Calculate the consumers' surplus (in dollars) at the indicated unit price p for the demand equation.
p = 8 − 2q^1⁄3; p = 4

Answer:

A

Step-by-step explanation:

Two vertical then probably two horizontal

Answer:

C

Step-by-step explaintion:

Answer:

y = x + 2

Step-by-step explanation:

We start by writing the coordinates pair

(x, f(x))

So we have;

(5,7) and (-2,0)

We start by getting the slope;

m = y2-y1/x2-x1

m = 0-7/-2-5 = -7/-7 = 1

The equation of a linear equation has the general form;

y = mx + c

m is the slope and c is the y-intercept

y = x + c

to get the value of c, we make a simple substitution

we can use the x and y values of any point

7 = 5 + c

c = 7-5

c = 2

So the equation is;

y = x + 2

The solution to the equation using the completing the square are 2 and -3

These are equation that has a leading degree of 2. Given the equation below

-x^2 +x+6=0

This can also be written as

x^2-x-6 = 0

Complete the square

x^2-x = 6

x^2-x+ (1/2)^2 = 6 + (1/2)^2

(x-1/2)^2 = 6 + 1/4

(x+1/2)^2 = 25/4

x+1/2 = ±√25/4

x = 5/2 -1/2  or -5/2-1/2

x = 4/2  or -6/2

x = 2 and -3

Hence the solution to the equation using the completing the square are 2 and -3

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Answer:

Step-by-step explanation:

Given function:

The vertex is (2, 3)

We know the vertex form:

Substitute coordinates to get:

Compare with given to find out:

The number of nickels and dimes that Ariana has are 58 and 91

Linear Equation:

The polynomial equation with 1 degree representing an unknown quantity is known as a Linear equation. Here to represent the unknown quantity we will use variables like x, y, z .... etc.

From the given problem,

The amount that Ariana = $12.00

As we know 1 dollar = 100 cents

⇒ $12.00 = 12 × 100 = 1200 cents  

Total number of nickels and dimes = 149

Since we don't know the number of nickels and dimes we will represent them with variables x and y respectively.

The amount of x nickels coins

= x × 5 cents = 5x cents   [ ∵ nickels = 5 cents ]  

The amount of y dimes coins

= y × 10 cents = 10y cents   [ ∵ dimes = 10 cents ]  

From the above calculations the equation that can be formed

Total amount that Ariana is 5x + 10y = 1200 cents

=> x + 2y = 240 ----- Equation (1)  

Total number of coins is  x + y = 149 ----- Equation (2)    

Now solve (1) and (2) to find the number of each coin  

Do (1) - (2)

=> x + 2y - [ x + y ] = 240 - 149

=> x + 2y - x - y  = 91  

=> y  = 91      

Substitute y = 91 in Equation (2)      

(2) => x + 91 = 149

=> x = 58

The number of nickels and dimes that Ariana has are 58 and 91

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3,4,5 is correct

as we know that ,

3² + 4² = 5²

9 + 16 = 5²

25 = 25

hence . 3,4,5 is correct

Answer:

I'm pretty sure it's 3,4,5 but I'm not sure (is it in cm,mm etc?)

Answer:

40

Step-by-step explanation:

8x = 56

8x + 16 = 40

x = 3

8x = 24

x = 7

8x – 16 = 40

8(x – 2) = 40

Answer:

2nd option

Step-by-step explanation:

Using the power rule

\(\frac{d}{dx}\) (a\(x^{n}\) ) = na\(x^{n-1}\)

Given

f(x) = \(\frac{3}{2\sqrt[3]{x} }\) = \(\frac{3}{2x^{\frac{1}{3} } }\) = \(\frac{3}{2}\) \(x^{-\frac{1}{3} }\) , then

f'(x) = - \(\frac{1}{3}\) × \(\frac{3}{2}\) \(x^{-\frac{4}{3} }\)

      = - \(\frac{1}{2}\) × \(\frac{1}{x^{\frac{4}{3} } }\)

      = - \(\frac{1}{2x^{\frac{4}{3} } }\) = - \(\frac{1}{2\sqrt[3]{x^4} }\) [ Note there should be a leading negative ]

Answer:

The number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.

Step-by-step explanation:

We will use the sin function for the height of the Ferris wheel.

\(y=A\ sin(B(x+C))+D\)

A = amplitude

C = phase shift

D = Vertical shift

2π/B = period

From the provided information:

A = 15/2 = 7.5 m

\(Period=2\\\\\frac{2\pi}{B}=2\\\\B=\pi\)

Compute the Vertical shift as follows:

D = A + Distance of wheel from ground

   = 7.5 + 1

   = 8.5

The equation of height is:

\(h(t)=7.5\cdot sin(\pi (t+C))+8.5\)

Now at t = 0 the height is, h (t) = 1 m.

Compute the value of C as follows:

\(h(t)=7.5\cdot sin(\pi (t+C))+8.5\)

\(1=7.5\cdot sin(\pi (0+C))+8.5\\\\-7.5=7.5\cdot sin\ \pi C\\\\sin\ \pi C=-1\\\\\pi C=sin^{-1}(-1)\\\\\pi C=\frac{3\pi}{2}\\\\C=\frac{3}{2}\)

So, the complete equation of height is:

\(h(t)=7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5\)

Compute the number of minutes of the ride that are spent higher than 15 meters above the ground as follows:

h (t) ≥ 15

\(h(t)=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))+8.5=15\\\\7.5\cdot sin(\pi (t+\frac{3}{2}))=6.5\\\\sin(\pi (t+\frac{3}{2}))=\frac{6.5}{7.5}\\\\(\pi (t+\frac{3}{2}))=sin^{-1}[\frac{13}{15}]\\\\\pi (t+\frac{3}{2})=60.074\\\\t+\frac{3}{2}=19.122\\\\t=17.622\\\\t\approx 18\)

Thus, the number of minutes of the ride that are spent higher than 15 meters above the ground is 18 minutes.

The normality assumption is valid.

The librarian can proceed to create a confidence interval for the population proportion of students in the school who have read the book.

The school librarian has a goal of estimating the proportion of students in the school who have read a particular book. The librarian sampled 50 students from the senior English classes, and out of those 50 students, 35 of them had read the book.

The question at hand is whether the conditions for creating a confidence interval for the population proportion have been satisfied.

Firstly, it is essential to establish that the sample was selected at random.

According to the question, this has been done.

It is a crucial condition because it helps to avoid bias in the sample.

If the sample had not been selected at random, there would be a risk of under- or over-representing certain groups, leading to an inaccurate estimation of the proportion of students who have read the book.

Secondly, sampling distributions of proportions are modeled with the normal model.

This condition has been met because the sample size (50 students) is greater than or equal to 30.

When the sample size is this large, the sampling distribution of proportions can be approximated to the normal distribution.

The normality assumption is valid when the sample size is large enough to satisfy the rule of thumb of np≥10 and nq≥10.

Thus, both conditions for creating a confidence interval for the population proportion have been met.

The sample was selected at random, and the sample size is greater than or equal to 30.

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Answer:

PR = 7.9

Step-by-step explanation:

By sine rule:

\( \frac{12.5}{ \sin \: 66 \degree} = \frac{PR}{ \sin \: 37 \degree} \\ \\ \frac{12.5}{ 0.9135454576} = \frac{PR}{ 0.6018150232} \\ \\ PR = \frac{12 \times 0.6018150232}{0.9135454576} \\ \\ PR = \frac{12 \times 0.6018150232}{0.9135454576} \\ \\PR = \frac{7.22178028}{0.9135454576} \\ \\ PR = 7.90522269 \\ \\ PR \approx \: 7.9\)

Step-by-step explanation:

I've been a substitute for a few day for College students so the answer is y equal s x2-5x+2

Answer: The comparison "3.4 < 3.36" is reasonable because 3.36 is greater than 3.4.

The decimal point separates the whole number part of a number from the fractional part. In this case, 3.36 has a greater whole number part (3) than 3.4, and both have the same decimal part (0.36). So, 3.36 is greater than 3.4.

Therefore, the statement "3.4 < 3.36" is a true and reasonable comparison.

Step-by-step explanation:

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

y=-5/2x+(Any number)

Step-by-step explanation:

First, find the slope of that line

3+2=5

-5+7=2

5/2 is the slope

Perpendicular lines have the slope that is opposite and a fliped sign

This means that the slope should be -2/5

The equation of the line would be y=-5/2x+(Any number)

Answer: 21 units²

Step-by-step explanation:

Since there is a pair of parallel sides, this figures is a trapezoid. The formula for the area of a trapezoid is \(\frac{1}{2}(a+b)h\), where a and b are the parallel sides and h is the height.

Here, a and b are 5 and 9, while 3 is the height. Let's put all 3 values into the formula.

\(A=\frac{1}{2}(5+9)*3\)

\(A=\frac{1}{2}(14)*3\) [Adding in the parentheses]

\(A=7*3\) [Multiplying one-half by 14]

\(A=21\) [Multiplying 7 and 3]

The area is 21 units².

Answer:

70 degrees.

Step-by-step explanation:

They are vertical angles, and vertical angles are always congruent.

Answer:

The minimum income level for this target group is of $51,253.6.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of $41,182 and a standard deviation of $11,990

This means that \(\mu = 41182, \sigma = 11990\)

Find the minimum income level for this target group.

The 100 - 20 = 80th percentile, which is X when Z has a p-value of 0.8, so X when Z = 0.84.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.84 = \frac{X - 41182}{11990}\)

\(X - 41182 = 0.84*11990\)

\(X = 51253.6\)

The minimum income level for this target group is of $51,253.6.

the 95% confidence interval for Mike's set of data is (65.89, 70.97). This means we can be 95% confident that the true population mean falls within this interval.

To find the 95% confidence interval for Mike's set of data, we first need to calculate the sample mean and the standard error of the mean:

Sample mean = (65 + 71 + 74 + 61 + 66 + 70 + 72) / 7 = 68.43

Standard error of the mean = sample standard deviation / sqrt(sample size) = 4.577 / sqrt(7) = 1.732

Next, we can use the formula for the confidence interval:

Confidence interval = sample mean ± (critical value) × (standard error of the mean)

The critical value for a 95% confidence interval with 6 degrees of freedom (n-1) is 2.015.

Plugging in the values, we get:

Confidence interval = 68.43 ± 2.015 × 1.732

Confidence interval = (65.89, 70.97)

what is mean?

In mathematics, the mean is a measure of central tendency of a set of numerical values. It is commonly known as the average, which is obtained by summing up all the values in a data set and dividing by the total number of values. The mean provides an overall idea of the "typical" value in a data set, and is widely used in statistics and data analysis.

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Answer:

Step-by-step explanation:

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

ln

(

6

x

)

=

ln

(

66

)

Expand

ln

(

6

x

)

by moving

x

outside the logarithm.

x

ln

(

6

)

=

ln

(

66

)

Divide each term by

ln

(

6

)

and simplify.

Tap for more steps...

x

=

ln

(

66

)

ln

(

6

)

The result can be shown in multiple forms.

Exact Form:

x

=

ln

(

66

)

ln

(

6

)

Decimal Form:

x

=

2.33829083

…

Answer:

X=19

Step-by-step explanation:

A full line must be 180 degrees and you already know that part of the line is 66 degrees. You do 180 minus 66 which gives you 114. That is the other unknown angle but it is asking for x, not the angle. You do 114 divided by 6 to get 19. Therefore, x=19.

Answer:

(-12+6+7+12-6+1)÷ 6

=8÷6

=1.3333

lim sin(pi/3+h) - sin(pi/3)/ h as h approaches 0 is  Non existent. The correct answer is option e.

To evaluate the limit, we can use the formula for the derivative of sin(x), which is:

lim f(x+h) - f(x) / h as h approaches 0 = f'(x)

where f(x) = sin(x).

So, in this case, we have:

lim sin(pi/3+h) - sin(pi/3) / h as h approaches 0

which can be rewritten as:

lim [sin(pi/3+h) - sin(pi/3)] / h as h approaches 0

Using the identity for the difference of two sines, we can simplify this expression to:

lim [2cos(2pi/6+h/2)sin(h/2)] / h as h approaches 0

Now, we can cancel out the factor of sin(h/2) in the numerator and denominator, and we are left with:

lim 2cos(2pi/6+h/2) / h as h approaches 0

We can evaluate the limit using direct substitution, and we get:

2cos(pi/3) / 0

Since the denominator is 0, the limit does not exist. Therefore, the answer is option E: Nonexistent.

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Answer:

a) The area of the triangle AQB is 43 square centimeters.

b) The length of the line segment AQ is approximately 14.866 centimeters.

Step-by-step explanation:

a) The procedure consist in subtracting the areas of triangles APQ, ASB and BRQ of the area the rectangle, that is to say:

\(A = (9\,cm)\cdot (14\,cm) - \frac{1}{2}\cdot (5\,cm)\cdot (14\,cm) - \frac{1}{2}\cdot (8\,cm)\cdot (9\,cm) -\frac{1}{2}\cdot (4\,cm) \cdot (6\,cm)\)

\(A = 43\,cm^{2}\)

The area of the triangle AQB is 43 square centimeters.

b) The length of the line segment AQ is determined by Pythagorean Theorem:

\(AQ = \sqrt{AP^{2}+PQ^{2}}\) (1)

\(AQ = \sqrt{(5\,cm)^{2}+(14\,cm)^{2}}\)

\(AQ \approx 14.866\,cm\)

The length of the line segment AQ is approximately 14.866 centimeters.

Answer:

C. g(x) = x^2 + 3

Step-by-step explanation:

Answer:

$430

Step-by-step explanation:

Let the weekly income be x

Money spent on food= $86

% of weekly income spent on food = 20

20% of weekly income in terms = 20/100 * x = x/5

This, income is equal to $86 as given

thus,

x/5 = 86

x = 86*5 = 430

Thus, weekly income is $430.

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The two unit vectors are (2/5 +√5/10, 3/10 + 2√5/15) and (2/5 -√5/10, 3/10 - 2√5/15).

Given that, Angle = 60°, v = 8, 6

Consider unit vector a = (x, y)

x² + y² = 1 …. (1)

Now apply the dot product of unit vector with v

a.v = |a||v|cos Ø

a.v = √ (x² + y²) √ (8² + 6²) cos 60º

8x + 6y = 1 × 10 × ½

So we get,

8x + 6y = 5 …. (2)

y = (5 - 8x) / 6

Substituting the value of y in equation (1)

x² + y² = 1

x² + [(5 - 8x)/6]² = 1

x² + 25/36 + 16x²/9 - 20x/9 = 1

25x²/9 - 20x/9 = 11/36

So we get,

4 × (25x² - 20x) = 11

100x² - 80x = 11

100x² - 80x - 11 = 0

Now solve the quadratic equation,

x = { 2/5 ± √5/10}

Substituting the value of x in equation (2)

y = 3/10 ± 2√5/15

Therefore, the two unit vectors are (2/5 +√5/10, 3/10 + 2√5/15) and (2/5 -√5/10, 3/10 - 2√5/15).

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Step-by-step explanation:

To calculate the minimum number of days required to finish this project, we need to use the critical path method (CPM), which involves identifying the longest sequence of dependent tasks and their durations.

First, we need to draw the network diagram for the project:

```

|---(T1-8)---(T3-10)---|

(T2-6) (T5-12)

| / |

|---(T4-7)---(T6-15)---|

```

Next, we need to calculate the earliest start time (EST), earliest finish time (EFT), latest start time (LST), and latest finish time (LFT) for each task. For the starting task, EST = 0 and EFT = 0.

```

EST EFT LST LFT

T1 (8 days) 0 8 22 30

T2 (6 days) 0 6 6 12

T3 (10 days) 8 18 22 32

T4 (7 days) 18 25 25 32

T5 (12 days) 18 30 32 44

T6 (15 days) 32 47 32 47

```

The critical path is the longest sequence of dependent tasks that have no slack (i.e., the difference between LST and EST, or LFT and EFT, is zero). In this case, the critical path is T1-T3-T5-T6.

Therefore, the minimum number of days to finish this project is the sum of the durations of tasks on the critical path:

8 + 10 + 12 + 15 = 45 days

Therefore, the minimum number of days required to finish this project is 45 days.