What is the solution to 9|x – 8| < 36?

4 < x < 12
x < –4 or x > 12
x > –12 or x < 8
–4 < x < 8

Answer:

The prices where the revenue is zero are $x = 0 and $x = 125.

When x = 0, the revenue is 0 since the function is equal to zero (R(0) = -40(0)^2 + 5000(0) = 0).

When x = 125, the revenue is 0 since the coefficient of the x^2 term is negative and the coefficient of the x term is positive. Since the equation is equal to zero, the two terms must cancel each other out, resulting in zero revenue (R(125) = -40(125)^2 + 5000(125) = 0).

Step-by-step explanation:

Answer:

Buying two T-shirts for 5 dollars is a better deal.

Step-by-step explanation:

If you bought one T-shirt for 3 dollars, that would be more than half of the money than two T-shirts. Therefore, it's a better deal to get 2 T-shirts for 5 dollars.

(a) Loan you can afford is $143097.67. (b) Total money will you pay the loan company is $378000. (c) Interest amount is $234902.33.

Loan interest is the additional cost that a borrower must pay on top of the principal amount of a loan. Interest is typically expressed as a percentage of the principal and is charged over a specific period of time. The rate of interest charged on a loan is determined by a variety of factors, including the borrower's creditworthiness and the type of loan. The purpose of interest is to compensate the lender for the risk and cost of providing the loan.

Given data:

Principal = $1050 per month

Time = 30 year

        = 30 × 12

        = 360 months

Interest rate = 8%  

                    = 0.08/12

                    = 0.006667 monthly

(a) We get here first maximum amount of loan by present value of annuity as

Present value of annuity = principal ×  [tex]\frac{1-(1+rate)^{-t} }{rate}[/tex]           .........(1)

Put here value we get

value of annuity = 1050 × [tex]\frac{1-(1+0.006667)^{-360} }{0.006667}[/tex]

value of annuity = $143097.67

(b) Total amount  = principal × time period

                            = $1050 × 360

                            = $378000

(c) Total amount of interest paid will be

interest amount = total amount paid - loan amount

interest amount  = $378000 - $143097.67

interest amount  = $234902.33

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Hello,

I hope you and your family are doing well!

The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. Since the sum of 5 consecutive odd numbers is 145, we can set up the equation:

(a + (a + 4)) / 2 * 5 = 145

where a is the first term in the sequence.

Solving this equation gives us:

a = -23

The third number in the sequence is the third odd number after a, which is a + 4. Substituting -23 for a gives us:

(-23) + 4 = -19

Therefore, the third number in the sequence is -19.

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Happy Holidays & New Year!

1a. No, the value of 60% of 400 is 240.

1b.  No, the value of 60% of 200 is 120.

1c.  No, the value of 60% of 120 is 72.

2. The equation the express the relation 60%, x, and 87 is 0.6x = 87. The value of x is 145.

3a.The equation is0.6c = 43.2. The value of c is 72.

3b. The equation is0.38e = 190. The value of e is 500.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

1.a

Compute the vale of  60% of 400.

Using the formula a% = a/100

60% of 400 = 60/100 of 400

Replace of by multiplication:

60% of 400 = (60/100) × 400

60% of 400 = 240.

1b.

Compute the vale of  60% of 200.

Using the formula a% = a/100

60% of 200 = 60/100 of 200

Replace of by multiplication:

60% of 200 = (60/100) ×2 00

60% of 400 = 120.

1c.

Compute the vale of  60% of 120.

Using the formula a% = a/100

60% of 120 = 60/100 of 120

Replace of by multiplication:

60% of 120 = (60/100) × 120

60% of 400 = 72.

2.

Given that 60% of x is 87.

Compute the vale of  60% of x.

Using the formula a% = a/100

60% of x = 60/100 of x

Replace of by multiplication:

60% of x = (60/100) × x

60% of x = 0.6x

Therefore the relationship is 0.6x = 87

Now divide both sides by 0.6:

x = 87/0.6

x = 145.

3a.

Given that 60% of c is 43.2.

Compute the vale of  60% of c.

Using the formula a% = a/100

60% of c = 60/100 of c

Replace of by multiplication:

60% of c = (60/100) × c

60% of c = 0.6c

Therefore the relationship is 0.6c = 43.2

Now divide both sides by 0.6:

c = 43.2/0.6

c =72.

3b.

Given that 38% of e is 190.

Compute the vale of  38% of e.

Using the formula a% = a/100

38% of e = 38/100 of e

Replace of by multiplication:

38% of e = (38/100) × e

38% of e = 0.38e

Therefore the relationship is 0.38e = 190

Now divide both sides by 0.38:

e = 190/0.38

e = 500.

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Probability p(Royal flush)= 4/2598960 = 1/649740

What is Probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

A royal rush in Poker Card is five of each of the following: ace, king, queen, jack, and ten.

The ten, Jack, Queen, King, and Ace of a single suit make up a royal flush. These hands come in fours.

Total no. of ways = selecting 5 cards out of 52 cards = 52 C5 = 2598960

So, P(royal flush)= 4/2598960 = 1/649740

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The measure of x = 64°

The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal.

Here we have

Three lines are intersected and formed a triangle  

Let's assume that the triangle formed is ΔABC

In ΔABC,  ∠C = 34°  

Since Vertical opposite angles are equal

=> ∠B = 30°  

As we know the sum of angles in a triangle = 180°

=> ∠A + ∠B + ∠C = 180°

=> ∠A = 180° -  30° - 34°  

=> ∠A = 116

From the line CL [ observe the given picture ]  

=> ∠A + x = 180°

=> 116° + x = 180°

=> x = 180° - 116°

=> x = 64°  

Therefore,

The measure of x = 64°

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Answer:

61 is the mode.

Step-by-step explanation:

Remember, the mode is the most repeated number in the list. 6|1 is repeated the most times (twice).

Answer:

61 is the correct answer

The minimum length of the slanted poles needed to support the fly is 20 feet.

What is a Pythagoras theorem?

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

To find the minimum length of the slanted poles, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the slanted pole) is equal to the sum of the squares of the other two sides (the heights of the tent and fly).

We are given that the height of the tent is 12 feet and the height of the fly is 16 feet. The Pythagorean theorem can be written as follows:

c² = a² + b²

where c is the length of the slanted pole, a is the height of the tent, and b is the height of the fly.

Substituting in the given values, we get:

c² = 12² + 16²

= 144 + 256

= 400

Taking the square root of both sides gives:

c = √400

= 20

Therefore, the minimum length of the slanted poles needed to support the fly is 20 feet.

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Answer:

The answer is in the picture

Step-by-step explanation:

The explanation is in the picture

The values shown by the thermometer of 87 °F and 94 °F which in degrees Celsius are 31 °C and 34 °C indicates that the relationship is not a proportional relationship. The correct option is therefore;

A proportional relationship is one in which one  variable is a constant multiple of the other, such that the ratio of each data pair is a constant.

The ratio of the two temperatures are therefore;

[tex]\dfrac{87}{31}[/tex] and  [tex]\dfrac{94}{34}[/tex]

31 is a prime number, therefore'

[tex]\dfrac{87}{31} \neq \dfrac{94}{34}[/tex]

The ratio of the ordered pair of a proportional relationship  is constant, the ratio of the specified values is not constant, therefore, the relationship is not a proportional relationship.

The correct option is therefore;

No there is not a proportional relationship because 87 over 31 does not equal 94 over 34

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The p-value for the hypothesis test in this problem is given as follows:

0.0258.

The first step in obtaining the p-value of the test is verifying the hypothesis that are test, to classify the test.

At the null hypothesis, it is tested if the mean carrier data speed is of 12 Mbps, that is:

[tex]H_0: \mu = 12[/tex]

At the alternative hypothesis, it is tested if the mean carrier data speed is different of 12 Mbps, that is:

[tex]H_1: \mu \neq 12[/tex]

Then we have a two-tailed test, as we are testing if the mean is different of a value, and the parameters are given as follows:

Using a t-distribution calculator with these parameters, the p-value for the test is given as follows:

0.0258.

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Answer:

Factor for this problem is

2(2c+1)(c+2)

Answer:(c+2)(4c+2)      

Step-by-step explanation:

Factor by grouping

(c+2)(4c+2)      

The solution of a compound inequality is the common region or intersection region of two inequalities.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

A sentence having two inequality statements connected by the words 'or' Or 'and' is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence.

For example, if in a compound inequality we get x > 3 and x > 5 so the final conclusion is x > 5.

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The two solutions of the quadratic equation are:

x  = 1.135

x= -1.468

A general quadratic equation:

a*x^2 + b*x + c = 0

Has solutions of the form:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Here the quadratic equation is:

3*x^2 + x - 5 = 0

So the values are:

a = 3

b = 1

c = -5

Replacing that in the quadratic formula for the solutions we will get:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*3*(-5)} }{2*3}\\\\x = \frac{-1 \pm 7.81 }{6}[/tex]

Thus, the two solutions are:

x = (-1 + 7.81)/6  = 1.135

x = (-1 - 7.81)/6 = -1.468

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According to the given information the slope of the linear function containing these points is of 1.

The graph of a linear function is a horizontal line. The following is the form of a linear transformation. a + bx = y = f(x). One regression coefficient or one predictor variables make up a linear function.

A linear function is modeled by:

y=mx+b

In which:

In this problem, the points given are: (-10, 22) and (14, 26), hence, the slope is given by:

[tex]y_2=26 ,y_1=22 ,x_2=14 , x_1=10\\\\\\text { m }=\frac{y_2-y_1}{x_2-x_1}\\\\\\text { m }=\frac{y_2-y_1}{x_2-x_1}\\\\\text { m }=\frac{26-22}{14-10}\\\\\m=1[/tex]

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The graph showing the transformation of the function y = 2ˣ, with points (0, -1), and (1, -4), as well as an horizontal asymptote of y = 2, indicates that the equation of the graph in the form y = A·2ˣ + k is; y = -3·2ˣ + 2

The asymptote is a line that can be drawn on the graph such that the curve of the graph approaches the line without touching it as the values of the variables increase.

The required form of the exponential equation is; y = A·2ˣ + k

Where;

k = The horizontal asymptote

The graph included in the question indicates that an horizontal asymptote is indicated by the line y = 2

= 2

Points on the graph of the transformed function are (1, -4), (0, -1)

When x = 0, y = -1, therefore;

-1 = A·2⁰ + 2

A·2⁰ + 2 = -1 - 2 = -3

A = -3

The equation for the graph is therefore;

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Using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, we know that:

Jenna has 50 pieces of laundry.

She removed her 10 favorite shirts.

50 - 10 = 40

She divided the rest into 8 piles.

40/8 = 5

Therefore, using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.

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Answer: a= (-10)

Step-by-step explanation:

step 1- move the -7 to the other side of the equal sign to combine with -17.

step 2- to do this we need to make -7 positive so instead of (-17) -7, it would be (-17) +7.

step 3- leaving you with

a= (-10) hope this helped :)

The probability of select 4 women from the group is, P = 35.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given: You have a group of 20 people, 7 are women and the remaining people are men.

7 are women then 13 are men.

No. of ways in which 4 women can be chosen from 7 women are 7C4.

So, the probability of select 4 women from the group is,

[tex]P = {7_C_4} \\P = \frac{7!}{4!*(7-4)!} \\P=\frac{7!}{4!*3!} \\P = 35[/tex]

Hence, the probability of select 4 women from the group is, P = 35.

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What is the maximum height of the ball 182.25 feet

How many seconds does it take until the ball hits the ground 6 seconds

The maximum height will occur at the vertex v(h', k)

h' = -b/2a

From the equation h = − 16 t^2 + 84 t + 72

a = -16

b = 84

h' = -84/(2 * -16)

h' = t = 2.625

k = h = − 16 t^2 + 84 t + 72 at t = 2.625

= − 16 * 2.625^2 + 84 * 2.625 + 72

= 182.25 feet

The ball hits the ground when h = 0

0 = − 16 t^2 + 84 t + 72

solving the quadratic equation gives

t = 6 OR -3/4

Use the positive value

t = 6 seconds

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Answer:

x = 5

Step-by-step explanation:

Since the lines with red arrows are parallel, we can use the ratios

(28 - 12)/28 = 4x/35

35(16) = 28(4x)

560 = 112x

x = 560/112

x = 5

Answer:

1:25

$0.04 or 4 cents per can

Step-by-step explanation:

The ratio of dollars to can is 2:50 = 1:25.

$1/25 = $0.04

She gets $0.04 or 4 cents per can

The amount of initial sample will be left in the sample after 25 years is $771.49.

What is isotope decay?

An unstable atomic nucleus loses energy via radiation during the process of radioactive decay. A substance is regarded as radioactive if it has unstable nuclei. The three most frequent types of decay are alpha decay, beta decay, and gamma decay, all of which involve the emission of one or more particles.

Given:

A sample of 200g of an isotope decays to another isotope according to the function [tex]A(t) = 200e^-^0^.^0^5^4^t[/tex],where t is the time in years.

We have to find the amount of  initial sample will be left in the sample after 25 years.

Plug t = 25 in the given equation.

[tex]A(25) = 200e^-^0^.^0^5^4^(^2^5^)\\A(25) = 771.4851\\A(25) = 771.49[/tex]

Hence, the amount of initial sample will be left in the sample after 25 years is $771.49.

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The number of handshakes that occur in Tom's workshop is 105

Given: Number of people in the workshop is 15 and Every person shakes hands once with every other person

To find: Number of handshakes

Since every person has to meet the other person only once and shake hands only once. So every handshake has only one possible combination.

Total number of combinations (handshakes) that can be possible with 15 people = [tex]15C_2[/tex]

The formula for a combination is

[tex]nC_r = \frac{n!}{r!(n-r)!}[/tex]

where n is the number of items and r is the unique arrangements.

Plugging in our numbers of n = 15 and r = 2, we get

[tex]15C_2= \frac{15!}{2!(15-2)!}\\= \frac{15!}{2! \times 13!} \\=\frac{15 \times 14 \times 13!}{2! \times 13!}\\[/tex]

On cancelling out 13! from numerator and denominator , we get

[tex]15C_2=\frac{15 \times 14}{2 \times 1}= 15 \times 7=105[/tex]

A combination is a method of picking things from a collection in which the order of selection is irrelevant. Assume we have three numbers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

It is feasible to count the number of combinations in smaller collections, but the possibilities of a set of combination increases with the number of groups of elements or sets. As a result, a formula has been developed to determine the number of things that can be selected.

The formula is

[tex]nC_r = \frac{n!}{r!(n-r)!} \, when \, n > r\\nC_r = 0 \, when \, n < r[/tex]

Where n = number of distinct objects to choose from

C = Combination

r = spaces to fill

The number of handshakes that occur in Tom's workshop is 105

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a) The equation is 10p + 80 = 180 and p = 10.

b) The three angles are 90°, 37°, 53°.

What is an equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given that, the angles of the triangles are 53°, 2p + 17°, and 8p + 10°.

The sum of all angles of a triangle is  53° + 2p + 17° + 8p + 10° = 80 + 10p

The sum of all angles of a triangle is 180°.

Therefore,

80 + 10p = 180

Subtract 80 from both sides:

10p = 100

divide both sides by 10:

p = 10.

Putting p = 10 in 2p + 17°, and 8p + 10°:

2p + 17° = 20° + 17° = 37°

8p + 10° = 80° + 10° = 90°

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The equation will be 44.50 w + 106.37 = 239.87, and it will take 3 weeks to collect money for gaming chair.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data provided in the question,

Cost of new gaming chair = $239

Savings for gaming chair = $106.37

Each week earning = $44.50

Then the expression will be,

44.50 w + 106.37 = 239.87

44.50 w = 239.87 - 106.37

w = 133.5/44.50

w = 3

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Answer:

Therefore, the value of k is 1.

Step-by-step explanation:

Vertical angles are pairs of angles that are opposite each other and are formed by two intersecting lines. If one angle measures 160°, the other angle must measure 180° - 160° = 20°. Therefore, if the other angle measures (3k + 61)°, we can set up the equation 20 = 3k + 61. Solving for k, we get k = -41. However, since the value of k must be a positive integer, the only possible value of k is k = 1. Therefore, the value of k is 1.

Answer:

k = 33

Step-by-step explanation:

Answer:

25.5 inches.

Step-by-step explanation:

To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have a right triangle with legs of length 19 inches and 17 inches. The length of the hypotenuse is the square root of the sum of the squares of the other two sides. We can calculate this as follows:

hypotenuse = sqrt(19^2 + 17^2)

hypotenuse = sqrt(361 + 289)

hypotenuse = sqrt(650)

hypotenuse = 25.495097568 inches

Rounding to the nearest tenth, the length of the hypotenuse is 25.5 inches.

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