How is a proportional relationship different from a non-proportional relationship?

Answer:

Step-by-step explanation:

14√5 - 50√2

Let's solve ourselves instead of believing anyone

\(\\ \rm\Rrightarrow (x^2)^7=x^4x^8\)

\(\\ \rm\Rrightarrow x^{14}=x^{4+8}\)

\(\\ \rm\Rrightarrow x^{14}=x^{12}\)

\(\\ \rm\Rrightarrow x^{14}-x^{12}=0\)

\(\\ \rm\Rrightarrow x^{12}(x^2-1)=0\)

\(\\ \rm\Rrightarrow x^2-1=0\)

\(\\ \rm\Rrightarrow x^2=1\)

\(\\ \rm\Rrightarrow x=\pm 1\)

Answer:

Joe is correct

Step-by-step explanation:

Given equation:

\((x^2)^?=x^4 \cdot x^8\)

The exponent outside the bracket is a question mark and the students are trying to determine the value of the question mark.

For ease of answering, let y be the unknown number (question mark):

\(\implies (x^2)^y=x^4 \cdot x^8\)

First, simplify the equation by applying exponent rules to either side of the equation:

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

\(\implies (x^2)^y=x^4 \cdot x^8\)

\(\implies x^{2y}=x^4 \cdot x^8\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c} \quad \textsf{to the right side}:\)

\(\implies x^{2y}=x^4 \cdot x^8\)

\(\implies x^{2y}=x^{4+8}\)

\(\implies x^{2y}=x^{12}\)

Now, apply the exponent rule:

\(x^{f(x)}=x^{g(x)} \implies f(x)=g(x)\)

Therefore,

\(x^{2y}=x^{12}\implies 2y=12\)

Finally, solve for y:

\(\implies 2y=12\)

\(\implies 2y \div 2 = 12 \div 2\)

\(\implies y=6\)

Therefore, Joe is correct as the unknown number is 6.

Answer:

342:9, 38 cans per bag

Step-by-step explanation:

In this number theory problem, we are given that the product of 36 and the square of a number is equal to 121. Let the number be x, so the equation is 36 * x^2 = 121. To solve for x, divide both sides by 36: x^2 = 121/36.

In number theory, we are given that the product of 36 and the square of a number is equal to 121. We can solve for the unknown number by using algebraic equations. Let the number be represented by x. Therefore, we can write the equation 36x^2 = 121. By dividing both sides by 36, we get x^2 = 121/36. Taking the square root of both sides, we obtain x = ±11/6. Thus, the two possible numbers are 11/6 and -11/6. To write the numbers from least to greatest, we can use the fact that negative numbers are smaller than positive numbers. Therefore, the numbers from least to greatest are -11/6 and 11/6. In conclusion, the product of 36 and the square of a number can be solved using algebraic equations to find the possible numbers and they can be ordered from least to greatest. Taking the square root of both sides gives us x = ±(11/6). The two numbers are -11/6 and 11/6. Writing these numbers from least to greatest, we have -11/6 and 11/6. In summary, the two numbers whose product with 36 equals 121 are -11/6 and 11/6, ordered from least to greatest.

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Answer:

2/3

Step-by-step explanation:

1-1/3 is the same that   3/3 - 1/3

3/3 - 1/3 = 2/3

Answer: The y-intercept is -6.

Step-by-step explanation: The line crosses through the y (Straight up and down line) on -6. I hope this helps! :)

Answer:

15 is the answer

Answer:

\({ \tt{27 = {3}^{3} }} \\ { \tt{}} \sqrt[4]{27} = {27}^{ \frac{1}{4} } \\ { \tt{ = {3}^{3( \frac{1}{4}) } }} \\ = { \tt{ {3}^{ \frac{3}{4} } }} \\ { \boxed{ \bf{a = 3 \: \: and \: \: k = \frac{3}{4} }}}\)

Answer:

96

Step-by-step explanation:

Let's assume that the marks needed in the next exam is \(x\). Then if the average becomes 90,

\(\frac{80 + 93 + 91 + x}{4}= 90\)

Now we can simply solve for \(x\):

⇒ \(\frac{264 + x}{4}= 90\)

⇒ \(264 + x = 360\)            [Multiplying both sides by 4]

⇒ \(x = 360 - 264\)            [Subtracting 264 from both sides]

⇒ \(x = \bf96\)

Therefore, you need to score 96 in your next exam to have an average of 90 on the four exams.

Answer:

40°, 80°, 120°, 120°

Step-by-step explanation:

sum the parts of the ratio, 1 + 2 + 3 + 3 = 9 parts

The sum of the interior angles of a quadrilateral is 360°

Divide this by 9 to find the value of one part of the ratio.

360° ÷ 9 = 40° ← value of 1 part of the ratio

Then

2 parts = 2 × 40° = 80°

3 parts = 3 × 40° = 120°

The 4 angles are 40°, 80°, 120°, 120°

Answer:

x=3

Step-by-step explanation:

substitute into the equation

Answer:

x = 3

Step-by-step explanation:

x = -b/2a  for a = 1 & b = -6

x = 6/2

x = 3

When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.

When you write your measurement as the mean ± standard deviation, it means that you are displaying how far the data is spread out from the mean value. In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. When you add the standard deviation to the mean and also subtract the standard deviation from the mean, you get the upper and lower bounds of the range that contains about 68% of the data. This range is called one standard deviation.The value of the standard deviation indicates how much the data varies around the mean. If the standard deviation is high, then the data is widely spread out and vice versa. Additionally, when you write a measurement as the mean ± standard deviation, it is assumed that the data is normally distributed. A normal distribution is one that is symmetrical and bell-shaped, where most of the data lies near the mean value.

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Hi student, let me help you out! :)

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

We are asked to find the slope of

\(\star~\mathrm{(-2,5)}\)

\(\star~\mathrm{(-1,3)}\)

This can be done with the help of the slope formula:

\(\star~\mathrm{\cfrac{y2-y1}{x2-x1}}\)

Where

y2 and y1 are y-coordinates

x2 and x1 are x-coordinates

Substitute the values:

\(\mathrm{\cfrac{3-5}{-1-(-2)}}\)

\(\mathrm{\cfrac{-2}{-1+2}}\)

Upon simplifying,

\(\mathrm{\cfrac{-2}{1}}\)

Finally,

\(\bigstar~\mathrm{\underline{Slope=-2}}\)

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer: Slope = -2

Step-by-step explanation:

Slope = change in y/change in x

Slope = y2-y1/x2-x1

Substitue:

Slope = 3-5/-1-(-2)

Solve:

Slope = -2/1

Simplify:

Slope = -2

The measure of angles inside the rhombus are:

∠1 = 56

∠2 = 56

∠3 = 34

∠4 = 34

We have,

In a rhombus,

The opposite angle is congruent.

So,

(56 + 56) = ∠1 + ∠2

And,

∠1 and ∠2 are equal angles.

So,

112 = 2∠1

∠1 = 56

∠2 = 56

Now,

All four angles in side the rhombus = 360

112 + 112 + ∠x + ∠x = 360

2∠x = 360 - 224

2∠x = 136

∠x = 68

This ∠x is the angle inside the rhombus.

And, ∠x/2 = ∠3 = ∠4

So,

∠3 = 68/2 = 34

∠4 = 34

Thus,

The measure of angles inside the rhombus are:

∠1 = 56

∠2 = 56

∠3 = 34

∠4 = 34

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Cyrstal earned more per hour. She earned 0.50 cents more that Xavier each hour.

Completed table is shown below. With this h number, we can calculate the cone's volume as V = (1/3)(72)h\(\pi\) = 49/3h\(\pi\) = 6\(\pi\)h = 131.88.

To complete the table relating the height and volume of cones with a radius of 7 units using the equation\(v = 6\pi h\), we need to substitute the radius value of 7 units into the formula for volume and then solve for height.

Height (h) Volume (V)

1                  131.88

2                  263.76

3                  395.64

4                  527.52

5                  659.4

To obtain volume for each height, we plug in radius value of 7 units into the formula for the volume of a cone, which is given by \(V = (1/3)\pi r^{2} h\). This gives us \(V = (1/3)\pi (7^{2} )h = 49/3\pi h\),

which simplifies to V = 16.33h. Then we substitute this expression for V into given equation \(v = 6\pi h\) to obtain \(16.33h = 6\pi h\), and solve for h to obtain h = 6.56.

Using this value of h, we can obtain the volume of the cone as \(V = (1/3)\pi (7x^{2} )h = \\49/3\pi h = \\6\pi h = \\131.88\)

After that, by multiplying the value of h by 16.33 and rounding to two decimal places, we can determine the volumes for the other heights in the table.

Therefore, the completed table is as shown above.

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Using a system of equations, it is found that the original number of students in Group B was of 120.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable.

In the context of this problem, the variables are described as follows:

There are 270 total students, hence:

x + y = 270.

x = 270 - y. (as we want to find y).

If 30 students move to Group B from Group A, then there will be twice as many students in Group A as in Group B, hence:

x + 30 = 2(y - 30).

Replacing the relation of the first equation on the second, it is found that:

270 - y + 30 = 2y - 60

3y = 360

y = 360/3

y = 120.

The original number of students in Group B is of 120.

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This type of validity is called concurrent validity.

Concurrent validity refers to the extent to which a new test measures the same construct as an established, well-validated test. In this scenario, the newly developed test is being compared to a traditional intelligence test that has already been shown to be valid, and the hypothesis is that there will be no significant differences between the results obtained from the two tests. By comparing the scores of the two groups, the researchers are attempting to determine whether the new test is measuring the same construct (intelligence) as the established test.

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There are 60,466,176 different sequences that are possible.

Permutation represents a method of arranging things in order. In a fair 6-sided die rolled 10 times and the resulting sequence of 10 numbers is recorded, the different possible sequences are calculated as shown below:

When rolling a die, the possible outcomes are 1, 2, 3, 4, 5, and 6. As there are ten rolls, each roll has six possible outcomes. Thus, the total number of different sequences will be calculated as follows:6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 60,466,176. Therefore, there are 60,466,176 different sequences that are possible.

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Using the given conditions that sin(20) = cos(2u) = tan(24) = 3, we can find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. By substituting the known values into the formulas, we can determine the exact values of these trigonometric functions.

Given sin(20) = 3, we can use the double-angle formula for sine to find sin(2u).

The double-angle formula for sine is sin(2u) = 2sin(u)cos(u). We know that sin(u) = -3/5, so we can substitute this value into the formula to calculate sin(2u).

Therefore, sin(2u) = 2(-3/5)(cos(u)).

Given cos(2u) = 3, we can use the double-angle formula for cosine to find cos(2u).

The double-angle formula for cosine is cos(2u) = cos^2(u) - sin^2(u). Since we already know sin(u) = -3/5 and cos(u) can be calculated using the Pythagorean identity (cos^2(u) = 1 - sin^2(u)), we can substitute these values into the formula to determine cos(2u).

Finally, given tan(24) = 3, we can use the double-angle formula for tangent to find tan(2u).

The double-angle formula for tangent is tan(2u) = (2tan(u))/(1 - tan^2(u)). By substituting the known value of tan(24) = 3 into the formula, we can calculate the exact value of tan(2u).

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The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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Answer:

x = -16

Step-by-step explanation:

Answer: X = -16

Step-by-step explanation:

1. -2(2x + 5) - 3 = -3(x - 1)

2. -4x-10-3=-3x+3

3. -13=x+3

4. x=-16

check: -2(-16*2+5)-3=-3(-16-1)

51=51

Answer:

5.5

Step-by-step explanation:

Answer: actually 5.504 rounded to 5.5

Step-by-step explanation:

Answer:

(a) To find the probability that at most 8 accidents involve a single vehicle, we need to calculate the probability of 0, 1, 2, ..., 8 accidents involving a single vehicle and then add them up. Using the binomial distribution formula with n=20 and p=0.6 (the probability of an accident involving a single vehicle), we get:

P(X ≤ 8) = Σi=0^8 (20 choose i) * 0.6^i * (1-0.6)^(20-i) = 0.000 + 0.002 + 0.014 + 0.062 + 0.178 + 0.345 + 0.409 + 0.262 + 0.068 = 0.999

Therefore, the probability that at most 8 accidents involve a single vehicle is 0.999.

(b) To find the probability that exactly 8 accidents involve a single vehicle, we simply plug in i=8 in the binomial distribution formula:

P(X = 8) = (20 choose 8) * 0.6^8 * (1-0.6)^(20-8) ≈ 0.167

Therefore, the probability that exactly 8 accidents involve a single vehicle is approximately 0.167.

(c) To find the probability that exactly 10 accidents involve multiple vehicles, we need to calculate the probability of exactly 10 accidents involving multiple vehicles and 10 accidents involving a single vehicle. Using the binomial distribution formula with n=20 and p=0.6, we get:

P(X = 10) = (20 choose 10) * 0.4^10 * 0.6^10 ≈ 0.117

Therefore, the probability that exactly 10 accidents involve multiple vehicles is approximately 0.117.

(d) To find the probability that between 5 and 8, inclusive, involve a single vehicle, we need to calculate the probability of 5, 6, 7, and 8 accidents involving a single vehicle and then add them up. Using the binomial distribution formula with n=20 and p=0.6, we get:

P(5 ≤ X ≤ 8) = Σi=5^8 (20 choose i) * 0.6^i * (1-0.6)^(20-i) ≈ 0.854

Therefore, the probability that between 5 and 8, inclusive, involve a single vehicle is approximately 0.854.

(e) To find the probability that at least 5 accidents involve a single vehicle, we need to calculate the probability of 5, 6, ..., 20 accidents involving a single vehicle and then add them up. Using the binomial distribution formula with n=20 and p=0.6, we get:

P(X ≥ 5) = Σi=5^20 (20 choose i) * 0.6^i * (1-0.6)^(20-i) ≈ 0.999

Therefore, the probability that at least 5 accidents involve a single vehicle is approximately 0.999.

(f) To find the probability that exactly 8 accidents involve a single vehicle and the other 12 involve multiple vehicles, we need to multiply the probability of 8 accidents involving a single vehicle by the probability of 12 accidents involving multiple vehicles. Using the binomial distribution formula with n=20 and p=0.6, we get:

P(X = 8) * P(X = 12) = (20 choose 8) * 0.6^8 * (1-0.6)^(20

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The pounds of the Earl Grey tea and Orange Pekoe tea are required from selling the new blend versus selling the other types is 225 pounds and 75 pounds.

Let x = amount of Earl Grey tea to mix

so, 300-x = amount of Orange Pekoe tea to mix

After putting the equations together,

6x+4(300-x)=5.5*300

6x+1200-4x=1650

2x=450

x=225

So amount of Earl Grey tea to mix is 225 pounds

amount of Orange Pekoe tea to mix = 300-x

300-225 = 75

So the amount of Orange Pekoe tea to mix is 75 pounds.

Amount of Earl Grey tea to mix=225 pounds

Amount of Orange Pekoe tea to mix=75 pounds

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The annual scholarship payment for a perpetual scholarship with a $100,000 endowment and a 7% discount rate would be $7,000.

To calculate the annual scholarship payment, we need to determine the amount that can be withdrawn from the endowment each year while still preserving its value over time. The discount rate of 7% represents the college's desired rate of return on investments.

Using the concept of present value, we can calculate the annual payment as a percentage of the initial endowment. The formula for present value is:

Present Value = Annual Payment / Discount Rate

In this case, we want to find the annual payment, so we rearrange the formula:

Annual Payment = Present Value * Discount Rate

Since the present value is the initial endowment of $100,000, and the discount rate is 7%, the calculation is as follows:

Annual Payment = $100,000 * 0.07 = $7,000

Therefore, to maintain the perpetual scholarship, the college would need to make an annual payment of $7,000. This amount is determined by the combination of the initial endowment and the discount rate, ensuring that the scholarship remains sustainable over time.

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Answer:

3.7

Step-by-step explanation:

The lenght of an arc with a radius of 3m and substended angle of 70 degrees is 3.7meters

The length of an arc is expressed as:

L = r theta

Given the following parameters

r = 3m

theta = 70 degrees = 70π/180

L = 3(70π/180)

L = 3.7 metres

Hence the lenght of an arc is 3.7meters

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