Simplify the following exponential expression. Show your work step by step and justify your steps using the Properties of Exponents you’ve learned in previous units. Use your class notes for the names of the Properties of Exponents.

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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Hey there!

3/4k + 3/8k = 1/2

COMBINE the LIKE TERMS

(3/4K + 3/8k) = 9/8k

NEW EQUATION: 9/8k = 1/2

MULTIPLY 8/9 to BOTH SIDES

8/9 * 9/8k = 8/9 * 1/2

CANCEL out: 8/9 * 9/8 because it gives you 1

KEEP: 8/9 * 1/2 because it helps solve for your result (also known as giving you the result of the k-value)

NEW EQUATION: k = 8/9 * 1/2

SIMPLIFY IT AND YOU WILL HAVE YOUR RESULT

k = 4/9

Therefore, your answer is: k = 4/9

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

\(n < -\frac{2}{21}\) or \(n > 0\).

\(\frac{1}{3n} -2+\frac{1}{2} > -5\)

From this point forward, we're not solving the inequation as we may solve a normal one. Since it's a rational inequation (the variable is dividing another number), let's write it in standard form.

Standard form. The inequality is expressed by only one fraction or term, compared to 0.

\(\frac{1}{3n} -2+\frac{1}{2}+5 > -5+5\\ \\\frac{1}{3n} -2+\frac{1}{2}+5 > 0\)

\(\frac{1}{3n} +(-2+\frac{1}{2}+5) > 0\\ \\\frac{1}{3n}+ (-\frac{4}{2} +\frac{1}{2}+\frac{10}{2} ) > 0\\ \\\frac{1}{3n}+ (\frac{-4+1+10}{2} ) > 0\\ \\\frac{1}{3n} +(\frac{7}{2} ) > 0\)

\(\frac{(1)(2)+(3n)(7)}{(3n)(2)} > 0\\ \\\frac{2+21n}{6n} > 0\)

\(2+21n=0\\ \\21n=-2\\ \\n=\frac{-2}{21}\)

Check attached image 1.

a. First, let's test with a value that goes from -∞ to -2/21 (Region 1).

\(\frac{1}{3(\frac{-2}{22} )} -2+\frac{1}{2} > -5\\ \\-5.167 > -5\)

The statement is true, therefore, this region is one of the solutions. Hence, one of the solutions is \(n < -\frac{2}{21}\)

b. Test with a value that goes from -2/21 to 0 (Region 2).

\(\frac{1}{3(\frac{-2}{10} )} -2+\frac{1}{2} > -5\\ \\-3.167 > -5\)

The statement is false, therefore, the region is not one of the solutions.

c. First, let's test with a value that goes from 0 to ∞ (Region 3).

\(\frac{1}{3(1)} -2+\frac{1}{2} > -5\\ \\-1.166 > -5\)

The statement is true, therefore, this region is one of the solutions. Hence, the second solution is \(n > 0\)

9. Express your results.

\(n < -\frac{2}{21}\) or \(n > 0\).

Answer:

-8+√20 to the nearest tenth =-3.5

Answer:

5 feet + 12 inches = 2 yards

48 inches = 1 foot + 1 yard

5 feet = 3 feet + 24 inches

Step-by-step explanation:

To help solve these equations, you must know how to convert feet to inches, inches to yards, etc. Use the information below:

1 feet = 12 inches

3 feet = 1 yard

To solve 5 feet + 12 inches = blank yard(s), convert 5 feet & 12 inches to yards. Since 5 feet would be complicated to convert, let's convert 12 inches to feet first.

12 inches = 1 feet

Instead of 12 inches, we can substitute it as 5 feet + 1 feet = blank yard(s). That would be 6 feet = ? yards. 3 feet = 1 yard, which tells us we must divide both sides by 3. Thus, 5 feet + 12 inches = 2 yards.

Blank inches = 1 foot + 1 yard

To find the # of inches in a yard, you must first know that 3 feet = 1 yard. If there are 12 inches in a foot, we must multiply 3 by 12, getting us 36. You add 12 inches (1 foot), getting us 48 inches in total. Thus 48 inches = 1 foot + 1 yard.

Blank feet = 3 feet + 24 inches

Since 3 feet is already feet, we do not need to convert it. If 12 inches is 1 foot, we must divide 24 inches by 12. So, there is 2 feet in 24 inches. 2 + 3 is 5. Thus, 5 feet = 3 feet +24 inches.

Answer:

Solution given:

<3+90=180[co interior angle ]

<3=180-90=90°

is your answer

The intervals in which the function is decreasing. \([-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ]\). Option 3

We're given a function f(x) = 2 sin x - x, which describes a curve on a graph. We want to find the intervals where this curve is decreasing (going down) within the range of -π to π.

To find when the function is decreasing, we look at its slope. The slope tells us if the curve is going up or down. We find the slope by taking the first derivative of the function: f'(x) = 2 cos x - 1.

We now have an equation for the slope, f'(x) = 2 cos x - 1. A negative slope means the function is decreasing. So, we want to find where f'(x) is less than 0 (negative).

We set up the inequality: 2 cos x - 1 < 0. We solve it to find the x-values where the slope is negative. The solution is cos x < 1/2.

From the inequality cos x < 1/2, we find the intervals within the range of -π to π where the function is decreasing. These intervals are [-π, -π/3] and [π/3, π].

The above answer is in response to the question below as seen in the picture.

Determine the interval(s) in \([-\pi, \pi ]\) on

which f(x) =  2 sin x - x

is decreasing.

1. \([-\frac{\pi }{3}, \frac{\pi }{3} ]\)

2. \([-\frac{\pi }{6}, \frac{\pi }{6} ]\)

3. \([-\pi , -\frac{\pi }{3} ], [\frac{\pi }{3}, \pi ]\)

4. \([-\pi , -\frac{-2\pi }{3} ], [\frac{2\pi }{3}, \pi ]\)

5. \([-\pi , - \frac{5x}{6} ], [\frac{\pi }{6}, \pi ]\)

6. \([-\frac{\pi }{6}, \frac{5\pi }{6} ]\)

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Answer:

Step-by-step explanation:

A

Answer: Imma say C

Step-by-step explanation:

Answer:

n = -8

Step-by-step explanation:

We need to work through the problem, to see how the individual got n = 8:

\(3(5n+8)=8(4+2n)\\15n+24=32+16n\\15n=8+16n\\-n = 8\\n = -8\)

It is clear that when the individual got to -n = 8, they forgot to divide by -n.

The - symbol simply represent -1 so to fully isolate n, we need to divide both sides by -1 to get n = -8.

Answer: 18√2(Decimal: 25.455844)

Step-by-step explanation:

Answer: The answer is 6!

Step-by-step explanation:

Sorry. If I’m late! & Explanation? I just took the test Nd scored an 100%

Answer:

The answer is -6!

Step-by-step explanation:

I promise you, I just took the USATestprep test and this is the answer. Good luck with the rest of the test!

Answer:

220

Step-by-step explanation:

Answer:

I would say the second one

Step-by-step explanation: Good luck! :)

Answer:

17.40

Step-by-step explanation:

no

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Option C is correct. Both a and b are valid options, but altering the scale to make the top bar appear four times as long as the bottom bar would be the more accurate representation of Phil's hits quadrupling.

To show that Phil's hits have quadrupled since last year, we need to compare the number of hits he received this year with the number of hits he received last year.

a. Using the same scale and making the top bar twice as thick as the bottom bar does not accurately represent the quadrupling of Phil's hits. It only shows that he received more hits this year than last year.

b. Altering the scale so that the top bar appears four times as long as the bottom bar would accurately represent the quadrupling of Phil's hits. This would show that Phil's hits have increased fourfold from last year to this year.

c. Option C is correct. Both a and b are valid options, but altering the scale to make the top bar appear four times as long as the bottom bar would be the more accurate representation of Phil's hits quadrupling.

d. Option D is incorrect because at least one of the options a or b is correct.

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Answer:

The answer are

B and C

Step-by-step explanation:

r=d/2=12/2=6

r=16/2=8

Circumference=2pir

C=2×6pi

C=12pi

C=2pir

C=2×8pi

C=16pi

Answer:

\(=729x^{30}\)

Step-by-step explanation:

So we have the expression:

\((3x^5)^6\)

To simplify, we can use the product of a power property, where:

\((ab)^x=a^xb^x\)

So, our expression will be equal to:

\(=(3)^6(x^5)^6\)

Let's evaluate 3⁶, which equates to:

\(=729(x^5)^6\)

For our x, we can use the power of a power property, where:

\((x^a)^b=x^{ab}\)

So, our expression is:

\(=729x^{5(6)}\)

Evaluate:

\(=729x^{30}\)

And we're done!

Answer:

Step-by-step explanation:

The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.

To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:

Step 1: Find the mean (average) of the data set.

Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5

Step 2: Calculate the difference between each data point and the mean.

Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|

Step 3: Calculate the absolute value of each difference.

Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10

Step 4: Find the average of the absolute differences.

MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20

The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.

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Answer:

No

Step-by-step explanation:

Tyler is incorrect. The only way you can set individual terms equal to the result is when the result is zero. This is due to zero times anything equalling zero. If one of the terms equals zero, then the other term does not matter because the whole thing will be zero. Let's say:

\((2 - x)(x + 1) = 0\)

If the first term equals zero, the entire left side is zero. For Priya's case, the right side is not zero, it is 11. If one term is 11, the other term will contribute. You can check this by plugging in Tyler's solutions. The correct way to solve this equation is to use FOIL on the two terms, then subtract 11 on both sides to get zero. Then use the quadratic formula.

Answer:

0.1056 = 10.56% probability that their average salary is more than $77,500.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean $75,000 and standard deviation $8,000.

This means that \(\mu = 75000, \sigma = 8000\)

Sample of 16

This means that \(n = 16, s = \frac{8000}{\sqrt{16}} = 2000\)

What is the probability that their average salary is more than $77,500?

This is 1 subtracted by the pvalue of Z when X = 77500. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{77500 - 75000}{2000}\)

\(Z = 1.25\)

\(Z = 1.25\) has a pvalue of 0.8944

1 - 0.8944 = 0.1056

0.1056 = 10.56% probability that their average salary is more than $77,500.

Answer:

  x = 9 inches

Step-by-step explanation:

You want the value of x in the similar triangles shown.

Corresponding sides are proportional. This means the ratio of the horizontal side of the triangle to the vertical side is the same for both.

  6/4 = (6+x)/10

  15 = 6 +x . . . . . . . . multiply by 10

  9 = x . . . . . . . . . subtract 6

The measure of x is 9 inches.

__

Additional comment

You could also write the proportion ...

  6/4 = x/(10 -4)

  x = 36/4 = 9 . . . . . . . multiply by 6

You can see this if you draw a horizontal line through the figure at the top of the side marked 4 in.

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Answer:

A

Step-by-step explanation:

fog(x) = f(g(x) = f(1/2x) = 4x/(1+6x)

Step-by-step explanation:

8x13 kkkxkgkgxkgxkkkxkkk

The probability that Aakesh will select a blue marble from each bag is 4/45.

To find the probability that Aakesh will select a blue marble from each bag, we need to calculate the probability of selecting a blue marble from each bag and then multiply those probabilities together.

Let's start with the first bag, which contains 5 marbles: 2 red marbles, 2 blue marbles, and 1 green marble. The probability of selecting a blue marble from the first bag is:

P(Blue from first bag) = Number of blue marbles / Total number of marbles in the first bag

P(Blue from first bag) = 2 / 5

Now, let's move on to the second bag, which contains 9 marbles: 3 red marbles, 2 blue marbles, and 4 green marbles. The probability of selecting a blue marble from the second bag is:

P(Blue from second bag) = Number of blue marbles / Total number of marbles in the second bag

P(Blue from second bag) = 2 / 9

To find the probability of both events happening (selecting a blue marble from each bag), we multiply the individual probabilities together:

P(Blue from both bags) = P(Blue from first bag) * P(Blue from second bag)

P(Blue from both bags) = (2 / 5) * (2 / 9)

P(Blue from both bags) = 4 / 45.

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According to question as both side are equal so it is an isosceles triangle and the value of X is 18.

An isosceles triangle is a triangle with two sides of equal length. Some properties of an isosceles triangle include:

so In this triangle ,

The mid point on horizontal side is given and 5m line cut the mid point of both the sides.

both side are equal as it is an isosceles triangle.

and given in the question,

side/2 =9

and  one side is equal to x.

and both sides are equal,

therefore

side = 9*2 = 18

so the value of x = 18.

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