Given r(x) =x' - 4x2 + 4x - 6, find the value of r(2). What does your answer tell you about x - 2 as a factor of r(x)? Explain.

The direct distance from home plate to the second base is 127.27  feet .

In the question ,

it is given that

the shape of base ball diamond = square ,

distance of one side =  90 feet ,

so , the distance of other side will be = 90 feet , because it is a square ,

the distance from home plate to the second base is represented by the diagonal ,

2 sides with length 90 feet and one diagonal forms a right angled triangle.

let the distance from home plate to the second base be " x" .

So , By Pythagoras Theorem ,

90² + 90² = x²

x² = 8100 + 8100

x² = 16200

x = √16200

x = 127.27

Therefore , The direct distance from home plate to the second base is 127.27  feet .

The given question is incomplete , the complete question is

A baseball diamond is in the shape of a square, 90 feet on a side. What is the direct distance from home plate to second base ?

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Answer:

$96 dollars in one year. 12 months in a year. and you get $96 in one year.

Step-by-step explanation:

I did it already in class.

The probability that if we select 4 fish from the tank, at least 2 will be white is 0.7863.

Given,

A fish tank in a pet store has 21 fish in it. 9 are orange and 12 are white. determine the probability that if we select 4 fish from the tank, at least 2 will be white;

The probability that the fish is white = 12/21

                                                      = 4/7

To find the probability that at least two will be white,

P(x ≥ 2) = 1 - P(x < 2) = 1 - ( P(0) + P(1) )

The binomial distribution formula [tex]P(x) = (^n_x)p^xq^n^-^x[/tex] where p is the probability of success and q is the probability of failure.

From the above formula;

P(x ≥ 2) = 1 + [ (3/7)⁴ + 4*(4/7)*(3/7)³ ]

            = 0.7863

Hence, the likelihood that if we select 4 fish from the tank, at least 2 will be white is 0.7863.

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The solution is

a) 1.412

b) 0.662

What is the place value chart?

A place value chart is a table that is used to determine the value of each digit in a number based on its numerical position. We place the given number in the place value chart to examine the place value of each digit in order to precisely identify the worth of distinct digits in a number.

Given data ,

Let the number be A = 4.236 / 3

So , the number A = 1.412

So , in order to place the number in place value chart

The digit 1 is in ones place

The digit 4 is in tenths place

The digit 1 is in hundredths place

The digit 2 is in thousandths place

b)

Let the number be B = 1.324 / 2

So , the number is B = 0.662

So , in order to place the number in place value chart

The digit 0 is in ones place

The digit 6 is in tenths place

The digit 6 is in hundredths place

The digit 2 is in thousandths place

Hence , the place value chart of numbers 1.412 and 0.662 are solved

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The yield on a corporate bond with a face value of $1000 after removal of discount would be =$60.

Interest rate can be defined as the payment received by an individual after investing a particular amount of money for a given period of time.

The principal amount after removal of $950 discount = $1000

The rate of interest (R) = 6%

The time of investment (T) = 1

Then the simple interest;

= P × T × R/100

= 1000 × 1 × 6/100

= 6000/100 = $60

Therefore, the yield of the corporate bond would be extra $60.

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Answer:

7 burgers

Step-by-step explanation:

1.96 #  /  .28 # / burger = 7 burgers

Answer: y = -2x -2

Step-by-step explanation:

First, we want to find the slope. We can see that every time x goes up by one, y goes down by two. Slope is y/x, so we can say that the slope is -2/1 or just -2. Now we have y = -2x + b. To find b, we need to plug in one of the points in the chart. We will use (1, -4). So:

-4 = -2(1) + b

-4 = -2 + b

-2 = b

Therefore our b is -2, making the linear function equate to: y = -2x -2.

As the sample size gets larger, the z value increases therefore we will more likely to  less likely to fail to reject the null hypothesis, thus the power of the test increases.

Statistical tests provide a mechanism for making quantitative decisions about one or more processes. The intent is to determine whether there is sufficient evidence to "reject" speculations or hypotheses about the process. If you want to keep pretending that you "believe" the null hypothesis is true, then not rejecting it can do you good. Alternatively, it may indicate that there is not yet enough data to "prove" something by rejecting the null hypothesis. A classic application of statistical testing is process control studies. Suppose a manufacturing process is interested in  a photomask with an average linewidth of 500 microns. The null hypothesis in this case is that the average linewidth is 500 microns. This statement implies the need to characterize photomasks with average linewidths much larger or  smaller than 500 microns. This leads to the alternative hypothesis that the average linewidth is not equal to 500 microns. This is a two-way substitution as it protects against substitution in the opposite direction. In other words, the line width is either too small or too large.

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Answer:

the area=16

Step-by-step explanation:

by ur calculations lol

The estimate should be 24 within a margin of error -4% with 90% confidence level.

In statistics, the margin of error is the degree of error in results from random sampling surveys. A wider margin of error in statistics suggests a reduced likelihood of relying on the results of a survey or poll, i.e. less trust in the results to represent a population.

A margin of error is a statistical parameter that compensates for the gap between actual and projected findings in a random survey sample. In layman's words, the margin of error measures the degree of unpredictability in data and research conclusions.

Given,

Confidence level=90%=0.90

Margin of error= -4%

α=1-0.9

α=0.1

α/2=0.05

P(z>[tex]z_{0.05}[/tex])=0.05

P(z>[tex]z_{0.05}[/tex])=1-0.05

P(z>[tex]z_{0.05}[/tex])=0.95

[tex]z_{0.05}[/tex])=1.96

Approximating P=0.5 and using E=0.2,

n=((1.96)²(0.5)(0.5))/(0.2)²

n=24.01

n=24

Therefore, the estimate should be 24 within a margin of error -4% with 90% confidence level.

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The capital gains his earned is $2,625

What is capital gains?
Capital gain is the profit obtained from the sale of assets whose value is higher or increased than when the asset was purchased.

The first is to calculate the difference price when selling and purchasing.

= ((100% + 20%) × $52.50) - $52.50

With the substitution formula, we can simplify it to:

= 20% × $52.50
= $10.5

Next is to multiply the difference price to share he purchased.

= $10.5 × 250
= $2,625

Thus, the capital gains his earned is $2,625

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Answer:

y = 9280 - 20x

Step-by-step explanation:

Using the normal distribution, it is found that there is a 0.5899 = 58.99% probability that on any given day it will take between 34 and 44  minutes to complete the task.

In a normal distribution with mean  and standard deviation, the z-score of a measure X is given by:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

Mean of 40 minutes, hence μ =40 .

Standard deviation of 6 minutes, hence σ=6 .

The probability that on any given day it will take between 34 and 44  minutes to complete the task is the p-value of Z when X = 44

subtracted by the p-value of Z when X = 34, hence:

X = 44:

[tex]Z={\frac{x-\mu}{\sigma} }[/tex]

[tex]Z={\frac{44-40}{6} }[/tex]

  =4/6

Z =0.67 has a p-value of 0.7486

X = 34:

[tex]Z={\frac{x-\mu}{\sigma} }[/tex]

[tex]Z={\frac{34-40}{6} }[/tex]

Z=-6/6

Z=-1 has a p-value of 0.1587

0.7486 - 0.1587 = 0.5899.

0.5899 = 58.99% probability that on any given day it will take between 34 and 44  minutes to complete the task.

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The volume increase when the radius changes from 7 to 7.1 ft is 62.45 ft³ i.e. 4.34%. of the previous volume.

We know that the volume of the sphere is 4/3πr³.

So, here the radius of the sphere is 7 ft,

Therefore the volume of the sphere will be = 4/3π(7)³.

so, V1 = 4/3*3.14*(7)³.

V1 = 1436.76  ft³.

When the radius of the sphere will increase tp 7.1 feet then the volume will also increase which will be :

V2 = 4/3*3.14*(7.1)³.

V2 = 1499.21 ft³.

Now the increase in volume is V2- V1 .

which is , 1499.21 ft³ -  1436.76  ft³

i.e. 62.45 ft³ is the increase of the volume of the sphere.

This increased volume is the 4.34% of the previous volume of the sphere.

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Answer:

12

Step-by-step explanation:

Answer: 201

Step-by-step explanation: Ok this is very simple for those of you who are stuck on this. First you divide 12 by 268. You would get 22 with a remainder of 4. This in fractions would be 22 1/3. So he would be driving 22 1/3 miles with 1 galloon of gas. If you multiply this by 9 you would get 201 miles which is how much he can drive in 9 gallons of gas.

Hoped this helped!

Answer:

12x² + 6xy - 30x

Step-by-step explanation:

Given expression,

→ 6x(2x + y - 5)

Simplifying the given expression,

→ 6x(2x + y - 5)

→ (6x × 2x) + (6x × y) - (6x × 5)

→ 12x² + 6xy - 30x

Thus, answer is 12x² + 6xy - 30x.

The actual width of dining room is 6m, if Tristan drew a scale drawing of an apartment. He used the scale 1 millimeter = 2 meters. In the drawing, the dining room is 3 millimeters wide.

The ratio that describes the relationship between the actual figure and its model is called the scale. It serves as a representation of the actual figures in smaller units on maps. A scale of 1:5, for instance, means that 1 on the map is equivalent to the size of 5 in the real world. A measurement on a model and its matching measurement on the real item are referred to as being on the same scale in mathematics. An organized system of numbering or indexing that serves as a measurement reference standard and in which each number is associated with a specific physical quantity.

Given,

Tristan drew a scale drawing of an apartment. He used the scale 1 millimeter = 2 meters. In the drawing, the dining room is 3 millimeters wide.

The actual width of dining room is 6m.

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The t-score of 2.779 is used to find the 99% confidence interval for the population mean.

Given,

Assume that orangutans' heights, measured in inches, are regularly distributed with an unidentified mean and standard deviation. The population means are calculated using the orangutan heights of 27 orangutans that were randomly selected.

What t-score should be applied to determine the population mean's 99% confidence interval?

n = 27

confidence level = 0.99

We have to find a critical value for the confidence level of 0.99.

To find the critical value we need degrees of freedom and significance level.

df = n-1 = 27 - 1 = 26

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

For α/2 = 0.005 and df = 26, the critical value using the above table is,

t-critical value = 2.779

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Answer: 90%

Step-by-step explanation: 36 divided by 40 = 0.9 x 100 = 90

The solution to the system of equation in the graph is (3, 4)

In algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."

In this problem, we simply need to look at where the lines intersect with one another and that will show us the solution to the equations.

If one carefully looks at this, the solution to this equations would be (3, 4)

This is because, at the point of intersection, the x - axis is at +3 and the       y-axis is at +4. This makes the solution to the system of equations (3, 4).

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Answer:

1/6

Step-by-step explanation:

y-1 = -6x -18

y = -6x - 18 + 1

y = -6x -17

slope of the perpendicular line: 1/6

Answer:

72.3

Step-by-step explanation:

72.381% as a recurring decimal using dot notation is 0.72381.

To express 72.381% as a recurring decimal using dot notation, we can follow these steps:

Convert the percentage to a decimal by dividing it by 100:

72.381% = 72.381 / 100 = 0.72381

Write the decimal part without the leading zero:

Decimal part: 0.72381

Place a dot above the repeating part of the decimal, which is the entire decimal in this case:

Decimal part with dot notation: 0.72381

Thus, 72.381% as a recurring decimal using dot notation is 0.72381.

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The number of pieces of tiles that are needed to pave a path 5 m long and 1 m wide is; 20 tiles

We are told that the size of each piece of tile is 50 cm by 50 cm.

Now, we are told that the area that needs to be paved with tiles measures 5 m by 1m. Thus;

Converting the area that needs to be tiles to cm, we have;

5m = 500 cm

1m = 100 cm

Thus;

Area to be tiled = 500 * 100 = 50000 cm²

Area of each tile = 50 cm * 50 cm = 2500 cm²

Thus;

Number of tiles that are required to pave the given path = 50000/2500 =20 tiles

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The expression <√2 / 10, 7√2 / 10> is the unit vector of the vector <1, 7>.

Vectors are characterized by two features: Magnitude and direction. The magnitude represents the "quantity" contained by the vector and the direction indicates the distribution of the "quantity" along the orthogonal axes of the vector, that is, the x and y axes.

We can obtain the unit vector of any non-zero vector by dividing it by its magnitude. The magnitude can be found by using Pythagorean theorem. Now we proceed to determine the unit vector associated with vector <1, 7>.

First, determine the magnitude of the vector:

||[tex]\vec v[/tex]|| = √(1² + 7²)

||[tex]\vec v[/tex]|| = √50

||[tex]\vec v[/tex]|| = 5√2

Second, calculate the unit vector:

||[tex]\vec u[/tex]|| = (1 / 5√2) · <1, 7>

||[tex]\vec u[/tex]|| = <1 / 5√2, 7 / 5√2>

||[tex]\vec u[/tex]|| = <√2 / 10, 7√2 / 10>

The unit vector is <√2 / 10, 7√2 / 10>.

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The number of Swiss francs received for each pound decreased by 3.82%

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

200 pounds = 262 Swiss francs.

1 pound = 262/200 = 1.31 Swiss francs.

450 pounds = 567 Swiss francs.

1 pound = 567/450 = 1.26 Swiss francs.

Difference in Swiss francs received for each pound = 1.31 - 1.26= 0.05

% decrease = (0.05/1.31)*100 = 3.82%

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The magnitude of b from the coordinate plane is 3 units. Therefore, option A is the correct answer.

We need to find the magnitude of b.

In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind.

If the number is negative, the magnitude becomes the absolute value of the number.

Now, magnitude of b is |-3|=3

The magnitude of b from the coordinate plane is 3 units. Therefore, option A is the correct answer.

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Jim needs a score of 115 on his third test to keep an average of 89 or greater.

A mean represents the average value among a set of values.

Mean = (sum of all values)/(total number of values)

In other words, mean is the value assigned to each member of set after fair distribution. It means that if a set of n values has a mean of x, we can assume the set to be 'x' value recurring n times over the sample.

In this case, we have 3 test results: 83, 69 & x, where x is the unknown result of 3rd test. Our required minimum average/mean is 89.

Substituting these in our formula for mean, we get:

[tex]89=\frac{83+69+x}{3} \\89*3=152+x\\x=267-152=115[/tex]

Thus, 115 is our required test result for maintaining average of minimum 89.

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