The Mean Value Theorem: If f is continuous on a closed interval (a,b) and differentiable on (a,b), then there is at least one point c in (a,b) such that f'(a) f(b) – f(a) b-a (a) (3 points) The dist

Answer:

If r=0, there is absolutely no relationship between the two variables.

Step-by-step explanation:

Inverse function:

f(x)= 9x - 14

Put y for f(x) and solve for x

y = 9x-14

Solve for x:

y-14=9x

(y-14)/9 =x

Answer:

A) A = 275 + 125x

B) 1850 - 100x

C) 7 months

D) 13 months

Step-by-step explanation:

He has $275 saved.

He plans to save $125 each month.

We are told that the computer is currently $1,850

And the price drops $100 each month.

Thus;

A) If x represents the number of months, then equation of the amount he will save is;

A = 275 + 125x

B) If x represents the number of months, then equation to represent the total cost is;

1850 - 100x

C) To find the Number of months he will need to save, we will equate gotten in question A to the equation gotten in question B. Thus;

275 + 125x = 1850 - 100x

Rearranging;

125x + 100x = 1850 - 275

225x = 1575

x = 1575/225

x = 7 months

D) If the price doesn't drop like he is anticipating, then the cost will still be $1850. Thus;

275 + 125x = 1850

125x = 1850 - 275

125x = 1575

x = 1575/125

x = 12.6 months

Approximating to the nearest whole number gives 13 months

The directional derivative of the function f(x, y) = 3ex sin y at the point (0, π/3) in the direction of the vector v = <0, -5, 12> is -15/26.

To find the directional derivative of a function f(x, y) at a point (a, b) in the direction of a unit vector v = <u, v>, we use the following formula:

Dv(f)(a, b) = ∇f(a, b) · v

where ∇f(a, b) is the gradient of f(x, y) at the point (a, b). The gradient is a vector that points in the direction of the steepest increase of the function and has a magnitude equal to the rate of change of the function in that direction.

In this problem, our function is f(x, y) = 3ex sin y, and the point is (0, π/3). The gradient of the function is:

∇f(x, y) = <∂f/∂x, ∂f/∂y> = <3ex sin y, 3ex cos y>

Evaluating the gradient at the point (0, π/3), we get:

∇f(0, π/3) = <3e0 sin (π/3), 3e0 cos (π/3)> = <0, 3/2>

Next, we need to find the unit vector in the direction of v = <0, -5, 12>. To do this, we first find the magnitude of v:

|v| = √(0² + (-5)² + 12²) = 13

Then, we divide v by its magnitude to get the unit vector:

u = v/|v| = <0, -5/13, 12/13>

Finally, we can use the formula for the directional derivative to find Dv(f)(0, π/3):

Dv(f)(0, π/3) = ∇f(0, π/3) · u = <0, 3/2> · <0, -5/13, 12/13> = -15/26

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The measure of ∠Z1 is 135°. We used parallel lines and transversals to find the answer by recognizing that corresponding angles are equal and that adjacent angles on a straight line sum up to 180°.

In order to find the measure of ∠Z1, we will use the fact that line p is parallel to line q and the properties of parallel lines and transversals. Here's the step-by-step explanation:

1. Extend both lines between the parallel lines p and q, as suggested in the clue. This creates a transversal line intersecting both parallel lines.
2. Identify the given angles: 45° and 30°.
3. Since line p is parallel to line q, the corresponding angles are equal. So, the angle on line q that corresponds to the 45° angle on line p will also be 45°.
4. Now, ∠Z1 and the 45° angle on line q are adjacent angles and together they form a straight angle (180°) because they are on the same side of the transversal and between the parallel lines p and q.
5. To find the measure of ∠Z1, use the straight angle property: ∠Z1 + 45° = 180°.

Solving for ∠Z1, we get:
∠Z1 = 180° - 45° = 135°.

Therefore, the measure of ∠Z1 is 135°. We used parallel lines and transversals to find the answer by recognizing that corresponding angles are equal and that adjacent angles on a straight line sum up to 180°.

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

3.0

Step-by-step explanation:

0.8 times -3 = -2.4

5.4-2.4=3.0

So the answer is 3.0

On solving the provided question, we can say that - by percentage we have what was the total number of products that joey sold, x= 30

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. Occasionally, the acronyms "pct.," "pct," and "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. It lacks any measurement devices. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 questions on an exam (75/100). Divide the money by the total and multiply the result by 100 to calculate percentages. The formula for calculating the percentage is (value/total) * 100%.

market affairs = 70 %

website sales = 30 %

difference = 70-30 = 40 %

40% = 12

100% = x

100/40 = x/12

5/2 = x/12

2x = 60

x = 30

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Step-by-step explanation:

\(5p = 35\)

Divide both sides of the equation by 5

\( \frac{5p}{5} = \frac{35}{5} \)

Simplify

\(5p \div 5 = p \\ 35 \div 5 = 7 \\ p = 7\)

Answer:

p = 7

Step-by-step explanation:

5 × p = 35.

35÷ 5 = 7

p=7

Answer:

Number 2

Step-by-step explanation:

I can explain if needed to, since you said asap ill tell u the answer rq

Part a:  What quantity order size would minimize the total annual inventory cost? Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying Cost At minimum Total Annual Inventory Cost, the formula for the Economic Order Quantity (EOQ) is used. EOQ formula is given below: EOQ = sqrt((2DS)/H)Where, D = Annual DemandS = Ordering cost

The company should place an order for 168 boxes at a time in order to minimize the total annual inventory cost.Part b: Determine the minimum total annual inventory cost.Using the EOQ, the company can calculate the minimum total annual inventory cost. The Total Annual Inventory Cost formula is:Total Annual Inventory Cost = Annual Ordering Cost + Annual Carrying CostAnnual Ordering Cost = (D/EOQ) × S = (16,800/168) × $60 = $6,000Annual Carrying Cost = (EOQ/2) × H = (168/2) × $30 = $2,520Total Annual Inventory Cost = $6,000 + $2,520 = $8,520Therefore, the minimum Total Annual Inventory Cost would be $8,520.Part c: Would you recommend the manager to use your quantity from part (a) rather than 300 boxes? Justify your answer (by determining the total annual inventory cost for 300 boxes)

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5 km = 5000 meters

66 minutes = 3960 seconds

Meters per second = 5000/3960 = 1.26

The answer is A.1.26

Answer:

the y intercept is five

Step-by-step explanation:

the line crosses the y axis at 5

Answer:

5

Step-by-step explanation:

The y intercept is where the line will cross the plane from one quadrant to another, and the number the line crosses on is the y int. Hope i helped :D

acknolegde requirements:

straight line.(horizontol or vertical? i dunno)

passes through 3,3

perpindicular to y=-x-4

perpidicular lines have negative recipricals

-1 ---- 1

y-3= 1(x-3)

y-3=x-3

cancel out

y=x

Answer:

30°

Step-by-step explanation:

x = 180° -60°-90° = 30°

Step-by-step explanation:

1 more time solve and answer is ready

Answer:

16.25

Step-by-step explanation:

6.5 + 5 = 32.5/2 = 16.25

The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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The amount you could save per month would be 25% of your discretionary money.

Discretionary income is the money you have left over after paying taxes and necessary cost-of-living expenses.

The formula for discretionary money is: Discretionary money = Realized income - Fixed expenses. Inputting data, we have: Discretionary money = $3,543.22 - Fixed expenses

Amount to be saved = 25% of discretionary money

Amount to be saved = 0.25 * (Realized income - Fixed expenses)

Therefore, the amount savable is calculated as 0.25 times the difference between your realized income and fixed expenses.

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Answer:

Step-by-step explanation:

7(3+4y)-15y=73

21 plus 28y-15y=73

21 plus 13y = 73

13y=51

y=4

Step-by-step explanation:

Step 1: Multiply the 7 into the bracket.(make sure that your signs are correct)

Step 2: Minus the 21 from the 73.( Because when you take a value over the equal sign the value's sign changes)

Step 3: Minus 15y from 28y.

Step 4: Divide 52 by 13( because when you take the 13 over it divides ,because on the other side lf the equal the 13 multiples with the y)

Answer:

22

Step-by-step explanation:

Answer:

6:5

Step-by-step explanation

boys : girls

= 18 : 15

Now time to simplify:

18/3: 15/3

= 6:5

The equation of the linear function is:

z = 10 + 4x + 6y

To find the equation of the linear function, we need to determine the values of c, m, and n in the function z = c + mx + ny.

Since the graph of the function intersects the xz-plane at z = 4x + 10 and the yz-plane at z = 6y + 10, we can use these equations to find the values of c, m, and n.

When the graph intersects the xz-plane (y = 0), we have:

z = c + mx + n(0) = c + mx

Comparing this with z = 4x + 10, we can equate the coefficients:

c = 10 (the constant term)

m = 4 (the coefficient of x)

When the graph intersects the yz-plane (x = 0), we have:

z = c + m(0) + ny = c + ny

Comparing this with z = 6y + 10, we can equate the coefficients:

c = 10 (the constant term)

n = 6 (the coefficient of y)

Therefore, the equation of the linear function is:

z = 10 + 4x + 6y

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Answer:

The correct option is;

69 cm

Step-by-step explanation:

The z-score, or standard score is a measure of how far a data is from the mean

The z-score, is given by the relation;

\(z = \dfrac{x- \mu}{\sigma}\)

Z = Standard score

x = Value observed

μ = The mean height of the plants = 52.5 cm

σ = Standard deviation = 7.2 cm

Given that the z-score = 2.25, we have;

\(2.25 = \dfrac{x- 52.5}{7.2}\)

Therefore, x = 7.2 × 2.25 + 52.5 = 68.7 cm ≈ 69 cm

Therefore, the minimum required height for this type of plant to be displayed in the main lobby is 69 cm.

Answer:

y = f(x) = a + bx

Step-by-step explanation:

Step-by-step explanation: A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the gradient of the line, and b represents the y-axis intercept (which is sometimes called the vertical intercept).

To find C the Pythagorean formula is used which would be = 7.6

The formula for the Pythagorean theorem is given as follows:

c² = a²+b²

where;

a = 7

b = 3

C = ?

c² = 7²+3²

c² = 49+ 9

c² = 58

C= √ 58

C = 7.6

Therefore, when the Pythagorean formula is being used, the value of the missing side of the triangle = 7.6.

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The hypotenuse of the right triangle is:

C = 7.6

On the image we can see a right triangle where C is the hypotenuse of said triangle.

Remember the Pithagorean's theorem, it says that if A and B are the two legs of the right triangle, then C can be written as:

C = √(A² + B²)

Here we can see that:

A = 3

B = 7

Replacing that we will get:

C = √(3² + 7²) =7.6

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The perimeter of the quadrilateral is approximately 50.47 units

Given the vertices of the quadrilateral: H(– 4,6), I(4,9), J(2,3), K(7, – 4).

Let us calculate the distances of HI , IJ , JK and KH

\({\displaystyle HI={\sqrt {(4-(-4))^{2}+(9-(6))^{2}}}.}\)

or, HI = 17 units

\({\displaystyle IJ={\sqrt {(2-(4))^{2}+(3-(9))^{2}}}.}\)

or, IJ = 10

\({\displaystyle JK={\sqrt {(7-(2))^{2}+(-4-(3))^{2}}}.}\)

or, JK = √74 = 8.602... ≈ 8.60

\({\displaystyle KH={\sqrt {(7-(-4))^{2}+(-4-(6))^{2}}}.}\)

or, KH = √221 = 14.866... ≈ 14.87

Now perimeter = HI + IJ + JK + KH

or, perimeter = 8.60 + 14.87 + 10 + 17 = 50.47 units.

Therefore the perimeter of the quadrilateral is 50.47 units.

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