What is the area of the shape?
24
10
25
hint: decompose the shape into rectangle and triangle

Point B of line segment AB = (-3 , 2)

The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

Given,

Midpoint of AB = (x , y) = (-5, 0)

A = (x₁ , x₂) = (-7, -2)

Let B = (x₂ , y₂)

Midpoint (x , y) = [(x₁ + x₂)/2 , (y₁ + y₂)/2]

(-5, 0) = [(-7 + x₂)/2 , (-2 + y₂)/2]

Comparing horizontal coordinates,

(-7 + x₂)/2 = -5

(-7 + x₂) = -10

x₂ = -10 + 7

x₂ = -3

Comparing vertical coordinates

(-2 + y₂)/2 = 0

(-2 + y₂) = 0

y₂ = 2

B = (x₂ , y₂) = (-3 , 2)

Hence, (-3 , 2) is point B of line segment AB.

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Answer:

The Panthers soccer team does not like to lose because they always try to be their best. One day, they were embarrassed when all their shirts were so loose they started to fall off during a game. Guess who did not win that day?

The value of the segment a for the similar triangles is equal to 6.

The triangles MNO and YXO are similar, this implies that the length OX of the smaller triangle is similar to the length ON of the larger triangle

and the length OY of the smaller triangle is similar to the length OM of the larger triangle

so;

a/(a + 18) = 4/(4 + 12)

16a = 4(a + 18) {cross multiplication}

16a = 4a + 72

16a - 4a = 72 {collect like terms}

12a = 72

a = 72/12 {divide through by 12}

a = 6.

Therefore, the value of the segment a for the similar triangles is equal to 6.

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The function  [tex]f(x) = (x^2 - 9)^3[/tex]   is continuous on the entire real number line because its domain is the entire real line and it is a polynomial, which is a continuous function.

The function   [tex]f(x) = (x^2 - 9)^3[/tex]   is continuous on the entire real number line because its domain is the entire real line and it is a polynomial, which is a continuous function. A function is considered continuous at a point if the limit of the function as the input approaches the point exists and is equal to the function's value at that point. In this case, the function's domain is the entire real line, meaning that it is defined for all real values of x. The function is also a polynomial, which is a continuous function by definition. Thus, the function is continuous on the entire real number line.

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The total amount of money that Allam will have to pay is given as follows:

$18.

The total amount of money that Allam will have to pay is obtained applying the proportions in the context of the problem.

The extra payments are given as follows:

Hence the extra percentage is given as follows:

5 + 15 = 20%.

Meaning that the price of the meal is multiplied by 1.2, which is equivalent to 100 + 20 = 120%.

Considering a meal of $15, the total price is given as follows:

1.2 x 15 = $18.

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Answer:

b

Step-by-step explanation:

The width of the rectangle is y = (8P - 2x) ÷ 2 and the maximum area of the rectangle is A = x x y.

The perimeter of a rectangle is given by the following equation: 2L + 2w = P, where P is the perimeter, L is the length, and w is the width. We are given that the rectangle has a perimeter of 8P units. Let x represent the length of the rectangle and let y represent the width. Then, the equation for the perimeter of the rectangle in terms of x and y is: 2x + 2y = 8P.

To solve for y, we can subtract 2x from both sides of the equation to get: 2y = 8P - 2x. Then, we divide both sides of the equation by 2 to get: y = (8P - 2x) ÷ 2.

Now, we can use the area formula for rectangles, A = L x w, to determine the maximum area of a rectangle with a perimeter of 8P units. Substituting the values for length and width, we get: A = x x (8P - 2x) ÷ 2. We can rearrange this equation to make x the subject: A = x x (8P - 2x) ÷ 2 → x2 - (8P/2)x + A = 0.

Now, we can use the quadratic equation to solve for the length of the rectangle, x. We get: x = (8P ± √(64P2 - 16A)) ÷ 4. Therefore, the width of the rectangle is y = (8P - 2x) ÷ 2 and the maximum area of the rectangle is A = x x y.

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The required complete table for the given function f(x) = 2x - 1 is given as,
  x =  1      0    -1     2
f(x) =  1     -1     -3    3

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Given function,
f(x) = 2x - 1

To complete the table,
Put x = 1
f(1) = 2(1) - 1
f(1) = 1

Similarly
f(0) = -1
f(-1) = -3
f(2) = 3

Thus, the required complete table for the given function f(x) = 2x - 1 is given as,
  x =  1      0    -1     2
f(x) =  1     -1     -3    3

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Answer: Looking at the unit price allows you to compare the price of different sized packages and different brands to find the best deal.

Step-by-step explanation: The "unit price" tells you the cost per pound, quart, or other unit of weight or volume of a food package. It is usually posted on the shelf below the food.

The unit rate price of an item at a supermarket is necessary to help buyers to understand and compare the prices for different things at the rate.

Shopkeepers sell their items according to some fixed unit rates. These rates can be used by the customer to compare within different qualities of that specific product and to understand how much quantity of goods they can purchase under their budget.

Everyone can easily learn about the amount of money to be paid to the shopkeeper. If we have unit rates we can compare the prices of items fairly in the market. So it is helpful to buy and sell the items at unit rates for a better economy.

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a) The function will be C(n) = 0.74 * min(n, 100) + 0.69 * max(n-100, 0)

b. The cost of 53 CDs will be $39.22

c. The cost of 201 CDs will be $143.69.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario

a) C(n) = 0.74 * min(n, 100) + 0.69 * max(n-100, 0)

b) C(53) = 0.74 * min(53, 100) + 0.69 * max(53-100, 0)

= 0.74 * 53

= 39.22

c) C(201) = 0.74 * min(201, 100) + 0.69 * max(201-100, 0) = 0.74 * 100 + 0.69 * (201-100) = 74 + 0.69 * 101

= 74 + 69.69

= 143.69

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The probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score of more than 700 points is 5.8%.

The distributed samples can be solved using the z-score formula:

We can set with mean  and standard deviation, the z-score of a measure X is given by:

[tex]Z=\frac{X-u}{sd}[/tex]

The Z-score defines how many standard deviations will be measured from the mean. After finding the Z-score, we should see the z-score table and find the p-value included with this z-score.

This p-value is the probability of the value measuring smaller than X, that is, the percentile of X. by Subtracting 1 from the p-value, we get the probability of the value of the measure is greater than X.

In this problem, we have that:

u=511 sd=120.

This is 1 subtracted by the value of Z when X = 700.

[tex]Z=\frac{X-u}{sd}\\\\Z=\frac{700-511}{120}[/tex]

Z=1.575.

Z=1.575 has a p-value of 0.942

1 - 0.942 = 0.058.

5.8% probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score of more than 700 points.

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The equation for a parabola that has x-intercepts (5,0) and (6,0) and y-intercept (0,1) is: [tex]y =[/tex] [tex]a(x + 0.5)^2 - 1[/tex]

The equation of a parabola can be found by using the vertex form of a parabolic equation, which is given by:[tex]y = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola. In this case, the x-intercepts (5, 0) and (-6, 0) can be used to find the value of h, which is the midpoint between the x-intercepts and is equal to (-6 + 5) / 2 = -0.5.

The y-intercept (0, -1) can be used to find the value of k. So, the equation is:[tex]y = a(x + 0.5)^2 - 1[/tex], where a is a constant that can be determined by substituting the vertex coordinates (h, k) into the equation.

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Answer:

6.375 cubic inches

Step-by-step explanation:

To find the volume of a cube using the formula V = s^3, where s represents the length of one side, we simply need to raise s to the power of 3.

Given that the length of one side, s, is 2 1/4 inches, we need to first convert the fractional part to decimal form:

[tex]\sf:\implies{2 1/4 inches = 2 + 1/4 inches}[/tex]

[tex]\sf:\implies{= 2.25 inches}[/tex]

Now, we can use this value in the formula:

[tex]\sf:\implies{V = s^3 = 2.25^3}[/tex]

To raise a number to the power of 3, we simply multiply the number by itself three times:

V = 2.25 × 2.25 × 2.25 = 6.375 cubic inches

Therefore, the volume of the cube with sides of length 2 1/4 inches is 6.375 cubic inches.

The maximum error of the calculator would be 0.0003 if it is increased to 4-digit accuracy.

2.345 * 0.678

the calculator will return

1.592

a. Determine the maximum error of the calculator

The maximum error of the calculator is 0.003 since the calculator retains only 3 digits to the right of the floating point.

b. If you increase the accuracy of the calculator to 4-digit, what would be the maximum error?

The maximum error of the calculator would be 0.0003 if it is increased to 4-digit accuracy.

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The square of a binomial, when the binomials are subtracted, is defined as follows:

(a - b)² = a² - 2ab + b².

When the two binomials are added, the square is given as follows:

(a + b)².

Expanding the square, we have that:

(a + b)² = (a + b) x (a + b).

(a + b)² = a² + ab + ab + b².

(a + b)² = a² + 2ab + b².

Which is the result presented in this problem.

Now, when the binomial has a minus sign, involving a subtraction, the pattern is obtained as follows:

(a - b)² = (a - b) x (a - b).

(a - b)² = a² - ab - ab + b².

(a - b)² = a² - 2ab + b².

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Yes, we would be more intrigued by looking so at mean, median, or mode for the below type of data set.

Choose the proper center measurement first, and then decide how to support your decision.

Correct center measurement

Justification:

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The correct question is-

For the following type of data set, would you be more interested in looking at the mean, median, or mode? State your reasoning.

The price of cars on a car lot-

At a significance threshold of 0.10, p-value(0.0005)< [tex]\alpha[/tex] =0.10, therefore we reject [tex]H_{0}[/tex].

Under the assumption of independence, the expected frequencies for contingency tables are

[tex]e_{ij} = \frac{(Row_{i}Total)(Column_{j} total)}{SampleSize}[/tex]

Using the formula for the number of freshmen without body art: (247*168)/490=84.69.

State the null and alternative hypotheses:

[tex]\alpha = 0.10[/tex]

[tex]H_{0}[/tex]: There is a connection between body art and class standing 

Ha: There is no connection between class standing  and rejection from body art. [tex]H_{0}[/tex] if the probability is less than 0.10.

the test statistic for independence is

[tex]X^2= \sum\limits_i \sum\limits_j\frac{(f_{ij}-e_{ij} )^2 }{e_{ij} }[/tex]

where fij = observed frequency for the contingency table category in rows i and j

eij = expected frequency for the contingency table category in rows i and j based on the assumption of independence

We only need to add up the values as they have already been obtained and are listed in the table to obtain the chi-square value.

Therefore,

[tex]X^2= 2.56+ 4.33+1.1+0.02+0.69+0.02+1.2+0+0.49+0.51+0.33+0.25+4.99+4.31+8.41+0.27[/tex]

[tex]X^{2} = 29.48[/tex]

Consequently, the probability of p-value=0.0005

Given DF=9.

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The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of linear equations is given below.

−2x + 3y = 15         ....1

x + y = 10

2x + 2y = 20           ...2

Add equations 1 and 2, then we have

5y = 35

y = 7

Then the value of the variable 'x' is given as,

x + 7 = 10

x = 3

The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.

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Answer:

Each change in the solution area makes the inequality true.

The dimensions of the rectangular region that will maximize the total area are 20ft x 50ft.

The goal is to find the dimensions of a rectangle that will maximize the total area when it is divided into 6 smaller rectangles.

Let the length of the rectangle be x and the width be y.

The total length of the fencing used to enclose the rectangle is 100 feet, so 2x + 2y = 100.

To divide the rectangle into 6 smaller rectangles, we need 5 partitions,

so we have x/6 = y, or y = x/6.

Substituting y = x/6 into 2x + 2y = 100 gives 2x + 2x/3 = 100, or x/3 = 50.

Solving for x, we find x = 150.

Then y = x/6 = 150/6 = 25.

The maximum area of the rectangle is 150 * 25 = 3750 square feet.

To maximize the area of the rectangular region, the width and length should be in the ratio of 1:2. This allows the rectangular region to be split into six smaller rectangles of equal area by placing five fences parallel to the width.

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The transformations that could be used to show that Henry's claim is incorrect are:

Horizontal stretch by a factor of 1/3.

Dilation by a factor of 2 units through origin.

Given that a a square is plotted on a coordinate plane.

Henry claims that any transformation on the square will preserve the length of its sides.

We need to check which claims is incorrect.

We must find transformations that do not maintain the length of the square's sides in order to refute Henry's assertion.

Analyzing each transformation now:

a) A translation of 5 units to the right:

The square's shape is unaltered by this transformation. The length of the sides does not change, but the square is merely moved 5 units to the right. The sides' length is preserved by this modification.

b) A horizontal stretch of the square by a factor of 1/3:

This change enlarges the square horizontally. The lengths of the original square's sides will not be kept because they will be multiplied by a factor of three-quarters. The sides' length is not preserved in this change.

c) Two-unit dilation through the origin:

This transformation uniformly scales the square by a factor of two. The lengths of the sides will alter as a result of multiplying all of them by 2. The sides' length is not preserved in this change.

d) Rotation of the square 45 degrees clockwise about its center:

This transformation spins the square, but the side lengths stay the same. The length of the sides are preserved by this translation because the rotation does not change the square's dimensions.

Therefore, the following transformations could be used to refute Henry's assertion:

b) Horizontal stretch by a factor of 1/3.

c) Dilation by a factor of 2 units through the origin.

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The functions for this problem are classified as follows:

a) q(x) is an odd function.

b) r(x) is an even function.

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Answer:

The width of the walkway is 5ft long

The general antiderivative of the rate of change function s(m) = 500m + 8 DVDs per month is [tex]S(m) = 250m^2/2 + 8m + C[/tex].

The general antiderivative of a rate of change function is calculated by integrating the rate of change expression over the given interval. In this case, the rate of change of DVD orders is given by s(m) = 500m + 8 DVDs per month. We can calculate the general antiderivative of this expression by integrating it over the given interval from m = 0 (the beginning of the year) to some arbitrary value m. This gives us the following expression for the general antiderivative: [tex]S(m) = 250m^2/2 + 8m + C[/tex], where C is the constant of integration. To calculate the value of S(m) for any given value of m, we simply plug the value of m into the expression above and solve for S(m). For example, if m = 5, then [tex]S(5) = 250(5)^2/2 + 8(5) + C = 1250 + 40 + C = 1290 + C[/tex]

The general antiderivative of the rate of change function s(m) = 500m + 8 DVDs per month is [tex]S(m) = 250m^2/2 + 8m + C[/tex].

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LAN: LAN messenger

WAN: SD-WAN

Some of the main differences between LAN and WAN are listed below:

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The sample correlation coefficient of 0.81 indicates a strong positive correlation between the number of rooms and the cost per night, which appears reasonable given the results of the scatter diagram.

a. The mean number of rooms is 1,346.5. To calculate this, we added up the number of rooms for each hotel and divided by 12, the total number of hotels in the sample.

b. The mean cost per night for a double room is $380. To calculate this, we added up the cost per night for each hotel and divided by 12, the total number of hotels in the sample.

c. The scatter diagram shows a positive correlation between the number of rooms and the cost per night. As the number of rooms increases, so does the cost per night. This makes sense because larger hotels tend to be more expensive than smaller ones.

d. The sample correlation coefficient is 0.81, which indicates a strong positive correlation between the number of rooms and the cost per night. This appears reasonable given the results of the scatter diagram.

The mean number of rooms in the sample of 12 top rated hotels in the US is 1,346.5, and the mean cost per night for a double room is $380. The sample correlation coefficient of 0.81 indicates a strong positive correlation between the number of rooms and the cost per night, which appears reasonable given the results of the scatter diagram.

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Let's call the event of flipping two tails in a row "success." The probability of success on any given flip is (1-p) ^2.

The number of flips required to get two tails in a row is a random variable, which we can calculate the expected value of. This expected value can be calculated as an infinite sum:

E = 1 * (1 - (1-p) ^2) + 2 * (1-p) ^2 * p + 3 * (1-p) ^2 * (p^2) + ...

This sum can be simplified using geometric series formula:

E = 1 / (1 - (1-p) ^2 * p)

So, the expected number of flips required to get two tails in a row with a biased coin with probability p of heads is given by the above formula.

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