Truck 202 started with a full tank of fuel on Monday morning and the odometer reading was 78467. On Friday, it took 241 gallons of diesel fuel to fill the tank and the odometer reading was 80293. How many miles was the truck driven between fill-ups?

The relationship between the variables x and y is a direct variation as the constant of variation 1/3 is the same for all values of x and y

If the values of y varies directly as does of x, then there is a constant say "k" that is true for them, else y does not vary directly as x.

For x = 3 when y = 9, we can solve for the constant k as follows:

3 = k9

we divide through by 9

3/9 = k9/9

k = 1/3

The constant 1/3 is same for x = 9 when y = 27, x = 13 when y = 39, and x = 20 when y = 60.

Therefore, the relationship between the variables x and y is a direct variation as the constant of variation 1/3 is the same for all values of x and y.

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Two ancient mathematics concepts are given as follows:

The Egyptians used fractions extensively in their calculations and were the first civilization to develop a notation for fractions. Their notation used a symbol for the numerator placed above a symbol for the denominator, similar to our modern fraction notation.

Euclid's Elements is one of the most influential works in the history of mathematics. It provided a systematic and rigorous approach to geometry, which has been the basis of mathematical education for over two thousand years.

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Thus, we can be 90% confident that the true proportion of men in the college is between 8.8% and 14.0%.

Percent, denoted by the symbol "%", is a way of expressing a number as a fraction of 100. For example, 50% is equivalent to the fraction 50/100, which can be simplified to 1/2. Percentages are commonly used to express ratios, proportions, or rates in various contexts such as finance, statistics, and everyday life. For instance, an interest rate of 3% means that for every $100 borrowed, the borrower will be charged $3 per year. Similarly, a score of 80% on an exam means that the student has answered 80 out of 100 questions correctly.

by the question.

To find the confidence interval of the true proportion of men in the college, we need to use the formula:

[tex]CI = p ± z\sqrt((p(1-p))/n)[/tex]

where p is the sample proportion (80/700 = 0.114), z is the z-score associated with the confidence level (90% in this case), and n is the sample size (700).

To find the z-score, we can use a standard normal distribution table or a calculator. For a 90% confidence level, the z-score is approximately 1.645.

Plugging in the values, we get:

[tex]CI = 0.114 ± 1.645\sqrt((0.114(1-0.114))/700)[/tex]

Simplifying, we get:

[tex]CI = 0.114 ± 0.026[/tex]

Therefore, the 90% confidence interval for the true proportion of men in the college is:

[tex]CI = 0.114 ± 0.026[/tex]

Rounding to the nearest tenth of a percent, we get:

CI = (8.8%, 14.0%)

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Therefore , the solution of the given problem of circle comes out to be the circle's radius is about 5.2 centimetres.

A circle is formed by each region of a plane that is a certain distance from this extra point (center). It thus consists of spots that are isolated from one another by the surface and is curved. It also revolves about the centre equally from all angles. In the constrained, the double sphere of a circular, every group of endpoints is uniformly separated from the "centre." By tracing a thread through a circle, one can create a line to circular symmetry. Additionally, it rotates evenly in all directions around the centre.

Here,

The following equation determines the extent of a circle's arc:

=> arc length = radius * central angle

We can determine the radius by solving for the centre angle,

which is known to be 2.3 radians, and the arc length, which is 12 cm:

=> radius = arc length / central angle

=> 12 cm / 2.3 radians

=> 5.22 cm

We calculate the radius to be 5.2 cm by rounding to the closest tenth. As a result, the circle's radius is about 5.2 centimetres.

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The total number of outcomes in the quiz is 8

From the question, we have the following parameters that can be used in our computation:-

Using the above as a guide, we have the following:

For each question, there are two possible outcomes: true or false.

So, the total number of outcomes for all three questions is:

Total = 2 x 2 x 2

Evaluate

Total = 8

Hence, there are 8 possible outcomes in total.

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Complete question

Find the total number of outcomes of the following experiment

There are 3 true-false questions on a quiz.

Answer:

Traingle=180 degrees

U=54

180-54

=126

126/2

=63

R=63

U=54

T=63

Answer:

368.49 cm3

Step-by-step explanation:

[tex]2.9kg=(2.9)(1000)=2900g[/tex]

[tex]V=2900/7.87[/tex]

[tex]368.49 cm^{3}[/tex]

nearest hundredth

Hope this helps.

If I were to run this company, I would be concerned about the discrepancy between the allocated budget and the actual spending in the graph.

Graph is a mathematical structure used to represent relationships between objects. It consists of vertices (also known as nodes) which represent the objects and edges (also known as arcs) which represent the relationships between the objects. Graphs are often used to represent networks, such as social networks, transportation networks, and communication networks. Graphs can also be used to represent data structures, such as trees and linked lists.

In particular, the finance, admin, marketing, HR, and developer departments all have allocated budgets that are greater than their actual spending. This could be a sign that the company is not utilizing its resources efficiently, since it is not spending up to its allocated budget. The discrepancy between allocated budget and actual spending could also indicate that the company is wasting money on unnecessary projects, or that its budget is not allocated correctly.

Furthermore, the customer support department has allocated budget of $100k, yet its actual spending is only $50k. This could indicate that the company is not providing adequate customer support, which could lead to customer dissatisfaction and a decrease in customer loyalty. It could also mean that the company is not taking advantage of its resources and not utilizing them to their fullest potential.

Overall, the discrepancy between the allocated budget and the actual spending could be a sign of inefficiencies and mismanagement within the company. As the company’s leader, I would be concerned about the implications of this discrepancy and would take steps to ensure that the company is utilizing its resources correctly and efficiently.

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Therefore , the solution of the given problem of triangle  comes out to be segments LM and MN have equal 10x measures.

A triangle is a polygon because it has two or more additional parts. It has the simple form of a rectangle. A triangle can only be distinguished from a conventional triangle by its three sides, A, B, but not C. So when borders are still not exactly collinear, Euclidean geometry results in a single area as opposed to a cube. Three edges and three angles are the characteristics of triangles.

Here,

Given that RS and LM are the respective sides of the two triangles, if we set x as the length of RS, then LM's length is 5x and ST's length is 2x. The duration of MN is five times that of ST, which is ten times longer.

We can now calculate the length of RS using the tangent of angle R:

=> tan R=RS/ST

=> 5/2.5=2

We thus have:

=> RS = 2

=> ST = 2x

We can determine the length of RT using the Pythagorean theorem:

=> RT/ST = sin R

=> RT = ST sin R

=>  2.5 (2/29) = 4.337 sin R = 2.5

We can now determine the lengths of LM and MN using the similarity of the triangles:

=> RM = 5 (2x) LM = 5 = 10

=> MN = 5 ST = 5 (two times) = 10

As a result, segments LM and MN have equal 10x measures.

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The values of LM = 12.5 and MN = 25

A triangle is a closed geometric figure consisting of three line segments or sides, connected to each other at three endpoints or vertices. Each side of a triangle intersects with exactly two other sides, and the vertices are the points where the sides meet.

From the given figures, both the triangles are right angle triangle.

[tex]tan R=\frac{5}{2.5} = \frac{ST}{RS}[/tex]

So, ST = 5 and RS = 2.5

Since, ΔRST is 5th to create ΔLMN,

its corresponding sides are 5 times the length LM corresponding sides of RS. So, its length

LM = 5×2.5 = 12.5

LM = 12.5

MN corresponding sides of ST. So, its length

MN = 5×5 = 25

MN = 25

Therefore, The values of LM = 12.5 and MN = 25.

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Answer:Answer:

median=10, 6 numbers, so median is between 3rd and 4th

.. 9 11 . .

mode=11

.. 9 11 11 .

range=4

7 8 9 11 11 11

Step-by-step explanation:

If the company sells more than 3,000 pairs of socks per month, it will make a profit.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To analyze the profit of the Sock Company, we need to consider the total cost and total revenue.

Let's start with the total cost:

The cost per pair of socks is $6.

If x is the number of pairs of socks sold, then the total cost is 6x.

There is also a fixed cost of $12,000 per month.

So, the total cost can be expressed as:

C(x) = 6x + 12,000

Now, let's move to the total revenue:

The selling price per pair of socks is $10.

If x is the number of pairs of socks sold, then the total revenue is 10x.

So, the total revenue can be expressed as:

R(x) = 10x

The profit is the difference between the total revenue and total cost:

P(x) = R(x) - C(x) = 10x - (6x + 12,000) = 4x - 12,000

To find the range of x where the company makes a profit, we need to set P(x) greater than 0:

4x - 12,000 > 0

4x > 12,000

x > 3,000

Therefore, if the company sells more than 3,000 pairs of socks per month, it will make a profit.

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Answer: 56 cm

Step-by-step explanation:

Answer:

the length of IJ is 7.2 units.

Step-by-step explanation:

Since IJ is parallel to LM, we can use the property of similar triangles to solve for IJ.

Triangles KIJ and KLM are similar, so we have:

IJ/KL = KI/LM

Substituting the given values, we get:

IJ/8 = 18/20

IJ/8 = 9/10

Multiplying both sides by 8, we get:

IJ = (8)(9/10)

IJ = 7.2

Therefore, the length of IJ is 7.2 units.

Answer:

PS=21.3

Step-by-step explanation:

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Individual insurance is designed tο prοtect individuals and their families against the financial impact οf events such as illness, disability, accidents, οr death.

Individual insurance and business insurance are similar in that bοth prοvide financial prοtectiοn against risks and uncertainties. Hοwever, there are alsο significant differences between the twο types οf insurance.

Individual insurance is designed tο prοtect individuals and their families against the financial impact οf events such as illness, disability, accidents, οr death.

Business insurance is designed tο prοtect businesses against the financial impact οf events such as prοperty damage, liability claims, οr lοss οf incοme due tο interruptiοn οf business οperatiοns.

The similarities between individual insurance and business insurance include:

The differences between individual insurance and business insurance include:

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Answer:

2 * 3 * 5

Step-by-step explanation:

The factors of 30 are 1,2,3,5,6,10,15, and 30. Lets just pick out the prime numbers from this and see if they multiply to 30.

[tex]2\times 3\times 5=30[/tex]

Therefore , the solution of the given problem of volume comes out to be  has a volume of 256 cubic centimetres.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The symbols cm3 and in3 are two examples of cubic measures. However, the bulk of an item may be employed to estimate its size. Usually, the weight of an item is converted into mass measures like grams and kilos.

Here,

The formula: gives the capacity of a pyramid.

=> V = (1/3)Bh

where B is the base's size and h is the pyramid's height.

The ratio of the volumes of the dilated pyramid to the initial pyramid is (1/4)3 = 1/64 if the scale factor of dilation is 1/4. In other terms, pyramid B's volume is 1/64 that of pyramid A's.

Let V(A) represent the pyramid A's volume. Then:

=> V(B) = (1/64)

=> V(A) = 4

When we multiply both parts by 64, we obtain:

=> V(A) = 256

Pyramid A, the preimage, therefore, has a volume of 256 cubic centimetres.

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Answer:

Since Khrysteen is paid semimonthly, she receives 24 paychecks in a year (12 months x 2 pay periods per month).

To calculate her annual pay, we can multiply her semi-monthly pay by the number of paychecks she receives in a year:

Annual pay = Semi-monthly pay x Number of paychecks in a year

Annual pay = $1,978.50 x 24

Annual pay = $47,484

Therefore, Khrysteen's annual pay is $47,484.

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In response to the given question, we can state that As a result, Igbo expressions experienced a N50.00 loss.

In mathematics, you can multiply, divide, add, or subtract. An expression is formed as follows: Expression, number, and math operator Numbers, parameters, and functions make up a mathematical expression. It is possible to contrast phrases and expressions. Every mathematical statement that comprises variables, numbers, and a mathematical action between them is referred to as an expression. For example, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, all separated by the mathematical symbol +.  

Igbo spent N40.00 on 5 books, for a total of N40.00.

N200.00 = 5 books x N40.00 each

Igbo lost money since he sold the books for N150.00. To find the amount of the loss, subtract the selling price from the cost price:

Cost Price - Selling Price = Loss

N200.00 - N150.00 = Loss

Loss = N50.00

As a result, Igbo experienced a N50.00 loss.

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The side x = 16.72 approximately to two decimal places using the cosine rule.

In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Considering the given triangle, we shall calculate for the side x is using the cosine rule as follows;

a² = b² + c² - 2(b)(c)cosA

x² = 7² + 12² - 2(7)(12)cos121°

x² = 49 + 144 - 168(-0.5150)

x² = 193 + 86.52

x² = 279.52

x = 16.7189 {take square root of both sides}

Therefore, using the cosine rule, we can conclude the value of the side x of the triangle is 16.7189.

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Answer:

26.0 years

Step-by-step explanation:

It will take approximately 16.79 years (to the nearest hundredth) for the initial mass of 20 grams to decay to four grams, given a constant decay rate of 6% per year.

To determine how long it will take for the 20 grams of the element to decay to four grams, we need to calculate the time using the given decay rate.

Given:

Initial mass (M₀) = 20 grams

Decay rate: 6% per year

Let's set up an equation to represent the decay of the element:

M(t) = M₀ * (1 - r)^t

Here, M(t) represents the mass at time t in years, M₀ is the initial mass, r is the decay rate (expressed as a decimal), and t is the time in years.

We want to find the value of t when M(t) = 4 grams:

[tex]4 = 20 * (1 - 0.06)^t[/tex]

Dividing both sides by 20:

[tex]0.2 = (1 - 0.06)^t[/tex]

Taking the natural logarithm of both sides:

[tex]ln(0.2) = ln[(1 - 0.06)^t][/tex]

Using logarithmic properties, we can simplify further:

[tex]ln(0.2) = t * ln(1 - 0.06)[/tex]

Now, we can solve for t by dividing both sides of the equation by ln(1 - 0.06):

t =[tex]ln(0.2) / ln(1 - 0.06)[/tex]

Using a calculator, we find:

t ≈ 16.79 years

Therefore, it will take approximately 16.79 years (to the nearest hundredth) for the initial mass of 20 grams to decay to four grams, given a constant decay rate of 6% per year.

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The statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" is false.

In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables (unknowns) and specifies a relationship between those variables. Equations are used to model real-world phenomena, solve problems, and make predictions. There are many types of equations in mathematics, including linear equations, quadratic equations, polynomial equations, exponential equations, trigonometric equations, and many more. Each type of equation has its own set of methods and techniques for solving it.

Here,

To determine which statements are true about the circle whose equation is x2 + y2 – 2x – 8 = 0, we can use the standard form of the equation of a circle, which is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Comparing the given equation to the standard form, we can complete the square by adding 1 to both sides:

x² - 2x + y² - 8 = -1

(x - 1)² + y² = 9

From this, we can see that the center of the circle is (1, 0) and the radius is 3 units. Therefore, the statements that are true are:

The center of the circle does not lie on the x-axis, so the statement "The center of the circle lies on the x-axis" is false.

The center of the circle does lie on the y-axis, so the statement "The center of the circle lies on the y-axis" is true.

The standard form of the equation is (x - 1)² + y² = 3, so the statement "The standard form of the equation is (x - 1)² + y² = 3" is true.

The radius of this circle is not the same as the radius of the circle whose equation is x² + y² = 9, so the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" is false.

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The area of trapezoid ABCD is 39 ft².

A trapezοid is a quadrilateral with twο sides that are parallel. It has fοur sides, fοur angles, and twο pairs οf οppοsite sides that are equal in length. The nοn-parallel sides, οr legs οf the trapezοid, are usually referred tο as the bases οf the trapezοid. The twο parallel sides are referred tο as the bases, the nοn-parallel sides are referred tο as the legs, and the line cοnnecting the twο parallel sides is called the midline. The angles created by the bases and the legs are called the base angles

Area of trapezoid = [tex]\dfrac{a + b}{2} h[/tex]

Here, a = 5ft

b = 21 ft

h = 3ft

Area of trapezoid = [tex]\dfrac{5 + 21}{2} (3)[/tex]

Area of trapezoid = 39 ft²

Thus, The area of trapezoid ABCD is 39 ft².

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Answer:

12

Step-by-step explanation:

7+5

Answer:

.

Step-by-step explanation:

The distance between two points (x1, y1) and (x2, y2) is given by the formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Here, (x1, y1) = (-7, 3) and (x2, y2) = (5, 3).

Substituting these values, we get:

d = sqrt((5 - (-7))^2 + (3 - 3)^2)

= sqrt((12)^2 + (0)^2)

= sqrt(144)

= 12

Therefore, the distance between (-7, 3) and (5, 3) is 12 units.

Answer:

for what value of y is the rational expression y+6÷2y-3 be yndefined?

The translation that maps K onto K' is a horizontal translation of 2.8 ft to the right, followed by a vertical translation of 5.6 ft downwards.

We first need to know the distance and direction of the two reflections in order to find the single translation that maps K onto K'.

When figure K is mirrored across line p, figure K" is the resultant image:

K'  K''

      |  |

      |  |

p ------   ------ d

      |  |

      |  |

     K   K'

We can see that the distances between K and p and K" and p, as well as K and d and K" and d, are the same. Because of this, K and K" are separated by a distance that is 2 2.8 feet longer than K and d.

When positioned above line D, figure K"s reflected image is K". This reflection, being perpendicular to p, has no impact on the horizontal placement of K" in regard to K'. K" is now beneath K', although the vertical axis has changed.

K'  K''

      |  |

      |  |

p ------   ------ d

      |  |

      |  |

     K'' K'

Consequently, a horizontal translation of 2.8 feet to the right, then a vertical translation of 5.6 feet downward, is the translation that maps K onto K'. The straightforward translation is:

(x, y) → (x + 2.8, y - 5.6).

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Answer: 1, 5, 11, 55

Step-by-step explanation:

Answer:

x=522/163

Step-by-step explanation:

14(12x−36)=5x+18

168x-504=5x+18

168x-504+504=5x+18+504

163x=522

163x/163=522/163

x=522/163

x=3.20

Answer:

I got 3.2 in decimal form or 522/163 in a fraction

Answer: Since the alloy is made up of 93.5 parts aluminum, 5 parts zinc, and 1.5 parts copper, we can express the weight of zinc and copper needed to make the alloy as a ratio to the weight of aluminum needed. Let x be the weight of aluminum needed in pounds, then we have:

Weight of aluminum: Weight of zinc: Weight of copper = 93.5: 5 : 1.5

We know that the foundry has 164 pounds of aluminum available, so we can substitute x = 164 into the above ratio and solve for the weights of zinc and copper:

164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5

Cross-multiplying, we get:

164 × 5 = 93.5 × Weight of zinc

Weight of zinc = (164 × 5) / 93.5

Weight of zinc = 8.76 pounds (rounded to two decimal places)

Similarly, cross-multiplying the above ratio gives us:

164: Weight of zinc: Weight of copper = 93.5: 5 : 1.5

164 × 1.5 = 93.5 × Weight of copper

Weight of copper = (164 × 1.5) / 93.5

Weight of copper = 2.63 pounds (rounded to two decimal places)

Therefore, the weight of zinc needed to make the alloy is 8.76 pounds and the weight of copper needed is 2.63 pounds.

Step-by-step explanation: