1. The population average fuel efficiency of U.S. light vehicles for 2005 was 21 mpg. If the standard deviation of the population was 2.9 and the gas ratings were normally distributed, what is the probability that the mean for a random sample of 25 light vehicles is under 20 mpg

Answer:

Step-by-step explanation:

To plot points P (-5/2), Q (2 3/4), R(1.25), and S(-3.5) on a number line, we can simply draw a horizontal line and mark off the positions of the points. The numbers on the number line will represent the values of the x-coordinates of the points.

[asy]

unit size(1cm);

draw((-7,0)--(5,0));

draw((-7,0)--(-7,1)--(5,1)--(5,0)--cycle);

dot("$P$", (-5/2,0), S);

dot("$Q$", (2 3/4,0), S);

dot("$R$", (1.25,0), S);

dot("$S$", (-3.5,0), S);

[/asy]

On the number line, point P is located at -5/2, point Q is located at 2 3/4, point R is located at 1.25, and point S is located at -3.5.

Answer:

B) 2 + 3x = 8

Step-by-step explanation:

Option B is not an expression as expressions do not have equal signs.

The table that is a justification for the given solution to the system of equations is table 1

The two linear equations are

y=4x-9 and

y=2x-5

We that the following points for x : -1, 0, 1, 2, 3

When we substitute the values in the two equations we will have

x           y₁              y₂

-1         -13             -9

0           -9             -5

1             -5            -3

2            -1              - 1

3            3                1

Conclusively the values of y₁, and y₂ are shown in the table above

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The value u > -16 that makes the inequality 5u > -80 is true.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

We have the inequality,

5u > -80

To find the solution set of the inequality;

Divide by 5 to both sides,

5u/5 > -80/5

u > -16.

That means, the inequality is true for u > -16.

Therefore, the inequality is true for u > -16.

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Answer:

[tex]b = 90[/tex]

[tex]d = 100[/tex]

[tex]c = 80[/tex]

Step-by-step explanation:

The problem is asking for the values of the variables [tex]b[/tex], [tex]c[/tex], and [tex]d[/tex] in the given parallelogram with angles [tex]d\textdegree[/tex], [tex]c\textdegree[/tex], [tex](b-10)\textdegree[/tex], and [tex](b+10)\textdegree[/tex].

To solve for these variables, we can construct three equations using the knowledge that any two adjacent angles of a parallelogram are supplementary (their measures add to 180º).

The first equation shows that the top two angles are supplementary:

[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]

The second equation shows that the bottom two angles are supplementary:

[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]

The third equations shows that the left two angles are supplementary:

[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]

First, we can solve for [tex]b[/tex] in the second equation using simple algebraic manipulation.

[tex](b-10)\textdegree + (b+10)\textdegree = 180\textdegree[/tex]

[tex](b+b)\textdegree + (10-10)\textdegree = 180\textdegree[/tex]

[tex]2b\textdegree = 180\textdegree[/tex]

[tex]b\textdegree = 90\textdegree[/tex]

[tex]b = 90[/tex]

Using this [tex]b[/tex]-value, we can solve for [tex]d[/tex] by rewriting the third equation, plugging [tex]90[/tex] in for [tex]b[/tex]:

[tex]d\textdegree + (b-10)\textdegree = 180\textdegree[/tex]

[tex]d\textdegree + (90-10)\textdegree = 180\textdegree[/tex]

[tex]d\textdegree + 80\textdegree = 180\textdegree[/tex]

[tex]d\textdegree = 100\textdegree[/tex]

[tex]d = 100[/tex]

Finally, we can solve for [tex]c[/tex] in the first equation by plugging [tex]100[/tex] in for [tex]d[/tex]:

[tex]d\textdegree + c\textdegree = 180\textdegree[/tex]

[tex]100\textdegree + c\textdegree = 180\textdegree[/tex]

[tex]c\textdegree = 80\textdegree[/tex]

[tex]c = 80[/tex]

Between the 100th and 400th kilometers, the average fuel consumption rate is 5/6 liters per kilometer.

A consequence of dividing the variation in a variable's function by the variation in the variable. For example The rate at which a distance changes in relation to time is known as velocity.

Given, Devin drove her truck. The fuel remaining in the truck's tank (in liters) as a function of distance (in kilometers) is graphed.

Since in the domain [100, 400] graph shows somewhat linear properties.

from the graph Fuel consumption at 100 = 375 liters

Fuel consumption at 400 = 125 liters

rate in a linear function between two points = (y₂ - y₁)/ (x₂ - x₁)

thus rate between [100, 400] = (375-125)/400-100

rate between [100, 400]  = 250/300

rate between [100, 400] = 5/6litere per kilometer

therefore, the average fuel consumption rate, between the 100th kilometer and 400th kilometer is 5/6 liters per kilometer.

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Therefore , the solution to the given problem of inequality comes out to be 120d + 1,500 = 110d + 2,500.

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right

Here,

Given : $1,500 a week to a wage

$55 per hour

Thus ,

Taking all the information in concern

We get,

where d is the is he number of hour

120d + 1,500 = 110d + 2,500

Therefore , the solution to the given problem of inequality comes out to br

120d + 1,500 = 110d + 2,500.

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Answer:

gay

Step-by-step explanation:

gayayayayayayaydyfyfaygaygagya

Only when each iteration is sufficiently time-consuming in terms of CPU usage does parallel programming become more effective.

The term "parallel processing" is used to deliver simultaneous data-processing activities, which is utilized to increase the computing performance of computer systems. Additionally, a parallel processing system has the ability to process input concurrently for quicker execution times.

As an illustration, when an instruction is being carried out in an ALU, the following instruction may be read from memory. The system may be equipped with two or more ALUs and be able to carry out multiple instructions at once.

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The domain and range of the function on the graph are:

Remember that for any function y = f(x), we define the domain as the set of possible inputs (possible values of x) and the range is the set of the possible outputs of the function (possible values of y).

To find the domain we need to look at the horizontal axis. The minimum is at x = -2 with a colored circle, so x = -2 belongs to the domain.

The largest value is at x = 1, now with an open circle, then this value does not belong to the domain. Thus the domain is:

D: [-2, 1)

For the range we need to look at the vertical axis, the minimum is at zero and the maximum at 4, then the range is:

R: [0, 4]

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Answer:

f(x + 2) = - 3x - 1

Step-by-step explanation:

substitute x = x + 2 into f(x) , that is

f(x + 2)

= 5 - 3(x + 2)

= 5 - 3x - 6

= - 3x - 1

Area of the region enclosed by one loop of the curve is pi/288.

To find the area of the region enclosed by one loop of the curve, we can use the formula for the area of a polar region:

A = 1/2 * ∫(r^2)dθ

We can use this formula with the equation for r given:

A = 1/2 * ∫(sin^2(6θ))dθ

This integral can be simplified by noting that sin^2(x) = (1/2)(1 - cos(2x))

Thus,

A = 1/2 * ∫(1/2)(1 - cos(12θ))dθ

This integral can be solved by noting that the antiderivative of (1/2)(1 - cos(12θ)) is (1/24)(sin(12θ) + θ).

Therefore, the area enclosed by one loop of the curve is

A = 1/2 * ((1/24)(sin(12θ) + θ)) evaluated from 0 to pi/6

A = (1/48)(sin(2pi) + pi/6)

   = (1/48)(0 + pi/6)

   = pi/288

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The goal of using similarity transformations is to make the evaluation of a matrix's eigenvalues less complicated. In fact, the computation of the eigenvalues would be instantaneous if a given matrix could be translated into a similar matrix in diagonal or triangular form.

A geometric similarity or a matrix transformation that produces a likeness are both covered by the term "similarity transformation."

A conformal mapping with a similarity transformation is one whose transformation matrix A' has the formula A'=BAB⁻¹, where A and A' are referred to as similar matrices.

Space-based items are converted to equivalent objects by similarity transformations. Fractals and iterated function systems have a lot to do with similarity transformations and the idea of self-similarity.

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(0.1), (2,5), (1/2,2), (-1,-1) are the points on graph.

In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph.

A graph is a type of non-linear data structure composed of nodes, also known as vertices and edges. Any two nodes, also referred to as vertices, in a graph are connected by edges. The vertex numbers in this graph are 1, 2, 3, and 5, and the edge numbers are 1, 2, 1, 3, 2, 4, and 5, respectively.

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The coefficient of the variable x  in the expression 4a+3x +a is 3

Given that,

The expression is 4a+3x +a which can be simplified as 4a+3x +a

To find : The coefficient of the variable x in the expression

The coefficient of x in 4a+3x +a is 3

A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6

Coefficient is the number that is beside the variable in the equation.

As we can see that the term that is in multiplication with x is 3

Hence, the coefficient of x in the equation  is 3

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The value for the blanks after calculating the as per the given data is found to be as 4 and 9 respectively.

On solving the question we will get the answer of the final blank as 0.

The question can be rephrased as ,

__x 9 - __ x 4 = ___ - ___ = ___.

Now if we will place 4 in first blank and 9 in second blank we will get the result as follows,

4 x 9 - 9 x 4 = 36 - 36 = 0

Therefore , we will get our desired answer.

A relationship between two quantities or, more broadly, two mathematical expressions that asserts that the quantities have the same value or that the expressions reflect the same mathematical object is referred to as equality.

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Answer: 5.6

Step-by-step explanation:

the opposite of an negative number...

So your answer would be....

        =5.6

Answer:

[tex]5.6[/tex] or [tex]\dfrac{1}{-5.6}[/tex]

Step-by-step explanation:

The additive inverse of [tex]-5.6[/tex] is [tex]-1 \cdot -5.6 = \boxed{5.6}[/tex]

or...

If you mean the multiplicative inverse of  [tex]-5.6[/tex], then the answer would be [tex]\dfrac{1}{-5.6}[/tex]

The solution of this system of linear equations is x=3, y=-5.

To solve this system of linear equations, you can use various methods such as substitution, elimination, or matrices. Here is one way to solve using the substitution method:

4((11+y)/2) + 8y = 24

3((11+y)/2) + 2y = 15

y = -5

x = (11 + (-5))/2

x = 3

4(3) + 8(-5) = 24

3(3) + 2(-5) = 15

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The question is -

Solving a system of linear equations in two variables,

joyce's painting rate in window frames per hour is 1.6 and her painting rate in hours per window frame 0.625.

A unit rate is a ratio between two separate units with one as the denominator. Examples include miles/hour, kilometers/hour, meters/sec, salaries/month, etc. The most fundamental and historically significant field of mathematics is arithmetic, which is also the one we use the most frequently in daily life.

Given, Joyce painted 8 window frames in 5 hours while earning money for college.

Her painting rate in window frames per hour is = 8 /5

Her painting rate in window frames per hour is = 1.6

Her painting rate in hours per window frame is = 5/8

Her painting rate in hours per window frame is = 0.625

therefore, The rate at which Joyce paints is 1.6 window frames per hour and 0.625 hours per window frame.

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Answer:

The value of x is 12.

i think it is correct.

The sequence is going to be {2,−5,2,−5,…}. Since we can see that options A and B are one and the same, the correct answer is options A and B.

A sequence is a successive arrangement of two or more things that are constructed on the basis of a given formula.

Here, the first term is = 2

Each previous term has been multiplied by = -1

And then, it has been subtracted by = 3

So, following the formula given, we conclude that the second value will be = 2×(-1)-3 = -5

Similarly, the formula is going to be applied to the second term now which is -5, and then the third term is going to be = -5×(-1)-3 = 2

In this fashion, we can make the sequence. Options A and B is the correct answer.

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Considering that the quadrilateral EFGH is similar to quadrilateral IJKL the side LI is calculated to be

The side LI is calculated using the concept of similar polygons. This concept allows for the sides to be proportionally equal to each other.

This implies that the factor used for any side will produce same result

let the factor be r and using side HG and JK to solve for the factor r

HG * r = JK

where

HG = 16

JK = 51

substituting the values and solving for r

HG * r = JK

16 * r = 51

r = 51/16

and HE * r = LI

where HE = 9.6

LI = 9.6 * 51/16

LI = 30.6

hence side LI = 30.6

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The probability is 5/32.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

To roll exactly 4 odds out of 5 rolls is [tex](\frac{1}{2} )^{4}\frac{1}{2}[/tex]  where the odds are 1, 3, and 5 for 3/6=1/2 and the other 1/2 is the probability of rolling an even since we want exactly 4 odds.

Since there are 5 dice being rolled there are 5 ways to order them.

So the probability is 5/32.

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Example of perfect square trinomial is: x² + 6x + 9 it is expressed as

(x + 3)²

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Example:

  x² + 6x + 9

= x² + 3x + 3x + 9

= (x +3) (x + 3)

= (x + 3)²

so, this is a perfect square trinomial.

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In order to pay for the sweets, Zachary intends to take $0.30 from each guest that attends the celebration. To pay for the total cost of the sweets, 4 guests are required to attend the party.

We suggest 8 ounces of sweets per visitor when utilizing ounces. A 5 pound bag of candy will thus be enough to satisfy 10 people. The candy bar may have been distributed evenly in the following manner. Since there are four individuals, split each according to who will receive. About half a pound of sweets is given to each visitor. Therefore, you should buy 50 pounds of sweets at the very least if 100 people are expected.

Setting up the confectionery should minimize guest contact with it for hygienic reasons. Tongs and candy scoops in your theme-coordinating color should be provided for bulk candies. Since you don't want your guests to consume too much sugar, smaller serving utensils are preferred.

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Answer:

3/7

Step-by-step explanation:

3 ponies + 3 goats = 6 total

8 rabbit + 6 sheep = 14 total

6/14 simplified is 3/7.

We can plot in the coordinate plane if an ordered pair is known to us.

The space or plane in where location of points is represented by a pair of numerical terms with respect to some reference lines or reference direction is called coordinate plane.

let we have some pair of numerical terms such as A (4, 9) and B (6, 10)

that is needed to plot in the coordinate plane.

At first, we will plot the point A (4, 9)

we will start from the origin and move horizontally along the direction of X axis up to 4 unit. In the next, start again and move up vertically in the direction of y axis up to 9 unit. And we will draw a point at the final location.

By the same way, we can plot the point B.

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Answer:

-225

Step-by-step explanation:

-30*7=-210

-210-15=-225

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