find the slope of a line perpendicular to y=- 1/2x+7

Using the interquartile range (IQR) method, the value 2 is considered an outlier in the given data.

To determine if there is an outlier in the given data, we need to calculate the lower and upper bounds using the interquartile range (IQR) method.

First, we need to calculate the first quartile (Q1), second quartile (Q2 or median), and third quartile (Q3) of the data.

Arranging the data in ascending order

2, 9, 13, 17, 18, 20, 23, 24, 33, 34, 43, 45, 53, 53

Q1 = 17

Q2 = 24

Q3 = 43

Next, we can calculate the IQR by subtracting Q1 from Q3

IQR = Q3 - Q1 = 43 - 17 = 26

Now we can calculate the lower and upper bounds

Lower bound = Q1 - 1.5 × IQR = 17 - 1.5 × 26 = -8

Upper bound = Q3 + 1.5 × IQR = 43 + 1.5 × 26 = 79

Any values outside the lower and upper bounds are considered outliers.

In this case, we have a value of 2 that is outside the lower bound of -8. Therefore, 2 is considered an outlier in the given data.

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Answer:

Let the cost of each pair of trousers be x dollars.

(i) Belle bought 40 pairs of trousers for a total of $2040, so we can set up an equation:

40x = 2040

Solving for x, we get:

x = 2040/40 = 51

Therefore, each pair of trousers cost Belle $51 to buy.

(ii) Belle made a loss of $200 on the entire sale of 40 pairs of trousers. The cost of 40 pairs of trousers is:

40 x $51 = $2040

So, Belle sold 40 pairs of trousers for:

$2040 - $200 = $1840

Belle's cost was $2040, and she sold the trousers for $1840, so her loss was:

$2040 - $1840 = $200

The loss per pair of trousers is the total loss divided by the number of pairs of trousers sold, which is:

$200/40 = $5

Therefore, Belle made a loss of $5 on each pair of trousers sold.

(iii) The selling price of each pair of trousers can be found by adding the loss per pair to the cost per pair:

Selling price = Cost + Loss

Selling price = $51 + $5

Selling price = $56

Therefore, Belle sold each pair of trousers for $56.

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The probability of selling more than 5 properties in a week is 0.7494 (rounded to four decimal places).

The probability of selling more than five properties in a week would be calculated using the binomial distribution method. Binomial distribution is used to calculate the probability of an event happening, given a specific number of trials and assuming that each trial is independent of the others. In this case, we want to know the probability of selling more than five properties in a week.

The formula for the probability of selling more than five properties in a week is:
P(X > 5) = 1 - P(X ≤ 5)
Where P is the probability of selling any one property in a week, and X is the number of properties sold in a week.
Using the binomial probability formula, we can determine the probability of selling exactly k properties in one week:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where
n = 12 (total number of properties)
k = number of properties sold
p = 0.40 (probability of selling any one property in a week)
We can now calculate the probability of selling more than 5 properties in a week:

P(X > 5) = 1 - P(X ≤ 5)
P(X > 5) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5))
P(X > 5) = 1 - [(12 choose 0) * (0.40)^0 * (0.60)^(12-0) + (12 choose 1) * (0.40)^1 * (0.60)^(12-1) + (12 choose 2) * (0.40)^2 * (0.60)^(12-2) + (12 choose 3) * (0.40)^3 * (0.60)^(12-3) + (12 choose 4) * (0.40)^4 * (0.60)^(12-4) + (12 choose 5) * (0.40)^5 * (0.60)^(12-5)]
P(X > 5) = 1 - [0.000015 + 0.0003 + 0.003 + 0.018 + 0.068 + 0.161]
P(X > 5) = 1 - 0.250583
P(X > 5) = 0.749417

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Answer:

(5 + 9) + 3 = 17

Step-by-step explanation:

The Associative Property of Addition states that no matter how you group the numbers to be added, the results will still be the same. In this case:

Original:

5 + (9 + 3) = 17

5 + 12 = 17

17 = 17 (True)

Associative Property of Addition:

(5 + 9) + 3 = 17

(14) + 3 = 17

17 = 17 (True)

As you can see, the grouping does not matter as the outcome is still the same.

~

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To solve a system of equations, you need to find the values of the variables that satisfy both equations simultaneously. There are different methods to solve systems of equations, including substitution, elimination, and graphing. Here's an example of using substitution:

Solve the system of equations:

2x + y = 5

x - y = 1

From the second equation, we get x = y + 1. Substitute this expression for x into the first equation:

2(y + 1) + y = 5

Simplifying and solving for y, we get:

3y + 2 = 5

3y = 3

y = 1

Then, substitute y = 1 into x = y + 1 to get:

x = 2

So the solution to the system of equations is x = 2 and y = 1.

To solve a system of inequalities, you need to find the values of the variables that satisfy both inequalities simultaneously. There are different methods to solve systems of inequalities, including graphing and substitution. Here's an example of using graphing:

Solve the system of inequalities:

x + y ≤ 3

x - y > 1

First, graph the boundary lines of each inequality. For the first inequality, the boundary line is x + y = 3, which is a line with intercepts (3, 0) and (0, 3). To decide which side of the line to shade, test a point that is not on the line, such as (0, 0):

0 + 0 ≤ 3, which is true

Therefore, shade the side of the line that contains the origin.

For the second inequality, the boundary line is x - y = 1, which is a line with intercepts (1, 0) and (0, -1). To decide which side of the line to shade, test a point that is not on the line, such as (0, 0):

0 - 0 > 1, which is false

Therefore, shade the side of the line that does not contain the origin.

The shaded region that satisfies both inequalities is the region that is below the line x + y = 3 and to the right of the line x - y = 1. This region is a triangle with vertices (1, 2), (2, 1), and (2, 2).

I hope this explanation helps you with your homework!

Answer:

False

Step-by-step explanation:

You can transform a function many times

:)

The factorizations of the given expressions are:

[tex]9x^{2}-6x+15[/tex] = 3(3x+5)(x-2)

[tex]2x^{2}+11x+5[/tex] = (2x+1)(x+5)

[tex]2x^{2}+3x-9[/tex] = (2x-3)(x+3)

[tex]10x^{2}+80x+70[/tex] = 10(x+1)(x+7)

[tex]3x^{2}-8x+4[/tex] = (x-2)(3x-2)

[tex]x^{2}-16[/tex] = (x+4)(x-4)

[tex]9x^{2}-6x+15[/tex]

We can first factor out the greatest common factor, 3:

[tex]9x^{2}-6x+15[/tex] = 3([tex]3x^{2}-2x-5[/tex])

[tex]3x^{2}-2x-5[/tex] = (3x+5)(x-2)

Putting it all together, we get:

[tex]9x^{2}-6x+5[/tex] = 3(3x+5)(x-2)

[tex]2x^{2}+11x+5[/tex]

We need to find two numbers that multiply to give 2x5=10 and add up to 11. Those numbers are 1 and 10:

[tex]2x^{2}+11x+5[/tex] = (2x+1)(x+5)

[tex]2x^{2}+3x-9[/tex]

We need to find two numbers that multiply to give 2x(-9)=-18 and add up to 3. Those numbers are 6 and -3:

[tex]2x^{2}+3x-9[/tex] = (2x-3)(x+3)

[tex]10x^{2}+80x+70[/tex]

We can first simplify the expression by factoring out 10:

[tex]10x^{2}+80x+70[/tex] = 10([tex]x^{2}+8x+7[/tex])

Now we need to factor the quadratic expression inside the parentheses:

[tex]x^{2}+8x+7[/tex] = (x+1)(x+7)

Putting it all together, we get:

10(x+1)(x+7)

[tex]3x^{2}-8x+4[/tex]

We need to find two numbers that multiply to give 3x4=12 and add up to -8. Those numbers are -2 and -6:

[tex]3x^{2}-8x+4[/tex] = (x-2)(3x-2)

[tex]x^{2}-16[/tex]

This is a difference of squares, which we can factor as:

[tex]x^{2}-16[/tex] = (x+4)(x-4)

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The correct option is:

Steering wheel the proper distance from the body, at least a foot from the body, right foot should reach behind the brake pedal and knee should be slightly bent.

What is distance?

Distance is a numerical measurement of the amount of space between two objects or points.

distance between steering wheel and body ≥ 1 foot

length of driver's leg + distance from seat to brake pedal = distance from seat to brake pedal when leg is slightly bent

These considerations help to ensure that the driver is seated in a safe and comfortable position while operating the vehicle.

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Answer:

168 ft^2

Step-by-step explanation:

18×8=144ft^2 for the area of the rectangle

8×6=48ft^2

48÷2=24ft^2 for the area of the triangle

144+24=168ft^2

A ship sails from port a, on a bearing of 050, to port b which is 80km to the east of a. it then sails on a bearing of 062 for 72km until it reaches pot c. West is 270 degrees. Hence Answer would be 80 km.

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Answer: Option C, (x - 4)(x - 5)

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Given:  [tex]\textsf{x}^2\textsf{ - 9x + 20}[/tex]

Find:  [tex]\textsf{Determine the factored form}[/tex]

Solution: In order to factor the given equation, we need to first determine two numbers which add up to -9 and multiply to become 20.  We can think of the factors of 20 which would add up to -9 and the one that matches that description would be -5 and -4.  These two numbers multiply to become 20 and combine to become -9.  Now that we have that information, we can break up the quadratic into two separate roots using the two numbers that we found.  

Therefore, the answer would be Option C, (x - 4)(x - 5).

The value of the angle a is 49 degrees and angle b is 139 degrees in the given triangle.

External angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle. For each vertex, there are two equivalent exterior angles.

Each vertex typically displays a single external angle. The exterior angles of a triangle are those that are formed outside of it. The exterior angle of a triangle is defined as the angle formed between one of a triangle's sides and its neighboring extended side. As a result, the exterior angle of a triangle is the angle formed by any extended side of a triangle and its neighboring side.

Given that the measure of angle y = 49 degrees.

We observe from the figure that angle a is vertically opposite angle of y thus,

angle y = angle a = 49 degrees.

Now, angle b is exterior angle and,

angle b = angle a + 90

angle b = 49 + 90

angle b = 139 degrees.

Hence, the value of the angle a is 49 degrees and angle b is 139 degrees in the given triangle.

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The value of x, the missing side which is the hypotenuse, is approximately 24.85 units.

To solve this problem, we can use the trigonometric function of sine, since we know the opposite side and we want to find the hypotenuse.

The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse:

sin(θ) = opposite/hypotenuse

In this case, θ is the angle 75 degrees, the opposite side is 24, and we want to find the hypotenuse x:

sin(75°) = 24/x

To solve for x, we can cross-multiply:

x * sin(75°) = 24

Then, we can divide both sides by sin(75°):

x = 24 / sin(75°)

Using a calculator, we get:

x = 24.85 units

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Answer:

#1. A. y=sin x + 2 Is the same as cos.

Step-by-step explanation:

Answer:

w ≥ 13.5

Step-by-step explanation:

-(4/ 9)w ≤ -6

Multiply both side by - 1

(4/ 9)w ≥ 6

Cross multiply

4w ≥ 54

Divide both side by the coefficient of w

4w/4 ≥ 54/4

w ≥ 13.5

Answer:

largest angle ≈ 109.6°

Step-by-step explanation:

the largest angle in the triangle is the angle opposite the longest side.

Here that is the angle opposite side of 7.8 cm

let a = 7.8, b = 5.4 , c = 4.1 and A the largest angle , then

cosA = [tex]\frac{b^2+c^2-a^2}{2bc}[/tex]

        = [tex]\frac{5.4^2+4.1^2-7.8^2}{2(5.4)(4.1)}[/tex]

        = [tex]\frac{29.16+16.81-60.84}{44.28}[/tex]

       = [tex]\frac{45.97-60.84}{44.28}[/tex]

       = [tex]\frac{-14.87}{44.28}[/tex]

then

A = [tex]cos^{-1}[/tex] ( [tex]\frac{-14.87}{44.28}[/tex] ) ≈ 109.6° ( to 1 decimal place )

Answer:

A.

Step-by-step explanation:

the solution to a relation (like an equation, but also inequalities and so on) is the set of values that make the whole thing true (or consistent).

every other value is not a solution.

The correct angle measures of triangle XWZ are m∠x = 55°, m∠w = 125°, m∠z = 125°.  The correct options are A, B and D.

The correct angle measures are m∠x = 55°, m∠w = 125°, m∠z = 125°

The option "m∠w = 55°" and "m∠z = 55°" are incorrect. Because "m∠w = 55°" and "m∠z = 55°" are incorrect is that there is only one angle measurement that can be equal to 55°, which is m∠x. This is because in any triangle, the sum of the interior angles is always 180°. Therefore, if m∠x is 55°, then the sum of the other two angles (m∠w and m∠z) must add up to 125° (i.e., 180° - 55°).

So, if m∠w is 125°, then m∠z must also be 55°, and if m∠z is 125°, then m∠w must be 55°. Hence, the options "m∠w = 55°" and "m∠z = 55°" cannot both be correct at the same time. So, the correct answers are A, B and D.

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_____The given question is incomplete, the complete question is given below:

Which angle measures are correct? select three options. A m∠x = 55°   B m∠w = 125°   C m∠w = 55°   D m∠z = 125°  E m∠z = 55°.

Answer:

A , B , E

Step-by-step explanation:

Just put A , B , D and got it wrong

The contrapositive of the given statement is: She will not hang out with her friends If she did not get off work early

Given that we have the following statement:

"If she gets off work early, she will hang out with her friends."

The contrapositive of a statement is defined as:

The above means that we have the contrapositive of the given statement to be:

She will not hang out with her friends If she did not get off work early,

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The digit information are:

A) 900,000,000

B) 40,000

900,000,000: Nine hundred million. The first three digits (900) represent the hundred millions place, the next three digits (000) represent the ten millions place, and the last three digits (000) represent the ones (or units) place.

Lastly, 7009: Seven thousand nine. The first digit (7) represents the thousands place, the next two digits (00) represent the hundreds place (which are omitted since they are zeroes), and the last two digits (09) represent the ones (or units) place.

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See full text below

3.- Anota el valor posicional de las cifras encerradas

=

a) (9) 1(5) 23(6) 470

b) 38(4) 1(7) 6(9)

3.- Write down the place value of the enclosed figures

=

a) (9) 1(5) 23(6) 470

b) 38(4) 1(7) 6(9)

By answering the presented question using inequality, , we may conclude that Therefore, the equation of the line passing through the points (1,2) and (2,3) is

An inequality in mathematics is a link between two expressions or values that is not equal. As a result, inequality results from imbalance. An inequality in mathematics is a relationship between two values that are not equal. Equality and inequality are not the same thing. The not equal sign is often used to indicate that two values are not equal (). To contrast values, various disparities—no matter how small or large—are used. By changing the two sides until just the variables are left, many fundamental inequalities can be resolved. Yet, a variety of causes fuel inequality: On both sides, negative values are divided or added. Trade right and left.

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation:

[tex]y-ylm(x-x1) = \\m = (y^2 - y1)/(x^2 − x^1) \\m = (3-2)/(2-1) = 1\\ m = y-2=1\\(x-1) y-2=x-1\\y = x+1[/tex]

Therefore, the equation of the line passing through the points (1,2) and (2,3) is

D) y=x+1

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Answer:

Each black pentagon in the soccer ball is surrounded by five white hexagons. Each white hexagon is, in turn, surrounded by three black pentagons and three other white hexagons. This pattern is repeated throughout the soccer ball.

To find the measures of the angles of the shapes that make the soccer ball, we need to first consider the angles of a regular pentagon and a regular hexagon.

A regular pentagon has five sides and five angles that are equal in measure. The formula for finding the measure of each angle in a regular pentagon is:

(angle measure) = (180(n-2))/n, where n is the number of sides.

In the case of a regular pentagon, n=5. Therefore, the measure of each angle in a regular pentagon is:

(angle measure) = (180(5-2))/5 = 108 degrees.

A regular hexagon has six sides and six angles that are equal in measure. The formula for finding the measure of each angle in a regular hexagon is:

(angle measure) = (180(n-2))/n, where n is the number of sides.

In the case of a regular hexagon, n=6. Therefore, the measure of each angle in a regular hexagon is:

(angle measure) = (180(6-2))/6 = 120 degrees.

Now, let's consider the angles of the shapes that make up the soccer ball.

Each black pentagon has five angles that are equal in measure. Therefore, each angle in a black pentagon measures:

(angle measure) = (180(5-2))/5 = 108 degrees.

Each white hexagon has six angles that are equal in measure. Therefore, each angle in a white hexagon measures:

(angle measure) = (180(6-2))/6 = 120 degrees.

Answer:

just do what the guy above me did

Step-by-step explanation:

i checked its correct

The perimeter of the figure which is a rectangle with a semicircle on its shorter side would be =34.28ft

To calculate the perimeter of the figure, the perimeter of both the rectangle and the semicircle is calculated separately and added together.

The perimeter of rectangle = 2(l+w)

where;

l = 10ft

w = 4ft

perimeter = 2(10+4)

= 2× 14

= 28ft

Perimeter of semicircle = 2πr/2 = πr

where

π = 3.14

r = 4/2 = 2ft

perimeter = 3.14×2 = 6.28

Therefore, the perimeter of the given figure = 28+6.28 = 34.28ft.

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To find the number of degrees the minute hand turned from its first position to its second position, we need to find the difference between the two angles formed by the minute and hour hands.

In the first position, the minute hand forms a 46° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 10 and 11, we know that the hour hand has moved 1/6th of the way from 10 to 11, or 30°. Therefore, the angle between the hour hand and the 12:00 position is 120° + 30° = 150°. So the minute hand is 46° away from 150°, or 104°.

In the second position, the minute hand forms an 84° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 11 and 12, we know that the hour hand has moved 1/2 of the way from 10 to 11, or 150°. So the minute hand is 84° away from 150°, or 234°.

To find the number of degrees the minute hand turned, we subtract the two angles: 234° - 104° = 130°.

Therefore, the minute hand turned 130° from its first position to its second position.

The probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI is approximately 0.304.

This problem can be solved using the binomial distribution, which models the probability of a certain number of successes in a fixed number of independent trials, each with the same probability of success.

Let X be the number of Indianapolis residents in a sample of 30 who wanted the Giants to beat the Patriots. Then X follows a binomial distribution with n = 30 and p = 0.97, since the probability of success (rooting for the Giants) is 0.97 for each resident.

We want to find the probability that fewer than 95% of the sample wanted the Giants to win. That is, we want to find P(X < 0.95*30) = P(X < 28.5), where X has the binomial distribution with parameters n = 30 and p = 0.97.

We can use a continuity correction and approximate this probability by the cumulative distribution function of a normal distribution with mean np and variance np(1-p). That is,

P(X < 28.5) ≈ P(Z < (28.5 - np) / sqrt(np(1-p)))

where Z is a standard normal random variable. Substituting the values of n and p, we get

P(X < 28.5) ≈ P(Z < (28.5 - 300.97) / sqrt(300.97*0.03))

≈ P(Z < -0.51)

Using a standard normal table or calculator, we find that P(Z < -0.51) ≈ 0.304. Therefore, the probability that fewer than 95% of the sample wanted the Giants to win is approximately 0.304.

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The given question is incomplete, the complete question is:

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city’s own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 97% of Indianapolis residents wanted the Giants to beat the Patriots.

What is the probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLIV?

The minimum score required for the job offer found using normal distribution is 629

To find the minimum score required for the job offer, we have to use the standard normal distribution formula.

Where Z-score can be calculated as,

Z = (x - μ) / σ

Z-score is the number of standard deviations from the mean.

μ = Mean = 455

σ = Standard Deviation = 124

Substituting the values, we get, Z = (x - μ) / σ= (x - 455) / 124

Probability value = 1 - 0.08 = 0.92

The probability of getting scores in the top 8% is 0.92.

By using the standard normal distribution table, we can find the corresponding z-value, where the area under the curve to the right of that value is 0.92.

So, the corresponding Z-value is 1.44.

Z-value = 1.4 = (x - 455) / 124

We can solve the above equation for x (minimum score required for the job offer).

x = Z * σ + μ = 1.4 * 124 + 455 = 628.6 ≈ 629

Round off the answer to the nearest whole number, we get the minimum score required for the job offer is 629.

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The approximate value of z for the given logarithm in base-e is found to be: z = 0.8959 (nearest thousandth).

A power wherein a number must all be increased in order to obtain another number is known as a logarithm.

The conception of hyperbolic sectors in calculating the area of a rectangular hyperbola gave rise to the concept of log. Several formats, such as exponential and integration of 1/x, can be used to express a log.

The given expression is-

9. [tex]e^{2z}[/tex] = 54.

On simplification:

[tex]e^{2z}[/tex] = 54 / 9

[tex]e^{2z}[/tex] = 6

Now, taking ㏑ both side:

㏑ [tex]e^{2z}[/tex] =  ㏑ 6

using the power rule of ㏑.

2z.  ㏑e =  ㏑6

we know that,  ㏑e = 1

2z * 1 =  ㏑6

z = ㏑6 / 2

z = 1.79 / 2

z = 0.8959

Thus, the approximate value of z for the given logarithm in base-e is found to be: z = 0.8959 (nearest thousandth).

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Answer:

-1

Step-by-step explanation:

Asaad having median salary makes more money in comparison to Amahle who makes minimum salary.

From the attached box plot we have,

Box plot always shows,

First Minimum → Lower quartile → Median → Upper quartile → Maximum

The minimum salary for an actuary is equals to

Approximately 35 dollars

And the median salary for a CPA from the box plot is equals to,

Approximately 60 dollars

Here , by comparing the both the values we have,

Median salary for CPA (60 dollars ) is greater than minimum salary for actuary ( 35 dollars ).

The median salary for a CPA is typically higher than the minimum salary for an actuary.

Therefore, Asaad representing median salary makes more money than Amahle .

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The above question is incomplete, the complete question is:

Amahle makes the minimum salary for an actuary. Asaad makes the median salary for a CPA. Who makes more money?

Box plot is attached.