(07.01, 07.02 LC) Factor the greatest common factor: −5k2 + 20k − 30.
−1(5k2 − 20k + 30)
−5(k2 − 4k + 6)
−5k(k2 − 4k + 6)
−5(k2 + 4k − 6)

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:

One triangle

Step-by-step explanation:

Since the sum of the shorter two sides is greater than the larger side.

Answer:

The question is an incomplete question

Answer:

minimum: 80 zeds

maximum: 137 zeds

Step-by-step explanation:

minimum price is where you choose all the cheapest options

lowest deck price is 40, lowest wheel set price is 14...

40+14+16+10

=40+30+10

=80

maximum price is where you choose all the most expensive options

highest deck is 65, highest price of wheels are 36, hardware 20

65+36+16+20

=65+72

=137

The value of the expression 4d ÷ c + 3 is 11.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression.

Given:

4d ÷ c + 3

Now, for d= 6 and c= 3

we have

4d ÷ c + 3

= 4(6) / 3 + 3

= 4(2) + 3

= 8+ 3

= 11

Hence, the value of the expression is 11.

Learn more about expression here:

https://brainly.com/question/14083225

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Answer:

it means it is less than one

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:

x=70

Step-by-step explanation:

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

8x+64=9x-6

x=70

Answer:

the area of the trapezoid is 32

Step-by-step explanation:

a (base)2

b (Base)6

h (height)8

Answer:

11/13

Step-by-step explanation:

4 out of the 26 marbles are blue, meaning that the rest of the 22 marbles are not blue. (26-4=22)

This means that out of the total 26, the chance of not picking a blue marble are 22/26=11/13

Answer:

3=4÷12

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

Answer:

(10-8) + n

Step-by-step explanation:

Good luck with your work!

Answer and Step-by-step explanation:

To subtract 8 from 10, it would look like this:

10 - 8.

Now, we add n to the result.

(10 - 8) + n

The question said not to simplify any part of this, so this is the expression.

(10 - 8) + n

#teamtrees #PAW (Plant And Water)

Answer:

Parameter of interest is the proportion of games won by a certain team.

H0 : p = 0.5

H1 : p ≠ 0.5

Step-by-step explanation:

Parameter refers to any statistical measure which is derived from the population data. Therefore, the parameter of interest in the scenario described above is the proportion of win or loss by a particular team. This could be either team A or team B.

Probability of either of either win or loss :

Proportion, p of win = 0.5

Null hypothesis ; H0 : p = 0.5

Alternative hypothesis ; H1 : p ≠ 0.5

Answer:

B

Step-by-step explanation:

Answer:

1) ASA

2) SAS

3) SAS

4) SAS

5) SSS

Answer:

A and D

Step-by-step explanation:

Unit circle is a circle described by the equation

x^2 + y^2 = 1

We can try each pair and check

A. [tex](\frac{6}{7})^2 + (\frac{\sqrt{13}}{7})^2 = \frac{36}{49} + \frac{13}{49} = \frac{49}{49} = 1[/tex]

B. [tex](\frac{4}{3})^2 + (\frac{4}{5})^2 > (\frac{4}{3})^2 > 1[/tex]

C. [tex](\frac{1}{3})^2 + (\frac{2}{3})^2 = \frac{1}{9} + \frac{4}{9} = \frac{5}{9} < 1[/tex]

D. [tex](\frac{5}{13})^2 + (\frac{12}{13})^2 = \frac{25}{169} + \frac{144}{169} = \frac{169}{169} = 1[/tex]

Answer:

480

Step-by-step explanation:

(16x10x8) divided by 2 = 480

Answer:

300%

Step-by-step explanation:

By increasing the down payment from 1,000 to 4,000, how does the total purchasing cost change?

If down payment is increased from 1000 to 4000

Icecrement = 4000-1000

Increment =3000

Percentage increase = 3000/1000×100

Percentage increase = 3000/10

Percentage increas=300%

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:

Kindly check explanation

Step-by-step explanation:

From the given information :

Linear model : y = - 0.04x + 29.83

Quadratic model : y = - 0.02x² + 0.16x + 29.35

Cubic model : y = 0.02x³ - 0.38x² + 2.11x + 26.88

Predicted y value for X = 1 ; X = 2

Linear model :

y = - 0.04(1) + 29.83 = 29.79

y = - 0.04(2) + 29.83 = 29.75

Quadratic model :

X = 1

y = - 0.02(1)^2 + 0.16(1) + 29.35 = 29.49

X = 2

y = - 0.02(2)^2 + 0.16(2) + 29.35 = 29.59

Cubic model :

X = 1

y = 0.02(1)^3 - 0.38(1)^2 + 2.11(1) + 26.88 = 28.63

X = 2

y = 0.02(2)^3 - 0.38(2)^3 + 2.11(2) + 26.88 = 28.22

Based on the R² value of the models given :

Linear ; R² = 0.001 ; R = sqrt(0.001) = 0.0316

Quadratic ; R² = 0.001 ; R = sqrt(0.001) = 0.0316

Cubic ; R² = 0.008 ; R = sqrt(0.008) = 0.089

Hence, the model which best fits the data is Cubic model.

Answer:

it 45

Step-by-step explanation:

u add 75 and 60 together which equals 135

then u subtract 135 from 180 and u get 45

Answer:

8 - 6 ÷ 2 + 3 × 5

8 - 3 + 15

5 + 15

20

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.

Answer:

3

Step-by-step explanation:

2×-3y = 12 ( multiply whit 4)

3x + 4y =1 (multiply whit 3 )

8x -12y =48

9X+ 12y = 3

if you add this equations

17X =51

X= 51 / 17

x=3

There's your answer buddy!

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:

x = 12 efg = 132

Step-by-step explanation:

Hi,

4x = 48

x = 12

Which means...

m < EFG is

4x

4 (12) = 48

m < EFG is 48 degrees

I hope this helps :)

Answer:

A. 3

Step-by-step explanation:

I just did it on a calculator and got it correct

Answer:

No lol that seems very confusing but was it 26.6?

Answer:  26.6

Step-by-step explanation:

7 times 1/5= 7/5

7/5 times 19= 26.6

I hope ti helps and may God bless you! have a nice day, bye!

Answer:

17/6 + 17/5

Step-by-step explanation: