The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 8 to 5. If there were 6336 yes votes, what was the total
number of votes?

Explanation:

Given f(x) : (2, -3)

f(x) + 2 then graph translates up by 2 units up =  \(\boxed{\sf (2, -1)}\)

f(x) - 3 then graph translates down 3 units down = \(\boxed{\sf (2, -6)}\)

f(x + 5) then graph translates left 5 units = \(\boxed{\sf (-3, -3)}\)

-f(x) then graph reflects over x axis = \(\sf \boxed{\sf (2, 3)}\)

f(-x)  then graph reflects over y axis = \(\sf \boxed{\sf (-2,-3)}\)

f(2x) then graph has horizontal compression = (2/2, -3) = \(\boxed{\sf (1, -3)}\)

2f(x) then graph has vertical compression = (2, (-3)2) = \(\boxed{\sf (2, -6)}\)

-f(x - 4) then graph reflects over x axis, moves 4 units to right = \(\sf \boxed{\sf (6, 3)}\)

Parent function: y = x²

Graph function: f(x) = (x + 8)² - 4

After Identification:

D. The graph has a translation of 8 units left and 4 units down.

Answer:

Translations

For \(a > 0\)

\(f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

\(y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a\)

\(y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}\)

\(y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}\)

\(y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}\)

Given:  \(f(x)=(2,-3)\)

\(f(x)+2 \implies (x, y+2)= (2,-3+2)=(2,-1)\)

\(f(x)-3 \implies (x,y-3)=(2,-3-3)=(2,-6)\)

\(f(x+5)\implies (x-5,y)=(2-5,-3)=(-3,-3)\)

\(-f(x) \implies (x,-y)=(2,-(-3))=(2,3)\)

\(f(-x) \implies (-x,y)=(-(2),-3)=(-2,-3)\)

\(f(2x) \implies \left(\dfrac{x}{2},y\right)=\left(\dfrac{2}{2},-3\right)=(1,-3)\)

\(2f(x) \implies (x,2y)=(2,2 \cdot -3)=(2,-6)\)

\(-f(x-4) \implies (x+4,-y)=(2+4,-(-3))=(6,3)\)

\(\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & &\\f(x)+2 & f(x)-3 & f(x+5) & -f(x) & f(-x) & f(2x) & 2f(x) & -f(x-4)\\& & & & & & &\\\cline{1-8} & & & & & & &\\(2,-1) & (2,-6) & (-3,-3) & (2,3) & (-2,-3) & (1,-3) & (2,-6) & (6,3)\\& & & & & & &\\\cline{1-8} \end{array}\)

Parent function:  \(y=x^2\)

Given function:  \(f(x)=(x+8)^2-4\)

\(f(x+8) \implies f(x) \: \textsf{translated}\:8\:\textsf{units left}\)

\(f(x)-4 \implies f(x) \: \textsf{translated}\:4\:\textsf{units down}\)

Therefore, a translation 8 units to the left and 4 units down.

The measure of side length x in the right triangle is approximately 6.03 cm.

The figure in the image is a right triangle having one of its interior angle at 90 degrees.

From the figure:

Angle θ = 37 degrees

Adjacent to angle θ = 8 cm

Opposite to angle θ = x

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( θ ) = opposite / adjacent

Plug in the given values and solve for x:

tan( 37 ) = x / 8

x = tan( 37 ) × 8

x = 6.03 cm

Therefore, the value of x is 6.03 cm.

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Answer:

Ordered pair: (- 8, 1)

x = - 8,y = 1

Step-by-step explanation:

\(1.5x-9y=-21\\-1.5x-3y=9\)

Add together.

- 12y = - 12

y = 1

1.5x - 9(1) = - 21

1.5x - 9 = - 21

1.5x = - 12

x = - 8

Answer:

6.8

Step-by-step explanation:

Add the numbers and divide by the amount of numbers and get 6.8

Answer: 6.8.

Step-by-step explanation: When finding the mean of a data set, you need to add all the numbers of the set, and then divide the answer by however many numbers you have on the data set.  The work is done below:

14 + 7 + 2  8 + 3 = 34.

34 / 5 = 6.8, because there are 5 numbers in the data set.

Have a great day! :)

a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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627 x 26 equals 16,302 when solved using the standard algorithm.

The steps below can be used to solve the multiplication issue 627 x 26 using the conventional algorithm:

627 and 26 should be written one above the other, with the larger number appearing above and the smaller number beneath.

Start by adding each digit of the top number to the ones digit of the bottom number (six). Write the answers below the line after multiplying 6 by 7 and then by 2.

1254 -- a 6 x 7 partial product

1254 -- a half 6 x 2 product

Repeat the process by moving the bottom number one position to the left after that. Multiply 2 by 7 and then by 2, and then write the results one space to the left of the line below the line.

1254 x 627

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Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

The total materials handling cost allocated to the modular homes is $246,372.84.

The total materials handling cost allocated to the Prefab Barns is closest to $108,000.

To allocate materials handling cost based on material moves, we must determine proportion of material moves for each product and then apply that proportion to the total materials handling cost.

Proportion of material moves for Modular Homes:

= (Total expected material moves for Modular Homes) / (Total expected material moves for both products)

= 590 / (590 + 190)

= 0.756

Total materials handling cost allocated to Modular Homes:

= Proportion of material moves for Modular Homes * Total materials handling cost

= 0.756 * $325,890

= 246 372.84

= $246,372.84.

To allocate the materials handling cost based on direct labor-hours, we need to determine proportion of direct labor-hours for each product.

For Modular Homes:

Total direct labor-hours for Modular Homes:

= 6,000 units * 800 hours/unit

= 4,800,000 hours

For Prefab Barns:

Total direct labor-hours for Prefab Barns:

= 9,000 units * 300 hours/unit

= 2,700,000 hours

Total direct labor-hours for both products:

= 4,800,000 hours + 2,700,000 hours

= 7,500,000 hours

Proportion of direct labor-hours for Prefab Barns:

= 2,700,000 hours / 7,500,000 hours

= 0.36

Allocated materials handling cost for Prefab Barns:

= Proportion of direct labor-hours for Prefab Barns * Total materials handling cost

= 0.36 * $300,000

= $108,000.

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The regression equation is y = 11.9799 + (-246.4420)x.

The chest size (x) is the independent variable.

Now,

X         Y          XY          X²          Y²

47      282     13254     2209     79542

61      495     30195     3721     245025

51      371     18921     2601     137641

47      349     16403     2209     121801

54      421      22734    2916     177241

56      389      21784    3136     151321

Table for the sum,

n                         6

sum(XY)          123291.00

sum(X)             316.00

sum(Y)             2307.00

sum(X²)            16792

sum(Y²)            912553

Numerator        10734

Denominator     11711.10

r                         0.9166

r²                        0.8401

Xbar(mean)       52.6667

Ybar(mean)       384.5

b                        11.9799

a                       -246.4420

Now,

b = [ ∑XY - (∑X)(∑Y) ] / [ n∑ X² - ( ∑X )² ]

Therefore,

b = 11.9799

a = [ ∑Y  - b ∑x ] / n

a  = - 246.4420

So, the regression equation is:

y = 11.9799 + (-246.4420)x

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Answer:

C

Step-by-step explanation:

Answer:

C. 40 and 50

Step-by-step explanation:

The median marks the mid-point of the data and is shown by the line that divides the box into two parts (sometimes known as the second quartile). Half the scores are greater than or equal to this value and half are less.

Answer: 0.35

Step-by-step explanation:

Times 7 = 2. 45kg

Answer:

C. \( f(-1) = 0 \)

Step-by-step explanation:

The value of \( f(-1) \), is the value of \( f(x) \) when x = -1.

What we are being asked to find what value of \( f(x) \) corresponds with x = -1. Or what output would an input of value of -1 give us.

From the table given, when x = -1, \( f(x) = 0 \).

Therefore, the value of \( f(-1) = 0 \).

Answer:

17 cm

Step-by-step explanation:

A box has a length of 5 cm, a width of 10 cm, and a height of 2 cm. the volume of the box is: 17 cm

Farid is able to produce 8 small pies.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Given: For the filling, Farid blends 1 pound of each blackberries, blueberries, and raspberries. Following that, he spoons 6 ounces of the filling into each tiny pie pan.

We need to find How many tiny pies can be made if he wants to use all of the filling.

Raspberries, blueberries, and blackberries, each weighing 1 pound, are combined by Faris for the filling.

3 pounds of filler total from 1+1+1= 3*16 ounces.

1 pound equals 16 ounces. = 48 ounces

Each little pie tin is filled with 6 ounces of filling by Faris.

48 ounces divided by 6 ounces equals 8 mini pies.

Hence, the Farid made 8 mini pies with 6 ounces.

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Answer:

1) 5m

2) 0.25tan

Step-by-step explanation:

Answer:

a < - 3

Step-by-step explanation:

Given

- 2a > 6

Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity, thus

a < - 3

Given that the integral is given as \(\int_{0}^{12} f(t) dt\), Hence, we are required to find the area under the graph where t is between 0 and 12. The correct answer is 2 (Option A) See the explanation below.

An integral is a function of which a given function is the derivative, that is, when differentiated, it returns that function, and it can express the area under the curve of a graph of the function.

Hence the areas under the graph for the above function are given as:

12 + 6 + 2 + (-2) + (-16)

= 20-18

= 2

Notice that the following figures were arrived at by dividing the areas under the graph into common geometric shapes and deriving their area.

For example, the first three positive values were derived by dividing the positive part of the graph into two triangles and a rectangle.

The length of the rectangle is 6 while its height is 2

Area of a rectangle is L x W

= 6 * 2

= 12

It is to be noted that the areas under the curve are negative hence the negative results. See the attached image.

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Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

Answer:

x = \(\frac{19+\sqrt{365}}{2}, \frac{19-\sqrt{365}}{2}\)

Step-by-step explanation:

1. Move everything to one side of the equation.

x^2 - 19x - 1 = 0

2. Use the quadratic formula where a = 1, b = -19, and c = -1.

x = (-b +- sqrt(b^2-4ac)) / 2a

If you plug those numbers into that formula, you will get the result listed above

Answer:

B

x₁ = \(\frac{19-\sqrt{365}}{2}\), x₂ = \(\frac{19+\sqrt{365} }{2}\)

Step-by-step explanation:

Answer: B

Step-by-step explanation:

from edge

Answer:

B

Step-by-step explanation:

Edge 2022

Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).

In order to find the missing expression in Step 1, let's analyze the given steps and the final expression.

Step 1: ?

Step 2: -9 + 2 + 3

Step 3: -7 + 3

To find the missing expression in Step 1, we need to work backwards from Step 3 to Step 1.

In Step 3, the expression "-7 + 3" gives us a result of -4.

In Step 2, the expression "-9 + 2 + 3" gives us a result of -4.

So, the missing expression in Step 1 should also evaluate to -4 when performed correctly.

Let's check the available options:

[-10 + -1 + 2] + (2 + 3) = -11 + 2 + 5 = -4

[-8 - 1] + (2 + 3) = -9 + 5 = -4

[-10 + 1] + (2 + 3) = -9 + 5 = -4

[8 + 1] + (2 + 3) = 9 + 5 = 14

Out of the given options, only option 2, [-8 - 1] + (2 + 3), correctly evaluates to -4. Therefore, the missing expression in Step 1 is [-8 - 1] + (2 + 3).

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From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC

The two column proof to show that ∠BAC ≅ ∠DAC is as follows:

Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD

Reason 1: Given

Statement 2: AB ≅ AD

Reason 2:  Definition of isosceles Triangles

Statement 3: ∠1 and ∠2 are right angles

Reason 3: Definition of perpendicular

Statement 4: AC ≅ AC

Reason 4: Reflexive Property

Statement 5: ΔABC and ΔADC are right triangles

Reason 5: Definition of right triangle

Statement 6: ΔABC ≅ ΔADC

Reason 6: HL Congruency

Statement 7: ∠BAC ≅ ∠DAC

Reason 7: CPCTC

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The probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

Since there are 8 cameras in the box, the total number of ways to choose 2 cameras from the box is given by the combination formula:

C(8,2) = 8!/(2!×(8-2)!) = 28

So there are 28 possible ways to choose a sample of 2 cameras.

Now, let's calculate the probability of each possible value of x:

When x = 0, both cameras in the sample are non-defective. The number of ways to choose 2 non-defective cameras from the 4 non-defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 0 is:

P(x=0) = (number of ways to choose 2 non-defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

When x = 1, one camera in the sample is defective and the other is non-defective. The number of ways to choose 1 defective camera from the 4 defective cameras in the box and 1 non-defective camera from the 4 non-defective cameras in the box is given by the product of the corresponding combinations:

C(4,1) × C(4,1) = 4×4 = 16

So the probability of x = 1 is:

P(x=1) = (number of ways to choose 1 defective camera and 1 non-defective camera)/(total number of ways to choose 2 cameras)

= 16/28

= 0.571

When x = 2, both cameras in the sample are defective. The number of ways to choose 2 defective cameras from the 4 defective cameras in the box is given by the combination formula:

C(4,2) = 4!/(2!×(4-2)!) = 6

So the probability of x = 2 is:

P(x=2) = (number of ways to choose 2 defective cameras)/(total number of ways to choose 2 cameras)

= 6/28

= 0.214

Therefore, the probability distribution for x is:

x P(x)

0 0.214

1 0.571

2 0.214

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Okay, let's list the 4 rational numbers from smallest to largest:

5/3

7/15

6/10

25/5

So:

5/3 is A

7/15 is B

6/10 is C

25/5 is D

Using it's concept, it is found that the domain of the function regarding the speed of the tidal wave is explained by:

[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.

It is the set that contains all possible input values for the function. In a graph, it is given by the x-values, that is, the horizontal axis values.

In this graph, the horizontal axis assumes values between 0 and 4, which is the time after the wave, and considering that the wave cannot be less than zero. Hence, the correct option is:

[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.

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Angle WZY is 50 degrees, angle WZX is also 50 degrees, and angle XZW is 160 degrees.

What is the inscribed angle theorem?

The inscribed angle theorem, also known as the central angle theorem, states that an angle formed by two chords in a circle is half the measure of the arc they intersect, or subtend, inside the circle.

To find all other angles in the circle with quadrilateral WXYZ inscribed in it and WY going through the center Q:

Since WY goes through the center, angle WYZ and angle WXY are both right angles (90 degrees)

By the inscribed angle theorem, angle WZY is equal to half the measure of the arc WX.

Since angle XYZ is given as 50 degrees, the measure of the arc WX is 2 times 50 degrees, which is 100 degrees.

Therefore, angle WZY is 50 degrees.

By the same logic, angle WZX is also 50 degrees.

Since angles WYZ and WXY are right angles, angles XZY and WZX are also right angles.

Finally, we can find angle WZY + angle XYZ + angle XZW + angle WZX = 360 degrees (sum of angles in a quadrilateral), and we can solve for angle XZW which is 160 degrees.

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Answer:

224

Step-by-step explanation:

360.-136.

Answer:

52kg

Step-by-step explanation:

it's just sum of the kgs bought

Answer:

1/3

Step-by-step explanation:

1/3