polynomial function
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The values of the variables t and k are 33 and 21, respectively.

We are given a system of two equations. The equations are linear in nature. Each equation represents a straight line. We need to find the solution to the system of linear equations. The coordinates of the intersection point of the straight lines are the solution. The equations are given below.

t - k = 12

3t + 2k = 141

We will substitute the value of t from the first equation into the second equation.

t = 12 + k

3t + 2k = 141

3(12 + k) + 2k = 141

36 + 3k + 2k = 141

5k = 105

k = 21

We will substitute the value of k into the first equation to find the value of t.

t = 12 + k

t = 12 + 21

t = 33

Hence, the values of t and k are 33 and 21, respectively.

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The constant of proportionality is: k = 0.45

The equation is: p = 0.45w.

The equation that models the proportional relationship between two variables, x and y, can be expressed in slope-intercept form as y = kx, here, the value of k is the constant of proportionality between the two variables x and y.

Thus, constant of proportionality, k = y/x.

In the table given, we can use the coordinates of one point, (3, 1.35), to find the constant of proportionality, k:

Constant of proportionality, k = 1.35/3

Constant of proportionality, k = 0.45

To write the equation of the relationship between weight (w) and price (p), substitute k = 0.45 into p = kw.

p = 0.45w

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As per the concept of correlation coefficient "tell us" that the model in question does not fit the data well, in whose case we need to find another that can do it.

Correlation coefficient:

Correlation coefficient refers the a statistical measure of the strength of a linear relationship between two variables. And its values can range from -1 to 1.

Given,

The correlation coefficient between two quantitative variables is approximately 0. 2.

Here we need to find the value of this correlation coefficient indicate about how well the model fits the data

While we looking into the given question, a correlation coefficient of 0.02 is near to zero. In this case, the correlation coefficient is "telling us" that the two variables do not follow the cases 1 and 2 above described. Instead, it follows the case 3.

Therefore, the model in question does not fit the data well, in whose case we need to find another that can do it.

Therefore, it is important to remember that the correlation coefficient does not tell us anything about that one variable causes the other variable, only behaviors as described above.

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The expression [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in simplified radical form obtained by using the laws of indices is presented as follows;

[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]

The laws of indices are a set of rules that can be used to simplify expressions of variables and numbers that consists of powers that have the same base.

The expression is; [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex]

The laws of indices which can be used to evaluate the expression includes;

Expressing the index in terms of 5, we get;

[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]

[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]

The expression, [tex]\sqrt[5]{36\cdot t^6\cdot w^{17}}[/tex] in the simplified form is [tex]2\cdot t\cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]

A second method evaluating the expression is presented as follows;

[tex]\sqrt[5]{32\cdot t^6\cdot w^{17}} = \sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2}[/tex]

[tex]\sqrt[5]{2^5\cdot t^5 \times t\cdot w^{15} \times w^2} = 2^\frac{5}{5} \cdot t^\frac{5}{5} \times t\cdot w^{\frac{15}{3} } \times w^\frac{2}{5}[/tex]

[tex]2^\frac{5}{5} \cdot t^\frac{5}{5} \times t^{\frac{1}{5} }\cdot w^{\frac{15}{3} } \times w^\frac{2}{5} = 2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5}[/tex]

[tex]2\cdot t \cdot w^3\times t^{\frac{1}{5} }\cdot w^\frac{2}{5} = 2\cdot t \cdot w^3 \cdot \sqrt[5]{t \cdot w^2}[/tex]

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Answer:

-27

Step-by-step explanation:

Answer:

-27

Step-by-step explanation:

Since the problem says that you are subtracting -5 you have to turn everything that is on the right to a positive number like so:

-32 - (-5) ---> -32 + 5

So now all you have to do is add 5 to -32

Therefore equaling -27

So your final answer is C. -27

Answer:

$7,686.77744

Step-by-step explanation:

19000-14%=16340

16340-14%=14052.4

14052.4-14%=12085.064

12085.064-14%=10393.155

10393.155-14%=8938.1133

8938.1133-14%=7686.77744

Answer:

The solution is A. 183

Step-by-step explanation:

112-38×14÷14+109

= 74×1+109

= 74+109

= 183

Using the theories of confidence interval, we got that 0.945 is critical value which should we use for constructing an 89% confidence interval from this population.

In statistics, a confidence interval is the range of values that is determined through the use of the observed data, calculated at a desired confidence level that may contains the true value of the parameter being studied.

Assuming this is asymmetrical confidence interval we have the diagram, and dealing with a Normal distribution

from the diagram we see that

P(Z<z)=0.89+0.055=0.945

Hence, if I were going to construct an 89% confidence interval from this population, critical value should use is 0.945

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If Mario will use all the rope as instructed right the number of 8 1/4 inch sections of  Mario that can come from the rope is: 6.

First step is to convert the 7 feet rope to inches

7 feet robes = 84 inches

Second step is to find the inches of rope left

Inches of rope left =84 inches - 34.5 inches

Inches of rope left = 49.5 inches

Now let find the number of 8 1/4 inch sections

Number of 8 1/4 inch sections =49.5 / 8.25

Number of 8 1/4 inch sections =6

Therefore 6 is the number of 8 1/4 inch sections .

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The sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D' is A'(3,-1) , B'(3,2), C'(4,3) and D'(4,0)

From the graph:

A(-4,5) , B(2,5) , C(4,3) ,D(-2,3)

transformations:

A'(-4+7,5-6)

= A'(3,-1)

B'(2+1,5-3)

= B'(3,2)

C'(4,3)

D'(-2+6,3-3)

= D'(4,0)

Therefore the sequence of transformation that maps quadrilateral ABCD onto quadrilateral A'B'C'D' is A'(3,-1) , B'(3,2), C'(4,3) and D'(4,0).

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The equation for straight line can be used to plot it on the graph. The amount of discount is 4.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

The given equation is as follows,

5x + (–2y) = 8

Here, x is the number of picture frames purchased after discount.

And, y is the total amount spent.

In order to find the discount, write the equation in terms of y as,

5x + (–2y) = 8

=> 2y = 5x - 8

=> y = 5 / 2 x - 4

The above equation can be plotted as a graph which is shown below,

It is found from the graph that slope is 5 / 2 which is the rate of per picture.

Since the frames are being purchased after the discount, from the above graph  discount can be obtained as 4.

Hence, the discount on the picture frames is given by 4.

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Answer:

30%

Step-by-step explanation:

60/200 = 3/10 = 30%

Answer:

through: (-4, 1) and (1, -3) how do u write the point slope form of the equation of the line through the given points ?

Step-by-step explanation:

to find slope you do delta y over delta x meaning 3 - 1 over 1 - (-4) you get 2/5 that is slope then you do to find b you take one of the points and you plug in for y = mx + b doesn't matter which one so -3 = 2/5 (1) + b

-3 = 2/5 + b

subtract 2/5 from both sides you get

-17/5 = b

so the equation is

y = 2/5x - 17/5

The 80 % confidence interval for the mean repair cost for the TVs will be [87.873,101.266] and the critical value that should be used in constructing the confidence interval is ±1.337 for 80% interval.

An area created using fixed-size samples of data from a population (sample space) that follows a particular probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability.

Here,

df = 17-1=16

critical value = ±1.337 for 80% interval

lower end value,

-1.337=(x-94.57)/[20.65/√17]

x = 87.87

higher end value,

1.337=(x-94.57)/[20.65/√17]

x = 101.27

hence, 80% interval:[87.87 101.27]

The range of values within which the mean repair cost for TVs falls within an 80% confidence interval is [87.873,101.266], and a critical value of ±1.337 should be used to construct the confidence interval.

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The total area of the shaded regions is 72 unit sq.

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = side x side

Given that square has an area of 196.

The region contains two overlapping squares that is the larger of these squares has an area 4 times that of the smaller and the area of their overlap is 1.

We can come up with equations as;

Since the area of their overlap is 1 then the side length is 1 unit.

Let the length of the smaller square is x.

The length of the larger square is 2x.

Therefore,

x + 2x - 1 = 3x - 1

Thus, 3x - 1 = 14

x = 5

The area of larger square = 100

The smaller one is 25

The area of shaded region;

196 - 124 = 72.

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Sandeep picked up 4.5 pounds of fresh apples from the field

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the standard form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.

Pounds of pre-picked apples picked up by Sandeep = 3 pounds

Charges per pound = $4

The total amount paid by Sandeep = $30

Let x be the pounds of fresh apples picked up by Sandeep

In the formulation of the equation we get the following:

Pounds of pre-picked apples*Charges per pound + Pounds of fresh apple picked*Charges per pound = Total amount paid by Sandeep

= 3*4 + x*4 = 30

12 +4x = 30

4x = 18

x = 4.5

So, fresh apples = 4.5 pounds

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The p-value is found to be 0.0006 by using the f-ratio.

Given that ,

SST = 10, 800 , SSTR = 4560

Sum of Square error SSE = SST- SSTR = 10800- 4560

SSE = 6240

df for treatment K= 1, where K are the level of treatment and given that K=3.

df treatment = k-1 = 3 - 1 = 2.

df error = n-k = 30- 3=27.

df total = n- 1 = 30 - 1= 29 .

Mean Square for treatment = SSTR / If treatment

=4560/ 2 = 2280

MSTR = 2280

MSE = SSE/ df error = 6240/27 = 231.11

F-ratio = MSTR/ MSE = 2280 / 231.11

= 9.8654 -=9.87 ( rounded to 2 decimal )

F ratio = 9.87

By using F-table the value of P-value in

F = 9.87 , and df1 = 2, df2=27 , with Significance level =0.05 , then the value is

P-value = 0.0006 .

Therefore, The p-value is 0.0006

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We have that the data is: (x₁ = 2, y₁ = 2) and (x₂ = 6, y₂ = 3).

The formula to calculate the slope of the line is:

m = y₂ - y₁/x₂-x₁

m = 3 - 2/6 - 2 = 1/4

The probability that at most 10% of the items in a given batch will be defective = 0.31333

We are aware that the item is broken.

Rate it 17.15 if X is either less than 16.85 or is.

Therefore, we simply found the area of one tail and multiplied it by two as we have seen their identical distance from the Min.

Therefore, let's choose 16.85.

We'll calculate a Z score for that.

Therefore, let's go on to the X value less the mean more than the standard deviation

This may be 16.85 -70, which will be 0.15 divided by.1 negative.

You will have a result of -1.5.

As a result, the Z distribution's region to the left of negative 1.5 will have a value of 0.0668. Divide that amount by two.

Z-score=0.0668/2=0.31333

You will also receive 0.31333.

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It take the speed of 299 m to travel 30 cm .

What is speed?

Speed is what it means. the speed at which an object's position changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed only has a direction and no magnitude, it is a scalar quantity.

Let us convert cm to m for distances

C = 2.998× 10^8 ms

The relationship between distance, speed, and time is

T =1 ×10^6/8

Because in this case you are being asked how long or time it takes, make it the subject.

Rounding the quotient produces.

Adjust it again to fit the scientific notation.

The result is -

d= c×t

d=2.998×10^8 m/s 10^6 m/s

d=2.998

As a mathematical expression, the time taken for light is 2.998

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If we use a × b, then it means that a is b times more than a and if we use a/b it means that we are making parts of a by the factors of b.

A mathematical expression that specifies the objects to be multiplied, known as a factor, produces a product. The other operations are multiplication, addition, and subtraction. When two natural numbers are divided with a remainder, or in the Euclidean method, the result is an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains after computing the quotient.

Rule of Division and Multiplication of Integers

Multiplication:

Rule 1: A positive integer and a negative integer cannot be added together.

Rule 2: A positive number is the result of two positive integers.

Rule 3: It states that the sum of two negative integers is positive.

Examples:

Rule 1: 1. (+4) x (-2) = -8 2. (-2) x (+5) = -10

Rule 2: 1. (+6) x (+8) = +48 2. (+6) x (+2) = +12

Rule 3: 1. (-6) x (-8) Equals +48 2. (-2) x (-4) = +8

Division:

Rule 1: A positive integer and a negative integer cannot be multiplied together.

Rule 2: A positive number is the quotient of two positive integers.

Rule 3: A positive number is the quotient of two negative integers.

Examples:

Rule 1: 1. (-8) / (+4) = -2 2. (-12) / (+6) = -2

Rule 2: 1. (+6) / (-3) = -2 2. (+24) / (-6) = -4

Rule 3. 1. (+9) / (+3) = +3 2. (+16) / (+4) = +4

Rule 4: 1. (-6) / (-2) = +3 2. (-42) / (-7) = +6

This is the summary of multiplication and division rules.

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Answer:

LCD is 18

Step-by-step explanation:

1/6 = 3/18

11/9 = 22/18

Answer: 20 shovelfuls of cement would be needed to be mixed with 80 shovelfuls of sand.

Step-by-step explanation:

First, we'd find out 4 divided by 1. This would equal 4.

Because we knew the amount of sand we had, we'd divide instead.

80 divided by 4

(If we had known the amount of cement we had, we would multiply)

This equals 20. This is how we get our answer, 20 to 80

Answer:

My teacher uses:

Please Excuse My Dear Aunt Sally : PEMDAS

Parenthesis, exponents, multiplication, division, addition, subtraction

Step-by-step explanation:

Answer:

parenthesis, exponents, multiplication, division, addition, subtraction

Step-by-step explanation:

The probability P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

For the probability,

The sample space of a die is, S = {1,2,3,4,5,6}

The probability of getting a number less than 2 is P(x < 2) = 1/6

The probability of getting an odd number is P(Odd) = 3/6

The required probability is calculated as:

P = 1/6 * 3/6

P = 1/12

Hence, the value of P (a number less than 2 on the blue cube and odd number on the green cube) is 1/12.

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Estimating 76.94 - 44.478 by first rounding each number to the nearest whole number gives 33

Rounding to the nearest whole numbers the figures are written s follows

rounding to the nearest whole is achieved by checking the number following the decimal.

If the number is up to 5 a number is added to the last number before the decimal as in here

76.94 = 77 (to the nearest whole number)

/when the number following the decimal is less than 5 is number is neglected as in here

44.478 = 44 (to the nearest whole number)

The subtraction is continued as follows

= 77 - 44

= 33

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