but if it's greater than the critical z-value, we will fail to reject the null hypothesis and say that the test was not statistically significant.

In this problem, the calculated z-value of -1.49 is greater than -1.645, so we will fail to reject the null hypothesis and say that the test was not statistically significant.

Thus, in this question, we fail to reject the null hypothesis because the calculated value of z was bigger the value of z_c.

Answer:

|b|= 4b+15

-b=4b+15

-b-4b= 15

-5b= 15

b= 15/-5

b= -3

the ans -3

If [tex]a<0[/tex] the [tex]|a|=-a[/tex]

So

[tex]|b|=4b+15\\-b=4b+15\\5b=-15\\b=-3[/tex]

Answer:

The standard deviation is  [tex]\sigma = 24.10[/tex]

Step-by-step explanation:

From the question we are told that

     The proportion of those that suffer from insomnia is  p  =  6%  =  0.06

      The  sample size is  n =  10300

Generally the proportion of those that do not suffer from  insomnia is mathematically represented as

               [tex]q = 1-p[/tex]

substituting values

               [tex]q = 1 -0.06[/tex]

               [tex]q = 0.94[/tex]

Generally the standard deviation is mathematically evaluated as

         [tex]\sigma = \sqrt{n * p * q }[/tex]

substituting values

         [tex]\sigma = \sqrt{ 10300 * 0.06 * 0.94 }[/tex]

        [tex]\sigma = 24.10[/tex]

Using the binomial probability concept, the standard deviation of the number of people who suffer from insomnia is 24.10

Recall :

Substituting the values into the equation :

[tex] standard \: deviation, σ = \sqrt{10300 \times \: 0.06 \: (1 - 0.06)} [/tex]

[tex] standard \: deviation, σ = \sqrt{10300 \times \: 0.06 \: 0.94} [/tex]

[tex] standard \: deviation, σ = \sqrt{580.92} = 24.10[/tex]

Hence, the standard deviation is 24.10.

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