Mr. Johnson predicted the average score on the vocabulary test he gave would be 85 points.
His prediction was 8% lower than the actual average score. What was the actual average
score on the vocabulary test?
Round your answer to the nearest tenth.

Answer:

1st answer option

Step-by-step explanation:

the 45° side angles make this an isoceles triangle (both legs are equally long).

therefore, x = y.

Pythagoras gives us

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), and a and b being the legs.

so, we have

(5 × sqrt(2))² = x² + y² (remember, x = y)

(5 × sqrt(2))² = x² + x²

25 × 2 = 2x²

25 = x²

x = 5

because of x = y

y = 5

Answer: Its. C. Line BC is longer than line BD

Step-by-step explanation:

Answer:

A. true

Step-by-step explanation:

I believe you pay most of your interest when you first receive the loan.

The cost of the tasks to surround the figures with a fence, equivalent to   perimeter of the fence and an extra percentage are as follows;

1. $143

2. $143.75

3. $147.84

4. $224.64

The perimeter of a figure is the length of the line that surrounds the plane area covered by the figure.

1. The perimeter of the fence = 2 ft +  4 ft + 2 ft + 4 ft + 2 ft + 4 ft + (4 ft - 2 ft)  = 20 ft

The perimeter needed = 110/100 × 20 ft = 22 ft

The cost of 4 feet of fence = $26

Cost per feet of fence = $26/4 = $6.5/ft

Cost of the task = 22 feet × $6.5/ft = $143

2. The perimeter of the fence = 3 ft + 3 ft + 2 ft + 3 ft + 1 ft + 2 ft + 1 ft + 2 ft + 3 ft = 20 ft

The perimeter of the fence needed = 115/100 × 20 ft = 23 ft

Cost of 4 feet = $25

Cost per ft = $25/4 = $6.25

Cost of the fencing = 23 ft × $6.25/ft = $143.75

3. The perimeter of the fence = 5 ft +  3 ft + (6 ft - 5 ft) + 2 ft +  6 ft + 2 ft + 3 ft = 22 ft

The fence needed = 120/100 × 22 ft = 26.4 ft

The cost of 5 ft of fencing = $28

The cost per feet = $28/5 ft = $5.6/ft

The cost of the fencing = 26.4 ft × $5.6/ft = $147.84

Cost of the Task = $147.84

4. The perimeter of the fence = 8 ft + 6 ft + (8 ft - 6 ft) + (8 ft - 6 ft) + 6 ft + 8 ft = 32 ft

The fencing needed = 104/100 × 32 ft = 33.28 ft

The cost for 4 feet = $27

The cost per feet = $27/4 ft = $6.75/ft

The cost of the task = 33.28 ft × $6.75/ft = $224.64

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Answer: 2nd first 1st second third 4th fourth 3rd and 5th in 5th

Step-by-step explanation:

Answer:

n = -1

Subtract and isolate

To solve this problem, the first thing we have to do is regroup the terms so that we can then subtract, simplify, subtract, and finally simplify again.

But first we must know.

Equations are those mathematical equalities divided between two expressions which are called members and separated by their equal sign, in which known elements and unknown or unknown data appear, related by mathematical operations.

Now we must check our results.

8n -7 = -12 + 3n

8 × - 1 - 7 = -12 + 3 × - 1

- 8 - 7 = - 12 - 3

- 15 = - 12 - 3

- 15 = - 15

So, our results are correct, the answer is n = - 1

¡Hope this helped!

Answer:

20

Step-by-step explanation:

5 x 4 = 20

(A)  The required inequality is,  -40°F  <  x  <  140°F.

(C) The gas has freezing point of -40°F, that means below that temperature the gas will freeze.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

(A) Let the liquid range is from -40°F to 140°F.

Let x be the range.

So, the required inequality is,

-40°F  <  x  <  140°F

(B) The graph of inequality is attached below.

(C) Since the gas has freezing point of -40°F, that means below that temperature the gas will freeze.

(-49°F < 40°F)

Hence, the gas will freeze.

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Answer:

3 / 5

Step-by-step explanation:

TOA-CAH-SOH are 3 trigonometry ratios. They are:

TOA - tan(theta) = Opposite ÷ Adjacent

CAH - cos(theta) = Adjacent ÷ Hypotenuse

SOH - sin(theta) = Opposite ÷ Hypotenuse

We are finding Cos(A)

Cos(A) = Adjacent ÷ Hypotenuse

= AB ÷ AC

=

[tex] \frac{30}{50} \\ = \frac{3}{5} [/tex]

Therefore Cos(A) = 3 / 5.

The difference between fundamental theorem of calculus part 1 and 2 is explained below:

The basic theorem of calculus is a theorem that connects the ideas of differentiating and integrating functions. A constant value that relies on where one begins to compute area makes the two procedures the inverses of one another. The relationship between the integral and derivative is established by the calculus fundamental theorem. Simply put, it says that the height of the area at a point x equals the rate of change of the area under the curve up to that point. We can find definite integrals with the aid of this theorem.

The connection between the integral and the derivative is demonstrated in The Fundamental Theorem of Calculus, Part 1. Take note. A definite integral can be assessed in terms of an antiderivative of its integrand using the Fundamental Theorem of Calculus, Part 2. This formula will calculate the total area under a curve.

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Answer:

120

Step-by-step explanation:

Using the theorems of geometry, you know that all angles of a triangle add up to 180º. We can use an equation after looking at both angles, and the total:

30 + 30 + x = 180

60 + x = 180

x = 180 - 60

x = 120

Answer:216

Step-by-step explanation:

Answer:

cis theanswerforthequwstion

The required expected number of women on the committee is 1/2 or 0.5.

The expected number of women on the committee can be found by calculating the probability that a woman is selected for the committee and then multiplying that probability by the number of people on the committee.

There are a total of 6 + 2 = 8 people in the club, and the committee has 2 people.

Given the committee is selected randomly, the probability that a particular person is selected for the committee is 2/8 = 1/4.

There are 2 women in the club, so the probability that a woman is selected for the committee is 2/8 = 1/4.

The expected number of women on the committee is the probability that a woman is selected for the committee multiplied by the number of people on the committee, which is (1/4) * 2 = 1/2.

Thus, the expected number of women on the committee is 1/2 or 0.5.

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Answer: Yes

Step-by-step explanation:

Parallel means that the lines are a constant distance away from each other and they never touch. As you can see lines C and D never touch.

The Lines D and C are Parallel since Parallel lines never touch

Hope this helps!

Statement C is correct

The line lies on the same plane as the points.

A 3-d or three-dimensional plane is called a hyperplane.

The three axes X-axis, Y-axis, and Z-axis are mutually perpendicular to each other.

We can represent a plane in vector form using the following equation. (p — p₀) . n = 0

Let the line is passing through two points on a given plane. Then,  this is the line joining the two points and so all the points lying on this line must also lie on the plane. This clearly tells that the line completely lies on the same plane as the points.

the correct option is Statement C. The line is on the same plane as the points

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Answer: (-3,-3)

Step-by-step explanation:

Sub in the numbers

3(0)-4(-4)<16

16<16 wrong

3(-3)-4(-3)<16

-9+12<16

3<16 Correct

(-3,-3)

The  equation that correctly solves for x in △RST is; x² + 11x - 42 = 0

We are given that ΔDEF ∼ △RST.

This means that ΔDEF is similar to △RST.

From the concept of similar triangles, all corresponding sides are usually in the same ratio. Thus, applying this to our given triangles, we have;

DE/RS = EF/ST = DF/RT

This means when we plug in the relevant values, we will get;

(x + 5)/12 = (x + 7)/(x + 12) = 6/(x + 6)

Thus, we can say that;

(x + 5)/12 = 6/(x + 6)

Cross multiply to get;

(x + 5)(x + 6) = 72

x² + 11x + 30 - 72 = 0

x² + 11x - 42 = 0

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Complete question is;

In the figure shown, ΔDEF ∼ △RST . Which equation can be used to find the value of x?

Answer: 2/1

Step-by-step explanation:

You can decide this by looking at the rise over the run.

Answer:

Answer: C. Oliver will knit eight rows each week for nine weeks and then he will still have nine rows to knit.

Step-by-step explanation:

to solve for m

distribute into parentheses

176 = -16 - 24m

get m on one side

176 + 16 = -24m

192 = -24m

divide by -24

-8 = m

m = -8

you think I know

Step-by-step explanation:

bro what

Triangle ABC has been translated 4 units to the right into triangle DEF. Then, the coordinates of point E is (6, -2).

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that, triangle ABC has been translated 4 units to the right into Triangle DEF.

From the given coordinate plane A(-8, -2), B(2, -2) and (-4, -9)

When the shape is moved towards the right by k units, then replace x with x + k.

Now,

A(-8, -2) → D(-8+4, -2)=D(-4, -2)

B (2, -2) → E(2+4, -2)=E(6, -2)

C (-4, -9) → F(-4+4, -9)=F(0, -9)

Therefore, the coordinates of point E is (6, -2).

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The area for the shaded region is obtained as 2 units.

In order to find the area, first find the intersection points of the two curves. Then, the area of the region can be found by taking the integration from the intersection point.

The curves in the graph in the form of equation are as follows,

y = x² + 3                     (1)

x = (y - 5)² - 2

=> y = √(x+ 2) + 5       (2)  

Part A :

The intersection points of the two curves are (-1.5, 5.5), (-1, 4) and (0.5, 3.5).

Thus, to calculate the area the limit is from x = -1.5 to x = 0.5.

Part B :

The expression of the integral is given as,

[tex]\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx[/tex]

Part C :

The area is found by evaluating the integral as follows,

[tex]\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx[/tex]

= [-1/3 + 3.375/3 + 3(-1 - (-1.5))] - [5(-1 - (-1.5)) + 2/3([tex]1^{3/2} - 0.5^{3/2}[/tex])] + [5(0.5 - (-1)) -(0.125/3 + 1/3 + 3(0.5 - (-1))]

= 2.291 - [2.5 + 2/3 × 0.647] + [5 × 1.5 - 4.8716]

= 2.291 - 2.927 + 2.6284

= 1.9924

Which is approximately 2.

Hence, the area between the curves is given as 2 units.

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Answer:

To find the value of the quartiles, we need to first find the median of the data set. The median is the middle value of the data set, or the value that separates the lower half of the data from the upper half. In this data set, the median is 68, as it is the middle value when the data is arranged in ascending order.

Once we have the median, we can find the first and third quartiles. The first quartile, also known as Q1, is the median of the lower half of the data set, and the third quartile, also known as Q3, is the median of the upper half of the data set. In this data set, the lower half of the data is {56, 58, 64}, and the upper half of the data is {72, 75, 78}. The median of the lower half is 58, and the median of the upper half is 75.

Therefore, the value of the quartiles is Q1 = 58, Q2 = 68, and Q3 = 75.

Option D, Q1 = 58; Q2 = 68; Q3 = 75, is the correct answer.

Step-by-step explanation:

Adding the times on A and B gets you 16 minutes and 3 seconds. 20 minutes minus 16 minutes and 3 seconds will leave you with

3 minutes, 57 seconds