Simplify the product using foil. (3x-4)(6x-2)

a. 18x^2 + 30x - 8

b. 18x^2 + 18x - 8

c. 18x^2 - 30x + 8

d. 18x^2 - 18x + 8

The area of the cross-section is 16 sq. cm. Thus, option C is the correct answer.

Vertices sides =  2, 3, 6, and 7

Divide part face = parallel to the face of vertices

It is given that a square face is present in the middle of the cube. The area of the cross-section of the cube results from the plane and cube intersection.

To find the distance between the square face of the cube and the length of the side:

distance = [tex]\sqrt{[(x^{2} - x1)^2 + (y^{2} - y1)^2 + (z^{2} - z1)^2]}[/tex]

we can use the coordinates of any two adjacent sides to find the distance.

distance = [tex]\sqrt{[(3-2)^2 + (3-2)^2 + (3-1)^2] }[/tex]

distance = [tex]\sqrt{11}[/tex]

To calculate the area of the face of the cube:

area = [tex]side^{2}[/tex]

area = [tex]\sqrt{(11)^2}[/tex]

area = 11

The area of the cross-section can be estimated as:

area = (1/2) x 11 x 4) + 5 vertices of plane

area = 16 sq. cm

Therefore we can infer that the area of the cross-section is 16 sq. cm

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This is the inequality that represents all possible widths, w, in feet of the garden is W^2 + 2W - 120 ≥ 0

The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. In this problem, we are given that the garden is rectangular and that the length is 2 feet longer than the width, so we can write L = W + 2.

We are also told that the area of the garden is at least 120 square feet, so we can write:
A = L x W ≥ 120
Substituting L = W + 2, we get:
(W + 2) x W ≥ 120

expanding the left side, we get:
W^2 + 2W ≥ 120
Rearranging, we get:
W^2 + 2W - 120 ≥ 0

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Lamar can spend at most $3.01 on a single pair of socks to stay within his budget.

a. The total cost of the socks and shorts can be represented by the expression:

Total cost = Cost of shorts + Cost of 5 pairs of socks

= $19.95 + 5x

where x is the price of one pair of socks.

b. To write an equation that says Lamar spent exactly $35 on the socks and shorts, we can equate the total cost expression to $35:

$19.95 + 5x = $35

To solve for x, we can first subtract $19.95 from both sides:

5x = $15.05

Then, divide both sides by 5:

x = $3.01

So, Lamar spent $19.95 + 5($3.01) = $35 on the socks and shorts.

c. Other possible prices for the socks that would still allow Lamar to stay within his budget of $35 can be found by plugging in values of x that satisfy the inequality:

Cost of 5 pairs of socks = 5x ≤ $15.05

For example, if the socks cost $2.99 per pair, then the total cost would be:

$19.95 + 5($2.99) = $34.90

which is within Lamar's budget.

d. We can write an inequality to represent the amount Lamar can spend on a single pair of socks as:

x ≤ (35 - 19.95)/5

This simplifies to:

x ≤ $3.01

So, Lamar can spend at most $3.01 on a single pair of socks to stay within his budget.

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The option of bank B investment will allow to reach goal of buying the car the fastest compare to bank A it will take approximately 8.4 years

Saved amount = $15,000

Value of the car = $26,795

Use the formula for compound interest to calculate the time it will take to reach $26,795 for each bank,

Bank A,

Initial investment ' P ' = $15,000

Annual interest rate ' r ' =5.45%

                                       =  0.0545

compounded continuously  'n'  = infinity

Target amount  'A' = $26,795

The formula for continuous compounding is,

A = P[tex]e^{rt}[/tex]

Substituting the values, we get,

⇒ 26,795 = 15,000 × [tex]e^{(0.0545t)}[/tex]

Solving for t, we get,

⇒ t = (log(26,795/15,000))/(0.0545)

     ≈ 9.4 years

It will take approximately 9.4 years to reach the target amount if we invest in Bank A.

Bank B,

Initial investment ' P ' = $15,000

Annual interest rate ' r ' =5.75%/12

                                       =  0.00479 (monthly interest rate)

n = 12 compounded monthly

Target amount 'A' = $26,795

The formula for monthly compounding is,

A = [tex]P\times( 1+ r/n)^{nt}[/tex]

Substituting the values, we get,

26,795 = [tex]15,000 \times(1+0.00479/12)^{12t}[/tex]

Solving for t, we get,

t = (1/12) × (log(26,795/15,000))/(log(1+0.00479/12))

  ≈ 8.4 years

It will take approximately 8.4 years to reach the target amount if we invest in Bank B.

Therefore, investment in Bank B will allow you to reach your goal of buying the car the fastest, taking approximately 8.4 years.

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Thus, the volume of cone for the given slant height and radius is found as:  314 cu. cm.

The distance from a cone's apex to its outer rim is referred to as the segment's slant height. It is corresponding to the hypotenuse's length of a right triangle that creates the cone.

Given data:

slant height of cone  l =  13 cm

radius r =  5 cm

Let h be the height

So, using Pythagorean theorem, find height.

l² = h² + r²

h² = l² - r²

h²= 13² - 5²

h² = 169 - 25

h = 12 cm

volume of a cone = 1/3 *π*r²*h

volume of a cone = 1/3 *3.14*5²*12

volume of a cone = 3.14*25*4

volume of a cone = 314 cu. cm

Thus, the volume of cone for the given slant height and radius is found as:  314 cu. cm.

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Probability is frequently used in news reports to convey the possibility of an event occurring.

Generally, in my opinion, probability is used well in the media space.

Probability is frequently used in news reporting to demonstrate the likelihood of an event occurring. A news story, for example, might mention that there is a 50% chance of rain tomorrow. Similarly, sports writers may use probability to forecast the outcome of games and goals to be scored.

Overall, I feel probability is utilized fairly responsibly in the media and entertainment industries, with a focus on informing or entertaining audiences rather than misleading them. However, in some cases, such as political polling or advertising, the use of probability may be incorrect or exploited to influence audiences.

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Choice D is correct: This situation satisfies each of the conditions for a binomial variable, so X has a binomial distribution.

A random variable X is said to have a binomial distribution if it satisfies the following conditions:

The variable X represents the number of successes in a fixed number of independent trials.

Each trial has only two possible outcomes: success or failure.

The probability of success is constant for each trial.

The trials are independent.

In this case, Yoshi attempts the same three-point shot until he makes the shot, so the number of attempts is not fixed. However, each attempt can be classified as a success (if he makes the shot) or a failure (if he misses the shot), so the variable X represents the number of successes in a sequence of independent trials with only two possible outcomes. Also, the probability of success is constant for each attempt, and the attempts are independent, so all four conditions for a binomial distribution are satisfied. Therefore, X is a binomial variable.

Choice D is correct: This situation satisfies each of the conditions for a binomial variable, so X has a binomial distribution.

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The area of the ring created by the two circles is approximately 1374.63 square feet.

Let's first find the radius of the circumscribed circle. We can draw a diagonal of the regular octagon, which will be twice the length of one of its sides, forming an isosceles triangle with two radii of the circle.

The angle at the center of the circle between two adjacent sides of the octagon will be 360 degrees divided by 8, or 45 degrees.

The angle at the top of the isosceles triangle will be half of that, or 22.5 degrees. Using trigonometry, we can find the radius of the circumscribed circle:

[tex]$\sin(22.5^\circ) = \frac{opposite}{hypotenuse}$$\sin(22.5^\circ) = \frac{10}{2r}$$r = \frac{10}{2\sin(22.5^\circ)} \approx 21.21$[/tex]

Next, we can find the radius of the inscribed circle. Drawing radii from the center of the octagon to the points where it touches the circle, we can form 8 congruent isosceles triangles, each with a base of length 10 and two equal legs.

The angle at the top of each triangle will be half of the central angle between two adjacent sides of the octagon, or 22.5 degrees. Using trigonometry again, we can find the length of each leg of the triangle:

[tex]$\tan(22.5^\circ) = \frac{opposite}{adjacent}$$\tan(22.5^\circ) = \frac{r'}{5}$$r' = 5\tan(22.5^\circ) \approx 2.93$[/tex]

Now we can calculate the area of the ring created by the two circles:

[tex]$A = \pi R^2 - \pi r'^2$$A = \pi (21.21)^2 - \pi (2.93)^2 \approx 1374.63$ square feetTherefore, the area of the ring created by the two circles is approximately 1374.63 square feet.\\\\\\\\[/tex]

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The critical value t Subscript c for a confidence level of 0.90 and sample size of 26 is 1.708. A t-value greater than or less than 1.708 in absolute value would lead to rejection of the null hypothesis at the 0.10 level of significance.

To find the critical value t Subscript c for the confidence level c=0.90 and sample size n=26, we can use a t-distribution table or calculator.

Since we have a sample size of n=26, we have n-1 = 25 degrees of freedom. Using a t-distribution table or calculator with 25 degrees of freedom and a confidence level of 0.90, we get

t Subscript c = 1.708

Therefore, the critical value t Subscript c for the confidence level c=0.90 and sample size n=26 is 1.708. This means that if we calculate the t-value from our sample data and it is greater than or less than 1.708 in absolute value, we can reject the null hypothesis at the 0.10 level of significance.

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The nearest year, we can estimate that the number of new cases would reach 1282 in the year 2017.

To find the linear regression equation, we need to use the formula:

y = a + bx

where y is the number of new cases, x is the number of years since 1995, a is the y-intercept and b is the slope of the line.

Using the given data, we can find the values of a and b using the formulas:

b = (nΣxy - ΣxΣy) / (nΣ[tex]x^2[/tex] - (Σx)[tex]^2)[/tex]

a = (Σy - bΣx) / n

where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x, Σy is the sum of y, and Σ[tex]x^2[/tex] is the sum of squares of x.

Using these formulas and the given data, we get:

n = 9

Σx = 36

Σy = 7386

Σx^2 = 162

Σxy = 3330

b = (93330 - 367386) / (9*162 - 36^2) ≈ -75.44

a = (7386 - (-75.44)*36) / 9 ≈ 2612.67

Therefore, the linear regression equation is:

y ≈ 2612.67 - 75.44x

To estimate the year in which the number of new cases would reach 1282, we can substitute y = 1282 into the equation and solve for x:

1282 ≈ 2612.67 - 75.44x

75.44x ≈ 2612.67 - 1282

x ≈ 22.36

This means that the number of new cases would reach 1282 approximately 22.36 years after 1995. Adding this to 1995 gives us an estimate of the calendar year:

1995 + 22.36 ≈ 2017.36

Rounding to the nearest year, we can estimate that the number of new cases would reach 1282 in the year 2017.

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To test the convergence of the given infinite series, we can use the Alternating Series Test. The series is in the form: Σ((-1)^n * (arctan(n)/n^2)), for n = 1 to infinity.

The Alternating Series Test requires two conditions to be met:

1. The absolute value of the terms in the series must be decreasing: |a_n+1| ≤ |a_n|.
2. The limit of the terms in the series as n approaches infinity must be zero: lim (n→∞) |a_n| = 0.

For the given series, let's check these conditions: 1.The absolute value of the terms: |arctan(n)/n^2|. Since arctan(n) increases with n and n^2 increases faster than arctan(n), the ratio (arctan(n)/n^2) decreases as n increases. Therefore, this condition is met.

2. Now, we need to check the limit: lim (n→∞) |arctan(n)/n^2|. As n approaches infinity, the arctan(n) approaches π/2, and n^2 approaches infinity.

Therefore, the limit is (π/2)/∞ = 0, so the second condition is also met. Since both conditions are met, the Alternating Series Test confirms that the given series converges.

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                          "Complete question"

Apply Any Appropriate Testing Method To: ∞X N=1 (−1)Narctan N N2

Apply any appropriate Testing Method to:

∞X

n=1

(−1)narctan n

n2

The entire expression is factored completely as: 5x2(x4 + 4)(x2 + 2)(x2 - 2)

Part A:

To factor out the greatest common factor, we need to find the largest number that divides evenly into both terms. In this case, the greatest common factor is 5x2.

5x10 − 80x2

= 5x2 (x8 - 16)

Therefore, we can rewrite the expression as 5x2(x8 - 16).

Part B:

To factor the entire expression completely, we need to use the difference of squares formula, which states that:

a2 - b2 = (a + b)(a - b)

In this case, we can rewrite the expression as:

5x2(x8 - 16) = 5x2[(x4)2 - (4)2]

Notice that x8 can be rewritten as (x4)2, and 80 can be factored into 4 x 20, which gives us 16 when squared.

Using the difference of squares formula, we can factor the expression further:

5x2[(x4 + 4)(x4 - 4)]

The expression (x4 + 4) cannot be factored further, but (x4 - 4) can be factored using the difference of squares formula again:

5x2[(x4 + 4)(x2 + 2)(x2 - 2)]

Therefore, the entire expression is factored completely as: 5x2(x4 + 4)(x2 + 2)(x2 - 2)

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The coordinates of the point prior to the dilation are (-2,-1) when the Scale factor is 1/3 and the new coordinates are (-6,3).

To find the coordinates of the point prior to the dilation, we need to use the formula for dilation:

(x’, y’) = (k x, ky)

where

(x’, y’) = the new coordinates

(x, y) = original coordinates

k = scale factor

Given data:

Scale factor =  1/3

New coordinates = (-6, 3)

By substuting the values in the equation we get:

(-6, 3) = (k x, ky)

Solving for x and y:

k x = -6

ky = 3

Dividing the ky equation by the k x  equation we get:

y/x = 3/-6

y/x = -1/2

From the above equation, we can assume that x = 2 and y = -1.

Therefore, the coordinates of the point prior to the dilation are (-2,-1).

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By 2009, it is projected that approximately 13,956 three-legged frogs will inhabit the area.

Recent studies have indicated a growing concern for the population of three-legged frogs in a specific area, as they have been exposed to chemical pollutants. In the year 2000, data estimated that there were about 5,000 three-legged frogs (N) in this area. With an annual increase of 15%, we can project the number of frogs in future years using the formula:

Future population = N * (1 + growth rate) ^ number of years

In this case, we want to determine the number of three-legged frogs in the area by 2009. To calculate this, we will use the given values:

Future population = 5,000 * (1 + 0.15) ^ (2009 - 2000)

Future population = 5,000 * (1.15)⁹

Future population ≈ 13,956

Therefore, by 2009, it is projected that approximately 13,956 three-legged frogs will inhabit the area, rounding to the nearest whole number. This increase in population highlights the potential ecological consequences of chemical pollutants on the environment and the need for further investigation and mitigation measures.

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Therefore, to the nearest hundredth, the value of x is 42.31 units.

A triangle is a three-sided polygon, which is a closed shape made up of straight lines. It is one of the simplest geometric shapes and is used extensively in mathematics, science, and engineering. In a triangle, each side connects two vertices or corners, and each vertex is where two sides intersect. The three angles of a triangle always add up to 180 degrees, and the sum of the lengths of any two sides is always greater than the length of the third side. Triangles can be classified by the lengths of their sides and the sizes of their angles, which gives rise to different types such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have many applications, such as in geometry, trigonometry, physics, and engineering, and they are fundamental to understanding the properties of other shapes and mathematical concepts.

Here,

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, for this triangle, we have:

sin(53°) = opposite / hypotenuse

sin(53°) = x / 53

To solve for x, we can rearrange the equation as follows:

x = 53 * sin(53°)

Using a calculator to evaluate sin(53°), we get:

sin(53°) = 0.7986 (rounded to four decimal places)

Substituting this value into the equation, we get:

x = 53 * 0.7986

x = 42.308 (rounded to two decimal places)

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APR is obtained by dividing the finance charge for the loan by the total amount borrowed, given by this formula APR = ((F / P) x 12) x 100

The formula for APR (annual percentage rate) is given as;

APR = ((F / P) x 12) x 100

Where;

The annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100, is calculated as follows;

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There is no convincing evidence that the proportion of Devon's serves that are good is more than 72%. The data collected does not provide sufficient evidence to support Devon's claim that he has a higher proportion of good serves than what his coach stated.

Based on Devon's hypotheses, H₀ states that p = 72%, while Hₐ states that p > 72%, where p represents the true proportion of Devon's good serves. To test this, 50 of his serves are randomly selected, and 42 are good. A simulation is conducted with 100 trials, resulting in an estimated P-value of 0.06. The significance level (α) is set at 0.05.

In this case, the P-value (0.06) is greater than the significance level (0.05). According to the rules of hypothesis testing, we should fail to reject the null hypothesis (H₀) when the P-value is greater than the significance level. Therefore, Devon should fail to reject H₀.

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Step-by-step explanation:

It looks as though ( from your post)  Sweden won 4 golds and 0 silver and 2 bronze medals

4:0:2     simplifies to   2 :0 : 1

Answer: 2,506 people

Step-by-step explanation:

786 + 908 + 812 = 2,506 people

For an individual with a femur length of 49 centimeters, we can expect their height to be approximately 177.15 centimeters.

When f=49, plugging it into the formula h=62.6+2.35f, we get h=62.6+2.35(49)=177.15.

This means that for an individual with a femur length of 49 centimeters, we would expect their height to be approximately 177.15 centimeters.

This provides an estimate of the individual's height based on the relationship between femur length and height indicated by the formula. It's important to note that this is an estimate and individual variation may exist.

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Answer:

v = -64

Step-by-step explanation:

First, you add 4 to both sides to isolate the variable term:

v/8 = -8

Next, you multiply both sides by 8 to isolate the variable on one side:

v = -64

So, the solution to the equation v/8 - 4 = -12 is v = -64.

Answer:

1/6

Step-by-step explanation:

The distance between bus stops A and C is exactly 1 km.

To find the distance between bus stops A and C, we can use the fact that the distance from A to D is 1 km and the distance from C to D is 5 km.

This means that the total distance from A to C, passing through D, is 6 km (1 km + 5 km).

However, we need to subtract the distance between B and D (3 km) and the distance between B and C (2 km) since we don't want to double count the stretch between B and D.

Therefore, the distance between A and C is 6 km - 3 km - 2 km = 1 km.

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The zeros of the quadratic equation are as follows

1. y = -x²+ 6x - 5:

zeros: (1, 0) and (5, 0)

2. y = x² + 2x + 1:

zeros: (-1, 0).

3. y = -x²+ 8x - 17:

zeros: (0, 0) and (0, 0)

4. y = x² - 4:

zeros: (1, 0) and (5, 0)

Zero in a quadratic equation are x values ​​that make the equation equal to zero. In other words, they are the x-intercepts or roots of a quadratic function.

Using graphical method, a zero is the point of intersection of the curve with the x -axis and this is shown in the graph attached.

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C(12) represents the total cost (in dollars) of renting the industrial cleaning unit for 12 hours.

The problem gives us a function C(t) = 60 + 24t, where t represents the number of hours that an industrial cleaning unit is rented for. The function tells us that the total cost (in dollars) of renting the unit is equal to $60 plus $24 per hour.

Now, we are asked to find what C(12) represents. To do so, we substitute t = 12 into the function, which gives us:

C(12) = 60 + 24(12)

We can simplify this expression by multiplying 24 by 12, which gives us:

C(12) = 60 + 288

Adding 60 and 288 together, we get:

C(12) = 348

So, C(12) represents the total cost (in dollars) of renting the industrial cleaning unit for 12 hours. Therefore, the correct answer to the question is: The cost of renting the unit for 12 hours.

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If the probability that this teacher is female is 3/5 , there are a total of 90 teachers at the school.

Let's denote the total number of teachers at the school as T. We know that the probability of choosing a female teacher is 3/5. Therefore, the probability of choosing a male teacher is 1 - 3/5 = 2/5.

We are also given that there are 36 male teachers at the school. We can use this information to set up an equation:

36/T = 2/5

To solve for T, we can cross-multiply:

36 x 5 = 2 x T

180 = 2T

T = 90

Therefore, there are a total of 90 teachers at the school.

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Complete question is:

One of the teachers at a school is chosen at random. The probability that this teacher is female is 3/5 There are 36 male teachers at the school. Work out the total number of teachers at the school.

Answer:

The y intercept of the scatterplot is 250 sweat shirts and the slope is 10/3

What is a linear function?

y = mx + b

where m is the rate of change and b is the y intercept.

Let y represent the number of sweat shirts sold and x represent the temperature.

The y intercept is at (0,250).

Using point (0,250) and (14,200):

Slope = (200-250) / (15-0) = 10/3

The y intercept of the scatter plot is 250 sweat shirts and the slope is (10/3)