In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded. A regression line was generated and shown to be an appropriate description of the relationship. The results of the regression analysis are below. Depend Variable: Top Speed Variable Constant Weight Coefficient 107.58 0.8710 s.e. of Coeff 11.12 0.4146 t-ratio 9.67 2.10 prob 0.000 0.062 R squared = 30.6% R squared (adjusted) = 23.7% s = 10.42 with 12 - 2 = 10 degrees of freedom Part A: What is the LSRL based on the analysis provided? Make sure to identify what the variables represent in the context of the problem. (4 points) Part B: What is the predicted value for the top speed of a boat if its weight is 4 tons? Show your work.

The rate at which the water is now flowing from the tap is 50 cubic centimeters per second.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

In other words it compares 1 unit of some quantity with different amount of another quantity.

Given that,

Time taken to fill the watering can of 4 liter = 40 seconds.

4 liter = 4000 cm³

Time taken to fill the watering can of 4000 cm³ = 40 seconds

Unit rate of flow of water = 4000 / 40 = 100 cm³ / sec

Now the rate at which water flows is halved.

Rate = 100 / 2 = 50 cm³ / sec

Hence the rate of the flow of water now is 50 cubic centimeters per second.

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The complete question is as follow :

Water flows at a steady rate from a tap it takes 40 seconds to fill a 4 liter watering can from the tap. The rate at which water flows is halved.

4litre=4000cm³

Find the rate at which the water is now flowing from the tap. Give your answer in cubic centimeters per second (cm³/s).

Answer:

Slope intercept form =  y=mx+b

So

y-1=x

Add 1 to both sides

y=x+1

For the given function C(x) = 0.37 + (x - 1)0.11 the cost of mailing a 1.6-ounce letter is $0.436

The term function in math is defined as a relation between a set of inputs having one output each.

Here we have given that certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces.

Let us consider that the term C refers that cost in dollars of a first class mailing and x refers the weight in ounces.

The the function for the given situation is written as,

=> C(x) = 0.37 + (x - 1)0.11

Here we have given that we need to find the cost of mailing a 1.6-ounce letter which defines that the value of x is 1.6, then the cost is calculated as,

=> C(x) = 0.37 + (1.6 - 1) 0.11

=> C(x) = 0.37 + 0.066

=> C(x) = 0.436.

Complete Question:

A certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces. Find the function of the situation and the cost of mailing a 1.6-ounce letter.

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The quotient of the expression,

9(7y - 15) /  (110 - 6y ÷ 4) is 18(7y - 15) / (55 - y).

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

We have an expression,

9(7y - 15) /  (110 - 6y ÷ 4)

Simplifying,

9(7y - 15) /  (110 - 6y ÷ 4),

= 9(7y - 15) x 4 / (110 - 6y)

= 36(7y - 15) / (110 - 6y)

= 18(7y - 15) / (55 - y)

Therefore, the quotient is 18(7y - 15) / (55 - y).

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Answer: The probability that all generators in a sample of 8 are defective can be calculated by finding the number of ways that 8 defective generators can be selected out of 48 total generators, divided by the total number of ways that any 8 generators can be selected out of 48 total generators.

The number of ways to select 8 defective generators out of 48 total generators is:

C(8,8)*C(40,0) = 1

The total number of ways to select 8 generators out of 48 total generators is:

C(48,8) = 1,907,725

The probability that all generators in a sample of 8 are defective is:

1/1,907,725

If a sample of 8 generators is selected, find the probability that none in the sample are defective.

The number of ways to select 8 non-defective generators out of 48 total generators is:

C(40,8) = 45,765

The total number of ways to select 8 generators out of 48 total generators is:

C(48,8) = 1,907,725

The probability that none in the sample are defective is:

45,765/1,907,725

Both of these are reduced fraction.

The values of x if the two expressions equal are all real numbers.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given expression ,

(x-2) (x+6) / 7 (x+6)  =  x-2/ 7

So, in LHS x+6 can be cancelled

and we get,

=x-2/ 7

which is same as the RHS from the given expression .

So, As the both LHS and RHS are equal , if put any value Both remains same

Hence, The values of x if the two expressions equal are all real numbers.

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The tension in each wire when a 180-lb cylinder is suspended from point d is 52.8

The term tension is defined as the tensile load in the wire as it is continuously fed between the wire guides that are used to keep the wire straight between said guides.

While we looking into the following diagram we have identified that the following values are known.

Here the width is 180 lb.

And the distance between the two wires on all the sides is 22 inches, 24 inches and 18 inches.

Then the tension is calculated as,

=> (22 x 24 x 18)/180

=> 9504/180

=> 52.8

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Answer:

It belongs in quadrant 3.

Legal precedent means that a decision on a definite principle or question of law has already been made by a court of higher authority, such as a call or supreme court. below such a decision, lower courts defer to, or adhere to, that prior decision in similar cases.

The commitment of lower courts may be used as precedent for courts of similar jurisdiction, but higher courts are not bound by the resolution of lower courts.

The use of legal precedent helps secure court rulings remain consistent among similar cases. To this end, courts are bound to cling to prior decisions made by a higher court on a same legal matter.

Because a judge is bound by these previously made decisions, this is mentioned to as binding precedent. anew, following the principle of glare decisis, binding precedent promotes the maintenance of answers to legal questions already established.

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The solution for the equations (2x + 5y = 18) and (3x + 1.5y = 9) will be x = 1.5 and y = 3.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

Given that the system of the equations is (2x + 5y = 18) and (3x + 1.5y = 9). The equations by substitution method can be solved as,

(2x + 5y = 18)

(3x + 1.5y = 9)

Rewrite the equation (2x + 5y = 18) as,

x = ( 18 - 5y) / 2

Substitute the value of x in the second equation,

3x + 1.5y = 9

3  ( 18 - 5y) / 2 + 1.5y = 9

( 54 - 15 y) /2 + 1.5y = 9

54 - 15y + 3y = 18

-12y = -54 + 18

-12y = -36

y = 3

The value of x will be calculated as:-

2x + 5y = 18

2x + ( 5x 3 ) = 18

2x + 15 = 18

2x = 3

x = 1.5

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The purchase cost of fixtures can become tax deductible is referred to as a true statement.

This is referred to as the imposition of compulsory levies on individuals or entities by governments in other to fund government spending and various public expenditures.

Office fixtures such as furniture would typically be considered a long-term asset because it isn't typically replaced on a yearly basis which is why they are not deductible from a business's taxable income. However in a scenario where the fixtures start going through the process of depreciation, amortization or depletion then it becomes tax deductible.

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In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.

A number's exponent tells you how long you will need to multiply it in order to get the result. For instance, because 8 is multiplied by itself 3 times, 8 8 8 can be written as 83.

Here, 3 is the "exponent" or "power," which indicates how many times the number 8 is multiplied by itself, and 8 is the "base," which stands for the number being multiplied.

The number of times a number must be multiplied by itself is what a power or exponent, in essence, indicates. The base in this situation can be any integer, fraction, or decimal. Any value, positive or negative, can be assigned to the exponent.

Given

[tex](1/4)^{x-2} = 16[/tex]

[tex](1/4^{x-2}) = 16[/tex]

1 = 16 × [tex]4^{x-2}[/tex]

1 = 16 × [tex](2^2)^{x-2}[/tex]

[tex]$1 = 16 \times \frac{ 2^{2x}}{2^4}[/tex]

[tex]$1 = \frac{ 16 \times2^{2x}}{2^4}[/tex]

[tex]$1 = \frac{ 16 \times2^{2x}}{16}[/tex]

[tex]$1 = 2^{2x}[/tex]

1 = 2²⁽⁰⁾ The only possible exponent that values in 1 is when exponent is 0

1 = 1

x = 0

Thus, In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.

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Answer:

H = 20

Step-by-step explanation:

Looks like you got everything correct. Nice!

For your last one, let's get H by itself. Since 1/2 is division, let's multiple it by 2 to turn it into one. Because you multiply by 2 on the left side, you have to on the right side also...

(1/2)(2) = 1

(1)(h) = h

On the other side, 10(2) = 20.

Combining the 2, H = 20

The rocket was at a height of 19.75 meters after 0.5 seconds

The rocket hit the ground after 8.02 seconds

The maximum height is 81 m.

An equation is an expression that shows the relationship between numbers and variables.

The height (h) of the rocket t seconds after launch is modeled by:

h(t) = -5t² + 40t + 1

a) After 0.5 seconds:

h(0.5) = -5(0.5)² + 40(0.5) + 1 = 19.75 meters

b) The rocket hit the ground when h(t) = 0, hence:

-5t² + 40t + 1 = 0

t = 8.02 s

c) The maximum height is at h'(t) = 0

h'(t) = -10t + 40

-10t + 40 = 0

10t = 40

t = 4 s

h(4) = -5(4)² + 40(4) + 1 = 81 meter

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Answer: The total cost for two people to go to the movies three times is 3x2 = 6x dollars.

The cost of a bag of popcorn is $4 and they share one bag of popcorn each time they go to the movie, so the total cost of popcorn is 4*3 = $12 dollars.

So the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12

So an expression to represent the total cost for two people to go to the movies three times and sharing a bag of popcorn each time is 6x + $12.

Step-by-step explanation:

Pareto chart is a type of bar graph which often displays the data in descending order of frequency.

It is made up of vertical bars, with the height of each bar representing the frequency of occurrence for each category. The chart is named after Vilfredo Pareto, who used it to analyze economic data in the late 19th century.

For the given data, we calculate the cumulative frequency of the data by adding the frequencies of each category.

Toga: 6

Hayride: 6 + 4 = 10

Beer Bash: 10 + 8 = 18

Masquerade: 18 + 2 = 20

The Pareto chart is created by plotting the cumulative frequency against the categories. The chart is plotted with the categories on the x-axis and the cumulative frequency on the y-axis.

Toga: 6 (30%)

Hayride: 10 (50%)

Beer Bash: 18 (90%)

Masquerade: 20 (100%)

Hence, the Pareto chart for the given data is as follows:

Toga: 30%

Hayride: 20%

Beer Bash: 40%

Masquerade: 10%

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Step-by-step explanation:

To get the total amount of sandwiches sold in the first week, we would need to add up all of the ham, tuna, and cheese sandwiches.

32 + 46 + 18 = 96

The shop sold 96 sandwiches in the first week.

To find out how many more sandwiches the store sold in the second week, we will need to add up all of the sandwiches again.

38 + 43 + 24 = 105

The shop sold 105 sandwiches in the second week.

Taking 105, we can subtract 96 from it to get how many more sandwiches the shop sold in week 2.

105 - 96 = 9

The shop sold 9 more sandwiches in the second week.

The circumference of the circle in terms of π  is 7π yards. Option B

The formula for calculating the circumference of a circle is expressed as;

C = 2πr

Given that the parameters are;

The formula for calculating the radius of a circle is given as;

Radius = d/2

Where; d is the diameter of the circle

From the information given,

Diameter = 7 yards

Radius = 3.5 yards

Now, substitute the value

Circumference = 2× 3. 5 ×π

Multiply the values

Circumference = 7π yards

Thus, the value is 7π yards

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Answer: 7 yards

Step-by-step explanation:

The probability that it is a caramel truffle is 6/13.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, A box contains only orange truffles, strawberry truffles, and caramel truffles and the ratio of orange truffles to strawberry truffles is 3 : 4.

Also given, The probability that it is an orange truffle P(O) is 3/13,

Hence  The probability that it is a strawberry truffle P(S) = 4/13.

Therefore, The probability that it is a caramel truffle P(C) is = 1 - 3/13 + 4/13.

= 1 - 7/13.

= 6/16.

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Answer: 311/500 and 62.22%

Step-by-step explanation:

Fraction: 0.622 = 622/1000 = 311/500

Percent: 0.6222 = 62.22 % (Move decimal 2 places down)

The decimal 0.622 in the form of simplest fraction as 311/500 and in percent is 62.2%.

To convert 0.622 to a fraction in simplest form, write it as follows:

0.622 = 622/1000

Now, simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

622/1000 = (311 × 2)/(500 × 2)

                 = 311/500

So, 0.622, when expressed as a fraction in simplest form, is 311/500.

To convert 0.622 to a percent, multiply it by 100:

0.622 × 100 = 62.2%

Therefore, 0.622 is equivalent to 311/500 or 62.2%.

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Answer:

You do not need to add any skim milk.

Step-by-step explanation:

Step-by-step explanation:

percentages are represented by hundredths in calculations.

2 1/2% = 2.5% = 0.025

2% = 0.02

we are mixing the 3 L 2.5% milk with x L of 0% milk.

and we are ending up with (3 + x) L of 2% milk.

so, we have

3×0.025 + x×0 = (3 + x)×0.02 = 3×0.02 + 0.02x

3×0.005 = 0.02x

0.015 = 0.02x

x = 0.015/0.02 = 0.75

so, 0.75 L have to be added to dilute the milk to 2%.

Answer:

7.5

Step-by-step explanation:

Since the segments are parallel, the side segment lengths are proportional.

8/10 = 6/x

4/5 = 6/x

4x = 30

x = 7.5

All normal density curves are symmetric and have a peak at the mean. 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.

All normal density curves are symmetric. This means that the curve looks the same to the right and left of the mean (μ). The curve reaches its peak at the mean, which is the highest point on the curve. The area under the curve is equal to 1. The area under the curve that is within one standard deviation (σ) of the mean is equal to 0.68. This means that 68% of the area under the curve is within one standard deviation of the mean and 95% of the area under the curve is within two standard deviations of the mean.

The formula for calculating the area under the curve within one standard deviation of the mean is:

Area = 0.68 * 1

The formula for calculating the area under the curve within two standard deviations of the mean is:

Area = 0.95 * 1

These formulas can be used to calculate the area under the curve for any normal density curve.

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Alicia made a quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.

The end-to-end measurement or size is called the length. In other words, the larger of the two or three dimensions of a geometric shape or object. For example, the length and width of a rectangle define its dimensions. In the international size system, length is also a dimensional distance quantity.

Blue Diamond fabric is 1/4" x 36" or 9" quarter yards.

5/6 yards of yellow bonnet fabric equals 5/6 x 36 inches or 30 inches.

Alicia made the quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.

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Answer:c

Step-by-step explanation:

The slope forms a uniform solution in each square box as shown in the drawing

here, s is the value or answer.

SOLUTION -

[tex] \frac{1}{2} = \frac{3}{6} \\ 1 \\ \frac{1}{2} = \frac{1}{2} \\ = \frac{1}{m } = \frac{1}{2} \\ m = 2[/tex]

4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.

An expression is combination of variables, numbers and operators.

Let m be the number of marbles.

The number of marbles April has be m.

Given that Carter has 10 fewer marbles than April.

If Carter has 10 less than m, that's m - 10.

Nicholas has 3 times as many marbles as April.

3m

marbles Carter and Nicholas have altogether

m-10+3m

4m-10

Hence, 4m-10 is the expression represents the number of marbles Carter and Nicholas have altogether.

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The property if VW+WY=ZY, and VW + WY=XZ, then XZ=ZY is referred to as a transitive property.

This states that “if two quantities are equal to the third quantity, then we can say that all the quantities are equal to each other”.

A good example of its application can be seen here which is if x = y, and y = 7, then x must equal 7 which when observed in what was given above corresponds with this type of property and is therefore the reason why it was chosen as the correct choice.

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The parametric equations for the line are:

x(t) = 5 + t, y(t) = 5 - t and z(t) = t

Given that the line through (5, 5, 0) and perpendicular to both i + j and j + k

We know that the symmetric form of the equation of the line is given by,

[tex]\frac{x-x_1}{a} =\frac{y-y_1}{b} =\frac{z-z_1}{c} =t[/tex]

Let us assume that x₁ = 5, y₁ = 5 and z₁ = 0

Evaluating the product of ( i + j) and ( j + k ) we get,

( i + j) × ( j + k )

= i - j + k

The value of a = 1, b = -1 and c = 1.

Substitute all the values in the above equation we get,

[tex]\frac{x-x_1}{a} =\frac{y-y_1}{b} =\frac{z-z_1}{c} =t[/tex]

[tex]\frac{x-5}{1} =\frac{y-5}{-1} =\frac{z-0}{1} =t[/tex]

so, the parametric form of the equation would be,

x(t) = x₁  + at

x(t) = 5 + (1)t

x(t) = 5 + t

y(t) = y₁  + bt

y(t) = 5 + (-1)t

y(t) = 5 - t

And z(t) = z₁  + ct

z(t) = 0 + (1)t

z(t) = t

Thus, the parametric equations: x(t) = 5 + t, y(t) = 5 - t and z(t) = t

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The complete question is:

Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (5, 5, 0) and perpendicular to both i + j and j + k

x(t), y(t), z(t) = ?