HOW GIAND
4. The circle graph shows the results of a middle
school survey about favorite states to visit on
vacation. If 400 students were surveyed, how
many more students favor visiting Florida than
Colorado? (Example 2)
New York
7%
Favorite State to Visit
Other
16%
North
Carolina
Colorado
Florida
38%
15% California
13%

The inverse function of f(x) = (x - 3)²- 4 is f-1(x) = 3 + √(x + 4)

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

f(x) = (x - 3)²- 4

Rewrite as

y = (x - 3)²- 4

Swap x and y

So, we have

x = (y - 3)²- 4

This gives

(y - 3)² = x +  4

Take teh square roots of both sides

y - 3 = √(x + 4)

So, we have

y = 3 + √(x + 4)

So, the inverse function is f-1(x) = 3 + √(x + 4)

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The correct option regarding the simplification of the expression is given as follows:

B. [tex]12\sqrt{2} + 4\sqrt{3}[/tex]

The expression in the context of this problem is defined as follows:

[tex]4\sqrt{18} - 2\sqrt{27} + 5\sqrt{12}[/tex]

To simplify the expressions, first we must obtain the simplest radical form of each expression, as follows:

Hence the simplified expression is obtained as follows:

[tex]4(3\sqrt{2}) - 2(3\sqrt{3}) + 5(2\sqrt{3}) = 12\sqrt{2} - 6\sqrt{3} + 10\sqrt{3} = 12\sqrt{2} + 4\sqrt{3}[/tex]

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Step-by-step explanation:

This is a composit figure of a 20 x 30 m rectangle and a circle of radius 10m

area of rectangle + area of circle = total area

     l x w                +     pi r^2           = total

       20 x 30         + pi (10^2)   = 914.2 m^2

The probability that (all 23 are not smokers is 0.0429

P(all 23 are not smokers 0.0429

P(exactly 6 smokers)  ≈ 0.1671

a) If 16% of the population are smokers, then the probability that an individual is not a smoker is 1-0.16=0.84.

P(all 23 are not smokers) = 0.84²³ ≈ 0.0429

b) The probability that any one individual smokes is 0.16, and the probability that any one individual does not smoke is 0.84.

P(all 23 are not smokers) = 0.84²³ ≈ 0.0429 (rounded to four decimal places).

c) Similarly, we can use the binomial distribution to find the probability of exactly 6 smokers in a sample of 23:

P(exactly 6 smokers) = (23 choose 6) * 0.16⁶ * 0.84^17 ≈ 0.1671

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Answer:

157.08 in.

Step-by-step explanation:

C=2πr=2·π·25≈157.07963

Answer:

A

Step-by-step explanation:

look at pic below.

Here are steps to find the circumference of a circle with a radius of 25 inches:

1. Recall the formula for the circumference of a circle:

C = 2πr

2. Substitute the value of the radius into the formula:

C = 2π(25)

3. Simplify the expression by multiplying 2π by 25:

C = 50π

4. Use the approximate value of π, which is 3.14, to get a numerical answer:

C ≈ 50(3.14)

5. Calculate the product:

C ≈ 157

Therefore, the circumference of a circle with a radius of 25 inches is approximately 157 inches.

Answer:

z = 4 , y = 6 , 4 and 13

Step-by-step explanation:

1

8z - 15 = 17 ( add 15 to both sides )

8z = 32 ( divide both sides by 8 )

z = 4

2

22 = 4y - 2 ( add 2 to both sides )

24 = 4y ( divide both sides by 4 )

6 = y

3

3(- 7) + 25 = - 21 + 25 = 4

4

16 - 6 ÷ 2 ← perform division before subtraction

= 16 - 3

= 13

For the middle par, using the answers associated to the colours

13 + (6 ÷ 4) - 4

= 13 + 1.5 - 4

= 14.5 - 5

= 10.5

Answer: 9 and 2/3

Step-by-step explanation:

Answer: The surface area of the rectangular prism is 424 square meters.

Step-by-step explanation: To find the surface area of a rectangular prism, we need to add up the areas of all six faces.

The front and back faces have an area of length x height, which in this case is 4 x 8 = 32 square meters each.

The top and bottom faces have an area of width x height, which in this case is 15 x 8 = 120 square meters each.

The left and right faces have an area of length x width, which in this case is 4 x 15 = 60 square meters each.

So the total surface area of the rectangular prism is:

32 + 32 + 120 + 120 + 60 + 60 = 424 square meters.

Therefore, the surface area of the rectangular prism is 424 square meters.

Using the net, the correct surface area of the prism is 216 square units

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

The triangular prism

Using the net, the surface area is

Surface area = Sum of areas of individual shapes

So, we have

Surface area = 2 * 1/2 * 3 * 4 + 17 * 5 + 17 * 4 + 17 * 3

Evaluate

Surface area = 216

Hence, the surface area of the prism is 216 square units

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Answer:  x=3   <W=27

Step-by-step explanation:

<Y is half of the arc XW

<Y=78/2 =39

The sum of all the angles in a triangle is 180

so add all angles ang make =180

114+39+7x+6=180          Simplify

159+7x=180                   Subtract 159 from both sides

7x=21                              Divide 7 to both sides

x=3

plug back in x to find <W

<W=7(3)+6

=21+6

27

Brett needs a complete of  [tex]322 \frac{5}{6} ^{2}[/tex]  inches of construction paper for his project.

The area of a rectangle is calculated through multiplying its length by its width. consequently, to discover the entire amount of square inches of construction paper Brett needs for his project, we want to calculate the area of each rectangle after which add them collectively.

The area of the primary rectangle is:

16 inches × 12 1/4 inches = 196 square inches

The area of 2nd rectangle is:

10 1/3 inches × 10 1/4 inches = (31/3) inches × (41/4) inches = 126 5/6 square inches

To add those areas collectively, we need to convert 2nd area to a mixed number:

126 5/6 square inches = 126 square inches + 5/6 square inches

Now we can add the 2 areas collectively:

196 square inches + 126 square inches + 5/6 square inches = 322 5/6 square inches

Therefore, Brett needs a complete of  [tex]322 \frac{5}{6}^{2}[/tex] inches of construction paper for his project.

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Answer:

Set your calculator to degree mode.

[tex] x = {cos}^{ - 1} \frac{5}{7} = 44.4[/tex]

Angle x measures 44.4 degrees.

The area of the decagon with side length 10 is 769.42 square units

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

side length, l = 10

The area of the decagon is calculated as

Area = 5/2l² * √[5 + 2√5]

Where

l = 10

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

Area = 5/2 * 10² * √[5 + 2√5]

Evaluate

Area = 769.42

Hence, the area is 769.42

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Answer: Answer

Step-by-step-explanation: 4:2 plays a sport 13:9 does not

The length of the side EF = 22.5 Units

The properties of the triangle are:

The sum of all the angles of a triangle (of all types) is equal to 180°.

The sum of the length of the two sides of a triangle is greater than the length of the third side.

In the same way, the difference between the two sides of a triangle is less than the length of the third side.

From the property of the similar triangle,

The ratio of the sides is always equal

So,

DE/EF = GH/EH

12/EF = 8/15

Cross multiply to get

(12*15)/8 = EF

180/ = 22.5

EF= 22.5 units

Therefore, the length of the EF is 22.5 Units.

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Answer:

x=28

x=-28

Step-by-step explanation:

The lower quartile, the median, and the upper quartile are 22, 31 and 90

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

11, 18, 22, 22, 31, 31, 63, 86, 90, 92, 98

Split the data values into 2

So, we have

11, 18, 22, 22, 31,

31,

63, 86, 90, 92, 98

The middle of each set is the quartiles

So, we have

Lower = 22

Median = 31

Upper = 90

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Answer:

Step-by-step explanation:

6v-19=3v-4

subtract 3v from both sides

3v-19=-4

add 19 to both sides

3v=15

divide both sides by 3

v=5

The better prediction of x when y = 7, based on the scatter plot, would be A. 11.

When looking at the scatter plot, we see that the potential y values below 10, correspond with potential x values below 20. This is why the only dots in the quadrant y < 10 are also x < 20.

When we have a y value that is 7, this is below 10. What this means therefore is that the most likely value of x is 11 because 52 would be much too high.

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Answer: 1.5

Step-by-step explanation:

To find the constant ratio of successive y-values, we need to divide each y-value by the previous one.

For example, to find the ratio between the second and first y-values:

7.5 ÷ 5 = 1.5

Similarly, we can find the other ratios:

11.25 ÷ 7.5 = 1.5

16.875 ÷ 11.25 = 1.5

25.3125 ÷ 16.875 = 1.5

Since all the ratios are the same, we can conclude that the constant ratio of successive y-values is 1.5.

Therefore, the answer is c. 1.5.

Answer:

The 3rd one or C

Step-by-step explanation:

A       B

C      D

Tatiana is the athlete who trains a weekly amount of kilometers equal to the median of the 11 competitors.

To find the median, we need to first arrange the values in order from lowest to highest:

4, 5, 5, 5, 5.5, 6, 7, 8, 8, 9, 10

Since there are 11 values, the median is the middle value. In this case, the middle value is 5.5. Therefore, the athlete who trains a weekly amount of kilometers equal to the median of the 11 competitors is Tatiana, who trains 5.5 kilometers per week.

None of the other athletes in the table trains exactly 5.5 kilometers per week, so Tatiana is the only correct answer.

It's worth noting that the median is a measure of central tendency that is less sensitive to outliers than the mean. In this case, the values range from 4 to 10, which is a relatively wide range, but the median still provides a useful measure of the typical training distance among the 11 athletes.

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a. The definite integral ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx = πr²/2

A definite integral is an integral evaluated on an interval.

Given the figure, to evaluate the definite integral ∫₀²f(x)dx and ∫₂⁴f(x)dx, we proceed as follows.

a.  The definite integral ∫₀²f(x)dx

Observe the graph, the integral ∫₀²f(x)dx is the area occupied by the square on the interval (0, 2).

So,  ∫₀²f(x)dx = lw

b.  The definite integral ∫₂⁴f(x)dx

Observe the graph, the integral ∫₂⁴f(x)dx is the area occupied by the circle on the interval (2, 4).

So,  ∫₂⁴f(x)dx = πr²/2

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The fraction can be represented as follows:

[tex]\frac{6^8}{6^8} = 6^0[/tex]

Remember the rule for exponents:

[tex]\frac{a^n}{a^m} = a^{n - m}[/tex]

So we just need to subtract the exponents

Here we have the following quotient:

[tex]\frac{6^8}{6^8}[/tex]

Using the rule above, we can rewrite that fraction as follows:

[tex]\frac{6^8}{6^8} = 6^{8 - 8} = 6^0[/tex]

So the exponent at the end is zero, this means that the correct option is B.

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Answer:

a)

[tex] log_{9}(7) - log_{9}(8) = log_{9}( \frac{7}{8} ) [/tex]

b)

[tex] log_{5}(11) + log_{5}(4) = log_{5}(44) [/tex]

c)

[tex] log_{9}(81) = log_{9}( {3}^{4} ) = 4 log_{9}(3) [/tex]

The missing side lengths in the triangles are c = 20 ft, b = 17.32 ft and x = y = 6√2

Triangle 1

The side length c is calculated as

sin(30) = 10/c

So, we have

c = 10/sin(30)

Evaluate

c = 20

This also means that the side length b is calculated as

b² = 20² - 10²

b² = 300

Take the square roots

b = 17.32

Triangle 2

Given that the acute angle in the right triangle is 45 degrees and the hypotenuse is 12 meters

The side lengths x and y are calculated as

x = y = 12/√2

Rationalise the expression

x = y = 6√2

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By simplification we get: [tex]2^4p^8q^1^2[/tex]

Simplify  the expression:

=> [tex](2p^2 q^3)^4[/tex]

We use the property for simplification i.e.,:

[tex](a^m)^n=a^m^n[/tex]

So, We solve by using above property:

[tex]p^2[/tex] raised to the 4 th power = [tex](p^2^.^4) =p^8[/tex]

[tex]q^3[/tex] raised to the 4 th power = [tex](q^3^.^4)=q^1^2[/tex]

Complete simplification, we get:

[tex](2p^2 q^3)^4=[/tex] [tex]2^4p^8q^1^2[/tex]

Hence, By simplification we get: [tex]2^4p^8q^1^2[/tex]

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The graph of the given inequalities is Attached below.

From the given inequalities:

As the first inequality is not strictly true, the graph of it is a straight solid line that passes through the points (0, 2) and (2/3, 0), with the shaded area being further from the origin ( as it fails the zero point test )

As the second inequality is not stringent, the graph of the inequality is a straight solid line that passes through the points (0,-4) and (8,0), with the shaded area pointing in the direction of the origin (since the inequality passes the zero point test)

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Complete question:

Which graph represents the system of inequalities?

y + 3x ≥ 2

y + 4 ≥ 1/2x

Yes, there are cases where the value of x or a would cause a problem in this equation.

A value of 0 for a would cause a problem because division by zero is undefined.

Therefore, we cannot have a=0 in this equation.

Additionally, if a fraction is being used as a value for a, there could be potential problems with rounding errors or decimal approximations that could cause issues in solving for x accurately.

It is also possible that certain values of x may make the left-hand side of the equation undefined, such as if x = 0 and a = 6.

However, these cases may not necessarily be problematic, depending on the context of the problem and the solutions being sought.

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The measures the angle 3 is given by 45°.

Hence the correct option is (B).

The quadrilateral which has four equal sides and the adjacent sides of which are in perpendicular that is called Square.

The given figure is a Square.

We know that the angle between two adjacent sides = 90°.

We also know that the diagonal of square divides angles into two equal parts of angles.

So here angle 3 is a one equal part of angle between two adjacent sides of  square.

So angle 3 is given by = (1/2)*90° = 45°.

Hence the correct option will be (B).

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Answer:10

Step-by-step explanation: