What is the rule to respresent this function?

Answer: $70 per year.

Step-by-step explanation:

Let's say that x is the number of years that has passed and y is how much the stamp is worth.

So we know that in zero years the stamp was worth $420 because that is the time Sheri gave her brother Sam the stamp. That could bring up the coordinates  (0,420) .

Now we know that in 8 years it was worth $980 and that could be the coordinates (8,980)

To find the rate of change we need to find the different between the y value and divide it by the difference in the x values.

420 - 980 = -560

 0-8 = -8

-560/-8 = 70

The rate of change is 70 which means that it grew by $70 every year.

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

3/8 + 3/8 = 6/8 = 3/4

Step-by-step explanation:

3 out of 8. or=+ 3 out of 8

Answer:

150 times

Step-by-step explanation:

Total outcome is 8

Favorable outcome is 6

\(\frac{6}{8}\) = \(\frac{3}{4}\)

\(\frac{3}{4}\) × 200 = 150 times

Answer:

Because when a number is raised to negative indice, it automatically becomes a fraction of 1, with the number raised to the positive indice. If the original expression becomes the other..its still equivalent and equal to the same value-just changed to make solving more easier

Answer:

see expression

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) ⇔ \(\frac{1}{a^{m} }\) , then

\(2^{-4}\)

= \(\frac{1}{2^{4} }\)

Thus

\(2^{-4}\) and \(\frac{1}{2^{4} }\) are equivalent expressions

Answer:

the answer is 2

Step-by-step explanation:

The number of lavender drops should be 2.

Given that,

Based on the above information, the calculation is as follows:

\(= 5 \div \frac{15}{6} \\\\= 5\div 2.5\)

= 2

Therefore we can conclude that the number of lavender drops should be 2.

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Answer:

NMHGJMHBNKJ6T76 5745

Step-by-step explanation:

7657457657776767

Answer:

18.95

Step-by-step explanation:

Answer: 7 students

Step-by-step explanation:

From the question, we are informed that there a camp is divided into2 groups and that there are 14 kids in Camp A and 21 kids in Camp B.

If the camps are divided into groups of equal size, there will be 7 students in a group. This will be gotten from :

Camp A = 14/2 = 7 students

Camp B = 21/3 = 7 students

By using implicit differentiation, the equations of the tangent line and normal line to the curve 2x^3 + 2y^3 = 9xy at the point (2, 1) can be determined.

a. Finding the marginal cost function:

The total cost function C(n) is given by C(n) = 250 + 3n + 20000/n.

To find the marginal cost, we need to find the derivative of the cost function with respect to the number of widgets produced, n.

C'(n) = dC/dn

Differentiating each term of the cost function separately:

dC/dn = d(250)/dn + d(3n)/dn + d(20000/n)/dn

The derivative of a constant term (250) is 0:

d(250)/dn = 0

The derivative of 3n with respect to n is 3:

d(3n)/dn = 3

Using the power rule, the derivative of 20000/n is:

d(20000/n)/dn = -20000/n^2

Therefore, the marginal cost function is:

C'(n) = 0 + 3 - 20000/n^2

= 3 - 20000/n^2

b. Finding C'(1000):

To find C'(1000), we substitute n = 1000 into the marginal cost function:

C'(1000) = 3 - 20000/1000^2

= 3 - 20000/1000000

= 3 - 0.02

= 2.98

c. Finding the cost of producing the 1001st widget:

The cost of producing the 1001st widget is the difference between the cost of producing 1000 widgets and the cost of producing 1001 widgets.

C(1001) - C(1000) = (250 + 3(1001) + 20000/(1001)) - (250 + 3(1000) + 20000/(1000))

Simplifying the expression and evaluating it to several decimal points:

C(1001) - C(1000) ≈ 280.408 - 280.000

≈ 0.408

The cost of producing the 1001st widget is approximately 0.408 dollars. Comparing it to the marginal cost (C'(1000) = 2.98), we can see that the marginal cost is higher than the cost of producing the 1001st widget. This suggests that the cost is increasing at a faster rate as the number of widgets produced increases.

d. Finding the number of widgets per day to minimize production costs:

To find the number of widgets per day that minimizes production costs, we need to find the critical points of the cost function. We can do this by finding where the derivative of the cost function is equal to zero or undefined.

C'(n) = 3 - 20000/n^2

To find the critical points, we set C'(n) = 0 and solve for n:

3 - 20000/n^2 = 0

Solving for n:

20000/n^2 = 3

n^2 = 20000/3

n ≈ √(20000/3)

Evaluating the approximate value of n:

n ≈ 81.65

Therefore, producing approximately 82 widgets per day should minimize production costs.

Implicit Differentiation:

To find the equations of the tangent line and the normal line to the curve 2x^3 + 2y^3 = 9xy at the point (2, 1), we can use implicit differentiation.

Differentiating both sides of the equation with respect to x:

6x^2 + 6y^2(dy/dx) = 9(dy/dx)y + 9xy'

To find the slope of the tangent line, we substitute the point (2, 1) into the derivative equation:

6(2)^2 + 6(1)^2(dy/dx) = 9(dy/dx)(1) + 9(2)(dy/dx)

24 + 6(dy/dx) = 9(dy/dx) + 18(dy/dx)

24 = 27(dy/dx)

(dy/dx) = 24/27

= 8/9

The slope of the tangent line at the point (2, 1) is 8/9.

Using the point-slope form of the line, the equation of the tangent line is:

y - 1 = (8/9)(x - 2)

To find the normal line, we can use the fact that the slopes of perpendicular lines are negative reciprocals.

The slope of the normal line is the negative reciprocal of 8/9:

m = -1/(8/9)

= -9/8

Using the point-slope form of the line, the equation of the normal line is:

y - 1 = (-9/8)(x - 2)

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The area of the parallelogram is 281.91 m²

A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

Therefore, the area of the parallelogram can be found as follows:

area of the parallelogram = bh

where

Therefore, let's find the height of the parallelogram using trigonometric ratios,

sin 70° = opposite / hypotenuse

sin 70° = h / 15

h = 15 sin 70°

h = 15 × 0.9396

h = 14.0953893118

h = 14.1 metres

Therefore,

area of the parallelogram = 14.1 × 20

area of the parallelogram = 281.907786236

area of the parallelogram = 281.91 m²

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Answer:

\(36\)

Step-by-step explanation:

The expression \(_nC_k\) is used to denote the number of ways you can choose \(k\) things from a set of \(n\) things. It is equal to:

\(_nC_k=\binom{n}{k}=\frac{n!}{k!(n-k)!}\)

In this case, \(n=9\) and \(k=2\), so:

\(\implies \frac{9!}{2!(9-2)!}=\frac{9!}{2!7!}=\boxed{36}\)

You can also think of it like this:

\(_9C_2\) is saying 9 choose 2. We are choosing 2 things from a set of 9 things, where order doesn't matter. For the first thing we choose, there are 9 options. Then 8 options, 7, and so on. Since we're only choosing two things, there are \(9\cdot 8=72\) permutations. However, the order of which we choose each thing does not affect what we've chosen overall (e.g. If we're choosing two donut flavors original and strawberry, it doesn't matter which flavor I choose first, because I'm still getting the same two flavors). Therefore, we must divide this by the number of ways we can arrange two distinct values, which is \(2!\). Our answer is thus \(\frac{72}{2!}=\frac{72}{2}=\boxed{36}\)

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

Explanation:

We have 9*8 = 72 different permutations. This is if we used the nPr formula with n = 9 and r = 2.

Notice the countdown from 9 to 8. This is because we don't reuse the same element twice.

Since order doesn't matter with nCr, we will divide by 2. This is because something like AB is the same as BA. So we go from 72 to 72/2 = 36

The value 36 is found in Pascal's Triangle in the row that has 1,9,... at the start of it. Start at the left hand side and count exactly 3 spaces to the right, and you should land on 36.

The height of the flagpole is 12.9 feet to the nearest tenth.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

The boy is 5' 3" tall and his shadow is 4 feet.

The shadow of the flagpole is 17 feet.

The boy is 5.25 feet tall.

Let the height of the flagpole is h feet.

So,

17/h = 5.25/4

h = 68/5.25

h = 12.95

h = 12.9 to one decimal place.

Therefore, h = 12.9 to one decimal place.

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Answer: Yes

Step-by-step explanation: Well 25% off of $20 is $15.

Answer:

Step-by-step explanation:

Take the amount, $4.75, multiplied by x will give you the total amount of money raised and just put that into the equation format:

$4.75 (x) = total amount of money raised

a. In a random sample of 1,000 births, the expected number of births that take place by Caesarian section is:

E(X) = n*p = 1,000 * 0.32 = 320 births

Therefore, on average, 320 births out of 1,000 will take place by Caesarian section.

b. The variance of the number of Caesarian section births in a sample of 1,000 births is:

Var(X) = np(1-p) = 1,000 * 0.32 * (1-0.32) = 217.60

The standard deviation is the square root of the variance:

SD(X) = sqrt(Var(X)) = sqrt(217.60) = 14.76

Therefore, the standard deviation of the number of Caesarian section births in a sample of 1,000 births is 14.76.

c. To form an interval that is likely to contain the number of Caesarian section births in a sample of 1,000 births, we can use the normal distribution and the central limit theorem. Since n*p = 320 is greater than 10, we can assume that the distribution of the number of Caesarian section births in a sample of 1,000 births is approximately normal.

The 95% confidence interval for the number of Caesarian section births is:

320 ± 1.96*(14.76) = (291.16, 348.84)

Therefore, we can be 95% confident that the number of Caesarian section births in a sample of 1,000 births will be between 291 and 349.

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Answer:

To write and solve an inequality that can be used to determine the number of 50-kilogram crates that can be loaded into the shipping container, we need to first find the total weight of the crates that can be loaded into the container. The maximum weight that can be loaded into the container is 27500 kilograms, and other shipments weighing 9500 kilograms have already been loaded, so the total weight of the crates that can be loaded is 27500 kilograms - 9500 kilograms = 18000 kilograms.

Next, we need to divide the total weight of the crates that can be loaded by the weight of each crate to find the number of crates that can be loaded. Since each crate weighs 50 kilograms, the number of crates that can be loaded is 18000 kilograms / 50 kilograms = 360 crates.

To express this as an inequality, we can use the following equation:

x <= 360

This inequality states that the number of crates that can be loaded into the shipping container (x) must be less than or equal to 360. Therefore, the number of 50-kilogram crates that can be loaded into the shipping container is x <= 360.

Step-by-step explanation:

43% of elementary students chose something other than blue, red, or yellow as their favorite color.

Blue: 24%

Red: 17%

Yellow: 16%

Total: 24% + 17% + 16% = 57%

Percentage chose something other:

100% - 57% = 43%.

Therefore, 43% of elementary students chose something other than blue, red, or yellow as their favorite color.

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The constant of proportionality from the proportional relationship is 3/2

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal. In other words, if x and y are in a proportional relationship, then y/x is always equal to a constant value, called the constant of proportionality. This can be expressed mathematically as y = kx, where k is the constant of proportionality and x and y are the variables in the relationship.

To determine the constant of proportionality, we need to use the proportional relationship given.

y = kx

k = constant of proportionality

3/8 = k(1/4)

Solve for k

k = [(3/8) / (1/4)]

k = 3/2

k = 1.5

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Answer: about 43.5298

Step-by-step explanation:

Answer : The probability that a randomly selected teacher earns more than $60,000 is 0.039.

Explanation :

Given data: The average annual salary for all U.S. teachers is $47,750 and standard deviation is $5680.  Now we need to find the following probabilities:

1. The probability that a randomly selected teacher earns less than $42,000.

2. The probability that a randomly selected teacher earns between $40,000 and $50,000.

3. The probability that a randomly selected teacher earns at least $52,000.

4. The probability that a randomly selected teacher earns more than $60,000.

We can find these probabilities by performing the following steps:

Step 1: Press the STAT button from the calculator.

Step 2: Now choose the option “2: normal cdf(” to compute probabilities for normal distribution.

Step 3: For the first probability, we need to find the area to the left of $42,000.

To do that, enter the following values: normal cdf(-10^99, 42000, 47750, 5680)

The above command will give the probability that a randomly selected teacher earns less than $42,000.

We get 0.133 for this probability. Therefore, the probability that a randomly selected teacher earns less than $42,000 is 0.133.

Step 4: For the second probability, we need to find the area between $40,000 and $50,000. To do that, enter the following values: normal cdf(40000, 50000, 47750, 5680) .The above command will give the probability that a randomly selected teacher earns between $40,000 and $50,000. We get 0.457 for this probability.

Therefore, the probability that a randomly selected teacher earns between $40,000 and $50,000 is 0.457.

Step 5: For the third probability, we need to find the area to the right of $52,000. To do that, enter the following values: normalcdf(52000, 10^99, 47750, 5680)The above command will give the probability that a randomly selected teacher earns at least $52,000. We get 0.246 for this probability. Therefore, the probability that a randomly selected teacher earns at least $52,000 is 0.246.

Step 6: For the fourth probability, we need to find the area to the right of $60,000. To do that, enter the following values: normalcdf(60000, 10^99, 47750, 5680)The above command will give the probability that a randomly selected teacher earns more than $60,000. We get 0.039 for this probability. Therefore, the probability that a randomly selected teacher earns more than $60,000 is 0.039.

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The inequality which represents the given phrase is 1/2(3x - 2/3) + 6 ≤  x+5​ and the solution are x ≤ -4/3.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

1/2(3x - 2/3) + 6 ≤  x+5​

3/2 x - 1/3 + 6 ≤  x+5​

3/2 x + 17/3 - x ≤ 5

x/2 ≤ -2/3

x ≤ -4/3

Hence "The inequality 1/2(3x - 2/3) + 6 ≤ x+5 represents the provided sentence, and the answer is x ≤  -4/3.".

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Hello!

-----------------------------------------------------------------------------------------------------------------

b:7

42:7

6

Hope it helps!

~SparklingFlower

-----------------------------------------------------------------------------------------------------------------

Step-by-step explanation:

given

b = 42

given expression,

b ÷ 7 or can be written as b/7

so a/q

42/7 = 6

therefore, 6 is the correct answer.

HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE

Answer:

X=18

Step-by-step explanation:

4.5 x 2=9  9x2 =18

Or 18/4.5-2=2

To find the four second-order partial derivatives of the function f(x, y) = 4x^4y - 5xy + 2y, we first differentiate the function with respect to x and y to obtain the first-order partial derivatives.

The first-order partial derivatives are:

f_x(x, y) = 16x^3y - 5y, and

f_y(x, y) = 4x^4 + 2. Now, we differentiate the first-order partial derivatives with respect to x and y to find the second-order partial derivatives:

1. The second-order partial derivative f_xx(x, y) is obtained by differentiating f_x(x, y) with respect to x:

f_xx(x, y) = (d/dx)(16x^3y - 5y) = 48x^2y.

2. The second-order partial derivative f_xy(x, y) is obtained by differentiating f_x(x, y) with respect to y:

f_xy(x, y) = (d/dy)(16x^3y - 5y) = 16x^3 - 5.

3. The second-order partial derivative f_yx(x, y) is obtained by differentiating f_y(x, y) with respect to x:

f_yx(x, y) = (d/dx)(4x^4 + 2) = 16x^3.

4. The second-order partial derivative f_yy(x, y) is obtained by differentiating f_y(x, y) with respect to y:

f_yy(x, y) = (d/dy)(4x^4 + 2) = 0 (since the derivative of a constant term with respect to y is zero).

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If the budget were to increase to $3000, allowing us to survey many more people from a simple random sample, the test statistic would likely be more accurate and reliable.

As per the given scenario,

if we have a limited budget of $500, we can only survey 50 people from a simple random sample. In order to study the relationship between social class and voting preferences, the budget must be increased to $3000.

On increasing the budget, we can survey more people from a simple random sample, which would lead to a better representation of the population.
Due to the small budget, the test statistic would be less accurate as only a small number of people are being surveyed. However, if the budget increases to $3000, it would allow for a larger sample size and therefore the test statistic would be more accurate.

This would result in a narrower confidence interval and a higher level of confidence in the accuracy of the results.
Moreover, with a larger budget, it would be possible to use more sophisticated sampling techniques such as stratified random sampling, which could further increase the accuracy of the test statistic.

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The general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

Given a recurrence relation tn = 120,-2 - 166n-3 + 2 we have to derive the general solution form for the recurrence sequence.

We have the recurrence relation tn = 120,-2 - 166n-3 + 2

We need to find the solution for the recurrence relation.

Associated Homogeneous Equation: First, we need to find the associated homogeneous equation.

                                     tn = -166n-3 …..(i)

The characteristic equation is given by the following:tn = arn. Where ‘a’ is a constant.

We have tn = -166n-3..... (from equation i)ar^n = -166n-3

                                Let's assume r³ = t.

Then equation i becomes ar^3 = -166(r³) - 3ar^3 + 166 = 0ar³ = 166

Hence r = ±31.10.3587Complex roots: α + iβ, α - iβ

Characteristics Polynomial:

                   So, the characteristic polynomial becomes(r - 31)(r + 31)(r - 10.3587 - 1.7503i)(r - 10.3587 + 1.7503i) = 0

The general solution of the Homogeneous equation:

Now we have to find the general solution of the homogeneous equation.

                  tn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)

                        nWhere C1, C2, C3, C4 are constants.

Computing a Particular Solution:

                Now we have to compute the particular solution.

                                  tn = 120-2 - 166n-3 + 2

Here the constant term is (120-2) + 2 = 122.

The solution of the recurrence relation is:tn = A122Where A is the constant.

The General Solution of Non-Homogeneous Equation:

        The general solution of the non-homogeneous equation is given bytn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)n + A122

Hence, we have derived the general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

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