The table shows how a leading automobile dealer plans to spend its advertising dollars for this year. If this company plans to increase its budget by 5% next year, approximately how much will it spend on social media ads?

Advertising Budget: $81,000
48.5% Television
23% Magazines
20% Newspapers
7% Radio
1% Billboards
0.5% Social Media
A.

The key underlying assumption of the single index model is that the return of a security can be explained by the return of a broad market index.

This assumption forms the basis of the single index model, also known as the market model or the capital asset pricing model (CAPM).

In this model, the return of a security is expressed as a function of the return of the market index. The single index model assumes that the relationship between the returns of a security and the market index is linear.

It suggests that the risk and return of a security can be explained by its exposure to systematic risk, which is represented by the market index.

The single index model assumes that the return of a security can be decomposed into two components: systematic risk and idiosyncratic risk.

Systematic risk refers to the risk that cannot be diversified away, as it affects the entire market. Idiosyncratic risk, on the other hand, is the risk that is specific to a particular security and can be diversified away by holding a well-diversified portfolio.

The single index model assumes that the systematic risk is the only risk that investors should be compensated for, as idiosyncratic risk can be eliminated through diversification.

It suggests that the expected return of a security is determined by its beta, which measures its sensitivity to the market index. A security with a higher beta is expected to have a higher return, as it is more sensitive to market movements.

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the length of the side of this square is \(4\sqrt{2} \:or \:5.65\)cm

Answer:

Solutions Given:

let diagonal of square be AC: 8 cm

let each side be a.

As diagonal bisect square.

let it forms right angled triangle ABC .

Where diagonal AC is hypotenuse and a is their opposite side and base.

By using Pythagoras law

hypotenuse ²=opposite side²+base side²

8²=a²+a²

64=2a²

a²=\(\frac{64}{2}\)

a²=32

doing square root on both side

\(\sqrt{a²}=\sqrt{32}\)

a=±\(\sqrt{2*2*2*2*2}\)

a=±2*2\(\sqrt{2}\)

Since side of square is always positive so

a=4\(\sqrt{2}\) or 5.65 cm

Answer:

Given :

↠ The diagonal of a square is 8 cm.

To Find :

↠ The length of the side of square.

Using Formula :

Here is the formula to find the side of square if diagonal is given :

\(\implies{\sf{a = \sqrt{2} \dfrac{d}{2}}} \)

Where :

Solution :

Substituting the given value in the required formula :

\({\dashrightarrow{\pmb{\sf{ \: a = \sqrt{2} \dfrac{d}{2}}}}}\)

\({\dashrightarrow{\sf{ \: a = \sqrt{2} \times \dfrac{8}{2}}}}\)

\({\dashrightarrow{\sf{ \: a = \sqrt{2} \times \cancel{\dfrac{8}{2}}}}}\)

\({\dashrightarrow{\sf{ \: a = \sqrt{2} \times 4}}}\)

\({\dashrightarrow{\sf{ \: a = 4\sqrt{2}}}}\)

\({\dashrightarrow{\sf{\underline{\underline{\red{ \: a = 5.65 \: cm}}}}}}\)

Hence, the length of the side of square is 5.6 cm.

\(\underline{\rule{220pt}{3pt}}\)

Answer:

Step-by-step explanation:

C

Answer:

B

Step-by-step explanation:

The point (0, 0) is a limit point of A because any neighborhood around (0, 0) contains points from A, specifically points satisfying 0 < x² + y² < 4. This means there are infinitely many points in A arbitrarily close to (0, 0).

To determine if the limit lim (x,y) → (0,0) f(x, y) exists, we need to evaluate the limit of f(x, y) as (x, y) approaches (0, 0).

Using polar coordinates, let x = rcosθ and y = rsinθ, where r > 0 and θ is the angle. Substituting these values into f(x, y), we have f(r, θ) = r(cosθ + sinθ)/√(r²(cos²θ + sin²θ)).

As r approaches 0, the denominator tends to 0 while the numerator remains bounded. Thus, the limit depends on the angle θ. As a result, the limit lim (x,y) → (0,0) f(x, y) does not exist since it varies based on the direction of approach (θ).

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The probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

What is the probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

An order does not matter so it is a Combination.

There are 16 men and we are going to choose 12 --> ₁₆C₁₂

There are 30 people and we are going to choose 12  --> ₃₀C₁₂

₁₆C₁₂ / ₃₀C₁₂

\(= \frac{16!}{(16 - 12)!} \div \frac{30!}{(30 - 12)!}\)  

= 0.00002104211

= 2.1 × 10⁻⁵

Hence, the probability that a randomly selected jury of 12 people is all male is 2.1 × 10⁻⁵.

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Answer:

Angle E is 53 degrees.

Step-by-step explanation:

Let's start with the ABC triangle first.

Since AC=BC, angle A and angle B are equal.

We know that the interior angles of a triangle add up to 180.

106 + A + B = 180

A + B = 74

A = B = 37

Moving on to the BDE triangle.

We have angle B = 37 (it's an opposite angle).

We know that angle D is 90, since this is a right triangle.

90 + 37 + E = 180

E = 53

Step-by-step explanation:

so, if I understand your text correctly, we need to bring

2 - (x+2)/(x-3) - (x-6)/(x+3)

into a form

(ax + b)/(x² - 9)

what we notice immediately is

(x+3)(x-3) = x² - 9

that makes sense, as we want to transform all terms into fractions with the same denominator.

and the necessary "criss-cross" multiplication leads to (x² -9) as denominator.

so, let's transform every term to a fraction with that denominator, and then we add or subtract them all up as per the original expression.

2 :

multiply by (x²-9)/(x²-9)

2(x²-9)/(x²-9) = (2x²-18)/(x²-9)

(x+2)/(x-3) :

multiply by (x+3)/(x+3)

(x+2)(x+3)/(x²-9) = (x²+3x+2x+6)/(x²-9) =

= (x²+5x+6)/(x²-9)

(x-6)/(x+3) :

multiply by (x-3)/(x-3)

(x-6)(x-3)/(x²-9) = (x²-3x-6x+18)/(x²-9) =

= (x²-9x+18)/(x²-9)

for the whole expression we get then

(2x²-18)/(x²-9) - (x²+5x+6)/(x²-9) - (x²-9x+18)/(x²-9) =

= (2x²-x²-x² -5x+9x -18-6-18)/(x²-9) =

= ( 0 + 4x - 42 )/(x²-9)

a = 4

b = -42

After the x-shearing transformation, the resulting coordinates of the rectangle/square are: (0,0), (0,2), (2,0), and (2,6). This transformation effectively shears the shape by shifting the y-coordinate of the top-right corner, resulting in a distorted rectangle/square.

To apply x-shearing with a shearing parameter of 2 units to a rectangle/square defined by the coordinates (0,0), (0,2), (2,0), and (2,2), we can transform the coordinates as follows: (0,0) remains unchanged, (0,2) becomes (0,2), (2,0) becomes (2,0), and (2,2) becomes (2,6). This transformation effectively shifts the y-coordinate of the top-right corner of the rectangle by 4 units while leaving the other coordinates unchanged, resulting in a sheared shape.

X-shearing is a transformation that shifts the y-coordinate of each point in an object while leaving the x-coordinate unchanged. In this case, we are given a rectangle/square with coordinates (0,0), (0,2), (2,0), and (2,2). To apply x-shearing with a shearing parameter of 2 units, we only need to modify the y-coordinate of the top-right corner.

The original coordinates of the rectangle/square are as follows: the bottom-left corner is (0,0), the top-left corner is (0,2), the bottom-right corner is (2,0), and the top-right corner is (2,2).

To perform the x-shearing, we only need to modify the y-coordinate of the top-right corner. The shearing parameter is 2 units, so we shift the y-coordinate of the top-right corner by 2 * 2 = 4 units. Therefore, the new coordinates of the rectangle/square become: (0,0) remains unchanged, (0,2) remains unchanged, (2,0) remains unchanged, and (2,2) becomes (2,2 + 4 = 6).

After the x-shearing transformation, the resulting coordinates of the rectangle/square are: (0,0), (0,2), (2,0), and (2,6). This transformation effectively shears the shape by shifting the y-coordinate of the top-right corner, resulting in a distorted rectangle/square.

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Answer:

x= -1

y= 2

Step-by-step explanation:

Notice that when x = 0 the value of y is 2/1 so this line "cuts" the y axis at y= 2

 y-intercept = 2/1  =  2

When y = 0 the value of x is 1/-1 Our line therefore "cuts" the x axis at x= -1

 x-intercept = 2/-2 = 1/-1  = -1

Answer:

c and d, b

Step-by-step explanation:

a - 49+64 = 113 so not a rt triangle

b - 16+100 = 116 again not rt triangle but 84+16 = 100 which is a rt triangle

c - 8+121 = 129 rt triangle

d - 1+3 = 4 rt triangle

Answer:

C and D

Step-by-step explanation:

The triple integral of the divergence over the region E is equal to the surface integral of F over the boundary surface of E, we have verified the Divergence Theorem for the given vector field F and the region E.

To verify the Divergence Theorem, we need to compute both sides of the equation for the given vector field F and the region E bounded by the paraboloid Z = 4 - X^2 - y^2 and the xy-plane.

First, we compute the divergence of F:

div F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 4x + 2

Next, we compute the triple integral of the divergence over the region E:

∫∫∫E div F dV = ∫∫∫E (4x + 2) dV

Since the region E is bounded by the xy-plane and the paraboloid, we can integrate over z from 0 to 4 - x^2 - y^2, over y from -√(4 - x^2) to √(4 - x^2), and over x from -2 to 2:

∫∫∫E div F dV = ∫-2^2 ∫-√(4 - x^2)√(4 - x^2) ∫0^4-x^2-y^2 (4x + 2) dz dy dx

= 128/3

Now, we compute the surface integral of F over the boundary surface of E:

∫∫S F dS = ∫∫P F dP + ∫∫D F dD

where P is the surface of the paraboloid and D is the disk at the bottom of E.

On the paraboloid, the normal vector is given by n = (∂f/∂x, ∂f/∂y, -1), where f(x,y) = 4 - x^2 - y^2. Therefore, we have:

∫∫P F dP = ∫-2^2 ∫-√(4 - x^2)√(4 - x^2) (2x^2, 2xy, 4 - x^2 - y^2) ∙ (∂f/∂x, ∂f/∂y, -1) dA

= ∫-2^2 ∫-√(4 - x^2)√(4 - x^2) (2x^2, 2xy, 4 - x^2 - y^2) ∙ (2x, 2y, 1) dA

= 16π/3

On the disk at the bottom, the normal vector is given by n = (0, 0, -1). Therefore, we have:

∫∫D F dD = ∫-2^2 ∫-√(4 - x^2)√(4 - x^2) (2x^2, 2xy, 0) ∙ (0, 0, -1) dA

= 0

Thus, we have:

∫∫S F dS = ∫∫P F dP + ∫∫D F dD = 16π/3 + 0 = 16π/3

Since the triple integral of the divergence over the region E is equal to the surface integral of F over the boundary surface of E, we have verified the Divergence Theorem for the given vector field F and the region E.

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The total surface integral is:

∫∫S F dS = ∫∫S F dS + ∫∫S F dS

= 8π/3 + 0

= 8π/3

To verify the Divergence Theorem, we need to show that the triple integral of the divergence of F over the region E is equal to the surface integral of F over the boundary of E.

First, let's compute the divergence of F:

div F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z

= 4x + 2y + 3

Next, we'll compute the triple integral of div F over E:

∭E div F dV = ∫∫∫ (4x + 2y + 3) dz dy dx

The region E is bounded by the paraboloid Z = 4 - X^2 - y^2 and the xy-plane. To determine the limits of integration, we need to find the intersection of the paraboloid with the xy-plane:

4 - x^2 - y^2 = 0

x^2 + y^2 = 4

This is the equation of a circle with radius 2 centered at the origin in the xy-plane.

So, the limits of integration are:

x: -2 to 2

y: -√(4 - x^2) to √(4 - x^2)

z: 0 to 4 - x^2 - y^2

∭E div F dV = ∫∫∫ (4x + 2y + 3) dz dy dx

= ∫-2^2 ∫-√(4-x^2)^(√(4-x^2)) ∫0^(4-x^2-y^2) (4x + 2y + 3) dz dy dx

= 32/3

Now, let's compute the surface integral of F over the boundary of E. The boundary of E consists of two parts: the top surface of the paraboloid and the circular disk in the xy-plane.

For the top surface of the paraboloid, we can use the upward-pointing normal vector:

n = (2x, 2y, -1)

For the circular disk in the xy-plane, we can use the upward-pointing normal vector:

n = (0, 0, 1)

The surface integral over the top surface of the paraboloid is:

∫∫S F dS = ∫∫D F(x, y, 4 - x^2 - y^2) ∙ n dA

= ∫∫D (4x + 2y, 2xy, 4 - x^2 - y^2) ∙ (2x, 2y, -1) dA

= ∫∫D (-4x^2 - 4y^2 + 4) dA

= 8π/3

The surface integral over the circular disk in the xy-plane is:

∫∫S F dS = ∫∫D F(x, y, 0) ∙ n dA

= ∫∫D (2x^2, 2xy, 0) ∙ (0, 0, 1) dA

= 0

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Therefore , the solution of the given problem of standard deviation comes out to be the CEO is informed that the mean scores for Cities A and B are identical.

Variance is a measure of difference used in statistics. The typical variance here between dataset and the mean is calculated using the multiplier of that figure. By comparing each figure to the mean, it incorporates those data points into its calculations, unlike other measurable measures of variability. Variations may result from internal or external factors and may include unintentional errors, inflated expectations, and changing economic or commercial circumstances.

Here,

It is clear that both offices share a comparable average score from the sentence "The CEO is informed that both City A or City B have the same mean score."

If City A is more reliable than City B, then City A will have a lower standard deviation.

A collection of data's variability or dispersion is measured by the standard deviation. The closer the data points are to the mean, the lower the standard deviation, and the less variable the data are.

So, the appropriate answer is:

The CEO is informed that the mean scores for Cities A and B are identical. However, due to the fact that City A's standard deviation is lower than City B's, City A is more reliable than City B.

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Answer:

65.5 apples

0.5 apples

7 bags

65 apples

Step-by-step explanation:

I'm no math expert but I hope this helps.

Answer:

65.5 a

0.5 a

7 bags

65 a

note

a=apples

Answer: C=5

Hope this helps!

The z-score for a 21-minute wait in a CPT-Memorial with a mean of 27 minutes and a standard deviation of 12 minutes is -0.5.

To calculate the z-score, follow these steps:

1. Write down the given values: mean (µ) = 27 minutes, standard deviation (σ) = 12 minutes, and the value you want to find the z-score for (x) = 21 minutes.

2. Use the z-score formula: z = (x - µ) / σ.

3. Plug in the values: z = (21 - 27) / 12.

4. Perform the calculations: z = (-6) / 12.

5. Simplify the result: z = -0.5.

The z-score represents how many standard deviations away from the mean the data point is. In this case, a 21-minute wait is 0.5 standard deviations below the mean wait time of 27 minutes.

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Angle A is 19 degrees.

Angle C is 90 degrees.

Side a is approximately 7.83.

Side c is approximately 34.50.

To solve the right triangle given that B = 71 degrees and b = 24, we can use the trigonometric ratios sine, cosine, and tangent.

Finding Angle A:

Angle A is the complementary angle to B in a right triangle, so we can calculate it using the equation:

A = 90 - B

Substituting the given value, we have:

A = 90 - 71

A = 19 degrees

Therefore, Angle A is 19 degrees.

Finding Angle C:

Since it is a right triangle, Angle C is always 90 degrees.

Therefore, Angle C is 90 degrees.

Finding Side a:

We can use the sine ratio to find the length of side a:

sin(A) = a / b

Rearranging the equation to solve for a, we have:

a = b * sin(A)

Substituting the given values, we have:

a = 24 * sin(19)

a ≈ 7.83

Therefore, the length of side a is approximately 7.83.

Finding Side c:

Using the Pythagorean theorem, we can find the length of side c:

c^2 = a^2 + b^2

Substituting the given values, we have:

c^2 = 7.83^2 + 24^2

c^2 ≈ 613.68 + 576

c^2 ≈ 1189.68

Taking the square root of both sides to solve for c, we have:

c ≈ √1189.68

c ≈ 34.50

Therefore, the length of side c is approximately 34.50.

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To estimate the proportion of all new cell phone batteries that fail to last through a claimed number of charges, a consumer group will use a random sample and construct a percent confidence interval based on the proportion of batteries that fail to last through the charges in the sample.

To construct a confidence interval to estimate the proportion of all such batteries that fail to last through charges, the following steps can be followed:

Determine the sample size:

The consumer group should select a random sample of cell phones with the new battery and use the phones through charges of the battery.

The sample size should be determined based on the desired level of precision and confidence level.

A larger sample size will provide a more precise estimate.

Calculate the sample proportion:

The consumer group should record the proportion of batteries that fail to last through charges in the sample.

Calculate the standard error:

The standard error can be calculated using the formula:

\(SE = \sqrt{(p_hat * (1 - p_hat) / n) }\)

where \(p_hat\) is the sample proportion and n is the sample size.

Calculate the margin of error:

The margin of error can be calculated using the formula:

ME = z * SE

where z is the critical value from the standard normal distribution corresponding to the desired confidence level.

For example, if the desired confidence level is 95%, then z = 1.96.

Calculate the confidence interval: The confidence interval can be calculated using the formula:

\(CI = (p_hat - ME, p_hat + ME)\)

This interval represents the range of values within which the true proportion of batteries that fail to last through charges is expected to fall with the desired level of confidence.

For example, suppose a random sample of 100 cell phones with the new battery is selected, and the proportion of batteries that fail to last through charges is found to be 0.10. If a 95% confidence level is desired, the standard error can be calculated as:

SE = \(\sqrt{(0.10 * 0.90 / 100)}\) = 0.03

The margin of error can be calculated as:

ME = 1.96 * 0.03 = 0.06

The 95% confidence interval can be calculated as:

CI = (0.10 - 0.06, 0.10 + 0.06) = (0.04, 0.16)

Therefore, we can say with 95% confidence that the proportion of all such batteries that fail to last through charges is expected to be between 0.04 and 0.16.

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Answer:

35 miles per hour

Step-by-step explanation:

175 -140 = 35

35/1 = 35

Answer:

35

Step-by-step explanation:

The dimensions of building lot are 396 feet width and 1980 feet length.

Let the width of building lot be x. So, the length of the same building lot will be 5x. According to the formula, the area will be length × width.

18 acre = x×5x

Keep the value of acre in the above mentioned relation

18 × 43,560 = 5x²

Performing multiplication on Left Hand Side of the equation

784,080 = 5x²

Performing division by 5

x² = 156,816

Now taking square root to find the value of x

x = ✓156,816

x = 396 ft

Thus, the width of building lot is 396 feet

The length of building lot = 5×396

Performing multiplication

The length of building lot = 1980 feet

Therefore, the length and width of building lot is 1980 feet and 396 feet respectively.

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Answer: The perimeter of the triangle is 69 cm.

Step-by-step explanation:

Let us consider the side of the triangle be 3x ,4x and 5x.

According to the question,

The longest side of the triangle be 30 cm.

. 5x=30cm

x=6 cm

So the side of the triangle are 18cm ,24 cm and 30 cm.

The perimeter of the triangle is the sum of sides of the triangle.

so perimeter is =15+24+30=69 cm



Answer:

36 days.

Step-by-step explanation:

60 + 15 = 75 soldiers.

By proportion the number of days that the provisions will last

=  45 * (60/75)

=  45 * 4/5

= 36 days.

The value of x when y = 37.5 if y varies directly as x and y = 5 when x = 0.4 is 3

y = k × x

Where,

k = constant of proportionality

If y = 5 when x = 0.4

y = k × x

5 = k × 0.4

5 = 0.4k

divide both sides by 0.4

k = 5/0.4

k = 12.5

If y = 37.5, find x

y = k × x

37.5 = 12.5 × x

37.5 = 12.5x

divide both sides by 12.5

x = 37.5 / 12.5

x = 3

Therefore, the value of x when y = 37.5 is 3

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The value of x from y is x = 3

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

y varies directly as x and y = 5 when x = 0.4,

The equation of direct variation is

k = y/x

So, we have

k = 5/0.4

Evaluate

k = 12.5

So, we have

y/x = 12.5

When y = 37.5. we have

37.5/x = 12.5

Solve for x

x = 3

Hence, the solution is x  3

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The rate of change of weight of the rabbit in pounds per week is 0.5 pounds per week.

To calculate the rate of change of weight of Samuel's rabbit in pounds per week, we need to look at how much the weight of the rabbit changes as the number of weeks since birth increases by one. This is also known as the slope of the linear relationship between the number of weeks and the weight of the rabbit.

Looking at the table below, we can see that when the rabbit is born (week 0), it weighs 0.5 pounds. As the number of weeks since birth increases by one, the weight of the rabbit increases by 0.5 pounds. This pattern continues for each subsequent week, with the weight of the rabbit increasing by 0.5 pounds each time.

| Number of Weeks Since Birth | Weight of Rabbit (in pounds) |
|-----------------------------|------------------------------|
|              0              |             0.5              |
|              1              |             1.0              |
|              2              |             1.5              |
|              3              |             2.0              |
|              4              |             2.5              |
|              5              |             3.0              |

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Answer:

14

Step-by-step explanation:

sum of three angles of a triangle is 180

(x-4) + (11x-11) + (x+13) = 180

13x -2 = 180

13x = 182

x=14

The geometric power series for the function f(x) = 1 / (9 + x), centered at 0, using long division is (9 - x) / ((9 + x) * (9 - x)).

To find a geometric power series for the function f(x) = 1 / (9 + x) using long division, we can start by expanding the function into a fraction:

f(x) = 1 / (9 + x)

To begin the long division process, we divide 1 by 9 + x:

1 ÷ (9 + x)

To simplify the division, we can multiply the numerator and denominator by the conjugate of the denominator:

1 * (9 - x) / ((9 + x) * (9 - x))

Simplifying further:

(9 - x) / (81 - x^2)

Now, we have expressed the function f(x) as a fraction with a simplified denominator. To find the geometric power series, we can rewrite the denominator using the concept of a geometric series:

(9 - x) / (81 - x^2) = (9 - x) / (9^2 - x^2)

We can see that the denominator is now in the form a^2 - b^2, which can be factored as (a + b)(a - b). In this case, a = 9 and b = x:

(9 - x) / (9^2 - x^2) = (9 - x) / ((9 + x)(9 - x))

Now, we can express the function f(x) as a geometric power series:

f(x) = (9 - x) / ((9 + x)(9 - x))

f(x) = 1 / (9 + x) = (9 - x) / ((9 + x)(9 - x))

f(x) = (9 - x) / (9^2 - x^2) = (9 - x) / ((9 + x)(9 - x))

f(x) = (9 - x) / ((9 + x) * (9 - x))

f(x) = 1 / (9 + x) = (9 - x) / ((9 + x) * (9 - x))

The geometric power series for the function f(x) centered at 0 is given by (9 - x) / ((9 + x) * (9 - x)).

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Answer:

1. LP

2. QR

3. LM

4. SNM

Step-by-step explanation:

hope this helps

Answer:

880

Step-by-step explanation:

600miles = 3168000feet

316800/3600=880

Answer:

13. you have to divide the numbers. hope this helps.

Answer:

25,000x1.06 or      25,000/100=250x106=26,500

Step-by-step explanation: