Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 4 ≤x≤7.
x
1
4
7
10
f(x)
90
87
84
81

Answer:

Step-by-step explanation:

x=2.3

Answer:

5. 1/2 & 3 , 6. 2 & 5

Step-by-step explanation:

5.

slope = 2

m = y2 - y1 / x2 - x1

m = 13-3/5-0

m = 10/5 or 2

y-intercept = 3

(0,3)

6.

slope = 1/2

m = y2 - y1 / x2 - x1

m = 6-5/2-0

m = 1/2

y-intercept = 5

(0,5)

The relation that is a function is (d) the graph

The list of options represents the given parameter

As a general rule;

For a relation to be considered a function, the following must be true:

One x value must not point to several y values

Using the above as a guide, the ordered pair in (a), relation in (b) and table in (c) are not functions

This is because one x value must not point to several y values

However, there are unique values in the graph of (d)

Hence, (d) the graph is a function

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Answer:

m∠5 = 91° (sorry if i got it wrong i tried my best)

Answer:

He gets $7.50 per cap

Step-by-step explanation:

I took the test

Answer:

$17.50

Step-by-step explanation:

The equation of each line in slope-intercept form are:

1. y = 3/4x + 4.

2. y = -x - 2

To express the equation of a line in slope-intercept form, y = mx + b, substitute the value of the slope (m) and the value of the y-intercept (b) into the equation.

1. Slope (m) = 3/4

y-intercept (b) = 4

Substitute m = 3/4 and b = 4 into the equation y = mx + b:

y = 3/4x + 4.

2. Slope (m) = -1

y-intercept (b) = -2

Substitute m = -1 and b = -2 into the equation y = mx + b:

y = -x - 2

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Answer:

Her weekly allowance is $18

Step-by-step explanation:

We can use an algebraic equation to solve this problem.

x/2 + 6 = 15

x/2 + 6 ( - 6) = 15 ( - 6)

x/2 ( · 2)= 9 ( · 2)

x = 18

Her weekly allowance is $18

Answer:

23 boxes of pasta

The population estimated minimum sample size will be 11 , and the critical value will be 1.28.

The average gorilla weight is being calculated as a range estimate by a researcher (in pounds).

She wants to be within 7.1 pounds of the actual average with 80% accuracy.

Previous research has shown that the standard deviation of the weights of gorillas is 18.2 pounds.

a)  Since the confidence is 0.80 or 80% then the value of α is 0.20 and  and we can calculate the critical value. Then the value of the z-score will be  z = 1.28.

b)  The margin of error is given as

M.E.= z*(standard deviation/√n)

We have,

Margin of error = 7.1

From the above formula we get;

n =  ((z* standard deviation )/marginal error)²

n =  ((1.28*18.2)/7.1)²

  =   10.76 ≈ 11

Therefore, the researcher should take 11 samples.

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Answer:

Step-by-step explanation:

-19y=-13x -14 to y=-13/-19 - -14/-19

New York City will indeed pay two men $36 million for their wrongful conviction in the 1965 assassination of a civil rights activist.

How is the chronology so that New York City pays for the incident of wrongful conviction of two people for the alleged murder of a civil rights leader?

After carrying out further investigations into the lawsuits against 2 people, in particular Muhammad A. Aziz and Khalil Islam who were accused of the murder of the leader of civil rights activist, Malcolm X, it was found that the two defendants were victims of wrongful conviction. It was previously stated that the police appeared to be withholding evidence to weaken the charges leading to acquittal. However, in the end, the court gave an acquittal because it was known that Muhammad Aziz and Khalil Islam had been proven innocent. As a form of accountability, New York City is willing to pay 26 million dollars to the victims and an additional 10 million dollars from New York state.

In conclusion, the amount of money paid by New York City is a form of responsibility that has been approved for the wrongful conviction of Muhammad Aziz and Khalil Islam.

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These are  two ways to indicate how quickly this issue is evolving.

Given;

Jamel bought 2.5 pounds of hamburger meat at the shop for $7. What are the two possible methods to state the rate in this case?

Since he buys 2.5-pound hamburger meat on 7$;

The two ways to explain the rate of this situation is

(I) the amount of meat per $ is 2.5/7 = 5/14

(II) the cost of meat is 7/2.5 = 14/5 = 2.8 /pound

a) The maximum amount of hamburger meat that can be purchased by spending 1 dollar pounds of hamburger meat can be purchased by spending 1 dollar

b) The maximum cost of 1 pound of hamburger meat dollar Thus, 1 pound of hamburger meat costs 2.8 dollars

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Answer: -4

Step-by-step explanation:

Answer: Real and Rational

Step-by-step explanation:

2/3 is a fraction. ALL numbers are are considered real numbers. Rational numbers are typically fractions and decimals.

Answer:

9.47

Rounded to the nearest 0.01 or

the Hundredths Place.

Explanation

9.4725

You rounded to the nearest hundredths place. The 7 in the hundredths place rounds down to 7, or stays the same, because the digit to the right in the thousandths place is 2.

9.47

When the digit to the right is less than 5 we round toward 0.

9.4725 was rounded down toward zero to 9.47

Hope this helps!

Answer:

26

Step-by-step explanation:

18 + (6 - 2) x 2

18 + (4) x 2

18 + 8

= 26

Answer:

  tan(θ) = 2/3

Step-by-step explanation:

You want the tangent of the angle θ between the x-axis and the line connecting the origin to point (3, 2).

The tangent ratio is given by ...

  Tan = Opposite/Adjacent

In the attachment, you can see that the side opposite the angle of interest is the y-coordinate of the point. The side adjacent is the x-coordinate. That means ...

  tan(θ) = y/x

  tan(θ) = 2/3

__

Additional comment

In general, the tangent of the angle a line makes with the x-axis is the slope of the line. Your line has slope 2/3, and that is the tangent of the angle it makes with the x-axis.

The diagram which represents Mason's ratio of made throws and missed throws in the story is option A.

The following are answers to like terms collected respectively

The following expressions are equivalent

If Mason made 20 free throws

Equate missed throws ratio made throws

2 : 5 = x : 20

2/5 = x/20

cross product

2 × 20 = 5 × x

40 = 5x

divide both sides by 5

x = 40/5

x = 8

Total free throws Mason attempted = Number of throws Mason missed + Number of throws Mason made

= 8 + 20

= 28 free throws

If Jennifer made 16 bracelet with neon

Equate neon made bracelet ratio pastel made bracelet

4 : 3 = 16 : x

4/3 = 16/x

cross product

4 × x = 3 × 16

4x = 48

divide both sides by 4

x = 48/4

x = 12

Combine the like terms

4d + 5d

= 9d

8r + 6 + 9r - 3

= 8r + 9r + 6 - 3

= 17r + 3

6r - r + 4

= 5r + 4

Determine if the following expressions are equivalent

3 + 4 = 2 + 5

7 = 7

4(2 + x) = 8 + 4x

8 + 4x = 8 + 4x

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Answer:

Step-by-step explanation:

You want the radius and water depth in a spherical bowl in which the water level is 10 cm above the center of the sphere, and the circular surface has a diameter of 30 cm.

The geometry of the diameter of the water surface can be modeled as shown in the attachment. The radius of that surface forms one leg of a right triangle with the other leg being 10 cm. The hypotenuse of the triangle is the radius of the sphere, so we have ...

  r² = 15² +10² = 325

  r = √325 = 5√13 ≈ 18.03 . . . . . cm

The water depth is 10 cm more than the radius, so is ...

  d = 10 +r = 10 +5√13 ≈ 28.03 . . . . . cm

The radius of the bowl is about 18.03 cm; the depth of water is about 28.03 cm.

2.Under feudalism, landowners were granted plots of land (called fiefs) by nobles in exchange for their loyalty and military service. The landowner, or vassal, was required to provide the lord with soldiers when needed and give him a portion of the land's produce. In return, the lord provided the vassal with protection from invaders.

Manorialism (how did it work)

Manorialism was an economic system that developed in medieval Europe. It was based on the control of land and the produce of that land by a lord. The lord would grant land to peasants in exchange for their labor and a portion of the produce. This system allowed for the development of large estates and the growth of a class of landowners.

Justinian ( identify and achivements)

Justinian was the Byzantine emperor from 527 to 565. During his reign, Justinian sought to revive the empire's greatness and reconquer the lost western half of the historical Roman Empire.

One of Justinian's most famous achievements was the construction of the Hagia Sophia, which was completed in 537. The Hagia Sophia is a former Greek Orthodox cathedral that was turned into a mosque after the Ottoman conquest of Constantinople in 1453. It is now a museum in Istanbul, Turkey.

Another of Justinian's accomplishments was the compilation of the Justinian Code, a collection of laws that codified Roman law and is still used as a reference today. The Justinian Code was instrumental in the development of modern legal systems.

vassal

The social position and duties of a vassal during the Middle Ages was to provide military service to their lord in exchange for land that they could then cultivate. Vassals were also required to attend their lord's court and give him counsel

Knights

Serve as a military support system for the king

. Helped keep the peace within the kingdom

. Provided protection for the king and queen

. Guarded the king's castle

serf

The serfs were the lowest class of society in medieval Europe and were bound to the land that they worked on. They were required to work for their lord for a certain number of days each week and were given a plot of land to farm for themselves. They were also required to pay taxes and fees to their lord.

The values of the variables associated ot translation operations are (w, x, y, z) = (3, 1, 0, 2 / 3).

Herein we find two translation cases of points set on Cartesian plane. Translations are rigid operations of the form:

P'(x, y) = P(x, y) + T(x, y)

Where:

Now we proceed to determine the values of the variables w, x, y, z behind each translation operation, substitute on each component and solve the resulting formula:

T(x, y) = A'(x, y) - A(x, y)

(2 · x + 1, 4) - (- 1, w) = (4, 1)

(2 · x + 2, 4 - w) = (4, 1)

(x, w) = (1, 3)

T(x, y) = B'(x, y) - B(x, y)

(3, 3 · z) - (8 · y - 1, 1) = (4, 1)

(4 - 8 · y, 3 · z - 1) = (4, 1)

(y, z) = (0, 2 / 3)

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Answer:

The slope is 1/3, calculate the rest from there

Step-by-step explanation:

We can picture this as a graph with the x value being the shoe size and the y being the length of a foot in inches. If we visualize it that way, we have two points on the graph: (5,9) and (11,11). From this, we can calculate the slope. The formula for slope is change in y value/change in x value, or rise/run. The slope in this case would be 2/6, simplified to 1/3. From this, we know that every time the X value increases by 1, the Y value increases by 3. Using this, you can find the two points on the line yourself. The equation formula for slope is y = mx + b. M is the slope, and Y is the y intercept (the value of Y when X = 0). Since the slope is 1/3, the equation is y = 1/3x+(y intercept). I am not going to fully solve this problem for you because I have a feeling you need this answer for a test of sorts (because of the level of urgency) but with this information you can probably solve this yourself! Good luck :)

The inequality that can be used to find the number of gigabytes used is 52.50+5g<75 and the value of g should be less than 4.5.

According to the question,

We have the following information:

Gabriel pays a flat cost of $52.50 per month and $5 per gigabyte. He wants to keep his bill under $75.

Now, the number of gigabytes used are represented by g.

So, we will have the following inequality:

52.50+5g<75

Now, we will solve this inequality.

Subtracting 52.50 from both the side:

5g<75-52.50

5g<22.5

Dividing by 5 on both the sides:

g<22.5/5

g<4.5

Hence, the inequality that can be used to find the number of gigabytes used is 52.50+5g<75 and the value of g should be less than 4.5.

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The equation of the line with a slope of one third and passes through (-2, 1) is y = one-third x + five-thirds.

The equation of a line can be represented in a slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line has a slope of 1 / 3. Let's find the y-intercept using the coordinates (-2, 1)

y = 1 / 3 x + b

1 = 1 / 3 (-2) + b

1 + 2 / 3 = b

b = 3 + 2 / 3

b = 5 / 3

Therefore, the equation is y = 1 / 3 x + 5 / 3

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