Type the correct answer in the box.
Diagram shows a small square inscribed in a large square such that its vertices lie on large square sides forming 4 right triangles. One right triangle (left) base as b. The other right triangle (right) base as a, vertical leg as b, hypotenuse as c.

In the figure, a square is inside another bigger square.

If a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is
units and the length of the diagonal of the inside square rounded to the nearest tenth is
units.

The earnings on an $18,500 savings account vary based on the compounding frequency. Annual compounding yields the highest earnings of $232, followed by quarterly, monthly, and daily compounding with earnings of $17.22, $3.32, and $0.60 respectively.

To compute the earnings for the year on a savings account, we can use the formula for compound interest:

A = \(P(1 + r/n)^{(n\times t)}\)

Where:

A = the total amount (including the principal and earnings)

P = the principal amount (initial savings)

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the number of years

Given:

P = $18,500

r = 1.2% = 0.012

(a) Annually:

n = 1 (compounded once a year)

t = 1 year

A = \(18,500(1 + 0.012/1)^{(1 \times 1)} - 18,500\)

= 18,500(1.012) - 18,500

= 18,732 - 18,500

= $232

The earnings for the year on an annual compounding basis are $232.

(b) Quarterly:

n = 4 (compounded four times a year)

t = 1 year

A = \(18,500(1 + 0.012/4)^{(4 \times 1)} - 18,500\)

= 18,500(1.003)⁽⁴⁾ - 18,500

= 18,517.22 - 18,500

= $17.22

The earnings for the year on a quarterly compounding basis are $17.22.

(c) Monthly:

n = 12 (compounded twelve times a year)

t = 1 year

A = \(18,500(1 + 0.012/12)^{(12 \times 1)} - 18,500\)

= 18,500(1.001)⁽¹²⁾ - 18,500

= 18,503.32 - 18,500

= $3.32

The earnings for the year on a monthly compounding basis are $3.32.

(d) Daily:

n = 365 (compounded daily)

t = 1 year

A = \(18,500(1 + 0.012/365)^{(365 \times 1)} - 18,500\)

= 18,500(1.00003287)⁽³⁶⁵⁾ - 18,500

= 18,500.60 - 18,500

= $0.60

The earnings for the year on a daily compounding basis are $0.60.

In conclusion, The earnings for the year on an $18,500 savings account depend on the compounding frequency. The earnings are highest when compounded annually ($232), followed by quarterly ($17.22), monthly ($3.32), and daily ($0.60).

The compounding frequency affects the frequency at which interest is added to the principal, resulting in different earnings over time. It is important to consider the compounding frequency when assessing the growth of savings and investments, as higher compounding frequencies can lead to greater overall earnings.

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The probability of a head on the 5th flip of the coin is 1/2 or 50%

The probability of getting a head on the 5th flip of the coin can be determined by understanding that each flip of the coin is an independent event. The previous flips do not affect the outcome of future flips.

Since the previous flips resulted in four consecutive heads (h h h h), the outcome of the 5th flip is not influenced by them. The probability of getting a head on any individual flip of a fair coin is always 1/2, regardless of the previous outcomes.

Therefore, the probability of getting a head on the 5th flip is also 1/2 or 50%.

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It can be seen that Plan 1 provides a greater total capacity.

To determine the greater total capacity, we need to compare the volumes of the tanks in both plans.

Plan 1: V1 = \(\pi * r1^2 * h1\) = \(3.14 * 50^2 * 150\)

≈ 11,78,500 cubic feet

Plan 2: V2 = \(\pi * r2^2 * h2 + \pi * r3^2 * h3\)

=\(3.14 * 30^2 * 75 + 3.14 * 25 ^2* 75\) ≈

2,12,100 + 1,47,187.5 ≈ 3,59,287.5 cubic feet

Plan 1 provides a total capacity of about 11,78,500 cubic feet, while Plan 2 provides a total capacity of about 3,59,287.5 cubic feet.

Therefore, Plan 1 provides a greater total capacity.

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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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The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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Answer:

Mean is the average of all of the numbers. Median is the middle number, when in order.

Answer:

x=7x/15

hope this helps

Answer:

D. 52

Step-by-step explanation:

105/2=52

The middle of 110 and 100 is 105. When you divide that by 2 you get 52.5 or 52. The answer is D

Answer:

D 52 is the answer

Answer:

1. previous clocks only showed the hours and minutes.

2. Maria asked, "wasn't he an inventor, too?"

3. Dr. B. Rimmins

4. 1157 Wakeshire Terrace

5. Fox Ridge, Indiana

6. Is Mt. Everest in nepal?

7. Jana's birthday is on the Fourth of July.

8.The girl scouts have an annual food collection in our town.

9. "Yesterday in Oxford Street"

10. My favorite movie is "The Parent Trap."

Step-by-step explanation:

1. Does not have proper capitalization.

Answer: The two factors are x+7 and x+2

The polynomial factors to (x+7)(x+2)

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

Explanation:

In the upper left corner we have x^2. We get this by multiplying x with x

So,

x*x = x^2

This means you'll have x to the left of x^2, and another copy of x above the x^2. These new terms are outside the box.

Now ask yourself, what goes in the blank x times ___ = 7x. The answer must be "7" since x times 7 = 7x. So we'll write 7 above the 7x, outside the box. Up top, the x and 7 help form the factor (x+7)

Along the left side, the other factor is (x+2) for similar reasoning. Notice how we effectively have x times ___ = 2x and '2' must go in the blank. So a '2' must go to the left of the 2x.

Putting everything together, the two factors are (x+7) and (x+2).

Therefore, x^2+7x+2x+14 fully factors to (x+7)(x+2)

This is the same as saying x^2+9x+14 factors to (x+7)(x+2)

The order of multiplication doesn't matter.

Answer:

7y + 15 - 2y = 5(y + 3)

Step-by-step explanation:

So two equations have infinitely many solutions, when they are exactly the same equation, in their most simplified form, for example: 2x = 3x-x which simplifies to 2x=2x. So in the options, three of the options have the same equation on the right side, so I'll distribute the 5. \(5(y+3) = 5y+15\). Now let's look at the options:

7y + 3-2y

5y+3 (this is not the same as 5y + 15)

7y + 15 (this is not the same as 5y + 15)

7y + 15 - 2y

5y + 15 = 5y + 15 (this is the same)

The equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

To find the slope of the tangent line to the parabola at the point (1,5), we need to find the derivative of the equation y = 6x - x² and evaluate it at x = 1.

Taking the derivative of y with respect to x:

dy/dx = d(6x - x²)/dx

= 6 - 2x

Now, we can substitute x = 1 into the derivative to find the slope at that point:

slope = 6 - 2(1)

= 6 - 2

= 4

So, the slope of the tangent line to the parabola at the point (1,5) is 4.

To find the equation of the tangent line, we need to use the point-slope form of a line.

The equation is given by:

y - y₁ = m(x - x₁)

Substituting the values we have:

y - 5 = 4(x - 1)

Expanding and simplifying:

y - 5 = 4x - 4

Moving the constant term to the other side:

y = 4x + 1

Therefore, the equation of the tangent line to the parabola at the point (1,5) is y = 4x + 1.

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Complete question =

Find the slope of the tangent line to the parabola at the point (1,5). y = 6x-x². find an equation of the tangent line.

Answer

triangle B is right angle because it is 90 degrees

triangle C is Obtuse because it equals 180

triangle D is obtuse angle because it equals 150

Step-by-step explanation:

sorry if i'm wrong

9514 1404 393

Answer:

  {58, 59, 60} kg

Step-by-step explanation:

Let x represent the mass of the heavier cow. Then the mass of the lighter cow is 96 -x.

The inequalities regarding the relative masses are ...

  x ≥ 96-x +20 . . . . . the heavy cow is at least 20 kg heavier

  96 -x > 35 . . . . . . . the lighter cow is more than 35 kg

__

Adding x to the first inequality makes it ...

  2x ≥ 116

  x ≥ 58

Adding x-35 to the second inequality makes it ...

  61 > x

So the mass of the heavier cow must be in the range ...

  58 ≤ x < 61

Possible whole-number masses for the heavier cow are ...

  58 kg, 59 kg, 60 kg

the derivative of the function y = (ln(x + 4))x using logarithmic differentiation is given by y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))].

To find the derivative of the function y = (ln(x + 4))x using logarithmic differentiation, we can follow these steps:

Step 1: Take the natural logarithm of both sides of the equation:

  ln(y) = ln((ln(x + 4))x)

Step 2: Use the logarithmic property ln(a^b) = b ln(a) to simplify the right-hand side of the equation:

  ln(y) = x ln(ln(x + 4))

Step 3: Differentiate both sides of the equation implicitly with respect to x:

  (1/y) * y' = ln(ln(x + 4)) + x * (1/ln(x + 4)) * (1/(x + 4))

Step 4: Simplify the expression on the right-hand side:

  y' = y * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))]

Step 5: Substitute the original expression of y = (ln(x + 4))x back into the equation:

  y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))]

Therefore, the derivative of the function y = (ln(x + 4))x using logarithmic differentiation is given by y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))].

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Answer:

(- ∞,∞)

there is no restriction when taking  cube roots

Step-by-step explanation:

Answer:

you need 32 eggs

Step-by-step explanation:

48 divided by 12=4

8x4=32

Answer:

2 eggs

Step-by-step explanation:

take the 48 and divide by 12 to get the answer, then take the 8 eggs and divide it by the answer you get to the first part, and you will get the amount of eggs.

Answer:

Step-by-step explanation:

The Answer is 203 Fahrenheit.

(95 x 9/5) + 32 = 203

The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).


To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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Answer:

False.

Step-by-step explanation:

Answer:

For 21: The first option (the uppermost) is correct for question 21. When it is no greater than, it implies that it can be equal to the number.

For 22: x+637 ≤ 2000, let x be the money he can spend for everything else.

Let me know if this helps!

Answer:

well when he buys the ticket he is left with 1,363 dollars

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Answer:

h = 8 inches

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

given A = 24 and b = 6 , then

\(\frac{1}{2}\) × 6 × h = 24 , that is

3h = 24 ( divide both sides by 3 )

h = 8 inches

Answer:

$18.00

Step-by-step explanation:

Answer: 18$

Step-by-step explanation:

17.59 is the current amount if you round to the nearest dollar the .5 will make the 7 go up in value meaning it will turn into a 8

Answer:

- 9 + 12x

Step-by-step explanation:

- 3(3 - 4x) ← multiply each term in the parenthesis by - 3

= - 9 + 12x

Answer:

x = -2

Step-by-step explanation:

3x - 1 × 3 = 5 × x + 1

3x - 3 = 5x + 1

3x - 5x = 1 + 3

-2x = 4

-2x/-2 = 4/-2

x = -2

Answer:

None of the given points satisfy the inequality 2x - 3y < 1.

Step-by-step explanation:

To determine which points satisfy the inequality 2x - 3y < 1, we can substitute the coordinates of each point into the inequality and check if the inequality holds true.

Let's consider the given points:

Point A: (1, 0)

2(1) - 3(0) < 1

2 - 0 < 1

2 < 1 (False)

Point B: (-1, -1)

2(-1) - 3(-1) < 1

-2 + 3 < 1

1 < 1 (False)

Point C: (3, -2)

2(3) - 3(-2) < 1

6 + 6 < 1

12 < 1 (False)

None of the given points satisfy the inequality 2x - 3y < 1.

Therefore, none of the points A, B, or C satisfy the inequality.

Answer:

175 is the answer

Step-by-step explanation:

\(700 = 8\)

\(700 \times 2 = 1400\)

\(1400 \div 8 = 175\)

Answer:

upper right corner

Step-by-step explanation:

just let x=0

then you know y>1

so those in left is wrong

and it's> not >=

y isn't equal to 1 so bottom right corner is wrong