Factor completely, then place the answer in the proper location on the grid. 9x^4 -225y8

In this scenario, we have a box containing 7 cameras, with 4 of them being defective. We are interested in the number of defective cameras in a sample of 2 cameras, represented by the random variable X.

To find the probability distribution for X, we calculate the chances for each possible  outgrowth. The probability of having 0  imperfect cameras( X =  0) is1/7, as there's only one way to  elect 2non-defective cameras out of the 7 available.  The anticipated value of X, denoted as E( X), provides an estimate of the average number of  imperfect cameras in a sample of 2. It's calculated by multiplying each possible  outgrowth by its corresponding probability and  casting  them up.

Probability distribution for X:

P(X = 0) = 1/7

P(X = 1) = 4/7

P(X = 2) = 2/7

Expected value of X: 1.1429

In this case, the anticipated value of X is1.1429, indicating that, on average, we'd anticipate to find  roughly1.1429  imperfect cameras in a sample of 2 cameras.   The anticipated value serves as a measure of central tendency and provides  perceptivity into the long- term average  outgrowth.

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Answer:

The original number is 572.

Step-by-step explanation:

Let the 3 digit number by xyz.

Where x is the hundreds digit, y is the tens digit and z is the units digit.

Hence, the digit is (100x + 10y + z).

From the question, the tens digit equals to the sum of the hundreds digit and the units digit.

That is,

y = x + z ...... (1)

Also, from the question, the hundreds digit of this number is 3 more than the units digit.

That is,

x = z + 3 ...... (2)

Also, from the question, If the digits were reserved, the new number is 11 less than half of the original number

If the digit were reversed, that is xyz becomes zyx. Then, the new number is (100z + 10y + x).

the new number is 11 less than half of the original number

That is,

(100z + 10y + x) + 11 = 1/2(100x + 10y + z)

This becomes

200z + 20y + 2x + 22 = 100x + 10y + z

200z - z +20y -10y +2x - 100x = -22

199z + 10y -98x = -22 ...... (3)

Solving the equations simultaneously,

Put the value of x in equation (2) into equation (1)

x = z + 3 ...... (2)

y = x + z ...... (1)

That is,

y = (z+3) + z

y = 2z + 3 ...... (4)

Put the value of y in equation (4) into equation (3)

199z + 10y -98x = -22

199z + 10(2z +3) -98x = -22

199z + 20z + 30 -98x = -22

219z -98x = -22-30

219z -98x = -52 ...... (6)

Put the value of x in equation (2) into equation (6)

219z -98(z+3) = -52

219z -98z -294 = -52

121z = -52 + 294

121z= 242

z = 242/121

∴ z = 2

Put the value of z into equation (2)

x = z + 3

x = 2 + 3

∴ x = 5

Put the values of z and x into equation (1)

y = x + z

y = 5 + 2

∴ y = 7

Hence, x = 5, y = 7 and z = 2.

Recall that the original number is 100x + 10y + z.

100x + 10y + z = 100(5) + 10(7) +2 = 500 + 70 + 2 = 572

Hence, the original number is 572.

Answer:

4 equation 4

Step-by-step explanation:

did math in head

Answer:

Equation 4.

Step-by-step explanation:

2+6=8

2 times 2+4=8

3 times 2+2=8

5 times 2-4=6

The 6 is different.

First, let's write on a table the information about the snow on the ground for the 11 hours it snowed:

period of time in hours amount of snow in inches

0 1

from 0 to 2 1 + t * 3 (initial amount plus 3 in/h * number of hours)

from 2 to 5 1 + 2*3 = 7 (the same amount as when it stopped raining)

from 5 to 11 7 + (t-5)/2 (amount at t = 5 plus 1 in/2h * number of

hours since hour 5)

Now, using this information on a graph, we obtain:

98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

What does a statistical random sampling entail?

P = x/n

= 89/168

= 0.53

α= 0.02

∴ Zc = Zi - α/2

= 2.326

Now, C.I = P ± Zc * √[P(1-P)/n]

= 0.5 ± 2.326 *√[(0.53(1-0.53)) / 168

= (0.440, 0.619)

∴98% C.I. = 0.440 < P < 0.619

Hence, 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

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Answer:

Following are responses to the given question:

Step-by-step explanation:

For Girls:

\(Range:66 \\\\Lower\ Quartile: 22 \\\\Upper\ Quartile: 56 \\\\IQ\ Range: 34 \\\\Mean\ Absolute \ Deviation: 19.4\\\\\)

For Boys:

\(Range: 75 \\\\Lower \ Quartile: 12\\\\Upper \ Quartile: 45\\\\IQ \ Range: 33 \\\\Mean\ Absolute\ Deviation: 20.8\\\\\)  

Companies that focus on specific product categories and employ aggressive and competitive pricing strategies to acquire a significant market share through everyday low price are often referred to as "category killers."

Category killers are companies that specialize in a specific product category and aim to dominate that particular market segment. They differentiate themselves by offering a wide range of products within the category and employing aggressive pricing strategies to attract customers and gain a significant market share. These companies often adopt a low-cost business model, leveraging economies of scale and operational efficiencies to maintain competitive pricing.

By focusing on a specific product category, category killers can become experts in that area and offer a comprehensive selection of products, often at lower prices than their competitors. They strive to create a one-stop shopping experience for customers looking for products within that category.

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Answer:

It's 25

Step-by-step explanation:

ooposite angle of 40 is the one between 2x and the 90 degree angle.

if that is 40 and another angle is 90, then

2x + 40 + 90 = 180

2x = 180 - 130

2x = 50

50/2 = x

x = 25

Answer:

Graph B

Step-by-step explanation:

The vertical intercept I am getting is (0,-1) and B is the only one with that point. Therefore, it should be B.

The inequalities are x + y < 5000 and 0.10x + 0.15y ≤ $450 which shows each month, you want to only spend up to $450 and use less than 5,000 minutes on both of the devices.c

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.

Let's suppose the total minutes for cell phone is x

and total minutes for tablet is y

Then total minutes will be:

x + y < 5000 (less than 5,000 minutes on both of the devices)

And total cost:

0.10x + 0.15y ≤ $450

Thus, the inequalities are x + y < 5000 and 0.10x + 0.15y ≤ $450 which shows each month, you want to only spend up to $450 and use less than 5,000 minutes on both of the devices.

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At office 826 they will meet if they leave at the same time.

It is given that,

Agent J has recently been relocated from office 2013 to office 1. But his former office neighbor, Agent K is still in office 2014.

So, there are  (2014 - 1) - 1 = 2012 offices in between them.

It is given that,

Agent J can walk at a rate of 25 offices per minute, and Agent K walks at 36 offices per minute.

So,

Per minute they cross

= 25 + 36

= 61 offices.  

Thus, the time required for crossing all the 2012 offices is,

= 2012/61

= 32.9 ≅ 33 minutes

Then,

They will meet at

1 + 25(33) = 826 office (or)

2014 - 36(33) = 826 office (Negative since opposite direction)

Therefore, both of them meet at office 826.

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Answer:

x=8 and y=2

Step-by-step explanation:

x+y=10

x=4y

x+y=10

4y+y=10

5y=10(divide both sides by 5)

y=2

x=4y=4*2=8

Answer:

2 and 8.

Step-by-step explanation:

y = -x + 10

y = 4x

If we subtract we eliminate y:

0 = -x + 10 - 4x

0 = -5x + 10

5x = 10

x = 2.

and y = 4 * 2 = 8.

The margin of error can be calculated using the formula:
Margin of error = (upper limit of the confidence interval - lower limit of the confidence interval) / 2

In this case, a margin of error of 9.55 suggests that the sample mean is quite precise, since it's relatively close to the true population mean (which we know to be 52.90).

In this case, the lower limit of the confidence interval is 43.85 and the upper limit is 61.95.
Margin of error = (61.95 - 43.85) / 2
Margin of error = 9.55
Therefore, the margin of error is 9.55. This means that if the sample size were to be repeated, we would expect the sample mean to be within 9.55 units of the true population mean 95% of the time.
It's worth noting that the confidence interval provides a range of values within which we can be reasonably certain that the true population mean lies. The margin of error, on the other hand, gives us an indication of the precision of our estimate. However, if the margin of error were larger, this would indicate that our estimate is less precise and that we need a larger sample size to obtain a more accurate estimate of the population mean.

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The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.

The ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.

12⅝ = 101/8 = 12.645

12.62 = 12.62

√146 = 12.0830

12.39 = 12.39

12¾ = 51/4 = 12.75

Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.

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Notice that:

Therefore, the given equation is factored as follows:

The solutions of the above equation are x=-7 and x=3.

Answer:

Answer:

Interest rate = 2.41%

Step-by-step explanation:

The total value of an investment was $305.33 after $240 was invested for 10 years compounded monthly. Find the interest rate.

The formula to calculate the Interest rate for a Compound Interest is given as:

Solving for rate r as a decimal

r = n[(A/P)^1/nt - 1]

r = 12 × [(305.33/240.00)^1/(12)(10) - 1]

r = 0.0240996

Then convert r to R as a percentage

R = r * 100

R = 0.0240996 * 100

R = 2.41%/year

Therefore, the Interest rate = 2.41%

Explanation:

-4x + 7y = 20 ... equation 1

y= 3x + 15 ...equation 2

Rewriting the equations:

7y - 4x = 20

y - 3x = 15

using elimination method:

I want to eliminate y. So, I multiply equation 2 by 7 so both equations can have same coefficient

7y - 4x = 20 ... equation 1

7y - 21x = 105 ...equation 2

subtract equation 1 from 2:

7y - 7y -21x - (-4x) = 105 - 20

-21x + 4x = 85

-17x = 85

divide both sides by -17:

-17x/-17 = 85/-17

x = -5

To get y, we insert the value for x in any of the equation

using equation 1

7y - 4(-5) = 20

7y + 20 = 20

7y = 20-20

7y = 0

y = 0/7

y = 0

x = -5 and y = 0

The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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Answer: See below.

Step-by-step explanation:

First table from left to right

7 12 14 11 6 8 13 12 9 15

Second table from left to right

1 9 6 12 7 8 5 9 4 3

Third table from left to right

12 33 21 15 24 36 9 27 6 18

Fourth table from left to right

2 5 9 6 12 3 8 7 11 10


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Answer:

55.22 salamanders

Step-by-step explanation:

Z score formula is given as:

Z score = x - μ/σ

x = 16.8 cm

μ = mean = 15cm

σ = standard deviation 2cm

Z score = 16.8 - 15/2

= = 0.9

Probability value from Z-Table:

P(x<16.8) = 0.81594

P(x>16.8) = 1 - P(x<16.8)

1 - 0.81594

= 0.18406

In a collection of 300 salamanders, about how many have length greater than 16.8cm?

= 300 × 0.18406

= 55.218 salamanders

Approximately to the nearest hundredth = 55.22 salamanders

Therefore, 55.22 salamanders have length greater than 16.8cm

Answer:

55.218

Step-by-step explanation:

correct for ethnic stats

Step-by-step explanation:

Our equation;

\(-5=\frac{y-7}{9}\)

Multiply each side by 9 to remove the fraction;

\(-45=y-7\)

Add 7 to each side;

\(\boxed{-38=y}\)

Answer:

11:40 in the morning

Step-by-step explanation:

Given that for every 550 m, Bella the eagle flies, she is blown back fifty meters by the wind. Her nest is 5 km and she flies 550 m in 1 minutes.

Therefore for Bella to reach her nest which is 5 km (5000 m) away, the required distance (d) she needs to travel is:

d - (d/550)50 = 5000

d - 50d/550 = 5000

500d / 550 = 5000

d = (550 * 5000) / 500 = 5500

d = 5500 m = 5.5 km

speed = distance / time = 550 m / 1 minutes = 550 meters per minute

The time t required to cover 5500 m is:

speed = distance / time

550 meters per minute = 5500 m / t

t =  5500 m  / 550 meters per minute

t = 10 minutes

If Bella lives at 11:30 am in the morning and then travels for 10 minutes to reach her nest, the time Bella will reach her nest is 11:40 am

By doing this, Pablo is likely trying to draw attention to the data on bottles, which may be of particular interest or importance in his analysis.

The yellow highlight can make the data stand out more visually, making it easier for viewers to quickly identify and understand the information presented.

Data visualization tools can be useful in helping to communicate complex information in a clear and concise way. By using different colors, shapes, and visual elements, it is possible to highlight key data points and make patterns and trends more apparent.

This can be especially useful in business, scientific, and academic settings, where data analysis and communication are important skills.

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By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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To find the amplitude, period, phase shift, and list the transformations of each function given below:

1. y = 3cos[2(x-π/8)] + 1Amplitude: The amplitude of the function can be found by dividing 1 by 3 and taking the absolute value: |1/3| = 1/3Period: The period of the function is calculated as follows: T = 2π/b = 2π/2 = π Phase shift: Since the standard equation for the cosine function is y = A cos (B(x-h)) + k, the phase shift can be determined by setting the argument equal to zero and solving for x:h = π/8Transformations: Vertical shift up 1 and horizontal shift to the right π/82.

2. y = 4sin[1/2(x+π/4)]Amplitude: The amplitude of the function is 4Period: The period of the function is calculated as follows: T = 2π/b = 2π/(1/2) = 4πPhase shift: Since the standard equation for the sine function is y = A sin (B(x-h)) + k, the phase shift can be determined by setting the argument equal to zero and solving for x:h = -π/4Transformations: Vertical shift up 0 and horizontal shift to the left π/4

3. y = -2sin[4(x-π/3)] - 5Amplitude: The amplitude of the function is 2 Period: The period of the function is calculated as follows: T = 2π/b = 2π/4 = π/2Phase shift: Since the standard equation for the sine function is y = A sin (B(x-h)) + k, the phase shift can be determined by setting the argument equal to zero and solving for x:h = π/3Transformations: Vertical shift down 5 and horizontal shift to the right π/3

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Answer:

D. 2 (1/3) hours

Step-by-step explanation:

'Of' means multiplication, so we are going to multiply

3 (1/2) x (2/3) = 2 (1/3)

or

3.5 x 0.66 = 2.333

I hope this helps!

Answer: \(2x^{2} y^{3} (\sqrt[3]{4x^{2} y} )\)

Step-by-step explanation:

\(\sqrt[3]{32x^{8} y^{10} } =\sqrt[3]{2^{3} \cdot 2^{2} \cdot x^{2} \cdot (x^{2} )^{3} \cdot y \cdot (y^{3})^{3} } =2x^{2} y^{3} (\sqrt[3]{4x^{2} y} )\)

Answer:

Option C :

               \(\sqrt[3]{32x^8y^10} = 2x^2 y^3 \sqrt[3]{4x^2 y}\)

Step-by-step explanation:

\(\sqrt[3]{32x^8y^{10}}} = ( 32 x^8 y^{10})^{\frac{1}{3}}\)

              \(= ( 2^5 \times x^8 \times y^{10})^{\frac{1}{3}}\\\\= ( 2^{5\times\frac{1}{3}} \times x^{8 \times \frac{1}{3}} \times y^{10 \times \frac{1}{3}})\\\\=(2^{\frac{3}{3} + \frac{2}{3}}} \times x^{\frac{6}{3} + \frac{2}{3}} \times y^{\frac{9}{3} + \frac{1}{3}})\\\\= 2 \times 2^{\frac{2}{3}} x^2 \times x^{\frac{2}{3}} \times y^3 \times y^\frac{1}{3}\\\\=2x^2 y^3 \times 2^{\frac{2}{3} \times }x^{\frac{2}{3}} \times y^{\frac{1}{3}}\\\\=2x^2 y^3 (2^2x^2 y)^{\frac{1}{3}}\\\\= 2x^2y^3 \ \sqrt[3]{ \ 4 x^2 \ y }\)

Answer:

A... 12

Step-by-step explanation: