Solve equation
10y=6y+5+3y
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The expression factoring out the greatest common factor is  (3pf - 21p²)(f + 2).

We have the expression as

3pf² - 21p²f + 6pf - 42p²

Now, factorising the expression as

= 3pf² + 6pf - 21p²f - 42p²

= 3pf(f +2) - 21p²(f + 2)

= (3pf - 21p²)(f +2)

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Considering the sequences given, the first number that appears in both sequences is given by: 45.

The rule is multiply by 3 starting from 5, hence the numbers are:

(5, 15, 45, 135, ...).

The rule is add 9 starting from 18, hence the numbers are:

(18, 27, 36, 45, ...).

45 is the first number that appeared in both sequences.

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Answer:

The explanatory variable is the type of program the people watched. The response variable is the number of calories consumed. This was an experiment.

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong

\(4\frac{2}{4}\) that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.

\(4\frac{2}{4} = \frac{16+4}{2}\)

=\(\frac{18}{4}\)

Then \(4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}\)

Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that \(\frac{18}{4}\) is less than \(\frac{37}{4}\) Hence, Darren is wrong.

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Answer:

You would tell them by labeling the x and y and the titles of the graph and what corresponds to it

Step-by-step explanation:

Every cardio class lasts for 41 minutes and every weightlifting class lasts for 35 minutes.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, Bridgette plans to attend 4 cardio classes and 5 weightlifting classes, which will last a total of 339 minutes. Next week, she hopes to attend 3 cardio classes and 1 weightlifting class, which will last a total of 158 minutes.

Let number of minutes spend in cardio be c and that of in weightlifting be w,

Establishing the equations, we get,

4c+5w = 339....(i)

3c+w = 158...(ii)

Multiplying eq(ii) by 5 and then subtracting eq(i) from eq(ii)

(15c+5w = 790) - (4c+5w = 339)

11c = 451

c = 41

Put c = 41 in eq(ii)

123+w = 158

w = 35

Hence, Every cardio class lasts for 41 minutes and every weightlifting class lasts for 35 minutes.

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This question is incomplete, the complete question is;

A sociologist wants to construct an 80 confidence interval for the proportion of children aged 8-10 living in New York who own a cell phone.

(a) A survey by the National Consumers League taken in 2012 estimated the nationwide proportion to be 036. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02?

Answer:

the required or needed sample size is 946

Step-by-step explanation:

Given the data in the question;

confidence level = 80%

⇒ 100( 1 - ∝ )% = 80%

100 - 100∝ = 80

100∝ = 100 - 80

∝ = 20/100

level of significance ∝ = 0.2

\(Z_{\alpha /2\) = \(Z_{0.10\) = 1.2816 { from z-table }

p = 0.36

Allowable margin of error E = 0.02

let n be the required sample size.

we know that

E = √( p( 1 - p) / n )

given that margin of error E = 0.02

⇒ √( p( 1 - p) / n ) × \(Z_{\alpha /2\) = 0.02

⇒ √( 0.36( 1 - 0.36) / n ) × 1.2816  = 0.02

⇒ √( 0.2304 / n ) × 1.2816 = 0.02

√( 0.2304 / n ) = 0.02 / 1.2816

√( 0.2304 / n ) = 0.01560549

( 0.2304 / n ) = ( 0.01560549)²  

0.2304 / n  = 0.000243531318

n = 0.2304 / 0.000243531318

n = 946

Therefore, the required or needed sample size is 946

Answer:

3

Step-by-step explanation:

(8x + 28) / ((x − 1) (x + 2) (x + 3)) = A / (x − 1) + B / (x + 2) + C / (x + 3)

Multiply both sides by (x − 1) (x + 2) (x + 3).

8x + 28 = A (x + 2) (x + 3) + B (x − 1) (x + 3) + C (x − 1) (x + 2)

If x = 1:

8 + 28 = A (3) (4)

36 = 12A

A = 3

Answer:

\(B.(2,1)\)

Step-by-step explanation:

Answer

approximately 0.0067

Step-by-step explanation:

If you multiply 0.0067 with 16,500 you get about 110.55 and the more you keep going with the 6, the closer it gets to 110$.

The required amount of the space available is 0.045 cubic meter.

We need to determine Space inside the steps.

The Volume is defined as the mass of object per unit density.

The required space = 0.3*0.4*0.5 - 0.15*0.5*0.2

                                 =  0.06 - 0.015

                                 =    0.045 cubic meter

Hence, the required amount of the space available will be 0.045 cubic meter.

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Answer:

$123

Step-by-step explanation:

238 + 365 = 603

603 - 480 = 123

Answer: It’s not correct, the equality is false. The reasoning behind this is the equality is the left-hand and right-hand side are different when you do the math.no

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

Answer:

Option A because functions only point to 1 output.

Answer: A) \(f(x)=\frac{6x^2-x+4}{2x^2-1}\)

Step-by-step explanation:

Line \(y=L\) is a horizontal asymptote of the function \(y=f(x)\), if either \(\lim_{x \to \infty} f(x)=L\) or \(\lim_{x \to \infty} f(x)=L\), and \(L\) is finite.

calculate the limits:

\(\lim_{x \to \infty} (\frac{6x^2-x+4}{2x^2-1})=3\)

\(\lim_{x \to -\infty} (\frac{6x^2-x+4}{2x^2-1})=3\)

Thus, the horizontal asymptote is \(y=3\)

The characteristic that is representative of a FUSION reaction is: B. The reaction happens predominantly in stars, like our sun.

A reaction is a process that involves the transformation of one or more substances into new substances with different physical and/or chemical properties. Reactions can be classified as either physical or chemical depending on the nature of the change that occurs. In a physical reaction, the identity of the substances remains the same, but their physical properties, such as size, shape, or phase, may change. Examples of physical reactions include melting, freezing, boiling, and condensation.

Here,

Fusion reactions involve the joining together of two atomic nuclei to form a heavier nucleus, releasing a large amount of energy in the process. These reactions occur naturally in stars, including our sun, where the high temperatures and pressures allow the atomic nuclei to overcome their mutual repulsion and come close enough to fuse. While scientists are working on developing fusion reactors for use on Earth, the technology is still in the experimental stage and is not yet cost-effective for widespread use. However, fusion reactions do not produce long-lasting radioactive waste as in the case of nuclear fission reactions.

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Answer:

21.72% is correct answer

Answer:

18.4

Step-by-step explanation:

The correct answer is Confidence interval lower bound: 32.52 cm,Confidence interval upper bound: 37.48 cm

To calculate the confidence interval for the true mean height of the loaves, we can use the t-distribution. Given that the sample size is small (n = 10) and the population standard deviation is unknown, the t-distribution is appropriate for constructing the confidence interval.

The formula for a confidence interval for the population mean (μ) is:

Confidence Interval = sample mean ± (t-critical value) * (sample standard deviation / sqrt(sample size))

For the first situation:

n = 15

Confidence level is 95% (which corresponds to an alpha level of 0.05)

x = 35 (sample mean)

s = 2.7 (sample standard deviation)

Using RStudio or a t-table, we can find the t-critical value. The degrees of freedom for this scenario is (n - 1) = (15 - 1) = 14.

The t-critical value at a 95% confidence level with 14 degrees of freedom is approximately 2.145.

Plugging the values into the formula:

Confidence Interval = 35 ± (2.145) * (2.7 / sqrt(15))

Calculating the confidence interval:

Lower Bound = 35 - (2.145) * (2.7 / sqrt(15)) ≈ 32.52 (rounded to 2 decimal places)

Upper Bound = 35 + (2.145) * (2.7 / sqrt(15)) ≈ 37.48 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 32.52 cm, and the upper bound is approximately 37.48 cm.

For the second situation:

n = 37

Confidence level is 99% (which corresponds to an alpha level of 0.01)

x = 82 (sample mean)

s = 5.9 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (37 - 1) = 36.

The t-critical value at a 99% confidence level with 36 degrees of freedom is approximately 2.711.

Plugging the values into the formula:

Confidence Interval = 82 ± (2.711) * (5.9 / sqrt(37))

Calculating the confidence interval:

Lower Bound = 82 - (2.711) * (5.9 / sqrt(37)) ≈ 78.20 (rounded to 2 decimal places)

Upper Bound = 82 + (2.711) * (5.9 / sqrt(37)) ≈ 85.80 (rounded to 2 decimal places)

Therefore, the lower bound of the confidence interval is approximately 78.20 cm, and the upper bound is approximately 85.80 cm.

For the third situation:

n = 1009

Confidence level is 90% (which corresponds to an alpha level of 0.10)

x = 0.9 (sample mean)

s = 0.04 (sample standard deviation)

The degrees of freedom for this scenario is (n - 1) = (1009 - 1) = 1008.

The t-critical value at a 90% confidence level with 1008 degrees of freedom is approximately 1.645.

Plugging the values into the formula:

Confidence Interval = 0.9 ± (1.645) * (0.04 / sqrt(1009))

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The average is 40 and  the margin of error is 10.95.

What is margin of error?

The margin of error is a statistic expressing the amount of random sampling in the result of a survey.

Average (A) = sum of all the value/ given set.

A = (51+ 41 + 28)/3 = 40

margin of error = 100/square root of 120 = 10.95.

Therefore, the average is 40 and  the margin of error is 10.95.

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Answer:

thx m8

Step-by-step explanation:

:)

Answer:

No idea but ok

Answer:

x<12

Step-by-step explanation:

subtract both sides by -3 because you need to isolate x. then you have x/4<3. now you need to get rid of the 4. so you do the opposite of division and multiply 4 by both sides so you get x<12

Answer:

074°

Step-by-step explanation:

the bearing of Y from X is the measure of the angle from the north line (N) at X in a clockwise direction to Y , that is ∠ NXY

∠ NXY = 180° - 106° = 74°

the 3- figure bearing of Y from X is 074°

Answer:

Step-by-step explanation:

-7-1=-8

Answer:

1 * 10^16 or 10000000000000000

Step-by-step explanation:

Answer: 1e+16 or 10000000000000000

Step-by-step explanation: Just multiply it