Which is the solution set of the inequality 15y - 9 < 36?
A. y > 9/5
B. y < 9/5
C. y > 3
D. y < 3

Answer:

\(3 {x}^{2} y - {y}^{2} \)

\(y(3 {x}^{2} - y)\)

is the answer

Answer:

\(3x {}^{2}y - y {}^{2} \\ 3x {}^{2} - \frac{y {}^{2} }{y} \\ 3x {}^{2} - y\)

Step-by-step explanation:

Answer:

\(x=14\)

Step-by-step explanation:

Since lines \(\overrightarrow{f}\) and \(\overrightarrow{g}\) are parallel, the angles labelled in the diagram must be supplementary (add up to \(180^{\circ}\)). Therefore, we have the following equation:

\(4x+(7x+26)=180,\\11x+26=180,\\11x=154,\\x=\boxed{14}\)

Answer:

x = 5

Step-by-step explanation:

14x + 1 + 14x + 1 + 38 = 180 , that is

28x + 40 = 180 ( subtract 40 from both sides )

28x = 140 ( divide both sides by 28 )

x = 5

The correct answer is "yes; all corresponding sides are proportional and angles are congruent."

To determine if two figures are similar, we need to examine two key properties: corresponding sides and corresponding angles.

If all corresponding sides of two figures are proportional and all corresponding angles are congruent, then the figures are similar. This means that the ratios of corresponding side lengths are equal, and the corresponding angles have the same measures.

Proportional sides: For two figures to have proportional sides, the ratios of corresponding side lengths must be equal. For example, if one figure has sides of lengths 2, 4, and 6 units, and the corresponding sides of the other figure have lengths 1, 2, and 3 units, then the ratios are 2/1, 4/2, and 6/3, which are all equal to 2/1. When the corresponding sides have these equal ratios, it indicates similarity.

Congruent angles: If all corresponding angles have the same measures, then the figures are said to have congruent angles. Congruent angles have the same degree of rotation and can be matched up directly with each other.

Therefore, if both the corresponding sides are proportional and the corresponding angles are congruent, the two figures are similar. The correct answer is "yes; all corresponding sides are proportional and angles are congruent."

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Aaron must get 570 score on exam b to be equivalent to the score in exam a.

The mean and Standard Deviation provides information about the average value and the average spread of values around it respectively.

Here in this question we are given that,

x1=50

mean=35

SD=5

then Z score will be,

z1=(x1-mean)/SD

z1=(50-35)/5

now we have,

x2

mean=40

SD=50

then Z score will be,

z1=(x2-mean)/SD

3=(x2-450)/50

x2=570

so Aaron must get 570 score on exam b to be equivalent to the score in exam a.

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Explanation:

The two parallel lines form a parallelogram.

For any parallelogram, the opposite angles are congruent.

So the angle adjacent to P is also 106 degrees.

The adjacent angles add to 180

P+106 = 180

P = 180-106

P = 74

Answer:

301.7 cm

Step-by-step explanation:

Given,

Height of cone (h)=8cm

base radius (r)=6cm

Volume of the cone (V)=

3

1

πr

2

h

=

3

1

×

7

22

×6×6×8

=

7

2112

=301.7cm

3

Hence, volume of the cone =301.7cm

3

Answer:

402.1402.1 cm

Step-by-step explanation

height = 6cm

Radius= 8cm

The slope of the given lines are:

Graph 1 = 1/3

Graph 2 = -1/3

Graph 3 = 3

Graph 4 = -3

To find the slope (m) of a given line on a coordinate plane, choose any two points on the line, (x1, y1) and (x2, y2), then find the slope by plugging in the values of the coordinates into the formula below:

Slope of a line (m) = change in y / change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\).

Find the slope of Graph 1:

Using two points on the line, (0, 0) and (3, 1):

Slope of graph 1 (m) = (1 - 0)/(3 - 0)

Slope of graph 1 (m) = 1/3

Find the slope of Graph 2:

Using two points on the line, (0, 0) and (-3, 1):

Slope of graph 2 (m) = (1 - 0)/(-3 - 0) = 1/-3

Slope of graph 2 (m) = -1/3

Find the slope of Graph 3:

Using two points on the line, (0, 0) and (1, 3):

Slope of graph 3 (m) = (3 - 0)/(1 - 0) = 3/1

Slope of graph 3 (m) = 3

Find the slope of Graph 4:

Using two points on the line, (0, 0) and (-1, 3):

Slope of graph 4 (m) = (3 - 0)/(-1 - 0) = 3/-1

Slope of graph 4 (m) = -3

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The volume of a cylinder is V=πr^2*h.

The volume of this cylinder is V=π(7)^2*12, which it V=588π.

Answer:

x = 15°

Step-by-step explanation:

the inscribed angle APB is half the measure of the central angle AOB , so

x = \(\frac{1}{2}\) × 30° = 15°

The student completed 9 courses worth 4 credits. The solution has been obtained by using the linear equation.

What is a linear equation?

It follows that a linear equation has the highest degree of one. As a result, it is evident that there are no variables in a linear equation with an exponent bigger than one. A straight line is produced by this equation on the graph.

Let the courses worth 3 credits be 'x' and worth 4 credits be 'y'.

We are given that the student earned a total of 54 credits.

So,

3x + 4y = 54   ...(1)

Also, we are given that in total 15 courses were completed.

So,

x + y = 15   ...(2)

From (2), we get

x = 15 - y

Substituting this value in (1), we get

⇒3(15-y) + 4y = 54

⇒45 - 3y + 4y = 54

⇒45 + y = 54

⇒y = 9

Therefore, x = 15-9 = 6

Hence, the student completed 9 courses worth 4 credits.

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Answer:

25°

Step-by-step explanation:

Since this angle is a right angle as shown by the mark in the corner, a right angle is 90°.

90° - 65° = 25°

Answer:

57.77% out of 100

john's father would pick pink because pink is in less number

Answer:

25%

Step-by-step explanation:

20 divided by 8 times 100 take away the zero

percentage = part/whole x 100

Answer:

y + 3 = 1/4(x -4)

Step-by-step explanation:

y - y = m (x - x)

y - -3 = 1/4 ( -4)

y + 3 = 1/4 ( x -4)

The equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0

Let

Since the rectangular plot of ground is 30 meters longer than it is wide, we have that

L = W + 30

Since the area of the rectangular plot is A = LW where

Since A = 20,000 m², we have that

LW = 20,000

(W + 30)W = 20,000

W² + 30W = 20,000

W² + 30W - 20,000 = 0

Using the quadratic formula, we have that

\(W = \frac{-30 +/- \sqrt{30^{2} - 4 X (-20000)} }{2 X 1} \\W = \frac{-30 +/- \sqrt{900 + 80000} }{2} \\W = \frac{-30 +/- \sqrt{80900} }{2} \\W = \frac{-30 +/- 284.43}{2} \\W = \frac{-30 +/- 284.43}{2}\\W = \frac{-30 - 284.43}{2} or \frac{-30 + 284.43}{2}\\W = \frac{-314.43}{2} or \frac{254.43}{2}\\W = -157.22 or 127.23\\\)

Since W cannot be negative, we have W = 127.23

Since L = W + 30

L = 127.23 + 30

L = 157.23

So, the dimensions are

So, the equation of the dimensions of the rectangular plot is W² + 30W - 20,000 = 0

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Answer:

Step-by-step explanation:

Which ones have four sides?

A

B

D

Answer:

Step-by-step explanation:

3

Answer:

1 - z/3

Step-by-step explanation:

2500 cubic centimetres

None of the available options match the parabola's equation.

To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.

A parabola's vertex form is given by:

\(y = a(x-h)^2 + k\)

where (h,k) is the parabola's vertex.

\(y = a(x-5)^2 - 3\)

These values are substituted into the equation to produce:

\(-15 = a(2-5)^2 - 3\)

\(-15 = 9a - 3\)

\(-12 = 9a\)

\(a = -4/3\)

\(y = (-4/3)(x-5)^2 - 3\)

This equation is expanded and simplified to produce:

\(y = (-4/3)x^2 + (32/3)x - 53\)

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Answer:

ready-steady paint

Step-by-step explanation:

if he needs 12 tins, and purchased from paint -O  mine, he would spend (12/3) X 7.50 = 4 x 7.50 = £30

from ready steady, he can buy 4 for £11. he needs 12.

so he will spend (12/4) X 11 = 3 X 11 = £33. but he can get 15% off. 15% off is the same as multiplying by 0.85.

33 X 0.85 = £28.05.

so he his better purchasing from ready steady paint

a) Alternatives:

1. Build a distribution center near Fresno

2. Build a distribution center near Henderson

States of nature:

1. Earthquake occurs near Fresno in the next 3 years

2. Earthquake does not occur near Fresno in the next 3 years

Payoff table:

                                     |Earthquake occurs | Earthquake does not occur |

Build near Fresno        | -$20 million            | $0 million                              |

Build near Henderson | -$40 million            | -$20 million                           |

b) Expected value calculation without hiring the geologist:

Probability of earthquake occurring near Fresno = 0.20

Expected value of building near Fresno = (0.20) x (-$20 million) + (0.80) x ($0 million) = -$4 million

Expected value of building near Henderson = (0.20) x (-$40 million) + (0.80) x (-$20 million) = -$28 million

Since the expected value of building near Fresno is higher, the optimal alternative is to build near Fresno.

c) Expected value of perfect information (EVPI):

The EVPI is the difference between the expected value with perfect information and the expected value without perfect information.

Without perfect information, the expected value of building near Fresno is -$4 million. With perfect information, Amazon would know whether an earthquake will occur or not and make the decision accordingly.

If an earthquake is predicted, Amazon will choose to build near Henderson and the expected value will be -$20 million.

If an earthquake is not predicted, Amazon will choose to build near Fresno and the expected value will be $0 million.

The probabilities of these two outcomes depend on the accuracy of the geologist's prediction.

If the geologist predicts an earthquake, the probability of an earthquake occurring is 0.90, and the probability of an earthquake not occurring is 0.10.

If the geologist predicts no earthquake, the probability of an earthquake occurring is 0.10, and the probability of an earthquake not occurring is 0.90.

Therefore, the EVPI can be calculated as follows:

EVPI = (0.10 x (-$20 million)) + (0.90 x $0 million) = -$2 million

This means that the maximum Amazon should pay for the geologist's prediction is $2 million.

d) Posterior probabilities:

If the geologist predicts an earthquake:

Probability of an earthquake occurring = 0.90 x 0.20 = 0.18

Probability of no earthquake occurring = 0.10 x 0.80 = 0.08

Normalization factor = 0.18 + 0.08 = 0.26

Posterior probability of an earthquake occurring = 0.18 / 0.26 = 0.6923

Posterior probability of no earthquake occurring = 0.08 / 0.26 = 0.3077

If the geologist predicts no earthquake:

Probability of an earthquake occurring = 0.10 x 0.20 = 0.02

Probability of no earthquake occurring = 0.90 x 0.80 = 0.72

Normalization factor = 0.02 + 0.72 = 0.74

Posterior probability of an earthquake occurring = 0.02 / 0.74 = 0.027

Posterior probability of no earthquake occurring = 0.72 / 0.74 = 0.973

e) Using the calculations from above, the expected value of sample information (EVSI) can be calculated as follows:

EVSI = E(EVSI | E)P(E) + E(EVSI | ¬E)P(¬E)

where E represents the event that an earthquake will occur and ¬E represents the event that an earthquake will not occur.

From the calculations in part (d), the posterior probabilities are P(E) = 0.144 and P(¬E) = 0.856.

If the geologist predicts an earthquake, then the expected value of perfect information (EVPI) is $8 million (calculated in part c).

If the geologist predicts no earthquake, then Amazon will build the distribution center near Fresno without hiring the geologist, so the expected value of sample information is simply the expected value without the geologist, which is $56 million.

Therefore, the EVSI can be calculated as follows:

EVSI = E(EVSI | E)P(E) + E(EVSI | ¬E)P(¬E)

    = ($8 million - $5.5 million) x 0.144 + ($56 million - $5.5 million) x 0.856

    = $44.896 million

Since the EVSI is positive and substantial, Amazon should hire the geologist to reduce uncertainty and improve the decision-making process.

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You have the following system of equations:

y = 9x - 9

y = 9

In order to solve the previous system of equations, replace y = 9 into the first equation and solve for x:

9 = 9x - 9 add 9 both sides and simplify

9 + 9 = 9x

18 = 9x divide by 9 both sides

18/9 = x

2 = x

x = 2

Hence, the solution to the system is x = 2 and y = 9.

Given:

The expression is:

\(\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}\)

To find:

The simplified form of the given expression

Solution:

Formula used:

\(x^2-y^2=(x-y)(x+y)\)

We have,

\(\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^7+4a^3b^4}{b^8-a^8}\)

It can be written as:

\(=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4)^2-(a^4)^2}\)

\(=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3(a^4+b^4)}{(b^4-a^4)(b^4+a^4)}\)

\(=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b^2-a^2)(b^2+a^2)}\)

\(=\dfrac{1}{a+b}+\dfrac{2a}{a^2+b^2}+\dfrac{4a^3}{(b-a)(b+a)(b^2+a^2)}\)

Taking LCM, we get

\(=\dfrac{1(b-a)(b^2+a^2)+2a(b-a)(b+a)+4a^3}{(b-a)(b+a)(b^2+a^2)}\)

\(=\dfrac{b^3+a^2b-ab^2-a^3+2a(b^2-a^2)+4a^3}{(b-a)(b+a)(b^2+a^2)}\)

\(=\dfrac{b^3+a^2b-ab^2-a^3+2ab^2-2a^3+4a^3}{(b-a)(b+a)(b^2+a^2)}\)

\(=\dfrac{b^3+a^2b+ab^2+a^3}{(b-a)(b+a)(b^2+a^2)}\)

Using the grouping method factories the numerator.

\(=\dfrac{b(b^2+a^2)+a(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}\)

\(=\dfrac{(b+a)(b^2+a^2)}{(b-a)(b+a)(b^2+a^2)}\)

Cancel out the common factors.

\(=\dfrac{1}{b-a}\)

Therefore, the value of the given expression is \(\dfrac{1}{b-a}\).

Answer:

6

Step-by-step explanation:

25 / 10 = 2.5

15 / 2.5 = 6

After 3 months, there will be 12 of each type of caregiver

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the daycare center in Seaside currently has 9 assistant caregivers and 6 senior caregivers. Since demand is high, the owner is going to be hiring 1 assistant caregiver per month and 2 senior caregivers per month.

This will be:

9 + m = 6 + 2m

where m= number of months

Collect the like terms

2m - m = 9 - 6

m = 3

The number of caregiver will be:

9 + m

9 + 3

= 12

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Answer:

Your answer is 1649 miles.

Step-by-step explanation:

\(5^{4} + 4^{5} = 1649\)

Answer:

\(\longmapsto \sf \: \: - 14x \cdot\sqrt{14x}\)

Step-by-step explanation:

\( \sf \: if \: x > 0 \)

\( \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } \)

\( \sf Let's \: solve \: for \sqrt{56 {x}^{3} } \: first, \\\longmapsto \sf \sqrt{56 {x}^{3} } = \sqrt{14 \times 4 {x}^{2} \times x } \\ \sf \longmapsto \sqrt{56 {x}^{3} } = 4x \sqrt{14x} \)

Substituting above value in given equation,

\(\longmapsto \sf 6x \sqrt{14x} - 5 \sqrt{56 {x}^{3} } \\ \longmapsto\sf 6x \sqrt{14x} - 5 \times 4x \sqrt{14x} \\ \longmapsto \sf \: 6x \sqrt{14x} - 20x \sqrt{14x} \\\longmapsto \sf \: \sqrt{14x}(6x - 20x) \\ \longmapsto \sf \: \: - 14x \cdot\sqrt{14x}\)

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The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

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