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

Answer:

B.

Step-by-step explanation\(\sqrt[3]{216} =6\)

Answer:

The problem statement suggests that the series of donations is arithmetic, as each student's donation increases by one as their number increases. Therefore, we can apply the formula for the sum of an arithmetic series to solve this problem.

In an arithmetic series, the sum S of n terms is given by:

S = n/2 * (a + l)

where:

- n is the number of terms (which represents the number of students in this case),

- a is the first term (in this case, the first student's number, which would be 1), and

- l is the last term (in this case, the last student's number, which we don't know yet).

Given that S = Rs. 13225, we have:

13225 = n/2 * (1 + l)

Since this is an arithmetic series starting from 1, the last term, l, is equal to n. Thus, we can substitute l with n:

13225 = n/2 * (1 + n)

Multiplying through by 2 to clear the fraction gives:

26450 = n * (1 + n)

Rearranging to a quadratic equation gives:

n^2 + n - 26450 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. To solve for n, we can use the quadratic formula, n = [-b ± sqrt(b^2 - 4ac)] / (2a). But since n cannot be negative in this context (as it represents the number of students), we will only consider the positive root.

Applying the quadratic formula, we find that the positive root is approximately 162.5. However, the number of students must be a whole number. Therefore, the number of students is 163, because the 163rd student did not donate fully as per their number, and that's why the total amount doesn't reach the full sum for 163 students.

So, there were 163 students who donated money to the fund.

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

Learn more about percentage on:

brainly.com/question/843074

#SPJ1

Answer:

give me more instructions so i can actually help

Step-by-step explanation:

Answer:

D. 1000 gallons per hour

Step-by-step explanation:

5000 / 5 = 1000

Answer: If it drained 5000 gallons and there were 5 hours, then 5000 divided by 5 is 1 so that would be answer D.

Hoped this helped!

Answer:

21=2w+2w+3    18=4w     w=4.5

Answer:

p= 40cm squared

a= 100cm squared

Step-by-step explanation:

. . . .

Let us check all the expression to find whose = 6h

6h = 6 x h

Then the 3rd answer is right

h + h + h + h + h + h = 6 (h) = 6h

Then the 2nd answer is right

Then the correct answers are 2nd and 3rd

Answer:

\(\sf 4.9 \times 10^{11}\)

Step-by-step explanation:

Given expression: \(\sf (7 \times 10^5)^2\)

Apply exponent rule \(\sf (ab)^2=a^2 \cdot b^2\) :

\(\sf \implies 7^2 \times (10^5)^2\)

\(\sf \implies 49 \times (10^5)^2\)

Apply exponent rule  \(\sf (a^b)^c=a^{bc}\) :

\(\sf \implies 49 \times 10^{5 \cdot 2}\)

\(\sf \implies 49 \times 10^{10}\)

Scientific notation:  \(\sf a \times 10^n\)

where  \(\sf 1\leq a < 10\) and n is an integer

We can write 49 as \(\sf 4.9 \times 10=4.9 \times 10^1\)

\(\sf \implies 4.9 \times 10^1\times 10^{10}\)

Apply exponent rule \(\sf a^ba^c=a^{b+c}\)

\(\sf \implies 4.9 \times 10^{11}\)

Answer:

Step-by-step explanation:

One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.

One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence

Answer:

B. is the correct answer

Step-by-step explanation:

Answer:

- 151 is the answers

Step-by-step explanation:

The number of days which it would take 1000 people to sign the petition as required in the task content is; 4.35 days.

It follows from the task content that the number of days which it would take Jan to get 1000 signatures on the petition be determined.

Since it is given in the task content that 230 people sign the petition each day.

It therefore follows from proportion that the number of days needed for 1000 people to sign the petition is;

= 1000/230

= 4.3478 days.

Hence, the number of days which it would take 1000 people to sign the petition is approximately; 4.35 days.

Read more on division;

https://brainly.com/question/870035

#SPJ1

Answer:

no, it isnt

Step-by-step explanation:

Answer:

18 t-shirts

Step-by-step explanation:

I got the question and this was the correct answer.

Answer: C

18 tshirts

Step-by-step explanation:

To solve a differential equation using the series method, you need to assume that the solution can be expressed as a power series of the form:

\(y(x) = a0 + a1x + a2x^2 + a3x^3 + ...\)

Substituting this expression into the differential equation and collecting the coefficients of each power of x will give you a recurrence relation for the coefficients of the series. You can then use this recurrence relation to find a fundamental pair of solutions y1 and y2.

For example, consider the following differential equation:

y'' + y = 0

We can assume that the solution can be expressed as a power series:

\(y(x) = a0 + a1x + a2x^2 + a3x^3 + ...\)

Substituting this expression into the differential equation and collecting the coefficients of each power of x gives us:

a2 + a0 = 0

a3 + a1 = 0

a4 + a2 = 0

...

This gives us the following recurrence relation:

a(n+2) + a(n) = 0

To find a fundamental pair of solutions, we can start by setting a0 = 1 and a1 = 0 in our power series, which gives us the following two solutions:

\(y1(x) = 1 + x^2 + x^4 + x^6 + ...\)

\(y2(x) = x + x^3 + x^5 + x^7 + ...\)

The first four terms of each of these solutions are:

\(y1(x) = 1 + x^2 + x^4 + x^6y2(x) = x + x^3 + x^5 + x^7\)

You can use similar steps to solve other differential equations using the series method. Just be sure to carefully substitute the power series into the differential equation and collect the coefficients of each power of x to find the recurrence relation for the coefficients of the series.

To learn more about differential equations, visit:

brainly.com/question/14620493

#SPJ4

Answer:

To make 10 liters of 20% alcohol solution, RSM would need to use a combination of the 18% and 40% alcohol solutions. Let's call the amount of 18% solution used "x" and the amount of 40% solution used "y".

To set up the equation, we'll use the fact that the amount of pure alcohol in the final solution must be equal to 20% of the total volume.

So:

0.18x + 0.40y = 0.20(10)

Simplifying:

0.18x + 0.40y = 2

We have one equation with two unknowns, which means we need another equation. Fortunately, we know that RSM is making a total of 10 liters of solution. So:

x + y = 10

We now have two equations with two unknowns, which we can solve simultaneously. One way to do this is to solve one equation for one variable, then substitute that expression into the other equation, like so:

x = 10 - y (from the second equation)

0.18(10-y) + 0.40y = 2 (substituting into the first equation)

1.8 - 0.18y + 0.40y = 2

0.22y = 0.2

y = 0.91

So RSM would need to use approximately 0.91 liters (or 910 milliliters) of the 40% solution, and the rest (9.09 liters or 9090 milliliters) of the 18% solution, to make 10 liters of 20% alcohol solution.

The results of the hypothesis test H0:β0 = 0 against the alternative H1:β1 ≠ 0 is Reject at α = 0.10, Do not reject at α = 0.05. Hence, option D is the accurate solution.

To determine the results of the hypothesis test H0:β0 = 0 against the alternative H1:β1 ≠ 0, we will calculate the t-statistic and compare it to the critical values from the t-distribution at the desired significance level.

The t-statistic for the null hypothesis is given by -

t = (Bo - 0) / SE(Bo)

where Bo is the estimate of the intercept, SE(Bo) is its standard error, and 0 is the hypothesized value under the null hypothesis.

Substituting the given values, we get,

t = 15.52 / 3.242 = 4.785

The degrees of freedom for this test are n - 2 = 10, where n is the number of observations.

At a significance level of 0.10, the critical values for a two-tailed test with 10 degrees of freedom are ±1.812. Since our calculated t-statistic of 4.785 is greater than the critical value of 1.812, we reject the null hypothesis at α = 0.10.

Similarly, at a significance level of 0.05, the critical values for a two-tailed test with 10 degrees of freedom are ±2.228. Since our calculated t-statistic is less than the critical value of 2.228, we do not reject the null hypothesis at α = 0.05.

Therefore, the correct answer is (D) Reject at α = 0.10, Do not reject at α = 0.05.

Read more about the null hypothesis:

brainly.com/question/25263462

#SPJ4

Answer:

Lion area: 60

Lion Perimeter: 34

Tiger Area: 60

Tiger perimeter: 64

Step-by-step explanation:

Answer:

c 57

Step-by-step explanation:

To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

For such more question on parentheses

https://brainly.com/question/172904

#SPJ8

Answer: 626 yd^2

Step-by-step explanation: First you need to split the figure into 2 rectangular prisms (see attached image). The tallest rectangular prism has a length of 12 yd, a width of 3 yd, and a height of 11 yd. The shorter one has a length of 12yd, a width of 4 yd, and a height of 4 yd. The surface area equation is SA=2(wl+hl+hw). First solve for the taller rectangular prism. SA=2(3x12+11x12+11x3). SA=2(36+132+33). SA=2(201). SA=402 yd^2. Now solve for the smaller rectangular prism. SA=2(4x12+4x12+4x4). SA=2(48+48+16). SA=2(112). SA=224 yd^2. Lastly, add both values together. 402+224=626 yd^2.

Answer:

$637.95

Step-by-step explanation:

convert 8.5% to a decimal by dividing by 100:

8.5÷100= 0.085

then multiply.

587.98×(0.085)=49.97

now add.

587.98+49.97=637.95

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

learn more on angles here: brainly.com/question/18854964

#SPJ1

The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

Learn more about bisecting of angles on https://brainly.com/question/23984603

#SPJ1

Answer:

He must survey 123 adults.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

Assume that a recent survey suggests that about 87​% of adults have heard of the brand.

This means that \(\pi = 0.87\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a p-value of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

How many adults must he survey in order to be 90​% confident that his estimate is within five percentage points of the true population​ percentage?

This is n for which M = 0.05. So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}\)

\(0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}\)

\(\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}\)

\((\sqrt{n})^2 = (\frac{1.645\sqrt{0.87*0.13}}{0.05})^2\)

\(n = 122.4\)

Rounding up:

He must survey 123 adults.

Answer:

See below

Step-by-step explanation:

We have the series

\($\sum _{ n=0 }^{ \infty }{ 3(0.8)^n}$\)

(a) To show that the sum of first \(n\) terms is \(S_n= 15(1-0.8^n)\)

Consider that the this sum is given as

\(S_n = 3\dfrac { 1-{ r }^n}{ 1-r }\)

In this case, the ratio is 0.8, thus, \(r=0.8\)

\(S_n = 3\dfrac { 1-{ 0.8 }^n }{ 1-0.8 }\)

\(3\dfrac { 1-{ 0.8 }^{ n } }{ 1-0.8 } = 15(1-0.8^n) \iff 3(1-{ 0.8 }^{ n }) = 15(1-0.8^n)( 1-0.8) \iff 3 = 15(1-0.8) \iff 3 = 15-12 = 3\)

Therefore,

\(S_n = 3\dfrac { 1-{ 0.8 }^n }{ 1-0.8 } = 15(1-0.8^n)\)

\(\dfrac{S_6}{S_4} = \dfrac{15(1-0.8^6)}{15(1-0.8^4)} = \dfrac{(1-0.8^6)}{(1-0.8^4)} = \dfrac{0.737856}{0.5904} = \dfrac{737856}{5904} = \dfrac{144\cdot 5124}{144\cdot 41} = \boxed{\dfrac{5124}{41} }\)

(b) Calculate the smallest integer value of \(n\) such that \(S_{40} -S_n < \dfrac{1}{2}\)

Once \(S_{40} \approx 15 \text{ and } S_n>14.5, \text{ thus } S_{40} \approx S_n, \text{ but } n \text{ is considerably smaller than 40}\)

I am considering \(S_{40}=15\), so

\(15-15(1-0.8^n) < \dfrac{1}{2} \implies 0.8^n < 0.03 \implies n> 15.71\)

\(\text{Once } n\in\mathbb{Z}, \text{ then } n=16\)

The cost per ounce of the premium walnut is $0. 23

To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such  that they are made equal to another.

From the information given, we have that;

54 ounces of premium walnuts costs $12.95

This is represented as;

54 ounces = $12. 95

Then 1 = x

cross multiply the values, we get;

x = $12.95/54

Divide the values, we get;

x = $0. 23

Hence, the value is $0. 23 per premium walnut

Learn more about proportion at: https://brainly.com/question/1781657

#SPJ1

Answer:

At least 8 rows

Step-by-step explanation:

45 divided by 9 is 5. That is 5 rows

9x3= 27 and there are 23 adults. So that is 3 rows

5+3=8

8 rows in total.