The ratio table shows the costs for different lengths of silver chain. Find the unit rate in dollars per inch

Length (inches) 16 18 20 22

Cost (dollars) $36.00 $40.50 $45.00 $49.50

The unit rate is $__ per inch.​

The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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The solutions to the equations are:

x = 21,

x = 7,

4 * 7 = 28,

3³ - 2³ = 19, and 30 - 2 = 28.

We have,

x + 7 = 28

To solve for x, we can subtract 7 from both sides of the equation:

x + 7 - 7 = 28 - 7

x = 21

So, the solution to the equation x + 7 = 28 is x = 21.

2x + 14 = 28

To solve for x, we can subtract 14 from both sides of the equation:

2x + 14 - 14 = 28 - 14

2x = 14

Next, we divide both sides of the equation by 2 to isolate x:

2x/2 = 14/2

x = 7

Therefore, the solution to the equation 2x + 14 = 28 is x = 7.

4 * 7 = 28

This equation is already solved.

The product of 4 and 7 is 28.

So, the equation 4 * 7 = 28 is true.

3³ - 2³ = 28

To solve this equation, we need to evaluate the exponentials:

3³ - 2³ = 27 - 8 = 19

Therefore, the equation 3³ - 2³ = 28 is not true; the correct value is 19.

30 - 2 = 28

This equation is already solved.

The difference between 30 and 2 is indeed 28.

So, the equation 30 - 2 = 28 is true.

Thus,

The solutions to the equations are:

x = 21,

x = 7,

4 * 7 = 28,

3³ - 2³ = 19, and 30 - 2 = 28.

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The complete question:

x + 7 = 28

2x + 14 = 28

4 * 7 = 28

3^3 - 2^3 = 28

30 - 2 = 28

The limit of the given expression is 0.

To evaluate the limit of the given expression, we need to use the trigonometric identities and the limit rules.

First, let's rewrite the expression using the trigonometric identities:
limx→0cot5xcsc5x = limx→0(cos5x/sin5x)(1/sin5x)

Next, we can simplify the expression by multiplying the fractions:
limx→0(cos5x/sin5x)(1/sin5x) = limx→0(cos5x/(sin5x)^2)

Now, we can use the limit rule for the product of two functions:
limx→0(cos5x/(sin5x)^2) = limx→0cos5x * limx→0(1/(sin5x)^2)

The first limit is simply the cosine of 0, which is 1:
limx→0cos5x = cos(0) = 1

The second limit is more complicated. We can use L'Hopital's rule to evaluate it. L'Hopital's rule states that if the limit of the quotient of two functions is in the form 0/0 or ∞/∞, then the limit is equal to the limit of the quotient of their derivatives.
limx→0(1/(sin5x)^2) = limx→0(0/(-10sin5xcos5x)) = limx→0(-1/(10sin5xcos5x))

Now we can use the trigonometric identity sin(2x) = 2sinxcosx to simplify the expression:
limx→0(-1/(10sin5xcos5x)) = limx→0(-1/(5sin(10x)))

Finally, we can use the limit rule for the quotient of two functions:
limx→0(-1/(5sin(10x))) = limx→0(-1) * limx→0(1/(5sin(10x))) = -1 * limx→0(1/(5sin(10x)))

The second limit is in the form 0/0, so we can use L'Hopital's rule again:
limx→0(1/(5sin(10x))) = limx→0(0/(50cos(10x))) = limx→0(0/50) = 0

Therefore, the final answer is:
limx→0cot5xcsc5x = 1 * (-1) * 0 = 0

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Answer:

Well, the full question needs to be explained first. It very well is 7.4 miles back to the grocery store.

Step-by-step explanation"

First you have to take the time from home to school, x2 then divided 1.2 because the grocery store is a different coordinate than school, and multiply by your needing.

Answer:

5 < y < 2 This asks for all whole numbers y which are greater than 5 and also less than 2. That's a contradiction so there are no such whole numbers.

Step-by-step explanation:

Answer:

250, 4000, 20250

Step-by-step explanation:

\(\frac{2}{5}a^{4}\)

2/5 × 5^4 = 250

2/5 × 10^4 = 4000

2/5 × 15^4 = 20250

Hope this helps! :)

Answer:

0.21428571428

Step-by-step explanation:

hope it helps

Answer:

3

Step-by-step explanation:

Answer:3

Step-by-step explanation: because half of 6 eggs are need to make 2 loaves so split that in half and you have 3

Answer:

48

Step-by-step explanation:

16+16+16 or 16 x 3

hope it helps <3

Answer:

48 yards

Step-by-step explanation:

To calculate the perimeter you have to add the outline of the triangle together.

16 + 16 + 16 = 48

You can also do 16 × 3 = 48

So, your answer is 48 yards.

Have a great day! :)

Answer:

16 cups

Step-by-step explanation:

In order to find the answer to this question we need to solve it using what we know about unit measurements.

3 cups = 12 oz

\(12\div 3 = 4\)

1 cup = 4 oz

1lb = 16 oz

\(4\times4=16\)

4 cups = 1lb

16 cups = 4lb

=16 cups

Hope this helps.

Answer:

97°

I forgot how to explain. Ah, I'm sorry. Please let me know if it's wrong but I'm sure it's right.

Answer:

5 Batches.

Step-by-step explanation:

5*1/6 = 5/6

To solve the given inequality, first we have to simplify the given inequality.38 < x + 10 After simplification we get, 38 - 10 < x or 28 < x.

The correct option is B.

The given inequality is 38 < 4x + 3 + 7 - 3x. Simplify the inequality38 < x + 10  - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. The given inequality is 38 < 4x + 3 + 7 - 3x. To solve the given inequality, we will simplify the given inequality.

Simplify the inequality38 < x + 10  - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. Combine the like terms on the right side and simplify38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18.So, the answer is  x > 28. In other words, 28 is less than x and x is greater than 28. Hence, the answer is x > 28.

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Answer:

Step-by-step explanation:

102

The option that is not a factor of capacity planning is the option d

d) Proximity to suppliers

The process of ascertaining the production capacity an organization needs in order to meet changing demand for the products and services of the organization is known as capacity planning.

The factors considered in capacity planning are factors which include the capacity measurement approach, the economies of scale, preparedness to deal with the capacity in chunks, and activities towards identifying the best operating level.

Therefore, from the listed options, the option that is not a factor in capacity planning is the option (d) proximity to suppliers

Other aspects of the operations of an organization, such as supply chain management and logistics can be affected by the proximity of suppliers, but the proximity of suppliers is not directly linked to the determination process for the production capacity needed to meet the market demand.

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Where is the Graph.

Step-by-step explanation:

LOL

Answer:

y = -1

Step-by-step explanation:

Right away, you should notice that the y-coordinate is the same between both points. If it's a straight line (which you can assume), that means it's a horizontal line at y = that y-coord, or y = -1 in this case.

Answer:

1: 2

3: 14

10: 56

Step-by-step explanation:

Just a simple equation.

Answer:

5. 7+3=10

6. 5+-2=3

7. -3+6=3

8. -6+1=-5

9. 4+-5=-1

10.6+-9=-3

11. 8+-13=-5

12.-10+3=-7

Answer:

(+7)+ (+3)

==+10

(+5)+(_2)

=+3

(_3)+(+6)

=+3

(_6)+(+1)

=_5

(+4)+(_5)

=_1

(+6)+(_9)

=_3

(+8)+(_13)

=_5

(_10)+(+3)

=_7

Over the past 10 years, you have paid off $1,80,000 - $1,12,681 = $67,319 of the original loan.

This amount represents the reduction in the loan balance over the years. It is essential to consider that your monthly payments were not entirely directed towards the loan principal; a portion went towards paying interest charges. As a result, the loan balance was gradually reduced over time.

The interest on the loan accumulated each month, which affected the allocation of your payments. Initially, a significant portion of your payments likely went towards interest, with a smaller fraction reducing the principal balance. However, as time progressed, the interest portion decreased, and more of your payments started chipping away at the loan's principal.

It is crucial to recognize the impact of interest on loans, especially over extended periods. The difference between the current value of your house and the remaining loan balance illustrates the progress you have made in building equity over the years. As you continue making payments, the loan balance will further diminish, and your equity will continue to grow.

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The number 72 is the initial height of the ball before being launched into the sky that is option A is correct.

The function h(t) = −16t² + 110t + 72 is about the equation of height of the ball when it is thrown from the ground. The ball will follow a projectile path and then fall on the ground again.

Now the equation is h(t) = −16t² + 110t + 72 where h(t) is height as a function of time and t is time.

If we put t = 0, then

h(0) = -16(0) + 110(0) + 72

h(0) = 72

that is the height at time t = 0 which is the initial height of the ball before it is thrown.

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Complete Question:

The function h(t) = −16t² + 110t + 72 models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?

A) The initial height, in feet, of the object

B) The maximum height, in feet, of the object

C) The initial speed, in feet per second, of the object

D) The maximum speed, in feet per second, of the object

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Step-by-step explanation:

sorry i sent the wrong image hold on

Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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The number of fliers that she has still not broadcasted will be 48 fliers.

Algebra is the study of ideational characters, while logic is the manipulation of all those opinions.

Linda had 90 fliers to post around town. Last week, she posted 1/5 of them. Then the number of fliers staying is given as,

⇒ (1 - 1/5) x 90

⇒ (4/5) x 90

⇒ 72 fliers

This week, she posted 1/3 of the remaining fliers. Then the number of fliers that she has still not broadcasted is given as,

⇒ (1 - 1/3) x 72

⇒ (2/3) x 72

⇒ 48 fliers

The number of fliers that she has still not broadcasted will be 48 fliers.

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Answer:

$550

Step-by-step explanation:

Answer:

The restaurant would take in $550 by selling 100 burritos

Step-by-step explanation:

First, we need to add all the expenses together and multiply by 100

1.50 + 1.00 = 2.50

2.50 x 100= 250

We know that the restaurant would charge $800 in total for the 100 burritos so now we subtract what it costs to make them.

800 - 250 = 550

Our final answer would be $550

Step 1: Multiply a and c

a = 1

c = 20

a * c = 20

Step 2: Find factors of +20 that add up to +9

Factors of 20 = 1, 2, 4, 5, 10, 20

The two factors that add up to 9 are 4 and 5.

Step 3: Factor

(x + 4)(x + 5) = 0

Answer: (x + 4)(x + 5) = 0

Hope this helps!

Answer:

$100

Step-by-step explanation:

From the question, we are given the following

Rental price of the truck

percentage off coupon = 50%

Required

Sale tax of the truck rental

Sale tax of the truck rental = 50% of the truck price

Sale tax of the truck rental = 50% of $200

Sale tax of the truck rental = 50/100 * 200

Sale tax of the truck rental = 0.5 * 200

Sale tax of the truck rental = $100

Hence the sale tax of the truck rental is $100