Evaluate: 47.6 - 5.342

A) -42.258

B) 52.942

C) 42.258

D) -5.82
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The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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Answer:

Therefore, the length of the ladder is 13 feet.

Step-by-step explanation:

This is a classic example of a right triangle problem in geometry. The ladder serves as the hypotenuse of the triangle, while the distance from the building to the ladder and the height of the window serve as the other two sides. Using the Pythagorean theorem, we can solve for the length of the ladder:

ladder^2 = distance^2 + height^2 ladder^2 = 5^2 + 12^2 ladder^2 = 169 ladder = √169 ladder = 13

Therefore, the length of the ladder is 13 feet.

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The probability of picking a cast member who sold more than 30 tickets is 2/5

Given that one cast member will be picked at random from the 20 cast members who sold tickets to receive a prize. We have to determine the probability of picking a cast member who sold more than 30 tickets.

To find the probability of picking a cast member who sold more than 30 tickets, we need to count the number of cast members who sold more than 30 tickets. Let A be the event of picking a cast member who sold more than 30 tickets. The number of cast members who sold more than 30 tickets is 8. Therefore, P(A) = 8/20 = 2/5.

The probability of picking a cast member who sold more than 30 tickets is 2/5.Answer: 2/5.

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Answer:

pi r squared

Step-by-step explanation:

A=pir2

pi is 3.14

hope it helps

The probability that suits of cards are spades, hearts, and spades is 39/850 or 0.046.

According to the give question.

Three cards are drawn from a standard deck of cards without replacement.

Since,

The total number of cards in a standard deck = 52

Total number of spade cards = 13

Total number of heart cards = 13

Now,

The probabbility of getting first card as a spade card = 13/52 = 1/4

The probability of getting second card as heart card

= 13/(52 -1)     (cards are drawn without replacement)

= 13/51

The probability of getting third card as a spade card

= (13 - 1)/52 -2

= 12/50

= 6/25

Therefore, the probability that suits of the cards are spades, hearts, spades

= 1/4 × 13/51 × 6/25

= 39/850

= 0.046

Hence, the probability that suits of cards are spades, hearts, and spades is 39/850 or 0.046.

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The equation of the tangent line to the curve \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at the point (1, 0) is y = (2/3)x - 2/3.

To find the equation of the tangent line to the curve at the point (1, 0), we need to find the slope of the tangent line and then use the point-slope form of a linear equation.
Let's differentiate \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) using the quotient rule:

\(y' = [(2x)(x^2 + x + 1) - (x^2 - 1)(2x + 1)] / (x^2 + x + 1)^2\)
Substituting x = 1 into the derivative expression:

\(y'(1) = [(2(1))(1^2 + 1 + 1) - (1^2 - 1)(2(1) + 1)] / (1^2 + 1 + 1)^2\)

        \(= [2(3) - (0)(3)] / (3)^2\)

        = 6/9

        = 2/3

Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) = (1, 0) and m = 2/3 we get,  
y - 0 = (2/3)(x - 1)

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

The point-slope form of a linear equation is given by y - y₁ = m(x - x₁) where (x₁, y₁) is a point on the line, and m is the slope of the line.

Therefore, the equation of the tangent line to the curve y = (x^2 - 1) / (x^2 + x + 1) at the point (1, 0) is y = (2/3)x - 2/3.

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The complete question is:

Find an equation of the tangent line to the given curve at the specified point, \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at (1,0).

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

fractions with the same denominator added together

You must add the numerators and keep the same denominator when adding fractions with the same denominator. Since the denominators of the two fractions are the same, we must add the numerators while maintaining the same denominator, which is 4.

What are the parts of fraction?

A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.

The number below the bar is called the denominator . It tells the number of equal parts into which the whole has been divided. The number above the bar is called the numerator. It tells how many of the equal parts are being considered.

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Based on the given options, the sample that can provide the most valid generalization is option C: 400 randomly chosen employees from the list of all employees. Option C

To determine the sample that can provide the most valid generalization regarding employees' preferences for team-building activities, we need to consider factors such as representativeness and diversity. Let's evaluate each option:

A) A group with one member from each department:

While this option includes representation from different departments, it may not capture the diversity of the company as a whole. Different departments might have varying preferences and dynamics that could influence their team-building activity preferences. Therefore, this sample may not provide a comprehensive view of the entire company's preferences.

B) All employees who have worked in the company for 5 years or more:

This sample includes employees who have long-term experience with the company. While it may capture their preferences accurately, it might not represent the preferences of newer employees who may have different perspectives and preferences. Therefore, it may not be the most valid sample for generalizing the preferences of all employees.

C) 400 randomly chosen employees from the list of all employees:

This option provides a random selection of employees from the entire company, which can help ensure representativeness. Random sampling helps minimize bias and provides a more accurate reflection of the overall employee population. Therefore, this sample has a higher likelihood of providing a valid generalization.

D) All 624 female employees in the company:

This sample includes only female employees, excluding male employees from the analysis. Consequently, it does not capture the preferences of the entire employee population and may introduce gender bias into the results. To obtain the most valid generalization, it is important to consider the preferences of all employees, irrespective of gender.

Option C is correct.

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The probability that a pupil uses neither pool nor gym is 11/70

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.

Number of pupil that can use pool and gym = 28

Number of people that can use pool = 48

Number of people that can use gym = 39

Number of people that can use pool only = 48 - 28 which is 20

Number of people that can use gym only = 39 - 28 = 11

Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59

Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.

Probability = required outcome / possible outcome

Required outcome = 11

possible outcome = 70

Probability = 11/70

In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70

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Check the picture below.

\(\cfrac{17.5+14}{17.5}~~ = ~~\cfrac{x}{12.5}\implies \cfrac{(17.5+14)(12.5)}{17.5}~~ = ~~x\implies 22.5=x\)

a)

Given,

3/x+2 = 1/7-x

Now further simplifying,

3(7-x) = x+2

21 - 3x = x + 2

19 = 4x

x = 19/4

Hence for the given expression the value of x is 19/4

b)

Given,

3-x/x-5 - 2x²/x² - 3x 10 = 2/x+2

Factorize the quadratic equation,

x² - 3x -10 = 0

(x+2)(x-5) = 0

3-x/x-5 - 2x²/ (x+2)(x-5) = 2/x+2

Taking LCM,

(3-x)(x-2) - 2x²/(x-5)(x+2) = 2/x+2

Further simplifying,

(3-x)(x-2) - 2x²= 2(x-5)

x² - 3x - 4 = 0

x² -4x +x - 4 = 0

x(x-4) + 1(x-4) = 0

(x+1)(x-4) = 0

x = -1 , 4 .

Hence for the given expression the value of x is -1, 4 .

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The limiting distribution for the given Markov chain is [0.25, 0.25, 0.25, 0.25].

a. The transition matrix P is given as follows:

P = [0 0.5 0.5; 0.5 0 0.5; 0.5 0.5 0 0 0.5 0.5; 0 0 0]

P is an ergodic Markov chain since all the states are communicating.

Therefore, the limiting distribution, denoted by π, exists and is unique.

We use the formula πP = π to find the limiting distribution, which yields [π₁, π₂, π₃, π₄] = [0.25, 0.25, 0.25, 0.25]

Thus the limiting distribution for the given Markov chain is [0.25, 0.25, 0.25, 0.25].

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Answer:

Minimum Values:

x = 0, y = 1, z = 3

Maximum Values:

x = 7 , y = 11 , z = 47

Step-by-step explanation:

FOR MINIMUM VALUES:

0<= x <= 7

It is clear from the above inequality that the minimum value of x must be 0.

y>= 1

This inequality shows that the minimum value of y must be 1. Using these minimum values of x and y to get the minimum value of z:

z = 2x + 3y

z = (2)(0) + (3)(1)

z = 3 (Minimum)

FOR MAXIMUM VALUES:

0<= x <= 7

It is clear from the above inequality that the maximum value of x must be 7.

x + y <= 11

To calculate maximum value of y we can use the minimum value of x in this inequality:

0 + y <= 11

y <= 11

Hence, the maximum value of y is 11.

Using these maximum values of x and y to get the maximum value of z:

z = 2x + 3y

z = (2)(7) + (3)(11)

z = 47 (Maximum)

For a sample of 72 batteries, the probability that the average battery life of the sample exceeds 1173.8 minutes is 0.9918.

It states a battery life variance of 8100 minutes and a median battery life of 1192 minutes.

In a sample of 72 batteries, find the probability that the average battery life (x) of the sample exceeds 1173.8 minutes.

Due to the large sample size (n = 72), we can use the central limit theorem to assume that the sample mean follows a normal distribution with mean μ = 1192 and standard deviation σ = sqrt(8100/72) = 30.

So the z-score for x= 1173.8 is

z = (x - μ) / (σ / sqrt(n))

= (1173.8 - 1192) / (30 / square(72))

= -2.4

You can use a standard normal distribution table or calculator to find the probability that a  standard normal random variable is greater than -2.4. This is 0.9918 (rounded to four decimal places).

Therefore, for a sample of 72 batteries, the probability that the average battery life of the sample exceeds 1173.8 minutes is 0.9918 (rounded to four decimal places) if the claim is correct. 

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Answer:

=5x⁴+3x

=-2x+4

=8x+4

=-2x-4

Step-by-step explanation:

hope it's help

Answer:

Step-by-step explanation:

2.02

x=21 so replace x with 21

3(21)+y/z

then do the same with y and z

3(21)+36/49

63+36/49

99/49

SOLUTION 2.02

The probability of a percentage increase in gasoline that is 4% or larger over the next quarter is approximately 25%.

Gasoline exhibits an average quarterly percentage change of 2.84% and a quarterly volatility of 8.22%. To determine the probability of a percentage increase in gasoline that is 4% or larger over the next quarter, we need to consider the distribution of the data.

The average quarterly percentage change of 2.84% provides us with a baseline expectation of how gasoline prices may change over time. However, the quarterly volatility of 8.22% indicates that there is significant variability in these price changes. This volatility suggests that gasoline prices can deviate considerably from the average.

To calculate the probability, we can use the concept of standard deviations. A 4% increase in gasoline prices is equivalent to a change of (4 - 2.84) / 8.22 standard deviations from the mean. By referring to a standard normal distribution table or using statistical software, we can determine the proportion of the distribution that falls above this threshold.

Based on the available information, the probability of a percentage increase in gasoline that is 4% or larger can be estimated to be approximately 25%.

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Answer:

21

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Step-by-step explanation:

Answer:21 students were on each bus.

Step-by-step explanation:

215-5=210

210/10=21 the number of students divided by the number of buses

Answer:

Step-by-step explanation:

Put them in your calculator. I think you'll find 2.95 is larger by 0.001

Do it like this 2.95 - 2.949 = 0.001

The measure of PS is 58 not 48 showing that the statement PS = 48 is false

A line is a shortest distance between two points. If the measure of PQ is equivalent to QR where;

PQ = 3x - 7

QR = 2x + 2

PQ = QR

3x - 7 = 2x + 2

Collect the like term

3x - 2x = 2 + 7

x = 9

Determine RS

RS = x + 9

RS = 9 + 9

RS = 18

PS =  PR + RS

PS = PQ + QR + RS
PS = 3x - 7 + 2x + 2 + 18

PS = 3(9) - 7 +. 2(9) + 20

PS = 27 - 7 + 38
PS = 20 + 38

PS = 58

Hence the measure of PS is 58 not 48 showing that the statement PS = 48 is false

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The parametric equation of the line drawn  ( 0. , 4.) and ( 4. , 0. ) is x + y - 4 = 0

A finite line segment is drawn from two points

Let the point be A and B

The co ordinates of the point A is (0, 4) and the co ordinates of the point B is (4, 0)

The equation of the line can be

y - y₁ =( (y₂-y₁)/(x₂ - x₁))(x - x₁)

y - 4 = ((4 - 0)/(0 - 4))(x - 0)

y - 4 = (4/-4)(x - 0)

y - 4 = -1(x - 0)

y - 4 = -x

y + x -4 = 0

Therefore, the parametric equation of the line drawn from  ( 0. , 4.) and ( 4. , 0. ) is x + y - 4 = 0

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The probability, P(not green) when choosing one marble from the bag is 88%.

The probability of an event is a number that indicates how likely the event is to occur.

Given is that Joseph has a bag filled with 3 red, 3 green, 9 yellow, and 10 purple marbles

We can write -

P(not green) = 1 - P(green)

So, we can write -

P(green) = n{g}/n{s}

P(green) = 3/25

So, we can write -

P(not green) = 1 - P(green)

P(not green) = 1 - 3/25

P(not green) = 22/25

Now -

Let -

22 is x% of 25

22 = x/100 x 25

x/4 = 22

x = 88%

Therefore, the probability, P(not green) when choosing one marble from the bag is 88%.

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Step-by-step explanation:

log both sides:

Compare both sides to get:

or

The interest rate is 10.89%

1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..

The size of the nominal money supply in the new short-run equilibrium is 121.07.

2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.

Real exchange rate will remain unchanged.

3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.

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Answer:

in 13 years it will be at 432,480

Step-by-step explanation:

(a) Number of groups: 3 groups. (b) P-value: Not provided in the given computer output.

(a) The number of groups can be determined from the given computer output in the "Source" column. In this case, it states "Groups" with a degree of freedom (DF) value of 3. Therefore, there are 3 groups.

(b) The p-value is not provided in the given computer output. The p-value represents the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. It is typically obtained from a statistical table or calculated using statistical software. Without the specific p-value mentioned in the output, it cannot be determined.

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Answer:

\(l = 6w - - - - 1 \\ \\ 2l + 2w = 70 - - - - - 2 \\ \\ solving \: simultaneously \\ put \: l = 6w \: into \: 2 \\ 2(6w) + 2w = 70 \\ 12w + 2w = 70 \\ 14w = 70 \\ w = 5 \\ \\ l = 6w \\ l = 6(5) \\ l = 30\)