As part of an exercise regimen, the probability of a person running outside is 0.45, the probability of a person joining a gym is 0.40, and the probability of a person both running outside and joining a gym is 0.25. what is the probability that a person either runs or joins a gym?

After 4 hours of discharging, the volume left in the tank would be 500 liters. The correct option is C.

Initially, the tank has a water capacity of 1500 liters.

After three hours of discharging, half of the water is discharged, which means 1500/2 = 750 liters have been removed from the tank.

To find the volume left after 4 hours of discharging, we need to subtract the additional amount discharged in the fourth hour.

Since the discharge rate remains the same, we can calculate the amount discharged in one hour as 750/3 = 250 liters.

Therefore, in the fourth hour, 250 liters would be discharged. Subtracting this from the remaining water after three hours (750 liters), we get 750 - 250 = 500 liters.

Therefore, the correct answer is c. 500 liters.

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Answer:

a) Given two perpendicular sides of a square (as given in the diagram), we can construct two more perpendicular lines that are parallel to the initial two (since we are given their slopes). The intersection of these two lines is the unknown point.

b) From points A and C we can construct lines perpendicular from the lines coming out of point B. The intersections of these lines will be our unknown point.

Step-by-step explanation:

So, the account is at 0 initially; after the 1st payment made to the statement, the only balance it'd have, is the first payment amount, so namely, what's the monthly amortized cost.

Ex.: the picture

So let's do the same!

pymt: 120,000 [0.049/12/1 - (1 + 0.049/12) -12 x 20]

Hope this helped!

Part A: The value of the printer after 9 years is $2060.

The printer depreciates at 8% of its original cost per year. After 9 years, the value of the printer is calculated as:

$7000 x (1-0.08)^9 = $2060.

Part B:The volume of loam required is 5400 cubic feet

The plot is 1080 feet by 20 feet and needs to be filled to a depth of 3 inches with loam. First, we need to convert the depth to feet by dividing by 12: 3/12 = 0.25 feet. The volume of loam required is then calculated as:

(1080 x 20 x 0.25) = 5400 cubic feet.

To convert to cubic yards, we divide by 27: 5400/27 = 200 cubic yards.

Part C: We need to hire 6 more women.

The team currently has 1/4 women and 3/4 men, so the number of women in the team is 16 x 1/4 = 4. To obtain a team with 40% women, we need to have a total team size of:

4 / 0.4 = 10 women.

So, we need to hire 10 - 4 = 6 more women.

Part D: The carpet would cost $576.

To account for waste, the company needs to order 4% more material than needed, which means they need to order:

68.5 x 1.04 = 71.24 square feet of carpet.

Since fractional parts cannot be ordered, they need to order 72 square feet of carpet. The cost of the carpet at $8.00 per square foot is:

72 x $8.00 = $576.

Thus, the carpet would cost $576.

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The percentage of the observations in a distribution that are greater than the first quartile is 75%

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

Observations = Greater than first quartile

By definition

first quartile = 25%

So, we have

Observations = 1 - 25%

Evaluate

Observations = 75%

Hence, the percentage is 75%

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The value c guaranteed by the Intermediate Value Theorem over the interval [0, 2], where f(0) = 2, and f(2) = 10 is c = 1.5, f(1.5) = 5

The inequalities, 0 < 1.5 < 2, f(0) < f(1.5) < f2), verifies the Intermediate Value Theorem.

The Intermediate value theorem states that a value p that is between the f(a) and f(b), such that f(a) < p < f(b) or f(a) > p > f(b), then a number, c, exists between a and b such that f(c) = p

The derivative of the function f(x), f'(x) = 4·x² - 4·x + 2

The interval over which the Intermediate Value Theorem is to be verified = [0, 2]

The value of the function at the boundaries of the domain [0, 2], are;

f'(0) = 4 × 0² - 4 × 0 + 2 = 2

f'(2) = 4 × 2² - 4 × 2 + 2 = 10

Therefore, the value, f(c) = 5, indicates that we get;

f'(0) < f(c) < f'(2), and 0 < c < 2

We get; 4·x² - 4·x + 2 = 5

4·x² - 4·x + 2 - 5 = 0

4·x² - 4·x - 3 = 0

Completing the square

4·x² - 4·x = 3

x² - x = 3/4

x² - x + (-1/2)² = 3/4 + (-1/2)²

(x - 1/2)² = 3/4 + (-1/2)² = 1

x - 1/2 = ± √1 = ±1

x = 1 + (1/2) = 1.5, and x = -1 + 1/2 = -1/2

A value of x that satisfies the equation, f'(x) = 4·x² - 4·x + 2, is x = 1.5

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Answer:

82/43 = 1 and 39/43

Step-by-step explanation:

When dividing 82 by 43 , the operation follows;

82/43 = 1 and 39/43

This means the quotient is 1 and reminder is 39

However;

82/43 = 1.907 ------nearest whole number is 2.

so the quotient can be approximated to the nearest whole number as 2.

The equation y = x² + 2 is a non linear equation.

Since,

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Here, We have;

The equation is,

y = x² + 2

Since, The degree of x is 2.

Hence, It is a quadratic equation.

Thus, The equation y = x² + 2 is a non linear equation

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Answer:

No Sanya is not correct because the point (1,34) actually means that for 1 pie, it needs 34 cups of sugar.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area = 72 m^2

L = 12m

Formula

w = Area / L

Perimeter = 2L + 2W

Solution

72m^2 = 12 W      Divide both sides by 12

72/12 = 12W / 12

W = 6 m

Perimeter = 2L + 2W

Perimeter = 2*12 + 2*6

Perimeter = 24 + 12

Perimeter = 36 m

The probability of getting the first two questions correct by randomly guessing is option D: 0.0625.

Since each question has four choices and you are randomly guessing, the probability of guessing the correct answer for each question is 1 out of 4, or 1/4 = 0.25.

To find the probability of getting both questions correct, we multiply the probabilities of each event since they are independent. So, the probability of getting the first question correct is 0.25, and the probability of getting the second question correct is also 0.25.

To find the probability of both events occurring, we multiply the individual probabilities:

P(both questions correct) = P(first question correct) * P(second question correct) = 0.25 * 0.25 = 0.0625.

Therefore, the probability of getting the first two questions correct by randomly guessing is 0.0625, which corresponds to option D.

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The lengths of LV and OE are 15cm, and the lengths of LD and EV are 3√7 cm and 9/√7 cm, respectively.

Since LOVE is a kite, LV and OE are perpendicular bisectors of each other. Let the length of LD be x, and the length of EV be y. Then, we can use the Pythagorean theorem and the fact that the diagonals bisect each other to set up two equations:

x² + (LV/2)² = DV²/4

y² + (OE/2)² = LE²/4

Simplifying each equation and substituting the given values, we get:

x² + (LV/2)² = 81/4

y² + (OE/2)² = 225/4

We also know that the diagonals bisect each other, so we can set up another equation:

LV/2 + OE/2 = LO = VE

Substituting the given value for LE, we get:

LV/2 + OE/2 = 15

Solving this equation for one of the variables, we get:

LV = 30 - OE

Substituting this expression into the first equation above, we get:

x² + ((30 - OE)/2)² = 81/4

Simplifying and rearranging, we get:

OE² - 60OE + 675 = 0

Using the quadratic formula, we get:

OE = (60 ± √(3600 - 2700)) / 2

OE = 15 or 45

If OE = 15, then LV = 30 - 15 = 15, and we can solve for x and y:

x² + 7.5² = 81/4

y² + 7.5² = 225/4

Solving these equations, we get:

x = 3√7

y = 9/√7

If OE = 45, then LV = 30 - 45 = -15, which is impossible for a length. Therefore, the solution is:

LV = OE = 15

x = 3√7

y = 9/√7

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Complete question:

LOVE is a kite. LV and OE are diagonals. The segments DV = 9cm and LE = 15cm are given. Find the lengths of the other segments of the diagonals, DV, OE, and LV.

in a class of 12 boys and 9 girls, the teacher selects three students at random to write problems on the board then the probability that all the students selected are boys is 0.165

given that a class consists of 12 boys and 9 girls. The teacher picks three students to present their work to the rest of the class  and says that the three students are being selected at random

Here selecting any 3 students from the group of total 21 students is combination because order does not matter.

Total no of ways of selecting any 3 from total 21 = 21C3 = 1330

No of ways of selecting only 3 boys = No of ways of selecting random 3 boys from total 12 boys

= 12C3 =220

the probability be that all three students

selected are boys=220/1330 = 0.165

Hence , the probability that all the students selected are boys is 0.165

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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To find all relative  extrema of the function f(x) = cos(x) - 8x on the interval [0, 4], we'll use the second derivative test where applicable.

Step 1: Find the first derivative of the function.
f'(x) = -sin(x) - 8

Step 2: Set the first derivative equal to zero to find critical points.
0 = -sin(x) - 8

Step 3: Solve for x.
sin(x) = -8 (Since the range of sin(x) is [-1,1], there are no solutions for this equation on the interval [0, 4].)

Step 4: Check endpoints of the interval.
f(0) = cos(0) - 8(0) = 1
f(4) = cos(4) - 8(4) ≈ -31.653

Step 5: Find the second derivative.
f''(x) = -cos(x)

Step 6: Apply the second derivative test.
Since there are no critical points, we don't need to use the second derivative test.

Conclusion: There are no relative extrema within the interval [0, 4] for the function f(x) = cos(x) - 8x. The extrema on the interval are the endpoints, with a maximum value of 1 at x = 0 and a minimum value of approximately -31.653 at x = 4.

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A relative maximum at x ≈ 2.301, a global minimum at x = 4, and no relative minimum.

To find all relative extrema of the function f(x) = cos(x) - 8x in the interval [0, 4], we will use the first and second derivative tests. Here's a step-by-step explanation:

1. Find the first derivative of the function:

f'(x) = -sin(x) - 8.

2. Find the critical points by setting f'(x) equal to 0:

-sin(x) - 8 = 0.

3. Solve for x to find the critical points within the interval [0, 4]. The equation is difficult to solve algebraically, so we can use a numerical method or graphing calculator to approximate the solution. We find one critical point x ≈ 2.301.

4. Find the second derivative of the function:

f''(x) = -cos(x).

5. Evaluate the second derivative at the critical point

x ≈ 2.301: f''(2.301) ≈ -cos(2.301) ≈ -0.74.

6. Since f''(2.301) < 0, the second derivative test tells us that there is a relative maximum at the critical point x ≈ 2.301.

7. Check the endpoints of the interval [0, 4].

For x = 0, f(0) = cos(0) - 8(0) = 1.

For x = 4, f(4) = cos(4) - 8(4) ≈ -31.653.

The relative extrema of the function f(x) = cos(x) - 8x in the interval [0, 4] are as follows:

a relative maximum at x ≈ 2.301,

a global minimum at x = 4,

and no relative minimum.

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The average velocity of the object after during the first three seconds is: 48m/s

The time at which the instantaneous velocity equals the average velocity within the first three seconds is 1.5 seconds.

Instantaneous velocity  is the speed of an object at a particular point in time.

Average velocity is the velocity of an object after covering a certain distance for a period of time

Analysis:

Given

initial height = 600 feet

Height with respect to time = f(t) = -16\(t^{2}\) + 600

a) Height at t = 0 = 600 feet

    Height at t = 3 seconds = f(3) = -16\((3)^{2}\) + 600 = 456 feet

Distance travelled  = 600 - 456 = 144 feet

Average velocity = distance travelled/time taken  = 144/3 = 48 feet/seconds

b) instantaneous velocity at time t = \(\frac{df(t)}{dt}\) = \(\frac{d(-16t^{2} + 600) }{dt}\) = -32t

  when instantaneous velocity equal average velocity

     -32t = -48

      t = 1.5 seconds

In conclusion, the Average velocity after 3 seconds is 48 feet per seconds and the time taken for the average velocity to equal the instantaneous velocity is 1.5 seconds.

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Answer:

$135

Step-by-step explanation:

Answer:

  6π cm

Step-by-step explanation:

For a circle, the perimeter is equal to the circumference. The formula for the circumference of a circle is ...

  C = 2πr

where r is the radius of the circle.

__

Substituting the given value of radius into the formula gives ...

  C = 2π(3 cm)

  C = 6π cm

The perimeter of the circle is 6π cm.

These relative frequencies demonstrate the relationship between high blood pressure and exercise habits in the population under study. The data suggests that a higher proportion of individuals with high blood pressure engage in regular exercise compared to those without high blood pressure.

Based on the information given, the study could provide the following relative frequency table:

Exercise ≥ 90 mins/week  86%  32%

Exercise < 90 mins/week  14%   68%

The table shows the relative frequencies of exercise habits among the population based on whether they have high blood pressure or not.

The study reveals that 72% of the population has high blood pressure, so the remaining 28% does not have high blood pressure. Out of the group without high blood pressure, 32% exercise for at least 90 minutes per week, while the remaining 68% exercise less than 90 minutes per week.

Among those with high blood pressure, 86% exercise for at least 90 minutes per week, while 14% exercise less than 90 minutes per week.

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The estimate for the number of cars that are red will be 9450000.

From the information, when Ben sat outside his school in Cambridge and made a note of the colour of the first 100 cars that passed, he found out that 27 of them were red.

Based on the above, the ratio of red cars to total cars is 27:100.

Therefore, if thee are 35 million cars, the red cars will be:

= Ratio of red cars × Total cars

= 27/100 × 3500000

= 9450000

The number of red cards is 9450000.

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The area of the semicircle is, 6.28 unit².

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

BC is the diameter of the semicircle.

And, The area of rectangle ABCD is 20 and the length of line AB is 5.

Now, We have;

The area of rectangle ABCD is 20 and the length of line AB is 5.

Let the width of rectangle = x

So, We can formulate;

⇒ 20 = x × 5

⇒ x = 4

Here, the width of rectangle is the diameter of the semicircle.

So, The radius of semicircle = 4 / 2

                                            = 2 units

We know that;

Area of semicircle = π r

Where, 'r' is radius of semicircle.

Hence, We get;

⇒ Area of semicircle = π r

⇒ Area of semicircle = 3.14 × 2

                                 = 6.28 unit²

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On solving the provided question we can say that - The Range of the given function, f(x) = sin(x) , Range = \(-1 < y < 1\)

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the variable and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The Range of the given function, f(x) = sin(x)

\(-1 < y < 1\)

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Answer:

14

73%

Step-by-step explanation:

The mean Number of years worked :

. (sum of service years) / employees in the

(8+13+15+3+13+28+4+12+4+26+29+3+10+3+17+13+15+15+23+13+12+1+14+14+17+16+7+27+18+24) /

(417 / 30)

= 13.9 years

= 14 years

The percentage of employees who have worked for atleast 10 years :

Number of employees with service years ≥ 10 years = 22 employees

Total number of employees

Percentage (%) = (22 / 30= * 100% = 0.7333 * 100% = 73.33% = 73%

The Probability of P(F/E) is 0.5  .

Baye's Theorem helps in finding the conditional probability probability of an event A given that event B has already occurred.

For Example : The probability of event A given that event B has already occurred is denoted by P(A/B) and is calculated by

\(P(A/B)=\frac{P(A.and.B) }{P(B)}\)

It is given in the question that

P(E and F)=0.1      and  

P(E)=0.2

Using Baye's Theorem ,we get

\(P(F/E)=\frac{P(F .and .E)}{P(E)}\)

Substituting the values ,we get

\(P(F/E)=\frac{0.1}{0.2}\\ \\ =\frac{1}{2} \\ \\ =0.5\)

Therefore , the probability of P(F/E) is 0.5  .

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Answer:

So Monica is 9 years old.

To find Amita's age, we substitute x into the expression for Amita's age:

Amita's age = 9 + 3 = 12

Therefore, Amita is 12 years old.

Answer:

Short leg = 10.4

Hypotenuse = 20.8

Step-by-step explanation:

For a 30-60-90 right triangle, rhw ahorter  leg will be opposite the 30° angle.

If we let this shorter leg be x, the longer leg will be √3  · x

The hypotenuse will be 2x

We are given longer leg = √3  · x = 18

x = 18/√3 = 10.39230...
= 10.4 rounded to the nearest tenth

Given x = 10.4, the hypotenuse = 2x = 2 x 10.4 = 20.8

Answer: Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Step-by-step explanation:

Given that;

U = 75

X = 78

standard deviation α = 10

sample size n = 20

population is normally distributed

PROBLEM is to test

H₀ : U = 75

H₁ : U ≠ 75

TEST STATISTIC

since we know the standard deviation

Z =  (X - U) / ( α /√n)

Z = ( 78 - 75 ) / ( 10 / √20)

Z = 1.3416 ≈ 1.342

Now suppose we need to test at ∝ = 0.05 level of significance,

Then Rejection region for the two tailed test is Zc = 1.96

∴ Reject H₀ if Z > Zc

and we know that Z is less than Zc ∴ 1.342 < 1.96

Therefore, Null hypothesis is not Rejected.

There is no sufficient evidence to claim that students turning in their test first score is significantly different from the mean.

Testing the hypothesis, it is found that since the p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

At the null hypothesis, we test if the mean is of 75, that is:

\(H_0: \mu = 75\)

At the alternative hypothesis, we test if the mean is different of 75, that is:

\(H_1: \mu \neq 75\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which:

For this problem, we have that:

\(X = 78, \mu = 75, \sigma = 10, n = 20\)

The value of the test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{78 - 75}{\frac{10}{\sqrt{20}}}\)

\(z = 1.34\)

Since this is a two-tailed test, the p-value of the test is P(|z| < 1.34), which is 2 multiplied by the p-value of z = -1.34.

Looking at the z-table, z = -1.34 has a p-value of 0.0901.

2(0.0901) = 0.1802

The p-value of the test is 0.1802 > 0.05, which means that the average test score earned by the first 20 students to turn in their tests was not significantly different from the overall mean.

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The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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