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Answer:

D) -4 (with imaginary roots ±2i)

Step-by-step explanation:

Since you cannot take the square root of a negative number to produce a real result, the only option that has two imaginary roots is D) -4, where the two imaginary roots are 2i and -2i.

Answer:

a) The mean is 18 and the standard deviation is 1.79.

b) The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

c) 0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 18 and a standard deviation of 8.

This means that [tex]\mu = 18, \sigma = 8[/tex]

Sample of 20:

This means that [tex]n = 20, s = \frac{8}{\sqrt{20}} = 1.79[/tex]

(a) Calculate the mean and standard deviation of the sampling distribution of x¯.

By the Central Limit Theorem, the mean is 18 and the standard deviation is 1.79.

(b) Interpret the standard deviation from part (a).

The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.

(c) Find the probability that a sample of 20 students has a mean score of 19.5 or more.

This is 1 subtracted by the pvalue of Z when X = 19.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{19.5 - 18}{1.79}[/tex]

[tex]Z = 0.84[/tex]

[tex]Z = 0.84[/tex] has a pvalue of 0.7995

1 - 0.7995 = 0.2005

0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.

Answer:

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

Step-by-step explanation:

For each runner, there are only two possible outcomes. Either they finished the marathon, or they did not. The probability of a runner completing the marathon is independent of any other runner. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

97.4% finished:

This means that 100 - 97.4 = 2.6% = 0.026 did not finish, which means that [tex]p = 0.026[/tex]

100 runners are chosen at random

This means that [tex]n = 100[/tex]

Find the probability that at least 5 of them did not finish the marathon

This is:

[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]

In which

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{100,0}.(0.026)^{0}.(0.974)^{100} = 0.0718[/tex]

[tex]P(X = 1) = C_{100,1}.(0.026)^{1}.(0.974)^{99} = 0.1916[/tex]

[tex]P(X = 2) = C_{100,2}.(0.026)^{2}.(0.974)^{98} = 0.2531[/tex]

[tex]P(X = 3) = C_{100,3}.(0.026)^{3}.(0.974)^{97} = 0.2207[/tex]

[tex]P(X = 4) = C_{100,4}.(0.026)^{4}.(0.974)^{96} = 0.1429[/tex]

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0718 + 0.1916 + 0.2531 + 0.2207 + 0.1429 = 0.8801[/tex]

[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.8801 = 0.1199[/tex]

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

Answer:

The answer would be B  [tex]120ft^{3}[/tex]

Step-by-step explanation:

volume of triangular prism is 30 and volume of the cube is 90 :)

Answer:

480

Step-by-step explanation:

(16x10x8) divided by 2 = 480

Answer:

Step-by-step explanation:

Base perimeter: 5 x 2 x π = 10π

LA = 10π x 2 = 20π

Base area : 5^2π = 25π

SA = 25π x 2 + 20π = 70π

V : 25π x 2 = 50π

Step-by-step explanation:

perimeter of the given figure=24cm+24cm+30cm+20cm+20cm+20cm+5cm+5cm

=148cm

Answer:

148mm aka 1.48cm aka 1cm48mm

Step-by-step explanation:

to obtain the small thing between the"24mm" and"20mm":

(30mm-20mm)÷2

=5mm

so add up all those given information:

24mm+24mm+20mm+20mm+20mm+30mm+5mm+5mm

comment below if you still don't get it ;)

Answer:

3=4÷12

3groups with 4 members (teachers)and we cannot make groups with 5 members

Answer:

40

Step-by-step explanation:

24^2+32^2=c^2

square root of 1600 is 40

Answer:40

Step-by-step explanation:Because

a^2 + b^2=c^2

Answer:

A. 3

Step-by-step explanation:

I just did it on a calculator and got it correct

9514 1404 393

Answer:

  (b)  x +2y = 8

Step-by-step explanation:

The only offered line that includes the given point is ...

  x +2y = 8

__

We can check the other choices:

  x + 2y = 2 +2(3) = 2+6 = 8 . . . matches B (not A)

  2x +y = 2(2) +3 = 4+3 = 7 . . . . not a choice

_____

Getting there from scratch

The standard form equation for a line can be written from ...

  (y2 -y1)x -(x2 -x1)y = constant

  (-4 -0)x -(4 -(-4))y = constant . . . . using the given points (-4, 0) and (4, -4)

  -4x -8y = constant

For standard form, we need the leading coefficient to be positive, and we need common factors removed. We can get there by dividing by -4.

  x +2y = constant

The value of the constant will be whatever it takes for the given point to lie on the line. For (x, y) = (2, 3) to be a solution, we must have ...

 x +2y = (2) +2(3) = constant = 8

The desired line has the equation ...

  x +2y = 8

Answer:

B on edge

Step-by-step explanation:

Answer:

Option (4)

Step-by-step explanation:

From the table attached,

Ratio of spores in day 2 and day 1 = [tex]\frac{400}{200}[/tex]

                                                         = 2

Ratio of spores in day 3 and day 2 = [tex]\frac{800}{400}[/tex]

                                                          = 2

There is a common ratio of 2 in each successive to the previous term of the Mold spores.

Therefore, spores are growing exponentially.

Let the function representing exponential function is,

y = a(b)ˣ

Here, y = Number of spores after time 'x'

x = Number of days

a and b are the constants.

On day 1,

x = 1

y = 200

By substituting these values in the exponential function,

200 = a(b)¹

ab = 200 -------(1)

On day 2,

x = 2

y = 400

400 = a(b)² -------(2)

Divide equation 2 by equation 1,

[tex]\frac{400}{200}=\frac{ab^{2} }{ab}[/tex]

b = 2

By substituting the value of b in equation (1),

a(2) = 200

a = 100

Therefore, equation of the function will be,

y = 100(2)ˣ

Option (4) will be the answer.

Answer:

30

Step-by-step explanation:

This problem can be done without the Distance Formula (which is a way to find the distance between any two points in the plane).

The attached image shows the points and segments joining them.

PQ = 5 because the points are on the same horizontal line, and you can count spaces between them (or subtract x-coordinates: 4 - (-1) = 5).

PR = 12 because the points are on the same vertical line; count spaces or subtract y-coordinates, 7 - (-5) = 12.

The triangle is a right triangle, so the Pythagorean Theorem can be used to find the length of the hypotenuse.

[tex](\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2[/tex]

[tex](QR)^2=5^2+12^2=25+144=169\\QR=\sqrt{169}=13[/tex]

The perimeter of the triangle is 5 + 12 + 13 = 30

Answer:

40 feet

Step-by-step explanation:

long sides are 16

short sides are 4

Perimeter is l + l + w + w

so 16 + 16 + 4 + 4

= 40

The perimeter of the given rectangle is 40 feet.

The perimeter of a rectangle is defined as the sum of all the four sides of the rectangle.

The perimeter of a rectangle = 2( l + b)

It is given that rectangle is 4 times as long as it is wide. If the area is 64 square feet,

The area is 64 square feet = l x w

So,

The long sides are 16

The short sides are 4

Perimeter = 2 (l + w)

Perimeter = 2( 16  + 4)

Perimeter = 40

Learn more about the area;

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Answer:

1/5

Step-by-step explanation:

I hope this helps you

Answer:

1/5

Step-by-step explanation:

each X is divided by 5 to get the Y

Answer:

180

Step-by-step explanation:

Answer:

[tex]Height=\boxed{10\sqrt{2}} [/tex]

[tex] Area =\boxed{165\sqrt{2}} [/tex]

Step-by-step explanation:

By geometric mean theorem:

[tex] AC=\sqrt{25\times 8}[/tex]

[tex] AC=\sqrt{5^2 \times 2^2 \times 2}[/tex]

[tex] AC=5\times 2\sqrt{2}[/tex]

[tex] AC=10\sqrt{2}[/tex]

So,

[tex]Height=\boxed{10\sqrt{2}} [/tex]

[tex] Area = \frac{1}{2} \times base\times height [/tex]

[tex] \therefore Area = \frac{1}{2} \times (25+8)\times 10\sqrt{2} [/tex]

[tex] \therefore Area =33\times 5\sqrt{2} [/tex]

[tex] Area =\boxed{165\sqrt{2}} [/tex]

Answer:

No solution

Step-by-step explanation:

1. Distribute the right side.

8w+5=8w+4

2. This has no solution.

Answer:

divide by avagadro number to get the amount of moles in the atoms you have

Answer:

B

Step-by-step explanation:

Answer:

The smallest sample size that will produce an interval with these specifications is 601.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

He would like you to report a 95% confidence interval with a margin of error no more than 0.04. What is the smallest sample size that will produce an interval with these specifications?

We have to find n for which M = 0.04.

We dont know the true proportion, so we use [tex]\pi = 0.5[/tex], which is when the smallest sample size needed will have it's largest value.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2[/tex]

[tex]n = 600.25[/tex]

Rounding up

The smallest sample size that will produce an interval with these specifications is 601.

9514 1404 393

Answer:

  x = 30

Step-by-step explanation:

The sum of exterior angles of a convex polygon is 360°. Here, that means ...

  3x° +x° +2x° +2x° +4x° = 360°

  12x = 360

  x = 360/12 = 30

The value of x is 30.

Answer:

Sum of all angles = 360⁰

[tex] \to \sf \: 2x + 2x + x + 4x + 3x = 360[/tex]

[tex] \to \: 12x = 360[/tex]

[tex] \to \: x = \dfrac{360}{12} [/tex]

[tex] \sf \: x = 30[/tex]

The calculated measure of the arc DEF is 204 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

The measure of the arc intercepted by the angle DEF is calculated as

Arc DF = 2 * DEF

When the given values are substituted in the above equation, we have the following equation

Arc DF = 2 * 78

So, we have

Arc DF = 156

The measure of arc DEF is then calculated as

Arc DEF = 360 - 156

Evaluate

Arc DEF = 204

Hence, the measure of the arc DEF is 204 degrees

Read more about angles at

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Answer:

Both are equal

Step-by-step explanation:

[tex]2^4 = 16 \\ \\ {4}^{2} = 16 \\ \\ \implies \: {2}^{4} = {4}^{2} [/tex]

Answer:

Step-by-step explanation:

2^4=16 and 4^2=16

They both equal the same thing so im guessing neither. They are both the same value.

Hope this helped!

PLS let me know if i'm wrong so i can correct my mistake!!

Answer:B

Step-by-step explanation:

Answer:

x=70

Step-by-step explanation:

(x+8)*8=(3x-2)*3

8x+64=9x-6

x=70

Answer:

I wanna say 1/3 because there 3 even numbers on a dice

Step-by-step explanation:

Answer:

70 in

Step-by-step explanation:

7 * 7 = 49 {that's the square}

(7 * 6) * 1/2 = 21 {that's the triangle}

49 + 21 = 70

Answer:

the square SxS= 7x7 = 49

the triangle is hxs÷2=(7×6 )÷2 =42 ÷2 = 21

Answer:

13.4±2.132(1.02/5)

Step-by-step explanation:

Khan Academy

The confidence interval for the mean life time is; CI = 13.4 ± 3.678(1.02/5)

Formula for confidence interval is;

CI = x' ± z(s/√n)

We are given;

Mean; x' = 13.4

Standard deviation; s = 1.02

Sample size; n = 5

z-score at confidence level of 90% = 1.645

Thus;

CI = 13.4 ± 1.645(1.02/√5)

CI = 13.4 ± 3.678(1.02/5)

Read more about Confidence Interval at; https://brainly.com/question/17097944