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The expression as a square of a monomial is (3a²b)²

From the question, we have the following parameters that can be used in our computation:

9a⁴b²

By definition, a monomial that is a perfect square is represented as

a²

Using the above as a guide, we have

9a⁴b² = (3a²b) * (3a²b)

When expressed as perfect square monomial, we have

9a⁴b² = (3a²b)²

Hence, the expression as a square of a monomial is (3a²b)²

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The sequence an=an−1+2 is an arithmetic sequence

The first three terms in the sequence are (a) 8, 10, 12

The sequence is given as:

an=an−1+2

Where:

a1 =8

Start by calculating a2 using:

a2=a1+2

This gives

a2=8+2 = 10

Calculate a3 using:

a3=a2+2

This gives

a3=10+2 = 12

So, we have:

a1 = 8, a2 = 10 and a3 = 12

Hence, the first three terms in the sequence are (a) 8, 10, 12

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If Mr. Phil T. Rich had a boat load of money. The original value of his estate is $152,000.

Let's call the original value of Mr. Phil T. Rich's estate "x".

After he gave 1/2 of the estate to his wife, he was left with x/2.

After he gave 30,000 to his daughter, he was left with x/2 - 30,000.

After he gave half of what was left to his butler Niles, he was left with (x/2 - 30,000)/2.

After he gave half of what was left to Bubbles, he was left with (x/2 - 30,000)/4.

Finally, after he donated the 8,000 to charity, he was left with (x/2 - 30,000)/4 - 8,000.

We know that the final amount after all these transactions was $0, so we can set up an equation to solve for x:

0 = (x/2 - 30,000$)/4 - 8,000

Multiplying both sides by 4 to isolate x/2:

0 * 4 = (x/2 - 30,000) - 8,000 * 4

Expanding the right side:

0 = (x/2 - 30,000) - 32,000

Adding 30,000 and 32,000 to both sides:

30,000+ 32,000 = (x/2)

Dividing both sides by 1/2:

62,000 * 2 = x

Multiplying both sides by 2:

62,000* 2 * 2 = x * 2

Expanding the left side:

62,000* 4 = x

Dividing both sides by 4:

62,000 * 4 / 4 = x / 4

Expanding the left side:

$62,000 = x

Therefore the original value of Mr. Phil T. Rich's estate was $62,000.

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Answer:sorry

Step-by-step explanation: i need points

Answer:

maybe 2 1/2 ÷4=0.625

5/8?

Answer:

310.5

Step-by-step explanation:

Answer:

310.5

Step-by-step explanation:

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 270 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 270 is 100%, so we can write it down as 270=100%.

4. We know, that x is 115% of the output value, so we can write it down as x=115%.

5. Now we have two simple equations:

1) 270=100%

2) x=115%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

270/x=100%/115%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 115% of 270

270/x=100/115

- we multiply both sides of the equation by x

- we divide both sides of the equation to get x

270/0.8695652173913=x

310.5=x

x=310.5

now we have:

115% of 270=310.5

Answer:

Option D. 10,779 feet

Step-by-step explanation:

Given from the figure attached,

PT = OB = 7000 ft

PB = OT = x feet

and angle of elevation (∠POT) = 30°

By applying Tan rule in the triangle POT,

tan33° = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\) = \(\frac{PT}{OT}\)

tan33° = \(\frac{7000}{x}\)

x = \(\frac{7000}{\text{tan}33}\)

x = 10779 feet

Therefore, distance between the bird (B) and plane (P) is 10,779 feet.

Option D. will be the answer.

Answer:

10,779 feet

Step-by-step explanation:

I took the test.

Sample size and the confidence level width have an inverse relationship. As the sample size increases, the confidence level width decreases.

When determining a confidence interval for a population parameter, such as the mean or proportion, a larger sample size provides more information about the population. This increased information leads to a narrower confidence interval.

The confidence level width is influenced by two factors: the sample standard deviation (or the variability of the data) and the critical value associated with the desired confidence level. As the sample size increases, the sample standard deviation becomes a more accurate estimate of the population standard deviation. This reduces the variability and leads to a narrower confidence interval.

A larger sample size leads to a decrease in the confidence level width, providing a more precise estimate of the population parameter with a higher level of confidence.

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560 miles would 35 inches be on the map.

What is distance?

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Given:

The distance between two cities on a map is 25 inches.

The actual distance between the two cities is 400 miles.

We have to find the how many miles would 35 inches be on the map.

As the distance between two cities on a map is 25 inches but the actual distance between the two cities is 400 miles.

⇒ 400/25 = 16 miles would be map in a one inches.

⇒ 16 x 35 = 560 miles would be map in a 35 inches.

Hence, 560 miles would 35 inches be on the map

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The height of the school building is 12.34 meters, rounded to the nearest hundredth of a meter.

Nakeisha's method of using a mirror on the ground to measure the height of her school building is based on the principles of similar triangles. When she places the mirror on the ground and steps away from it, she creates two triangles, one from her eyes to the mirror and the other from the mirror to the top of the school building. These two triangles are similar, which means that they have the same shape but different sizes.

To find the height of the school building, we need to use the ratios of the corresponding sides of the two similar triangles. Let's call the height of the school building "h". Then, the distance from Nakeisha's eyes to the mirror is (1.25 + 1.65) = 2.9 meters, and the distance from the mirror to the school building is (8.65 - 1.65) = 7 meters.

Using the ratios of the corresponding sides, we can set up the proportion:

h/7 = 2.9/1.65

Cross-multiplying and solving for h, we get:

h = 7 x (2.9/1.65) = 12.34 meters

It's important to note that this method of measuring height using a mirror on the ground assumes that the ground is flat and level. If there are any slopes or uneven surfaces, the results may be inaccurate. Additionally, it's crucial to take all necessary safety precautions when conducting any measurements from heights or near busy roads.

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S = {4t − t^2, 5 + t^3, 5 + 3t, −3t^2 + 2t^3} is a basis for P₃ because it spans P₃ and is linearly independent.

To check if S spans P₃, let's take an arbitrary polynomial in P₃, say p(t) = a + bt + ct^2 + dt^3. We need to show that we can write p(t) as a linear combination of the elements in S. Let's try

p(t) = a + bt + ct^2 + dt^3

= (5 + t^3) + (5 + 3t) + (4t - t^2) - (3t^2 - 2t^3) + (c - 5 - 3) + (b - 4)t + (a + 3)d

We can see that we can express p(t) as a linear combination of the elements in S plus some constants. Since the constants can be absorbed into the coefficients of the elements in S, we have shown that S spans P₃

Now, let's check if S is linearly independent. To do this, we need to show that no element in S can be written as a linear combination of the other elements in S. Let's set up the equation

c₁(4t - t^2) + c₂(5 + t^3) + c₃(5 + 3t) + c₄(-3t^2 + 2t^3) = 0

Expanding and collecting like terms, we get

(c₂ + c₃) + (-c₁ + c₄)t + (c₁ - 3c₄)t^2 + (2c₄)t^3 = 0

Since this equation must hold for all values of t, we can equate the coefficients of the corresponding powers of t to get the system of equations

c₂ + c₃ = 0

-c₁ + c₄ = 0

c₁ - 3c₄ = 0

2c₄ = 0

The last equation implies that c₄ = 0. Substituting this into the second equation gives -c₊ = 0, so c₁ = 0. Substituting c₁= c₄ = 0 into the first equation gives c₂ + c₃ = 0. Since c₂ and c₃ cannot both be zero (otherwise the equation is trivial), this implies that S is linearly independent.

Since S satisfies both conditions for a basis, we can conclude that S is a basis for P₃

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Determine whether S is a basis for P_3.

S = {4t − t^2, 5 + t^3, 5 + 3t, −3t^2 + 2t^3}

Answer:

20/893

Step-by-step explanation:

of means to multiply

i did it on a calculator

hope this helps

Answer:

20/893 or 0.0224

Step-by-step explanation:

Of means "multiply".

So, 2/47 of 10/19 is 2/47 * 10/19.

Now simplify:

2/47 * 10/19

20/893 or 0.0224

Answer:

176

Step-by-step explanation:

Apply PEMDAS

Solve the parenthesis first

11 ( 7 + 9 )

11 ( 16 )

Now open the parenthesis and you will have your answer

11 times 16

176

Answer:

the answer should be A Hope this helps!

Answer:

\(\frac{2}{3}\)

Hope this helps!

Step-by-step explanation:

Slope = \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

b = ( -2, 0 )

a = ( -5, -2 )

\(slope = \frac{0 - (-2) }{-2 - ( -5)}\)

slope = \(\frac{2}{3}\)

Answer:

17cm is the answer

Step-by-step explanation:

27×2 = 54

88 - 54 = 34

34 ÷ 2 = 17

Responda:

270, 00

Explicação passo a passo:

Dado o seguinte:

Pagamento diário até as 18h00

Pagamento por hora trabalhada = 5,00

Em um determinado mês:

Trabalhou 25 dias: (25 * 20) = 500,00

20 horas à noite: (20 * 5) = 100,00

Ganho total = 500 + 100 = 600,00

Despesas:

Transporte = 1/10

= (1/10) × 600 = 60,00

Quantidade restante = (600 - 60) = 540,00

Renda:

1/2 de 540 = 270,00

Valor total restante após a dedução das despesas:

600 - (270 + 60)

600 - 330 = 270,00

Kevin is correct. He needs to know how much of his college expenses will be covered so he knows how much he should save.

Kevin is correct. By filling out the FAFSA and sending it in, he will not have to pay anything because grants and scholarships will cover the costs.

Kevin is incorrect." Beacause It is never too early to start saving for college. Even if he earns scholarships, he could use the money for other expenses.

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Answer:

45%

Step-by-step explanation:

The computation of the percentage increase from the first week is shown below:

Given that

In the first week there is 3,200 views

And, in the second week, there is 4,640 views

So, the percentage increase is

= (Second week views - first week views) ÷ (first week views)

= (4,640 - 3,200) ÷ (3,200)

= 45%

Answer:

y = x - 4

Step-by-step explanation:

Given the slope (m) = 1, and the point (7, 3):

We can determine the  equation of the line in its slope-intercept form, y = mx + b by plugging in the given numbers to identify the y-intercept.

Let the slope (m) = 1

x = 7

y = 3

We'll plug these values into the slope-intercept form to solve for the y-intercept.

The y-intercept is the point on the graph where it crosses the y-axis. It is also the value of y when x = 0, hence having the coordinates of (0, b).

y = mx + b

3 = 1(7) + b

3 = 7 + b

Subtract 7 from both sides to solve for the y-intercept, b:

3 - 7 = 7 - 7 + b

-4 = b

Therefore, the y-intercept is -4.

Now that we have our slope, m = 1, and the y-intercept (b) = -4, we can establish our linear equation in slope-intercept form:

y = x - 4

The correct answer is: Diverges by the Ratio Test. To determine whether the series \(\( \sum_{n=0}^\infty \frac{n!}{2^n} \)\) converges, we can use the Ratio Test.

The Ratio Test states that for a series \(\( \sum_{n=0}^\infty a_n \), if the limit \( \lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right| \)\) exists and is less than 1, then the series converges. If the limit is greater than 1 or does not exist, the series diverges.

Let's apply the Ratio Test to the given series:

\(\[ \lim_{n \to \infty} \left|\frac{\frac{(n+1)!}{2^{n+1}}}{\frac{n!}{2^n}}\right| = \lim_{n \to \infty} \left|\frac{(n+1)!}{2^{n+1}} \cdot \frac{2^n}{n!}\right| \]\)

Simplifying the expression:

\(\[ \lim_{n \to \infty} \left|\frac{(n+1)!}{2^{n+1}} \cdot \frac{2^n}{n!}\right| = \lim_{n \to \infty} \left|\frac{(n+1)(n!)}{2(n!)}\right| \]\)

The factor of \(\( (n+1) \) cancels with \( (n!) \):\)

\(\[ \lim_{n \to \infty} \left|\frac{n+1}{2}\right| \]\)

As \(\( n \)\) approaches infinity, the limit diverges to infinity. Therefore, the series \(\( \sum_{n=0}^\infty \frac{n!}{2^n} \)\) diverges.

Hence, the correct answer is: Diverges by the Ratio Test.

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Answer:

61.3

Step-by-step explanation:

Hint: triangles will always equal 180

21.6 +7 +90+x=90

Add your  constants or numbers that are alike

21.6

 90

+ 7

_______

 118.6  

subtract  to both sides

     118. 6 +x =180

    -118.6        -118.6

  _______     ______

         X        = 61.3

Step-by-step explanation:

What is the formula for mean median and mode?

Mean: is the average of values

Median: center most value when values are arranged in numerical order

Mode: most frequent occurring value

_______________________________________

Example

Given values: 0 , 3 , 2 , 10 , 11 , 31 , 2

mean: (0 + 3 + 2 + 10 + 11 + 31 + 2)/7  = 8.429

median: 0 , 2 , 2 , 3 , 10 , 11 , 31

mode: 2 (because 2 shows up twice and the others numbers only once)

Answer: 20

Step-by-step explanation:

Answer: 54 bricks

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:  

Volume of a rectangular prism (V) : length x width x height  

Replacing with the values given and solving for v (Volume)  

V = 10 x 6 x 4

V = 240 cm3 (volume of one brick)

Finally, we have to divide the amount of concrete used by the volume of each brick:

13,000cm³ /240 cm3 = 54.16 = 54 bricks

Feel free to ask for more if needed or if you did not understand something  

Answer:

8/81

Step-by-step explanation:

8/18 x 4/18 = 32/324 = 8/81

The probability of drawing a blue and then a green and replacing the candy after the draw is 8/81.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

It is given that in a bag of M&MS there are 4 green, 6 yellow, and 8 blue candies.

The probability for blue = 8/18

The probability for green = 4/18

The probabilities of drawing a blue then green if you replace the candy after the draw will be calculated as below:-

Probability = 8/18 x 4/18

Probability = 32/324

Divide the number 32 by 324 to get the probability.

Probability = 8/81

Therefore, the probability of drawing a blue and then a green and replacing the candy after the draw is 8/81.

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1: no solution

2: infinitely many solutions

3: one solution