What is the next term in the following sequence: 0, 5, 11, 18, … 24 26 23 25

We can rewrite the radical expression:

\(\frac{a^3}{\sqrt{ab} } = b\)

To get the one in option D:

\(a^5 = b^3\)

Here we start with the following expression:

\(\frac{a^3}{\sqrt{ab} } = b\)

Such that a*b > 0, so the denominator is never equal to zero.

First, remember two properties of the square root:

√(a*b) = √a*√b

And:

√a = a^(1/2)

Thus, we can rewrite:

\(\frac{a^3}{\sqrt{ab} } = b\\\\\frac{a^3}{a^{1/2}*b^{1/2}} = b\\\)

Now we can solve this as:

\(\frac{a^3}{a^{1/2}*b^{1/2}} = b\\\\\frac{a^3}{a^{1/2}} = b*b^{1/2}\\\\a^{3 - 1/2} = b^{1 + 1/2}\\\\a^{5/2} = b^{3/2}\)

Now we can apply a power of two in both sides to get:

\(a^{5/2} = b^{3/2}\\\\(a^{5/2})^2 = (b^{3/2})^2\\\\a^5 = b^3\)

So the correct option is D.

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Answer:

so the Domain:

{5, -5, 6,−6}

Range:  {1,4,2,8,3}

functon no

Since x=−5 produces y=4 and y=3, the relation (5,1),(−5,4),(6,2),(−6,8),(−5,3)is not function.

Step-by-step explanation:

domain is normally x and range in most the time y, this is what i was taught and i hope it helps and is right

To achieve a margin of error of +3 for a 90% confidence interval for the average number of lawn mowings during summer in a large city with a mean of u and a standard deviation of 0-8.7, a simple random sample of size 18 should be selected.

To determine the sample size needed to achieve a margin of error of +3 for a 90% confidence interval, we can use the formula:

n = (z * σ / E)^2

where n is the sample size, z is the z-score for the desired confidence level (in this case, 1.645 for 90% confidence), σ is the standard deviation, and E is the margin of error.

Substituting the given values into the formula, we get:

n = (1.645 * 0.8 / 3)^2 = 17.18

Rounding up to the nearest whole number, we get a sample size of 18.

Therefore, to achieve a margin of error of +3 for a 90% confidence interval for the average number of lawn mowings during summer in a large city with a mean of u and a standard deviation of 0-8.7, a simple random sample of size 18 should be selected. This sample size ensures that the estimate of the population means based on the sample mean is within +3 of the true population mean with 90% confidence.

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Answer:

solution

5x4=20

20-10=10

:kenza need 10 cookies

next method

solution

friends of kenza are =5

wanted cookies for per friends is=4

now

5x4

=20

again

20divide 10=2

then

: she need 2 box .

Answer:

Kenza should get 2 boxes.

Step-by-step explanation:

Total number of cookies needed

= 5×4

= 20

Number of boxes needed

= 20÷10

= 2

Answer:

The answer is 1250

Step-by-step explanation:

5×250=1250

Answer:

1250

Step-by-step explanation:

number of words on one page= 250

number of pages= 5

total number of words=250 x 5

=1250

There 1250 words in the report

PLEASE MARK ME AS BRAINLIEST!!!!!

Answer:

15,420 cm

Step-by-step explanation:

Given the actual distance between the library and train station to be 500 ft, to find the distance between them in centimeters, we ill convert 500 ft to cm as shown;

Given the conversion:

1 ft = 30.48cm

500ft = x cm

Cross multiply

x cm * 1ft= 30.48 cm * 500ft

x cm = 30.48 cm * 500ft/1ft

x cm = 15,240 cm

Hence the distance between them in centimeters on the map is 15,420 cm

Answer:

  B.  -2, 2

Step-by-step explanation:

Apparently, we're to presume that f(x) is the line that is graphed. It has a y-intercept of +1 and a slope (rise/run) of 1/2. Its equation is ...

  f(x) = 1/2x +1

If we want points of intersection, we want to solve the equation f(x) = g(x) for the values of x that make it so.

  1/2x +1 = √(x +2)

Squaring both sides, we get ...

  1/4x² +x + 1 = x +2

  1/4x² = 1 . . . . . . . . . . . . subtract x+1 from both sides

  x² -4 = 0 . . . . . . . . . . multiply by 4, subtract 4

  (x -2)(x +2) = 0 . . . . factor the difference of squares

  x = -2, 2 . . . . . . . . . values of x that make the factors zero

The solutions to f(x) = g(x) are x = -2 and x = 2.

_____

Additional comment

The attached graph shows the x- and y-values at the points of intersection. The solutions to f(x) = g(x) are only the x-values, -2 and 2.

The square of (ax +b) is ...

  (ax +b)² = a²x² +2abx +b²

The point-slope equation of a line is ...

  y = mx + b . . . . . line with slope m and y-intercept b

Answer:

last one

Step-by-step explanation:

Answer:

The equation of a line parallel to the line and passing through (1, -1) is:

Step-by-step explanation:

Given the line

y = -3

We know that the slope-intercept form of the line equation is

\(y=mx+b\)

where m is the slope and b is the y-intercept

Thus, the slope of the equation y=-3 will be m = -3

We know that the parallel lines have the same slopes.

Thus, the slope of the parallel line will also be -3.

Thus, using the point-slope form to find the line equation is

\(y-y_1=m\left(x-x_1\right)\)

substituting the values m = -3 and the point (1, -1)

y-(-1) = -3(x-1)

y+1 = -3x+3

y=-3x+3-1

y=-3x+2

Thus, the equation of a line parallel to line and passing through (1, -1) is:

The monthly payment for this loan is 291.735

Given,

Faith is taking an $8,100.

and, 2.5 year loan with an APR of 3.22%.

To find the monthly payment for this loan.

Simple Interest:-

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = A(0)(1 + rt)

In which:

A(0) is the initial amount.

r is the interest rate, as a decimal.

In this problem, the parameters are A(0) = 8100, r = 0.0322, t = 2.5, hence, the total amount is:

A(t) = 8100[1 + 0.0322(2.5)]

A(t) = 8,752.05

It will be paid over 2.5 x 12 = 30 months, hence the monthly payment is given by:

M = 8,752.05/30

M = 291.735

Hence,  The monthly payment for this loan is 291.735

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Answer:

a. 754cm³ (3 s.f.)

b. 415cm² (3 s.f.)

Step-by-step explanation:

Formulas (for easier reference):

Volume of cone: \(\pi\)r²\(\frac{h}{3}\)

Volume of hemisphere: \(\frac{2}{3}\)\(\pi\)r³

Surface area of cone without base: \(\pi\)rl

Surface area of hemisphere without base: 2\(\pi\)r²

We can just apply the formulas for the question:

Volume of toy = (\(\pi\) × 6² × \(\frac{8}{3}\)) + (\(\frac{2}{3}\) × \(\pi\) 6³)

                        = 96\(\pi\) + 144\(\pi\)

                        = 240\(\pi\)

                        = 754cm³ (3 s.f.)

Surface area of toy = (\(\pi\) × 6 × 10) + (2 × \(\pi\) × 6²)

                                = 60\(\pi\) + 72\(\pi\)

                                = 132\(\pi\)

                                = 415cm² (3 s.f.)

Answer:

Should be 20.

Step-by-step explanation:

360-120=240

240/12=20

the question is about porportionality

y=kx

120=k(12)

k=120/12

k=10

360=10(x)

360=10x

x=360/10

x=36

Answer:

525/50=10.5 it will take 10.5 weeks to get rid of every car we however only need to have below 75 so 525/50w<75

Step-by-step explanation:

First you need to divide 525 by 50 to show how many weeks it will take to sell all the cars. And then it should be one less week than the answer you just reacieved.

Investor purchased 50 shares of stock in a company for $40.

So, the total initial amount he invested is

Then the rate of return is:

So, the requied rate of return is 10.0%.

Answer:

x = 136°

Step-by-step explanation:

We can use a theorem to help us.

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

For exterior angle x, the remote interior angles are z and <CBD.

From the theorem, we get this equation.

x = z + m<CBD

We know z = 52°.

We need to find m<CBD.

Angles CBD and y are a linear pair. They are supplementary, so the sum of their measures is 180°. We are given y = 96°.

m<CBD + y = 180°

m<CBD + 96° = 180°

m<CBD = 84°

x = z + m<CBD

x = 52° + 84°

x = 136°

Answer:

x = 136°

Step-by-step explanation:

∠ABD = y = 96°, ∠ABD + ∠DBC must be equal to 180° because they form a straight angle.

\(y + B = 180\\96 + B = 180\\B = 180 - 96 = 84\)

∠BDC = z = 52° and ∠DBC = B = 84.

Angles ∠BDC, ∠DBC, and ∠BCD must have a sum of 180° because the sum of the interior angles in a triangle is 180°.

\(180=(180 - y) + 52 + C\\180=(180 - 96) + 52 + C\\180 - (52 + 84) = C\\C = 44\)

The interior angle at C is 44. Line DCE forms a straight line, therefore having an angle of 180°. To find x, the sum of x and interior angle C is 180°.

\(180 = C + x\\180 = 44 + x\\x = 180-44\\x = 136\\\)

Angle ∠BCE = x = 136.

The width of the freezer is 2.25ft

The formula for calculating the volume of rectangular prism is expressed as:

V = lwh

Given the following

length l = 8feet

w is the width

height h = 3feet

Substitute

54 = 8*3w

54 = 24w

w = 54/24

w = 2.25ft

Hence the width of the freezer is 2.25ft

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Answer:

Probability = A. 2 / 5

Step-by-step explanation:

Probability = ( Number of Favorable Outcomes ) / (Total Number of Outcomes )

So the Total Number of Students = 20

Number of Students ( Dots ) scored more than 15 = 3+2+1+2 = 8

Probability = 8 / 20 = 2 / 5

Glad to Help

Answer: 12/20= 3/5

Step-by-step explanation:

you have to count all the dots on the dot plot to find your denominator which is 20.

then you count all the dots that are fifteen or more and there are 12 so 12/20 is the probability which is simplified into 3/5.

Answer:

- 18\(\sqrt{10}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

Given

(6\(\sqrt{2}\) )(- 3\(\sqrt{5}\) )

= 6 × - 3 × \(\sqrt{2}\) × \(\sqrt{5}\)

= - 18 × \(\sqrt{10}\)

= - 18\(\sqrt{10}\)

The proportions of the adults who took the 1944 and recent surveys, which were total abstainers, are 0.380 and 0.33, respectively.

(a) Sample proportion for the 1944 survey is calculated as follows: From the 1100 adults surveyed, 418 indicated that they were total abstainers. Therefore, the sample proportion for the 1944 survey is calculated as follows:

p = 418/1100

p = 0.380
(b) Hypotheses:H0: The proportion of adults who abstain from alcohol is equal to 0.380.H1: The proportion of adults who abstain from alcohol is not equal to 0.380. Level of significance = α = 0.05. The test statistic: Z = (p - P) / sqrt [(PQ) / n]

Where: P = Proportion of adults who abstain from alcohol in the 1944 survey = 0.380, Q = 1 - P = 1 - 0.380 = 0.620

p = Proportion of adults who abstain from alcohol in the recent survey = 0.330 n = Total number of adults surveyed = 1100Substituting the values into the equation:

Z = (0.330 - 0.380) / sqrt [(0.380 x 0.620) / 1100]

Z = -2.413

Suppose the calculated Z-value is less than -1.96 or greater than +1.96. In that case, we reject the null hypothesis H0 at α = 0.05 level of significance and conclude that there is a significant difference in the proportion of adults who abstain from alcohol between the two surveys.

At α = 0.05 level of significance, the critical value is ±1.96. Since the calculated Z-value (-2.413) is less than -1.96, we reject the null hypothesis H0 at α = 0.05 significance level. Therefore, there is sufficient evidence to conclude that the proportion of adults who abstain from alcohol has changed between the two surveys.

The sample proportion for the 1944 survey is calculated as follows:

p = 418/1100

p = 0.380

The sample proportion for the recent survey is calculated as follows:

p = 363/1100

p = 0.330.

Therefore, the proportions of adults who took the 1944 and recent surveys, total abstainers, are 0.380 and 0.330, respectively. (Round to three decimal places as needed.

At α = 0.05 level of significance, the critical value is ±1.96. Since the calculated Z-value (-2.413) is less than -1.96, we reject the null hypothesis H0 at α = 0.05 significance level. Therefore, there is sufficient evidence to conclude that the proportion of adults who abstain from alcohol has changed between the two surveys.

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(a)The sample proportion for the 1944 survey is approximately 0.380, and for the recent survey, it is approximately 0.330.(b) The proportion of adults who totally abstain from alcohol has changed at the 0.05 level of significance. Therefore, based on the given data and the hypothesis test, there is evidence to suggest that the proportion of adults who totally abstain from alcohol has changed.

(a) To determine the sample proportion for each sample, we divide the number of total abstainers by the total number of adults surveyed.

For the 1944 survey:

Sample proportion = Number of total abstainers / Total number of adults surveyed

Sample proportion = 418 / 1100

Sample proportion ≈ 0.380 (rounded to three decimal places)

For the recent survey:

Sample proportion = Number of total abstainers / Total number of adults surveyed

Sample proportion = 363 / 1100

Sample proportion ≈ 0.330 (rounded to three decimal places)

The sample proportion for the 1944 survey is approximately 0.380, and for the recent survey, it is approximately 0.330.

(b) To determine if the proportion of adults who totally abstain from alcohol has changed, we can perform a hypothesis test. We can use the chi-square test for proportions to compare the two sample proportions.

The null hypothesis (H_(0)) is that there is no difference in the proportion of adults who totally abstain from alcohol between the two surveys.

The alternative hypothesis (H_(a)) is that there is a difference in the proportion of adults who totally abstain from alcohol between the two surveys.

Using the chi-square test for proportions, we can calculate the test statistic and compare it to the critical value at a significance level of 0.05.

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the proportion has changed. Otherwise, if the test statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that the proportion has not changed.

Since we do not have information about the observed frequencies in each category, we cannot calculate the test statistic directly. However, we can compare the sample proportions using a normal approximation.

The test statistic can be calculated as follows:

z = (p_(1) - p_(2)) / (\sqrt((p × (1 - p)) × ((1 / n_(1)) + (1 / n_(2)))))

Where:

p_(1) = Sample proportion for the 1944 survey

p_(2) = Sample proportion for the recent survey

p = Pooled proportion ([(p_(1) × n_(1)) + (p_(2) × n_(2))] / [n_(1) + n_(2)])

n_(1) = Sample size for the 1944 survey

n_(2) = Sample size for the recent survey

Using the provided values:

p_(1) = 0.380

p_(2) = 0.330

n_(1) = 1100

n_(2) = 1100

Let's calculate the test statistic:

p = [(p_(1) × n_(1)) + (p_(2) × n_(2))] / [n_(1) + n_(2)]

= [(0.380 × 1100) + (0.330 × 1100)] / (1100 + 1100)

= (418 + 363) / 2200

≈ 0.377 (rounded to three decimal places)

z = (p_(1) - p_(2)) / (\sqrt((p × (1 - p)) × ((1 / n_(1)) + (1 / n_(2)))))

= (0.380 - 0.330) / (\sqrt((0.377 × (1 - 0.377)) × ((1 / 1100) + (1 / 1100))))

≈ 2.639 (rounded to three decimal places)

Using a significance level of 0.05, we can compare the test statistic to the critical value from the standard normal distribution. The critical value for a two-tailed test with a significance level of 0.05 is approximately ±1.96. Since the test statistic (2.639) is greater than the critical value ( (1.96), we reject the null hypothesis. We conclude that the proportion of adults who totally abstain from alcohol has changed at the 0.05 level of significance.

Therefore, based on the given data and the hypothesis test, there is evidence to suggest that the proportion of adults who totally abstain from alcohol has changed.

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Answer:

If you can buy four bulbs of garlic for $8, then with $32, you can buy 4 times as many bulbs. That means buying 4 * 4 = 16 garlic bulbs for $32.

Answer:

16 garlic bulbs for 32

Step-by-step explanation:

you can buy 4 times as many

Given:

\(a_n\) is an arithmetic sequence.

To find:

The value of \(\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\).

Solution:

We have,

\(\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\)

It can be written as:

\(=\dfrac{d}{d}\left[\dfrac{1}{a_1a_2}+\dfrac{1}{a_2a_3}+...+\dfrac{1}{a_{39}a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{d}{a_1a_2}+\dfrac{d}{a_2a_3}+...+\dfrac{d}{a_{39}a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{a_2-a_1}{a_1a_2}+\dfrac{a_3-a_2}{a_2a_3}+...+\dfrac{a_{40}-a_{39}}{a_{39}a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_2}+\dfrac{1}{a_2}-\dfrac{1}{a_3}+....+\dfrac{1}{a_{39}}-\dfrac{1}{a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{1}{a_1}-\dfrac{1}{a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{a_{40}-a_1}{a_1a_{40}}\right]\)

\(=\dfrac{1}{d}\left[\dfrac{a_1+(40-1)d-a_1}{a_1a_{40}}\right]\)       \([\because a_n=a_1+(n-1)d]\)

\(=\dfrac{1}{d}\left[\dfrac{39d}{a_1a_{40}}\right]\)

\(=\dfrac{39}{a_1a_{40}}\)

Therefore, the value of given expression is \(\dfrac{39}{a_1a_{40}}\).

We can identify a correct system of equations after draw the graph of the system. The point of intersection indicates the correct solution of the system.

Two or more equations which have the same variables, and we can use these all together. The equations are called a set of equations. We get the solution from the system while plotting in the XY coordinate system.

Such as we have two or more linear equations, and we solve each equation and draw a graph for each. We will notice a point of intersection of the straight lines and that refers the solution of the system of equation.

There are many sets or system of equation. Some systems have infinity many solutions and graph of the equations never intersect each other. In the next, there are system of equations such as a set of linear function from where we get a point of intersection after plotting the graphs together. The line of intersection is the correct solution of the system.

On the other hand, there are some sets which have no solution, and they are called inconsistent.

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Answer: view below

Step-by-step explanation:

a. \(-\frac{2}{3}x \geq 7\)

\(x\leq -\frac{21}{2}\)

b. 32>23-x

x>-9

c. 2(x+6)<10

x+6<5

x<-1

d. 15-4x\(\leq 3x-6\)

21\(\leq\)7x

3\(\leq\)x

x\(\geq\)3

Answer:

I-11I

Step-by-step explanation:

To find the distance between two numbers, find the absolute value of each number and add them together.

I-11I = 11

I0I = 0

11 + 0 = 11

Answer:

Hope this helps!

Step-by-step explanation:

The answer is 11. To find the distance between two numbers, find the absolute value of each number and add them together.

The desired statistical measures are given as follows:

1. The margin of error is of \(M = \frac{6.75}{\sqrt{n}}\).

2. The margin of error is of 0.02 = 2%.

3. The point estimate is of 0.655.

We also have to be given the sample size n, along with the standard deviation s, and the margin of error is given by:

\(M = \frac{s}{\sqrt{n}}\)

In item 1, we have that s = 6.75, hence the margin of error is:

\(M = \frac{6.75}{\sqrt{n}}\)

The margin of error is given by half the subtraction of the bounds, hence, for item 2:

(0.37 - 0.33)/2 = 0.02.

The margin of error is of 0.02 = 2%.

The points estimate is given by the mean of the bounds, hence, for item 3:

M = (0.61 + 0.70)/2 = 0.655.

The point estimate is of 0.655.

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The 90% confidence interval estimate for the population mean of hotel room prices in New York City is $256.01 to $289.99.

A confidence interval is a range of values that is likely to contain the true population mean with a certain degree of confidence.

To calculate the confidence interval for the population mean of hotel room prices in New York City, we need to use the formula:

CI = x ± (Zα/2)(σ/√n)

where x is the sample mean, σ is the sample standard deviation, n is the sample size, and Zα/2 is the critical value of the standard normal distribution for the chosen confidence level (in this case, 90%).

Plugging in the given values, we have:

CI = 273 ± (1.645)(65/√45)

Simplifying this expression, we get:

CI = 273 ± 16.99 =  [256.01 , 289.99].

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Answer:

Step-by-step explanation:

The total balance he will have in the accounts at the end of 2 years

is D. $870.88.

What are simple and compound interests?

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

The formula for simple interest is SI = (p×r×t)/100 and the formula for compound interest is A = P(1 + r/100)ⁿ.

∴ P + (p×r×t)/100 + P(1 + r/100)ⁿ is the total amount after 2 years.

= 450 + (450×4.5×2)/100 + 350(1 + 4.25/100)².

= 450 + 40.5 + 350(1.0425)².

= 490.5 + 380.38.

= $870.88.