F-Tests Past results indicate that the time for a CSM student to finish a departmental exam in Statistics is a normal random variable with a standard deviation of 5 minutes. Test the hypothesis that o=5 against the alternative that a<5 if a random sample of 20 students have a standard deviation s =4.35 . Use a 0.05 level of significance.

The value of the function (g o f) (x) = 12x + 49.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

Given that the value of f(x) = x + 4 and g(x) = 12x + 1.

The value of (g o f)(x) is:

g(x) = 12x + 1

Substitute the value of f(x) in x for the function of g(x):

(g o f) (x) = 12(x + 4) + 1

(g o f) (x) = 12x + 48 +1

(g o f) (x) = 12x + 49

Hence, the value of the function (g o f) (x) = 12x + 49.

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The value of the function (gof) (x) would be 12x + 49.

The set of all x such that x is in the domain of g and g(x)) is in the domain of f is the domain of f composed with g, as you should be aware of. A composite function's domain is the set of inputs x in the domain of g for which g(x) is in the domain of the function.

A composite function is also known as f of g of x. It is formally represented as f(g(x)) or (f g)(x), which indicates that x = g(x) should be substituted in f. (x). It can alternatively be written as "f circle g of x." It is a process that merges two functions into one new function.

Let the given value be f(x) = x + 4 and g(x) = 12x + 1.

The value of (g o f)(x) is:

Substitute the value of f(x) in x for the function of g(x):

(g o f) (x) = 12(x + 4) + 1

simplifying the above equation, we get

(g o f) (x) = 12x + 48 +1

(g o f) (x) = 12x + 49

Therefore, the value of the function (gof) (x) be 12x + 49.

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Answer:

self realization, confidence

Step-by-step explanation:

also these concepts are used in real life jobs but most people think otherwise because you dont use them in a grocery store... yeah people think that, but also its so these concepts that were figured out thousands of years ago dont fade away with the newer generations

To solve the differential equation 2yy' + 1 = y^2x, we can use separation of variables.

First, we can rearrange the equation to get:

2yy' = y^2x - 1

Next, we can divide both sides by y^2x - 1 to get:

(2y)/(y^2x - 1) dy/dx = 1

We can now integrate both sides with respect to x and y, respectively:

∫(2y)/(y^2x - 1) dy = ∫1 dx

For the left-hand side, we can use substitution by letting u = y^2x - 1, which means du/dy = 2yx.

Substituting this into the integral gives:

(1/2)∫du/u = (1/2)ln|y^2x - 1| + C1

For the right-hand side, we can integrate with respect to x:

∫1 dx = x + C2

Combining the two integrals gives:

(1/2)ln|y^2x - 1| + C1 = x + C2

We can simplify this to:

ln|y^2x - 1| = 2x + C

where C = 2C2 - C1.

Finally, we can exponentiate both sides to get rid of the natural logarithm:

|y^2x - 1| = e^(2x+C)

Since the absolute value of y^2x - 1 can be either positive or negative, we need to consider both cases:

y^2x - 1 = e^(2x+C) or y^2x - 1 = -e^(2x+C)

Solving for y in each case gives:

y = ±sqrt((e^(2x+C) + 1)/x)

Therefore, the general solution to the differential equation 2yy' + 1 = y^2x is:

y = ±sqrt((e^(2x+C) + 1)/x)

where C is a constant of integration.
Hello! To solve the given differential equation 2yy' = y^2x, you can follow these steps:

1. Divide both sides by y^2 to isolate y':

  y' = (x/2) * (1/y)

2. Now, we have a separable equation, so we can separate the variables by multiplying both sides by y:

  y dy = (x/2) dx

3. Integrate both sides with respect to their respective variables:

  ∫y dy = ∫(x/2) dx

  (1/2)y^2 = (1/4)x^2 + C₁

4. To solve for y, multiply both sides by 2:

  y^2 = (1/2)x^2 + 2C₁

5. Take the square root of both sides:

  y = ±√[(1/2)x^2 + 2C₁]

This is the general solution of the given differential equation, where C₁ is an arbitrary constant.

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Answer:

C (-3,2)

Step-by-step explanation:

Well point Q on the parabola is located on point (1,2),

The corresponding point means the point located all the way to the left of Q which is (-3,2).

Thus,

the point that is corresponding to point Q is C. (-3,2).

Hope this helps :)

Answer:

x= 8

Step-by-step explanation:

Half of a circle or a straight line is equal an angle of 180 degrees. Therefore, both the measurements of angles RPS and QPR are equal to 180 degrees.

3x + 12 + 7x + 88 = 180

Add like terms

10x + 100 = 180

-100. -100

10x = 80

/10. /10

x = 8

Answer:

25

Step-by-step explanation:

25 is the answer because the sum of angles add up to 90

There are a total of 7 ways to seat eight people around a table if Alice and Bob won't sit next to each other. This is because the seating arrangement must be a permutation of the seven people not including Alice and Bob.

We can calculate this by taking the factorial of the number of people not including Alice and Bob, which is seven. Since a factorial is the product of an integer and all the integers below it, we can calculate the factorial of seven by multiplying all the integers from one to seven.

This gives us 7=5040, which is the total number of ways to seat eight people around a table if Alice and Bob won't sit next to each other.

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Answer: I am terrible at these kinds of "sit-uating" problems (haha). My idea is that the three people can be situated in (3−1)!

ways and that the rest can be situated in (5−1)!

ways. Then, the ordering of the five people depends on the partitions of 5 into 3 groups:

Step-by-step explanation:

Answer: 85 degrees

Step-by-step explanation: 20x+5+24x-1=180

                                                         44x+4=180

                                                           -4         -4

                                                              44x=176

               division property of equality  x=4

20(4)+5=

80+5=  85 degrees

Answer:

x + y ≥ 6 (Melissa exercises for at least 6 hours per week)

x ≤ 11 (Melissa spends at most 11 hours doing cardiovascular work)

y ≤ 4 (Melissa spends at most 4 hours on weight training)

To graph this region, you can plot the constraints on the x-y coordinate plane and shade the area that satisfies all of them.

The first constraint x+y>=6 can be represented by the line y = -x +6

The second constraint x<=11 can be represented by the line y = 11

The third constraint y<=4 can be represented by the line y = 4

The shaded area will be the region that is above and to the right of the line y = -x + 6, below the line y = 11 and below the line y = 4.

Kind of hard to shade a graph without having it in front of me. Hope this helps!

Answer:

livirav737 has provided the correct answer first.

I am merely providing the graph

Step-by-step explanation:

Plotted using online graphing tool Geogebra

The heavily shaded region with ABCD as its corners represents the region corresponding to all 5 inequalities

Note
Though not explicitly stated

You must also have the two additional constraints

x ≥ 0, y ≥ 0

These are called non-negativity constraints to ensure that x and y are not negative. The number of hours exercised on each platform cannot be less than 0

In this particular case, these are not necessary but standard practice is to include them whenever you have a system of inequalities with non-negative variables

Answer:

14.49

Step-by-step explanation:

Answer

$7.82

Step-by-step explanation:

12 hrs=$93.84

1 hr= 93.84/12

1 hr=$7.82

The integral of (3x^4 + x - 2 + √x^3) * x is (x^6/2) + (x^3/3) - x^2 + 3ln|x| + C, where C represents the constant of integration.

To solve the given integral ∫(3x^4 + x - 2 + √x^3) * x, we can break it down into separate terms and integrate each term individually.

In the first term, 3x^4 * x, we can simplify it by multiplying the exponents: 3x^5. We apply the power rule for integration, which states that the integral of x^n is (x^(n+1))/(n+1). Applying this rule to our first term, we get (3/6)x^6 = x^6/2.

Moving on to the second term, x * x, we simply have x^2. Again, applying the power rule, the integral of x^2 is (x^3)/3.

In the third term, -2 * x, we have a constant multiple of x, which can be integrated as -(2/2)x^2 = -x^2.

Lastly, in the fourth term, √x^3 * x, we can simplify √x^3 as 3/x^2. Therefore, the term becomes (3/x^2) * x = 3/x.

Combining all the integrated terms, the final result of the integral is (x^6/2) + (x^3/3) - x^2 + 3ln|x| + C, where C is the constant of integration.

In summary, the integral of (3x^4 + x - 2 + √x^3) * x is (x^6/2) + (x^3/3) - x^2 + 3ln|x| + C, where C represents the constant of integration.

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It would take Dr. Wong 18 hours to see 72 patients at her current rate.

To find the unit price in dollars per pound, we need to divide the total cost of the package by its weight in pounds.

The cost of a 1.5-lb package of seedless grapes is $3.95.

So, the unit price in dollars per pound can be calculated as follows:

Unit price = Total cost ÷ Weight in pounds

Unit price = $3.95 ÷ 1.5 lb

Unit price = $2.63 per pound (rounded to the nearest cent)

Therefore, the unit price of seedless grapes is $2.63 per pound.

To find how long it would take Dr. Wong to see 72 patients, we can use proportions.

If Dr. Wong can see 12 patients in 3 hours, then she can see 1 patient in 3/12 hours or 0.25 hours (15 minutes).

So, to see 72 patients, she would need:

Time = Number of patients × Time per patient

Time = 72 × 0.25 hours

Time = 18 hours

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Step-by-step explanation:

i believe the awnser is 5 holp this helps

Answer: -30

Let's call the original number "x". Then, we can write the equation as follows:

-3/10 x + 1 = 10

To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:

-3/10 x = 9

x = (9 * 10)/(-3)

x = -30

So, the original number is -30.

The linear function which represents the line is y = - 3x + 14.

What is Point slope form?

Point slope form is used to represent a straight line using its slope and a point on the line. It means that the equation of a line whose slope is 'm' and which passes through a point (x1, y1) is found using the point-slope form.

Main body:

y - y1 = m (x - x1)

where, (x, y) is a random point on the line and m is the slope of the line.

The given point-slope equation is

y + 1 = - 3 (x - 5)

By further calculation

y + 1 = -3x + 15

y = -3x + 15 - 1

y = -3x + 14

Therefore, the linear function which represents the line is y = - 3x + 14.

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Deangelo's pace for the last 1.5 hrs of his half-marathon practise was p = 7 miles/hr.

By using the basic principles of speed and distance, we answer this question. Let's evaluate this question step-by-step.

After Deangelo starts the practice half-marathon, he jogs for half an hour at a pace of 5.5 miles per hour.

His speed  = 5.5 miles/hr

Time = 1/2 hr

From the Speed formula:

Speed = distance/time

Distance = Speed * Time

              = 5.5 * (1/2)

              = 5.5/2

              = 2.75 miles.

Since he completes his track, we can assume he traveled the rest of the distance in the last 1.5 hrs.

Distance Left = 13.25 - 2.75

                      = 10.5 miles.

Time Taken = 1.5 hrs.

His pace = 'p' miles/hr

Again applying the same formula,

p = 10.5/1.5

p = 7 miles/hr

Thus, we can complete the given statement as follows.

p = 7  = Deangelo's rate for the last 1.5 hrs of his run, in miles per hour.

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Answer:

its 24 you welcome

Step-by-step explanation:

Answer:

24!!!

Step-by-step explanation:

PLS GIVE BRAINLYIST

Answer:

Length of rectangle parking lot = 94 m

Width of rectangle pool = 85 m

Step-by-step explanation:

Given:

Perimeter of rectangle = 300 m

Width of rectangle parking lot = 56 m

Find:

Length of rectangle parking lot

Area of rectangle pool = 8,245 m²

Length of rectangle pool = 97 m

Find:

Width of rectangle pool.

Computation:

1. Perimeter of rectangle = 2[l+b]

2[56 + l] = 300

56 + l = 150

Length of rectangle parking lot = 94 m

2. Area of rectangle = L x B

97 x Width of rectangle pool = 8,245

Width of rectangle pool = 85 m

Answer:

The length of the rectangle parking lot is 94 meters.

Rectangle pool width = 85 m

Step-by-step explanation:

i hope it helpss

The shortest length of fence is thus equal to P1 = x + 1,300,000/x.

Let the width of the rectangular field be "x" feet and the length be "y" feet, then the area of the field, A = x y square feet. The area of the field is given as 1,300,000 square feet, so we can write; x  y = 1,300,000 Therefore, y = 1,300,000/x feet. Now, if we divide the rectangular field into two halves parallel to one side, we can write the new dimensions of each half as follows: Half 1: Length = x, Width = y/2 = 1,300,000/2x = 650,000/x Half 2: Length = x, Width = y/2 = 1,300,000/2x = 650,000/x

The total length of fence needed to enclose the rectangular field is given by; P = 2x + 2y = 2x + 2(1,300,000/x)P = 2x + 2(1,300,000/x)The total length of fence needed to divide the rectangular field into two halves is given by;P1 = x + 2(650,000/x)P1 = x + 1,300,000/x Thus, the shortest length of fence that the rancher can use is the length of the fence needed to divide the field into two halves. Therefore;P1 = x + 1,300,000/x.

The shortest length of fence is thus equal to P1 = x + 1,300,000/x.

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Answer:

The distance is 7.81 when rounded to the nearest hundredth

Answer:

109.090909%

Step-by-step explanation:

Answer:

9.09091%

Step-by-step explanation:

From 11 friends to 12 friends find the percent

from 11 friends to 12 friends. The number of friends is increased by 1.

To get the percentage of increase:

(12 - 11) / 11 = 1 / 11 = * 100% =

The increase of 1 friend is equivalent to 9.09091% increase

11 is the basis. It is the 100%

 1 is the increase. It is the 9.09091%

12 is the total number of friends.

The Dollar Price of the bond $4813.26

The bond's present value (PV) represents the estimated future cash payments that will result from the bond. The value is equal to the sum of the discounted present values of the interest payments and the redemption value (RV).

Bond value equals PV of interest plus PV of RV

The Local School District's bond amount can be calculated as follows:

PV of interest payments

Semi annual interest payment:

= 2.9% × 5000× 1/2= 72.5

Semi-annual yield = 2.7/2 = 1.65%

Total period to maturity = (2 × 16) = 32 periods

PV of interest payment:

=72.5× (1- (1+0.016)^(-32)/0.016)

= 1804.66

PV of Redemption Value

= 5000× (1.016)^(-32)

= 3008.6

Price of bond

=1804.66 + 3008.6

=$4813.26

Therefore, The dollar Price of the bond is $4813.26

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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Answer:

Height above ground =  2 m  

Water level = - 15 m

Difference = 2 - (-15)  = 17 m

Hence minimum length of the rope is 17 m

Step-by-step explanation:

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The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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Answer: 13/25

Step-by-step explanation: it is equal to 52% which is greater than 50%

50% is greater than 13/25. To compare these two values, you can convert both of them to a common denominator, such as 50%. 50% is equal to 1/2, so 13/25 is equal to 52/50, which is less than 1/2 or 50%. Alternatively, you can also express both fractions as decimals and compare the two values that way. 50% is equal to 0.5, and 13/25 is equal to 0.52, so 50% is still greater than 13/25.

To eliminate the roots in 1.1 and 1.2, we can use trigonometric substitution. In 1.1, we can substitute x = 4 sin(theta) to eliminate the root of 4. In 1.2, we can substitute z = 7 sin(theta) to eliminate the root of 7.

1.1. V64+2 + 1 We can substitute x = 4 sin(theta) to eliminate the root of 4. This gives us:

V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3 1.2. V4z2 – 49

We can substitute z = 7 sin(theta) to eliminate the root of 7. This gives us:

V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta) (2 – 1) = 7 sin(theta)

Here is a more detailed explanation of the substitution:

In 1.1, we know that the root of 4 is 2. We can substitute x = 4 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 2.

When we substitute x = 4 sin(theta), the expression becomes V64+2 + 1 = V(16 sin^2(theta) + 2 + 1) = V16 sin^2(theta) + V3 = 4 sin(theta) V3

In 1.2, we know that the root of 7 is 7/4. We can substitute z = 7 sin(theta) to eliminate this root. This is because sin(theta) can take on any value between -1 and 1, including 7/4.

When we substitute z = 7 sin(theta), the expression becomes: V4z2 – 49 = V4(7 sin^2(theta)) – 49 = V28 sin^2(theta) – 49 = 7 sin(theta) V4 – 7 = 7 sin(theta)

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