Directions - Answer the questions based on the following scenario and graph.
Jim and Cassie are both saving money each week in order to buy an awesome Bulls snapback hat (and leave the price stickers on it, of course). The hat costs $27.

Notice that the coefficients of the expression 12x+18y-60 are all divisible by 3, then, we have:

now notice that the coefficients on the expression inside the parenthesis are divisible by 2, then, we have:

therefore, the expression as a product of two factors is 6(2x+3y-10)

The 19th term of a geometric sequence is 1048576.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

We have,

a = 4 and r = 2

The nth term of a geometric sequence.

= a\(r^{n-1}\)

Now,

The 19th term of a geometric sequence.

= a\(r^{n-1}\)

Substituting a and r values.

= 4 x \(2^{19 - 1}\)

= 4  x \(2^{18}\)

= 4 x 262144

= 1048576

Thus,

The 19th term of a geometric sequence is 1048576.

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Answer:

D

Step-by-step explanation:

the equation tells you that 1 yard is 3 feet

so when you move one unit to the right on the x-axis, you should move three units up on the y-axis

The amount of juice served this year is given as follows:

513 gallons.

The amount of juice served this year is obtained applying the proportions in the context of the problem.

The amount last year was given as follows:

540 gallons.

The percentage of this year's amount relative to last year's amount is given as follows:

95%, due to the decay of 5%, 100 - 5 = 95%.

Hence the amount of juice served this year is given as follows:

0.95 x 540 = 513 gallons.

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Answer:

No evidence .because the configurations factors and failure mode are independent

Step-by-step explanation:

Determine if there is sufficient evidence to conclude that configuration affects the type of failure

Number of configurations = 3

Number of failures = 4

assuming Pij represents proportion of items in pop i of the category j

H0 : Pij = Pi * Pj,  I = 1,2,-- I,  j = 1,2,---J

Hence the expected frequencies will be

16.10 , 43.58 , 18, 12.31

7.5,  19.37, 8 , 5.47

10.73, 29.05, 12, 8.21

x^2 = 13.25

test statistic = 14.44. Hence the significance level where Null hypothesis will be acceptable will be = 2.5%

The y-intercept of the linear function means that her initial distance from the finish line is of 10 kilometers.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 10, hence the intercept b is given as follows:

b = 10.

The y-values represent the distance in the context of this problem, hence the initial distance is of 10 km.

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Answer:

slope = \(\frac{5}{9}\) , y- intercept = - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

5x - 9y = 45 ( subtract 5x from both sides )

- 9y = - 5x + 45 ( divide through by - 9 )

y = \(\frac{-5}{-9}\) x + \(\frac{45}{-9}\) , that is

y = \(\frac{5}{9}\) x - 5 ← in slope- intercept form

with slope m = \(\frac{5}{9}\) and y- intercept c = - 5

Answer:

c) 78 miles

Step-by-step explanation:

12²+5²=c²

144+25=c²

169=c²

√169=√c²

13=c

13x6=78

The value of AB is,

⇒ AB = 5.9

(rounded to nearest tenth)

We have to given that,

A right triangle ABC is shown.

Now, By trigonometry formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

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Answer:\(a^2-b^2=3\)

Step-by-step explanation:

We need to find the value of the below expression i.e.

\(a^2-b^2\) when a = 2 and b = 1.

So,

Put a = 2 and b = 1 in the above expression. So,

\(a^2-b^2=(2)^2-1^2\\\\=4-1\\\\=3\)

Hence, the value of the expression is equal to 3.

Answer:

Step-by-step explanation:

Probability is defines as the likelihood or chance that an event will occur.

Probability = expected outcome of event/total outcome.

Since a single die with 9 sides was rolled, the total event outcome will be 9*9 = 81

Expected outcome will be the event that the sum of the two rolls equals 3. The possible outcomes are {(1,2), (2,1)}. The expected outcome is 2

Probability that the sum of the two rolls equals 3 = 2/81

The probability that the sum of the two rolls equals 3 is \(\dfrac{2}{81}\).

Important information:

We need to find the probability that the sum of the two rolls equals 3.

If a die with 9 sides is rolled twice, then the number of total possible outcomes is:

\(9\times 9=81\)

The sum of the two rolls equals 3, if we get 1, 2 and 2, 1. It means the number of favorable outcomes is 2.

\(P=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\)

\(P=\dfrac{2}{81}\)

Therefore, the probability that the sum of the two rolls equals 3 is \(\dfrac{2}{81}\).

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Answer:

1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, 3/2 eggs, and 3/4 cups flour.

Step-by-step explanation:

There are several ways to solve this, I like using proportions.

(You could also find 3/4 of every ingredient since 12 is 3/4s of 16)

We can do this by temporarily naming the amount of each ingredient a variable, and then using the proportion to find the variable.

Note that in a given proportion such as:

a/b=c/d

will always equal

a*d=b*c

This is known as cross multiplying.

For each ingredient I'm going to set up the following proportion:

\(\frac{amount of given ingredient in 16 brownies}{16 (number of brownies)} = \frac{variable (amount of given ingredient in 12 brownies}{12 (new number of brownies)}\)

Now we can start setting up proportions for every ingredient.

Butter:

(2/3)/16=b/12

(2/3)(12)=16b

8=16b

b=1/2

Chocolate:

5/16=c/12

60=16c

c=60/16

c=15/4

Sugar:

(3/2)/16=s/12

(3/2)(12)=16s

18=16s

s=18/16

s=9/8

Vanilla:

2/16=v/12

24=16v

v=24/16

v=3/2

Eggs:

2/16=e/12

24=16e

e=3/2

Flour:

1/16=f/12

12=16f

f=3/4

Therefore, the ingredients for 12 brownies would be:

1/2 cups butter, 15/4 ounces unsweetened chocolate, 9/8 cups sugar, 3/2 teaspoons vanilla, 3/2 eggs, and 3/4 cups flour.

To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.

To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.

First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.

Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.

Using the formula for the present value of an ordinary annuity, we have:

PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.

Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.

Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.

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The volume of the hemisphere with a diameter of 60.9 inches rounded to the nearest tenth is 59131.7 inches³.

Given that,

Diameter of a hemisphere = 60.9 inches

We have to find the volume of the hemisphere.

We know that, radius is half the measure of the diameter.

Radius of the hemisphere = 60.9 / 2 = 30.45 inches

Volume of a hemisphere is,

Volume = 2/3 π r³

Here r is the radius

Substituting,

Volume = 2/3 π (30.45)³

             = 59131.7 inches³

Hence the volume is 59131.7 inches³.

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Answer:

Step-by-step explanation:

y = -1(x + 2)(x - 3)(x - 3)(x + 0)(x + 0)(x + 1)(x + 1)(x + 1)

The 8 degree polynomial for the given roots can be written as  p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

The factor theorem states that for a polynomial p(x) if there exists a real number a such that p(a) = 0, then (x - a) is one of the factors of p(x).

The roots of the polynomial are given as follows,

Number of roots at -2 = 1

Number of roots at 3 = 2

Number of roots at 0 = 2

And, number of roots at -1 = 3.

Now, the polynomial can be written using factor theorem as,

p(x) = x²(x + 2)(x - 3)²(x + 1)³

      = x²(x + 2)(x²- 6x + 9)(x³ + 3x² + 3x + 1)

      = x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x²

Hence, the polynomial for given roots can be written as p(x) =  x⁸ - x⁷- 12x⁶ - 4x⁵ + 30x⁴ + 51x³ + 18x².

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Answer:

The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.

Step-by-step explanation:

Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing

In this case:

Probability of Winning = 0.05

Payout for Win = $5

Cost of Playing = $1

Expected Value = (0.05 * $5) - $1

Expected Value = $0.25 - $1

Expected Value = -$0.75

An exponential equation in the form \(y=a(b)^x\) that can model the amount of caffeine, y, in Kendall's body x hours after drinking the coffee is

The amount of caffeine that will be in Kendall's body after 12 hours is 18 milligrams.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

f(x) = a(b)^x

Where:

Since Kendall drank a cup of coffee that had 95 milligrams of caffeine which is decreasing at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:

Rate of change (decay rate) = 100 - 13 = 87% = 0.87.

By substituting the parameters into the exponential equation, we have the following;

\(f(x) = 95(0.87)^x\)

When x = 12, we have;

\(f(12) = 95(0.87)^{12}\)

f(12) = 17.86 ≈ 18 milligrams.

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Answer:

Tens

Step-by-step explanation:

Decimal Place Values:

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones

. decimal point

tenths

hundreths

thousandths

ten thousandths

Given that cos (0) = 0, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the value of sin (0).

sin^2(0) + cos^2(0) = 1

sin^2(0) = 1 - cos^2(0)

sin^2(0) = 1 - 0^2

sin^2(0) = 1

So, sin (0) = sqrt(sin^2(0)) = sqrt (1) = 1.

However, the given value is sin (0) = v3/6. This means that sin (0) = sqrt (3)/2, which is the value of sin (60). Therefore, the correct value of sin (0) is sqrt (3)/2, not 1.

trigonometry, the branch of mathematics deal with specific functions of angles and their application to calculations. There is total six functions of an angle commonly used in trigonometry.

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Answer:

12

Step-by-step explanation:

Answer:

2.4

Step-by-step explanation:

The vertex form of the quadratic equations in standard form are, respectively:

Case 9: y = 2 · (x + 2)² - 12

Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11: y = 3 · (x - 4 / 3)² - 16 / 3

Case 12: y = - 3 · (x - 3)²

Case 13: y = (x - 4)² + 3

Case 14: y = (x - 1)² - 7

Case 15: y = (x + 3 / 2)² - 9 / 4

Case 16: 2 · (x + 1 / 4)² - 1 / 8

Case 17: y = 2 · (x - 3)² - 7

Case 18: y = - 2 · (x + 1)² + 10

In this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.

The two forms are introduced below:

Standard form

y = a · x² + b · x + c

Where a, b, c are real coefficients.

Vertex form

y - k = C · (x - h)²

Where:

Now we proceed to determine the vertex form of each quadratic equation:

Case 9

y = 2 · x² + 4 · x - 4

y = 2 · (x² + 2 · x - 2)

y = 2 · (x² + 2 · x + 4) - 12

y = 2 · (x + 2)² - 12

Case 10

y = - (1 / 2) · x² - 3 · x + 3

y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]

y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)

y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11

y = 3 · x² - 8 · x

y = 3 · [x² - (8 / 3) · x]

y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)

y = 3 · (x - 4 / 3)² - 16 / 3

Case 12

y = - 3 · x² + 18 · x - 27

y = - 3 · (x² - 6 · x + 9)

y = - 3 · (x - 3)²

Case 13

y = x² - 8 · x + 19

y = (x² - 8 · x + 16) + 3

y = (x - 4)² + 3

Case 14

y = x² - 2 · x - 6

y = (x² - 2 · x + 1) - 7

y = (x - 1)² - 7

Case 15

y = x² + 3 · x

y = (x² + 3 · x + 9 / 4) - 9 / 4

y = (x + 3 / 2)² - 9 / 4

Case 16

y = 2 · x² + x

y = 2 · [x² + (1 / 2) · x]

y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)

y = 2 · (x + 1 / 4)² - 1 / 8

Case 17

y = 2 · x² - 12 · x + 11

y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)

y = 2 · (x - 3)² - 7

Case 18

y = - 2 · x² - 4 · x + 8

y = - 2 · (x² + 2 · x - 4)

y = - 2 · (x² + 2 · x + 1) + 2 · 5

y = - 2 · (x + 1)² + 10

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yes. It would be an irrational number if it didn't repeat in a pattern.

hope it helps comment if u have any questions

Answer:

Yes.

Step-by-step explanation:

Yes 1 \(\frac{1}{2}\) is a rational number because because it can be converted to a decimal, which is 1.5

The cost of the new heating and air conditioner equipment is:

A = $4122

They make a down payment of 20%

A. The down payment is:

B The amount of the loan is the remaining amount after paying the down payment:

L = $4122 - $824.40

L = $3297.60

For given function function f(x)=-x+3-2, the domain is x > -3 and the range is y ≤ 2. So, correct option is D.

The function f(x)=-x+3-2 is a linear function in the form y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is -1 and the y-intercept is 1. Therefore, the graph of the function is a straight line that intersects the y-axis at (0,1) and has a slope of -1, meaning that it decreases by 1 for every 1 unit increase in x.

The domain of the function is the set of all possible values of x for which the function is defined. Since there are no restrictions on the value of x in the equation f(x)=-x+3-2, the domain is all real numbers, or (-∞, ∞).

The range of the function is the set of all possible values of y that the function can output. In this case, the lowest possible value of y occurs when x approaches positive infinity, and the highest possible value of y occurs when x approaches negative infinity. Therefore, the range is all real numbers less than or equal to 2, or y ≤ 2.

So, the domain is x ∈ (-∞, ∞) and the range is y ≤ 2. Alternatively, the domain can also be expressed as x > -3, since that is the minimum value of x at which the function is defined.

Correct option is D.

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Complete question is:

What are the domain and range of the function f(x)=-x+3-2?

A) domain: -3 -2

B) domain: -3 -3 range: y<-2

C) domain: x>-3 range:y>-2

D) domain : x>-3 range: y ≤ 2

Given

The function is

\(f(x)=3\sqrt{x}\)

The function g(x) transform by shifting f(x) right 3 units.

To find:

The function g(x).

Step-by-step explanation:

The translation is defined as

\(g(x)=f(x+a)+b\)

where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The function f(x) shifts only 3 units right. So,

\(a=-3,b=0\)

Now,

\(g(x)=f(x+(-3))+0\)

\(g(x)=f(x-3)\)

\(g(x)=3\sqrt{x-3}\)               \([\because f(x)=3\sqrt{x}]\)

Therefore, the required function is \(g(x)=3\sqrt{x-3}\).

Answer:

y=2w im not shure tell me if this is wong

Answer:

(2, -1)

Step-by-step explanation:

Given system of equations:

\(\begin{cases}y=-2x+3\\y+9=4x\end{cases}\)

To solve the given system of equations, we can use the method of substitution.

Substitute the first equation into the second equation to eliminate the y term:

\((-2x+3)+9=4x\)

Solve for x:

   \(-2x+3+9=4x\)

       \(-2x+12=4x\)

\(-2x+12+2x=4x+2x\)

                  \(12=6x\)

                 \(\dfrac{12}{6}=\dfrac{6x}{6}\)

                   \(2=x\)

                   \(x=2\)

Substitute the found value of x into the first equation and solve for y:

\(y=-2(2)+3\)

\(y=-4+3\)

\(y=-1\)

Therefore, the solution to the system of equations is (2, -1).

To verify the solution by graphing the system, find two points on each line by substituting two values of x into each equation. Plot the points and draw a line through them. The solution is the point of intersection.

Graphing y = -2x + 3

\(\begin{aligned} x=0 \implies y&=-2(0)+3\\y&=0+3\\y&=3\end{aligned}\)            \(\begin{aligned} x=-2 \implies y&=-2(-2)+3\\y&=4+3\\y&=7\end{aligned}\)

Plot points (0, 3) and (-2, 7) and draw a straight line through them.

Graphing y + 9 = 4x

\(\begin{aligned} x=0 \implies y+9&=4(0)\\y+9&=0\\y&=-9\end{aligned}\)                 \(\begin{aligned} x=3 \implies y+9&=4(3)\\y+9&=12\\y&=3\end{aligned}\)

Plot points (0, -9) and (3, 3) and draw a straight line through them.

The solution to the graphed system of equations is the point of intersection of the two lines: (2, 1).

Answer:

y dónde está la pregunta de imagen?????????????

Answer:

114.29

Step-by-step explanation: