I really need help solving this practice problem from my ACT prep guide It has an additional picture with a graph to use, I will send this pic

Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The system of equations with no solution is:

y + 3x = -7

4z - 2y = 10

The system of equations with exactly one solution is:

y = 6z+8

y = 6x-4

y = 3x + 2

2z-y = 5

y=-2z+8

The system of equations with infinitely many solutions is:

4z + y = 8

Answer: buy all the crop tops

Step-by-step explanation:

Answer:

Well with that amount of money u should most definitely buy them, if you liked the of course

Step-by-step explanation:

I'm just saying

Answer:

65 degrees

Step-by-step explanation:

All angles of a triangle have to add up to 180 degrees. After establishing that, we can see that there are two angles given. 25 degrees and a 90-degree symbol. So if two angles add up to 115 degrees, we can do 180-115=65 to find the angle of C.

Answer:

m∠C=65°

Step-by-step explanation:

m∠B=90°

m∠A=25°

m∠A+m∠B+m∠C=180°

25°+90°+m∠C=180°

m∠C=180°-(90°+25°)

m∠C=65°

Hope it helps! :)

Answer:

The rate of interest may vary , totally depends on the market value of that agency or company or the financial agency which is providing the mortgage money at certain rate. So, option (B) the interest rate may change depending on the condition of the economy is true statement regarding adjustable rate mortgage.Step-by-step explanation: hope it helps

9514 1404 393

Answer:

  y = 2(x -2)^2 +1

Step-by-step explanation:

Start by factoring the leading coefficient from the x-terms.

  y = 2(x^2 -4x) +9

Now identify the coefficient of x, -4, and figure half of that: -2. Square this number and add it inside the parentheses. At the same time, subtract the equivalent value outside parentheses. (The leading coefficient must be taken into account.)

  y = 2(x^2 -4x +4) +9 -2(4)

Put in the desired form.

  y = 2(x -2)^2 +1

This matches vertex form ...

  y = a(x -h)^2 +k . . . . . . . . . vertical scale factor 'a'; vertex (h, k)

Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

The perimeter and area of a rectangle are (5,6) and (6,5).

The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.

A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.

The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.

The perimeter of the rectangle:

P=2l+2w=22

divide 2 into both sides

l+w=11 -------------> (1)

w=11-l

Area of the rectangle:

l*w=30

l(11-l)=30

11l-l^2-30=0

l^2-11l+30=0

By factor method,

(l-5)(l-6)=0

l=5,6.

Substitute this value in w,

l=5 implies w=6

l=6 implies w=5

There we have two solutions.

The length and breadth of the rectangle is

(5,6) and (6,5).

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Answer:

25.9615099715

Step-by-step explanation:

Answer:

I believe the answer is neither

Step-by-step explanation:

Step-by-step explanation:

Given the equation that modeled the total public debt D (in trillions of dollars) in the United States at the beginning of each year from 2000 through 2008 can be approximated by;

D = 0.032t^2 + 0.21t + 5.6, 0 ≤ t ≤ 8

We are to find the total public debt with the time interval;

when t = 0;

D = 0.032(0)^2 + 0.21(0) + 5.6

D = 5.6 trillion dollars

when t = 1;

D = 0.032(1)^2 + 0.21(1) + 5.6

D = 0.032+0.21+5.6

D = 5.842 trillion dollars

when t = 2;

D = 0.032(2)^2 + 0.21(2) + 5.6

D = 0.128+0.42+5.6

D =  6.148 trillion dollars

when t = 3;

D = 0.032(3)^2 + 0.21(3) + 5.6

D = 0.288+0.63+5.6

D = 6.518 trillion dollars

when t = 4;

D = 0.032(4)^2 + 0.21(4) + 5.6

D = 0.512+0.84+5.6

D = 6.952 trillion dollars

when t = 5;

D = 0.032(5)^2 + 0.21(5) + 5.6

D = 0.8+1.05+5.6

D = 7.45 trillion dollars

when t = 6;

D = 0.032(6)^2 + 0.21(6) + 5.6

D = 1.152+1.26+5.6

D = 8.012 trillion dollars

when t = 7;

D = 0.032(7)^2 + 0.21(7) + 5.6

D = 1.568+1.47+5.6

D = 8.638 trillion dollars

when t = 8;

D = 0.032(8)^2 + 0.21(8) + 5.6

D = 0.032(64)+1.68+5.6

D = 2.048+1.68+5.6

D = 9.328 trillion dollars

From the values gotten, we can see that the total public debt reached or surpassed 7 trillion dollars in 2005

To get the public debt in 2017, we can simply substitute t = 17 into the expression D = 0.032t2 + 0.21t + 5.6

D = 0.032(17)^2 + 0.21(17) + 5.6

D = 0.032(289)+3.57+5.6

D = 9.248+3.57+5.6

D(17) = 18.418 trillion dollars

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The total number of people want in all is 531.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of buses = 9

Number of buses that has 63 people = 5

Number of buses that has 54 people = 4

The total number of people in all the buses.

= 5 x 63 + 4 x 54

= 315 + 216

= 531

Thus,

The total number of people want in all is 531.

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Answer:

1/3

Step-by-step explanation:

-4 - (-3)= - 1

-12 -(-9)=-3

two negatives make a positive

-1/-3 = 1/3

Answer:

(-4)^3 * y^2

Step-by-step explanation:

hope it helps.

Answer:

The answer is 4.797752129

The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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For the correlation between the fund returns is .0459, the reward-to-volatility ratio of the best feasible CAL is equals to 0.1621 or 16.21%.

A probability distribution is helps to determine the future what frequency distribution is to the past. Standard deviation is used in the concept of risk of portfolio of investment. Risk refer to the dispersion of a probability distribution.

Stock fund (S) Bond fund (B)

Expected Return 14% 7%

Standard Deviation 43% 37%

Risk-free returns , Rf = 5.3%

Correlation coefficient = 0.459

Covariance : 0.459 = COV(s,b)/0.43×0.37

Covariance = 0.073

Stock Fund =( (σB)²− σS× σB× correationco, SandB)/((σS)²(σB)² - 2 × σS× σB× correationco, SandB)

= ((0.37)²− 0.43× 0.37× 0.0459) /((0.43)²(0.37)² −2× 0.43× 0.37× 0.0459)

Weight of S = 42.18%

Weight of B = 1 - 42.18 = 57.82%

Expected Return of the portfolio (Rp) = WS× E(RS) + WB × E(RB) = 42.18 × 14% + 57.82 × 7%

= 5.90 + 4.05 = 9.95

Standard Deviation of the portfolio (SDp)

= (WS²SD² + WB²× lSD²+ 2WS WBCov(S,B))1/2

= 28.68

Reward to volatility = (Expected return - Rf) / SD of Portfolio

= (9.95- 5.3) / 28.68

=0.1621

Hence, the required volatility is 0.1621 or 16.21%.

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Answer:

x= - 52

Step-by-step explanation:

we need to multiply  both sides by 4 to leave the x alone

so

\(\frac{-x}{4} *4= 13*4\\-x= 52\\\frac{-x}{-1}=\frac{52}{-1}\\ x=-52\)

On factoring the polynomial 6z² + 6z the values for length and width are obtained as 6z and z + 1.

What is a polynomial?

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

We can factor the polynomial 6z² + 6z by taking out the greatest common factor, which is 6z -

6z² + 6z = 6z(z + 1)

This means that the area of the wall is equal to 6z(z + 1) square meters. Since the area of a rectangle is given by the product of its length and width, we can write -

6z(z + 1) = length × width

Therefore, the possible expressions for the length and width of the wall are -

length = 6z

width = z + 1

or

length = z + 1

width = 6z

Both of these expressions give a product of 6z(z + 1), which is equal to the area of the wall.

We can switch the roles of length and width, so there are two possible expressions for the dimensions of the wall.

Therefore, the length is 6z and width is z + 1.

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As a result, we have demonstrated that GE≅  HF, assuming that ABCD is a parallelogram, BG ≅ DH, and AE≅  FC.

A parallelogram is a two-dimensional geometric figure that is defined by two pairs of parallel and congruent sides. It is a flat shape that is similar to a rectangle, but with the important difference that its opposite sides do not have to be equal in length. A parallelogram can be described by its base, height, and diagonals. The base and height of a parallelogram are the lengths of two parallel sides. The diagonals of a parallelogram are the lines that connect opposite vertices of the figure. In mathematical terms, a parallelogram can be defined as a quadrilateral (a four-sided figure) with the property that its opposite sides are both parallel and congruent. This means that if two sides of a parallelogram are equal in length and parallel, then the other two sides are also equal in length and parallel. Parallelograms are important in geometry and are used in various applications, such as calculating area, finding the length of diagonal lines, and solving problems involving similar figures. They are also useful in understanding concepts in physics and engineering, such as force and velocity vectors.

Here,

To prove that GE ≅ HF, we can use the fact that opposite sides of a parallelogram are equal.

Since ABCD is a parallelogram, we know that AB ≅ CD and AD ≅ BC.

Since BG ≅ DH and AE ≅ FC, we can write:

BG + AE ≅ DH + FC

Now, using the fact that opposite sides of a parallelogram are equal, we have:

AB ≅ CD and AD ≅ BC

So, substituting these equalities into our previous equation, we get:

BG + AE ≅ DH + BC

Finally, since GE is equal to BG + AE and HF is equal to DH + BC, we have:

GE ≅ HF

Therefore, we have proven that GE ≅ HF, given that ABCD is a parallelogram, BG ≅ DH and AE ≅ FC.

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The percent of the bags of chips weigh less than 176 grams is b 16%

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

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

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Answer:

0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.

Step-by-step explanation:

Manufacturer’s claim that the average nicotine content does not exceed 3.5 mg

This means that the null hypothesis is given by:

\(H_{0}: \mu = 3.5\)

And the alternate hypothesis is:

\(H_{a}: \mu > 3.5\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

3.5 is tested at the null hypothesis

This means that \(\mu = 3.5\)

A random sample of 8 cigarettes of a certain brand has an average nicotine content of 4.2 milligrams and a standard deviation of 1.4 milligrams.

This means that \(n = 8, X = 4.2, \sigma = 1.4\)

Value of the z-statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{4.2 - 3.5}{\frac{1.4}{\sqrt{8}}}\)

\(z = 1.41\)

Pvalue of the test:

We are testing if the mean is higher than 3.5.

The sample mean found is of 4.2, and we have to find the probability of finding a sample mean at least as large as this, which is 1 subtracted by the pvalue of z = 1.41.

z = 1.41 has a pvalue of 0.9207

1 - 0.9207 = 0.0793

0.0793 > 0.01, which means that we have a result in line with the manufacturer's claim.

The surface area of the composite figure is 2005 in².

To find the surface area of the composite figure, we need to calculate the sum of the areas of its individual components.

Let's break down the figure into its different parts and calculate the surface area step by step:

Rectangular Prism: The rectangular prism has dimensions of 20 in, 11 in, and 5 in. The surface area of a rectangular prism can be found by adding the areas of its six faces. The total surface area of the rectangular prism is given by:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(20)(11) + 2(20)(5) + 2(11)(5) = 440 + 200 + 110 = 750 in²

Rectangular Prism: Another rectangular prism has dimensions of 19 in, 12 in, and 12 in. Following the same process as above, we can calculate the surface area of this rectangular prism:

Surface Area of Rectangular Prism = 2lw + 2lh + 2wh

Plugging in the values, we have:

Surface Area of Rectangular Prism = 2(19)(12) + 2(19)(12) + 2(12)(12) = 456 + 456 + 288 = 1200 in²

Base: The base is a rectangle with dimensions 11 in and 5 in. The surface area of a rectangle is given by the formula:

Surface Area of Rectangle = lw

Plugging in the values, we have:

Surface Area of Rectangle = (11)(5) = 55 in²

Finally, to find the total surface area of the composite figure, we add the surface areas of the individual components:

Total Surface Area = Surface Area of Rectangular Prism + Surface Area of Rectangular Prism + Surface Area of Rectangle

Total Surface Area = 750 in² + 1200 in² + 55 in² = 2005 in²

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Sara should expect a paycheck of $91.80 from her first full of work.

In the question, we are given that Sara just started her first job as an assistant at an after-school child care center. She works 12 hours a week and makes $9 per hour. She has been told that 15% of her paycheck will be deducted for federal, state, and local taxes.

We are asked for the amount that Sara should expect her paycheck of, from her first full week of work.

The time for which Sara works weekly = 12 hours.

The per hour earning of Sara = $9.

Thus, the total earnings after working for 12 hours at the rate of $9 per hour is 12*$9 = $108.

Now, the deduction is given to be 15%.

Thus, the total deduction = 15% of $108 = $16.20.

The amount on the paycheck = The total earnings less the deduction,

or, the amount on the paycheck = $108 - $16.20 = $91.80.

Thus, Sara should expect a paycheck of $91.80 from her first full of work.

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The production cost of ONE small chicken pie is R9.40. Option C.

To calculate the production cost of 1 litre of homemade ginger beer:

The cost of ingredients to produce 30 litres of ginger beer is R120, so the cost of ingredients per litre is 120/30 = R4.

They added 75% to the production costs to cover their overheads, so the total production cost per litre is 4 + 0.75(4) = R7.

Therefore, the production cost of 1 litre of homemade ginger beer is R7.

To calculate the profit of 60 litres of homemade ginger beer if the mark-up is 30%:

The cost of producing 60 litres of ginger beer is 60 x 7 = R420.

The mark-up is 30%, so the selling price of 60 litres of ginger beer is 420 + 0.3(420) = R546.

The profit is the selling price minus the production cost, so the profit is 546 - 420 = R126.

Therefore, the profit of 60 litres of homemade ginger beer with a 30% mark-up is R126.

To calculate the production cost of ONE small chicken pie:

The cost of ingredients to produce ten small chicken pies is R63, so the cost of ingredients per pie is 63/10 = R6.30.

The overheads to make ten small chicken pies is R31, so the overhead cost per pie is 31/10 = R3.10.

The production cost of ONE small chicken pie is the sum of the cost of ingredients and the overhead cost, so it is 6.30 + 3.10 = R9.40.

Therefore, the production cost of ONE small chicken pie is R9.40.

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Answer: b

Explanation:

The given graph is the graph of a piecewise function. The equations of the lines are

Considering the First line on left, the equation is

y = - 2x + 1

The line extends towards the right and terminates at a point. The endpoint has an open circle. This means that the coordinates of that point are not inclusive. The x coordinate of the endpoint is 1, Thus, only all values of x less than 1 satisfy this function. The domain is

x < 1

Considering the second line on right, the equation is

y = - x + 2

The line extends towards the right from a point(x = 1). The start point has a closed circle. This means that the coordinates of that point are inclusive. Thus, only all values of x greater than or equal to than 1 satisfy this function. The domain is

x ≥ 1

The correct option is B

Answer: the wise man is 79

Step-by-step explanation:

400 - 3x = 163

400–163 =3x

237 = 3x or 3x = 237 or x = 79…

Answer: Let "T" denote households with television

"I" denote households with internet

and "N" denote households with neither of these.

Since P(N) = 0.05 then it means P(TuI) = 0.95. We know from set theory that P(TuI) = P(T) + P(I) - P(TnI). Thus,

0.95 = 0.92 + 0.72 - P(TnI) ==> P(TnI) = 0.69. This means P(T/I) = P(T) - P(TnI) = 0.92 - 0.69 = 0.23, and P(I/T) = P(I) - P(TnI) = 0.72 - 0.69 = 0.03. So,

a)

House                 Probability

Nothing                0.05

Only television      0.23

Only internet         0.03

Both                   0.69

b) P(internet but no television) = P(only internet) = 0.03

c) P(internet | there is television) = (By Bayes' Rule) P(TnI) / P(T) = 0.69 / 0.95 = 0.726 (rounded to 3 decimal points)

d) P(internet | there is no television) = (By Bayes' Rule) P(I/T) / P(T') = 0.03 / 0.08 = 0.375

e) From (c) and (d) ==> In Canada, it is (0.726/0.375 ≈ 2 ) twice more likely that if there's television in the household, then there is internet.

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Because we know both figures have the same perimeter, we can set them equal to each other.

3x + 4 + 5x + 1 + 2x + 5 = x + 13 + x + 13 + 2x + 2x

10x + 10 = 6x + 26 (Added like terms.)

4x + 10 = 26 (Subtracted 6x on both sides.)

4x = 16 (Subtracted 10 on both sides.)

x = 4 (Divided 4 on both sides.)