The speeds of vehicles traveling on a highway are normally distributed with an unknown population mean and standard deviation. A random sample of 13 vehicles is taken and results in a sample mean of 55 miles per hour and a sample standard deviation of 7 miles per hour. find the margin of error for a 95% confidence interval estimate for the population mean using the Student's t-distribution

14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.

What is the Central Limit Theorem (CLT)?

According to the CLT, the distribution of sample means from a population with mean μ and standard deviation σ, will be approximately normal with mean μ and standard deviation σ/√n, where n is the sample size.

In this case, the population mean is 589 grams and the population standard deviation is 16 grams. We are picking a sample of 23 fruits at random, so the standard deviation of the sample means will be:

σ/√n = 16/√23 ≈ 3.33

To find the value of x such that 14% of the time the sample mean will be greater than x, we need to find the z-score that corresponds to the 86th percentile of the standard normal distribution. We can use a table or a calculator to find that z-score:

z = invNorm(0.86) ≈ 1.08

The sample mean is normally distributed with a mean of 589 grams and a standard deviation of 3.33 grams. Using the formula for z-score:

z = (x - μ) / (σ / √n)

We can solve for x:

x = z × (σ / √n) + μ

x = 1.08 × (16 / √23) + 589

x ≈ 594.33 grams

Therefore, 14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.

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Answer:

[tex]\sf{x = 2}[/tex]

Step-by-step explanation:

Question type: solving equations with variables on both sides.

[tex]\textsf{This is a question with variables on both sides, to solve this we need to get the variable x }[/tex]

[tex]\textsf{alone. (getting the x on one side)}[/tex]

--------------------------------------------------------------

[tex]\sf{-2x~+~4~=~2x~-~4[/tex]

Subtract 4 from both sides.

[tex]\sf{-2x~=~2x~-8[/tex]

Subtract 2x from both sides.

[tex]\sf{-4x~=~-8}[/tex]

Divide both sides by -4.

[tex]\bf{x~=~2[/tex]

Therefore, x would be 2.

[tex]-jurii[/tex]

Answer:

x=2

Step-by-step explanation:

The numeric value of the function at x = 4 is given as follows:

f(4) = 0.

The expression for the numeric value of the function in this problem is given as follows:

f(4).

This means that the input is given as follows:

x = 4.

Passing a vertical line through x = 4 the value of y in which the vertical line crosses the graph is given as follows:

y = 0.

Hence the numeric value is given as follows:

f(4) = 0.

The graph is given by the image presented at the end of the answer.

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Using percentage, the correct answer is "The value of P is $3,500 and it corresponds to 70% of her salary".

The denominator of a percentage, also known as a ratio or a fraction, is always 100. For instance, Sam would have received 30 points out of a possible 100 if he had received a 30% on his maths test. In ratio form, it is expressed as 30:100, and in fraction form, as 30/100. Here, "percent" or "percentage" is used to translate the percentage symbol "%." The percent symbol can always be changed to a fraction or decimal equivalent by using the phrase "divided by 100".

First, we need to calculate L.

1/3 or 33.33% of L spend on gift.

2/5 or 40% of L spent on savings.

This would leave her with $200 for miscellaneous expenses:

= 100% - (33.33% + 40%)

= 100% - 73.33%

= 26.67%

So, 26.67% = $200 for miscellaneous expenses

Rule of three, to calculate L.

26.67% is $200.

100% will be:

= (100 X 200) ÷ 26.67

= 20000 ÷ 26.67

= $750

L= $750

Now we going to calculate K.

"K is twice the amount of L".

K = L X 2

K = 750 X 2

K= $1,500

Finally, we going to calculate P.

P = J - K

J = $5,000

K = $1,500

P =$5,000 - $1500

= $3,500

Rule of three

5000 is 100%

3500 will be:

= 3500 x 100 ÷ 5000

= 350000 ÷ 5000

P = 70%

The value of P is $3,500 and it corresponds to 70% of her salary.

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this is the total cost for the round trip, the answer is (C) 583.20.

what is round trip ?

A round trip refers to a journey from a starting point to a destination and then back to the starting point. In other words, it involves traveling to a place and then returning to the original location.

In the given question,

To calculate the cost of gasoline for the round trip, we need to first find the total amount of gasoline they will use. We can calculate this by dividing the distance of the trip by the RV's average gas mileage:

Total gasoline used = distance ÷ gas mileage

Total gasoline used = 1,701 miles ÷ 10.5 miles per gallon

Total gasoline used = 162 gallons (rounded to the nearest whole number)

Now, we can find the total cost of gasoline by multiplying the total amount of gasoline used by the average cost of a gallon of gasoline:

Total cost of gasoline = total gasoline used × cost per gallon

Total cost of gasoline = 162 gallons × 3.60 per gallon

Total cost of gasoline = 583.20

Since this is the total cost for the round trip, the answer is (C) 583.20.

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Answer:

To compare the texting rates of Student A and Student B, we need to calculate their respective rates of change.

For Student A, we can use the formula for the slope of a line:

slope = (change in y) / (change in x)

In this case, the "y" variable represents the number of texts sent, and the "x" variable represents the number of tests sent. Looking at the table, we can see that Student A sent 10.5 texts after sending 1 test, and 10 texts after sending 2 tests. So the change in y is -0.5 (10.5 - 10), and the change in x is 1. Therefore:

slope = (-0.5) / 1 = -0.5

So Student A's texting rate is -0.5 texts per test.

For Student B, we can look at the graph and find the slope of the line connecting any two points. Let's choose the points (2, 15) and (5, 23) because they are easy to read off the graph. The change in y is 8 (23 - 15), and the change in x is 3 (5 - 2). Therefore:

slope = 8 / 3 = 2.67

So Student B's texting rate is 2.67 texts per minute.

To find the difference in their texting rates, we simply subtract:

difference = Student B's rate - Student A's rate

difference = 2.67 - (-0.5) = 3.17

So the difference in their texting rates is 3.17 texts per test.

Step-by-step explanation:

The cost of capital for the second option, issuing new preferred stock, is 0.00356, or 0.356%. This means that for every dollar of capital raised through issuing preferred stock, the company will need to pay 0.356 cents in annual interest or dividend payments.

To calculate the cost of capital for the second option, we need to first calculate the cost of the preferred stock. The cost of preferred stock is the dividend yield, or the annual dividend divided by the market price of the stock. In this case, the annual dividend is $5.00 and the market price is $56,000.

Cost of preferred stock = Annual dividend / Market price of stock

Cost of preferred stock = $5.00 / $56,000

Cost of preferred stock = 0.000089

To calculate the cost of capital, we need to weight the cost of preferred stock with the proportion of capital that is financed by preferred stock. Let's assume that the preferred stock will finance 40% of the total capital.

Cost of capital = Cost of preferred stock * Proportion of capital financed by preferred stock

Cost of capital = 0.000089 * 0.40

Cost of capital = 0.0000356

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All the values are,

Compound interest = $1280.2

Future value = $1280.2 + $x

Given that;

P = $865

r = 4%

T = 10 years

Formula is,

Compound Interest = P(1 + r)^t

Where, Principal = P, Interest rate = r, Number of compounds = n, Interest time = t

Plug, p = 865, r = 0.04, t = 10

Compound Interest = 865 (1 + 0.04)¹⁰

Compound Interest = 865 (1.04)¹⁰

Compound Interest = 865 x 1.48

Compound Interest = 1280.2

Hence, We get;

Future value = Compound Interest + Principal

Future value = $1280.2 + $x

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Answer: 5.26

Step-by-step explanation:

458,930/87,178 =
5.264 =
5.26

Answer:

Answer is B. 3x^2 +2x - 2.5

Step-by-step explanation:

Just factor out and simplify.

[tex]\frac{0.25x^2*(3x^2+2x-2.5)}{0.25x^2}[/tex]

x cannot be 0 or else the denominator is 0 making the function undefined.

Answer:

it is B

Step-by-step explanation:

If each person drove at a constant rate, the person who drove the fastest (in miles per hour) is: C. Nathan.

In Mathematics and Science, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;

In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

For Hank, we have:

Speed = 176/3.2 = 55 miles per hour.

For Laura, we have:

Speed = 150/2.5 = 60 miles per hour.

For Nathan, we have:

Speed = 112.5/2.25 = 50 miles per hour (Fastest).

For Raquel, we have:

Speed = 286/4.4 = 65 miles per hour.

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The length of the hypotenuse is 28.3

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.

If a and b are the legs of the triangle and c is the other side(hypotenuse) then,

c² = a²+b²

c² = 19² +21²

c² = 361+441

c² = 802

c = √802

c = 28.3

therefore , if the two legs are 19 and 21, the length of the other side is 28.3

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The length of the hypotenuse is 28.3

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.

If a and b are the legs of the triangle and c is the other side(hypotenuse) then,

c² = a²+b²

c² = 19² +21²

c² = 361+441

c² = 802

c = √802

c = 28.3

therefore , if the two legs are 19 and 21, the length of the other side is 28.3

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The distance of P at north of Q is 34.98 km.

The distance of P at east of Q is 19.39 km.

The distance of P at the given directions is calculated by resolving the vector into vertical and horizontal components.

The distance of P at north of Q is calculated as follows;

Py = d sinθ

Py = 40 km x sin (61)

Py = 34.98 km

The distance of P at east of Q is calculated as follows;

Px = d cosθ

Px = 40 km x cos (61)

Px = 19.39 km

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Answer: x=22

Step-by-step explanation:

see image for explanation

Answer:

Step-by-step explanation:

To calculate the stock price, you can multiply the earnings per share (EPS) by the benchmark PE ratio.

The stock price would be:

$3.64 x 21 = $76.44

So you would pay $76.44 per share for the stock of The Dahlia Flower Company.

Answer:

155000 milliliters of water

Step-by-step explanation:

We Know

The platoon drank 155 liters of water.

How many milliliters did the platoon drink?

1 liter = 1000 milliliters

155 liters = 155 x 1000 = 155000 milliliters of water

So, the platoon drank 155000 milliliters of water.

The platoon drank 155,000 milliliters of water.

1 liter = 1000 milliliters

Therefore, 155 liters = 155,000 milliliters

So, the platoon drank 155,000 milliliters of water.

Answer:

a. The linear model that represents the height of the plant after d days can be expressed as:

h(d) = 1.5d + 5

where h(d) is the height of the plant in centimeters after d days, and 1.5d represents the growth rate of 1.5 cm per day multiplied by the number of days (d). The constant term 5 represents the initial height of the plant, which is 5 cm.

b. To find the height of the plant after 20 days, we can substitute d = 20 into the linear model:

h(20) = 1.5(20) + 5

= 30 + 5

= 35

So, the height of the plant after 20 days will be 35 cm.

The six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

To find 6 rational numbers between 3 and 4, we can start by finding the difference between 4 and 3, which is 1.

We can then divide this difference by any number and add it to 3

So that the number will be less than 4 but greater than 3

Now, we can add this gap size successively to 3, starting with the first rational number after 3, to find the six rational numbers between 3 and 4:

3.1, 3.2, 3.3, 3.4, 3.5, 3.6

So, the six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

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Answer:

We can solve this equation by using substitution. We substitute each value of x in the given set and check which one makes the equation true.

Let’s start with A. 8(x - 20) = 304 becomes 8(49 - 20) = 304 which simplifies to 8(29) = 304 which is not true.

Let’s try B. 8(x - 20) = 304 becomes 8(none of these - 20) = 304 which simplifies to 8(-20) = 304 which is not true.

Let’s try C. 8(x - 20) = 304 becomes 8(29 - 20) = 304 which simplifies to 8(9) = 304 which is not true.

Finally, let’s try D. 8(x - 20) = 304 becomes 8(21 - 20) = 304 which simplifies to 8(1) = 304 which is not true.

Therefore, none of these values of x make the equation true

Step-by-step explanation:

The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

In mathematics, an inequality is a statement that compares two values, often using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequality graphs show the region of the coordinate plane that satisfies an inequality. The graph of inequality can be determined in a similar way to the graph of an equation, but with some additional steps.

Here we have

The inequality |2x + 2| > 6

To graph the solution to the inequality |2x + 2| > 6,

we can start by rewriting the inequality as two separate inequalities without the absolute value:

2x + 2 > 6 or 2x + 2 < -6

Simplifying these inequalities, we get:

2x > 4 or 2x < -8

x > 2 or x < -4

Therefore,

The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

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The standard form equation of the ellipse as described in the task content is;

It is evident from the task content that the standard form equation of the ellipse is to be determined.

Recall, the equation of an ellipse takes the form;

(x - h)²/a² + (y - k)²/b² = 1

where (h, k) is the center and a represents the distance of the center to each vertex on the x-axis and b represents the distance from the center to each vertex on the y-axis.

Therefore, for the given scenario where center is at the origin; the equation of the ellipse is;

x²/2² + y²/5² = 1

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The polynomial function of lowest degree with rational coefficients P(x) = x⁴ + 20x² - 125

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

To find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. √5,5i​.

Since √5 and 5i​ are zeros, then their conjugates -√5, and -5i​ are also zeros.

So,

So, the factors of the polynomial are

So, multiplying the factors together, we get the polynomial.

So, P(x) = (x  - √5)(x - 5i)(x + √5)(x + 5i)

= (x  - √5)(x  + √5)(x - 5i)(x + 5i)

= [x² - (√5)²][x² - (5i)²]

= [x² - 5][x² - (5²i²)]

= [x² - 5][x² - 25(-1))]

= [x² - 5][x² + 25]

Expanding the brackets, we have

= [x² - 5][x² + 25]

= [x² × x² + 25x² - 5x² + 25 × (-5)]

= x⁴ + 20x² - 125

So, P(x) = x⁴ + 20x² - 125

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The nearest kilometers to 999.09344471 km is 1000 km.

Given value is 999.09344471 Km.

We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.

Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only  the value after the decimal (934) is to be rounded off which is (900).

So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.

Again rounding off 999.900 km to nearest km so it becomes 1000 km.

The nearest kilometers to 999.09344471 km is 1000 km.

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3√4x/5

the / slash before the 5 is over so you put the 3√4x at the top of the fraction and the 5 at the bottom, so it would be 3√4x divide 5

Answer:

a) 1/6

b) 1/2

c) 1/2

d) 1

e) 1/6

Step-by-step explanation:

a)Getting a six

=1/6

b)Gettingan even number =3/6=1/2

c)number greater than 3

=3/6=1/2

d)number greater than 0

=6/6=1

e)number greater than 4 and an odd number

=1/6

The height of the Zeta Tower as a percentage of the height of the Delta tower is the 94.72%

Here we know that:

The epsilon tower is 23% taller than the delta one, then the height is:

H = 55m*(1 + 0.23) = 67.65 m

And we know that the Zeta tower is 23 short than the epsilon one, then the height of this twoer is.

H' = 67.65m*(1 - 0.23) = 52.0905 m

The height of the delta tower is 55m, this is our 100%.

Then the height of the zeta tower written as a percentage will be:

(52.0905 m/55m)*100% = 94.72%

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Answer:

Step-by-step explanation:

The approximate solution(s) to the given functions are x= -4/3, 3/2.

The given functions are f(x)=6x² and g(x)=x+12.

Set the functions equal to each other, then solve for the variable.

f(x)=g(x)

6x² = x+12

6x²-x-12=0

By splitting middle term we get

6x²-9x+8x-12=0

3x(2x-3)+4(2x-3)=0

(2x-3)(3x+4)=0

2x-3=0 and 3x+4=0

x= -4/3, 3/2

Therefore, the approximate solution(s) to the given functions are x= -4/3, 3/2.

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Answer: you pay 18$

Step-by-step explanation:96 ounce×1pound/16ounce×3$/1pound=18$

The amount the cashier charged is incorrect. Based on the given information, the amount of fruit purchased is 96 ounces, which is equivalent to 6 pounds. Therefore, the total cost of the fruit should be 6 pounds x $3 per pound = $18.

The error the cashier made was converting ounces to pounds incorrectly. 96 ounces is equivalent to 6 pounds, not 1,536 pounds. The cashier multiplied 96 by 16 (the number of ounces in a pound) instead of dividing by 16 to get the number of pounds.

Answer:

16

Step-by-step explanation:

starting from month 2, how many more months will A be as tall as B?

A grows at 1.75 in per month

B grows at 1.5in per month

so 7.5+1.75x = 11+1.5x

solve for x

x=14

so from month 2, need to go for another 14 mos.

so at month 16, they'll be same height