write the vertices of each figure​

\(\\ \sf\longmapsto y=\dfrac{2}{7}x+\dfrac{1}{3}\)

Compare to slope intercept form of a line

\(\\ \sf\longmapsto y=mx+b\)

Answer:

131°

Step-by-step explanation:

Sum of all angles of a quadrilateral = 360°

We can find the unknown angle ∠B, by subtracting the sum of the angles ∠A, ∠C, ∠D from 360°.

∠A + ∠B + ∠C + ∠D = 360

105 + ∠B + 34 + 90  = 360

           ∠B +  229      = 360

                     ∠B       = 360 - 229

                           ∠B = 131°

Answer:

The measure of m<GHE is 49°, the correct option is B.

What is a Quadrilateral?

A quadrilateral is a polygon with four sides.

It is of various types,

Trapezoid, which have one pair of parallel sides,

Parallelogram, it has two pairs of parallel sides,

Rhombus, it has all sides equal,

Rectangle, opposite sides are parallel and equal, and,

Square, all sides are equal and opposite sides are parallel, and all angles have measure of 90 degree.

The quadrilateral ABCD is ≅ quadrilateral EFGH

When two figures are congruent then by CPCTC, corresponding parts of congruent figures are congruent.

The measure of the angle

B = m<BCD = 90°

m<BAD = 131°

As the quadrilaterals are congruent,

By CPCTC

∠F = ∠FGH = 90°

m ∠FEH =  131°

The measure of m<GHE has to be determined.

The sum of the measures of all angle so of a quadrilateral is 360 degree.

The ∠F + ∠FGH + ∠FEH + ∠GHE = 360

90 +90+ 131 +∠GHE = 360

∠GHE = 49°

Step-by-step explanation:

a) The average rate of change over the interval [−2,2] is 4.

b) The instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4).

A) To find the average rate of change of g(x) over the interval [-2,2], we need to calculate the slope of the line passing through the points (-2,g(-2)) and (2,g(2)).

g(-2) = (-2)³ - 6 = -8 - 6 = -14

g(2) = (2)³ - 6 = 8 - 6 = 2

Therefore, the slope of the line passing through these two points is:

(g(2) - g(-2))/(2 - (-2)) = (2 - (-14))/(2 - (-2)) = 16/4 = 4

B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivative of g(x):

g'(x) = 3x²

At x=-2, the instantaneous rate of change of g(x) is:

g'(-2) = 3(-2)² = 12

At x=2, the instantaneous rate of change of g(x) is:

g'(2) = 3(2)² = 12

We can see that the instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4). This is because the function g(x) is not a straight line and its rate of change varies across the interval.

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The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.

According to the given statement

we have to find the explicit rule for the nth term of the given sequence,.

So, For this purpose

The given sequence is :

2, 8, 26, 80, 242.

And according to the ap series formula

\(a_{n} = (a_{n-1} -1)*3 +2\)

If we put the terms in it then we get the exact value as the value in the sequence.

So,

\(a_{n} = (a_{n-1} -1)*3 +2\)

For \(a_{2}\)

\(a_{2}\) \(= a_{1} *3 +2\)

\(a_{2}\) \(= 2*3 + 2\)

\(a_{2}\) \(= 8\)

and by this way we get all the values as same as the sequence.

So, The explicit rule for the nth term of the sequence is an = (an-1)*3 +2.

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Complete question:

A 90 percent confidence interval is to be created to estimate the proportion of television viewers in a certain area who favor moving the broadcast of the late weeknight news to an hour earlier than it is currently. Initially, the confidence interval will be created using a simple random sample of 9,000 viewers in the area. Assuming that the sample proportion does not change, what would be the relationship between the width of the original confidence interval and the width of a second 90 percent confidence interval that is created based on a sample of only 1,000 viewers in the area?

Answer:

original interval is 3 times narrower than the second interval with a sample. Size of 1000

Step-by-step explanation:

The width of the two different intervals, created with sample sizes of 9000 and 1000 samples :

Width = 2z√(pq)/n

q = 1 -p

For :

The only difference between the intervals Is the sample size, n

For Interval1, with sample size, n = 9000 ;

2z√(pq)/9000 ---(1)

For Interval1, with sample size, n = 1000 ;

2z√(pq)/1000 ----(2)

Dividing 1 by 2 :

2z√(pq)/9000 ÷ 2z√(pq)/1000

2z√(pq)/9000 * 1000 /2z√(pq)

Hence, we have :

√9000 / √1000

300 / 100

= 3

This means the original interval is 3 times narrower than the second interval with a sample. Size of 1000 ; the width of confidence interval narrows as sample size increases

The average percentage of downsizing among the five randomly selected companies can be calculated by multiplying the survey percentage (13%) by the sample size (5), which gives an average of 0.65 companies downsizing. However, we cannot determine the standard deviation based solely on the given information. Therefore, we need additional data to calculate the standard deviation.

To find the average number of companies downsizing, we can multiply the survey percentage (13%) by the sample size (5). This gives us an average of 0.65 companies. However, this only provides us with the expected value or mean of the sample, and it doesn't give us any information about the variation or spread of the data.

To calculate the standard deviation, we would need the individual downsizing percentages or the overall distribution of downsizing percentages among the companies. Without this data, it is not possible to determine the standard deviation.

Regarding the likelihood of exactly three companies downsizing, we don't have enough information to make a definitive judgment. Since we don't know the distribution of downsizing percentages or have individual company data, we can't accurately estimate the probability of exactly three companies downsizing.

However, if we assume that the downsizing percentages are independent and identically distributed, we can use the binomial distribution to make an estimate. In this case, the probability of exactly three companies downsizing would be calculated as follows:

P(X = 3) = (5 choose 3) * (0.13)^3 * \((0.87)^2\)

Here, (5 choose 3) represents the number of ways to choose 3 companies out of 5, 0.13 is the probability of a single company downsizing, and 0.87 is the probability of a single company not downsizing.

To calculate the probability of a cold sufferer experiencing symptoms for at least four days, we can use the cumulative distribution function (CDF) of the normal distribution. We subtract the probability of experiencing symptoms for less than four days from 1 to get the probability of experiencing symptoms for at least four days.

To find the probability of a cold sufferer experiencing symptoms between seven and nine days, we can use the CDF again. We calculate the probability of experiencing symptoms for less than or equal to nine days and subtract the probability of experiencing symptoms for less than seven days.

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The upper limit of the confidence interval is 0.243 at 99% confidence and the interval for the proportion of adults that prefer honey is 0.157 and 0.243.

We have the information available from the question:

A random sample of 815 adults surveyed.

Sample proportion  = 20% = 0.2

Confidence = 99%

We have to find the 99% confidence interval for the proportion of adults that prefer honey. and also a UL, Upper limit of the confidence interval.

Now, According to the question:

We can utilize the following formula:

CI = p ± z x \((\sqrt(p(1-p)/n))\)

The z-score corresponds to a 99% confidence level = 2.576.

CI = 0.2 ± 2.576 × \((\sqrt(0.2(1-0.2)/815))\)

CI = 0.2 ± 0.043

CI upper limit = 0.2 + 0.043

CI upper limit = 0.243

CI lower limit = 0.2 - 0.043

CI lower limit =0.157

Therefore, we can conclude that the 99% confidence interval for the proportion of adults that prefer honey is 0.157 and 0.243. The upper limit of the interval is 0.243.

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Answer:

Step-by-step explanation:

16-2t=t+9+4t  

7=7t  
t=1

The error represented in this scenario is an inappropriate task allocation or a mismatch between job responsibilities and the assigned task during the interview process.

The primary role of a customer service representative is to interact with customers, address their concerns, and log calls professionally and efficiently. In contrast, performing a detailed analysis of call-in data falls under the domain of data analysis or business intelligence roles.

By asking the candidate to perform a task unrelated to their potential job responsibilities, the company may not accurately assess the candidate's aptitude for customer service tasks. This error could lead to selecting a candidate who may excel in data analysis but may not possess the necessary communication and problem-solving skills required for a customer service representative position.

To avoid this error, the company should focus on evaluating candidates based on their skills, experience, and performance in tasks directly relevant to the customer service role.

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Answer:

Mode: 91

Median: 91

Mean: 107

Answer:

Zeb will pay $119.84 per month from next year.

Step-by-step explanation:

Given

Monthly Payment of Zeb's health insurance = $107

Percentage increase = 12%

In order to find the insurance premium for next year we have to find the 12% of current insurance

\(increase = 12\%\ of\ 107\\= 0.12*107\\=12.84\)

Zeb will have to pay previous monthly insurance plus increase each month from next year

\(= 107+12.84 = 119.84\)

Hence,

Zeb will pay $119.84 per month from next year.

Answer:

-5x-1/6=3/2

-5×1/6+1/6=3/2+1/6

-5×÷5×=10/6/-5x

x=-10/30

Answer:

The value of the expression is 11

Step-by-step explanation:

Evaluate Expressions

An algebraic expression consists of a set of variables and constants related by algebraic operations like addition, subtraction, multiplication, etc.

To evaluate an algebraic expression, we replace the variables for the constant value they are assigned.

Let's consider the expression:

\(x-y+ z(x + y)\)

for x=10, y=-1, z=0

Substituting the variables for their values:

\(10-(-1)+ (0)(10 -1)\)

\(=10+1+ (0)(9)\)

\(=11+0=11\)

The value of the expression is 11

The constant of proportionality is 2.02.

According to the concept of proportion, two ratios are in proportion when they are equal.

Two ratios or fractions are equal when an equation or a declaration to that effect is utilised. A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Four dozen gourmet donuts cost a total of $96.96.

So, if y be the total cost of the donuts and x be the number of donuts.

then the proportionality is

y= kx

k= y/x

k = 96.96 / (4 x 12)

k= 96.96/ 48

k= 2.02

Hence, the constant of proportionality is 2.02.

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Answer:

a = -10

r = 4/5

Step-by-step explanation:

formula

nth term = ar^n

a1 -a2 = 2

a(1-r)= 2

(1-r) = 2/a

a/(1-r) = 50

a = 50(1-r)

replace the value of (1-r) with 2/a

a = 50(2/a)

a = 100/a

a^2 = 100

a = \(\sqrt{100}\)

a = ± 10

a(1-r)= 2

10(1-r) = 2

1-r = 2/10

1 - r = 1/5

1 + 1/5 = r

r = 4/5

10*4/5 = 8

10 , 8 , 32/5......

since it states that the second term exceeds by two... this means that the second term has to be greater than the first

Hence:

a = -10

meaning the sequence becomes:

-10 , -8 , -32/5

a = -10

r = 4/5

Answer:

(1,  2), (3,  4), (5, 6), (8, 7)

Step-by-step explanation:As we can observe from the answers the representation is about the pair of points. We can sort it out by excluding the wrong options.

Answer:

6 ducks and 13 horses

Step-by-step explanation:

Let H and D be the numbers of Horses and Ducks, respectively.

We are told that:

H + D = 19

Our biology book confirms that:

1 horse = 4 legs, and

1 duck = 2 legs

[In most cases on Earth]

So we can say that:

4H + 2D = 64 legs

Rewrite

H + D = 19 as:   H = 19 - D

and then substitute:

4H +2D = 64 legs

4(19-D) +2D = 64 legs

76 - 4D + 2D = 64 legs

-2D = - 12

D = 6  [We have 6 ducks]

Then:

H + D = 19

H + 6 = 19

H = 13  [There are 13 horses]

=============================

Check:

Do 6 ducks and 13 horses have a total of 64 legs?

6*2 + 4*13 = 64?

12 + 52 = 64?

YES

100 - j = j - 40

100 + 40 = j + j

140 = 2j

140/2 = j

70 = j

_____

RainbowSalt2222 ☔

Arc length formula is L = ∫a^b √[1 + (dy/dx)^2] dx . The arc length of a curve is the length of the curve between two points, and it can be calculated using the arc length formula in calculus.

The arc length formula can be used to find the length of a curve in terms of the function that describes the curve.

The arc length formula is given by:

L = ∫a^b √[1 + (dy/dx)^2] dx

where L is the arc length of the curve, a and b are the endpoints of the curve, dy/dx is the derivative of the function that describes the curve with respect to x, and ∫ represents the integral of the function over the interval from a to b.

To use the formula, we first find the derivative of the function that describes the curve, dy/dx. Then we plug this expression into the arc length formula and integrate the expression over the interval from a to b to find the arc length of the curve.

The arc length formula is useful in many applications, such as physics, engineering, and geometry, and it allows us to find the length of a curve even when it is not a straight line.

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The surface area, SA, of the composite figure, obtained from the sums of the areas of the rectangular surfaces is 488 square inches

SA = 488 in.²

A composite figure is a figure that comprises of two or more simpler figures.

The surface area of the composite figure can be calculated as follows;

The area of the rare of the figure = 11 in × 9 in = 99 in²

The area of the four surfaces of the top cuboid = 2 × 3 × 3 + 11 × 3 + 11 × 3 = 84 in²

The area of the exposed surface of the lower cuboid = 6 × 11 + 2 × 6 × 8 + 5 × 11 + 8 × 11 = 305 in²

The surface area, A, of the composite figure is therefore;

A = 99 + 84 + 305 = 488 in²

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The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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a. The linear equation that models the temperature T as a function of the number of chirps per minute N is: T(N) = (1/9)N + 60

b. If the crickets are chirping at 155 chirps per minute, the estimated temperature is approximately 77.22 degrees Fahrenheit.

a. Let's first find the slope of the line using the formula:

slope (m) = (y2 - y1) / (x2 - x1)

where (x1, y1) = (117, 73) and (x2, y2) = (180, 80).

slope = (80 - 73) / (180 - 117)

= 7 / 63

= 1/9

Now, let's use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Using the point (117, 73):

T - 73 = (1/9)(N - 117)

Simplifying the equation:

T - 73 = (1/9)N - (1/9)117

T - 73 = (1/9)N - 13

Now, let's rearrange the equation to solve for T:

T = (1/9)N - 13 + 73

T = (1/9)N + 60

Therefore, the linear equation that models the temperature T as a function of the number of chirps per minute N is: T(N) = (1/9)N + 60

(b) If the crickets are chirping at 155 chirps per minute, we can estimate the temperature T using the linear equation we derived.

T(N) = (1/9)N + 60

Substituting N = 155:

T(155) = (1/9)(155) + 60

T(155) = 17.22 + 60

T(155) ≈ 77.22

Therefore, if the crickets are chirping at 155 chirps per minute, the estimated temperature is approximately 77.22 degrees Fahrenheit.

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