Karen worked her 40 regular hours last week, plus 6 hours at the time-and-a-half rate. Her gross pay was $650. What was her hourly rate?

Answer:

The area of the rectangle is given by:

Area = Length x Width

Substituting the given values, we get:

90 = (x+3)(x+2)

Expanding the right side:

90 = x^2 + 5x + 6

Rearranging the terms:

x^2 + 5x - 84 = 0

Factoring the quadratic equation:

(x + 12)(x - 7) = 0

Therefore, x = -12 or x = 7. Since the length and width cannot be negative, we take x = 7.

So, the length is (x+3) = 10 and the width is (x+2) = 9.

The perimeter of the rectangle is given by:

Perimeter = 2(Length + Width)

Perimeter = 2(10 + 9)

Perimeter = 2(19)

Perimeter = 38

Therefore, the answer is (C) 38.

Step-by-step explanation:

In 30 years, the amount Alex can withdraw (future value) if the investment earns 6% annual interest, is $876,292.95.

The future value (FV) is the compounded present value for a period in the future.

In addition, the FV can be the present value of annual investments compounded to the coming period at an interest rate.

In this situation, the future values are computed for the initial investment today for 30 years and the annual investments, which started a year from today ( for 29 years).

N (# of periods) = 30 years

I/Y (Interest per year) = 6%

PV (Present Value) = $50,000

PMT (Periodic Payment) = $0

Results:

FV = $287,174.56

Total Interest =$237,174.56

N (# of periods) = 29 years

I/Y (Interest per year) = 6%

PV (Present Value) = $0

PMT (Periodic Payment) = $8,000

Results:

FV = $589,118.39

Sum of all periodic payments = $232,000 ($8,000 x 29(

Total Interest = $357,118.39

Future Value of $50,000 in 30 years = $287,174.56

Future Value of $8,000 annual for 29 years = $589,118.39

Total Future Value = $876,292.95 ($287,174.56 + $589,118.39)

Thus, Alex can withdraw a future value of $876,292.95 in 30 years.

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The distance between the points A ( -12 ) and B ( -7 ) on the number line is given by distance d = -5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first point be A ( x₁ )

The value of A ( x₁ ) = A ( -12 )

Let the second point be B ( x₂ )

The value of B ( x₂ ) = B ( -7 )

Let the distance between the two points on the number line be = D

Now , the equation will be

The distance between the points A and B is calculated by

The distance D = B - A

Substituting the values in the equation , we get

The distance D = -12 - ( -7 )

Distance D = -12 + 7

Distance D = -5

Therefore , the value of D is -5

Hence , The distance between the points A ( -12 ) and B ( -7 ) on the number line is given by distance d = -5

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Answer:

D

Step-by-step explanation:

The number that has a 4 in the hundred places.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A 4 with a value ten times less than the 4 in the number 123,469.

First, the value of the 4 in the number 123,469 can be found by separating each digit as:

123,469 = 100,000 + 20,000 + 3,000 + 400 + 60 + 9

Then the value of the 4 is 400.

Now we want a number that has a 4 with a value then times less than 400. Then we have

400/10 = 40

Then we want a number that has a 4 in the hundred places.

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Answer:

x = 11

Step-by-step explanation:

The two angles measuring (7x + 14)° and (9x - 8)° are corresponding angles, which are always congruent to each other and thus equal to each other.  

Step 1:  Thus, we can find the value of x by setting the two angles equal to each other:

7x + 14 = 9x - 8

7x + 22 = 9x

22 = 2x

11 = x

Optional Step 2:  We can check that we've found the correct answer by plugging in 11 for x in both (7x + 14) and (9x - 8) and checking that we get the same number:

7(11) + 14 = 9(11) - 8

77 + 14 = 99 - 8

91 = 91

Hope it helps.

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Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)

Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).

The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,

 A' = 2A

 A'(8, -12) = 2×A(4, -6)

These facts are all you need to know to choose the correct answer (shown above).

Answer: 1/2

Step-by-step explanation:

I took the quiz!

The multiplication 3/4×8/9 can be used to address the problem in response (B). which is the correct answer that would be an option (B).

In mathematics, Multiplication operations perform Multiplying values on either side of the operator.

For example 4×2 = 8

As per option (B),

Jada rode her bike for 3/4 mile. Sarah rode her bike 8/9 the distance that Jada rode her bike.

Sarah rides her bike = Sarah rode (8/9) of the (3/4) that Jada rode.

Sarah rides her bike = 3/4 × 8/9

Therefore, this problem can be solved by performing the above multiplication.

Hence, the correct answer would be an option (B).

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(I) \(3x + 2y = 45\)

(II) \(4x - y = 5\)

Get \(y\) alone in equation (II)

\(4x - y = 5\\y = 4x - 5\)

Insert new equation (II) in equation (I)

\(3x + 2(4x - 5) = 45\\3x + 8x - 10 = 45\\3x + 8x = 45 + 10\\11x = 55\\x = 5\)

Insert \(x = 5\) in equation (II)

\(y = 4 \cdot 5 - 5\\y = 20 - 5\\y = 15\)

40 + 30 + 18

= 70 + 18

= 88

Answer:

88

Step-by-step explanation:

40+30+18=70+18=88

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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The curved surface area of the cylinder is 48.06 cm².

The circumference of a cylinder is given by the formula:

C = 2πr

where C is the circumference and r is the radius of the base.

In this case, the given circumference is 6 cm.

So, 6 = 2πr

r = 6 / (2π)

r ≈ 0.955 cm

Now, the curved surface area (CSA) of the cylinder using the formula:

CSA = 2πrh

Given the height as 8 cm, we can substitute the values into the formula:

CSA = 2π(0.955 cm)(8 cm)

CSA ≈ 48.06 cm²

Therefore, the curved surface area of the cylinder is 48.06 cm².

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See graph below

Given:

Rate water is added = 30 l/min

The initial amount in the pond = 600l

To find:

The equation relating the amount of water in the pond to the number of minutes the water is being added

W = amount of water in the pond

T = number of minutes that water has been added

Amount of water in the pond = rate water is added (number of minutes that water has been added) + the initial amount in the pond

Graphing the equation:

To graph the equation, we will assign values to T

when T = 0, W = 600

when T = 2, W = 660

when T = 4, W = 720

when T = 6, W = 780

Answer:

12 people are need to walk 24 dogs

Step-by-step explanation:

12/2=6

24/2=12

Answer:

12 people can walk 24 dogs.

Step-by-step explanation:

Given information,

→ 6 people can walk 12 dogs.

→ People required for 24 dogs = ?

Let us assume that,

→ Missing value = p

Forming the equation,

→ 6/12 = p/24

Then the value of p will be,

→ 6/12 = p/24

→ p/24 = 6/12

→ p × 12 = 6 × 24

→ 12p = 144

→ p = 144/12

→ [ p = 12 ]

Hence, the value of p is 12.

Answer:

Step-by-step explanation:

a) The formula for the regression function is:

Maintenance Cost = 54.7757 + 120.689 x Age of Car

b) The slope of the regression equation is 120.689. This means that on average, for every one year increase in the age of a car, the maintenance cost is expected to increase by $120.689.

c) To construct a 95% interval to predict the maintenance cost for a car that is 7 years old, we can use the formula:

Y = a + bX ± tα/2 * SE

where Y is the predicted maintenance cost, a is the intercept, b is the slope, X is the age of the car, tα/2 is the t-value for the 95% confidence level with n-2 degrees of freedom (11 in this case), and SE is the standard error of the estimate.

Plugging in the values, we get:

Y = 54.7757 + 120.689 * 7 ± 2.201 * 11.8442

Y = 923.167 ± 26.010

Therefore, we can be 95% confident that the maintenance cost for a car that is 7 years old will be between $897.16 and $949.17.

d) The null hypothesis is that there is no significant linear relationship between the average maintenance cost and the age of a car in years. The alternative hypothesis is that there is a significant linear relationship between the average maintenance cost and the age of a car in years.

To test the hypothesis, we can perform a t-test on the slope coefficient using the t-statistic and the p-value provided in the output. The t-statistic is 10.1898, which is much greater than the critical t-value at the 0.05 level of significance for a two-tailed test with 11 degrees of freedom (2.201). The p-value is 0.0000, which is less than the significance level of 0.05. Therefore, we can reject the null hypothesis and conclude that there is a significant linear relationship between the maintenance cost and the age of the car in years.

Answer:

200 lbs.

Step-by-step explanation:

Divide mass value by 16 to convert oz to lbs.

3,200/16=200

About 80 necklaces have more than 28 beads. Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and the standard deviation is 4 beads.

P(x > 28) = P(x - 24 / 4 > 28 - 24 / 4)

P(x > 28) = P(x - 24 / 4 > 1)

P(x > 28) = 1 - ∅1

P(x > 28) = 1 - 0.8413

P(x > 28) = 0.1587

Multiply both sides by 500, then we have

500 P(x > 28) = 0.1587 × 500

500 P(x > 28) = 79.35

500 P(x > 28) ≈ 80

About 80 necklaces have more than 28 beads. Then the correct option is C.

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The missing options are given below.

A. About 24 devices have more than 28 beads.

B. About 48 necklaces have more than 28 beads.

C. About 80 necklaces have more than 28 beads.

D. About 96 necklaces have more than 28 beads.

sorry me too don't know

Step-by-step explanation:

anybody try

Answer:

5/5 which simplifies to 1

Step-by-step explanation:

Answer:

m= 5/5

Step-by-step explanation:

y2= 9

y1=4

x2=8

x1=3

9-4 = 5

8-3 = 5

Therefore the slope/rate of change is 5/5

Answer:

r = -27/16

Step-by-step explanation:

We have:

8r - 3/2 = -15

To find r, we have to isolate the term which contains this variable. Then, we can use the least common multiple:

So,

r = -27/16

Answer: The summer monsoon rains are a crucial source of rainfall for India, bringing in 80% of the country's annual rainfall. These rains are essential for the country's agriculture as they provide the necessary water for crops to grow and thrive. The monsoon season typically runs from June to September, and the amount of rainfall received during this time period can greatly impact the success of the agricultural season. With the majority of the rainfall coming during this season, farmers and agricultural experts closely monitor the monsoon forecast to ensure that enough rainfall is received to support the crops. Without the summer monsoon rains, the agricultural production of the country would be greatly impacted and the livelihoods of many farmers would be at risk.

Step-by-step explanation:

Answer:

\( \sqrt{ {( - 4 - 2)}^{2} + {(1 - 0)}^{2} } = \sqrt{ {( - 6)}^{2} + {1}^{2} } = \sqrt{36 + 1} = \sqrt{37} \)

The number 37 goes beneath the radical symbol.

Answer:

1. \( P(x) \) ÷ \( Q(x) \)---> \( \frac{-3x + 2}{3(3x - 1)} \)

2. \( P(x) + Q(x) \)---> \(\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}\)

3.  \( P(x) - Q(x) \)---> \( \frac{-2(12x - 5)}{(3x - 1)(-3x + 2)} \)

4. \( P(x)*Q(x) \) --> \( \frac{12}{(3x - 1)(-3x + 2)} \)

Step-by-step explanation:

Given that:

1. \( P(x) = \frac{2}{3x - 1} \)

\( Q(x) = \frac{6}{-3x + 2} \)

Thus,

\( P(x) \) ÷ \( Q(x) \) = \( \frac{2}{3x - 1} \) ÷ \( \frac{6}{-3x + 2} \)

Flip the 2nd function, Q(x), upside down to change the process to multiplication.

\( \frac{2}{3x - 1}*\frac{-3x + 2}{6} \)

\( \frac{2(-3x + 2)}{6(3x - 1)} \)

\( = \frac{-3x + 2}{3(3x - 1)} \)

2. \( P(x) + Q(x) \) = \( \frac{2}{3x - 1} + \frac{6}{-3x + 2} \)

Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:

\( \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)} \)

\( \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)} \)

\( \frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)} \)

\( \frac{12x - 2}{(3x - 1)(-3x + 2)} \)

\( = \frac{2(6x - 1}{(3x - 1)(-3x + 2)} \)

3. \( P(x) - Q(x) \) = \( \frac{2}{3x - 1} - \frac{6}{-3x + 2} \)

\( \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)} \)

\( \frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)} \)

\( \frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)} \)

\( \frac{-24x + 10}{(3x - 1)(-3x + 2)} \)

\( = \frac{-2(12x - 5}{(3x - 1)(-3x + 2)} \)

4. \( P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2} \)

\( P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)} \)

\( P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)} \)

Composite functions involve combining multiple functions to form a new function

The functions are given as:

\(P(x) = \frac{2}{3x - 1}\)

\(Q(x) = \frac{6}{-3x + 2}\)

\(P(x) \div Q(x)\) is calculated as follows:

\(P(x) \div Q(x) = \frac{2}{3x - 1} \div \frac{6}{-3x + 2}\)

Express as a product

\(P(x) \div Q(x) = \frac{2}{3x - 1} \times \frac{-3x + 2}{6}\)

Divide 2 by 6

\(P(x) \div Q(x) = \frac{1}{3x - 1} \times \frac{-3x + 2}{3}\)

Multiply

\(P(x) \div Q(x) = \frac{-3x + 2}{3(3x - 1)}\)

Hence, the value of \(P(x) \div Q(x)\) is \(\frac{-3x + 2}{3(3x - 1)}\)

P(x) + Q(x) is calculated as follows:

\(P(x) + Q(x) = \frac{2}{3x - 1} + \frac{6}{-3x + 2}\)

Take LCM

\(P(x) + Q(x) = \frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}\)

Open brackets

\(P(x) + Q(x) = \frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}\)

Collect like terms

\(P(x) + Q(x) = \frac{18x-6x + 4 - 6}{(3x - 1)(-3x + 2)}\)

\(P(x) + Q(x) = \frac{12x - 2}{(3x - 1)(-3x + 2)}\)

Factor out 2

\(P(x) + Q(x) = \frac{2(6x -1)}{(3x - 1)(-3x + 2)}\)

Hence, the value of P(x) + Q(x) is \(\frac{2(6x -1)}{(3x - 1)(-3x + 2)}\)

P(x) - Q(x) is calculated as follows:

\(P(x) - Q(x) = \frac{2}{3x - 1} - \frac{6}{-3x + 2}\)

Take LCM

\(P(x) - Q(x) = \frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}\)

Open brackets

\(P(x) - Q(x) = \frac{-6x + 4 - 18x +6}{(3x - 1)(-3x + 2)}\)

Collect like terms

\(P(x) - Q(x) = \frac{-18x-6x + 4 + 6}{(3x - 1)(-3x + 2)}\)

\(P(x) - Q(x) = \frac{-24x +10}{(3x - 1)(-3x + 2)}\)

Factor out -2

\(P(x) - Q(x) = \frac{-2(12x -5)}{(3x - 1)(-3x + 2)}\)

Hence, the value of P(x) - Q(x) is \(\frac{-2(12x -5)}{(3x - 1)(-3x + 2)}\)

P(x) * Q(x) is calculated as follows:

\(P(x) \times Q(x) = \frac{2}{3x - 1} \times \frac{6}{-3x + 2}\)

Multiply

\(P(x) \times Q(x) = \frac{12}{(3x - 1)(-3x + 2)}\)

Hence, the value of P(x) * Q(x) is \(\frac{12}{(3x - 1)(-3x + 2)}\)

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It can be concluded that triangle ABC and triangle CDE have the same shape, but possibly different sizes, and their corresponding sides are in proportion to each other.

In mathematics, a graph is a set of vertices (or nodes) and edges connecting pairs of vertices. Graphs can be used to represent relationships between objects or to visualize data. In a graph, the vertices usually represent the objects being studied, while the edges represent the connections or relationships between the objects. Graphs can be used to model a wide range of phenomena, from social networks to chemical reactions to the flow of traffic in a city. There are many different types of graphs, including directed graphs, undirected graphs, weighted graphs, and many others.

Slope is a measure of how steep a line is. It is the ratio of the change in the y-coordinates of two points on the line to the change in their x-coordinates. Symbolically, if (x1, y1) and (x2, y2) are two points on a line, then the slope of the line is given by:

slope = (y2 - y1) / (x2 - x1)

In other words, the slope is the amount by which the y-coordinate changes for every unit increase in the x-coordinate. It can be positive, negative, zero, or undefined depending on the direction and steepness of the line.

If the slopes of AC and CE are the same in the given graph, it means that the two sides are parallel to each other. By the corresponding angles theorem, angle C in triangle ABC is congruent to angle C in triangle CDE, as they are opposite angles formed by the intersection of parallel lines. Therefore, triangles ABC and CDE are similar by the angle-angle (AA) criterion.

This means that they have the same shape, but possibly different sizes, and their corresponding sides are in proportion to each other.

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The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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