Find the slope of the line represented
by the data below.
x 2 4 6 8
-3 39
3
9 15
y|-3
Simplify completely.
Slope = [?
Hint: The slope of a line is the
Change in y
Change in x

When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)

First, we shall determine the value of A. Details below:

Quadratic equation is expressed as:

x² - (sum of root)x + product of root

Comparing the above with x² - 11x + 30, we have

x² - 11x + 30 = x² - (sumof root)x + product of root

Product of roots = 30

Thus,

A = 30

Next, we shall determine the value of B. details below:

f(x) = x² + 5

f(2) = 2² + 5

f(2) = 9

Thus,

B = 9

Next, we shall determine the value of C. Details below:

Let

x + 4 = 0

Thus,

x = -4

Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:

Remainder = x² - 2x - 24

Remainder = (-4)² - 2(-4) - 24

Remainder = 0

Thus,

C = 0

Finally, we shall determine value of A/5 + √(B - C). Details below:

A/5 + √(B - C) = 30/5 + √(9 - 0)

A/5 + √(B - C) = 6 + √(9

A/5 + √(B - C) = 6 + 3

A/5 + √(B - C) = 9

Thus, the value of A/5 + √(B - C) is 9 (option B)

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Answer: A) Let's first calculate how far the van would have traveled in the half hour before the car started. The van's speed is 50 km/h, which means in half an hour it would have traveled 50/2 = 25 km.

Now let's consider the time it takes for the car to catch up to the van. We can represent this using the formula:

distance = rate × time

Let's call the time it takes for the car to catch up "t". We know that during this time, the van is also traveling. In fact, it has been traveling for t + 0.5 hours (the half hour before the car started plus the time it takes for the car to catch up). So the distance the van has traveled is:

distance van = 50 × (t + 0.5)

The distance the car has traveled is:

distance car = 60t

When the car catches up to the van, they will have traveled the same distance. So we can set the two distances equal to each other:

50(t + 0.5) = 60t

Simplifying this equation:

50t + 25 = 60t

Subtracting 50t from both sides:

25 = 10t

So t = 2.5 hours.

But we're not done yet! We need to add the 0.5 hours that the van traveled before the car started to get the total time it took for the car to catch up:

t + 0.5 = 2.5 + 0.5 = 3 hours

So the car catches up to the van 3 hours after the van started, or at 12:15 pm.

B) We can use the formula:

distance = rate × time

to find the distance between the two towns. We know the car traveled for 6 hours (from 9:45 am to 3:45 pm) and its speed was 60 km/h. So the distance it traveled is:

distance car = 60 × 6 = 360 km

We also know that the van traveled for 6.5 hours (from 9:15 am to 3:45 pm) and its speed was 50 km/h. So the distance it traveled is:

distance van = 50 × 6.5 = 325 km

The distance between the two towns is the difference between these two distances:

distance = distance car - distance van = 360 - 325 = 35 km

So the distance between the two towns is 35 km.

The [tex]f^{-1}[/tex] inverse of f  of each

1) (x + 1)/2

2) [tex]\sqrt{\frac{x+1}{4} } \\[/tex]

3) 3 - 4x

4) [tex](x+5)^{1/3}[/tex]

5) [tex]\sqrt{x + 4}[/tex]

1) function f(x) = 3x + 1

let f(x) = y

y = 3x + 1

y - 1 = 3x

(y - 1)/3 = x

x obtained is [tex]f^{-1}[/tex]

and y will be x

[tex]f^{-1}[/tex] = (x-1)/3

2) equation f(x) = 4x² - 1

let f(x) = y

y = 4x² - 1

y + 1  = 4x²

(y + 1 )/4 = x²

x = [tex]\sqrt{\frac{x + 1}{4} }[/tex]

x obtained is [tex]f^{-1}[/tex]

and y will be x

[tex]f^{-1}[/tex] =  [tex]\sqrt{\frac{x + 1}{4} }[/tex]

similarly,

3) f(x) = 3-x/4

y = 3-x/4

4y = 3 - x

x = 3 - 4x

[tex]f^{-1}[/tex] =  3- 4x

4) y = x³ - 5

y + 5 = x³

x = [tex](y + 5)^{1/3}[/tex]

[tex]f^{-1}[/tex] = [tex](x+5)^{1/3}[/tex]

5) y = x² - 4

y + 4 = x²

x = √y + 4

[tex]f^{-1} = \sqrt{x + 4}[/tex]

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The length of AB is 27.3m and AD is 113 m.

Using Trigonometry in Triangle ABC

tan 50. 8 = P / B

tan 50.8 = AB / 22.3

1.2261 = AB/ 22.3

AB =  27.34 m

Now, again using Trigonometry

tan 25.4 = P / B

tan 50.8 = AD / 27.34

0.474 = AD/ 27.34

AD =  12.95916 m

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Using trigonometry and the Pythagorean theorem, the length of the hypotenuse AC is found to be 3.5 cm, and using the Pythagorean theorem again, the length of BC is found to be approximately 1.75 cm.

Using trigonometry and the given angle and side length information, we can solve for the length of side BC (x).

We know that

sin(A) = opposite/hypotenuse

sin(30) = AC/7

AC = 7 × sin(30)

AC = 3.5 cm

Using the Pythagorean theorem, we have

BC² = AC² - AB²

BC² = (3.5)² - (7)² sin²(30)

BC² = 3.0625

BC = √3.0625

BC = 1.75 cm (rounded to two decimal places)

Therefore, the value of x is approximately 1.75 cm.

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Answer:

Step-by-step explanation:

In November 1998, former professional wrestler Jesse “The Body” Ventura was elected governor of Minnesota. Up until right before the election, most polls showed he had little chance of winning. There were several contributing factors to the polls not reflecting the actual intent of the electorate:

Ventura was running on a third-party ticket and most polling methods are better suited to a two-candidate race.

Many respondents to polls may have been embarrassed to tell pollsters that they were planning to vote for a professional wrestler.

The mere fact that the polls showed Ventura had little chance of winning might have prompted some people to vote for him in protest to send a message to the major-party candidates.

But one of the major contributing factors was that Ventura recruited a substantial amount of support from young people, particularly college students, who had never voted before and who registered specifically to vote in the gubernatorial election. The polls did not deem these young people likely voters (since in most cases young people have a lower rate of voter registration and a turnout rate for elections) and so the polling samples were subject to sampling bias: they omitted a portion of the electorate that was weighted in favor of the winning candidate.

SAMPLING BIAS

A sampling method is biased if every member of the population doesn’t have equal likelihood of being in the sample.

So even identifying the population can be a difficult job, but once we have identified the population, how do we choose an appropriate sample? Remember, although we would prefer to survey all members of the population, this is usually impractical unless the population is very small, so we choose a sample. There are many ways to sample a population, but there is one goal we need to keep in mind: we would like the sample to be representative of the population.

Returning to our hypothetical job as a political pollster, we would not anticipate very accurate results if we drew all of our samples from among the customers at a Starbucks, nor would we expect that a sample drawn entirely from the membership list of the local Elks club would provide a useful picture of district-wide support for our candidate.

One way to ensure that the sample has a reasonable chance of mirroring the population is to employ randomness. The most basic random method is simple random sampling.

I can't see the chart...

A linear function would be the best fit for the given data because as x increase the y-values change linearly.

Rounded to the .5 the slope of the function is approximately 32.5

A linear relation means that any increase of 1 unit in the independent variable (x) has always the same impact in the other variable (y).

In this particular case, the increases in the y-value are:

56 - 24 = 32

88 - 56 = 32

122 - 88 = 34

The mean of that, rounded to .5, is (32 + 32 + 34)/3 = 32.5

So the change is almost the same one, then this seems to be a linear relation.

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Answer:

36 °

Step-by-step explanation:

The markings imply equal sides*

So both of the angles are 27° there

To find angle a we do 180 - (27+27) and obtain 126°

Then to find angle y, we do 180-angle a which is 180-126 and we get 54°

We now have reached the triangle where you're supposed to find x right?

So x is equal to 180 - both other angles, which is 180 - (90 and angle y) = 180- (90+54) = 180 - 144 = 36 which is your final answer

Therefore , the solution of the given problem of unitary method comes out to be 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).

The well-known simple approach, real variables, and any crucial elements from the very initial And specialised inquiry can all be used to finish the work. Customers may then be given another chance to try the product in response. If not, significant impacts on our understanding of algorithms will vanish.

Here,

The circumference of the circle the bike tyre forms is equal to the distance travelled in one rotation of the tyre. The following formula determines a circle's circumference:

=> C = 2πr

where the mathematical constant is roughly equivalent to 3.14159 and r is the circle's radius.

Your bicycle tyre's radius in this instance is 12 inches. The tyre's circumference is as follows:

=> C = 2π(12) = 24π inches

You may easily calculate how far you will travel after 50 spins by multiplying the tyre's circumference by the number of turns:

=> Covered distance:  50 × 24π ≈ 376.99 inches

As a result, after 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).

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An equation for this linear function that describes how height varies with age is y = 1/5(x) + 2.

The predicted height at 9 is 3.8 feet.

The predicted height at 31 is 8.2 feet.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Conversion:

1 feet = 12 inches

24 inches = 24/12 = 2 feet.

Next, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 2)/(10 - 0)

Slope (m) = 2/10

Slope (m) = 1/5

At data point (0, 2) and a slope of 1/5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 1/5(x - 0)  

y = 1/5(x) + 2

When x = 9, the predicted height is given by;

y = 1/5(9) + 2

y = 3.8 feet.

When x = 31, the predicted height is given by;

y = 1/5(31) + 2

y = 8.2 feet.

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Shawn's phone is 36 cubic cm larger than Ellie's phone.

To get difference in volume between the two phones, we must calculate  volume of each phone and subtract the volume of Ellie's phone from the volume of Shawn's phone.

The volume of a rectangular prism is: length*width* height. The height of both phones is 3/4 centimeters.

The volume of Ellie's phone is:

= length x width x height

= 12 cm x 6 cm x (3/4) cm

= 54 cubic centimeters

The volume of Shawn's phone is:

= length x width x height

= 15 cm x 8 cm x (3/4) cm

= 90 cubic centimeters

The difference in volume is:

= Volume of Shawn's phone - Volume of Ellie's phone

= 90 cubic centimeters - 54 cubic centimeters

= 36 cubic centimeters

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A. Using the formula for area of rectangle, the length of the rectangular space is: 2x - 3

B. The expression to prove this is: (2x - 3) * 4x = 8x² - 12x

To find the area of a rectangle, multiply the width and the length together. This means: Area = length * width.

Part A: We are given that area of the rectangular space is expressed as 8x² - 12x, if the width is 4x, then:

Length of the rectangular space = (8x² - 12x) / 4x = 4x(2x - 3)/4x

Length = 2x - 3

Part B: To prove this, we have:

length * width = 8x² - 12x

Substitute:

(2x - 3) * 4x = 8x² - 12x

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Answesar:

Step-by-step explanation:

SA = 10(5)² = 250cm²

Volume² = 2 (5)³ = 250cm³

They are not equal.

Surface area is in square cm and volume is in cm³.

Answer:

[tex]y = -x/5 -4.[/tex]

Step-by-step explanation:

To simplify the line x + 5y = 20 into y = mx + b form:

x + 5y = 20.

5y = -x + 20.

y = -x/5 + 4.

The line parallel to the line y = -x/5 + 4 will have the same slope of -1/5.

We get the equation:

y = -x/5 + b.

To find b, we plug in the point (5, -5).

-5 = -5/5 + b.

-5 = -1 + b.

b = -4.

[tex]y = -x/5 -4.[/tex]

The calculated value of the surface area of the cylinder is 138π square inches

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

Height, h = 5 1/2 inches

Diameter, d = 12 inches

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

SA = 2πr(r + h)

Where

Radius, r = d/2

r = 12/2

r = 6

Substitute the known values in the above equation, so, we have the following representation

SA = 2 * π * 6(6 + 5 1/2)

Evaluate

SA = 138π

Hence, the surface area of the cylinder is 138π square inches

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The interest rate if Ted made $56 in interest for 1 year on a principle of $700 will be 8%.

Given, the interest amount is $56.

The principal amount is $700.

The time period of investment is 1 year.

Now, we have to find the interest rate.

The formula to find the simple interest is,

  S.I = PTR/100.

Now, we need to substitute the values in the above formula.

S.I = PTR/100

56 = 700×1×R / 100

56 = 700R/100

5600 = 700R

R = 5600/700

R = 8

Therefore, the interest rate is 8%.

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False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.

What is Algebraic expression ?

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.

The tax incidence (the division of the burden of a tax between buyers and sellers) does not depend on which side of the market the tax is levied on, but rather on the relative elasticities of supply and demand. In this case, we don't have information about the elasticities of supply and demand, so we cannot determine the tax incidence. However, we can infer that the tax on consumers did reduce the quantity sold (from 30 million liters to 25 million liters), so it's unlikely that a tax on producers would have had a larger effect.

Therefore, False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.

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Answer:

Ned has 20 white marbles.

Step-by-step explanation:

Let's call the number of red marbles "r".

We know that Ned has twice as many white marbles as red marbles, so the number of white marbles would be 2r.

We also know that he has five more blue marbles than white marbles, so the number of blue marbles would be 2r + 5.

The total number of marbles in Ned's collection is 55, so:

r + 2r + (2r + 5) = 55

Simplifying this equation, we get:

5r + 5 = 55

Subtracting 5 from both sides:

5r = 50

Dividing by 5:

r = 10

So Ned has 10 red marbles.

We can use this to find the number of white marbles:

2r = 2(10) = 20

So Ned has 20 white marbles.

If a turtle lives in a garden and a hedgehog lives in the woods. The distance between the garden and the woods is 450m.

Let d represent the distance between the turtle's garden and the hedgehog's wood

Let h represent the  speed of the hedgehog

Let the  turtle's speed = h-10

Le the time it takes for the hedgehog to walk from the woods to the meeting point= t

Set up two equations

d = (h-10)(t+4.5) + ht (Equation 1)

d - 150 = ht (Equation 2)

Solve for d by substituting equation 2 into equation 1:

ht + (h-10)(t+4.5) = ht + 150

(h-10)t + 45h = 150

t = (150 - 45h) / (h-10)

Substitute t into equation 2:

d = ht + 150 - (h-10)(t+4.5)

d = h(150 - 45h)/(h-10) + 150 - (h-10)(45h/(h-10) + 4.5)

d = 2250/(h-10) (distance between the garden and the woods)

Since the turtle and hedgehog meet in 5 hours

Thus,

d = ( h-10 ) (5) + h( 5- 4.5 )

d = 5h - 25

Substitute

5h - 25 = 2250/(h-10)

Multiplying both sides by h-10

5h² - 75h + 250 = 0

Dividing both sides by 5

h²- 15h + 50 = 0

Using the quadratic formula

h = (15 ± sqrt(15^2 - 4(1)(50))) / (2*1)

h = (15 ± 5) / 2

So,

h = 10 or h = 5

Distance between the garden and the woods :

d = 2250/(h-10)

d= 2250/(5-10)

= 450 meters

Therefore the distance is 450m.

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The equation of the line passing through the points (-7, -3) and (1, 2) is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

First, we determine the slope of the line.

Given the two points are (-7, -3) and (1, 2)

We can find the slope of the line by using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values, we get:

m = (2 - (-3)) / (1 - (-7))

m = 5/8

Using the point-slope form, plug in one of the given points and slope m = 5/8 to find the equation of the line.

Let's use the point (-7, -3:

y - y₁ = m(x - x₁)

[tex]y - (-3) = \frac{5}{8}( x - (-7) ) \\\\y + 3 = \frac{5}{8}(x + 7 )\\\\y + 3 = \frac{5}{8}x + \frac{35}{8} \\ \\y = \frac{5}{8}x + \frac{35}{8} - 3\\\\y = \frac{5}{8}x + \frac{11}{8}[/tex]

Therefore, the equation of the line is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].

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The equation of the line passing through the given points is y = 6x

Given that are the values of x and y coordinates we need to find the equation of the line using them,

So, considering the points (4, 24) and (5, 30),

We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here (x₁, y₁) and (x₂, y₂) are (4, 24) and (5, 30),

Therefore, the required equation is =

y-24 = 30-24/5-4 (x-4)

y-24 = 6(x-4)

y-24 = 6x-24

y = 6x

Hence, the equation of the line passing through the given points is y = 6x

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The result of the row 1 multiplication by 1/4 is determined as  [¹/₂  0 ].

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [2 0]

To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;

[2 0] x 1/4 = 1/4(2 0)

= [¹/₂  0 ]

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that is 2, and 0 by 1/4.

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Answer:

x = 16.2

Step-by-step explanation:

Using trig functions:

cos theta = adjacent side/ hypotenuse

cos 72 = 5/x

Solving for x

x = 5 /cos 72

x=16.18033

Rounding to the nearest tenth

x = 16.2

Answer: x = 16.2 units

Step-by-step explanation:

     We are given an angle (72°), the adjacent side (5), and the hypotenuse (x). We will use the cosine function to solve.

cos(θ) = [tex]\frac{adjacent}{hypotenuse }[/tex]

cos(72°) = [tex]\frac{5}{x }[/tex]

xcos(72°) = 5

x = [tex]\frac{5}{cos(72\°)}[/tex]

x = 16.1803398 ≈ 16.2

Answer:

Step-by-step explanation:

4x - 5 = 7

4x = 7 + 5

4x = 12

x = 12/4

x = 3

The sum of all the number is found to be 630 which is not given in the options.

Let the middle number be x. Then the five numbers smaller than x have an average of 44, so their sum is 544 = 220. Similarly, the five numbers larger than x have an average of 68, so their sum is 568 = 340.

The total of all the numbers is 9x since x is the median and average of all the numbers. The total of all the numbers equals 9x since we know that x is the average of all the numbers.

Therefore, we have,

9x = 220 + x + 340

Simplifying and solving for x, we get,

8x = 560

x = 70

Therefore, the sum of all the numbers is 9x = 970 = 630.

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Complete question - Nine numbers are written in ascending order, the middle number is the average of all the numbers, the average of the five largest numbers is 68, and the average of the five smallest is 44. What is the sum of all the numbers? ?

a) 112

b) 504

c) 144

d) 560

d) 122

Answer: 12

Step-by-step explanation:

We have to find h so the first step is to subtract the 11 from the 20

3/4h=9

Then to move the 3/4 over to the other side, you must multiply it by it's reciprocal, 4/3.

h= 4/3 x 9

This equals 12.

Answer:

(r, y)=(10,-2)

Step-by-step explanation: Hope this helps :)

The total money raised is (15/7) * $88,000 = $188,571.43.

a) Let x be the total amount raised.

Charity A received (1/3)(x - A), Charity C received (1/4)(x - C). We have A = (1/3)(B+C) and C = (1/4)(A+B).

Solving these equations, we find B's share to be 7/15 of the total amount.

p) Since Charity B received $88,000, which is 7/15 of the total amount, the total money raised is (15/7) * $88,000 = $188,571.43.

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