Find the length of each segment:

According to Chebyshev's theorem, at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.

Chebyshev's theorem states that for any set of data, regardless of its distribution, a certain percentage of the data lies within a certain number of standard deviations from the mean. Specifically, Chebyshev's theorem states that for any data set, at least 1 – 1/k² of the data values will lie within k standard deviations of the mean, where k is any number greater than 1. If k=2, at least 75% of the data values lie within 2 standard deviations of the mean. If k=3, at least 89% of the data values lie within 3 standard deviations of the mean.

Therefore, for a data set with a mean of 63.6 minutes and a standard deviation of 2.5 minutes, we can use Chebyshev's theorem to determine that at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.

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Answer:

the answer without a doubt it b B B

Step-by-step explanation:

Answer:

s = 2r + 1

Step-by-step explanation:

Number of sunflower (s) is 1 more than twice the number of roses (r)

Mathematically ;

Number of sunflower = 1 + 2 * number of roses

Sunflower = s ; roses = r

s = 2r + 1

We want to study the relation between the number of sunflowers and roses, we will see that it is an equation and the equation is:

s = 2*r + 1

So we know that the number of sunflowers is one more than twice the number of roses, notice that it represents an equation (so it is not an inequality)

And the equation can be written as:

s = 2*r + 1

The number of sunflowers is 2 times the number of roses, plus 1.

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The z-scores for the given weights of 2700 g, 4000 g, 4250 g, and 6300 g are -1.88, -0.25, 0.06, and 2.63, respectively.

Z-score is a measure of the deviation of the raw data points from the mean value of the data set, measured in terms of standard deviations.

To find the z-score, subtract the average weight from the given weight and then divide it by the standard deviation. The calculations and solutions are as follows:

Given average weight of penguin = 4200 g

Standard deviation of penguin weight = 800 g

Z-score formula: z = (x - μ) / σwhere z is the z-score, x is the given weight, μ is the mean weight, and σ is the standard deviation of the weights.

Weight = 2700 g

z-score = (2700 - 4200) / 800

            = -1.88 (rounded to two decimal places)

Weight = 4000 g

z-score = (4000 - 4200) / 800

            = -0.25 (rounded to two decimal places)

Weight = 4250 g

z-score = (4250 - 4200) / 800

            = 0.06 (rounded to two decimal places)

Weight = 6300 g

z-score = (6300 - 4200) / 800

= 2.63 (rounded to two decimal places)

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To find the z-scores associated with each of the given penguin weights, we can use the formula:

z = (x - μ) / σ

where x is the given weight, μ is the mean weight, and σ is the standard deviation.

For weight = 2700 g:

z-score = (2700 - 4200) / 800 = -1.875

For weight = 4000 g:

z-score = (4000 - 4200) / 800 = -0.25

For weight = 4250 g:

z-score = (4250 - 4200) / 800 = 0.0625

For weight = 6300 g:

z-score = (6300 - 4200) / 800 = 2.625

These are the respective z-scores associated with each given penguin weight.

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Answer:

\(gradient = - 3 \\ y = mx + c \\ 2 = ( - 3 \times 0) + c \\ c = 2 \\ \therefore \: y = - 3x + 2 \\ y = 2 - 3x\)

Answer:

23

Step-by-step explanation:

We Know

The sequence (1,3,5,7)

Each time it increases by 2

What is the 12th term in the sequence (1,3,5,7)?

Let's list it out

1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,....

So, the 12th term in the sequence is 23.

The probability that a total of four tries will be necessary for both of you to get through is 0.1728.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

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The bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.

To find the correlation between the bacterial count after 24 hours and 48 hours, we would need the actual numerical values of the bacterial counts for each strain. Without that information, we cannot calculate the correlation coefficient. However, it is important to note that a positive correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours also increases. A negative correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.

The complete question is-

Five strains of the Staphylococcus aureus bacteria were grown for 24 hours either at 35 degrees Celsius or at 43 degrees Celsius. Here are the resulting bacterial counts for each condition:

24 hr: 66, 71, 93, 102, 62

48hr: 110,123,146,136,113

If we had plotted bacterial count at 35 degrees Celsius on the y-axis instead of the x-axis, the value of the correlation coefficient would be

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The equations of the lines are y = 3x - 5 and y = (1/2)x - 7

An equation is an expression that shows how numbers and variables are related to each other.

A linear function is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Two lines are parallel if they have the same slope

1) y = 3x + 6; (4, 7)

The parallel line would have a slope of 3 and pass through (4, 7), hence:

y - 7 = 3(x - 4)

y = 3x - 5

2) y = (1/2)x + 5; (4, -5)

The parallel line would have a slope of 1/2 and pass through (4, -5), hence:

y - (-5) = (1/2)(x - 4)

y = (1/2)x - 7

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(ANB)' = {1, 5, 11} is the complement of intersection of sets A and B.

The complement of the intersection of sets A and B, denoted as (ANB)', can be found by first determining the intersection of the two sets and then finding the elements that are not in this intersection.

Step 1: Intersection of Sets A and B

Set A = {7, 6, 9, 2, 5, 1}

Set B = {3, 6, 2, 10}

Intersection (ANB) = {2, 6}

Step 2: Complement of the Intersection

To find the complement, we need to consider the elements that are not present in the intersection. In this case, the universal set U consists of natural numbers less than 11, which means it includes all numbers from 1 to 10.

The complement of (ANB) in U is the set of elements from 1 to 10 that are not in the intersection (ANB). Therefore, (ANB)' = {1, 5, 11}.

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If the number of cups of water w, needed for f cups of flour is described by the equation w = 0.75f, 0.75 represents the number of cups of water needed for one cup of flour

The equation is

w = 0.75f

Where w is the number of cups waters needed for f cups of flour.

Here w is is dependent variable and f is the independent variable

We can see that w is proportional to the f, the 0.75 is the constant.

w = 0.75f

Move the f to left hand side of the equation

w/f = 0.75

Hence, If the number of cups of water w, needed for f cups of flour is described by the equation w = 0.75f, 0.75 represents the number of cups of water needed for one cup of flour

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Answer:

5 boxes

Step-by-step explanation:

multiply the crayons (7) by the number of children (8) to see how many crayons are need (56). Then dived that by how may crayons come in a box(12). that gives you 4.6 so round that up and your are left with the answer 5 . 5 boxes

the vector from vertex C to the midpoint of side AB is 7/2 i + 5/2 j + 3 k.

To find the midpoint of side AB, we can use the midpoint formula:
M = (A + B)/2

Substituting the coordinates of A and B, we get:
M = ((5,5,4) + (4,2,4))/2
M = (9/2, 7/2, 4)

Now, to find the vector from vertex C to the midpoint M, we can subtract the coordinates of C from the coordinates of M:
M - C = (9/2, 7/2, 4) - (1, 1, 1)
M - C = (9/2 - 1, 7/2 - 1, 4 - 1)
M - C = (7/2, 5/2, 3)

Therefore, the vector from vertex C to the midpoint of side AB is 7/2 i + 5/2 j + 3 k.

It seems that the answer you got, 4i + 5/2j + 7/2 k, is the result of using the coordinates of point B instead of point A in the midpoint formula. If we use B instead of A, we get the midpoint as (5/2, 3/2, 4), which leads to the vector 4i + 5/2j + 7/2k from C to the midpoint.
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Answer: 124

Step-by-step explanation:

Corresponding angles are congruent

Opposite angles are congruent

A tax of 7.5 percent was added to the product to make it equal to 27.95.

Answer:

Lexi can read 60 pages in 36 minutes.

Step-by-step explanation:

Answer:

13%

Step-by-step explanation:

the area of the flag is 4x6=24 the circle has an area of 3.14.  3.14/24 is 13%

The  percent of the flag is gold should be considered as the 13%.

Since

In a 4-by-6-foot Colorado state flag, the gold-colored disk has a 1-foot radius.

So here the area of the flag should be

= (4) (6)

= 24

Now the percentage be like

= 3.14/24

= 13%

hence, The  percent of the flag is gold should be considered as the 13%.

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Answer:

the building is thirty feet tall

Step-by-step explanation:

so make a ratio of shadow to joey

5:45

simplify that to

1:9

so you can now divide 270 by nine

30

the building is thirty feet tall

The estimated cost of producing 600 lb of paper once 10 tons have been produced is approximately $23,000.

To estimate the cost of producing 600 lb of paper once 10 tons have been produced, we can use the concept of submissions used.

First, we need to convert 10 tons to pounds, which is 10 x 2000 = 20,000 lb.

Next, we can use the formula C(x) = S(x) / 1000, where C(x) is the cost in thousands of dollars and S(x) is the submissions used.

We know that C(10) = 380, which means that at 10 tons produced, the cost is $380,000.

To find the submissions used at 10 tons, we can use the formula S(x) = kx, where k is a constant.

So, S(10) = k(10) = 10k

We don't know the value of k, but we can find it by using the given cost and submissions used.

C(10) = S(10) / 1000

380 = 10k / 1000

k = 38

Now we can find the submissions used at 20,000 lb by using S(x) = kx.

S(20,000) = 38(20,000)

S(20,000) = 760,000

Finally, we can find the cost of producing 600 lb of paper by using the submissions used and the formula C(x) = S(x) / 1000.

C(600) = S(20,000) / 1000 / (20,000 / 600)

C(600) = 760 / 33

C(600) ≈ 23

Therefore, the estimated cost of producing 600 lb of paper once 10 tons have been produced is approximately $23,000.

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Answer:

There are 8 boys for every 10 girls. This is 6 equal groups. Equal ratio

Step-by-step explanation:

1.  The simultaneous solution of the given equations is X=12/5 and Y=4/5

2.1)The combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.

2)The combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.

To find the simultaneous solution of the given equations 4X+3Y=12 and 2X+4Y=8, we can use the method of elimination, also known as the addition method. Multiplying the second equation by 2, we get 4X+8Y=16.

Now, we can subtract the first equation from the second equation: 4X+8Y - (4X+3Y) = 8Y - 3Y = 5Y and 16 - 12 = 4. Thus, 5Y=4 or Y = 4/5.

Substituting this value of Y in any of the two equations, we can find the value of X. Let's substitute this value of Y in the first equation: 4X+3(4/5)=12 or 4X

= 12 - (12/5)

= (60-12)/5

= 48/5.

Thus, X = 12/5. Hence, the simultaneous solution of the given equations is X=12/5 and Y=4/5.2. To find the optimal values of X and Y that will maximize the objective function Z=$10X+$50Y, we need to use the method of linear programming.

First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 3X+4Y=12, 2X+5Y=10, X=0, and Y=0.

To find the optimal solution, we need to evaluate the objective function at each of the corner points of the feasible region, and choose the one that gives the maximum value.

Let's denote the corner points as A, B, C, and D, as shown above. The coordinates of these points are: A=(0,3), B=(2,1), C=(5/2,0), and D=(0,0). Now, let's evaluate the objective function Z=$10X+$50Y at each of these points:

Z(A)=$10(0)+$50(3)

=$150, Z(B)

=$10(2)+$50(1)

=$70, Z(C)

=$10(5/2)+$50(0)

=$25, Z(D)

=$10(0)+$50(0)=0.

Thus, we can see that the maximum value of Z is obtained at point A, where X=0 and Y=3. Therefore, the combination of X and Y that will yield the optimum for this problem is X=0 and Y=3.3.

To find the combination of X and Y that will provide a minimum for the problem Minimize Z=X+5Y subject to: 4X+3Y≥12 and 2X+5Y≥10, we need to use the same method of linear programming as above.

First, let's plot the feasible region defined by the given constraints:We can see that the feasible region is bounded by the lines 4X+3Y=12, 2X+5Y=10, X=0, and Y=0.

To find the optimal solution, we need to evaluate the objective function Z=X+5Y at each of the corner points of the feasible region, and choose the one that gives the minimum value.

Let's denote the corner points as A, B, C, and D, as shown above.

The coordinates of these points are: A=(3,0), B=(5,1), C=(0,4), and D=(0,0).

Now, let's evaluate the objective function Z=X+5Y at each of these points:

Z(A)=3+5(0)=3,

Z(B)=5+5(1)=10,

Z(C)=0+5(4)=20,

Z(D)=0+5(0)=0.

Thus, we can see that the minimum value of Z is obtained at point A, where X=3 and Y=0. Therefore, the combination of X and Y that will provide a minimum for this problem is X=3 and Y=0.

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Brand A sells their product for 36 dabloons per 6 kg. Brand B sells their product for 4 dabloons per 2 kg. Therefore, Brand B is cheaper than Brand A by 2 dabloons per kg in price.

To determine which brand is cheaper and by how much per kg, we compare the prices of both brands based on the cost per kg.

Brand A sells their product for 36 dabloons per 6 kg. We can simplify this to find the cost per kg:

Cost per kg for Brand A = 36 dabloons / 6 kg = 6 dabloons/kg.

Brand B sells their product for 4 dabloons per 2 kg. We can simplify this to find the cost per kg:

Cost per kg for Brand B = 4 dabloons / 2 kg = 2 dabloons/kg.

Comparing the cost per kg, we find that Brand B has a lower cost per kg than Brand A. Therefore, Brand B is cheaper.

To calculate the difference in price per kg between the two brands, we subtract the cost per kg of Brand B from the cost per kg of Brand A:

Difference in price per kg = Cost per kg of Brand A - Cost per kg of Brand B

= 6 dabloons/kg - 2 dabloons/kg

= 4 dabloons/kg.

Therefore, Brand B is cheaper than Brand A by 4 dabloons per kg.

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Answer:

X = 24

Step-by-step explanation:

Answer:

the answer is 24

Step-by-step explanation:

Answer:

y = -x/4 + 30

y = -2x/3 + 490

Step-by-step explanation:

5x+20y=600

5x-5x+20y=-5x+600

20y=-5x+600

20y/20=(-5x+600)/20

20y/20=-5x/20+600/20

y = -x/4 + 30

2x+3y=1470

2x-2x+3y=-2x+1470

3y=-2x+1470

3y/3=(-2x+1470)/3

3y/3=-2x/3+1470/3

y = -2x/3 + 490

When the thermometer reads 6 degrees the temperature drops 15 degrees overnight, the temperature at 9:00pm will be 16°.

From the information, the thermometer reads 6 degrees the temperature drops 15 degrees overnight the it rises 25 degrees at 9:00am.

Therefore, the temperature at 9:00pm will be:

=6° - 15° + 25°

= 16°

Therefore, the temperature at 9:00pm will be 16°.

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Answer:

8

Step-by-step explanation:

The following expression  →  |- 5| + |3| is equivalent to 8

The absolute value of a number is the magnitude of number. Absolute value describes the distance from zero that a number is on the number line, without considering direction.

We have the following expression -

|- 5| + |3|

For a number [x], such that [x] < 0, the absolute value would be -

v[a] = - x

and for [x] > 0

v[a] = x

So, for x = |- 5| + |3| , the equivalent expression would be -

5 + 3

8

Therefore, the following expression  →  |- 5| + |3| is equivalent to 8.

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