A company selling widgets has found that the number of items sold, x, depends upon the price, p at which they're sold, according the equation x= 50000/(√4p+1)
Due to inflation and increasing health benefit costs, the company has been increasing the price by $5 per month. Find the rate at which revenue is changing when the company is selling widgets at $290 each.

The perimeter P of rectangle R with a constant area of 4ft² can be expressed as a function of the length l as 2l+8/l. The function is linear, and its domain includes all positive values of l.

Let's consider a rectangle with length l and width w, such that its area is constant at 4ft². The area of a rectangle is given by A = l * w.

In this case, we have A = l * w = 4ft².

To find the perimeter P, we use the formula P = 2l + 2w.

Since we want to express P as a function of the length l, we need to eliminate the variable w. From the area equation, we can solve for w:

w = 4ft² / l.

Substituting this value of w into the perimeter formula, we have:

P = 2l + 2(4ft² / l).

Simplifying further, we get:

P = 2l + 8ft² / l.

This expression represents the perimeter P as a function of the length l. It is a rational function, as it involves the division of polynomials. The domain of this function includes all positive values of l, as length cannot be negative or zero in this context.

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In the context of this poem, people overcome adversity through hope.

Hope is described as a bird with feathers that perches in the soul and never stops singing. It is a source of comfort and solace, heard in the chillest lands and on the strangest seas, even in extremities. Despite the challenges people may face, the presence of hope is enough to keep them warm and to overcome adversity.

In my own experience, hope has been a driving force in overcoming adversity. When faced with challenges, having a positive outlook and focusing on a brighter future can help to overcome difficulties and find resilience.

This idea is echoed in other literature and art, where hope is often depicted as a source of strength and comfort in the face of adversity.

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--The given question is incomplete; the complete question is

"In the context of this poem, how do people overcome adversity? Use evidence from the poem 'hope is the thing with feathers', your own experience, and other literature or art in your answer. The poem is

"Hope" is the thing with feathers

That perches in the soul

And sings the tune without the word

And never stops - at all-

And sweetest in the gale is heard

And sore must be the storm

That could abash the little bird

That kept so many warm

I've heard it in the chillest land

And on the strangest sea

Yet never in extremity.

It asked a crumb of me."--

Answer:

Option C, 93.6 mi³

Step-by-step explanation:

Volume of the triangular prism,

base area × height

= (8×3.9/2)×6

= 93.6 mi³

Answer:

Step-by-step explanation:

The first step makes the figures be same by size but the second step, reflection over line AE doesn't map them together.

Correct line of reflection would be a vertical line through the point D.

First step is fine

But then

It should be reflecting using a line through D

Step 2 is wrong

By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.

To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.

Since a van can ferry a maximum of 12 people, we can write the inequality as:

12v ≥ 80

Now, let's solve for "v":

Divide both sides of the inequality by 12.
v ≥ 80/12

Simplify the inequality.
v ≥ 6.67

Since we cannot have a fraction of a van, we need to round up to the nearest whole number:

v ≥ 7

Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.

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By using two points ont he given graph, we can see that the rate of change is -60 miles per hour

For any line that passes through two points (x₁, y₁) and (x₂, y₂) the rate of change is given by:

r = (y₂ - y₁)/(x₂ - x₁)

Here using the graph we can identify two points, these are:

(0, 120) and (2, 0)

Where the first value is time and the second is distance, then the rate of change will be:

R = (0 - 120)/(2 - 0) = -60

Adding the units, it would be -60 miles per hour.

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The inverse of matrix B is:

     25   -560

     -1     23

To find the inverse of matrix B, we need to perform a series of operations. First, we calculate the determinant of B, denoted as |B|. In this case, |B| = (23 * 0) - (1 * 560) = -560.

Next, we need to find the adjugate of B, denoted as adj(B). The adjugate of a matrix is obtained by taking the transpose of the cofactor matrix. In this case, the cofactor matrix of B is:

      0     560

     -1     23

Taking the transpose of the cofactor matrix gives us the adjugate:

      0    -1

    560    23

Finally, we can find the inverse of B by dividing the adjugate by the determinant:

     0    -1

    -560/(-560)    23/(-560)

Simplifying the fractions, we get:

     0     -1

     1    -23/560

Therefore, the inverse of matrix B is:

     25   -560

     -1     23

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Answer:

Answer = D

Step-by-step explanation:

If you add all of the heights up you get 480. divide that by ten (because there were 10 students whose height was taken) then you get 48. therefore, the typical second-grade student is about 48 inches tall.

I hope this helps have a good day :)

The typical second-grade student is about 48 inches tall.

'Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.'

According to the given problem,

Given data = { 44, 45, 47, 49, 48, 48, 49, 50, 48, 52 }

Sum of the given data = 44 + 45 + 47 + 49 + 48 + 48 + 49 + 50 + 48 + 52

                                     = 480

Average of the given heights = \(\frac{480}{10}\)

                                                 = 48

Hence, we can conclude,  The typical second-grade student is about 48 inches tall since the average of the given data is 48.

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Small market orders copies of a certain magazine for its magazine rack each week. The number of copies to order to generate more revenue is 4.

Let the profit y, the demand for the magazine be x , the number owner ordered k , then we get :

y = 4x - 2m ( m > x)

y = 2m        ( m ≤ x)

If m = 3 we get

E (y) = 1/14 (4 - 2x3) + 2/14 (4x2 - 2x3) + 3/14 (2x3) + 3/14 (2x3) + 2/14 (2x3) + 3/14 (2x3)

E(y) = 68/14

If m = 4 get,

E (y) = 1/14 (4 - 2x4) + 2/14 (4x2 - 2x4) + 3/14 (4x3 -2x4) + 3/14 (2x4) + 2/14 (2x4) + 3/14 (2x4)

E(y) = 72/14

E (y)m=4 > E(y)m=3

So order number is 4.

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The values of x and y in the given system of equations are x = 4.00 and y = 5.00. These values are obtained by solving the system using the method of substitution.

The given system of linear equations is:

0.50x + 0.20y = 3.00 ...(Equation 1)

x + y = 9.00 ...(Equation 2)

To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the method of substitution:

From Equation 2, we can express x in terms of y:

x = 9.00 - y

Substituting this expression for x in Equation 1, we have:

0.50(9.00 - y) + 0.20y = 3.00

Expanding and simplifying:

4.50 - 0.50y + 0.20y = 3.00

-0.30y = -1.50

Dividing both sides by -0.30:

y = -1.50 / -0.30

y = 5.00

Now, substitute this value of y back into Equation 2 to find x:

x + 5.00 = 9.00

x = 9.00 - 5.00

x = 4.00

Therefore, the values of x and y in the given system of equations are x = 4.00 and y = 5.00.

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The programs of engineering corresponding to the given events are as follows: 1. A′ = {electronics, mechanical, electrical, industrial} 2. A∪C = {civil, computer, aeronautical, industrial} 3. (A∩B′)∪C′ = {civil, aeronautical, industrial} 4. B′∩C′ = {} (empty set) 5. (A′∪B′)∩(A′∩C) = {electronics, electrical, industrial}

1.A′ represents the complement of event A, which includes all the programs in the sample space S except those in A. Therefore, A′ = {electronics, mechanical, electrical, industrial}.2.A∪C represents the union of events A and C, which includes all the programs that belong to either A or C. Therefore, A∪C = {civil, computer, aeronautical, industrial}.

3.(A∩B′)∪C′ represents the union of the intersection of A and the complement of B with the complement of C. The intersection of A and B′ includes the programs that are in A but not in B, which are {civil, aeronautical}. The complement of C is {}. Therefore, (A∩B′)∪C′ = {civil, aeronautical}.4.B′∩C′ represents the intersection of the complement of B with the complement of C. The complement of B is {civil, electrical, industrial, aeronautical}. The complement of C is {}. Therefore, B′∩C′ = {} (empty set).

5.(A′∪B′)∩(A′∩C) represents the intersection of the union of the complement of A with the complement of B, with the intersection of the complement of A and C. The complement of A is {electronics, mechanical, electrical, industrial}. The complement of B is {civil, electrical, industrial, aeronautical}. The intersection of the complement of A and C is {industrial}. Therefore, (A′∪B′)∩(A′∩C) = {electronics, electrical, industrial}.
Hence, the programs of engineering corresponding to the given events are as mentioned above.

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Given:

Radius of the circle = 10 in

Central angle of the sector = 45 degrees

To find:

The area of the sector.

Solution:

Area of a sector is

\(A=\dfrac{\theta}{360^\circ}\pi r^2\)

Where, \(\theta\) is the central angle in degrees.

Putting r=10 and \(\theta=45^\circ\), we get

\(A=\dfrac{45^\circ}{360^\circ}\pi (10)^2\)

\(A=\dfrac{1}{8}\pi (100)\)

\(A=12.5\pi\)

Therefore, the area of the sector is 12.5π sq. inches.

The radius of gyration of the plate about the x-axis is \(6 \sqrt{6} / 5\) units.

To find the radius of gyration of a plate covering the region bounded by \(y = x^2\), x = 6, and the x-axis with respect to the x-axis, we need to use the formula:

\(k_x = \sqrt{(I_x / A)}\)

where \(k_x\) is the radius of gyration, \(I_x\) is the moment of inertia of the plate about the x-axis, and A is the area of the plate.

We can calculate the area A of the plate as follows:

\(A = \int\limits^6_0 { x^2}\, dx\\= [x^3/3]\ from\ 0\ to\ 6\\= 72\)

To find the moment of inertia \(I_x\), we can use the formula:

\(I_x = \int\ {y^2} \, dA\)

where y is the perpendicular distance of an element of area \(dA\) from the x-axis. We can express y in terms of x as y = x². Therefore, we have:

\(dA = y dx = x^2 dx\\I_x = \int\limits^6_0 { x^2 (x^2)} dx\\= \int\limits^6_0 {x^4}\, dx\\= [x^5/5]\ from\ 0\ to\ 6\\= 6^5/5\)

Substituting these values into the formula for \(k_x\), we get:

\(k_x = \sqrt{(I_x / A)}\\= \sqrt{((6^5/5) / 72)}\\= \sqrt{(6^3 / 5)}\\= 6 \sqrt{6} / 5\)

Therefore, the radius of gyration of the plate about the x-axis is \(6 \sqrt{6}/ 5\) units.

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Answer:

Below

Step-by-step explanation:

6, 8, 10, 10

Mode = 10

Median = 9

Answer:

A. median

explain i just aced the test rn

Answer:

Angle bisector

Step-by-step explanation:

The line AD bisects both sides of the triangle. Both angles are congruent to each other since both sides are congruent to each other.

a. The probability that X is at most 1 is 0.7627.

b. The probability that X is at least 4 is 0.0146.

c. The probability that X is less than 1 is 0.2373.

These probabilities were calculated using the binomial formula with n=5 and p=0.25.

To calculate the probabilities using the binomial formula, we need to plug in the values of n (the number of trials) and p (the probability of success). In this case, n = 5 and p = 0.25.

a. To find the probability that x is at most 1 (P(X ≤ 1)), we sum the individual probabilities of x = 0 and x = 1. The formula for the probability of exactly x successes in n trials is:

\(P(X = x) = (nCx) * p^x * (1-p)^(^n^-^x^)\)

Using this formula, we calculate the probabilities for x = 0 and x = 1:

\(P(X = 0) = (5C0) * (0.25^0) * (0.75^5) = 0.2373\)

\(P(X = 1) = (5C1) * (0.25^1) * (0.75^4) = 0.5254\)

Adding these probabilities together gives us the probability that x is at most 1:

P(X ≤ 1) = P(X = 0) + P(X = 1) = 0.2373 + 0.5254 = 0.7627

b. To find the probability that x is at least 4 (P(X ≥ 4)), we sum the probabilities of x = 4, 5. Using the same formula, we calculate:

\(P(X = 4) = (5C4) * (0.25^4) * (0.75^1) = 0.0146\\P(X = 5) = (5C5) * (0.25^5) * (0.75^0) = 0.00098\)

Adding these probabilities together gives us the probability that x is at least 4:

P(X ≥ 4) = P(X = 4) + P(X = 5) = 0.0146 + 0.00098 = 0.01558

c. To find the probability that x is less than 1 (P(X < 1)), we only consider the probability of x = 0:

\(P(X = 0) = (5C0) * (0.25^0) * (0.75^5) = 0.2373\)

Therefore, the probability that x is less than 1 is equal to the probability that x is equal to 0:

P(X < 1) = P(X = 0) = 0.2373

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The statistical procedure used to describe the strength and direction of the linear relationship between two factors is called correlation analysis.

Correlation analysis is a statistical technique that examines the relationship between two variables to determine the strength and direction of their association. It focuses specifically on the linear relationship between the variables, which means it assumes that the relationship can be represented by a straight line.

The result of a correlation analysis is often expressed as a correlation coefficient, which measures the degree of association between the variables. The correlation coefficient ranges from -1 to 1, where:

A correlation coefficient of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other variable decreases in a consistent manner.

A correlation coefficient of 1 indicates a perfect positive correlation, meaning that as one variable increases, the other variable also increases in a consistent manner.

A correlation coefficient close to 0 indicates a weak or no linear correlation between the variables.

Correlation analysis helps to understand the relationship between variables and can provide insights into patterns, trends, and dependencies in the data. However, it is important to note that correlation does not imply causation, meaning that a strong correlation between two variables does not necessarily imply that one variable causes the other to change.

In addition to determining the correlation coefficient, correlation analysis can also involve generating a scatter plot to visualize the relationship between the variables and conducting hypothesis tests to assess the statistical significance of the correlation.

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Answer:

y ≥ 9 = -28

y ≥ -28-9

y ≥ -37

Answer:

098765

Step-by-step explanation:

Answer:

no se perdon

Step-by-step explanation:

GG

Answer:

Step-by-step explanation:

Sine ratio: In a right triangle, the side adjacent to an acute angle over the hypotenuse.

Similar polygons: Polygons whose vertices can be matched in a one-to-one correspondence so that corresponding angles are equal and corresponding sides are in proportion.

Tangent ratio: In a right triangle, the side opposite an acute angle over the hypotenuse.

Ratio: The comparison of two numbers by division. The quotient is the ratio of the two numbers.

Projection of a point on a line: The point where a perpendicular through the point to the line intersects the line.

Cosine ratio: In a right triangle, the side adjacent to an acute angle over the hypotenuse.

Geometric mean: For any positive real numbers a, b, and x if then x is called the geometric mean between a and b.

Proportion: In a right triangle, the side opposite an acute angle over the side adjacent to the acute angle.

Projection of a segment on a line: The portion of a line with endpoints that are the projections of the endpoints of the segment.

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If the man invested at 5% interest rate and get an amount of GH¢840, then the amount invested at the beginning in the bank was GH¢16,800.

The "Simple-Interest" is defined as a method of calculating the interest on a principal amount based on a fixed percentage rate and a specific period of time.

⇒ Simple Interest (SI) = Principal Amount (P) × Rate of Interest (R) × Time (T)

Where : P = initial amount invested, R = Rate-of-Interest (in decimal form)

T = Time (in years);

⇒ The interest-rate is = 5% per annum, = 0.05 , and

⇒ total amount in bank at end of year is = GH¢840,

Substituting the values,

We get,

⇒ 840 = P × 0.05 × 1,

⇒ 840 = 0.05×P,

⇒ P = GH¢16,800,

Therefore, the man invested GH¢16,800 in bank.

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Answer:

y is correct but x is not

Step-by-step explanation:

because x+ 118°=180°[ co- interior angle ]

Answer:

A is right answer

Step-by-step explanation:

because - - = +

Answer:

11 and 44

Step-by-step explanation:

let the 2 numbers be x and y ( with x the larger number ), then

x + y = 55 → (1)

3y + 11 = x → ()

substitute x = 3y + 11 into (1)

3y + 11 + y = 55

4y + 11 = 55 ( subtract 11 from both sides )

4y = 44 ( divide both sides by 4 )

y = 11

substitute y = 11 into (1)

x + 11 = 55 ( subtract 11 from both sides )

y = 44

smaller number is 11 and larger number is 44

Answer:

one solution

Step-by-step explanation:

the solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is (1, 2 )

Since there is only 1 point of intersection then there is only one solution.