Write an expression for the height of the flag after t seconds

The sum of the n first terms in an arithmetic series is given by the following formula

Where a_1 represents the first term, a_n represents the n-th term, and n the amount of terms we want to sum.

The first term of our sequence is 13, the tenth term is 89 and the amount of terms is 10. Plugging those values in our formula, we have

This sum is equal to 510.

We know by the figure that angles

We will solve it as follows:

1.3.1: We transform liters to cubic centimeters:

So, there are 875 000 cubic centimeters.

1.3.2: We transfrom cubic centimenters into liters:

So, there are 35.853 liters.

The Solution:

Given:

Required:

Find the equivalent of the given expression.

Answer:

[option A]

The formula to use for solving simple interest rate problems is:

Where

i is interest accumulated

P is the initial, or principal, amount

r is the rate of interest [in decimal]

t is the time

Given,

Total amount in account is 80 [principal plus interest]

rate is 2%

time is 8 years

Let's write:

The amount in the account was around $68.97

Solution:

Given:

Using the inverse trigonometric function,

However, since the sine of the angle is negative, it shows that the angle is in the third or fourth quadrant.

Hence, the possible values of the angle are,

Therefore, the value of the angle to the nearest tenth of a degree is 264.0 degrees or 276.0 degrees.

After simplification, the option 2, [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex] is correct option.

In the given question,

We have to find which simplifications is incorrect.

Option 1: [tex]\sqrt{48x^4}\times\sqrt[4]{16x^{10}}=8x^4\sqrt[4]{3x^2}[/tex]

To check whether the given expression is true or not simplifying the left hand side expression.

We simplifying the left hand side by writing it as

[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=\sqrt{16\times3\times (x^2)^2}\times\sqrt[4]{(2)^4\times x^{8}\times x^2}[/tex]

[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=\sqrt{(4)^2\times3\times (x^2)^2}\times\sqrt[4]{(2)^4\times (x^{2})^4\times x^2}[/tex]

Now simplifying the roots

[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=4\times x^2\times\sqrt{3}\times2\times x^2\times\sqrt[4]{ x^2}[/tex]

Now writing it in a simplified form

[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=8\times x^{2+2}\times\sqrt{3}\sqrt[4]{ x^2}[/tex]

[tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}=8x^{4}\sqrt{3}\sqrt[4]{ x^2}[/tex]

Hence, the simplified form of [tex]\sqrt{48x^4}*\sqrt[4]{16x^{10}}[/tex] is [tex]8x^{4}\sqrt{3}\sqrt[4]{ x^2}[/tex].

So the given statement is wrong.

Option 2. [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex]

To check whether the given expression is true or not simplifying the left hand side expression.

We simplifying the left hand side by writing it as

[tex]\sqrt{4x}\times \sqrt{12x^8}=\sqrt{(2)^2\times x}\times \sqrt{3\times4\times (x^4)^2}[/tex]

[tex]\sqrt{4x}\times \sqrt{12x^8}=\sqrt{(2)^2\times x}\times \sqrt{3\times(2)^2\times ({x^4})^2}[/tex]

Now simplifying the roots

[tex]\sqrt{4x}\times \sqrt{12x^8}=2\sqrt{x}\times 2\times x^4\times\sqrt{3}[/tex]

[tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex]

Hence, the simplified form of [tex]\sqrt{4x}\times \sqrt{12x^8}[/tex] is [tex]4x^4\sqrt{3x}[/tex].

Hence, the option 2 is correct.

Since we get the write answer so we haven't solve the next option.

The next 2 options also can be solved in the way that we use in previous option to solve.

So the option 2 [tex]\sqrt{4x}\times \sqrt{12x^8}=4x^4\sqrt{3x}[/tex] is correct option.

To learn more about the simplification of expression link is here

https://brainly.com/question/14575743

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Explanation

The question wants us to determine the amount $2400 will yield after 7 years if compounded annually at a rate of 8.75%

To do so, we will use the formula:

Thus, if we substitute the values above we will have

Therefore, after 7 years, the investment will be worth $4317.34

In the expression, there are 3 terms so polynomial is trinomial.

In trinomial the highest degree of term

is 5. So degree of the polynomial is 5.

Anwer:

Trinomial

Degree is 5.

Given equation:

Open the bracket:

Collect like terms:

Divide both sides by 2:

Answer:

x = 70

solve for y

Answer:

y = -41/4 or 10.25

Step-by-step explanation:

7 - 4y = 48

Move 7 across the equals sign to make y stand alone

-4y = 48 - 7

= 41

Divide both sides by the coefficient of y, which is -4

-4y/4 = 41/4

y = -41/4 or 10.25

SOLUTION:

The one that is not a correct description of these anles is tption D. (They are supplementary angles)

EXPLANATION:

Two angles are said to be supplementary if they add up to be 180 and considering the sum of these angles which is 90 (right angle)

Given that angle ABC is a right angle, then:

21° + x° + 32° = 90°

x = 90° - 21° - 32°

x = 37°

This corresponds to the option: subtract 21° and 32° from 90°, x = 37°.

y= 6x-22

Explanation

Step 1

Let

slope=6

Point (3,-4)

to find the equation in slope intercept form use

Step 2

Replace,

I hope this helps you

To find:

Round $43,569.14 the nearest dollar

Solution:

The number after the decimal is less than 50. So, the amount $43,569.14 rounded to the nearest dollar is $43,569.

Thus, the answer is $43569.

He will need to take sample of at least two different sample of pet food in order to analyze it more accurate. So, the researcher should:

divide the pet foods into two different groups, cat and dog, and take a sample from each group.

Answer: The graph of the P(t) has been provided, we have to find the instantaneous slope of P(t) at t = 8:

Therefore we need two y values and two x values, which can be obtained as follows:

Equation (1) corresponds to the third, option, therefore that is the answer.

Table 1

3:5 , 6 : 10 , 9 :15 , 12 : 20

Table 2

7 : 10 , 14 : 20 , 21 : 30 , 28 : 40

Notice that all ratios in each table are equal. Additionally, since:

And 6<7, then the ratio 3:5 is less than the ratio 7:10.

Therefore, all ratios in table 1 are less than all ratios in table 2.

Some specific comparisons between ratios may apply as well. For example:

The ratio 14:20 (table 2) is greater than the ratio 9:15 (table 1).

We have here a case of a normally distributed variable. We can solve this kind of problem using the standard normal distribution, and the cumulative standard normal table (available in any Statistic Book, or on the internet).

We have that we can find z-scores to normalized the situation, and then, using the cumulative standard normal table, we can find the percentile. Then, we have:

In this case, we need to find the raw value, x. We need to find a z-score that represents that before it there are 33% of the cases for this distribution: in this case, the value for z is approximately equal to z = -0.44.

Now, we have the mean (253 lbs), and the standard deviation (1.12 lbs):

And now, we can determine the value, x, which is, approximately, the 33% percentile of this normal distribution:

1. Multiply by 1.12 to both sides of the equation:

2. Add 253 to both sides of the equation:

Therefore, the weight that would be the 33rd percentile, is, approximately, x= 252.5072 or 252.51lbs (rounding to the nearest hundredth).

6 + 42i

Expanding the expression, by using FOIL acronym

(-4+2i)(3-9i)​

-12+36i+6i-18i²

-12 +42i -18i² Remember i²= -1

-12 + 42i -18(-1)

-12 + 42i +18

6 + 42i

2) Now we have that complex number in the form a +bi

-

Hello there. To solve this question, we'll simply have to multiply the percent and the salary to find how much will the raise of the worker.

Given his salary: $35,868 and knowing he'll get a 3% raise, we make:

3/100 * 35,868

107,604/100 = 1,07604

Rounding up the answer to the nearest tenth, we have that his raise will be $1,1.

Answer:

Step-by-step explanation:

Divide 6 by 4:

Answer:

p(x) = f(x) - g(x) = -0.04x² + 20.96x - 71

Explanation:

The sales are given by f(x) = 24.96x and the cost are represented by g(x) = 0.04x² + 4x + 71.

Then, the profit is equal to

p(x) = f(x) - g(x)

p(x) = 24.96x - (0.04x² + 4x + 71)

p(x) = 24.96x - 0.04x² - 4x - 71

p(x) = -0.04x² + 20.96x - 71

Therefore, the answer is

p(x) = f(x) - g(x) = -0.04x² + 20.96x - 71

For an initial amount P with an annually compounded interest rate r, after t years the total amount A is is given by:

Then we have:

For P = $10,000, A = $23,750 and r = 0.05, we have:

books are on sale for $8

Peter has $25 dollar in his wallet

let the numbers of book be x

so,

if a book cost $8

x number of books cost $25

lets put it into mathematical statement

1 = $8

x = $25

lets cross multiply

1 X 25 = 8 X x

25 = 8x

8x = 25

divide both sides by 8

8x/8 = 25/8

x = 25/8

x = 3.125

x = 3 (approximately)

recall, we say x is the numer of books

so,

the number of books peter can by with is $25 in his wallet is 3atement

1

we know that

The volume of the sphere is equal to

In this problem we have

r=14/2=7 in ----> the radius is half the diameter

pi=3.14

substitute the given values

Recall that:

Therefore:

Now, the above function is well defined as long as x+2 remains positive, therefore, it is well defined as long as x is greater or equal to -2.

Answer: The domain is:

The composition is:

Problem Statement

We have been given random sample of 100 observations and we have been asked to find the probabilities of getting certain observed values given the population mean of 30 and a standard deviation of 21.

Method

To solve this question, we need to:

1. Find the z-score of the observations. The formula for calculating the z-score is:

2. Convert the z-score to probability using the z-score table.

Implementation

Question A

1. Find the z-score of the observations.:

2. Convert the z-score to probability using the z-score table.:

Using a z-score calculator, we have the probability to be:

This probability is depicted in the drawing below:

If the mean is represented by 0 and the right-hand side of 0 has a probability of 0.5, then the probability of getting greater than or equal to 28, is the addition of the probability 0.037938 gotten above with the 0.5 on the right-hand side of zero.

Thus, the answer to Question A is:

Question B: