y = f(x) = -1x
find f(x) when x = 3

The total number of cars sold by two dealerships is 294.

Let x be the number of cars and y be the number of trucks.

As, there are total 164 cars then

x+ y= 164   ........(1)

The second dealership sells twice as many cars and half as many trucks as the first dealership and sold a total of 229 cars and trucks.

so, 2x+ y/2 = 229.....(2)

Solving the equation as

y= 164- x

and, 2x + (164-x)/2 = 229

4x + 164 -x = 458

3x= 458 - 164

3x = 294

x= 294/3

x = 98

Thus, the total number of cars sold by two dealerships is 294.

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The probability that a randomly selected permutation of the letters A, A, B, C, S, U would spell "abacus" is:  

(A) 1/720

Probability is the likelihood of a desired event happening. Mathematically:

Probability = Number of occurrence / Number of possible outcomes

The number of permutations of 6 letters is:

6! =720

Out of these 720 permutations, only one spells "abacus" (based on the arrangement of letters).

Thus, the probability that a randomly selected permutation of the letters A, A, B, C, S, U would spell "abacus" is:  

1/720

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The value of x to the nearest hundredth of a foot as required to be determined in the task content is; Choice A; 7.51.

It follows from the task content that the value of x as indicated is to be determined.

As the given triangle is a right triangle whose hypothenuse and side x is opposite the angle whose measure is 28°.

It follows from trigonometric ratios that;

sin 28° = x / 16

x = 16 sin 28°

x = 7.51.

Ultimately, the value of x to the nearest hundredth is; Choice A; 7.51.

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The statement that best describes the effect on the graph of y=(x-9)² if the equation is changed to y = (x + 9)² is:O C. The graph moves left 18 units.

The graph shifts horizontally when the equation is modified from y = (x - 9)2 to y = (x + 9)2. The graph's points' x-coordinates are impacted by the inclusion of 9 inside the brackets.

The graph is moved 9 units to the left by adding 9 to the x-coordinate. As a result, the phrase "The graph moves left 18 units" is the most correct way to describe the effect on the graph.

Therefore the correct option is C.

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We transformed 630 square yards to square inches, resulting in a value of 816,480 square inches.

To convert 630 square yards to square inches, we can utilize the following unit multipliers:

1 yard = 3 feet (since there are 3 feet in a yard)

1 foot = 12 inches (since there are 12 inches in a foot)

1 square yard = 1 yard × 1 yard = 3 feet × 3 feet = 9 square feet

1 square foot = 12 inches × 12 inches = 144 square inches

Now, we can set up the conversion using the unit multipliers:

630 square yards × (9 square feet / 1 square yard) × (144 square inches / 1 square foot) = 630 × 9 × 144 square inches

Simplifying the calculation:

630 × 9 × 144 square inches = 816,480 square inches

Therefore, 630 square yards is equal to 816,480 square inches.

By using the four unit multipliers and converting yards to feet and then to inches, we successfully transformed 630 square yards to square inches, resulting in a final value of 816,480 square inches.

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The function which is modeled by the graph is y=2x+4.

We have to find the function in the given graph.

The line is passing through the points (-1, 2) and (0, 4).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope = 4-2/0+1

=2

Now let us find the y intercept.

4=2(0)+b

b=4

So the function is y=2x+4.

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Answer:

y= -3/2x+1

Step-by-step explanation:

slope intercept is y = mx + b form

so the answer is y= -3/2x+1

The percentage of age-groups has more male customers than female customers is approximately 50%.

The given graph depicts a company's customer analysis based on gender and age group.

Male percentage is more between the age 30-34, 45-49, 50-54 and 55-59.

Here, percentage = 20/41 ×100

= 0.487×100

= 48.7%

≈ 50%

Therefore, option B is the correct answer.

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To find the value of x, we can use the fact that the sum of the lengths of the line segments in a triangle is equal to the total length of the triangle.

In this case, we have:

AC = 8x - 9

AB = 3x + 1

BC = 4x - 5

The sum of the lengths of the line segments AB, BC, and AC should be equal to the total length of the triangle ABC. Therefore, we can set up the equation:

AB + BC + AC = total length of triangle ABC

(3x + 1) + (4x - 5) + (8x - 9) = total length of triangle ABC

Simplifying the equation, we get:

15x - 13 = total length of triangle ABC

Since we don't have any additional information about the triangle, we can't determine the exact length of the total triangle. Therefore, we cannot find the exact value of x using the given figure.

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The perimeter (P) by multiplying the side length by 4:
P = 4 * (4√2) = 16√2
The answer: b. 16√2

To find the perimeter of a square with a diagonal length of 8 feet, first, you need to determine the side length. In a square, the diagonal length (d) is related to the side length (s) through the Pythagorean theorem as follows:

d = s√2

Now, plug in the given diagonal length (8 feet) and solve for s:

8 = s√2
s = 8/√2
s = 4√2 (simplified by multiplying both numerator and denominator by √2)

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Answer:

Step-by-step explanation:

speed= distance/time taken

45=300/t

t=300/45

t=6.7

from 18:00 to 12:00, it's 6hours

so mark won't be on time

The measure of arc MN include the following: B. 45°.

In Mathematics and Geometry, the theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, the value of arc MN can be calculated as follows:

37= 1/2(arc MN + 29)

37(2) = arc MN + 29

74 = arc MN + 29

arc MN = 74 - 29

arc MN = 45 degrees.

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The required answer is: it is not possible to determine Alvin's average paddling rate based on the given information.

Given that table of terms Distance, Rate and  Time

Against the current d r - 2 km/hr 8 hours

With the current d r + 2 km/hr 3 hours

To set up an equation to solve for Alvin's average paddling rate, we can use the formula: rate = distance/time.

For the first row : (r - 2 km/hr) = d/8.

For the second row: (r + 2 km/hr) = d/3.

To solve for r, we can equate the rates against the current and solve for r.

(r - 2 km/hr) = (r + 2 km/hr)

Simplifying the equation, we get: r - 2 = r + 2.

By solving this equation, we find that the "r" terms cancel out, resulting in -2 = 2, which is not a true statement. This indicates that there is no solution for Alvin's average paddling rate in this scenario.

Therefore, it is not possible to determine Alvin's average paddling rate based on the given information.

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There are 5040 different passwords that can be created from the word "Alabama" when using all the letters.

To calculate the number of different passwords that can be created from the word "Alabama," we need to consider the total number of permutations.

The word "Alabama" contains 7 letters. To find the number of different passwords, we need to calculate the number of permutations of these 7 letters.

The formula to calculate permutations is given by:

nPr = n! / (n - r)!

Where n is the total number of items (letters in this case), and r is the number of items selected (length of the password).

For the word "Alabama," let's assume we want to create passwords of length 7, using all the letters.

n = 7 (number of letters in "Alabama")

r = 7 (length of the password)

Using the formula, we can calculate the number of permutations:

7P7 = 7! / (7 - 7)!

= 7! / 0!

= 7! / 1

= 7 × 6 × 5 × 4× 3 × 2 × 1

= 5040

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Answer:

I think answer is D but it could be wrong not sure

The sum of the first 33 terms of the following series, to the nearest integer is 4818.

The sum of the first 33 terms of the following series, to the nearest integer is calculated as follows;

n = (n/2)(2a + (n-1)d)

where;

From the given parameters, we have;

n = 33

a = 2

d = 9

The sum of the first 33 terms is calculated as;

S(33) = (33/2)(2x2 + (33-1)(9))

S(33) = (33/2)(4 + 32(9))

= (33/2)( 4 + 288)

= (33/2)(292)

= 33(146)

= 4818

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The matrix corresponding to the vertices of the triangle after the rotation is given as follows:

[0 -1 -2]

[0 -3 1]

The five more known rotation rules are given as follows:

The vertices of the original triangle are given as follows:

(0,0), (-3,1) and (1,2).

The rotation rule is given as follows:

(x,y) -> (-y, x).

Hence the vertices of the rotated figure are given as follows:

(0,0), (-1, -3) and (-2, 1).

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The Watkins family should install a chlorine pool to be more cost-efficient.

In order to compare the two graphs we take a value on the x-axis and then measure the output of the two graphs. This can be done with the help of the graph or by substituting the value of x in the function to measure the output y.

As in the given graph, the x-axis denotes the year while the y-axis denotes the cost of maintaining the pool in that year.

If we compare the two of the given graph we will find the cost of maintaining a chlorine pool is less as compared to a salt water pool at x=10, therefore, after 10 years.

Hence, the Watkins family should install a chlorine pool to be more cost-efficient.

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The area of the shaded region is 61.76 square feet.

The given figure has a rectangle and circle.

Let us find the area of both rectangle and circles.

The length of rectangle is 14 ft and width is 8 ft.

Area = length × width

=14×8

=112 square feet.

The diameter of the circle is 8 feet because diameter is equal to width of rectangle.

Radius =diameter/2

= 4 ft.

Area of circle =πr²

=3.14×4²

=3.14×16

=50.24

To find the area of shaded region subtract area of circle from area of rectangle.

Shaded area = 112-50.24

=61.76 square feet.

Hence, the area of the shaded region is 61.76 square feet.

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This example demonstrates a two-step inequality where we first express the savings equation and then solve for the variable 'w' to determine the number of weeks needed to reach the savings goal.

Liam is saving money to buy a new video game console. He has already saved $50 and is saving $10 per week from his allowance. He wants to determine how many weeks it will take for his savings to reach at least $150.

Let:

number of weeks Liam saves = w

total amount of money he saves = S

Step 1: Express the first step of the problem as an inequality.

Liam saves $10 per week, so the amount of money he saves after w-weeks is 10w. We can write the first step of the inequality as:

10w + 50 ≥ 150

Step 2: Solve the inequality.

To isolate 'w', we can subtract 50 from both sides of the inequality:

10w ≥ 150 - 50

10w ≥ 100

Finally, divide both sides of the inequality by 10 to solve for 'w':

w ≥ 10

Therefore, it will take Liam at least 10 weeks to save enough money to reach $150 for the video game console.

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The coordinates of P' after rotating triangle PQR counterclockwise by 270 degrees about the origin are P'(-3, 1).

To rotate a point counterclockwise about the origin, you can use the following rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

In this case, we want to rotate the triangle PQR 270 degrees counterclockwise. We can calculate the coordinates of each point after the rotation.

For point P(-1, -3):

x' = (-1) * cos(270°) - (-3) * sin(270°)

y' = (-1) * sin(270°) + (-3) * cos(270°)

We can simplify these equations using the values of cosine and sine for 270 degrees:

x' = (-1) * 0 - (-3) * (-1)

y' = (-1) * (-1) + (-3) * 0

Simplifying further:

x' = 0 - 3

y' = 1 + 0

x' = -3

y' = 1

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Let "x" be the number of years it takes for the two plants to be the same height.The first plant has an initial height of 7 inches and grows at a constant rate of 3 inches each year. So, the two plants will be the same height after 5 years.

Therefore, after "x" years, its height will be:7 + 3xThe second plant also grows at a constant rate and has an initial height of 2 inches. After 3 years, its height is 14 inches.

Therefore, its rate is: Rate = (Final height - Initial height) / TimeRate = (14 - 2) / 3Rate = 12 / 3Rate = 4So, after "x" years, the second plant's height will be:2 + 4x.

To find when the plants are the same height, we can set the expressions for their heights equal to each other:7 + 3x = 2 + 4xSolving for "x":3x - 4x = 2 - 73x = -5x = -5/(-1). Therefore, x = 5, the two plants will be the same height after 5 years.

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An inequality that represents the state's hourly wage requirement include the following: C. m ≥ $9.25 per hour.

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Assuming the variable m represent the state's hourly wage requirement. Additionally, each interval on the number line represent 0.25 per hour.

Since the shaded circle (dot) is located at point 9.25 and the arrows points or increases to the right, an inequality that represents the state's hourly wage requirement is m ≥ $9.25 per hour.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Dolma will receive Rs.153,486.69 at the beginning of BS 2080 as detailed below

What is effective after-tax rate of return?

The effective after-tax rate of return in this case is determined as the 9% deposit return rate multiplied by 1 minus the tax rate as stated below:

effective after-tax rate of return= gross rate of return*(1-tax rate)

The gross rate of return is the return on the deposit before considering the tax rate.

gross rate of return=9%

tax rate=5%

effective after-tax rate of return=9%*(1-5%)

effective after-tax rate of return=8.55%

The future value of the deposit after three years(beginning of 2077-2080=3years), is determined using the future value formula of a single cash flow below:

FV=PV*(1+r)^N

FV=future value after 3 years=unknown

PV=Rs.120,000

r=8.55%

N=3

FV=120000*(1+8.55%)^3

FV=120000*(1,0855)^3

FV=120,000*1.279055776375

FV=Rs.153,486.69

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Answer:

Because the P-value < α = 0.05, the correct decision is to reject H0.

Step-by-step explanation:

When the p-value is less than our given significance level, it's outside the rejection region, so there is strong evidence that suggest the null hypothesis is not true and that the alternate hypothesis is favored instead.

As per the given equation, when a = 3 and b = -2, the value of the expression [tex]b^2[/tex] - 4ab is 28.

When a = 3 and b = -2, we replace the given values into the formula and make the necessary calculations to evaluate the expression b² - 4ab.

Now,

[tex](-2)^2 - 4 * 3 * (-2)[/tex]

4 - 4 * 3 * (-2)

Multiplying -4 and 3 gives us -12, so the expression becomes:

4 - (-12) * (-2)

Multiplying -12 and -2 gives us 24, so the expression further simplifies to:

4 + 24

Adding 4 and 24 together yields:

28

Therefore, when a = 3 and b = -2, the value of the expression b² - 4ab is 28

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Your question seems incomplete, the probable complete question is:

Using quadratic formula, Evaluate b²-4ab when a= 3, b = -2

Answer:

[tex]\Huge \boxed{\text{13.66$\%$}}[/tex]

Step-by-step explanation:

To find the rate, we need to use the following formula:

[tex]\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}[/tex]

Where "Portion" is the part of the whole and "Base" is the whole.

Now, let's plug in the given values:

[tex]\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}[/tex]

Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).

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To multiply the given binomials, we use the distributive property. So, the multiplication of the given binomials (2√3x - 2) and (3√3x + 5) is 18x + 4√3x - 10.

Using the distributive property which is given as: (a+b) (c+d) = a*c + a*d + b*c + b*d.

To multiply the binomials (2√3x - 2) and (3√3x + 5), we need to apply the distributive property which will result in four different terms.

Using the distributive property: (2√3x - 2) (3√3x + 5)= (2√3x * 3√3x) + (2√3x * 5) - (2 * 3√3x) - (2 * 5)= 6√(3x*3x) + 10√3x - 6√3x - 10= 6√9x² + (10-6)√3x - 10= 6 * 3x + 4√3x - 10= 18x + 4√3x - 10.

Therefore, the multiplication of the given binomials (2√3x - 2) and (3√3x + 5) is 18x + 4√3x - 10.

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Answer:

y=x/3+2

Step-by-step explanation:

y=x/3+2 would be (-6,0) and (0,2)