Given the geometric sequence an with the following information, find a10.
a2=-36 a7=128/27

3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer:

16n-4

Step-by-step explanation:

2(2n-3) +2(6n+1)=

4n-6+12n+2

16n-4

Answer:

Let `f` be a function defined on [0,2]. Then find the domain of function `g(x)=f(9x^2-1)

Step-by-step explanation:

I'm not sure if that's right

Answer:

1) \(Six\)

Step-by-step explanation:

1)     \(30\ seconds\div5\ seconds=6\ seconds\)          \(\left\{every\ 5\ seconds\ one\ time\right\}\)

I am going to work on the other several tonight/tomorrow and will post when I get them done.

Answer:

Explanation:

First, you put the equation into the standard “slope/intercept” form.

4x -y = 2 subtract 4x from both sides ; -y = -4x + 2 Multiply by -1 :

y = 4x - 2

In this standard form we see that the slope of the line (coefficient of x) is 4. ANY line parallel to this one must thus also have a slope of 4.

y = 4x - a (generic)

ANY other combination of slope multiples and constant terms will therefore also be lines parallel to this one. The one that passes through a specific point will simply have a different constant term.

We find this by putting our point value into the equation:

3 = 4(-2) + a ; 3 = -8 + a ; a = 11

Thus, our “parallel line equation” through the point (-2,3) is:

y = 4x + 11

Answer:

y = 4x + 1

Step-by-step explanation:

first put the equation 4x-y=2 into the form y = mx + b where m is the slope and b is the y-intercept (for example, y = 2x - 1 would have 2 is the slope and -1 is the y-intercept)

4x - y = 2

subtract 4x from both sides

-y = -4x + 2

multiply both sides by -1

y = 4x - 2

That means the slope of this line is 4.

Parallel lines always have the same slope, so the slope of the new line is also 4. You can again put the new equation into the form y = mx + b. You already know that the slope is 4, so y = 4x + b.

Next, you need to find b. You know that (-1, -3) is a solution, so if you plug x = -1 and y = -3 into the equation, it should be true.

You can put that into the equation to solve for b:

-3 = 4 * -1 + b

-3 = -4 + b

1 = b

This means the equation is y = 4x + 1

Using statistics, the upper value and lower value of the range of outcomes associated with the middle 25% = (41, 53)

Understanding the data and focusing on various applications are the two main goals of statistics. The study of data gathering, analysis, and mathematical synthesis is known as statistics. As part of their state science studies, statisticians used to collect and evaluate data about a country's economy, population, and other aspects. Mathematical statistics is the application of mathematical ideas such as linear algebra, differential equations, mathematical analysis, and probability theories.

Given, the mean of the normal distribution = 47.

μ =47

The standard deviation is 6.

σ = 6

The formula for range = (μ-σ, μ+σ)

Putting the values of μ and σ,

Range= (47-6, 47+6)

Range= (41, 53)

Hence, the range of outcomes associated with the middle 25%'s upper and lower values are equal to (41, 53)

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The number that can complete the equation 5y + 2(3y − 1) = ⬜y − (y + 2) is

5y + 2(3y − 1) = 12 y − (y + 2)

The number that can complete the equation is computed by simplifying the equation at the left hand side of the equality sign and comparing with the right side of the equality side

The comparison will show the number that can fit in the blank

Simplifying the equation at the left hand side of the equation

= 5y + 2(3y − 1)

= 5y + 6y − 2

= 11y - 2

Simplifying the equation at the right hand side of the equation

=  ⬜y − (y + 2)

let x represent the missing number

=  xy − (y + 2)

=  xy − y - 2

comparing both equations

11y - 2 =  xy − y - 2

11y =  xy − y

11y + y =  xy

12y = xy

x = 12

The missing value = 12

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if x = 8, we put this value in the expression to get

Hence, the answer is 23.

Answer:

A tape diagram. StartFraction part Over whole EndFraction = StartFraction 300 Over 100 EndFraction = StartFraction 75

Step-by-step explanation:

Answer: (D)

Start Learning and Start Growing! edge2023!

*DROPS THE MIC*

The expression that represents this inequality must relate both temperatures, then it would look like this: -40°F < x < 140°F.

To express this situation in an inequality we must include the temperature values. Additionally, we must include the greater than (>) or less than (<) symbols to relate the values.

According to the above, the expression would look like this:

Note: This question is incomplete because some information is missing. Here is the information:

A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.

Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form.

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Answer:

Step-by-step explanation:

\(1c-0.25c=0.75c\)

a. In the integrand ∫[x/(6x² + 5)²]dx, we make the substitution u =  (6x² + 5)

b. Writing the integrand ∫[x/(6x² + 5)²]dx in the form ∫f(u)du, f(u) = u²/12

Integration is the reverse of differentiation

a. Since we want to find the substitution in order to evaluate the following integrand ∫[x/(6x² + 5)²]dx, we proceed as follows

In the integrand ∫[x/(6x² + 5)²]dx, we see that the other function is the polynomial in the denominator which is (6x² + 5). So, we make the substitution u =  (6x² + 5)

b. To rewrite the integrand in terms of u so that ∫[x/(6x² + 5)²]dx is int he form ∫f(u)du, we proceed as  follows

Since  integrand ∫[x/(6x² + 5)²]dx and u = 6x² + 5. Differentiation u with respect to x, we have that

du/dx = d(6x² + 5)/dx

= d(6x²)/dx + d5/dx

= 12x + 0

= 12x

So, du/dx = 12x

xdx = du/12

So, substituting this into the integrand, we have that

∫[x/(6x² + 5)²]dx = ∫[x/u²]dx

= ∫[xdx/u²]

= ∫[du/12/u²]

=  ∫[du/12u²]  

So, comparing  ∫[f(u)du]  = ∫[du/12u²]  

So, f(u) = u²/12

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Answer:

\(f(u)=\dfrac{1}{12u^5}\)

Step-by-step explanation:

Integration by substitution is a technique used to simplify the integration of complex functions. It involves writing part of the function in terms of a new variable u, where u is some function of x.

Given integral:

\(\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x\)

Substitute u for 6x² + 5.

Differentiate u with respect to x and rearrange the equation to isolate dx:

\(\dfrac{\text{d}u}{\text{d}x}=12x \implies \text{d}x=\dfrac{1}{12x}\; \text{d}u\)

Substitute the expressions for u and dx into the original expression to rewrite the original integral in terms of u and du:

\(\begin{aligned}\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x &= \int \dfrac{x}{u^5} \cdot \dfrac{1}{12x}\; \text{d}u\\\\&= \int \dfrac{1}{12u^5}\; \text{d}u\\\\\end{aligned}\)

Therefore:

\(f(u)=\dfrac{1}{12u^5}\)

Answer:5

Step-by-step explanation:

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Using newton's method to find all real roots of the equation, 4x = 1+ x³ is

x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.

We have the equation,

4x = 1+ x³

To find the real roots of equation we have,

x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.

The cubic equation formula in mathematics is how the cubic equation is represented. An equation with degree three is said to be cubic. In nature, the roots of all cubic equations are either one real root and two real roots or three real roots. Cubic polynomials are the name given to three-degree polynomials.

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Answer:

11/7is your answer ....

Step-by-step explanation:

hope its help you

Step-by-step explanation:

substitute the angle of sine with a variable and differentiate

it was the oted entrepreneur, inventor, and philanthropist George Eastman of the Eastman-Kodak Company gave a lot to the world before he passed. His experiments with 35mm roll film helped popularize photography in the late 1800s and led to the invention of motion pictures. He was also responsible for perfecting the first Kodak camera.

The required amount paid in FICA taxes this year would be $2,295. The correct answer is $2,295.

To calculate the FICA taxes paid for the given scenario, we need to multiply the salary by the FICA rate.

Given:

Salary: $30,000

FICA rate: 7.65%

FICA taxes are split between employers and employees, with both parties paying 7.65% of their income to FICA, totaling 15.3% combined.

To calculate the FICA taxes paid by the employee, we multiply the salary by the FICA rate:

$30,000 * 7.65% = $2,295

Therefore, the amount paid in FICA taxes this year would be $2,295. The correct answer is $2,295.

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Answer:

7225 LOL

Step-by-step explanation:

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer:

The critical value for a 99% confidence interval is T = 2.9768

Step-by-step explanation:

We have the standard deviation of the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

Critical value

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.99}{2} = 0.995\). So we have T = 2.9768

The critical value for a 99% confidence interval is T = 2.9768

Answer: Length = 13 ft. , Width = 9 ft.

Step-by-step explanation:

Rectangle area = Length x width

Area = 117 ft.

Length = x + 4

Width = x

To solve

(x)(x + 4) = 117

x^2 + 4x = 117

x^2 + 4x - 117 = 0

(x - 9)(x + 13)

x = 9, -13

x = 9 (measurement cannot be negative)

Length

x + 4

9 + 4 = 13

Answer:

x = \(\sqrt{99}\)

Step-by-step explanation:

Based on the Pythagoras theorem, where a and b are the legs of the triangle and c is the hypotenuse.

\(c^{2}= a^{2} + b^{2} \\c = \sqrt{a^{2} + b^{2} } \\x = \sqrt{7^{2} + (5\sqrt{2})^{2}} \\x = \sqrt{99}\)

Therefor x = \(\sqrt{99}\)

Answer:

the Pythagorean theorem states:  

a^2 + b^2 = c^2  in your case a=24 and c=40

Step-by-step explanation:

24^2 + b^2 = 40^2

24x24 + b^2 = 40x40

(576 + b^2 = 1600)  

b^2 = 1600 - 576

b^2 = 1024

b= √1024

b = 32

Final answer: 32

The length of b is 32 units in triangle ΔABC.

Pythagoras theorem states that, a right-angled triangle, the square of the one side is equal to the sum of the squares of the other two sides.

a² + b² = c²

Given data as :  a=24 and c=40

Substitute the values of a and c in the equation,

24² + b² = 40²

24x24 + b² = 40x40

(576 + b² = 1600)  

b² = 1600 - 576

b² = 1024

b= √1024

b = 32

Hence, the length of b is 32 units.

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