A random sample of 9th-grade students was asked if they prefer taking notes on a computer or using a paper and pencil. Of the 180 students who were surveyed, 75 said they preferred using the computer. The resulting 99% confidence interval for the proportion of students who prefer taking notes on the computer was (0.322, 0.511). The school newspaper ran a story saying that less than half of the student body prefers taking notes on a computer. Based on the interval, is the newspaper justified in this statement?

Answer:

x = 5√2

y = 15

Step-by-step explanation:

By applying sine rule in the given right triangle,

sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{\sqrt{3} }{2}=\frac{y}{10\sqrt{2}}[/tex]

y = [tex]\frac{\sqrt{3} \times 10\sqrt{2} }{2}[/tex]

y = 15

Similarly, by applying cosine rule in the given triangle,

cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{2}=\frac{x}{10\sqrt{2}}[/tex]

x = 5√2

Answer:

9.71 ÷ 9.82 = .9987 or 1% .

The percentage increase is 1.1% to the nearest tenth

The calculation can be done as follows

Original price= $9.82

increase= $9.71

Change in price= 9.82-9.71

= 0.11

percent increase= 0.11/9.82 × 100

= 1.12

= 1.1 (to the nearest tenth)

Hence the percent increase is 1.1%

Please see the link below for more information

https://brainly.com/question/10613149?referrer=searchResults

Answer:

#1 - a mathematical relationship or rule expressed in symbols which help you solve something

#2 - variables, which represent an aspect of the problem

#3 P is perimeter, L is length, W is width, A is area

#4 Because in order to find the perimeter, you need to multiply the length and the width twice then add them.

Step-by-step explanation:

Domain:(−∞,∞),{x|x∈R}

Range:[2,∞),{y|y≥2}

The Domain is {1, 2, 3, 4} and the range is { 11, 18, 27, 38}

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x) make up this set. A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

Y=x^2+4x+6

As, we know that domain is the input value and range is the output value.

Then, x = 1

y = 1 + 4 +6

y= 11

and, x= 2

Y = 4 + 8 +6

Y = 18

and, x= 3

Y = 9 + 12 + 6

Y = 27

and, x = 4

Y = 16 + 16 + 6

Y = 38

Learn more about Domain and Range here:

https://brainly.com/question/28135761

#SPJ2

Answer:

$48 in savings

Step-by-step explanation:

1.

150-(150*32%)=102

150-102=48

2.

30% of 150 is 45

2% of 150 is 3

45 plus 3 is 48

Please brainliest! I did both methods and explained!

Answer:

the boxes are this

top left: 9

top right is 7

bottom right is 9

Step-by-step explanation:

Answer:

The minimum sample size required for the estimate is of 3820.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Variance is known to be 5.76

This means that [tex]\sigma = \sqrt{5.76} = 2.4[/tex]

What is the minimum sample size required for the estimate?

Maximum error of 0.1 means that we find n for which M = 0.1. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.1 = 2.575\frac{2.4}{\sqrt{n}}[/tex]

[tex]0.1\sqrt{n} = 2.575*2.4[/tex]

Multiplying both sides by 10

[tex]\sqrt{n} = 2.575*24[/tex]

[tex](\sqrt{n})^2 = (2.575*24)^2[/tex]

[tex]n = 3819.2[/tex]

Rounding up:

The minimum sample size required for the estimate is of 3820.

Answer:

log_7(6)

Step-by-step explanation:

log_7(2)+log_7(3)

log_7(2×3)

log_7(6)

Answer:

81a²b²

Step-by-step explanation:

(-9ab)² = (-9ab)(-9ab) = 81a²b²

Answer:

[tex]81a^{2} b^{2}[/tex]

Step-by-step explanation:

(-9ab)^2

(-9)^2×a^2b^2

Evaluate the power

81a^2b^2

81a^2b^2

hope it helps...

have a great day!!

Answer:

15

Step-by-step explanation:

Answer:

The answer is

Step-by-step explanation:

Mean 7

Median  6

Mode 3

Range 12

Answer:

x = 3

Step-by-step explanation:

Move all terms containing x to the left

5x + 2 = 17

Move all terms not containing x to the right

5x = 15

Divide each term by 5 and simplify

x = 3

Answer: 4 Units

Step-by-step explanation:

Answer:

Step-by-step explanation:

The mean for brand A is higher than the mean for brand B

The mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.

It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.

We have:

For brand A:

The number of hours per lightbulb:

1000, 4200, 1400, 1500, 1800, 2000

Mean for brand A:

[tex]\rm Mean(A) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}[/tex]

[tex]\rm Mean(A)= \frac{1000+4200+1400+1500+1800+ 2000}{6}[/tex]

[tex]\rm Mean(A)= \frac{11900}{6}\\\\\rm Mean(A) = 1983.33[/tex]

For Brand B:

The number of hours per lightbulb:

1200, 1400, 1600, 1800, 2000

Mean for brand B:

[tex]\rm Mean(B) = \frac{Sum \ of \ all \ data \ values}{Number \ of \ data \ in \ the\ set}[/tex]

[tex]\rm Mean(B)= \frac{1200 +1400 +1600 +1800 +2000}{6}[/tex]

[tex]\rm Mean(B)= \frac{8000}{5}\\\\\rm Mean(B) = 1600[/tex]

We can see that:

Mean(A) > Mean(B)

Thus, the mean for brand A is higher than the mean for brand B because the mean for A is 1983.33 and the mean for B is 1600 statement (C) is correct.

Learn more about the mean here:

https://brainly.com/question/22871228

Answer:

log 81 = 1.90849

Step-by-step explanation:

log 81 = log 9^2 = 2 log 9 = 2(0.95424) = 1.90849

Using the limit definition of the derivative, you have

[tex]\displaystyle f'(-5) = \lim_{x\to-5} \frac{f(x) - f(-5)}{x - (-5)} = \lim_{x\to-5} \frac{(2x^2+4x+7) - 37}{x + 5}[/tex]

Simplify the numerator:

(2x ² + 4x + 7) - 37 = 2x ² + 4x - 30

… = 2 (x ² + 2x - 15)

… = 2 (x + 5) (x - 3)

Then

[tex]\displaystyle f'(-5) = \lim_{x\to-5}\frac{2(x+5)(x-3)}{x+5} = \lim_{x\to-5} 2(x-3) = \boxed{-16}[/tex]

• • •

For your second question in the comments, if f(x) = -2x ² + 3x - 7, then by the definition of the derivative, you have

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0}\frac{(-2(x+h)^2+3(x+h)-7) - (-2x^2 + 3x - 7)}h[/tex]

Simplify the numerator:

(-2 (x + h)² + 3 (x + h) - 7) - (-2x ² + 3x - 7)

… = (-2x ² - 4xh - 2h ² + 3x + 3h - 7) - (-2x ² + 3x - 7)

… = -4xh - 2h ² + 3h

Now compute the limit:

[tex]\displaystyle f'(x) = \lim_{h\to0}\frac{-4xh-2h^2+3h}h = \lim_{h\to0}(-4x-2h+3) = \boxed{-4x+3}[/tex]

Answer

Assalam waliakum

Answer:

Step-by-step explanation:

If I add Gary's money

9+ 6 = 15

Emily have to begin with, $ 24

15 + 9 = 24

Fred have to begin with $ 21

15 + 6 =21

Answer:

7

Step-by-step explanation:

2+2+3

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The tank can not keep 30 tropical fish in it.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Since there needs to be an average of 2 gallons of water for each fish and there are a total of 30 tropical fish. Therefore, the amount of water needed for a total of 30 fish to flourish is,

Amount of water needed = 30 fish × 2 gallons = 60 gallons

Since One gallon is equal to 19.2152 cups. Therefore, the amount of water needed for the fish to flourish is,

60 gallons = 60 × 19.2152 cups = 1152.912 cups

Since the tank has a capacity of 976 cups only, the tank is not big enough to keep 30 fish.

Hence, the tank can not keep 30 tropical fish in it.

Learn more about Multiplication:

https://brainly.com/question/14059007

#SPJ1

Answer:

It takes 7.37 hours for the size of the sample to double.

Step-by-step explanation:

Continuous exponential growth model:

The continuous exponential growth model for populations is given by:

[tex]P(t) = P(0)e^{rt}[/tex]

In which P(0) is the initial population and r is the growth rate parameter, as a decimal.

Growth rate parameter of 9.4% per hour.

This means that [tex]r = 0.094[/tex]

So

[tex]P(t) = P(0)e^{rt}[/tex]

[tex]P(t) = P(0)e^{0.094t}[/tex]

How many hours does it take for the size of the sample to double?

This is t for which P(t) = 2P(0). So

[tex]P(t) = P(0)e^{0.094t}[/tex]

[tex]2P(0) = P(0)e^{0.094t}[/tex]

[tex]e^{0.094t} = 2[/tex]

[tex]\ln{e^{0.094t}} = \ln{2}[/tex]

[tex]0.094t = \ln{2}[/tex]

[tex]t = \frac{\ln{2}}{0.094}[/tex]

[tex]t = 7.37[/tex]

It takes 7.37 hours for the size of the sample to double.

Answer:

500000mm

Step-by-step explanation:

First to have to convert the meters into millimeters (25mm×1000mm=25000mm) than you have to times the answer by 20 (25000mm×20mm=500000mm) and your answer is 500000mm

Answer:

The owner will have to pay $ 125 after 2 hours.

Step-by-step explanation:

Given that the line graph shows the amount of water loss in a leaking tank during 7 hours, and the owner pays $ 1 for every 8 liters of water lost, to determine how much will he have to pay after 2 hours the following calculation must be performed :

((6000 - 5000) / 8) x 1 = X

(1000/8) x 1 = X

125 x 1 = X

125 = X

Therefore, the owner will have to pay $ 125 after 2 hours.

Answer: 31,672 mi2

Step-by-step explanation:

The area of the state of Nevada can be estimated using a trapezoid

Answer:

n=6

Step-by-step explanation:

[tex]\frac{1}{2} n=3[/tex]

Multiply both sides by 2

2*1/2n=3*2

Simplify;

n=6

Answer: n=6

Step-by-step explanation:

6*1/2=3 so this is y n=6.

Answer:

I hope this ans helps you

Answer:

1.330391 ; 1.734064 ; 1.713872 ; 1.670649 ;

Step-by-step explanation:

a) t0.10, 18

α = 0.10 ; df = 18

From table, critical value = 1.330

(b) t0.05, 18

α = 0.05 ; df = 18

From table, critical value = 1.734

(c) t0.05, 23

α = 0.05 ; df = 23

From table, critical value = 1.714

(d) t0.05, 60

α = 0.05 ; df = 60

From table, critical value = 1.671

(e) t0.005, 60

α = 0.05 ; df = 60

From table, critical value = 2.660