There are 38 buses in the parking lot and each bus holds 74 people how many people are able to ride the buses

Answer:

Step-by-step explanation:

gave $50  - got back $10.50 = it payed $39.50 for 2 pots

$39.50 /2 = $19.75 payed for one pot taxes included

A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

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The approximate equation of the line of best fit is y = x + 5 and the money spent on entertainment is $13

From the question, we have the following parameters that can be used in our computation:

Scatter plot

The line of best fit is added as an attachment

From this graph, we have the following points

(x, y) = (0, 5) and (4, 9)

A linear equation is represented as

y = mx + b

Where

b = y when x = 0

This means that

b = 5

So, we have

y = mx + 5

At (x, y) = (4, 9), we have

9 = 4m + 5

So, we have

4m = 4

Divide by 4

m = 1

So, we have

y = x + 5

This means that

x = 8

Substitute the known values in the above equation, so, we have the following representation

y = 8 + 5

Evaluate

y = 13

Hence, the money spent on entertainment for working for 8 hours is $13

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Answer:

18049/14= 1289 with a remainder of 3

Answer:

3

Step-by-step explanation:

Answer:

4 mph

Explanation:

8 miles / 2 hours = 4 miles each hour

The equation for the first option would be

Where "x" is the number of copies and y the cost.

The second equation will be

If we graph both equations we have

As we can see, they will be equal in terms of cost with 2 copies. The cost will be 50.

We can see it at the intersection of the two graphs! we can also do it with algebra, if the costs are equal (same "y") we can say

The number of copies is 2.

Answer:

5x6 - 20 + 8

Answer:

5 X k = 30

10X2 = 20+8 = 28

Step-by-step explanation:

Answer:

9%

Step-by-step explanation:

8000 x 9%= 720

Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.

A graph can be described  as a pictorial representation or a diagram that represents data or values in an organized manner.

The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.

In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.

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Answer:

  (c)  y = 3^x

Step-by-step explanation:

A function is described as exponential if the independent variable is found in the exponent.

  y = x^(1/2) . . . a square root function, not exponential

  y = 2x^3 . . . . a cubic (polynomial) function, not exponential

  y = 3^x . . . . . an exponential function

Step-by-step explanation:

n×2=?

The n means 1 then. 1×2 series

1 × 2 = 2

The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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Answer:

\(\begin{array}{cc}{Outcome} & {X's} & {FFF} & {0} & {SFF} & {1} & {FSF} & {1} & {FFS} & {1} & {FSS} & {2}& {SFS} & {2}& {SSF} & {2}& {SSS} & {3} \ \end{array}\)

Step-by-step explanation:

Given

\(S_S = \{FFF, SFF, FSF, FFS, FSS, SFS, SSF, SSS\}\)

\(X \to\) Number of beams failed by shear

Required

List each outcome and the value of X

To do this, we simply count the occurrence of S in each outcome.

This is tabulated as follows:

\(\begin{array}{cc}{Outcome} & {X's} & {FFF} & {0} & {SFF} & {1} & {FSF} & {1} & {FFS} & {1} & {FSS} & {2}& {SFS} & {2}& {SSF} & {2}& {SSS} & {3} \ \end{array}\)

Answer:

The probability that he took the CFA I exam is 0.297.

Step-by-step explanation:

We are given that the pass rates for levels I, II, and III are 0.51, 0.76, and 0.86, respectively. Suppose that 3,000 candidates take the level I exam, 2,500 take the level II exam and 2,000 take the level III exam.

Let the probability that the candidate take the level I exam = P(A) = \(\frac{3000}{7500}\) = \(\frac{2}{5}\)

The probability that the candidate take the level II exam = P(B) = \(\frac{2500}{7500}\) = \(\frac{1}{3}\)

The probability that the candidate take the level II exam = P(C) = \(\frac{2000}{7500}\) = \(\frac{4}{15}\)

Let P = event that the candidate is passed

Also, the probability of the pass rate for level I = P(P/A) = 0.51

The probability of the pass rate for level II = P(P/B) = 0.76

The probability of the pass rate for level III = P(P/C) = 0.86

Now, a randomly selected candidate who took a CFA exam tells you that he has passed the exam, the probability that he took the CFA I exam is given by = P(A/P)

We calculate this probability using the Bayes' Theorem;

       P(A/P) = \(\frac{P(A) \times P(P/A)}{P(A) \times P(P/A)+P(B) \times P(P/B)+P(C) \times P(P/C)}\)

                  = \(\frac{\frac{2}{5}\times 0.51 }{\frac{2}{5}\times 0.51+\frac{1}{3}\times 0.76+\frac{4}{15}\times 0.86}\)

                  = \(\frac{0.204}{0.687}\) = 0.297

Hence, the probability that he took the CFA I exam is 0.297.

The probability will be "0.2971".

According to the question,

The passing rate for the levels 1, 2 and 3 are:

Now,

The no. of students who passes CFA 1 will be:

= \(3000\times 0.51\)

= \(1530\)

The no. of students who passes CFA 2 will be:

= \(2500\times 0.76\)

= \(1900\)

The no. of students who passes CFA 3 will be:

= \(2000\times 0.86\)

= \(1720\)

So,

The total number of students who passes,

= \(1530+1900+1720\)

= \(5150\)

hence,

The probability that randomly selected candidates who took the CFA 1 will be:

= \(\frac{Favorable \ events}{Total \ events}\)

= \(\frac{1530}{5150}\)

= \(0.2971\)

Thus the above approach is correct.

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Answer:

the volume of the toy house is 66cm3

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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Answer:

51.3

Step-by-step explanation:

Tan(y) like all Tan Trig functions, is defined as the side opposite divided by the side adjacent.

The side adjacent is part of the reference angle.

The side opposite is not connected to the reference angle at all.

Side Opposite = 10

Side Adjacent = 8

Tan(y) = 10/8

Tan(y) = 1.25

y = Tan-1(1.25)

y = 51.34

y = 51.3

Answer is \(\frac{33}{8}\)

Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°

The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.

Now, for the transverse line theorem we can say that:

Angle 1 will be composed of two angles namely:

48 degrees and (180 - 153) degrees.

Thus:

m∠1 = 48° + 27°

m∠1 = 75°

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The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Step-by-step explanation:

5.02 is the answer as five and two hundredths

Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.

how many were there? well, really there were "x", which oddly enough is the 100%, we also know that 40% of "x" is 80, so

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 80& 40 \end{array} \implies \cfrac{x}{80}~~=~~\cfrac{100}{40} \\\\\\ \cfrac{ x }{ 80 } ~~=~~ \cfrac{ 5 }{ 2 }\implies 2x=400\implies x=\cfrac{400}{2}\implies x=200\)

(a) The conditional PMF P X∣B (x) of X given the event B={X<4} can be calculated using the formula

P(X=x|B) = P(X=x and B)/P(B).

Since the event B={X<4} includes the events X=1, X=2, and X=3, we can calculate P(B) as the sum of the probabilities of these events:

P(B) = P(X=1) + P(X=2) + P(X=3) = (1/4) + (3/4)(1/4) + (3/4)^2(1/4) = 13/16.

Therefore, the conditional PMF P X∣B (x) is given by:

P(X=1|B) = P(X=1 and B)/P(B) = (1/4)/(13/16) = 4/13
P(X=2|B) = P(X=2 and B)/P(B) = (3/4)(1/4)/(13/16) = 3/13
P(X=3|B) = P(X=3 and B)/P(B) = (3/4)^2(1/4)/(13/16) = 6/13

(b) The probability that your favourite character is eliminated in one of the first two episodes given the spoiler is P(X=1|B) + P(X=2|B) = 4/13 + 3/13 = 7/13.

(c) The expected value of X conditioned on the event B can be calculated using the formula E[X|B] = sum(x*P(X=x|B)) for all x in the support of X. Therefore, E[X|B] = 1*(4/13) + 2*(3/13) + 3*(6/13) = 20/13.

(d) The conditional PMF P X∣C (x) of X given the event C={X>2} can be calculated using the formula P(X=x|C) = P(X=x and C)/P(C). Since the event C={X>2} includes the events X=3, X=4, ..., we can calculate P(C) as the sum of the probabilities of these events: P(C) = P(X=3) + P(X=4) + ... = (3/4)^2(1/4) + (3/4)^3(1/4) + ... = (3/4)^2/(1-(3/4)) = 12/16. Therefore, the conditional PMF P X∣C (x) is given by:

P(X=3|C) = P(X=3 and C)/P(C) = (3/4)^2(1/4)/(12/16) = 1/3
P(X=4|C) = P(X=4 and C)/P(C) = (3/4)^3(1/4)/(12/16) = 1/4
...

(e) The conditional PMF P Y∣C (y) of Y given the event C={X>2} can be obtained by shifting the conditional PMF P X∣C (x) of X given the event C={X>2} by 2 units to the left. Therefore, P Y∣C (y) = P X∣C (y+2) for all y in support of Y. This conditional PMF belongs to the family of geometric random variables with parameter 1/4.

(f) The conditional mean E[X|C] can be calculated using the formula E[X|C] = sum(x*P(X=x|C)) for all x in the support of X. Since the conditional PMF P X∣C (x) is a geometric distribution with parameter 1/4 shifted by 2 units to the right, we can use the formula E[X|C] = 2 + 1/(1/4) = 6.

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Answer:

im not sour if this is what you want but i got 1.3 repeating

Step-by-step explanation:

u simplify in ur head

Answer:

b = 310

Step-by-step explanation:

192 + 118 = b

b = 310

The probability distribution of the number of customers that enter the store on a given day is described as follows:

Poisson with a mean of 70 customers.

In a Poisson distribution, the mass function probability that X represents the number of successes of a random variable is given by the equation presented as follows:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

A combination of Poisson variables is a Poisson variable, hence the daily distribution is a Poisson variable with mean given by the sum of these following observations:

Hence the mean is of:

8 + 16 + 18 + 28 = 70 customers.

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We got sales revenue= $31500, cost of goods sold =$8300 and gross profit =$23200

The income that someone earn from his product and services before the deduction of any charges or expenses.

All direct and indirect cost needed to make a product such as raw materials, transportation cost and labor cost is called cost of goods sold.

The profit earns by a business organization after deducting all the costs associated with manufacturing and selling products.

we calculated gross profit by using the formula, Gross profit= sales revenue- cost of goods sold.

We calculate cost of goods sold by using the formula

beginning inventory + purchases during the period - ending inventory

= 550×24+950×28-900×35

costs of goods sold =$8300

given, number of units sold = 900

average sales price per unit= $35

Now sales revenue= 900 × $35

                                =$31500

Now gross profit= $31500-$8300

                                 $23200

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