when the x-value is 100, what is the corresponding y-value? How do you know?

We know that the area of a rectangle is the width multiplied by its length, basically

But here, we have the area, which is a polynomial, same for the length, then, to find out the width we must do a division of polynomial, I'll call the unknown polynomial as P, we have

So now we got to solve

There is a lot of ways to solve it, first, I'll factor 3 in the denominator

As well the numerator

Then we can already simplify 3, and get an easier expression

Now I'll factor using the grouping method, I want the numerator to be something like (x+1)*(another polynomial), doing that we can "cut" the (x+1).

One way to do it is to expand it in some simple sums, look at 3x³, we want a 3x² to match with him, but look that 9x² is 3x²+6x², let's write that way

It doesn't seem to help us at all, but look that now we can factor 3x², then

Look, we have our first (x+1) in the numerator. Let's use the same idea but now for the term 6x², we want a 6x to match with him, we have 12x, so let's write it as 6x + 6x.

Similar to what we did before, factor 6x, and again

Now we have one more (x+1).

Now the easiest one, factor 6

As we can see we have (x+1) multiplied by something in all terms in the numerator, then we can factor (x+1) now

Now we can cancel (x+1), and our final expression will be

Therefore, the width is

Answer:

Step-by-step explanation:

i would say a

The probability of rolling a total of 7 on the two dice is 8/63

Probability:

In Mathematics, Probability is a branch that deals with the occurrence of possible outcomes in a random event or experiment. It is also defined as the ratio of the number of favorable outcomes and the total number of outcomes.

The probability of an event is denoted by P(E). And the probability of all the events in the sample space will equal to 1.  

Probability P(E) = No of favorable outcomes /Total No of outcomes  

Here we have,

The probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die, are in the ratio 1: 2: 3: 4: 5: 6  

Let x, 2x, 3x, 4x, 5x, and 6x are the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die [ since they are in ratio 1: 2: 3: 4: 5: 6 ]  

As we know the total events in a probability = 1

=> x + 2x + 3x + 4x + 5x + 6x = 1  

=> 21 x = 1

=> x = 1/21  

From the above calculations,

The probabilities of rolling 1, 2, 3, 4, 5, and 6 are  [tex]\frac{1}{21} , \frac{2}{21}, \frac{3}{21}, \frac{4}{21}, \frac{5}{21}, \frac{6}{21}[/tex] respectively.  

The possible combinations of two dies that can give a total of 7 are

(1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1)

Therefore, the probability of rolling a total of 7 on the two dice

=  the sum of the probabilities of rolling each combination

=  [tex]\frac{1}{21} . \frac{6}{21} + \frac{2}{21} .\frac{5}{21} + \frac{3}{21} . \frac{4}{21} + \frac{4}{21} . \frac{3}{21} + \frac{5}{21} .\frac{2}{21} + \frac{6}{21} .\frac{1}{21}[/tex]  

=  [tex]\frac{6}{441} + \frac{10}{441} + \frac{12}{441} + \frac{12}{441} + \frac{10}{441} + \frac{6}{441}[/tex]  

=  [tex]\frac{56}{441}[/tex]

=  [tex]\frac{8}{63}[/tex]

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The complete question is

For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die are in the ratio 1:2:3:4:5:6. What is the probability of rolling a total of 7 on the two dice

First step

We want to find the cost of each shirt Blair paid. In order to find it we want to find the total price Blair paid for the whole order and then divide it by 150 (total number of shirts).

She chose Company B.

They charge $3.10 per shirt, plus 4% of the total order for shipping.

There are 150 shirts, then the total order for shipping is:

150 · $3.10 = $465

we want to add the 4%. The 4% of $465 is

$465 · 4/100 = $465 · 0.04

= $18.60

If we add it to the total order for shipping:

$465 + $18.60 = $483.60

Second step

Now we divide the total price of 150 into 150: this is the cost for one shirt.

$483.60/150 = $3.224

If we round it to the nearest hundredth:

$3.224 ≅ $3.22

Answer- The total cost Blair paid for one T-shirt is $3.22

We know that she needs to add 75% to the total cost.

Let's remember that every percentage is equivalent to it divided by 100: for example 100% is equivalent to 1. For 75%:

75% = 75/100 = 0.75

Then 75% is equivalent to 0.75.

This means that if we want to find the 75% of something we multiply it by its equivalent: 0.75.

Answer- She can calculate the markup by multiplying her total cost by 0.75

Based on the previous parts, we know that we want to add the 75% (0.75) of the cost of each T-shirt Blair paid ($3.22).

We first find the 75% of $3.22 and then add it to it: it will be the cost of sell.

First step

The 75% of the total cost of each shirt ($3.22) is:

0.75 · $3.224 = $2.418

Second step

Adding the 75% to the total price:

$3.224 + $2.418 = $5.642

If we round it to the nearest hundredth:

$5.642 ≅ $5.64

Answer- Blair will sell each T-shirt at the carnival for $5.64.

The percentage increase of the value of Tessa's stock is 49%.

Stock is a term used to describe the shares of ownership of a company. It is sometimes also called equity.

To find the percentage value change, we use the formula given below

P = (N-O)/O*100

Here, P = percentage change, N = new value, O = old value.

P = (263.73-177)/177*100

P = 86.73/177*100

P =  8673/177

P = 49%

Therefore, we can conclude that the total percentage increase of the value of Tessa's stock is 49%.

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The equation for the direct linear variation that models the given information is: C. r = 64.5t.

The equation of a direct linear variation can be modelled as y = kx, where the variables are x and y, while the value of k is the constant of proportionality between the variables, x and y.

Given that:

We are told that r varies directly with t. Where k is the constant of proportionality, the equation of the direct linear variation between r and t can be expressed as r = kt.

Constant of proportionality, k = r/t

Number of shirts Rebecca can fold and restock (r) = 129

Amount of time she would spend (t) = 2

Find the constant of proportionality, k:

k = r/t = 129/2

k = 64.5

To write the equation for the direct linear variation, substitute k = 64.5 into r = kt:

r = 64.5t

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The relative intensity of the sound is 2.14 * 10 greater than the minimum threshold

The loudness equation is given as

L = 10log(R)

Where

R represents the relative intensity of the sound

From the question, we have the value of R to be

R = 138

Next, we substitute 138 for R in the loudness equation L = 10log(R)

So, we have

L = 10log(138)

Evaluate the logarithmic expression

L = 10* 2.14

Rewrite as

L = 2.14 * 10

Hence, the number of times is 2.14 * 10 times

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Answer:

Step-by-step explanation:

solution = (4 , 5)

y = 5 / x = 4

y = 2x - 13

5 = 2(4)- 3

5 = 8 - 3

5 = 5

the equation does make sense

y = x + 1

5 = 4 + 5

5 = 5

the equation does make sense

However, the questions asks if the solution works for both equations, and the solution does work for the first equation and the second one as well. The answer is yes, the solution does work for this system of equations.

Answer:

y = -1/4

Step-by-step explanation:

If the slope is o, that means that it is a horizontal line.  The line passes though the point (4, -1/4)  The horizontal line will have y as -1/4, no matter what x is.

Answer:

[tex]\sf y =\dfrac{-1}{4}[/tex]

Step-by-step explanation:

Equation of the line with slope 0 is y = c.

where c is the y-co-ordinate.

 The line with slope 0 is a horizontal line that is parallel to x-axis.

          [tex]\sf y =\dfrac{-1}{4}[/tex]

Given that points A, B, and C are the midpoints of their respective sides, A)  1/2YZ = AC is true about the figure according to SSS congruent rule.

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and angles have the same measure. Slides, rotations, flips, and turns can be used to make these triangles appear identical. They would be in alignment if they were moved. Congruence is represented by the letter "."

When two figures are similar to one another in terms of their size and shape, this is what mathematicians mean by congruence. It can be demonstrated that two triangles are congruent using four congruence rules in general.

However, all six dimensions must be discovered. In light of this, it is possible to determine the congruence of triangles using just three of the six values. Triangles that are congruent have equal corresponding sides and angles.

YX = 2 × AX (A = midpoint of YX)

ZX = 2 × CX (C = midpoint of ZX)

∠X and ∠X are congruent as the Reflexive property rule.

Therefore, triangle XAC is congruent to triangle XYZ (SAS similarity theorem)

Since 2AX = XY and 2XC = XZ Then 2AC = YZ which SSS congruent rule.

So, the correct option is A)  1/2YZ = AC

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Given that the length of one of the sides of the triangle is the radius, the length of the other leg of the triangle is also 6 units.

Therefore, this is an instance of a 45-45-90 triangle. The value of x can now be solve by

Given that the side length of the 45-45-90 triangle is 6 units, the length of the hypotenuse x is

Answer:$19.575

Solution

135/100of $14.50

=$19.575

or 35/100 of $14.50

=$5.075

$14.50+5.075

=$19.575

The expression which is equivalent to the given expression as in the task content is; 4.5⁶.

It follows from the task content that the expression which is equivalent to the given expression is to be determined.

Since the given expression is;

(4.5)-⁵ • (4.5)¹¹

Hence, it follows from the product of exponents law of indices that we have;

(4.5)^(-5 + 11)

= (4.5)⁶

Therefore, the expression which is equivalent is; 4.5⁶.

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The pairs of points that on the linear equations are:

a) (1, 7) and (0, 10).

b)  (1, 7/3) and (0, 2)

First, we need to find the slope of the equation of the line that passes through the points (-2, 6) and (1, -3).

Remember that if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know that the line passes through the points (-2, 6) and (1, -3), then the slope is:

a = (-3 - 6)/(1 + 2) = -9/3 = -3

a) A parallel equation will have the same slope, so it will be of the form:

y = -3*x + b

To find the value of b w euse the fact that this line should pass through the point (2, 4), so:

4 = -3*2 + b

4 = -6 + b

4 + 6 = b = 10

The linear equation is:

y = -3*x + 10

To find two points we can evaluate in x = 1 and x = 0, we will get:

y = -3*1 + 10 = 7

y = -3*0 + 10 = 10

So we have the pair of points (1, 7) and (0, 10).

b) A perpendicular equation will have a slope equal to the inverse of the opposite, so we will have a line like:

y = (1/3)*x + c

To find the value of c we use the fact that this line passes through (3, 3), them:

3 = (1/3)*3 + c

3 = 1 + c

3 - 1 = c

2 = c

This line is:

y = (1/3)*x + 2

Again we evaluate in 0 and 1 to get the two points:

y = (1/3)*1 + 2 = 1/3 + 6/3 = 7/3

y = (1/3)*0 + 2 = 2

So we have the pair of points (1, 7/3) and (0, 2)

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Answer:

[tex]5x^{2} +12x-7[/tex]

Step-by-step explanation:

Answer:

3.75

Explanation:

Given the equation 4x+4y = 15, we are to find the x coordinate of equation

To do this we will find the x intercept of the equation.

when y = 0

4x+4y = 15

4x + 4(0) = 15

4x = 15

x = 15/4

x = 3.75

Hence the x coordinate of the equation is 3.75

Answer:

5 batches

Step-by-step explanation:

60÷ 12=5 batches

Answer:

Yes, it is a positive correlation. It is a positive correlation because as the amount of calories goes up, the amount of fat goes up.

Answer:

x equals four

Step-by-step explanation:

collect like terms

then it will be minus 8 x equals minus 13 minus 19 which gives minus 32. Divide both sides by the coefficient of x i.e minus 8

Then x is less than 4

Because you divided with minus so the sign will change

The equation of the line that passes through the point (-8,6) is x + 4y = 16.

What is a slope?

A line's slope often indicates the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Given:

point = (-8,6)

equation : x+4y=20

x+4y=20

=> 4y = -x + 20

=> y = - x/4 + 5

Here the slope  m is -1/4.

Now  as the lines are parallel therefore the slope will be equal.

Therefore from the slope intercept form,

y - y1 = m (x - x1)

=> y - 6 = -1/4 ( x + 8 )

=> y - 6 = -x/4 - 2

=> x/4 + y = 4

=> x + 4y = 16

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First option is correct. A t - shirt cost $7.50 and a pair of shorts cost $23

First, it's crucial to understand linear equations.

Equation connects the two algebraic expressions with an equal to sign to demonstrate the equality between them.

Linear equations are those with one degree.

Simultaneous linear equations are two or more linear equations that can be solved simultaneously to find a common solution.

Let the price of one t-shirt be $x and price of one pair of shorts be $y

A t-shirt and two pairs of shorts cost $53.50

So, x + 2y = 53.50 .................... (1)

Two t-shirts and three pairs of shorts cost $84.

So, 2x + 3y = 84 ................ (2)

Multiplying (1) by 2,

2x + 4y = 107 .............(3)

Subtracting (2) from (3),

4y - 3y = 107 - 84

y = 23

Putting the value of y in (1)

x + 2[tex]\times[/tex]23 = 53.50

x = 53.50 - 46

x = 7.50

A t shirt cost $7.50 and a pair of shorts cost $23

First option is correct

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Answer:

 g(x) = f(5x)

Step-by-step explanation:

We assume that "shrink by a factor of 1/5" means that horizontal distances on the graph of g(x) are 1/5 of those on the graph of f(x).

Dividing x by a dilation factor will cause horizontal dilation of a graph. Here, that factor is 1/5, so the desired function is ...

 g(x) = f(x/(1/5))

 g(x) = f(5x)

Answer: x=3

Step-by-step explanation:

6x-15-4x+8=-1

2x-7=-1

2x=6

x=3

(a) Approximate the population standard deviation (?) with the sample standard deviation (s).

Approximate the standard normal distribution with the Student's t distribution.

(b) The lower bound is 40.35 and the upper bound is 41.65.

(a) Approximate the population standard deviation (?) with the sample standard deviation (s).

Approximate the standard normal distribution with the Student's t distribution.

(b) The degree of freedom =n-1=60-1=59

Given a=0.1, t(0.05, df=59) =1.67 (from student t table)

So the lower bound is

xbar -t*s/vn = 41 -1.67*3/sqrt(60) =40.35

So the upper bound is

xbar +t*s/vn = 41 +1.67*3/sqrt(60) =41.65

The standard deviation is a statistical metric that determines how much a bunch of values deviate from the mean. Simply said, standard deviation quantifies the distance between integers in a data collection. The square root of the variance is used to construct this measure.

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The plot of the data in the table is shown below.

And the plot of the answer choices is plotted in the following figure.

As we can clearly see, the exponential function of choice D best fits the data in the table,

Hence, choice D is the correct one.

A major weakness of the Articles of Confederation is that: B. States could ignore laws passed by the Congress.

The Articles of Confederation can be defined as the first written documents that were regarded as the Constitution of the United States of America, which was agreed upon by the thirteen (13) original states.

Under the Articles of Confederation, the national government was unable to raise revenue due to lack of enforcement powers of the confederate Congress.

In conclusion, we can reasonably infer and logically deduce that one of the limitations of the Articles of Confederation was the inability of Congress to enforce the laws it made because they can be ignored by states.

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Complete Question:

What was one major weakness of the Articles of Confederation?

A. State governments lost most of their political power.

B. States could ignore laws passed by the Congress.

C. The national government could not negotiate treaties.

O D. There was no way for new territories to become states.

The colored pencils does jaime have more than talisa is 24

An arithmetic operator is a mathematical function that takes two operands and performs a calculation on them.

They are used in common arithmetic and most computer languages contain a set of such operators that can be used within equations to perform a number of types of sequential calculation. Basic arithmetic operators include:

:-Addition (+)

:-Subtraction (-)

:-Multiplication (×)

:-Division (÷)

so;

     A.T.Q:-

     The colored pencils does talisa have are 34

     The colored pencils does  jaime have are 58

   ∴ by using arithmetic operator Subtraction (-) , we conclude that how more colored pencils does jaime have than talisa

 ∵ jaime's colored pencils - talisa's colored pencils

 ⇒ 58-  34

 ⇒24

 hence; jaime have 24 pencils more than talisa

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The midpoint, that is the middle point of any given line segment can be calculated if the endpoints have been made available.

The endpoints for the line segment is,

(7, 5) and (-3, -5) for points X and Y respectively.

The middle point can be found at this position;

(x1 + x2) / 2 and (y1 + y2) / 2

The points are shown as

(7, 5) = (x1, y1)

(-3, -5) = x2, y2)

Therefore we now have,

Midpoint = (7 + [-3])/2 and (5 + [-5])/2

Midpoint = (7-3)/2 and (0)/2

Midpoint = 4/2 and 0/2

Midpoint = (2, 0)

We're given : x+y+z = 4
x = -2y
z = -3y

So, we replace x = -2y and z = -3y in the original equation.

-> -2y + y + -3y = 4
-> -4y = 4
-> y = -1

Now we have the value of y, we substitute it into x and z
x = -2y = -2(-1) = 2
z = -3(-1) = 3