Apply the distributive property to the expression to write an equivalent expression. Complete the statements.

4x + 16

Find the GCF of
_______
.
Now factor out the GCF by dividing each term in the expression by
.__________
4x divided by the GCF is _________
, and 16 divided by the GCF is _______
.

The equivalent expression is _______
.

Answer:

80 feet per second

Step-by-step explanation: At 55 mph, your vehicle is traveling at about 80 feet per second. Feet-per-second is determined by multiplying speed in miles-per-hour by 1.47 (55 mph x 1.47 = 80 feet per second.)

The correct option is (B) Since the tSTAT value is greater than the critical value, reject H0.

A one-tailed hypothesis test, critical value = 2.485, tSTAT = +3.114.

In a one-tailed hypothesis test, we have:

1. Null hypothesis H0: The population parameter is less/greater than or equal to a certain value.

2. Alternative hypothesis H1: The population parameter is greater than/less than a certain value.

We reject the null hypothesis if the test statistic tSTAT is greater than the critical value, otherwise we fail to reject the null hypothesis.

Here, tSTAT = +3.114 is greater than the critical value of 2.485. Therefore, our statistical decision is to reject the null hypothesis H0.

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The part of the circle with the term is given.

A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.

The matches of the part of the circle with the respective term is given below:

GH ↔ chord

M ↔ point of tangency

MJ ↔ diameter

J ↔ center

MH ↔ radius

GH ↔ secant

Therefore, all the part of the circle are matched with the respective term.

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Answer:

in any quadrilateral, the sum of the interior angles is 360 degrees, so angles

a+b+c+d = 360 degrees.

But a = 2b

and b = 2c

and c = 2d so...

b = 4d and

a = 8d so we have:

8d+4d+2d+d = 360

15d = 360 and

d = 24 degrees

c = 2(24) = 48 degrees and

b = 4(24) = 96 degrees and

a = 8(24) = 192 degrees.

(x+1)^2 + 3

you just put the value of g(x)in f(x)

Answer:

1/2

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

Answer:

4 and 6

Step-by-step explanation:

After one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

To calculate the amount of money you will have in the savings account after one year with compound interest, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

Let's solve it step by step:

Given:

P = $3,000 (principal amount)

r = 6% = 0.06 (annual interest rate as a decimal)

n = 1 (compounded annually)

t = 1 (one year)

Using the formula:

A = 3000 * (1 + 0.06/1)^(1*1)

A = 3000 * (1 + 0.06)^1

A = 3000 * (1.06)^1

A ≈ $3180

So, after one year of compounding at a 6% interest rate, you would have approximately $3,180 in your savings account.

It seems there was a discrepancy in the answer provided. Based on the given information, the correct calculation yields $3,180, not $5,372.54.

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The relationship between x and y is a strong negative relationship.

For this question, we need to determine the correlation coefficient,

Thus,

The correlation coefficient

= (21 - 5*6)/ \(\sqrt{9 * 10}\)

= -0.948

The above answer is too close to -1. Therefore correlation coefficient is a strong negative.

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The cables need to be about 159.10 feet long and anchored about 86.81 feet from the base of the tower.

Let's call the length of each cable "x" and the distance from the base of the tower to the point where each cable is anchored "y".

Since there are four cables, we can think of them as forming a square around the tower. The diagonal of that square is equal to the length of one cable multiplied by the square root of 2. So we have:

x * sqrt(2) = 225

Solving for x, we get:

x = 225 / sqrt(2) ≈ 159.10 feet

Now we can use trigonometry to find y. We know that the sine of the angle between the ground and each cable is equal to y divided by x, so we have:

sin(32.5) = y / x

Solving for y, we get:

y = x * sin(32.5) ≈ 86.81 feet

So the cables need to be about 159.10 feet long and anchored about 86.81 feet from the base of the tower.

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Answer:

A

Step-by-step explanation:

you must distribute the 3 into the parenthsis first.

The volume of the solid generated when the region bounded by y = 9x and y = 27x/x is revolved around the x-axis is given by V = 27lnx - 9x + c

To calculate this volume, we need to calculate the area of the cross-section of a shell at x.

The cross-section is found by taking the difference of the two curves, y = 9x and y = 27x/x, at that particular x in the form of a rectangle.

The height of the rectangle is y₂ - y₁ and the width is the interval dx. Therefore, the area of the cross-section is given by

A(x) = (y₂ - y₁)dx = [(27x/x - 9x)dx].

The volume of the solid is then given by the formula

=> V = ∫A(x)dx.

Substituting in the expression for A(x), we have

=>  V = ∫(27x/x - 9x)dx.

Integrating this expression, we get V = 27lnx - 9x + c, where c is an arbitrary constant.

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The mean for grouped data can be calculated when data has been grouped into class intervals in a frequency distribution. (Option A)

When data has been grouped into class intervals, it is not possible to calculate the exact mean of the data. Instead, we use the midpoint of each class interval as a representative value for that interval. Then, we calculate the weighted average of these midpoints to find the mean for grouped data.

Options C and D, the variance and standard deviation, respectively, cannot be directly computed from grouped data. However, we can estimate them using the assumed normal distribution of the data within each class interval and the mean for grouped data.

Therefore, the correct answer is option A: the mean for grouped data can be calculated when data has been grouped into class intervals in a frequency distribution.

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SAT math scores for an ap statistics class of 20 students: 664, 658, 610, 670, 640, 643, 675, 650, 676, 575, 660, 661, 520, 667, 668, 635, 671, 673, 645, and 650 the distribution of scores is

skewed to the left. The correct answer is (b).

To determine the shape of the distribution of SAT math scores for the AP statistics class, we can create a histogram or a box plot. From the provided scores, we can see that the range of the scores is 520 to 676.

The distribution appears to be slightly skewed to the left as there are a few scores on the lower end, but most of the scores are grouped in the middle and upper end of the range. Additionally, the mean score is 648.6, which is slightly lower than the median score of 658, indicating that the distribution is slightly negatively skewed.

The distribution of SAT math scores for the AP statistics class is slightly skewed to the left, which means that there are more scores on the higher end of the range, and a few lower scores.

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The probability that over 2000 gallons were used during the month if the firm uses more than 900 gallons is 0.004190082 which is approximately equal to 0.0042. Hence, the correct option is D) 0.446.

In order to find the probability that over 2000 gallons were used during a particular month if the firm uses more than 900 gallons, we will have to use Poisson distribution.

Poisson distribution is a statistical technique that allows us to model the probability of a certain number of events occurring within a given time interval or a given area.

A Poisson distribution can be used when the following conditions are satisfied:

Let's assume λ is the average rate of occurrence which is 900.Since we are given that the average rate of occurrence is 900, the probability of exactly x events occurring in a given time interval or a given area is given by:P(x; λ) = (e-λλx) / x!For x > 0 and e is

Euler’s number (e = 2.71828…).

We can write:

P(X > 2000)

= 1 - P(X ≤ 2000)P(X ≤ 2000) = ΣP(x = i; λ) for i = 0 to 2000.

We can use the Poisson Probability Calculator to find ΣP(x = i; λ).

When λ = 900, the probability that X is less than or equal to 2000 is:ΣP(x = i; λ) for

i = 0 to 2000 is 0.995809918The probability that X is greater than 2000 is:1 - P(X ≤ 2000)

= 1 - 0.995809918

= 0.004190082 (Approx)

Therefore, the probability that over 2000 gallons were used during the month if the firm uses more than 900 gallons is 0.004190082 which is approximately equal to 0.0042. Hence, the correct option is D) 0.446.

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The value of nickels is $76.80.

The height of each nickel is 6.25 / 100 = 0.0625 inches.

Divide 8 feet by 0.0625 inches to find that there are

8×12 / 0.0625 = 1536 nickels in an 8 ft stack.

Their value is $76.80.

Nickel is a chemical detail with the symbol Ni and atomic range 28. It is silvery-white lustrous steel with a mild golden tinge. Nickel belongs to the transition metals and is hard and ductile.

Pure nickel, powdered to maximize the reactive surface vicinity, indicates a widespread chemical interest, but large pieces are slow to react with air underneath fashionable conditions because an oxide layer paperwork at the floor stops further corrosion (passivation).

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Answer:

Step-by-step explanation:

52 predicted that they will pass which means that (80-52) = 28 predicted that they will fail.

people who passed among the predicted ones = 52 * 3/4 = 39 people

54 people pass altogether so people who passed among the ones who predicted they will fail = 54 -39 = 15 people

percentage = 15/28 * 100 = 53.6 %

The z-test statistic for testing the claim that the proportion of people in the population who rent an apartment is 0.30, based on a random sample of 400 people with a sample proportion of 0.60, and assuming a population standard deviation of 0.25, is approximately 10.67.

The z-test statistic is used to assess whether a sample proportion significantly differs from a hypothesized population proportion. In this case, the economist wants to determine if the sample proportion of 0.60 is significantly different from the hypothesized population proportion of 0.30.

To calculate the z-test statistic, we use the formula:

z = (sample proportion - hypothesized proportion) / standard deviation

Plugging in the given values, we have:

z = (0.60 - 0.30) / 0.25

Simplifying the equation, we get:

z = 0.30 / 0.25

Performing the division, we find:

z ≈ 1.20

Therefore, the z-test statistic is approximately 1.20. This means that the sample proportion of 0.60 is 1.20 standard deviations away from the hypothesized population proportion of 0.30. The larger the absolute value of the z-test statistic, the stronger the evidence against the null hypothesis (the claim being tested). In this case, since the z-test statistic is 1.20, which is not very large, we would not have strong evidence to reject the claim that the proportion of people who rent an apartment is 0.30 in the population.

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The two values of x in the equation are x = -8 and x = 8

The equation is given as

x² - 14 = 50

Add 14 to both sides of the equation

So, we have the following equation

x² - 14 + 14 = 50 + 14

Evaluate the like terms

So, we have the following equation

x² = 64

Take the square roots of both sides

√x² = ±√64

Evaluate the square roots

So, we have the following equation

x = ±8

Split

x = -8 and x = 8

Hence, the values are x = -8 and x = 8

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Answer:

D) 8ft

Step-by-step explanation:

Let width=w

Let length=w+6

w(w+6)=112

w^2+6w=112

subtract 112 from both sides

w^2+6w-112=0

factor

(w-8)(w+14)=0

w=8

w=-14

since you can't have a negative length, your answer would be 8

Answer:

Step-by-step explanation:

Start with where it tells you the value of x. The value of x is 3. That's given by    f(x) = f(3)

Next see which one of the functions you use. x > 0 is given by x^4 - 7. Since 3 is greater than zero you use x^4 - 7

f(3) means that wherever you see an x on the right side, you put a 3.

f(x) = x^4 - 7

f(3) = 3^4 - 7

f(3) = 81 - 7

f(3) = 74

Answer:

\(\textsf{a) \quad $\dfrac{2}{5}$}\)

\(\textsf{b) \quad $\dfrac{5}{2}$}\)

Step-by-step explanation:

Given expression:

\(\left(\dfrac{4}{25}\right)^{\frac{1}{2}}\)

Rewrite 4 as 2² and 25 as 5²:

\(\implies \left(\dfrac{2^2}{5^2}\right)^{\frac{1}{2}}\)

\(\textsf{Apply the exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:\)

\(\implies \dfrac{(2^2)^{\frac{1}{2}}}{(5^2)^{\frac{1}{2}}}\)

\(\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies \dfrac{2^{(2\cdot\frac{1}{2})}}{5^{(2\cdot\frac{1}{2})}}\)

\(\implies \dfrac{2^1}{5^1}\)

\(\implies \dfrac{2}{5}\)

Given expression:

\(\left(\dfrac{4}{25}\right)^{-\frac{1}{2}}\)

Rewrite 4 as 2² and 25 as 5²:

\(\implies \left(\dfrac{2^2}{5^2}\right)^{-\frac{1}{2}}\)

\(\textsf{Apply the exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:\)

\(\implies \dfrac{(2^2)^{-\frac{1}{2}}}{(5^2)^{-\frac{1}{2}}}\)

\(\textsf{Apply the exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies \dfrac{2^{(2\cdot -\frac{1}{2})}}{5^{(2\cdot -\frac{1}{2})}}\)

\(\implies \dfrac{2^{-1}}{5^{-1}}\)

\(\textsf{Apply the exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:\)

\(\implies \dfrac{1}{2^1 \cdot 5^{-1}}\)

\(\implies \dfrac{1}{2 \cdot 5^{-1}}\)

\(\textsf{Apply the exponent rule} \quad \dfrac{1}{a^{-n}}=a^n:\)

\(\implies \dfrac{5^1}{2}\)

\(\implies \dfrac{5}{2}\)

9514 1404 393

Answer:

  16.  134°

  17.  20°

  18.  94°

Step-by-step explanation:

An inscribed angle is half the measure of the arc it intercepts.

__

16. Arc QT is twice the measure of inscribed angle QST, given as 67°.

  Arc QT = 2×67°

  Arc QT = 134°

__

17. Angle STR is half the measure of arc SR, so is ...

  m∠STR = (arc SR)/2 = 40°/2

  m∠STR = 20°

__

18.  Arc RST is a semicircle, so has a measure of 180°. Then arc ST is the difference between that and arc RS:

  arc ST = 180° -40° = 140°

Angle RST subtends a semicircle, so is 180°/2 = 90°. We know angle QST is 67°, so the remaining portion, angle QSR must be the complement of that:

  m∠QSR = 90° -67° = 23°

Arc RQ will be twice this measure, or 46°.

So, the desired difference is ...

  mST -mRQ = 140° -46° = 94°

According to the information the correct match would be: 3 1/2 - This is a rational number, but not an integer, 0.56 - This is a rational number, but not an integer, 5 - This is an integer, Square root of 11 - This is an irrational number, -3 1/2 - This is a rational number, but not an integer.

To determine the type of number, we need to understand the properties of each number.

3 1/2 can be expressed as the fraction 7/2, which is a rational number (a number that can be expressed as a fraction), but not an integer (a whole number without a fractional or decimal part).

0.56 is a rational number as it can be expressed as the fraction 28/50, but it is not an integer as it has a decimal part.

5 is an integer because it is a whole number without any fractional or decimal part.

The square root of 11 is an irrational number since it cannot be expressed as a fraction or a terminating or repeating decimal.

-3 1/2 can be expressed as the fraction -7/2, which is a rational number (a number that can be expressed as a fraction), but it is not an integer (a whole number without a fractional or decimal part).

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Answer:

1 1/2

Step-by-step explanation:

[Given]

5 1/3 − 3 5/6

[Subtract whole numbers

5 - 3 = 2

[Get common denominters]

1/3 -> 2/6

[Subtract fractions]

2/6 - 5/6 = -3/6 = -1/2

[Simplify

2 - 1/2 = 1 1/2

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Therefore, Drug C has a stronger impact on cell survival compared to Drug A, making it the drug with the greatest effect.

To draw a representation of the survival curve and identify the drug that has the greatest effect on cell survival, we can use a graph where the x-axis represents the drug concentration in μg/ml, and the y-axis represents the percentage of cell survival.

Since Drug B has no IC90 value, it means that it does not reach a concentration that causes a 90% reduction in cell survival. Therefore, we can assume that Drug B has no significant effect on cell survival and can omit it from the survival curve.

For Drug A and Drug C, we have IC90 values of 5 and 3 μg/ml, respectively. This means that when the drug concentration reaches these values, there is a 90% reduction in cell survival.

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Answer:

3/10 liters more

Step-by-step explanation:

8/10 - 5/10 = 3/10

PreAlg students spend significantly less time doing homework compared to ElemAlg and InterAlg students, while there is no significant difference in homework time between ElemAlg and InterAlg students.

What is significantly ?

Significantly" is the keyword that indicates a notable or meaningful difference or result in the context of statistical analysis. It is often used to describe findings that have a high level of confidence and statistical significance, indicating that the observed difference or relationship is unlikely to have occurred by chance.

Based on the given data and statistical analysis, the conclusion is as follows:

PreAlg compared to ElemAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for ElemAlg (3.18) with a t-value of 5.08 and a p-value of 0.000. Therefore, we can conclude that PreAlg students spend significantly less time doing homework compared to ElemAlg students.

PreAlg compared to InterAlg:

The sample mean for PreAlg (1.32) is significantly different from the sample mean for InterAlg (4.42) with a t-value of 3.64 and a p-value of 0.003. Hence, we can conclude that PreAlg students spend significantly less time doing homework compared to InterAlg students.

ElemAlg compared to InterAlg:

The sample mean for ElemAlg (3.18) is not significantly different from the sample mean for InterAlg (4.42) with a t-value of 1.49 and a p-value of 0.163. Therefore, we fail to reject the null hypothesis, and we cannot conclude a significant difference in homework time between ElemAlg and InterAlg students.

In summary, the PreAlg students have significantly lower homework time compared to both ElemAlg and InterAlg students. However, there is no significant difference in homework time between ElemAlg and InterAlg students.

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Answer:

48 cents

Step-by-step explanation:

divsion sorry im not a math lord

Answer:

F. 1.978 > 18979

Step-by-step explanation: