A student is comparing the mass of four bananas to the mass of four apples what is the difference in mass in grams between the bananas and the apples

5N² is expressed as a product of prime factors in index form as  \(5^{5} * 3^{2} * x^{10}\) .

In the expression of a number as the product of its prime factors, known as prime factor index form, each prime factor is only mentioned once, either as itself or, if necessary, to a required power.

Given:

N is a number that is expressed as a product of its prime factors in index form.

N = \(3x * 5x^{2} * x^{3}\)

We have to express 5N² as a product of prime factors in index form.

5N² = 5(\(3x * 5x^{2} * x^{3}\))²

       = \(5 * 9x^{2} *5^{4} x^{2} *x^{6}\)

       = \(5 * (5^{2}x)^{2}* (3x )^{2} *x^{6}\)

( using exponential properties  \(a^{m} *a^{n} = a^{m+n} and (a^{m} )^{n} = a^{mn}\))

    = \(5^{5} * 3^{2} * x^{10}\)

The prime factors of 5N² are 5,3 and x respectively.

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Answer:

x = -8

Step-by-step explanation:

all the angles in a triangle add up to 180 degrees

55 + 70 + x + 63  = 180

188 + x = 180

x = -8

To determine if the yearbook photo is a dilation of the original photo, we need to compare the dimensions and check if there is a consistent scaling factor between the two.

Original photo dimensions: 4 inches by 6 inches.

Yearbook photo dimensions: 6 2/3 inches by 10 inches.

To check if it's a dilation, we can compare the ratios of corresponding sides:

Ratio of width:

Yearbook photo width / Original photo width = (6 2/3) / 4 = (20/3) / (12/3) = 20/12 = 5/3

Ratio of height:

Yearbook photo height / Original photo height = 10 / 6 = 5/3

The ratios of the corresponding sides are equal, with both being 5/3. This indicates that there is a consistent scaling factor of 5/3 between the original photo and the yearbook photo.

Therefore, the yearbook photo is indeed a dilation of the original photo, and the scale factor is 5/3. This means that each dimension of the yearbook photo is 5/3 times the corresponding dimension of the original photo.

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Answer:

1/3 or 3/9

Step-by-step explanation:

The dart board can be split into 9 1x1 squares. 3 of those squares are in the 10 point zone. So, there is a 3 out of 9 (or 1 out of 3) chance to get 10 points.

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

Answer:

Ok, the rules of the exponent come from a logic construction.

If we have x^n

this means that n is multiplied by itself n times.

If we decompose n into a + b, we have:

x by itself a times, and then x by itself b times, and for how the product works, this is equivalent:

if n = 5, a= 2 and b = 3

x^5 = (x*x*x*x*x)   5 times-

x^5 = x^(2 + 3) = (x^2)*(x^3) = (x*x*)*(x*x*x) = x*x*x*x*x = x^5

And the same for the other rules:

(x^n)^b = x^n*b and such.

Obviusly, this only works when we have a common base.

So the correct answer is that we constructed the exponential rules in a way that only can be used when we have a common base, and this happens because to construct them, we started with common bases.

Answer:

x = 7.

Step-by-step explanation:

-18 = 6 (x - 10)

-18 = 6x - 60

6x = -18 + 60

6x = 42

x = 42/6 = 7.

Answer:

\(x=7\)

Step-by-step explanation:

\(-18=6(x-10)\)

Use distributive property.

\(-18=6x-60\)

Add 60 on both sides.

\(-18+60=6x\)

\(42=6x\)

Divide by 6 on both sides.

\(\frac{42}{6} =x\)

\(7=x\)

Another method.

\(-18=6(x-10)\)

Divide by 6 on both sides.

\(-18/6=x-10\)

\(-3=x-10\)

Add 10 on both sides.

\(-3+10=x\)

\(7=x\)

Give me Brainliest if my answer helped you.

Answer:

c=55t

Step-by-step explanation:

..

It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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Hope the picture will help you...

Answer:

Statiscal

Step-by-step explanation:

A statistical question is a question that can be answered by collecting data that vary. and this question can have more then one varitve of answers

Answer:

Step-by-step explanation:

We'll use the Pythagorean theorem. (a^2 + b^2 = c^2)

Triangle 1- 4^2 + 5^2 = 6^2 (16 + 25\(\neq\)41)

Triangle 2- 15^2 + 20^2 = 25^2 (225 + 400=625) 625 = 25^2

Triangle 3- 15^2 + 36^2 = 39^2 (225 + 1296 = 1521) 1521 = 39^2

Triangle 4- 5^2 + 13^2 = 14^2 (25 + 169 \(\neq\) 194) 14^2= 196

Therefore Triangles 2 and 3 are correct

Answer:

b. the two lines are perpendicular

Step-by-step explanation:

carry on learning

Answer:

4

Step-by-step explanation:

12-(3×3)+1

do the multiply first

3×3=9

so,

12-9+1 = 4

Answer:

35/6

Step-by-step explanation:

Answer:

5.83

Step-by-step explanation:

-1 is the z-score corresponding to a raw score of 32 from a population.

To find which Z-score could correspond to a raw score of 32 from a population with a mean of 33, we can use the Z-score formula, which is:

Z = (X - μ) / σ

Where:

Z is the Z-score

X is the raw score

μ is the population mean

σ is the population standard deviation

First, we need to know the Z-score corresponding to the raw score of 33 (since that is the population mean). Then, we can use that Z-score to find the Z-score corresponding to the raw score of 32.

Here's how to solve the problem:

Z for a raw score of 33:

Z = (X - μ) / σ

Z = (33 - 33) / σ

Z = 0 / σ

Z = 0

This means that a raw score of 33 has a Z-score of 0.

Now we can use this Z-score to find the Z-score for a raw score of 32:

Z = (X - μ) / σ

0 = (32 - 33) / σ

0 = -1 / σ

σ = -1

This tells us that the Z-score corresponding to a raw score of 32 from a population with a mean of 33 is -1.

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The best least squares approximation to\(x^{1/3\)on [-1,1] by a linear function l(x) = c_1 1 + c_2 x is given by: \(l(x) = (2/5)^{(3/2)\)

To show that 1 and x are orthogonal, we need to show that their inner product is zero:

\((1, x) = \int^1_1 1\times x dx = [x^{2/2}]^{1_1 }= 0\)

Therefore, 1 and x are orthogonal.

To compute ||1||, we use the norm formula:

\(||1|| = (1, 1)^{1/2 }= \int^1_1 1\times 1 dx = [x]^1_1 = 0\)

Similarly, to compute ||x||, we use the norm formula:

\(||x|| = (x, x)^1/2 = \int^1_1 x\times x dx = [x^3/3]^1_1 = 2/3\)

To find the best least squares approximation to\(x^{1/3\) on [-1,1] by a linear function l(x) = c_1 1 + c_2 x, we need to minimize the squared error:

\(||x^{1/3 }- l(x)||^2 = \int^1_-1 (x^1/3 - c_1 - c_2 x)^2 dx\)

Taking partial derivatives with respect to c_1 and c_2 and setting them to zero, we get the normal equations:

\(c_1 = (2/5)^{(3/2)} and c_2 = 0\)

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Answer:

I would say not enough information.

Step-by-step explanation:

because you cant calculate the angle DAC unless you have at least 1 or two of the angles.

Answer:

(1,1)

Step-by-step explanation:

Really simple, just see where they cross because that shows if you plug in the x or y value into the either equation you will get the same value in return.

Beth is correct for write these formulas to find the area of sector COB.

We have to given that,

In circle O,

Diameter AB, chord BC, and radius OC are drawn,

And, the measure of arc BC is 108°.

Now, We know that,

Area of sector is,

A = (θ/360) πr²

Where, θ = central angle and r is radius.

Substitute all the values, we get;

⇒ Area of sector = (108/360) π × (OC)²

Hence, Beth is correct for write these formulas to find the area of sector COB.

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A little over 95% of the curve's area lies within plus and minus two standard deviations of the mean.

When applying a conventional normal distribution,

One standard deviation from the mean is shared by about 68% of the values.

The values are within two standard deviations of the mean in almost 95% of the cases.

99.7% of the values, or nearly all of them, are within three standard deviations of the mean.

The 68 95 99.7 rule is based on these facts. Because the rule was initially based on observations (empirical means "based on observation"), it is occasionally referred to as the Empirical Rule.

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Answer:

9

Step-by-step explanation:

given an ordered pair (x, y )

Then x is the input and y the output

Given

(1, 9 )

Then y = 9 represents the output

12/25 as a percentage is 48%.

Answer:

48 percent

have a great day ahead

To solve the equation m/F = 1/a for F, we can rearrange the equation as F = a/m.

To solve for a specific variable in an equation, we isolate that variable on one side of the equation. In this case, we want to solve for F when given the equation m/F = 1/a. To do this, we need to isolate F.

We can start by cross-multiplying the equation to eliminate the fractions. Multiply both sides of the equation by F and a to obtain ma = F. Then, we can rearrange the equation to solve for F by dividing both sides by m, resulting in F = a/m.

This means that F is equal to the ratio of a divided by m. By rearranging the equation in this way, we have isolated F on one side and expressed it in terms of the given variables a and m.

In summary, to solve the equation m/F = 1/a for F, we rearrange the equation as F = a/m. This allows us to express F in terms of the given variables a and m.

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Answer:

12a+62b

Step-by-step explanation:

4a(2+3b)-5b(4a-10)

opening brackets

=8a+12b-20a+50b

=8a-20a+12b+50b

=-12a+62b

Answer:

20

Step-by-step explanation:

Most likely this is a triangle triangle have 180 always

According to the question Approximately 60% of Americans are in the working class and 80% of the people in the U.S. are lower middle class. The correct answer is D. \(\(60\%\)\) and \(\(10\%\)\).

The working class typically comprises individuals involved in manual labor, skilled trades, or service-oriented jobs. They often earn wages and may have lower income levels compared to other classes.

The percentage of Americans in the working class can vary based on factors such as economic conditions, industry trends, and societal changes. The lower middle class generally includes individuals who have achieved some level of education beyond high school and hold white-collar or technical jobs.

They often have moderate incomes and may have attained some level of financial stability. The percentage of people in the U.S. who fall into the lower middle class can also fluctuate based on economic factors and social dynamics.

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .