for the line of fit p = -26t + 5,649 , where t is the number of years since 1990 , what is the residual of the data point at t = 5?

To answer how many Jugs would be needed to treat an are of 168 square feet, we can use proportional relationships:

No, the sample of celebrities is not likely to be representative

Here, we should understand if the sample collected is likely to be representative or not

We need to understand what is meant by a representative sample or representative sampling

When a sampling is representative, it means that the sample that we have obtained looks like the population in which we are taking the sample from

Now, from what we have selected as a sample, we only considered the early comers while we have left out the late comers

What this mean in this case is that whatever sample we have is in fact not representative of the total

So we conclude that the sample of celebrities is not likely to be representative

The way in which the given ordered pairs represent a function is: b. For every x value, there is only one y value - a function.

A function simply refers to a mathematical expression (equation) which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for uniquely mapping an input variable (x-value) to an output variable (y-value).

In this context, we can reasonably infer and logically deduce that these ordered pairs represent a function because it has different input variables (x-values) for different or the same output variables (y-values).

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Answer: The answer is either $83 or $70

We are given a data set and we are asked to write the model that fits the data. We notice that for each step of "x" the values of "y" increase by the same amount. That means that the data follow a linear model, therefore, we will use:

Where:

To determine the slope "m" we will use the following formula:

Where:

Are data points. From the table we choose the following points:

Now, we substitute in the equation for the slope:

Solving the operations:

Therefore, the slope is -7. Substituting in the equation of the line we get:

Now, we substitute one of the points to get the value of "b". We will substitute the value x = -8, y = 47, we get:

Solving the product:

Now we subtract 56 from both sides:

Now, we substitute the value of "b" in the equation of the line:

And thus we get the line equation.

The rate of change of elevation is 0.18

Given the function:

To find the rate of change, we take the derivative of f(x)

At the point x = 1, we have:

The rate of change of elevation is 0.18

The percent of eighth graders who voted for Luke is  64 %.

Given that:-

Number of eighth graders who voted for Luke = 192

Number of eighth graders who voted for Alice = 60

Number of eighth graders who voted for Chris = 48

Total number of eighth graders at Wilson Middle School = 300

We have to find the percent of eighth graders who voted for Luke.

We know that:-

Percent of eighth graders who voted for Luke =

(Number of eighth graders who voted for Luke/Total number of eighth graders)*100

Hence, we can write,

Percent of eighth graders who voted for Luke = (192/300)*100 = 64 %

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The linear equation that passes through the point (4, -6) that is perpendicular to the line y = -3 is:

x = 4.

Im only answering the first question, like the guidelines say.

We want to find a line that passes through the point (4, -6) that is perpendicular to the line y = -3.

Now, line y = -3 is an horizontal line, so a line perpendicular to this one will be a vertical line of the form:

x = a.

Where a is a real number.

this line x = a must pass through (4, -6) where the x-value is 4, then the equation for the line will be:

x = 4.

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Answer:

√20 miles

Step-by-step explanation:

a² + b² = c²

                                           |

                     ?                    |   2 miles ↓

                                           |

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

                     ← 4 miles  

2² + 4² = c²

4 + 16 = c²

20 = c²

√20 = c

I hope this helps!

The length of the straight path they must run to get back to the starting line is 4.47 miles.

Displacement [x] of an object is the length of the straight line joining the initial and final position of the object. Mathematically, displacement can be written as-

Δx = x[2] - x[1]

Now -

Δx = vΔt              {[v] is velocity}

So we can write -

vΔt = x[2] - x[1]

Given are the runners at a cross-country meet such that they ran 2 miles to south and then 4 miles to west from the starting line.

We can find the straight path they must run to get back to the starting line using the Pythagoras theorem. The base will be equal to distance ran towards south and height will be equal to the distance ran towards west. The length of the hypotenuse will be equal to that of displacement or the straight path they must run to get back to the starting line. Using Pythagoras theorem -

[h]² = [b]² + [p]²

[h]² = (2 x 2) + (4 x 4)

[h]² = 4 + 16

[h]² = 20

[h] = 4.47 miles

Therefore, the length of the straight path they must run to get back to the starting line is 4.47 miles.

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We have a sample of size n=250. They are normally distributed with mean 88 and standard deviation of 15.

We have to find how many values from the sample are expected to be below 78.

We can calculate the z-score for 78 as:

Then, we can calculate the percentage of values below 78 as the probability P(z<-0.67):

This percentage is independent of the sample size: it is the same percentage for 100 numbers, 250 numbers or 1000 numbers.

For 250, 63 numbers are expected to be below 78, as 0.25*250=63 approximately.

Answer: 25%

Step-by-step explanation:

you can use proportions to convert molecules to moles and then moles to grams.

To convert molecules to moles, use the Avogadro number (6,022 × 10²³ atoms)

The proportion is:

1 : Avogadro number = x : number of molecules

so

1 : 6,022 × 10²³ = x : 4,5 × 10²⁴

solve. x = 7,47 moles

From the moles you can get the grams of SO2. To find grams, first find the mass of SO2.

S = 32,06

O2 = (16×2) = 32

so mass of SO2 is 64,06

Now use the proportion:

mass of SO2 : 1 = moles : x

so

64,06 : 1 = 7,47 : x

solve. x = 0,11 grams

The MAD tells you that most of the data values are greater than the mean.

MAD is an abbreviation for mean absolute deviation. Mean absolute deviation measures the variation of a data set. It measures the spread of the dataset from the mean. The higher the value of the mean absolute deviation compared to the mean, the greater the spread or variation of the dataset.

MAD =  (1 / n) ∑ l x - m(x) l

Mean is a measure of the center of a data set. It is the sum of the dataset divided by the total number in the dataset. Mean is also known as average.

Mean = sum of the data / total number in the dataset

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The rule of reflection over the x-axis is:

as shown in the figure:

The coordinates of point A = ( 2, 5 )

the coordinates of point B = (6, 3)

Apply the rule to the given points:

So,

A' = ( 2, -5)

B' = ( 6, -3)

So, the answer is option B

The simple interest earned on $8,350 principal deposited for 6 years at an interest rate of 2.28% is $ 1, 141. 28

It is of great importance to know the formula for calculating the simple interest. It is expressed as;

I = PRT/100

Where;

Now, let's substitute the values into the formula, we have;

Simple interest, I = $8,350 × 2. 28 × 6/100

Multiply the denominators

Simple interest, I = 114228/100

Find the quotient

Simple interest, I = 1, 141. 28

Hence, the simple interest is $ 1, 141. 28

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The points on the curve for the tangent is horizontal will be;

⇒ (1, -6) and (-2, 21)

What is mean by Tangent?

The tangent is defined by the line touching the ellipse and the circle at the only one point.

Given that;

The function is;

⇒ y = 2x³ + 3x² - 12x + 1

Now, Find the point on which the tangent is horizontal is find as;

The function is;

⇒ y = 2x³ + 3x² - 12x + 1

Differentiate it with respect to x as;

⇒ dy/dx = d/dx (2x³ + 3x² - 12x + 1)

⇒ dy/dx = 2 × 3x² + 3 × 2x - 12 × 1 + 0

⇒ dy/dx = 6x² + 6x - 12

Equate it to zero;

⇒ dy/dx = 0

⇒ 6x² + 6x - 12 = 0

Take common 6;

⇒ 6 (x² + x - 2) = 0

⇒ x² + x - 2 = 0

Solve for x, by the factorization as;

⇒ x² + 2x - x - 2 = 0

⇒ x (x + 2) - 1 (x + 2) = 0

⇒ (x - 1) (x + 2) = 0

We get two condition;

⇒ (x - 1) = 0 or (x + 2) = 0

⇒ x = 1 or x = -2

Substitute x = 1 in equation , we get;

y = 2x³ + 3x² - 12x + 1

y = 2 × 1 + 3 × 1 - 12 × 1 + 1

y = 2 + 3 - 12 + 1

y = - 6

Hence, The point = (1, -6)

Substitute x = -2 in equation , we get;

y = 2x³ + 3x² - 12x + 1

y = 2 × (-2)³ + 3 × (-2)² - 12 × -2 + 1

y = - 16 + 12 + 24 + 1

y = 21

Hence, The point = (-2, 21)

Therefore, The points on the curve for the tangent is horizontal will be;

⇒ (1, -6) and (-2, 21)

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Answer:

7 [tex]\frac{1}{73}[/tex]

Step-by-step explanation:

Set up a proportion

[tex]\frac{words}{minutes}[/tex] = [tex]\frac{words}{minutes}[/tex]

[tex]\frac{438}{6}[/tex] = [tex]\frac{512}{m}[/tex]  Cross multiply

438m = 6(512)

438 m = 3072  Divide both sides by 438

m = 7 [tex]\frac{1}{73}[/tex]

According to the compound interest concept, the total amount he will be paid is  $8,864.73

Compound interest:

The general form of the compound interest is,

A = P(1 + r/n)ⁿˣ

where

A = Accrued amount (principal + interest)

P = Principal amount

r = Annual nominal interest rate as a decimal

R = Annual nominal interest rate as a percent

r = R/100

n = number of compounding periods per unit of time

x = time in decimal years;

Given,

Ryan has an eight–year loan for $6,000. He is being charged an interest rate of 5 percent, compounded annually.

Here we need to find the total amount he will pay.

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)ⁿˣ

A = 6,000.00(1 + 0.05/1)⁽¹⁾⁽⁸⁾

A = 6,000.00(1 + 0.05)⁸

A = $8,864.73

Therefore, the total amount that he will pay is $ 8,864.73

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The volume of the cylinder is 3418.1 cubic feet

The volume of a cylinder is given by the formula:

Where r is the radius and h is the height.

The radius of the given cylinder is is 8 ft, the height is 17 ft

Volume is:

In triangle, value of QS = 12 ft .

What is a triangle answer?

ΔPQR and ΔQSR ,

         QS/SR = PO/OS

           y/9 =      16/12

           12 *  y =  16 *  9

                y = 16 *  9 /12

                 y = 12

value of QS = 12ft

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Given the system of equations

Solve by elimination method as shown below.

Multiply the first equation by 3 and subtract it from the second equation,

Then,

Use the value of y in the first equation,

Therefore, the answers are x=-5 and y=2, (x,y)=(-5,2)

Step 1

Given;

Step 2

Thus;

Answer;

aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾ is the explicit formula for the geometric sequence: 4, 20, 100, 500.

A geometric progression is simply a sequence of non-zero numbers, every term after the first can be determine by multiplying the previous number by a common ratio.

The nth term of a geometric sequence is expressed as;

aₙ = a₁ × r⁽ⁿ ⁻ ¹⁾

Where a₁ is the first term, r is the common ratio and n is the number of terms.

Given the sequence in the question;

4, 20, 100, 500, ...

First determine the common ratio.

r = any term / previous term

r = 20/4

r = 5

Th first term in the sequence is 4.

Plug these into the geometric sequence formula and simply.

aₙ = a₁ × r⁽ⁿ ⁻ ¹⁾

aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾

Therefore, the explicit formula for the sequence is aₙ = 4 × 5⁽ⁿ ⁻ ¹⁾

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Since the profit equation has been given to us as

Where m is the number of megaphones sold.

Since m can only take integer values from zero and above.

When no megaphone was sold, p(m)=p(0)=-875

Therefore, the range is;

However p(m) is not all real numbers.

When 500 megaphones were sold, the profit is;

This is the correct range.

Therefore, the range is represented as;

Thus the correct option is a. II

Answer:

The number of blueberry muffins Jake sold.

Step-by-step explanation:

Since Jake sold $38 of muffins, we know that 3 pertains to Jake.

Y is the price of a blueberry muffin, so 3 must be how many blueberry muffins were sold.

Answer:

y= -1/8x+3.5

Step-by-step explanation:

Plot your points and draw a line thru them. Find the slope: -1/8. Find the y-int: 3.5.

y = mx+b where x and y are variables, m is the slope and b is the y-int

y=-1/8x+3.5

Hope that helps

The product of 6000 and 50 can be found below

SOLUTION:

From the Z-score probability table;

P < 81 = 0.7123

CONCLUSION:

If one adult female is randomly selected, the probability that her pulse rate is less than 81 beats per minute is 0.7123