Julieta recorded the grade-level and instrument of everyone in the middle school School of Rock below. Seventh Grade Students Instrument # of Students Guitar 12 Bass 3 Drums 10 Keyboard 5 Eighth Grade Students Instrument # of Students Guitar 4 Bass 3 Drums 6 Keyboard 2 Based on these results, express the probability that a student chosen at random will play an instrument other than guitar as a fraction in simplest form.

Kevin will need to get a score of 109 on his next test to raise his mean score to exactly 91.

To find out what score Kevin will need to get on his next test to raise his mean score to exactly 91, we can use the formula for the mean:

mean = (sum of all scores) / (number of scores)

We know the current mean score is:

mean = (85 + 94 + 98 + 88 + 85 + 92 + 97 + 81) / 8

          = 89.5

To raise the mean to 91, we can set up the equation:

(85 + 94 + 98 + 88 + 85 + 92 + 97 + 81 + x) / 9 = 91

where x is the score Kevin needs to get on his next test.

Multiplying both sides of the equation by 9, we get:

85 + 94 + 98 + 88 + 85 + 92 + 97 + 81 + x = 819

Simplifying, we get:

710 + x = 819

Subtracting 710 from both sides, we get:

x = 109

Therefore, Kevin will need to get a score of 109 on his next test to raise his mean score to exactly 91.

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Answer:

(-3, -2)

Step-by-step explanation:

In terms of a scatterplot, an outlier is an individual data point that lies at an unusually extreme position relative to the other data points in the scatterplot.

To determine which of the given ordered pairs would be considered an outlier for the given scatterplot, plot the ordered pairs and observe how far away they are from the line of best fit.

After plotting the ordered pairs on the scatterplot (see attachment), we can see that point (-3, -2) is farthest away from the line of best fit. The other three points are very close to the line of best fit.

Therefore, (-3, -2) would be considered an outlier comparatively to the other ordered pairs.

Answer: Your answer is (-3, -2)

Step-by-step explanation: Outlier means the one that stands out in the bunch. So when you look at the coordinates of (-3, -2) you can see it is the farthest of the bunch. If you look at the other answers you can see that they are not as far away as (-3, -2)

The median total of amount Franky earned is A = $81.67 per day.

Given data ,

For the first five days: $(100 + x) per day

For the next two days: $(175 + 2x) per day

For the final three days: $(75 + 2x) per day

Now , the average amount she earns is $80 per day

So , Average earnings = Total earnings / Total number of days

Average earnings = [(100 + x) * 5 + (175 + 2x) * 2 + (75 + 2x) * 3] / 10

Simplifying the equation:

80 = [500 + 5x + 350 + 4x + 225 + 6x] / 10

Multiplying both sides by 10:

800 = 1075 + 15x

Subtracting 1075 from both sides:

15x = -275

Dividing both sides by 15:

x = -18.33

For the first five days: $(100 - 18.33) = $81.67 per day

For the next two days: $(175 + 2*(-18.33)) = $138.34 per day

For the final three days: $(75 + 2*(-18.33)) = $38.34 per day

Arranging the earnings in ascending order: $38.34, $38.34, $38.34, $81.67, $81.67, $81.67, $81.67, $138.34, $138.34

The median is the middle value when the earnings are arranged in ascending order. In this case, the middle value is $81.67

Hence , the median is $81.67

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Answer:

653.3 bacteria

Step-by-step explanation:

A continuously growing population of bacteria is modeled by the function:

[tex]P(t) = P_0 \cdot e^{rt}[/tex]

where:

In this problem, we are given the following values:

We can plug these into the function to solve for [tex]P(2)[/tex].

[tex]P(t) = P_0 \cdot e^{rt}[/tex]

[tex]P(2) = 484 \cdot e^{(0.15 \, \cdot \, 2)}[/tex]

[tex]P(2) = 484 \cdot e^{0.3}[/tex]

Finally, the right side of this equation can be evaluated using a calculator to solve for the population of the bacteria after 2 hours.

[tex]\huge{\text{P(2) = 653.3 bacteria}}[/tex]

a) The triangles are congruent by the AAA criterion.

b) The triangles are congruent by the SAS criterion.

a) In the first triangle the interior angles are 40 degrees and 30 degrees.

The other interior angle would be 180 - (40 + 30) = 110 degrees.

As per the diagram, the triangles have equal proportionate-sized side lengths.

Therefore, the triangles are congruent by the AAA criterion.

b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.

Therefore, the triangles are congruent by the SAS criterion.

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The values of  x and y is x=8 and y=12.

We are given that;

The dimensions=7 and 24

Now,

(x+y)^2= 7^2 + 24^2

x^2+y^2+2ab=49+416

x^2+y^2+2xy=465

Also, 7^2=x2+h2

49=x2+15

x2=49+15

x2=64

x=8

Substituting the values of x

8+y=20

y=12

Therefore, by Pythagoras theorem the answer will be x=8 and y=12.

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Answer:

Step-by-step explanation:

use gauth math it helps with maths

If this week there are 144 members at the meeting, which is 90% of the total group, the total number of members on the green team is 160.

If 144 members represent 90% of the total group, we can set up the equation:

144 = 0.9x

where x is the total number of members on the green team.

To solve for x, we can divide both sides of the equation by 0.9:

144 ÷ 0.9 = x

This simplifies to:

160 = x

To check our answer, we can verify that 144 is indeed 90% of 160:

144 ÷ 160 = 0.9

which confirms that our answer is correct.

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The circle graph percentage is solved and the measure of ∠KL = 54° and the measure of ∠LMJ = 198°

Given data ,

Let the circle graph gives the percentage of students who favor the different lunch menus offered by the school cafeteria

Now , the measures of the angles are given by

The measure of ∠KL = 15 %

15 % ( 360 ) = 54°

Therefore , the measure of ∠KL = 54°

And , the measure of ∠LMJ = ( 24 % + 21 % ) of 360

The measure of ∠LMJ = 198°

Hence , the circle graph percentage is solved

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Donald traveled approximately 100 kilometers on each of his trips to the amusement park.

Now, the distance Donald traveled on each of his trips to the amusement park.

If he drove a total of 399 kilometers over the course of four trips, we can find the average distance he traveled per trip by dividing the total distance by the number of trips.

So, We get;

= 399 divided by 4

= 399 / 4

= 99.75 kilometers per trip

≈ 100 kilometers per trip.

Therefore, Donald traveled approximately 100 kilometers on each of his trips to the amusement park.

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a) The triangles are congruent by the AAA criterion.

b) The triangles are congruent by the SAS criterion.

a) In the first triangle the interior angles are 40 degrees and 30 degrees.

The other interior angle would be 180 - (40 + 30) = 110 degrees.

As per the diagram, the triangles have equal proportionate-sized side lengths.

Therefore, the triangles are congruent by the AAA criterion.

b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.

Therefore, the triangles are congruent by the SAS criterion.

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5. GH= 3

HI= 3x-9 and x=4

HI= 3(4)-9=

= 12-9

= 3

so, GH = HI

Do the same for GJ and JI.

6. 36=2x

18=x

So, the angles are the same.

4x-11=61

4(18)-11=61

So, the sides are also the same meaning the triangles are congruent.

The quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).

By dividing each term of the numerator by 4ab:

(7a³ + ab + 3) / (7a³ + ab - 3) ÷ 4ab

= (7a³ / 4ab) + (ab / 4ab) + (3 / 4ab)

Simplifying each term individually:

= (7/4a²) + (1/4b) + (3/4ab)

Thus, the quotient of the expression (7a³ + ab + 3) / (7a³ + ab - 3) divided by 4ab is (7/4a²) + (1/4b) + (3/4ab).

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The value of the equation 6 sinθ=5 for θ is 56.4 degrees

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

6 sinθ=5

Express the equation properly

So, we have the following representation

6 sin(θ) = 5

Divide both sides of the equation by 6

This gives

sin(θ) = 5/6

Evaluate the quotient

sin(θ) = 0.833

Take the arc sin of both sides

θ = sin⁻¹(0.833)

Evaluate

θ = 56.4

Hence, the value of the equation for θ is 56.4 degrees

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Complete question

Approximate θ in the equation, to the nearest 0.1 degrees

6 sin(θ) = 5

Answer:

Step-by-step explanation:

5/12 pounds more

The manufacturer made 1,890 non-defective light bulbs and 210 defective light bulbs.

Let represent number of non-defective light bulbs with x

Let represent number of defective light bulbs with y.

The profit from selling non-defective light bulbs is €0.60x

The loss from selling defective light bulbs is €0.80y.

Given that the manufacturer made a profit of €966, we can form the equation:

0.60x - 0.80y = 966 ---(1)

The total number of light bulbs produced is 2,100, so we have:

x + y = 2,100 ---(2)

To solve this, we will use method of elimination.

We multiply equation (2) by 0.60.

0.60x + 0.60y = 1,260 ---(3)

Now, subtract equation (3) from equation (1):

0.60x - 0.60x - 0.80y - 0.60y = 966 - 1,260

-1.40y = -294

y = -294 / -1.40

y = 210

Substituting value of y into equation (2):

x + 210 = 2,100

x = 2,100 - 210

x = 1,890.

Translated question:

A light bulb manufacturer earns €0.60 for each bulb that leaves the factory but loses €0.80 for each one that is defective. On a certain day when he manufactured 2,100 light bulbs, he made a profit of €966. How many light bulbs of each type did he make?

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Answer:

The correct statements are:

A) There are no zeroes

D) The vertex is (1, 14)

H) The axis of symmetry is x = 1

J) The "a" of the parabola is positive

M) The parabola has a minimum

Therefore, the options B, C, E, F, G, I, K, N, O, P, Q, and R are all false.

Step-by-step explanation:

Step-by-step explanation:

Remember that, this is quadratic function graph.

Let's analyze fact the graph. We get :

There are two roots/zeroes

Two roots are x1 = -2 , x2 = 6

Vertex is maximum value of parabola (2,14)

Symmetry function is x = 2 (you can show that, x-axis from vertex)

"a" parabola indicated negative

The parabola with "a" negative, thus have maximum value (show that vertex is (2,14))

Conclusion :

The true statements are C,F,I,K,N,O (6 statements are shown)

Subject : Mathematics

Level : JHS

Chapter : Quadratic Functions

The required target debt/equity ratio is 0.5 or 1:2.

To calculate the target debt/equity ratio,

Use the following formula,

⇒ Target D/E Ratio = (Target Equity / Target Debt)

First, we need to calculate the weights of equity and debt in the firm's capital structure.

We can use the following formula,

Weight of Equity = Equity / (Equity + Debt)

Weight of Debt = Debt / (Equity + Debt)

Since the firm is unlevered,

its capital structure consists only of equity.

Therefore,

The weight of equity is 1 and the weight of debt is 0.

Now we can use the weighted average cost of capital (WACC) formula to find the firm's current cost of equity.

The WACC formula is as follows,

WACC = (Weight of Equity Cost of Equity)

                        + (Weight of Debt Cost of Debt x (1 - Tax Rate))

Substituting the given values, we get:

⇒ 10% = (1 Cost of Equity) + (0 9% x (1 - 34%))

Solving for Cost of Equity, we get:

Cost of Equity = 10% - (0 9% (1 - 34%))

Cost of Equity = 10%

Since the firm desires a cost of equity of 14%,

we can set up an equation to solve for the target debt/equity ratio:

⇒ 14% = (1 / (1 + Target D/E Ratio)) 10% + ((Target D/E Ratio) / (1 + Target D/E Ratio)) 9% x (1 - 34%)

Simplifying the equation, we get:

⇒ 14% = 10% / (1 + Target D/E Ratio) + 0.0594 x Target D/E Ratio

Multiplying both sides by (1 + Target D/E Ratio), we get:

⇒ 0.14 + 0.14 Target D/E Ratio = 0.1 + 0.0594 Target D/E Ratio

Subtracting 0.0594 x Target D/E Ratio from both sides, we get:

⇒ 0.08 x Target D/E Ratio = 0.04

Dividing both sides by 0.08, we get:

⇒ Target D/E Ratio = 0.5

Therefore, the firm's target debt/equity ratio is 0.5 or 1:2.

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The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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The value of the expression 0.36 × 4.2 - 0.008 ÷ 25.5 is approximately 1.5116863.

To evaluate the expression 0.36 × 4.2 - 0.008 ÷ 25.5, we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, let's simplify the division: 0.008 ÷ 25.5 = 0.0003137 (rounded to six decimal places).

Now, we can substitute the simplified division back into the expression: 0.36 × 4.2 - 0.0003137.

Next, we perform the multiplication: 0.36 × 4.2 = 1.512.

Finally, we subtract the result of the multiplication from the simplified division: 1.512 - 0.0003137 = 1.5116863 (rounded to seven decimal places).

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The expression (yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp) is simplified to obtain

2/y

The given expression is

(yx + y + px + p) / (5x² + 10x +5) * (10x + 10) / (y² + yp)

The expression is simplified individually, using different each equation in the expression

yx + y + px + p

= y(x + 1) + p(x + 1)

= (y + p)(x + 1)

5x² + 10x +5

= 5(x² + 2x + 1)

= 5(x² + 1)

(10x + 10)

= 10(x + 1)

(y² + yp)

= y(y + p)

bringing the equations together and simplifying further

(y + p)(x + 1) / 5(x² + 1) * 10(x + 1) / y(y + p)

= 10(x + 1)(x + 1) / 5y(x² + 1)

= 10(x² + 1) / 5y(x² + 1)

= 2/y

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The  quotient of 302 ÷ (9.1 x [tex]10^4)[/tex] in scientific notation is approximately 3.31868131868 x [tex]10^1[/tex]

Dividing 302 by 9.1 gives:

302 ÷ 9.1 ≈ 33.1868131868

Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:

33.1868131868 ≈ 3.31868131868 x[tex]10^1[/tex]

Therefore, the quotient of 302 ÷ (9.1 x [tex]10^4[/tex]) in scientific notation is approximately 3.31868131868 x[tex]10^1[/tex]

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The angle formed by the cable between chairs B and J, and then

continue chair G is

75 degrees

The angle is determined with the knowledge of the total angle in a circle which is 360 degrees. Also, intercepted arc = 2 * inscribed angle

Assuming each chair is equal distance apart, then they will subtend equal angle.

The number of chairs for A to L is 12

angle per chair = 360 / 12 = 30 degrees

number of chairs from B to G = 5 and angle intercepted arc = 30 * 5 = 150 degrees

Inscribed angle = 1/2 * intercepted arc

Inscribed angle = 1/2 * 150

Inscribed angle = 75 degrees

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The volume of the pyramid is 18069333.33 units³ and the surface area is 391600 units ²

A pyramid is a three-dimensional figure. It has a flat polygon base. All the other faces are triangles and are called lateral faces.

Surface area of a pyramid is expressed as;

area of 4 lateral face + area of base

area of base = 440²

= 193600 units²

area of a lateral = 1/2 bh

= 1/2 × 440 × 356

= 78320

For four surfaces = 4 × 78320 = 313280

Total surface area = 313280+78320

= 391600 units ²

Volume of a pyramid is expressed as;

V = 1/3base area × height

V = 1/3 × 440² × 280

V = 18069333.33 units³

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The circumference of the circle whose diameter is 2x + 2 is (44x + 44)/7

The formula for the circumference of a circle is 2πr

r = radius of the circle

Diameter of circle = radius  of circle × 2

The radius of the circle = ( diameter of the circle ) / 2

The radius of circle = (2x+2)/2

Taking 2 commons from 2x + 2

we get 2( x + 1 )

The radius of circle = 2(x+1)/2

The radius of the circle = x + 1

Circumference =  2 × 22/7 × (x+1)

Circumference = 44(x+1)/7

Circumference = (44x + 44)/7

Or in the form of π circumference can be written as (2x + 2)π

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The student that gets the rule of the transformation correctly is Raheem

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

Point N = (-2, -4)

Image of the point N = (2, 4)

This means that

N = (-2, -4)

N' = (2, 4)

From the above, we can see that

N' = -1 * N

This means that

N' = (-2, -4) * -1

So, we have

N' = (-2* -1 , -4 * -1)

So, the rule is (x * -1, y * 1)

Hence, the student that gets the rule correctly is Raheem

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Question

Four students are trying to find the rule that translates point N(-2,-4) to N'(2,4). Each student’s reasoning is shown below.

Raheem: The rule is (x * -1, y * -1)

Casey: The rule is (x + 2, y + 4)

Andrew: The rule is (x + 4, y + 0)

Lo: The rule is (x + 4, y + 8)

Which student is correct?

Raheem

Casey

Andrew

The height of the plane is 5 miles.

To solve this problem, we can visualize it as a right triangle. The horizontal distance traveled by the plane forms the base of the triangle, which is 12 miles. The total distance traveled by the plane forms the hypotenuse of the triangle, which is 13 miles. We need to find the height, which corresponds to the vertical side of the triangle.

Using the Pythagorean theorem, we can calculate the height as follows:

height^2 + 12^2 = 13^2

height^2 + 144 = 169

height^2 = 169 - 144

height^2 = 25

Taking the square root of both sides, we get:

height = √25

height = 5

Therefore, the height of the plane is 5 miles.

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The given information is,$37.60 interest earned on a $460 investment at 8%.

Part:The amount of interest earned is called the part. Here, the amount of interest earned is $37.60. Hence the part is $37.60.

Percent:The rate per 100 units of the base is called the percent. Here, the percent rate is 8%.

Base:The original amount invested or borrowed is called the base. Here, the original investment amount is $460. Hence the base is $460.

Thus,

Part: $37.60

Percent: 8%

Base: $460.

Part: The part is the interest earned, which is $37.60.

Percent: The percent is 8%, which represents the annual interest rate.

Base: The base is the amount of the investment, which is $460.

Answer:

[tex]\sf 2\sqrt{17}[/tex]

Step-by-step explanation:

To find the distance of a line using distance formula:

The line from point X intersect the line p at (0 , -3).

          ( -2 , 5) ⇒  x₁  = -2 & y₁ = 5

          (0 , -3)  ⇒ x₂ = 0    & y₂ = -3

    [tex]\boxed{\bf Distance = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}}[/tex]

                       [tex]\sf = \sqrt{-2-0)^2+(5-[-3])^2}\\\\=\sqrt{(-2-0)^2 + (5+3)^2}\\\\=\sqrt{(-2)^2+(8)^2}\\\\=\sqrt{4+64}\\\\=\sqrt{68}\\\\=\sqrt{2*2*17}\\\\=2\sqrt{17}[/tex]

Answer: 19

Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).

Hope this helps!