Three machines A, B and C operate independently in a factory. Machine A is out of action for 10% of the time, while machine B is out of action for 5% of the time and machine C for 20% of the time. A rush order has to be commenced at midday tomorrow. What is the probability that at this time: g

Answer:

Follow the steps above

Answer:

y = 5x -3

Step-by-step explanation:

slope = 5

y int = -3

Answer:

17.7 cm

Step-by-step explanation:

One of the legs of a right triangle measures 12 cm and the other leg measures 13 cm find the measure of the hypotenuse if necessary round the nearest 10th

To find the Hypotenuse of a right angle triangle, we solve using Pythagoras Theorem

Hypotenuse ² = Opposite ² + Adjacent ²

Hypotenuse = √Opposite ² + Adjacent ²

Opposite = 12 cm

Adjacent = 13 cm

Hence,

Hypotenuse = √12² + 13²

= √144 + 169

= 17.691806013 cm

Approximately = 17.7 cm

Therefore, the measure of the Hypotenuse is 17.7 cm

The mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The mean-square end-to-end distance for the fractal line is as follows.⟨R2⟩ = ⟨(R(u)- R(v))^2⟩ for u = 0 and v = L where L is the length of the line.⟨R2⟩ = b²/L^2.D.L = b².L^(1-D).

Thus, the mean-square end-to-end distance for the fractal line is ⟨R2⟩ = b².L^(1-D).

The radius of gyration Rg is defined as follows.

Rg² = (1/N)∑_(i=1)^N▒〖(R(i)-R(mean))〗²where N is the number of monomers in the fractal line and R(i) is the position vector of the ith monomer.

R(mean) is the mean position vector of all monomers.

Since the fractal dimension is D, the number of monomers varies with the length of the line as follows.N ~ L^(D).

Therefore, the radius of gyration for the fractal line is Rg² = (1/L^D)∫_0^L▒〖(b/v^(1-D))^2 v dv〗 = b²/L^2.D(1-D). Thus, Rg² = b².L^(2-D).

The ratio R²/Rg² is given by R²/Rg² = L^(D-2).

When D = 1, R²/Rg² = 1/L. When D = 1.7, R²/Rg² = 1/L^0.7. When D = 2, R²/Rg² = 1/L.

This provides information on mean-square end-to-end distance and radius of gyration for fractal line with a given fractal dimension.

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Jack can sell 12 bird feeders with 4 lb of birdseed. We can use Proportion method to calculate this :

Assuming that Jack mixes 1/3 pound of birdseed for each bird feeder, we can find out how many bird feeders he can sell with 4 pounds of birdseed by using a proportion.

Let x be the number of bird feeders Jack can make with 4 pounds of birdseed. We can set up the proportion:

1/3 pounds of birdseed per bird feeder = 4 pounds of birdseed / x bird feeders.

Simplifying this equation, we get:

1/3 = 4/x

To solve for x, we can cross-multiply:

1x = 12

x = 12

Therefore, Jack can make and sell 12 bird feeders with 4 pounds of birdseed.

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To find the equation of the line perpendicular to the line x - 6y = 3 and passing through the point (-1, 3), we need to determine the slope of the perpendicular line and use the point-slope form of a line. The standard form of the equation will be in the form Ax + By = C, where A, B, and C are constants.

The given line x - 6y = 3 can be rewritten in slope-intercept form as y = (1/6)x - 1/2, where the slope is 1/6. Since the line perpendicular to this line will have a slope that is the negative reciprocal of 1/6, the slope of the perpendicular line is -6.

Using the point-slope form of a line, we have y - y1 = m(x - x1), where (x1, y1) is the given point (-1, 3) and m is the slope of the perpendicular line (-6). Plugging in the values, we get y - 3 = -6(x + 1).

Simplifying the equation, we have y - 3 = -6x - 6, which can be rewritten as y = -6x - 3. This is the equation of the line perpendicular to x - 6y = 3 and passing through the point (-1, 3).  

To convert this equation into standard form Ax + By = C, we rearrange the terms and get 6x + y = -3. Therefore, the standard form of the equation of the line is 6x + y = -3.  

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The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

7 and 12

Step-by-step explanation:

x - y = 5

y = (5+x)

x+ (5+x) = 19

2x +5 = 19

2x = 14

x = 7

           19-7 = 12

12 +7  = 19

12-7 = 5

The two factors that add up to 6 are 3 and 3. This is because 3 + 3 = 6.

However, there are no two factors that can be multiplied together to give a product of -7. This is because if we multiply two factors, the result is positive if both factors have the same sign (both positive or both negative), and negative if the factors have opposite signs. Therefore, we cannot find two factors that multiply to give -7, as there are no two factors with opposite signs whose product is 7.

In other words, if we let x and y be two factors that multiply to give -7, then either x and y are both positive or both negative. If they are both positive, then their product is positive, which is not equal to -7. If they are both negative, then their product is positive as well, which is also not equal to -7. So there are no two factors that can be multiplied together to give -7.

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(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).

(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.

a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).

The formula for the two-sample t-test is:

t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]

where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.

Using the data from the plots, we get:

Xf = 917.5, sf = 348.0137, nf = 15

Xm = 783.7273, sm = 276.0625, nm = 28

Plugging in these values, we get:

t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895

Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.

The confidence interval for the difference between female and male times is:

(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))

= 133.7727 ± 121.8187

= (11.954, 255.591)

Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.

b) Assumptions and conditions for the two-sample t-test:

Independence, We assume that the observations for each group are independent of each other.

Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.

Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,

F = s^2f / s^2m

where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.

Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.

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All four measurement pairs could be the dimensions of Rectangle B.

If the corresponding components of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Since Rectangle B is a scaled copy of Rectangle A, its dimensions will be some multiple of the dimensions of Rectangle A.

The dimensions of Rectangle A are 8 inches by 4 inches. So, Rectangle B could have dimensions of:

4 inches by 2 inches: This is half the length and half the width of Rectangle A, so it is a scaled copy of Rectangle A.

8 inches by 2 inches: This is half the width of Rectangle A, but the same length, so it is also a scaled copy of Rectangle A.

10 inches by 4 inches: This is the same length as Rectangle A, but a little more than double the width, so it is a scaled copy of Rectangle A.

80 inches by 40 inches: This is ten times the length and ten times the width of Rectangle A, so it is also a scaled copy of Rectangle A.

Therefore, all four measurement pairs could be the dimensions of Rectangle B.

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Answer:

1260 springs

Explanation:

From 1 pm to 6 pm, the machine will work for 5 hours.

In the first part of the day, the machine made 450 paper clips, which took it:

So, the machine will start making springs at 2:30 pm.

From 2:30 pm to 6 pm, the machine will work for 3.5 hours.

During this time, the machine can make:

Therefore, the machine will make 1260 springs by 6 pm.

________________________________________________________

In one hour a machine can make 300 paper clips 300 paper clips or 360 springs. At 1 pm the machine starts working. It makes 450 paper clips and then changes to making springs. How many springs will the machine make by 6 pm?

The machine will make 1260 springs by 6 pm.

We are given that the machine can make 300 paper clips in one hour or 360 springs in one hour.

Let's first find out how many hours the machine will make paper clips before switching to making springs.

We know that the machine has made 450 paper clips. So,

Hence, the machine will make paper clips for 1.5 hours before switching to making springs.

Now, we need to find out how many hours the machine will make springs. We know that the machine starts working at 1 pm and we need to find out how many hours it will work making springs before 6 pm.

There are 5 hours between 1 pm and 6 pm. However, we need to subtract the 1.5 hours that the machine will work making paper clips.

So, the machine will make springs for:

Now, we can use the information that the machine can make 360 springs in one hour to find out how many springs it will make in 3.5 hours.

Therefore, the machine will make 1260 springs by 6 pm.

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Answer:

14/9

Step-by-step explanation:

9/9 = 1

Therefore,

-5/9 + x/9 = 9/9

x/9 = 9/9 + 5/9

x/9 = 14/9

To check the answer,

-5/9 + 14/9 = 9/9    answer checks out!

We have shown that if a is an integer, then either a² = 0 mod 4 or a² = 1 mod 4.

Let's prove that if a is an integer, then either a² = 0 mod 4 or a² = 1 mod 4.Let's start by considering that an integer is always one of the following:

even, i.e., 2k, where k is an integer.odd, i.e., 2k+1, where k is an integer.We have two cases to consider:

Case 1: Let a be an even integeri.e., a = 2k, where k is an integer.

Then, a² = (2k)² = 4k².We know that every square of an even integer is always divisible by 4.

Therefore, a² is always a multiple of 4.So, a² ≡ 0 (mod 4)

Case 2: Let a be an odd integeri.e., a = 2k+1, where k is an integer.

Then, \(a² = (2k+1)² = 4k² + 4k + 1\).Rearranging the above equation, we get:a² = 4(k²+k) + 1.

Observe that \(4(k²+k) i\)s always an even integer, since it is a product of an even and an odd integer.

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Answer:

hdjdkurjfiotnbbteuurjrhrt

In order to find the number of hours it takes to do the full rotation we separate into pieces the days, hours, and minutes and convert each of them separately.

using the conversion factor from days to hours we get that

then we get that

hours does not need a conversion factor, meaning that

continue by converting the minutes using the following conversion factor

then,

To complete add all the results together

It takes mercury 922.5 hours to complete a full rotation.

Answer:

A. Transitive

A randomly selected high school student taking the 2015 SAT has an approximately 79.3% chance of having an SAT score between 400 and 700 for standard deviation.

To calculate probabilities, we need to standardize the values ​​using the Z-score formula. A Z-score measures how many standard deviations a given value has from the mean. In this case, we want to determine the probability that the SAT score is between 400 and 700 points.

First, calculate the z-score for the given value using the following formula:

\(z = (x - μ) / σ\)

where x is the score, μ is the mean, and σ is the standard deviation. For 400 points:

z1 = (400 - 484) / 115

For 700 points:

z2 = (700 - 484) / 115

Then find the area under the standard normal curve between these two Z-scores using a standard normal table or statistical calculator. This range represents the probability that a randomly selected student falls between her two values for standard deviation.

Subtracting the cumulative probability corresponding to z1 from the cumulative probability corresponding to z2 gives the desired probability. Multiplying by 100 returns the result as a percentage rounded to one decimal place.

Doing the math, a random high school student who took her SAT in 2015 has about a 79.3% chance that her written SAT score would be between 400 and 700. 

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Given:

2x + 4y = 14

4x + y = 20

Required:

We need to find the equivalent to the given system.

Explanation:

Consider the equation

Multiply both sides of the equation by -4, it will not affect the equations of the system

Final answer:

The equivalent system of the equation is

Answer:

a < 4

Step-by-step explanation:

7 + a < 11

Subtract 7 from each side

7+a-7 <11-7

a < 4

Answer: a=3

Step-by-step explanation:

Option C is correct.  Less than 100  is closest to total deaths resulting from ladder misuse each year.

According to the Consumer Product Safety Commission (CPSC), on average, approximately 300 people die each year in the United States from falls involving ladders.

However, not all of these deaths are due to ladder misuse. In fact, the number of deaths resulting specifically from ladder misuse is likely to be lower. It is estimated that a significant portion of ladder-related fatalities are caused by factors such as overreaching, misusing the ladder, or failing to follow proper safety guidelines.

To reduce the number of deaths and injuries resulting from ladder misuse, it is important to follow safety guidelines and to choose the right ladder for the job, taking into consideration factors such as height, weight, and stability.

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Answer:

69.3 meters squared

Step-by-step explanation:

1) Think of the shape as being divided into two sections (a rectangle and a triangle)

2) multiply 5.2 times 7 to find the area of the rectangle (36.4)

3) subtract 5.2 from 14.6 to find the base of the triangle (9.4)

4) multiply 9.4 by the height of the triangle 7 (65.8)

5) divide 65.8 by two because a triangle is half of the needed rectangle

6) this leaves 32.9

7) add 32.9 and 36.4 to get your final answer of 69.3 meters squared

hope this helps :)

The least squares solution of the equation is x = (C, D) = (7, 0).

To find the least squares solution for the line equation b = C + Dt and draw the closest line, we need to set up a system of equations using the given data points.

Using the line equation b = C + Dt, substitute the values to form the following equations:

Equation 1: 7 = C - D

Equation 2: 7 = C + D

Equation 3: 21 = C + 2D

To find the least squares solution x = (C, D),

we want to minimize the sum of squared differences between the actual data points and the line.

This can be done by solving the system of equations using the method of least squares.

Let's solve the system of equations:

Add (1) and (2)

7 + 7 = C - D + C + D

14 = 2C

C = 7

Solving for D, we find:

7 = 7 - D

D = 0

Therefore,

The least squares solution of the equation is x = (C, D) = (7, 0).

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Answer:

8.9

Step-by-step explanation:

1.move down 5.7 into the box below it

2. add the numbers

3.awnser is 8.9

Answer:

(-3,2)

Step-by-step explanation:

To solve this system, you first have to find what either x or y is.

In the top equation, x is by itself, so it is the easiest route to find.

x+3y=3

Subtract the 3y to get x by itself

x=3-3y

Now that we know that x=3-3-3y, plug it into the other equation for x.

3y-2(3-3y)=12

3y-6+6y=12

Solve to get y by itself

9y=18   Divide by 9

y=2

Finally, now that you have y, you can plug 2 back into x=3-3y for y.

x=3-3(2)

x=3-6

x=-3

Therefore, (-3,2)

If you want to double-check, just plug both x and y back into one of the equations

x+3y=3

-3+3(2)=3

-3+6+3

3=3

The loads carried by an elevator are found to follow a normal distribution with a mean weight of 1812 lbs, and a standard deviation of 105.3 lbs. The answer is c) [1606, 2018].

To answer this question, we need to use the concept of confidence intervals. A 95% confidence interval means that in 95% of all cases, the true population parameter (in this case, the weight of the elevator load) will fall within the interval.

To find the interval centered about the mean, we need to calculate the margin of error first. The formula for margin of error is:

Margin of Error = z*(standard deviation/square root of sample size)

Since we do not have a sample size here, we will use the population standard deviation instead.

For a 95% confidence level, the z-value is 1.96. So, plugging in the values we have:

Margin of Error = 1.96*(105.3/square root of 1)

Margin of Error = 205.97

Now, we can find the interval by adding and subtracting the margin of error from the mean:

Interval = [1812 - 205.97, 1812 + 205.97]

Interval = [1606.03, 2017.97]

Therefore, the answer is c) [1606, 2018].

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As the average is 5 out of 8 baskets. You multiply the total shots for 5/8 to find how many she makes:

Therefore, the infinite geometric series representing the decimal 0.44444... converges to the fraction 4/9.

To represent the decimal 0.44444... as an infinite geometric series, we can start by noticing that this decimal can be written as 4/10 + 4/100 + 4/1000 + ...

The pattern here is that each term is 4 divided by a power of 10, with the exponent increasing by 1 for each subsequent term.

So, we can express this as an infinite geometric series with the first term (a) equal to 4/10 and the common ratio (r) equal to 1/10.

The infinite geometric series can be written as:

0.44444... = (4/10) + (4/10)(1/10) + (4/10)(1/10)^2 + ...

To find the fraction to which this series converges, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

Plugging in the values, we have:

S = (4/10) / (1 - 1/10)

= (4/10) / (9/10)

= (4/10) * (10/9)

= 4/9

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Answer:

x = 30, and the measure of NMO is 64°

Step-by-step explanation:

Since MO bisects LMN, it follows that LMO is congruent to NMO, and the measure of LMN is twice the measure of LMO and of NMO. So we have:

\(5x - 22 = 2(x + 34)\)

\(5x - 22 = 2x + 68\)

\(3x = 90\)

\(x = 30\)

So the measure of NMO is equal to the measure of LMO:

\(30 + 34 = 64\)

LMO and NMO are 64°.

Answer:

x=30

MO bisects LMN

so LMO = NMO

then LMO+NMO=LMN