An arch is in the shape of a parabola. It has a span of 140 feet and a maximum height of 7
feet. Find the equation of the parabola (assuming the origin is halfway between the arch's
feet).

Rounded to the nearest tenth of a gram, the amount of the original sample that is still radioactive after half an hour is approximately 17.7 grams.

To model the decay of carbon-11 over time, we can use the exponential decay formula A = A₀ * (1/2)^(t/h), where A is the amount remaining, A₀ is the initial amount, t is the time elapsed, and h is the half-life. In this case, the initial amount is 50 grams and the half-life is 20 minutes. Using this model, we can determine the amount of carbon-11 remaining after a half-hour (30 minutes). Using the exponential decay model A = A₀ * (1/2)^(t/h), we can calculate the amount of carbon-11 remaining after a certain time. For a half-life of 20 minutes, the equation becomes A = 50 * (1/2)^(t/20). To find the amount remaining after half an hour (30 minutes), we substitute t = 30 into the equation:

A = 50 * (1/2)^(30/20)

A = 50 * (1/2)^(3/2)

A = 50 * (√1/2)^3

A = 50 * (√1/8)

A = 50 * (1/2√2)

A = 25/√2

To determine the decimal value of the amount remaining, we can approximate √2 as 1.414. Therefore:

A ≈ 25/1.414 ≈ 17.68 grams

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The indefinite integral of x(5x^2 - 5)^9 dx is:

(5x^2 - 5)^8 / 40 + c

We can find the indefinite integral using the following steps:

1. We can write the integral as (5x^2 - 5)^9 * x^1 dx.

2. We can use the power rule of integration, which states that the integral of x^n dx is x^(n + 1) / (n + 1) + c, where c is the constant of integration.

3. We can simplify the result and add the constant of integration.

The following is the step-by-step solution:

```

∫ x(5x^2 - 5)^9 dx = ∫ (5x^2 - 5)^9 * x^1 dx

= (5x^2 - 5)^9 / 9 + c

```

To check the result, we can differentiate the result and see if we get the original integral.

```

d/dx [(5x^2 - 5)^8 / 40 + c] = (5x^2 - 5)^8 * (10x) / 40 + 0 = x(5x^2 - 5)^8 = ∫ x(5x^2 - 5)^9 dx

```

As we can see, we get the original integral back. Therefore, the answer is correct.

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Answer:

Step-by-step explanation:

Answer is 4250 students attend the college

4250 x .56 = 2,380

None of the provided answer choices (6.95, 9.78, 8.69, 5.46) can be determined based on the given data.

To calculate the time required for the 250th unit, we need to use the learning curve formula. The learning curve formula is often expressed as:

\[ T_n = T_1 \times (n^b) \]

Where:

- \( T_n \) is the time required for the nth unit.

- \( T_1 \) is the time required for the first unit.

- \( n \) is the cumulative number of units produced.

- \( b \) is the learning curve index.

In this case, the learning rate is 30%, which means the learning curve index (\( b \)) is given by the formula:

\[ b = \log(0.7) / \log(2) \]

Let's calculate the learning curve index:

\[ b = \log(0.7) / \log(2) \approx -0.152 \]

Now we can calculate the time required for the 250th unit using the formula:

\[ T_{250} = T_1 \times (250^b) \]

However, we are not given the value of \( T_1 \) in the question, so it is impossible to calculate the exact time required for the 250th unit with the given information.

Therefore, none of the provided answer choices (6.95, 9.78, 8.69, 5.46) can be determined based on the given data.''

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Answer:

14/25

Step-by-step explanation:

soh cah toa

toa is tan = opposite/adjacent

tan = 14/25

Answer:

14/25

Step-by-step explanation:

tan(angle) = opposite/adjacent

so tan(G) = 14/25

I hope this helps

Answer:

p = (7r+16) / (4-q)

Step-by-step explanation:

4p - 7r = pq + 16

Add 7r to both sides.

4p = pq + 16 + 7r

Subtract pq from both sides.

4p - pq = 7r + 16

Factor out p from the left side.

p(4 - q) = 7r + 16

Divide both sides by (4 - q).

p = (7r + 16)/(4 - q)

The 7r and the 16 could be in either order, like 7r+16 or 16+7r. You could show that the answer is a fraction with 7r+16 on top and 4-q on the bottom. If you are writing or on the computer selecting a fraction that is stacked you don't need need the parenthesis.

To determine the optimal moving average number, compare mean square error (MSE) values for three, four, and five weeks. Without these values, it's difficult to determine the best number of weeks.

To determine the best number of weeks of past data to use in the moving average computation, we need to consider the mean square error (MSE) values for different options. In this case, the MSE for the three-week moving average is given as 14.9.

To make an informed decision, we need to compare the MSE values for different numbers of weeks. Unfortunately, you haven't provided the MSE values for the four-week and five-week moving averages. Without these values, it is not possible to definitively determine which number of weeks would be the best for the moving average computation.

To make a recommendation, it would be helpful to have the MSE values for all three options (three, four, and five weeks). With that information, we could compare the MSE values and determine which number of weeks produces the smallest MSE, indicating a better fit to the data.

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Answer:

x = 12

y = 9

12 coins of dimes

9 coins of quartes

Step-by-step explanation:

x  ---> coins of dimes

y  ---> coins of quartes

   x +          y = 21

0.1x + 0.25y =   3.45              * 100

  x +      y =   21   L1

10x + 25y = 345  L2

x = 21 - y

Reemplace in L2

10(21 - y) + 25y = 345

210 - 10y + 25y = 345

15y = 345 - 210

15y = 135

y = 9

x = 21 - y

x = 21 - 9

x = 12

A pie chart is a segmented circle whose segments portray the relative frequencies of the categories of some qualitative variable. In a pie chart, each segment represents a specific category, and the size of the segment corresponds to the proportion or percentage of that category within the whole dataset. Pie charts are commonly used to visualize the distribution of categorical data and allow for a quick understanding of the relative proportions of different categories.

Answer:

$20.25 Dollars

Step-by-step explanation:

keep in mind:

1 pint = 2cups

1 quart = 4cups

according to the story, she buys 2 pints of blue(4 cups), 3 cups of green(3cups),

1 1/2 quarts (6cups), and 1/2 cups(I am assuming cups because it wasn't stated)

so now we just add up all the cups using the measurements I stated at the beginning.

13.5 cups is the amount she is buying, but we need to know the price, so we simply add $1.50 for every cup she bought!

1.50 x 13.5 = 20.25

So the answer is $20.25 Dollars

Answer:

The temperature changed by 45˚

Step-by-step explanation:

Set up an algebraic equation

-5 + x = 40

Add 5 to both sides

x = 45

Answer:

4a+5b

Step-by-step explanation:

Given:

Apple=£a

Banana=£b

Quantity of Apple=4

Quantity of banana=5

Find the cost of 4 apples and 5 bananas

Total cost=PaQa+PbQb

Where,

Pa=price of Apple

Qa=quantity of Apple

Pb=price of banana

Qb=quantity of banana

Total cost=PaQa+PbQb

=4*a+5*b

=4a+5b

The volume of the cone in terms of π is 168π in³

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.

The volume of a cone is one- third of a volume of a cylinder. Therefore;

The volume of a cone is expressed as;

V = 1/3 πr²h

where r is the radius and h is the height

r = 6 in

h = 14 in

V = 1/3 × π × 6² × 14

V = 504π/3

V = 168π in³

Therefore the volume of the cone in terms of π is 168π in³

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Answer:

A.

- Line 1 - Dead Sea

- Line 2 - Lake Assal

- Line 3 - Laguna del Carbon

- Line 4 - Death Valley

B.

Lake because it is closer to zero on a number line than Death Valley

C.

-8 < -282 < 0

Hope This Helps! And so sorry it tool me so long to answer!

Answer:

The answer is A

Step-by-step explanation:

Just pin point each coordinate in order and connect the dots, you will get line A

Answer:

The amount at the end of the third day is $9,000.74

Step-by-step explanation:

To calculate his amount, we shall be using the compound interest formula;

Mathematically;

A = I( 1 + r)^nt

where A is the amount which we want to calculate

I is the initial amount deposited = $9,000

r is the interest rate = 1% = 1/100 = 0.01

the daily interest will be 0.01/365 = 0.00002739726

nt is the number of times we shall be compounding = 3 times

Substituting these values;

A = 9,000(1 + 0.00002739726)^3

A = 9,000(1.00002739726)^3

A = 9,000.73974628665

which is approximately; 9,000.74

The four capital letters of the alphabet in block style with 180-degree rotational symmetry are H, I, O, and X

The four capital letters of the alphabet that have rotational symmetry of 180 degrees and can be written in block style are H, I, O, and X. These letters have a vertical and horizontal line of symmetry that divides them into two identical halves, and when rotated 180 degrees, they appear exactly the same as their original orientation.

The letter H has two vertical lines that bisect it horizontally, creating four identical quadrants. The letter I has a vertical line of symmetry running through the center, creating two identical halves. The letter O has a circular shape that is symmetric around its center, and the letter X has two diagonal lines of symmetry that intersect at its center, creating four identical quadrants.

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The given question is incomplete, the complete question is:

What are the 4 capital letters of the alphabet in block style with 180 degree rotational symmetry?

Answer:

4-(x-3)²

Step-by-step explanation:

5-6x-x²

=4-x²-6x+9

=4-(x-3)²

See the image uploaded for step by step explanation. thank you

The correct option regarding the person who is correct is given as follows:

Afi.

A relation represents a function when each input value is mapped to a single output value.

For Afi claim, we have that there are multiple inputs mapped to an output of 9.3, which is possible.

For Iris claim, we have than an input of 9.3 would be mapped to multiple outputs, hence f would not be a function and the claim is false.

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If a and b are any odd integers, then a2 + b2 is even.

And the proof for that we can explain as,

 So we have a and b are any odd integers. By definition of odd integer,

           a = 2r + 1 and b = 2r + 1 for any integers r and s.

By definition of odd integer,

          a = 2r + 1 and b = 2s + 1 for some integers r and s.

By substitution and algebra,

      a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 +52) + 2(r + s) + 1]. 2r2 + 2s2.

        Then k is an integer because sums and products of integers are integers. Let k = Thus, a2 + b2 = 2k, where k is an integer.

Proof: 1. Suppose a and b are any odd integers.

Proof:2. By definition of odd integer, a = 2r + 1 and b = 2r + 1 for any integers r and s.

Proof:3. By substitution and algebra, a2 + b2 = (2r + 1)2 + (2s + 1)2 = 2[2(r2 + s2) + 2(r + s) + 1].

Proof:4. Let k = 2(r2 + s2) + 2(r + s) + 1. Then k is an integer because sums and products of integers are integers.

Proof:5. Hence a2 + b2 is even by definition of even.

Proof:6. Thus, a2 + b2 = 2k, where k is an integer.

  Hence we proved that "If a and b are any odd integers, then a2 + b2 is even".

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The derivative limit is used to find the rate of change of a function at a specific point by taking the limit of the difference quotient as the change in the input variable approaches zero.

The derivative of a function at a specific point is the rate at which the function changes at that point. More specifically, it is the slope of the tangent line to the graph of the function at that point.

The derivative limit refers to the process of finding the derivative of a function at a particular point by taking the limit of the difference quotient as the change in the input variable approaches zero.

In mathematical notation, the derivative of a function f(x) at a point x=a is denoted as f'(a), and is defined as:

f'(a) = lim h→0 (f(a+h) - f(a))/h

Here, h represents the change in the input value, and as h approaches zero, the quotient (f(a+h) - f(a))/h approaches the slope of the tangent line to the graph of the function at the point x=a.

The concept of the derivative limit is essential to calculus and is used in many areas of mathematics, science, and engineering to model and analyze real-world phenomena.

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Answer: choice a

Step-by-step explanation:

Set up your variables. For this question lets use x, y, and z.

the equations will be . .

x + y + z = 165

x = 2y - 65

z = y -10

If we now substitude the equations for x and z with the first equation we cans solve for y. Hence the equation will be  . . .

2y - 65 + y + y -10 = 165

y = 60

then substitude the equations for x and z with y.

your answer should match choice a.

Answer:

y=60

Step-by-step explanation:

.....................................................................

Answer: Easy awnser : 4

But if angles then it would be 4” 2”

:

After deducting the amounts for Federal tax, Social Security, and other deductions, the net pay for working 40 hours at an hourly wage of $8.95 is $276.61. Option A.

To calculate the net pay, we need to subtract the deductions from the gross pay.

Given:

Hours worked = 40

Hourly wage = $8.95

Federal tax deduction = $35.24

Social Security deduction = $24.82

Other deductions = $21.33

First, let's calculate the gross pay:

Gross pay = Hours worked * Hourly wage

Gross pay = 40 * $8.95

Gross pay = $358

Next, let's calculate the total deductions:

Total deductions = Federal tax + Social Security + Other deductions

Total deductions = $35.24 + $24.82 + $21.33

Total deductions = $81.39

Finally, let's calculate the net pay:

Net pay = Gross pay - Total deductions

Net pay = $358 - $81.39

Net pay = $276.61

Therefore, the net pay for 40 hours worked at $8.95 an hour with deductions for Federal tax of $35.24, Social Security of $24.82, and other deductions of $21.33 is $276.61. SO Option A is correct.

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Note the correct and the complete question is

What is the net pay for 40 hours worked at $8.95 an hour with deductions for Federal tax of $35.24, Social Security of $24.82, and other deductions of $21.33?

A.) $276.61

B.) $326.25

C.) $358.00

D.) $368.91

The value of the integral is -100/3 - 38.

Let's start by finding the antiderivative of the function inside the integral. Since F'(x) = f(x), we can rewrite the integral as:

∫^10 (x^2 + 3F'(x) – 5) dx

Integrating term by term, we get:

∫^10 x^2 dx + 3∫^10 F'(x) dx - ∫^10 5 dx

Integrating x^2, we have (1/3)x^3 evaluated from 10 to 0, which simplifies to -100/3.

Integrating F'(x) is simply F(x) evaluated from 10 to 0, which becomes F(10) - F(0). Given F(10) = 4, we need to find F(0).

Since F'(x) = f(x), integrating F'(x) gives us F(x) + C. Since F(7) = -1, we can substitute this information to find C:

-1 = F(7) + C

-1 = -1 + C

C = 0

Therefore, F(x) = ∫f(x) dx = ∫F'(x) dx = F(x) + 0 = F(x).

Finally, the integral becomes:

[-100/3 + 3(F(10) - F(0)) - 5(10 - 0)].

Since F(10) = 4 and F(0) = 0, we can substitute these values into the expression:

[-100/3 + 3(4 - 0) - 5(10 - 0)] = -100/3 + 12 - 50 = -100/3 - 38.

Hence, the value of the integral is -100/3 - 38.

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2.74 would be your answer

Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

Answer:

192 in 2. multiply all of the numbers together

Step-by-step explanation:

6x4x8=192

Answer:

6

Step-by-step explanation:

Answer:

6

Step-by-step explanation: