Scores on an exam follow an approximately Normal distribution with a mean of 76.4 and a standard deviation of 6.1 points. What is the minimum score you would need to be in the top 4%?
A.87.08 B.86.08 C.64.72 D.65.72

Answer:

20

Step-by-step explanation:

If 50% of machines are washing machines and there are 10, then add 10 again to get 100% of the total machines

A two-sample t-test is a statistical test used to determine if there is a significant difference between the means of two independent groups or populations.

In research and experimental investigations, the two-sample t-test is frequently used to assess if there is a statistically significant difference between the mean values of two samples or groups.

The average test results of two separate student groups, for instance, may be compared by a researcher to see if one group performs noticeably better than the other.

The two-sample t-test makes the assumption that the two samples are independent, have nearly normal distributions, and have identical variances.

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The width he need to make the pasture with the given rectangle is 4x³y⁶.

Area of a rectangle is the product of its length and width.

If a rectangle has length L units and width of W units, then

Area = L × W squared units.

We are given that;

Area= 20x6y5

Length= 5x³y4

We can start by using the formula for the area of a rectangle:

Area = length x width

We know that the area of the rectangular pasture is 20x6y5, and we know the length is 5x³y4. So we can plug in these values and solve for the width:

20x6y5 = (5x³y4) x width

To solve for width, we can divide both sides by 5x³y4:

width = 20x6y5 / (5x³y4)

Simplifying the expression on the right-hand side, we can divide each term in the numerator by 5x³y4:

width = (4x³y¹) x (4y5)

Simplifying further, we can add the exponents of the common factor y:

width = 4x³y⁶

Therefore, the farmer would need to make the width of the rectangular pasture will be 4x³y⁶.

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The common ratio of the geometric sequence -10, 20, -40 is -2.A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed number called the common ratio.

To find the common ratio of the sequence -10, 20, -40, we can divide each term by the previous term.

The second term divided by the first term gives:

20 / (-10) = -2

The third term divided by the second term gives:

(-40) / 20 = -2

We can see that the quotient is the same in both cases, which means that the common ratio of the sequence is -2.

This tells us that to find the next term in the sequence, we multiply the previous term by -2. For example, to find the fourth term, we would multiply -40 by -2 to get 80, which would be the next term in the sequence.

In summary, the common ratio of the geometric sequence -10, 20, -40 is -2.

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The required, fourth term of the geometric sequence is 64.

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
We can use the formula for the nth term of a geometric sequence to solve the problem. The nth term of a geometric sequence with first term a and common ratio r is given by:

[tex]an = ar^(n-1)[/tex]

In this case, the first term is 14 and the common ratio is 2. So the nth term is:

[tex]an = 14*2^{n-1}\\[/tex]

So

[tex]14(2^{n-1}) = 64\\2^{n-1} = 64/14 = 32/7[/tex]

To solve for n, we can take the logarithm of both sides of the equation. We can use any base for the logarithm, but it's usually convenient to use base 2 since the equation involves powers of 2. So

[tex]log_2(2^{n-1}) = log_2(32/7)\\(n-1) = log_2(32/7)\\n = log_2(32/7) + 1[/tex]

Using a calculator, we can approximate log_2(32/7) as 2.665. So:

n = 2.665 + 1

n ≈ 3.665

Since n must be a whole number (we're looking for a specific term of the sequence), we can round up to the nearest integer to get:

n = 4

Therefore, the fourth term of the sequence is 64.

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An ellipse's form is determined by two locations inside the ellipse known as its foci.

The lengths of the main and minor axes of an ellipse may be used to calculate its foci.

The foci of an ellipse may be calculated using a variety of online calculators.

These calculators normally ask the user to enter the main and minor ellipse axes' lengths before calculating the foci's coordinates. Depending on the calculator in question, some may additionally ask for more details like the ellipse's eccentricity or center of rotation.

Understanding an ellipse's shape and characteristics requires knowing its foci since they are what characterize an ellipse.

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Answer:

Step-by-step explanation:

The strength of a linear relationship between two variables is typically measured by the correlation coefficient (r) or the coefficient of determination (r^2). A value of r or r^2 closer to 1 indicates a stronger positive linear relationship, whereas a value closer to -1 indicates a stronger negative linear relationship. A value of r or r^2 closer to 0 indicates a weaker or no linear relationship.

Looking at the given regression equations and their correlation coefficients, the regression with the weakest linear relationship between x and y is Regression 3:

Regression 1: y = -5.8x - 6.5, r = -0.7621

Regression 2: y = 2.4x - 14.7, r = 0.809

Regression 3: y = -7.4x - 17.4, r = -0.233

Regression 4: y = -3.4x - 8.5, r = -0.6121

Regression 3 has the lowest absolute value of r (0.233), indicating the weakest or no linear relationship between x and y. Therefore, Regression 3 represents the weakest linear relationship between x and y among the given options.

Answer:

The polygon has 13 sides.

Step-by-step explanation:

The sum of the interior angles of a polygon is (n - 2) * 180, where n is the number of sides. This formula can be set equal to the sum of the interior angles to determine how many sides it has.

(n - 2) * 180 = 1980

180n - 360 = 1980

180n = 2340

n = 13

Answer:

18.00 cm

Step-by-step explanation:

This composite heart shape consists of two semi-circles and a rectangle.

[tex]r_{ssc}[/tex] = radius of small semi-circle

     = [tex]\frac{3 cm}{2}[/tex] = 1.5 cm

[tex]r_{bsc}[/tex] = radius of big semi-circle

     = [tex]\frac{4 cm}{2}[/tex] = 2 cm

Perimeter of this composite shape

= Perimeter of big semi-circle + Perimeter of small semi-circle + 2 outer sides of the rectangle

= [tex](\frac{2}{2} \pi r_{bsc} + \frac{2}{2} \pi r_{ssc} + 3 + 4)[/tex] cm

= [tex](\pi r_{bsc} + \pi r_{ssc} + 3 + 4)[/tex] cm

= [tex][\pi (2) + \pi (1.5) + 3 + 4][/tex] cm

= [tex](2\pi + 1.5\pi + 7)[/tex] cm

= [tex](3.5\pi + 7)[/tex] cm

= 17.995 cm

= 18.00 cm (Rounded to two decimal places)

Answer:

{-4, 2, 6, 9}

Step-by-step explanation:

I took the quiz lol

Answer:

20%

Step-by-step explanation:

10 of 50 can be written as:1050To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 1001050 × 100100= (10 × 10050) × 1100 = 20100 Therefore, the answer is 20%

Answer:

aabc

Step-by-step explanation:

200 mph is approximately equal to 321.86 km per hour ( rounded to two decimal places )

The conversion factor to convert mph to km per hour is 1.6093

1 mph = 1.6093 km per hour

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The speed in km per hour = The speed in mph × conversion factor

Substitute the values in the equation

1 mph = 1.6093 km per hour

200 mph = 1.6093 × 200

Multiply the numbers

= 321.86 km per hour  ( rounded to two decimal places )

Therefore, 200 mph is 321.86 km

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The value 0.9375 as a fraction is 15/16 .

In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.

Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations

to convert in fraction we will muliply and devide by 100.

0.9375*100/100 = 15/16

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The value of volume 750 ml after converting to cups is 3.17 cups.

The conversion is useful when you need to measure liquids in cups instead of milliliters, especially if you are following a recipe that is written in cups instead of milliliters.

To convert 750ml to cups, you need to know that one cup is equal to 236.6ml. Knowing how to make the conversion can help you get the right measurements and produce accurate results in your cooking or baking. To do the conversion, divide 750 by 236.6 to get the answer in cups.

So, 750ml / 236.6ml per cup = 3.17 cups (rounded to the nearest hundredth).

Therefore, volume of 750ml is equivalent to 3.17 cups.

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hese two equations can be used to solve for the values of c and m.

Let's define:

c = the number of commercials on which Nakeisha's songs were played

m = the number of movies on which Nakeisha's songs were played

Based on the problem statement, we can set up the following system of equations:

Nakeisha's songs were played on 2 more commercials than movies:

c = m + 2

Nakeisha's total earnings on the royalties from all commercials and movies was $760:

30c + 110m = 760

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The number of students who travel to school by bus will be equal to 651. Hence, option "a" is correct.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

here, we have,

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the information given in the question,

Total students in the school = 1860

Percentage of students who come by bike or walk = 45%

So,

(1860 × 45)/100 = 837

Number of students who drive to school = 372

So, the number of students traveling by school bus will be,

1860 - (837 + 372).

= 1860 - 1209

= 651

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The correct inequality is the one in option A.

2x – 3 > 7 + 8

Here we know that:

"Three less than twice a number (x) is greater than the sum of seven and eight."

The first part:

"Three less than twice a number (x)"

Is written as:

2x - 3

The last part "... is greater than the sum of seven and eight."

Would be:

2x - 3 > 7 + 8

So that is the correct inequality, then the correct option is A.

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The conversion of 2000 pound sterling to dollars is 2,740 US dollars.

The conversion of 2000 pounds sterling to dollars depends on the current exchange rate between the two currencies.

The exchange rate was approximately 1.37 US dollars per 1 British pound.

Using this exchange rate, we can convert 2000 pounds sterling to US dollars as follows:

2000 pounds * 1.37 dollars/pound = 2,740 US dollars

Therefore, 2000 pounds sterling is equivalent to approximately 2,740 US dollars using the exchange rate mentioned above. However, please note that exchange rates can fluctuate over time, so the exact conversion may be different depending on the current exchange rate.

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Correct Question :

What is the conversion of 2000 pound sterling to dollars ?

Answer:The width of the rectangle is 1 unit

Step-by-step explanation:Let the length of the rectangle be x

let the breadth be x-5

Since ,area of rectangle=length*breadth

           area = x*(x-5)

           6=x^2-5x

           x^2-5x-6=0

solving the above equation,

x^2-(6x-x)-6=0

x^2-6x+x-6=0

x(x-6)+1(x-6)=0

(x-6)(x+1)=0

x=6 and x=-1

since the breadth cannot have negative value

Hence ,the breadth of rectangle is 1 unit

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The correct answer is option C. f(x) = x(x - 1)(x - 2)(x + 1)(x + 2)

Explanation:

To determine the correct answer, we need to look at the zeros of the given functions and compare them to the zeros shown on the graph. The zeros of a function are the values of x that make the function equal to zero. These are also the points where the graph of the function crosses the x-axis.

Option A: f(t) = (x - 1)(x - 2)(x + 1)(x + 2)
The zeros of this function are x = 1, x = 2, x = -1, and x = -2.

Option B: f(x) = x(x - 1)(x + 1)
The zeros of this function are x = 0, x = 1, and x = -1.

Option C: f(x) = x(x - 1)(x - 2)(x + 1)(x + 2)
The zeros of this function are x = 0, x = 1, x = 2, x = -1, and x = -2.

Option D: f(r) = x(x - 1)(x - 2)
The zeros of this function are x = 0, x = 1, and x = 2.

Comparing the zeros of these functions to the zeros shown on the graph, we can see that option C is the correct answer. The graph shows zeros at x = 0, x = 1, x = 2, x = -1, and x = -2, which are the same zeros as the function f(x) = x(x - 1)(x - 2)(x + 1)(x + 2).

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Answer:

Octagon.

Octa comes from the Greek word "okto", which means eight.

After converting 72 inches into inches, we will get it as: 72 inches equal to 6 feet.

Length conversion is the process of converting length measurements between different units.

The metric system uses length units like kilometres (km), metres (m), centimetres (cm), and so on.

As we know,

1 Foot equal to 12.000005 Inches.

But actually, we can consider it as:

The 12 inches is equal to 1 foot.

We have to convert the 72 inches into feet,

So, We will simply divide the value of given inches by 12

Thus, we will get it as:

72 inches = (72/12) feet = 6 feet

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The complete question may be:

What is the conversion of 72 inches into feet?

10 feet to meters can be find out by simply dividing the 10 feet by 3.081 so the  value will be 3.048 meters.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

One foot is equal to 0.3048 metres, or 3048/10000 metres. So, you multiply 10 by either 0.3048 or 3048/10000 to convert 10 feet to metres.

For the decimal answer, we use 0.3048, and for the fractional answer, we use 3048/10000. The math, formulas, and conversions from 10 feet to metres are shown below.

0.3048 metres divided by feet

10 feet = 3.048 metres, or 10 divided by 0.3048.

metres equal 3048/10000 feet.

10 × (3048/10000) = 3 6/125

10 feet equals 36/125 metres.

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The volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8 is approximately 1483.6 cubic units.

To find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8, we can use the method of cylindrical shells.

To find the volume of the solid, we need to integrate the area of each cylindrical shell over the height of the solid. Let r be the radius of a cylindrical shell at height y, and let h be the thickness of the shell. Then the volume of the shell is given by:

dV = 2πrh × h

where the factor of 2 comes from the fact that there are two cylindrical shells (one on either side of the line x = 8).

We can express r and h in terms of y:

r = 8 - y

h = e^8 - e^-x

Substituting these expressions into the formula for dV and integrating from y = 0 to y = 1, we get,

V = ∫(0 to 1) 2π(8 - y)(e^8 - e^-x) dy

= 2π ∫(0 to 1) (8e^8 - 8e^-x - ye^8 + ye^-x) dy

= 2π [8e^8 - 8e^-1 - (1/2)e^8 + (1/2)e^-1]

= 2π [15e^8 - 4e^-1]

≈ 1483.6 cubic units

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The given question is incomplete, the complete question is:

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8.

All the three statements given in the question are valid.

(a) Two real numbers satisfy a^2 < b^2 if and only if |a| < |b|. This is a valid statement, and the justification follows from the fact that the square of any real number is non-negative, i.e., a^2 ≥ 0 and b^2 ≥ 0, and if a^2 < b^2, then taking square roots of both sides yields |a| < |b|.

(b) Two real numbers satisfy a^2 > b^2 if and only if |a| > |b|. This is also a valid statement, and the justification follows from the fact that the square of any non-zero real number is positive, i.e., a^2 > 0 and b^2 > 0, and if a^2 > b^2, then taking square roots of both sides yields |a| > |b|.

(c) Two real numbers satisfy if and only if |a| ≤ |b|. This statement is also valid, and the justification follows from the fact that the square of any real number is non-negative, i.e., a^2 ≥ 0 and b^2 ≥ 0, and if a^2 ≤ b^2, then taking square roots of both sides yields |a| ≤ |b|.

Therefore, all three statements are valid.

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In statistics, p-value significance is the measure of the strength of evidence against the null hypothesis.

P-value significance is used to determine whether or not a result is statistically significant. The p-value is the probability of obtaining the observed results or more extreme results if the null hypothesis is true. If the p-value is below the chosen significance level, usually 0.05, the null hypothesis is rejected, indicating that the results are statistically significant.

This means that the observed data is unlikely to have occurred by chance alone and that there is strong evidence to support the alternative hypothesis. P-value significance is an essential concept in hypothesis testing, and it is widely used in scientific research, medical trials, and other statistical analyses.

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The fewest number of whole years the Banks family would need to include in the mortgage agreement in order to have a monthly payment of no more than $720 is 25 years.

Let's denote the number of years by y. Then the total number of monthly payments will be 12y.

The formula to calculate the monthly payment for a mortgage loan is:

M = P * (r/12) * (1 + r/12)^(12y) / ((1 + r/12)^(12y) - 1)

where:

M = monthly payment

P = principal (the amount borrowed)

r = annual interest rate

Plugging in the given values, we get:

720 = 120000 * (0.048/12) * (1 + 0.048/12)^(12y) / ((1 + 0.048/12)^(12y) - 1)

To solve for y, we can use trial and error or a numerical solver. Using trial and error, we can start with a few values of y and check if the monthly payment is less than or equal to $720.

Trying y = 20, we get:

720 = 120000 * (0.048/12) * (1 + 0.048/12)^(1220) / ((1 + 0.048/12)^(1220) - 1)

This results in a monthly payment of $753.81, which is higher than $720.

Trying y = 25, we get:

720 = 120000 * (0.048/12) * (1 + 0.048/12)^(1225) / ((1 + 0.048/12)^(1225) - 1)

This results in a monthly payment of $715.48, which is lower than $720.

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