In ∆ABC, AB//QR and AP:PB =BR: RC. With reasons, prove that PQ// BC​

The maximum profit of $3330 can be obtained by manufacturing 80 model A motors and 70 model B motors.

Let A and B denote the number of model A and model B motors to be manufactured, respectively. The goal is to maximize the total profit, which is given by the expression 22A + 15B

The given constraints imply that [tex]$3A + 2B \le 240$, $2A + B \le 210$, and $1.5A + 0.5B \le 120$.[/tex]

We can solve this problem using linear programming. Let P = 22A + 15B denote the total profit. Then, the optimization problem can be written as follows:

Maximize P = 22A + 15B

Subject to [tex]$3A + 2B \le 240$, $2A + B \le 210$, and $1.5A + 0.5B \le 120$.[/tex]

Using the Simplex Method, we obtain the optimal solution: A = 80, B = 70, and P = 2280 + 1050 = 3330$. This implies that the maximum profit is 3330, which is obtained by manufacturing 80 model A motors and 70 model B motors.

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As in the given circle, the measure of the value of ∠X is 115°.

Now, let's look at point X. This point is on the same line as point B and is also on the circle. Since the angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circle, we can find the measure of ∠AXB by first finding the measure of arc ACB. Since arc ACB is subtended by ∠AOC, which measures 90°, we can find the measure of arc ACB by subtracting 40° (the measure of ∠ABC) from 90°. Therefore, arc ACB measures 50°. This means that ∠AXB is half the measure of arc ACB, so ∠AXB measures 25°.

Therefore, the measure of ∠X is 180° minus the sum of ∠AXB and ∠ABC, which gives us:

∠X = 180° - (25° + 40°) = 115°.

So, the measure of ∠X is 115°.

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Complete Question:

If O is the center of the circle of the figure and the ∠ABC = 40°, then the measure of ∠X

The flat fee that the stοre charge $14 and the cοst fοr 7 hοurs is $56. we sοlve this questiοn using linear equatiοn.

An equatiοn is said tο be linear if the maximum pοwer οf the variable is cοnsistently 1. A linear equatiοn with οne variable has the cοnventiοnal fοrm Ax + B = 0. In this case, the variables x and A are variables, while B is a cοnstant.

let f be the tοtal rental cοst οf a vacuum cleaner fοr x hοurs

And, f(x) = 6x + 14 (Given)

Sο The flat fee that the stοre charge $14.

Reasοnable dοmain is 1  ≤  x  ≤  12

The cοst fοr 7 hοurs is,

f(7) = 6(7) + 14 = 56.

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Answer: A. ; [tex]2x-3=7[/tex]

Step-by-step explanation: We are solving for when the value of x is equal to five. Here is proving that the answer to the first question is correct.

[tex]2x-3=7[/tex]

Add 3 to both sides

[tex]2x=10[/tex]

Divide both sides by 2

[tex]x=5[/tex]

Please Mark Brainliest

Answer: A

Step-by-step explanation:

When an equation has a solution for x = some number n, that means the equation is true when you substitute for x=n. In this case, n=5, so we substitute x=5 in all 4 equations. We can notice that A yields 2*5-3=7 -> 10-3=7, which is true. Therefore, A yields a solution for x=5. We can also put in x=5 for the other 3 equations and we can spot that the equation does not hold for x=5 for any of them.

A sample size of 11 would give a standard deviation of 10 pounds for the Florida Manatees

An equation is an expression that shows how two numbers and variables are related using mathematical operations such as addition, subtraction, exponent, division and multiplication.

The standard deviation of a sample is:

[tex]\sigma_n=\frac{\sigma}{\sqrt{n} } \\\\Where\ n\ is\ sample\ size,\sigma\ is\ standard\ deviation\ and\ \sigma_n\ is\ standard\ deviation\ of\ sample[/tex]

Given that:

[tex]\sigma_n=10,\sigma=33,hence:\\\\10=\frac{33}{\sqrt{n} } \\\\n=10.89[/tex]

A sample size of 11 would give a standard deviation of 10 pounds

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Answer:

plot the point at -3

Step-by-step explanation:

-3 is 6 points away from t and 4 away from s. thus 3/5

The proper formula states that a sphere with a radius of [tex]15[/tex] has a volume of 4/3π([tex]15^{3}[/tex]).

The equation for a sphere's size is V = 3/3 r3, wherein r represents the radius and V is its volume. 1⁄2 of an object's circumference makes up its radius. Therefore, you may determine the radius first, then by the volumes, to get the contact area of a globe given its diameter.

Both a circle as well as a sphere are round, if you compare them. The difference among the two forms is that while a sphere has three dimensions, a circle only has two, which is why we can measure a sphere's volume and surface area.

The formula for the volume of a sphere is V = 4/3π[tex]r^{3}[/tex], where r is the radius of the sphere.

Substituting [tex]r=15[/tex], we get

V = 4/3π([tex]15^{3}[/tex])

Therefore, the expression 4/3π([tex]15^{3}[/tex]) gives the volume of a sphere with radius [tex]15[/tex].

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The transformation from f(x) to g(x) involves a horizontal shift and a change in the slope of the graph.The function g(x) is obtained from the function f(x) by a vertical shift of 3 units to the left.

Specifically, the denominator of g(x), x+3, represents a horizontal shift of 3 units to the left compared to the denominator of f(x), x. As a result, g(x) is shifted to the left relative to f(x). Furthermore, the shift causes the graph of g(x) to be steeper than that of f(x) at x=0. This is because, for small values of x, the difference between (1)/(x) and (1)/(x+3) becomes larger as x gets smaller. Therefore, the transformation from f(x) to g(x) involves a horizontal shift and a change in the slope of the graph.

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Answer:

Let's assume Karl rents the bike for x hours. Then the cost of renting the bike can be expressed as:

Cost = 7x + 9.5

We know that the maximum cost Karl can afford is $55. So we can set up an equation:

7x + 9.5 ≤ 55

Subtracting 9.5 from both sides:

7x ≤ 45.5

Dividing both sides by 7:

x ≤ 6.5

Since Karl can only rent the bike for whole hours, the maximum number of hours he can rent the bike is 6 hours (which costs $49 plus the $9.5 flat fee, for a total of $58.5). If he rented it for 7 hours, it would cost $60.5, which is over his budget.

Answer:

103

Step-by-step explanation:

157-54= 103

Answer: 103

Step-by-step explanation:

subtract 54 from 157

Answer:

Multiplying the first equation by 3 and the second equation by 9, we get:

-27y + 12x - 33 = 0

-27y + 90x + 279 = 0

Now, we can subtract the first equation from the second to eliminate y:

-27y + 90x + 279 - (-27y + 12x - 33) = 0

78x + 312 = 0

78x = -312

x = -4

Substituting x = -4 into the first equation, we get:

-9y + 4(-4) - 11 = 0

-9y - 27 = 0

y = -3

Therefore, the solution to the system of equations is (x, y) = (-4, -3).

The sum of 10 3/4 and 12 1/4 is 23.

To add the mixed numbers 10 3/4 and 12 1/4, follow these steps:

Step 1: Add the whole number of parts.

Add the whole numbers 10 and 12 to get:

10 + 12 = 22

Step 2: Add the fractional parts separately.

Add the fractions 3/4 and 1/4 separately. To do this, find a common denominator, which in this case is 4. Then convert each fraction to have the same denominator and add the numerators.

For 10 3/4, the fraction 3/4 has the same denominator, so we keep it as is.

For 12 1/4, the fraction 1/4 also has the same denominator, so we keep it as is.

Then we add the numerators of the fractions:

3/4 + 1/4 = 4/4 = 1

Step 3: Add the results from Step 1 and Step 2.

Add the result from Step 1 (the sum of the whole numbers) to the result from Step 2 (the sum of the fractions):

22 + 1 = 23

Therefore, the sum of 10 3/4 and 12 1/4 is 23.

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satisfied=88%

The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%.What is probability?Probability is the branch of mathematics that studies the probability of an occurrence, as well as the likelihood of its occurrence. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.Probability formula is P(E) = n(E) / n(S), where P(E) refers to the probability of occurrence of event E, n(E) is the number of outcomes in event E, and n(S) is the total number of possible outcomes.What is proportion?The proportion is a percentage, a fraction, or a ratio that compares the number in the group to the total number. When looking at a sample from the population, the sample proportion is calculated as the number in the sample with the attribute of interest divided by the total number of people in the sample. It gives us the proportion of people who have the attribute of interest in the sample.Answer:Therefore, the probability will be 88% ±5% and the proportion satisfied is 88%.

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Answer:

B.) x(x+2)

Step-by-step explanation:

Hope this helps! :)

The surface area of the mentioned rectangular prism is calculated to be 168 yd².

The surface area of ​​a three-dimensional object is the total area of ​​all its faces. In real life, we use the concept of the surface of different objects when wrapping something, painting something, and finally getting the best possible design when building things.

Area of rectangle 1

= 6 × 2

= 12 yd²

Area of rectangle 2

= 9 × 2

= 18 yd²

Area of rectangle 3

= 9 × 6

= 54 yd²

Since the prism is made of 2 faces of each type of rectangle and the area of prism is the sum of area of each face:

Area of prism = (12 × 2) + (18 × 2) + (54 × 2)

Area of prism = 24 + 36 + 108

Area of prism = 168 yd²

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Answer:

Step-by-step explanation:

You can do 6x+the number of the amount of squares. Then find find the units of the square unit.

The elevation at point B is 740 ft. So, option B is correct.

The elevation is the height above or below a specified reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation.

There are Four points that are displayed on the given map whose range are from A to D.  There are few additional lines in between these four places. The height between these points and lines is indicated on the map in feet, and from point A onwards there is an elevation difference of 20 feet. Point A is at the 700 ft and there is one more line between A and B, and the elevation difference in between one line is 20. So the elevation difference at point B is = 700 + 20 +20= 740 ft. So, option answer is B.

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1.   If the first envelοpe cοntains the largest amοunt, then yοu take it and stοp. The prοbability οf this happening is 1/4.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

a) If yοu take the first envelοpe, the prοbability that it cοntains the largest amοunt is 1/4.

b) If yοu οpen the first envelοpe, nοte that it cοntains the amοunt x, and take the next amοunt which is larger than x (if nο such amοunt shοws up, yοu must take the last envelοpe), the prοbability that yοu get the largest amοunt is 1/3.

Tο see why, cοnsider the fοllοwing cases:

2.   If the first envelοpe dοes nοt cοntain the largest amοunt, but the secοnd envelοpe dοes, then yοu discard the first envelοpe and take the secοnd οne. The prοbability οf this happening is (3/4) x (1/3) = 1/4.

3.   If the first twο envelοpes dο nοt cοntain the largest amοunt, but the third οne dοes, then yοu discard the first twο envelοpes and take the third οne. The prοbability οf this happening is (3/4) x (2/3) x (1/2) = 1/4.

4.   If the first three envelοpes dο nοt cοntain the largest amοunt, then yοu must take the last envelοpe, which has the largest amοunt with prοbability 1/4.

c) If yοu οpen the first twο envelοpes, call the amοunts x and y, and discard bοth and take the next amοunt that is larger than bοth x and y, the prοbability that yοu get the largest amοunt is 1/2.

Tο see why, cοnsider the fοllοwing cases:

1.   If the largest amοunt is in the first twο envelοpes, then yοu must take the last twο envelοpes, and the prοbability οf getting the largest amοunt is 1/2.

2.   If the largest amοunt is nοt in the first twο envelοpes, then yοu must take the third οr fοurth envelοpe, and the prοbability οf getting the largest amοunt is 1/2.

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The probability that among 10 such cars tested, 3 will average less than 28 miles per gallon, 6 will average from 28 to 32 miles per gallon, and 1 will average more than 32 miles per gallon is given by 0.0020125

Let X be the number of cars among ten that averages less than 28 miles per gallon. Let Y be the number of cars among ten that average from 28 to 32 miles per gallon. Let Z be the number of cars among ten that average more than 32 miles per gallon. We are to find P(X = 3, Y = 6, Z = 1).

Firstly, let us find the probability of getting 3 cars among 10 cars that will average less than 28 miles per gallon.

The probability of getting exactly 3 cars among 10 cars that will average less than 28 miles per gallon is given by the probability mass function:

P(X = 3) = (10C3) (0.4)³ (0.6)⁷
= (10 x 9 x 8 / 3 x 2 x 1) (0.064) (0.096)
= 0.23 (approximately)

Similarly, the probability of getting 6 cars among 10 cars that will average from 28 to 32 miles per gallon is given by the probability mass function:

P(Y = 6) = (10C6) (0.5)⁶ (0.5)⁴
= (10 x 9 x 8 x 7 x 6 x 5 / 6 x 5 x 4 x 3 x 2 x 1) (0.156) (0.063)
= 0.25 (approximately)

Finally, the probability of getting 1 car among 10 cars that will average more than 32 miles per gallon is given by the probability mass function:
P(Z = 1) = (10C1) (0.1)¹ (0.9)⁹
= (10) (0.1) (0.348)
= 0.035

Therefore, the answer is:
P(X = 3, Y = 6, Z = 1) = P(X = 3) P(Y = 6) P(Z = 1)
= 0.23 x 0.25 x 0.035
= 0.0020125 (approximately)

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According the question given above the area of ABK is  100 square cm.

a) ACD = 50 square cm

b)AMCN = 225 square cm

c)ABK = 100 square cm

a) Tο calculate ACD, we need tο use the fοrmula fοr the area οf a trapezοid, which is:

Area = (base1 + base2) × height ÷ 2

Since CD is twice the length οf AB, we can let AB = x and CD = 2x. Let's alsο call the height οf the trapezοid h.

Then we have:

450 = (AB + CD) × h ÷ 2

450 = (x + 2x) × h ÷ 2

450 = 3xh ÷ 2

300 = 3xh

100 = xh

Nοw, we can use the fact that MA = MB tο find the area οf triangle ACD:

ACD = AB × h ÷ 2

ACD = xh ÷ 2

ACD = 100 ÷ 2

ACD = 50 square cm

b) Tο calculate AMCN, we need tο first find the length οf MN. Since MA = MB and NC = ND, we can use the fact that οppοsite sides οf a trapezοid are parallel tο find that AMCN is a parallelοgram. Therefοre, MN is equal tο AB.

Using the fοrmula fοr the area οf a parallelοgram, which is base × height, we have:

AMCN = AB × CD

AMCN = x × 2x

[tex]AMCN = 2x^2[/tex]

AMCN = 900 ÷ 2

AMCN = 225 square cm

c) Tο find the area οf triangle ABK, we need tο find the length οf BK. Since AB = x and CD = 2x, we knοw that AK and KC are alsο equal tο x. Therefοre, BK is equal tο DA, which is 2x.

Using the fοrmula fοr the area οf a triangle, which is base × height ÷ 2, we have:

ABK = AB × BK ÷ 2

ABK = x × 2x ÷ 2

[tex]ABK = x^2[/tex]

ABK = 100 square cm

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After calculating, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.

Considering that Bert's maximum speed is 270 meters per minute, then his speed when he is paddling at one-third of his top speed is:

270 m/min * (1/3) = 90 m/min

If he is paddling at this speed for 8 minutes, then the distance that he covers is:

distance = speed * time = 90 m/min * 8 min = 720 meters

Therefore, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.

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Answer:

w = 102

m = 78

n = 58

Step-by-step explanation:

Three angles of a triangle add up to 180°

∴ w = 180 - (36 + 42)

= 180 - 78

= 102

w and m are supplementary angles:
m + w = 180

m + 102 = 180

m  = 180 - 102 = 78

Three angles of a triangle add up to 180°

m + 44 + n = 180

78 + 44+ n = 180

122 + n = 180

n = 180 - 122

n = 58

a. The utility of going to Western is 6.4/10

b. The utility of going to York would also be 5.15/10

Decision theory is a branch of mathematics that deals with decision making in the face of uncertainty.

a. If Martha accepts the early admission offer from Western, her utility would be 5/10, since that is the utility of going to Queens.

If Martha waits and gets admitted to Queens, her utility would be 5/10 as well, since that is the utility of going to Queens.

If Martha waits and gets admitted to UTM, her utility would be 9/10.

The probability of getting admitted to Queens is 1, since she is guaranteed admission. The probability of getting admitted to UTM is 6/10. The probability of accepting the early admission offer from Western is 4/10, since it is the complement of the probability of getting admitted to UTM.

Therefore, the expected utility of waiting is ⇒ (1 * 5/10) + (6/10 * 9/10) = 8.4/10. The expected utility of accepting the early admission offer is

⇒ (4/10 * 5/10) = 2/10.

Since Martha is indifferent between the two options, the utility of going to Western is 8.4/10 - 2/10 = 6.4/10

b. If Martha is indifferent between accepting an early-admissions offer from York and gambling on a 3/4 chance at going to Western vs. a 1/4 chance of having to go to Queens, then the utility of going to York must be the same as the expected utility of gambling.

If Martha gambles, her expected utility would be (3/4 * 6.4/10) + (1/4 * 5/10) = 5.15/10.

Therefore, the utility of going to York would also be 5.15/10.

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Answer: The radius of a circle is half of its diameter. Therefore, if the diameter of the circle is 3 cm, then the radius is 1.5 cm.

To set a pair of compasses to draw a circle with diameter 3 cm, open the compasses to a distance of 1.5 cm (which is the radius of the circle). The correct diagram in the link provided shows the compasses set to the correct radius.

So its A

The radius of the circle is 1.5cm.

A circle's diameter is divided in half by its radius. Thus, if the circle's diameter is 3 cm, the radius is:

radius = diameter/2 = 3cm/2 = 1.5cm

Any circular object's radius is the measurement from the centre to its outermost border or boundary. A radius is a dimension that applies to spheres, semispheres, cones with circular bases, and cylinders with circular bases in addition to circles.

It is possible to define a circle as the locus of a point travelling on a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its centre. The fixed point is referred to as the centre of the circle.

The distance along a line drawn between two points on a circle and through the centre of the circle is the diameter of the circle. It is equivalent to double the circle's radius. It is typically indicated with a d or a D.

Diameter = 2 x Radius

Or

Radius = diameter / 2.

The circle's longest chord equals its diameter.

Moreover, we may relate a circle's area and circumference to its diameter.

Circle circumference equals (Diameter)

Circle area equals /4 (Diameter[tex])^2.[/tex]

from the question;

A circle's diameter is divided in half by its radius. Thus, if the circle's diameter is 3 cm, the radius is:

radius = diameter/2 = 3cm/2 = 1.5cm

Therefore, the radius of the circle is 1.5cm.

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The algebra Property used to get  Equation B from Equation A is:

Rewrite one side (or both) using the distributive property​

The 2 equations given are:

A. 5 = -2(x - 1)

B. 5 = -2x + 2

Some of the popular properties of algebra are:

Commutative Property: This states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. For example: a + b = b + a , a b = b a

Associative Property: This is defined as when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped. For example: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c

Distributive Property: This is defined as multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together. For example, a(b + c) = ab + bc

Equation A is given as 5 = -2(x - 1)

To get equation B, we rewrite one side (or both) using distributive property

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Complete question is:

A. 5=-2(x-1)

B. 5=-2x+2

How can we get equation B from equation A?

A. rewrite one side (or both) by combining like terms

B. rewrite one side (or both) using distributive property

C. multiply or divide both sides by the same non zero constant.

D. multiply or divide both sides by the same variable expression.

Therefore, it will take about 11 years for the account value to reach 5100 dollars.

Percent is a way of expressing a quantity as a fraction of 100. The symbol "%" is used to represent percent. For example, if we say that an interest rate is 5%, it means that the interest is 5/100 or 0.05 as a decimal. Percentages are commonly used in finance, economics, and everyday life to express rates, proportions, and changes in quantities.

Here,

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)ⁿˣ

where A is the amount of money in the account after x years, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and x is the time (in years).

We are given that P = 2100, r = 0.05, and we want to find the value of x when A = 5100. Let's assume that the interest is compounded annually (n = 1). Substituting the given values into the formula, we get:

5100 = 2100(1 + 0.05)ˣ

Dividing both sides by 2100, we get:

(1 + 0.05)ˣ = 5100/2100

Simplifying the right-hand side, we get:

(1 + 0.05)ˣ = 2.42857

Taking the natural logarithm of both sides, we get:

ln(1 + 0.05)ˣ = ln 2.42857

Using the power rule of logarithms, we can simplify the left-hand side:

x ln(1 + 0.05) = ln 2.42857

Dividing both sides by ln(1 + 0.05), we get:

x= ln 2.42857 / ln(1 + 0.05)

Using a calculator, we get:

x≈ 11.4

Rounding this to the nearest year, we get:

x ≈ 11 years

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Answer:

[tex] \frac{45}{136} [/tex]

Step-by-step explanation:

The probability of selecting a girl on the first pick is 10/17, since there are 10 girls out of 17 students in total.

After the first pick, there are 16 students remaining, including 7 boys and 9 girls. So the probability of selecting a girl on the second pick, given that a girl was not selected on the first pick, is 9/16, since there are now only 9 girls and 16 total students left to choose from.

To find the probability of both events occurring (i.e., both students being girls), we need to multiply the probabilities of each event. Therefore, the probability of selecting two girls in a row is:

[tex] \frac{10}{17} \times \frac{9}{16} = \frac{90}{272} [/tex]

So the probability of selecting two girls in a row is

[tex] \frac{90}{272} [/tex]

which can be simplified to

[tex] \frac{45}{136} [/tex]

Answer:

68

Step-by-step explanation:

Answer:

u=4

Step-by-step explanation:

u+6/12 = 4+6/12 = 10/12 ÷ 2/2 = 5/6

Answer: u = 4

Step-by-step explanation:

The speed at which the driver travelled the 175 miles in 5 hours is  35 miles/hour.

The speed can be calculated by dividing the distance travelled (175 miles) by the amount of time taken (5 hours).

Formula: Speed = Distance/Time

Speed = 175/5 = 35 miles/hour

Therefore, my speed was 35 miles/hour.

To calculate the speed, the formula mentioned above is used. The formula states that speed is equal to the distance travelled divided by the amount of time taken. In this case, the distance travelled was 175 miles, and the time taken was 5 hours. When the distance travelled is divided by the time taken, the result is 35 miles/hour. This is the speed at which the driver travelled the 175 miles in 5 hours.

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