Design an expression that can be used to find the surface area of tower n cubes tall

Answer:

[tex] (759-658) -1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 74.54[/tex]

[tex] (759-658) +1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 127.46[/tex]

And the confidence interval for the difference of the two means is given by (74.54, 127.46)

Step-by-step explanation:

Information given:

[tex]\bar X_1 = 759[/tex] the sample mean for construction workers

[tex] s_1 =73[/tex] the sample standard deviation for construction workers

[tex]n_1 =30[/tex] sample size of construction workers

[tex]\bar X_2 = 658[/tex] the sample mean for manufacturing workers

[tex] s_2 =65[/tex] the sample standard deviation for manufacturing workers

[tex]n_2 =28[/tex] sample size of construction workers

Confidence interval

The confidence interval for the difference of means are given by:

[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]

We need to find the degrees of freedom given by:

[tex] df = n_1 +n_2 -2= 30+28-2=56[/tex]

The confidence is 0.85 and the significance level would be [tex]1-0.85=0.15[/tex] and [tex]\alpha/2 = 0.075[/tex]. We need to find a critical value in the t distribution who accumulates 0.075 of the area on each tail and we got:

[tex] t_{\alpha/2}= \pm 1.46[/tex]

And then we can replace and we got:

[tex] (759-658) -1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 74.54[/tex]

[tex] (759-658) +1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 127.46[/tex]

And the confidence interval for the difference of the two means is given by (74.54, 127.46)

Part (a): The 80% confidence interval for the earnings difference is $77.51 to $124.49.

Part (b): The interval suggests 80% confidence in the true earnings difference falling within $77.51 to $124.49.

Part (c): Since zero isn't in the interval, there's a significant pay difference between construction and manufacturing workers.

Part (a): Construct an 80% confidence interval for the difference between the mean weekly earnings

Step 1: Identify the given data

- Construction workers:

 - Mean [tex](\(\bar{X_1}\)) = \$759[/tex]

 - Standard deviation [tex](\(s_1\)) = \$73[/tex]

 - Sample size [tex](\(n_1\))[/tex] = 30

- Manufacturing workers:

 - Mean [tex](\(\bar{X_2}\)) = \$658[/tex]

 - Standard deviation [tex](\(s_2\)) = \$65[/tex]

 - Sample size [tex](\(n_2\)) = 28[/tex]

Step 2: Determine the formula for the confidence interval

We use the formula for the confidence interval of the difference between two independent means:

[tex]\[ (\bar{X_1} - \bar{X_2}) \pm t_{\alpha/2} \cdot \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]

Step 3: Calculate the standard error (SE) of the difference

[tex]\[ SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]

[tex]\[ SE = \sqrt{\frac{73^2}{30} + \frac{65^2}{28}} \][/tex]

[tex]\[ SE = \sqrt{\frac{5329}{30} + \frac{4225}{28}} \][/tex]

[tex]\[ SE = \sqrt{177.63 + 150.89} \][/tex]

[tex]\[ SE = \sqrt{328.52} \approx 18.12 \][/tex]

Step 4: Determine the degrees of freedom (df) using the Welch-Satterthwaite equation

[tex]\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1-1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2-1}} \][/tex]

[tex]\[ df \approx \frac{328.52^2}{\frac{(177.63)^2}{29} + \frac{(150.89)^2}{27}} \][/tex]

[tex]\[ df \approx \frac{107,922.4}{1090.15 + 843.48} \][/tex]

[tex]\[ df \approx \frac{107,922.4}{1933.63} \approx 55.83 \approx 56 \][/tex]

Step 5: Find the t-value for an 80% confidence interval

For df ≈ 56 and [tex]\(\alpha/2 = 0.10\),[/tex] the t-value [tex](\(t_{0.10}\))[/tex] is approximately 1.296.

Step 6: Construct the confidence interval

[tex]\[ (\bar{X_1} - \bar{X_2}) \pm t_{\alpha/2} \cdot SE \][/tex]

[tex]\[ (759 - 658) \pm 1.296 \cdot 18.12 \][/tex]

[tex]\[ 101 \pm 23.49 \][/tex]

[tex]\[ (77.51, 124.49) \][/tex]

So, the 80% confidence interval for the difference between the mean weekly earnings is [tex]\((77.51, 124.49)\).[/tex]

Part (b): Explanation of the Confidence Interval

The 80% confidence interval [tex]\((77.51, 124.49)\)[/tex] means that we are 80% confident that the true difference between the mean weekly earnings of construction workers and manufacturing workers lies between [tex]\$77.51[/tex] and [tex]\$124.49[/tex]. In other words, if we were to take many samples and compute the confidence interval for each, about 80% of those intervals would contain the true difference in mean earnings.

Part (c): Is there a significant difference in pay?

To determine if there is a significant difference in pay, we look at whether the confidence interval includes zero. Since the 80% confidence interval for the difference in mean earnings (\(77.51, 124.49\)) does not include zero, we can conclude that there is a statistically significant difference in pay between construction workers and manufacturing workers at the 80% confidence level.

Complete Question:

Answer:

S = 85cm^2

Step-by-step explanation:

The surface area of a square pyramid is given by the following formula:

[tex]S=2hb+b^2[/tex]

where it has taken into account the sum of the area of a square and four triangles:

[tex]4(\frac{hb}{2})+b*b=2bh+b^2[/tex]

h: slant height = 6cm

b: base = 5cm

By replacing in the formula you obtain:

[tex]S=2(5cm)(6cm)+(5cm)^2=85cm^2[/tex]

hence, the surface area is 85cm^2

Answer:

Step-by-step explanation:

Answer:

[tex]x = p( m - n)[/tex]

Step-by-step explanation:

[tex]m = n + \frac{x}{p} \\ m - n = \frac{x}{p} \\ p(m - n) = \frac{x}{p} \times p \\ \\ x = p(m - n)[/tex]

Answer:

The median of this set is 45.

Step-by-step explanation:

Answer:

See Below

Step-by-step explanation:

The equation estimating the number of cellphones in the country is:

[tex]f(x)=114.8 e^{0.125x}[/tex]

Where x = 0 corresponds to year 2000

thus,

x = 1 is year 2001

x = 2 is year 2002

x = 3 is year 2003

and so on...

We want approx. number of cellphones in the country in 2003. This corresponds to x = 3. So substituting in the equation we get:

[tex]f(x)=114.8 e^{0.125x}\\f(3)=114.8 e^{0.125(3)}\\f(3)= 167.03[/tex]

So, approximately there were 167.03 million cellphones in the country in 2003

Answer:

Work done by george = 35.28J

Step-by-step explanation:

We are given;

Mass; m = 2 kg

Height;h = 1.8 m

Now, we want to find how much work does George do on a 2-kg package at the height of 1.8m.

This is a potential energy problem.

The formula for work done is therefore;

W = mgh

Where;

m is mass

g is acceleration due to gravity which has a constant value of 9.8 m/s²

h is height

Thus, plugging in relevant values;

W = 2 x 9.8 x 1.8

W = 35.28 J

Final answer:

The work done by George on the 2-kg package when he lifts it to a height of 1.8 meters is calculated using the equation W = mgh, which results in 35.28 joules.

Explanation:

The question How much work does George do on a 2-kg package when he lifts it to a height of 1.8 m? requires the calculation of the work done against the force of gravity. To find the work done, the equation W = mgh is used, where W is the work done in joules, m is the mass in kilograms, g is the acceleration due to gravity (9.8 m/s2), and h is the height in meters.

To solve for the work done in this case: W = (2 kg)(9.8 m/s2)(1.8 m).

When you calculate this, it gives you the work done by George as W = 35.28 J (joules).

Answer:

89 units

Step-by-step explanation:

-The population's mean point estimate is equivalent to the sample mean.

Given the 5 month units sold is 94,80,85,94 and 92

-Mean is the average of the units sold over the 5 month period:

[tex]\bar X=\frac{\sum {x_i}}{n}\\\\=\frac{94+80+85+84+92}{5}\\\\=89[/tex]

Hence, the point estimate for the population mean is 89 units

Okay, to find the answer,

All we need to do it multiply !

[tex]\frac{f}{-3.2}[/tex] = 0.01

f = (0.01) × (-3.2)

f = -.032

I hope I helped :) Just comment if you have any questions and remember to vote me "brainliest" if you like my answer !!!

You would use the POINT SLOPE FORMULA and the Slope Formula

which is as follows ...

slope formula : [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

point slope formula:  [tex]y - y_{1} = m(x - x_{1} )[/tex]

Answer:

d

Step-by-step explanation:

The function y = tan(x) + 2 is shown in the provided graph option fourth is correct.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The missing figure is in the picture please refer to the picture.

As we have a trigonometric function.

In the picture, the graph of a tanx is shown but 2 units up.

Thus, the function y = tan(x) + 2 is shown in the provided graph option fourth is correct.

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Answer:

2931 + 51.4n/7 degrees where n is the number of animal from the lion to the zebra in the clockwise direction.

Step-by-step explanation:

We don't have details on the positions of the lion and the zebra prior to revolution but suppose the zebra is n animal away from the lion where n could be in the range of 0 to 6 in the clockwise direction. If n = 0, the zebra is next to the lion in line, and if n = 6, the zebra is right behind the lion.

In angular term, since all 8 animals are evenly spaced, there are 7 space in between them, each of them would span an angle of 360/7 degrees

Then the angular distance between the zebra and the lion is (n+1)360/7 degrees

If the carousel makes between 8 and 9 revolutions then the total angular distance is 8*360 + (n+1)360/7 = 2931 + 51.4n/7 degrees

Answer:

-2970, -3320

Step-by-step explanation:

The carousel makes between 8 and 9 clockwise revolutions

the position of the lion rotated to that of the zebra is two steps

now,

1 revolution = 360 degrees accomplished in 8 steps

1 step = 360/8 = 45 deg

=> position of  lion rotated to zebra = 2 × 45 = 90 deg

if 1 revolution = 360 accomplished in 9 steps

then

1 step = 360/9 = 40 deg

=> position of  lion rotated to zebra = 2 × 40 = 80 deg

since the rotation is in clockwise direction, a negative sign is required

FOR 8 Revolutions

in total the carousel rotates

-[8(360) + 90] degrees

= -2970 degrees

FOR 9 revolution

in total the carousel rotates

-[9(360) + 80] degrees

= -3320 degrees

Answer:

Probability that the next car passing will be travelling more than 66 miles per hour is 0.10565.

Step-by-step explanation:

We are given that the the speeds are normally distributed with a population mean of 61 miles per hour and a population standard deviation of 4 miles per hour.

Let X = speed of car

The z-score probability distribution for normal distribution is given by;

           Z = [tex]\frac{ X-\mu}{\sigma}} }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean speed = 61 miles per hour

            [tex]\sigma[/tex] = standard deviation = 4 miles per hour

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, Probability that the next car passing will be travelling more than 66 miles per hour is given by = P(X > 66 miles per hour)

        P(X > 66) = P( [tex]\frac{ X-\mu}{\sigma}} }[/tex] > [tex]\frac{ 66-61}{4}} }[/tex] ) = P(Z > 1.25) = 1 - P(Z [tex]\leq[/tex] 1.25)

                                                     = 1 - 0.89435 = 0.10565                       

So, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.25 in the z table which has an area of 0.89435.

Hence, the probability that the next car passing will be travelling more than 66 miles per hour is 0.10565.

Final answer:

The probability that the next car passing will be traveling more than 66 miles per hour, given a mean speed of 61 mph and standard deviation of 4 mph, is approximately 10.56%.

Explanation:

To calculate the probability that the next car passing will be traveling more than 66 miles per hour, given the speeds are normally distributed with a mean of 61 miles per hour and a standard deviation of 4 miles per hour, we use the Z-score formula.

The Z-score formula is: Z = (X - μ) / σ, where μ is the mean, σ is the standard deviation, and X is the value we're interested in.

Substitute the given values into the formula to find the Z-score for 66 miles per hour.

Z = (66 - 61) / 4 = 5 / 4 = 1.25.

Next, we look up the Z-score of 1.25 on the standard normal distribution table or use a calculator to find the area to the left of Z. The area to the left of Z=1.25 is approximately 0.8944. To find the probability of a car traveling more than 66 miles per hour, we subtract this value from 1.

Probability = 1 - 0.8944 = 0.1056.

Therefore, the probability that the next car passing will be traveling more than 66 miles per hour is approximately 10.56%.

Answer:

$1.9

Step-by-step explanation:

2 pound bag (when he bought) =.30×2=$0.6

when he sells, price is $2.50.

Profit for each bag= $2.5-$0.6=$1.9

Answer:

2 g/cm^3

Step-by-step explanation:

D=m/V

=20g/10cm^3

=2g/cm^3

Density calculation based on mass and volume of an object is  2 g/cm³.

The density of an object is calculated by dividing its mass by its volume. In this case, with a mass of 20 g and volume of 10 cm³, the density can be calculated as:

Density = Mass / Volume = 20 g / 10 cm³ = 2 g/cm³

Answer:

D

Step-by-step explanation:

All of the other functions are functions that are just multiplicative. When we substitute any x for A, B,or C, y/x will be the same. In D y/x will vary.

Answer:

Step-by-step explanation:

A nonlinear function with at least one term raised to the power of two is known as a quadratic function

FOR :

A non-linear system of equations is a set of equations where one or more terms have a variable of power two or higher .

In Algebra, linear functions are polynomials with highest exponent equal to 1 or of the form y = c where c is constant. Non-linear functions are all other rest functions with exponent atleast 2.

Hence A nonlinear function with at least one term raised to the power of two is known as a quadratic function

Answer:

42%

Step-by-step explanation:

Answer:

Since the events are independent, 30% of his customers have neither a foreign car nor a dog.

Step-by-step explanation:

Let the total number of his customers = 100.

Since the events are independent,

customers with foreign cars + customers that own dogs + customers that have neither a foreign car nor a dog = 100.

But,

Customers with foreign cars = 30% = 30

Customers that own dogs = 40% = 40

Customers with neither foreign car nor dog  = x%

So that,

     30 + 40 + x = 100

       70 + x = 100

      x = 100 - 70

      x = 30

Customers with neither foreign car nor dog  = 30.

Converting this value to percentage,

             =  [tex]\frac{30}{100}[/tex] × 100                      

             = 30%.

Therefore, 30% of his customers have neither a foreign car nor a dog.

Answer:

I like it when im high marks a lil by and he say he fly but he dono ha ta fly OoOoooOoOoOOoO

Step-by-step explanation:

Answer:

Event is not unusual(p>0.05).

Step-by-step explanation:

Given that :

[tex]p=0.10\\\\n=1100\\\\x=121[/tex]

#The sample proportion is calculated as:

[tex]\hat p=\frac{x}{n}\\\\=\frac{121}{1100}\\\\=0.1100[/tex]

#Mathematically, the z-value is the value decreased by the mean then divided  the standard deviation :

[tex]z=\frac{\hat p- p}{\sqrt{\frac{p(1-p)}{n}}}\\\\\\\\=\frac{0.11-0.10}{\sqrt{\frac{0.10(1-0.10)}{1100}}}\\\\\\=1.1055[/tex]

#We use the normal probability table to determine the corresponding probability;

[tex]P(X\geq 121)=P(Z>1.1055)\\\\=0.1314[/tex]

Hence, the probaility is more than 0.05, thus the event not unusual  and thus  this is not necessarily evidence that the proportion of Americans who are afraid to fly has increased.

The theoretical probability of rolling a 6 on a standard number cube is 1/6 or approximately 0.1667.

The theoretical probability of rolling a 6 on a standard number cube is 1/6 or approximately 0.1667.

To find the probability, we divide the number of successful outcomes (rolling a 6) by the total number of possible outcomes (numbers 1 to 6), which is 6.

So the probability is 1/6 or 0.1667.

Since a standard number cube has equal chances of landing on any number from 1 to 6, each outcome has the same probability of occurring, which is 1/6.

Thus, the theoretical probability of the event when rolling a standard number cube is found to be  1/6 or approximately 0.1667.

Final answer:

The theoretical probability of rolling a six on a standard six-sided die is 1 in 6, or P(6) = 1/6.

Explanation:

The student has asked about finding the theoretical probability of rolling a six, P(6), with a standard six-sided die. In a fair six-sided die, the outcomes are equally likely, meaning the probabilities for each number 1 through 6 are the same. Given that there are six possible outcomes, the probability of rolling any one specific number, for example 6, is 1 out of the 6 total possible outcomes. Therefore, P(6) = 1/6. This probability reflects that, theoretically, if we were to roll the die many times, we'd expect to roll a 6 in approximately one-sixth of all the rolls.

x=10

Step-by-step explanation:

7x - 5=65

+5 +5 so the 5's cancel so add 5 to 65

7x =70 because you add 5 to 65 to get 70

7x 7

7 x cancels out so you answer will be

x=10

Answer:

Step-by-step explanation:

7 x -5  = 65

7 times what? (x) - 5 equals 65

Well we know that x has to be less than 65 and more than 7 and -5.

So 7 must be multiplied by numbers 8, and up.

7 * 8 -5  = 51, NOT 65.

7 * 9 -5  = 58, NOT 65.

7 * 10 -5  = Does equal 65.

Therefore, x is equivalent to 10.

Answer:

d

Step-by-step explanation:

Answer:

you are not aloud to cheat on tests please don't do that sorry can't answer to a cheater

Step-by-step explanation:

Answer:

the answer is B,C,F

Step-by-step explanation:

The correct options are,
1. Add 3.4 to both sides of the equation.
2. 12.7 + 3.4 = 16.1, so j = 16.1.
3. Substitute 16.1 for j to check the solution.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

The steps to solve the equation: 12.7 = j - 3.4 are as follows,

Add 3.4 to both sides of the equation,

12.7 + 3.4 = j

Solve for j,

16.1 = j

So the solution is j = 16.1

To check the solution, you would substitute 16.1 for j in the original equation and see if both sides are equal.

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7.  tails, odd, 4

P(tails) = 1/2

P(odd) = 3/6 = 1/2

P(4) = 1/6

P(tails then odd then 4) = (1/2)×(1/2)×(1/6) = 1/24 ≈ 0.041666

Answer: 1/24, 4.2%

8.  tails, 6 or 1, 3

P(6 or 1) = 2/6 = 1/3

P(3) = 1/6

P( tails, 6 or 1, 3) = (1/2)(1/3)(1/6) = 1/36 ≈ 0.027777

Answer: 1/36, 2.8%

9.  heads, not 2, even

P(heads) = 1/2

P(not 2) = 5/6

P(even) = 1/2

P(heads, not 2, even) = (1/2)(5/6)(1/2) = 5/24 ≈ 0.208333

Answer: 5/24, 20.8%

Answer:

7. 1/24  = 4.2%

8. 1/36  = 2.8%

9. 1/6 = 16.67%

All percentages are rounded

Answer:

In my opinion I think the answer is C.12/33

Step-by-step explanation:

this would be the answer because...

1. First, add up the amount of boys and girls

21 girls+ 12 boys= 33 total

2. Next, since its asking for the probability for a boys name to de drawn at random, your going to divide 12 by 33

Answer:

it is c i took test good luck

Step-by-step explanation:

sike i lied your a is mine lol

Answer:

The first one is matched with 700,000

The second one is matched with 7

The third one is matched with 70

The fourth one is matched with 70,000

Step-by-step explanation:

Look at where the 7 is in the number, and replace all the digits to the right of it with 0's. Get rid of the digits to the left of the 7, if any

Answer:

1-->1

2-->3

3-->2

4-->4

Step-by-step explanation:

In the first number the 7 is in the the hundred thousands place. In the second the 7 is in the ones place. In the third the 7 is in the tens place. In the fourth the 7 is in the ten thousands place.