Jason uses his car for business. He must keep accurate records so his company will reimburse him for his car expenses. When he started his trip, the odometer read 42,876. 1. When he ended the trip, it read 43,156. 1. Jason's car gets 35 miles per gallon. His tank was full at the beginning of the trip. When he filled the tank, it cost $17. 20. What price did he pay per gallon of gas on this fill-up?.

Answer:

A 5 and -5

Step-by-step explanation:

You take the root of both sides to solve.

The method used by Horace to select his sample is Systematic Sampling.

A form of probability sampling technique called systematic sampling selects sample members from a broader population using a predetermined, periodic interval in addition to a random beginning point. The population size is divided by the intended sample size to arrive at this range, which is known as the sampling interval.

Horace desires to select every 1000th person to enter the park, starting with the 364th person. So he selects the 364th person, 1364th person, 2364th person, and so on. This is a perfect situation for Systematic Sampling.

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By entering the values of m and b into the slope-intercept form of a line (y = mx + b), you may obtain the equation for the line.

Given,

Equation of a line;

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

We have to find the equation of a line with 2 points;

Here,

Slope, m = (y₂ - y₁) / (x₂ - x₁)

The x and y of your equation y = mx + b can be replaced by one of your points, and the m can be replaced by the slope you just calculated. The only variable remaining is b in such case. To solve for b, use the same methods you would to solve for a variable.

Therefore,

You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of a line (y = mx + b).

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0.0405 is the number that contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.

According to collect from the data

Let us assume that the data as followed by

How many eight digit numbers contain the digit 2 exactly once, the digit 3 exactly twice, the digit 4 exactly thrice and more 5s than threes.

Let many eight digit numbers contain the digit 2 once, the digit 3 twice the digit 4 thrice and more 5s than threes.

2,3,3,4,4,4

now then:

= 8!/2!3!3!4!4!4!

= 8.7.6.5.4!/2×6×6×24×24×4!

= 35/864

Now 0.405 then the eight digit number contains the digit 2 once the digit 3 .

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The teenager whom attended a football game will be 575 people.

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The number of pens the store manager purchase, if A store manager purchased a total of 15 pens and markers, is 7.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

A store manager purchased a total of 15 pens and markers. Each pen cost $3.50, and each marker cost $1.75, the manager spent a total of $38.50,

Write the equation of the statement as shown below,

x + y = 15  and 3.5x + 1.75y = 38.5

Here, x is the number of pens and y is the number of markers,

Solve the equations by using the elimination method,

x = 7, y = 15 - 7 = 5

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The number of times to get a 3 will be 24 times.

It should be noted that the expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables

In this case, Jimm tossed a die several times and he got the number "3" on 8 of the tosses.

Therefore, when there are 64 tosses, the estimate will be:

= 3/8 × 64

= 3 × 8

= 24

The number of times is 24.

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Jimm tossed a die several times. He got the number "3" on 8 of the tosses. What is the best estimate of the total number of times he tossed the die 64 times?

The required coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3) are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].

To determine the coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3), we need to apply these transformations to the coordinates of the original vertices in the order given.

First, we rotate the triangle 90 degrees counterclockwise around the origin. This transformation can be represented by the matrix:[cos(90) -sin(90)][sin(90) cos(90)]

Applying this matrix to the coordinates of the vertices of △ABC, we get:A' = [-5, 4]B' = [6, -3]C' = [8, -1]

Next, we reflect the triangle across the line y=0.

This transformation can be represented by the matrix:[-1 0][0 1]

Applying this matrix to the coordinates of the vertices of △ABC', we get:A'' = [5, 4]B'' = [-6, -3]C'' = [-8, -1]

Finally, we translate the triangle according to the rule (x+3,y-3).

This transformation can be represented by the matrix:[1 0][0 1]

Applying this matrix to the coordinates of the vertices of △ABC'', we get:A''' = [8, 1]B''' = [-3, -6]C''' = [-5, -4]

Therefore, the coordinates of the vertices of △ABC after given transformations are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].

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The radius of a circle with equation is x² + y² + 8x - 6y + 21 = 0 is 2  units .

In the question ,

it is given that ,

the equation of circle is ⇒ x² + y² + 8x - 6y + 21 = 0 ,

we know that the general equation of the circle is x²+y²+2fx+2gy+c=0

so , the radius of the circle is calculated using the formula ,

radius = √(f² + g² - c)

On comparing the given equation with general equation

we get , the values of f as 4 and g as -3 .

So after substituting the values of f , g and c in the radius formula ,

we get ,

radius = √(16 + 9 - 21)

= √(16 + 9 - 21)

= √(25 - 21)

= √(4) = 2 .

Therefore , the radius of given circle is 2 units .

The given question is incomplete , the complete question is

What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0  ?

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The area of the rectangular park is 143360 square yards.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 hour = 60 minutes

1 minute = 60 second

1 km = 1000 m

We have,

Scale drawing of a rectangular park:

Wide = 5 inches

Length = 7 inches

Actual rectangular park:

Wide = 320 yards

Length = 448 yards

Now,

5 inches = 320 yards

7 inches = 7/5 x 320 yards

7 inches = 7 x 64 yards

7 inches = 448 yards

Now,

The area of the actual park.

= Length x Wide

=  448 x 320

= 143360 square yards.

Thus,

143360 square yards is the area of the actual park.

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Answer:

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

Linear function is:

Given points:

The first point represents the y-intercept, b = - 4.

Find the slope:

The function is:

The number of peanuts that Alex had initially will compute to a total of 108 in the observations of the situation provided above.

The computation of the peanuts in the hands of Alex can easily be ascertained using the given information, and input of values from the same into the generalized formula, as shown below,

Let p be the number of peanuts. Thus, it can be stated that

3p = 444 – 9 – 25 – 5

3p = 409

p = 409/3 = 135.3

Now, it can also be stated that

p+9=144

[tex]\[\dfrac{144}{k} + 144 + k \cdot 144 = 444 \\\\ \\\dfrac{144}{k} + k \cdot 144 = 300\\\\ \\ \dfrac{12}{k} + k \cdot 12 = 25\\\\\\k= \dfrac{4}{3} \\\\\\\\ \dfrac {144\cdot 3}{4} =108}\][/tex]

Therefore, Alex has a total of 108 peanuts initially.

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Complete question

Initially, Alex, Betty, and Charlie had a total of 444 peanuts. Charlie had the most peanuts, and Alex had the least. The three numbers of peanuts that each person had formed a geometric progression. Alex eats 5 of his peanuts, Betty eats 9 of her peanuts, and Charlie eats 25 of his peanuts. Now, the three numbers of peanuts each person has forms an arithmetic progression. Find the number of peanuts Alex had initially.

The slope of Line P Q is (v - z) divided by (w - x). The slope of Line P prime Q prime is

(v + b) - (z +b) divided by (w + a) - (x + a). Both lines have a slope that is (v - z) divided by (w - x). Therefore, the lines are parallel.

Slope of line :

Line slope is a measure of the slope and direction of a line. Finding the slope of a line in the coordinate plane helps predict whether the line is parallel or perpendicular without actually using a compass. The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line.

The formula for the slope is

m = (y₂ - y₁)/ (x₂ - x₁)

Where (x₁, y₁) and (x₂, y₂) are the points

We have given a line PQ passing through points (x,z ) and (w,v) then slope of line is

m = ( v- z)/(w-x) --(1)

that is line lie in XZ- plane .

The slope of line p prime and q prime

m' = (( v- b) - (z-b))/(w-a)- (x-a)

= (v -b -z + b) /(w-a -x + a)

= (v-z)/(w-x) --(2)

from (1) and (2) we get , m = m'

So, both lines are parallel lines .

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Complete question:

The slope of Line P Q is (v - z) divided by ________. The slope of Line P prime Q prime is _________ divided by (w + a) - (x + a). Both lines have a slope that is _______ divided by _______. Therefore, the lines are _______.

Answer: in the picture

Step-by-step explanation:

The point-slope form of the equation of Street D is; y = 0.8·(x - 5)

The point-slope of the equation of straight line can be expressed mathematically as (y - y₁) = m·(x - x₁)

The coordinates of the point

The x-intercept of the street D = 5

The y-intercept of the street D = -4

The x-intercept is the point the graph of the equation of the street intersects the x-axis.

At the x-intercept, the y-coordinate of the point of the graph is 0, therefore, the coordinate of the x-intercept is (5, 0)

The y-intercept is the point at which the graph of the function intersects the y-axis, therefore, the x-coordinate of the graph at the y-intercept is 0

The y-intercept of the street D is therefore; (0, -4)

The slope, m, of the equation of the street is therefore;

m = (-4 - 0)/(0 - 5) = 4/5 = 0.8

The point-slope form of the equation, using the x-intercept, (5, 0) is therefore;

y - 0 = 0.8·(x - 5)

y = 0.8·(x - 5)

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The two-column proof shows that LP = LQ

LP = √(LM² + PM²)

LQ² = √(LM² + PM²)

LP = LQ

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Point M is the midpoint of PQ.

This means,

PM = QM ______(A)

LM is the perpendicular bisector of PQ .

           L

      /    |    \

   /       |       \

/          |         \

P         M         Q

Applying the Pythagorean theorem.

Triangle LMP is a right triangle.

LP = LM² + PM² _____(1)

Triangle LMQ is a right triangle.

LQ² = LM² + QM² _____(2)

Thus,

From (A), (1), and (2) we get,

LP = √(LM² + PM²)

LQ² = √(LM² + PM²)

LP = LQ

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Answer:

a. shen's car

8 gallons

b. 400 miles

shen's car

The rules SSS SAS ASA and AAS are the rule that is used to prove the congruence of the triangle

The rules  SSS SAS ASA and AAS are used to prove the congruence of the triangles .

The congruence  means if shape and size of the one shape is same as the shape and size of the another shape, then we can say that both the shapes are congruent

If you consider the case of triangle, two triangle can be prove as congruent if the specifics sides and angles of the triangle is equal to the other triangles.

The rules that used to prove the congruence of the triangles are

SSS - side-side-side rule of congruence

SAS = side-angle-side rule of congruence

ASA = angle-side-angle rule of congruence

AAS = angle-angle-side rule of congruence

Therefore, these rules are used to prove the congruence of the triangle

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Answer:

Step-by-step explanation:

180=28+73+x

180-28-73=79

79=x

Answer:

To turn the given statement into an inequality, we can write it in the form "m - s >= 8", which means that the amount of money you have (m) minus the amount you spend on snacks (s) must be greater than or equal to 8. This inequality represents the constraint that your mom has placed on your spending, requiring you to spend at least $8 on the pizza. In mathematical notation, the inequality would be written as:

m - s >= 8

This inequality states that the amount of money you have, minus the amount you spend on snacks, must be greater than or equal to 8 in order for you to be able to buy the pizza.

Step-by-step explanation:

The range of the data-set in this problem has a value given as follows:

7.7.

The range of a data-set is calculated as the difference between the largest value of the data-set and the smallest value of the data-set.

The data-set in this problem is defined as follows:

{6.2, 9.1. 2.9, 1.6, 9.3, 5.5, 8.3}

Hence to obtain it's range we have to obtain the smallest and the highest values from these values between the brackets.

The smallest value of the data-set and the highest value of the data-set are defined as follows:

Hence the range of the data-set is given by the difference of 9.3 and 1.6, as follows:

Range = 9.3 - 1.6 = 7.7.

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Answer:

The right answer is C.

Step-by-step explanation:

The parent function is:

[tex]f(x)=x^3[/tex]

If something is subtracted from variable [tex]x[/tex] it means the graph shifted toward right and something is added to [tex]y[/tex] value then the graph is shifted up.

[tex]f(x)=(x-8)^3[/tex]

graph shifted toward right by [tex]8[/tex] units right

[tex]f(x)=(x-8)^3+3[/tex]

graph shifted toward right by [tex]3[/tex] units up

Thus the new function is:

[tex]g(x)=(x-8)^3+3[/tex]

Answer:

12%

Step-by-step explanation:

Christy Peterson's total income last year was $77,340. Of that amount, she spent $7,240 on transportation costs and $2,100 on clothing. What percent of Christy's total income did she spend on transportation and clothing combined? Round your answer to the nearest percent.

7,240 + 2,100 = $9,340

9,340 / 77,340 = 0.120765

0.120765 * 100 = 12.0765%

rounded = 12%

The side JE is equal to side IE because all the sides of the square are congruent.

It is a polygon with four sides. The total interior angle is 360 degrees. In a square, all the sides of the square are equal and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.

JH is opposite to JE and Hello is opposite to IE. Also, JH is congruent with HE.

Let 'm' be the side of the square.

HI = JE         (Congruent)

HJ = IE         (Congruent)

∠H = ∠J = ∠I = ∠E = 90°

Then the shape that is defined will be a square.

The side JE is equal to side IE because all the sides of the square are congruent.

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Answer: 5/4, -7/11, 1/2

Step-by-step explanation:

Slope of ordered pairs (y2-y1/x2-x1): -5/4

Y intercept (b in y=mx+b): (0, -7/11)

Slope of graph (rise over run) : 1/2

Length and width should the rectangle have so that its area is a maximum are 4.242 and 2.121 respectively.

From the question, we have

Area = A = xy

A = xsqr(9-x^2)

Taking the derivative and set = 0

A' = (x/sqr(9-x^2)(-2x) + sqr(9-x^2) = 0

A' = -x^2 + 9 -x^2 = 0

-2x^2 =-9

x^2 = 9/2

x = 3/sqr2 = (3/2)sqr2 = 4.242

y = sqr(9-x^2) = sqr(9-9/2) = 3sqr2/2 = 2.121

Dimensions of the rectangle are 4.242 and 2.121 respectively

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

Complete question:

A rectangle is bounded by the x-axis and the semicircle y = radical 9 − x^2 (see figure). What length and width should the rectangle have so that its area is a maximum?

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Answer:

7) d (21)

6) a (102)

Step-by-step explanation:

For the first question, we should start with what we know first:

When angles are complementary then, their angles add up to 90.

So here we have 69 + something = 90.

We find out that the missing angle (angle B) is 21.

For this second question, we know that a straight line has an angle of 180. Here we have a straight line, but only part of the angle in which we only have 78.

Since we know 78 + x = 180

Then we can figure out that x = 102.

Answer:

Since there are no abcd options, I'll just give the answer here: 3/4 divided by 5/7 is 21/20

Step-by-step explanation:

First, we have to convert the division sign to a multiplication sign, so we do that by using the reciprocal of the second fraction:

3/4 divided by 5/7 will turn into 3/4 * 7/5

Here is how to solve that:

3           7

--     *    --

4           5

3*7 is 21, and 4*5 is 20, so the final fraction is 21/20, final answer.

Answer:

6

Step-by-step explanation:

The y intercept is when x=0

Answer:x2 - 2x = 4x + 1" and "9x2 + 6x - 3 = 0

Step-by-step explanation: that will be your quadratic equation

The population standard deviation of the data is gotten from using the sum of squares and count which gave us 1.5

Standard deviation is used to find the values of a particular data that is dispersed or scattered. Standard deviation can be defined as the deviation of the values or data from an average mean. Lower standard deviation assumes that the values are very close to their average. Meanwhile higher values mean the values are far from the mean value. Note that the value of standard deviation value can never be negative.

The data given is

5, 8, 8, 5

The formula is given as

δ = √(μ / n)

δ = √(9/4)

δ = √2.25

δ = 1.5

The standard deviation is 1.5

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