If I have a mean of 40 and a standard deviation of 35, would the normal distribution be an adequate model?

For conducting experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.

As given in the question,

To conduct a experiment based on the effect of net force applied to an object the dependable quantities are as follow:

Force = mass × acceleration

As object remain same ⇒ mass is constant as object remain same.

And there is change in the acceleration.

Acceleration depends change in velocity over total time taken.

Acceleration depends on velocity and time.

Net force also depends on velocity and time.

Two measurements need to know  while conducting trail experiments are velocity and time.

Therefore, to conduct experiment based on effect of a net force , to apply net force on the object two other quantities should be measured in each trial of the experiment is given by velocity and time.

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The number of trucks needed to deliver the rock in one trip will be 6.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

V =  a x b x c

A transport company needs to deliver 500,000 pounds of rocks to a construction site.

The company owns a set of dump trucks- each with a container in the shape of a rectangular prism (figure A).

If each pound of rock has a volume of 0.01 cubic feet.

Then the total volume of rock that the transport company is responsible for.

Volume of rocks = 0.01 x 500,000

Volume of rocks = 5,000 ft³

Then the maximum volume of each dump truck will be

Volume of truck = 12 x 9 x 8

Volume of truck = 864 ft³

Then the number of the trucks are needed to deliver the rock in one trip will be

Number of trucks = 5000 / 864

Number of trucks = 5.787

Number of trucks ≅ 6

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recall that

sin(x) = cos(90-x)

therefore

cos((2/3)x + 20) = cos(90 - [2x - 10])

(2/3)x + 20 = 100 - 2x

2x + (2/3)x = 80

divide through by 2

x + (1/3)x = 40

(4/3)x =40

4x = 40*3

4x = 120

x = 30

since it is a right angled triangle, the angles are 30, 60 and 90

Answer: A=40 B=50

I just took the test

Answer:

135 meters

Step-by-step explanation:

h = 60t - 5t²

t is in seconds and it says to find out the height after 3 seconds

Sub the value '3' into 't'

h = 60(3) - 5(3)²

h = 180 - 5(9)

h = 180 - 45

h = 135 m

The dimensions of the rectangular prisms are:

Prism M: l=4 cm , w=1 cm and h=6 cm

Prism W: l=2 cm , w=2 cm and h=6 cm

Prism Z: l=6 cm , w=1 cm and h=4 cm

Prism J: l=2 cm , w=4 cm and h=3 cm

Prism R: l=2 cm , w=3 cm and h=4 cm

Prism F: l=1 cm , w=8 cm and h=3 cm

Given, a rectangular prism with a volume of 24 cm³

Dimensions of the prism if the volume is 24 cm³.

Prism M:

l=4 cm and w=1 cm

we know that volume = h×l×w

h×4×1=24

4h=24

h=24/4

h=6 cm

Prism W:

l=4 cm and w=2 cm

we know that volume = h×l×w

h×2×2=24

4h=24

h=24/4

h=6 cm

Prism Z:

l=4 cm and w=1 cm

we know that volume = h×l×w

h×6×1=24

6h=24

h=24/6

h=4 cm

Prism J:

l=2 cm and w=4 cm

we know that volume = h×l×w

h×2×4=24

8h=24

h=24/8

h=3 cm

Prism R:

l=2 cm and w=3 cm

we know that volume = h×l×w

h×2×3=24

6h=24

h=24/6

h=4 cm

Prism F:

l=1 cm and w=8 cm

we know that volume = h×l×w

h×1×8=24

8h=24

h=24/8

h=3 cm

hence we get the required dimensions.

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Yes, that is correct. The Gaussian elimination rules are essentially the same as the three basic row operations, which allow you to algebraically manipulate a matrix's rows.

You can interchange two rows, multiply a row by a constant, or add a row to another row. These rules are essential in solving systems of linear equations and finding the reduced row echelon form of a matrix. By applying these rules, you can transform a matrix into an equivalent matrix that is easier to work with and reveals important information about the system of equations or the matrix itself. The Gaussian elimination rules, also known as the three basic row operations, allow you to algebraically manipulate a matrix in order to solve systems of linear equations. These operations include:
1. Interchanging two rows (R2 ↔ R3)
2. Multiplying a row by a nonzero number (R1 → kR1, where k is a constant)
3. Adding a row to another row (R2 → R2 + 3R1)
These rules help simplify the matrix and ultimately obtain the unique solution for the system of equations.

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Answer:

50.27 in

Step-by-step explanation:

Answer: The slope is infinite

Step-by-step explanation:

An infinite slope is simply a vertical line. When you plot it on a line graph, an infinite slope is any line which runs parallel to the y-axis. You can also describe this as any line that doesn't move along the x-axis but stays fixed at one constant x-axis coordinate, making the change along the x-axis.

The minimum number of tons of ore that the mining company must produce to meet the contract is 44 tons.

Explanation:

A mining company owns two mines, each of which produces three grades (high, medium, and low) of ore. The company has a contract to supply a smelting company with at least 12 tons of high-grade ore, at least 8 tons of medium-grade ore, and at least 24 tons of low-grade ore.

What is the minimum number of tons of ore that the mining company must produce to meet the contract?

The mining company needs to produce at least 12 tons of high-grade ore, at least 8 tons of medium-grade ore, and at least 24 tons of low-grade ore. There are three grades of ore in total, and each mine produces three grades of ore. So, to meet the contractual requirements, the mining company will need to produce at least one ton of each grade of ore from each mine.

We know that the mining company has two mines, and both produce three grades of ore (high, medium, and low).

As a result, each mine should produce the following minimum quantities of ore:High-grade: 1 tonMedium-grade: 1 tonLow-grade: 1 tonIn total, each mine will produce three tons of ore (1 + 1 + 1).The mining company owns two mines, as previously mentioned, and each produces three tons of ore. As a result, the total ore generated by both mines will be:High-grade: 12 tons (2 × 6)Medium-grade: 8 tons (2 × 4)Low-grade: 24 tons (2 × 12)

Therefore, the minimum number of tons of ore that the mining company must produce to meet the contract is 44 tons.

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Answer:

75 km

Step-by-step explanation:

Answer: 234 inches

Step-by-step explanation:

The billboard is 6 meters long and we are given the conversion factor for centimeters to inches.

To convert the length to inches therefore, convert the length from meters to centimeters first:

1 meter = 100 cm

6 meters would therefore be:

= 6 * 100

= 600 cm

1 cm = 0.39 inches so 600 cm is:

= 600 * 0.39

= 234 inches

The probability of the sum of the two recorded numbers being less than 4 is $\frac{3}{4}$.

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.
This is because there are three possible scenarios in which the sum of the two numbers can be less than 4:

1) both numbers are 1 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$)

2) one number is 1 and the other is 2 (probability of $\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$).

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The probability of the sum of the two recorded numbers being less than 4 is \(\frac{3}{4}\).

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur. Probability is used in mathematics, statistics, and other sciences to measure the chances of a certain outcome. Probability is also used in gambling and other forms of betting to determine the likelihood of a certain outcome occurring.

This is because there are three possible scenarios in which the sum of the two numbers can be less than 4.

1) both numbers are 1 (probability of \(\frac{1}{4}\) × \(\frac{1}{4} = \frac{1}{16}\))

2) one number is 1 and the other is 2 (probability of \(\frac{1}{4}\) × \(\frac{1}{4} =\) \(\frac{1}{16}\))

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Answer:

P=1538.461

Step-by-step explanation:

do it by the formula of

I=PRT, I=750 R=3.25% T=15

Answer:

x=10

Step-by-step explanation:

since the angles seem similar they're most likely to be the same but since its 3x and you have to find the value of x then we will do 3 x ?=30, which is 10. if you want to check there is one way, since the angle on a straight line is 180 you can do 180 - 30 =150 which will be the unknown value next to the given angle. Since the unknown angle is on the line with the 150 degree angle we can do 180 - 50 to get the unknown angle (3x) which is 30. So in conclusion x will be 10

Answer: x = 10

Step-by-step explanation:

The angles are voa which means vertically opposite angles which means they are conguerent and also equal

ATQ

⇒3x = 30

⇒x = 30/3

⇒x = 10

Therefore x = 10 degrees

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The features of function gif g(x) = f(x + 4) + 8 is vertical asymptote of r = -4.

Since they enable us to convert an exponential equation into a logarithmic equation and vice versa, logarithmic functions are employed to solve equations involving exponents. They are also used in a variety of disciplines, including science, finance, and engineering.

Given equation:

g(x) = f(x + 4) + 8.

f(x) → f(x + 4)

Horizontal translation less 4 unit.

(x, y) → (x - y), y

f(x, y) + 8

Vertical translation up 4 unit.

(x, y) → (x, y + d)

f(x)

Vertical Asymptote x = 0,

f(x + 4) + 8

Vertical Asymptote x+ 4 = 0

x = -4

Therefore, the features of function gif g(x) = f(x + 4) + 8 is vertical asymptote of r = -4.

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True, The range of a linear transformation defined by the matrix transformation t(x) = Ax is equal to the column space of matrix A.


The range of a linear transformation defined by the matrix transformation t(x) = ax is equal to the column space of matrix A (col A).

The range of a linear transformation is the set of all possible output values. In this case, the matrix A represents the transformation, and the column space of matrix A represents the span of the columns of A. The column space of matrix A is the set of all possible linear combinations of the columns of A.

To prove that the range of the linear transformation t(x) = Ax is equal to the column space of matrix A, we can show that every vector in the column space of A can be obtained as an output of the transformation t(x) = Ax. Additionally, we can show that every output of the transformation t(x) = Ax belongs to the column space of A.


Therefore, it is true that the range of a linear transformation defined by the matrix transformation t(x) = Ax is equal to the column space of matrix A.

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Answer:

I think it's alternate interior angle

a. Jump with a bobbing motion: Shortest jump  b. Jump from deep knee flexion: Intermediate jump

c. Jump with fully extended knees: Longest jump ,In the long jump activity, three different jumping techniques were observed:

a) The bobbing motion involved bending and extending the knees and arms during the jump.

b) Starting from deep knee flexion meant initiating the jump from a position with knees bent and no motion prior to the jump.

c) Starting with fully extended knees involved jumping with the knees straight and no motion before the jump. During the performance, the lengths of each jump were measured. Trial results consistently indicated that the jump with the bobbing motion had the shortest length, while the jump starting from deep knee flexion had an intermediate length. The jump with fully extended knees consistently achieved the longest distance.

The observations reveal that starting the jump with fully extended knees and no knee motion results in the longest jump. The bobbing motion with knee and arm movements leads to the shortest jump. Deep knee flexion position falls between the two in terms of jump length.

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Answer:

x = 7, y = 60

Step-by-step explanation:

Given the 2 equations

50x - 2y = 230 → (1)

50x - 3y = 170 → (2)

Subtract (2) from (1) term by term on both sides

y = 60

Substitute y = 60 into either of the 2 equations and evaluate for x

Substituting into (1)

50x - 2(60) = 230

50x - 120 = 230 ( add 120 to both sides )

50x = 350 ( divide both sides by 50 )

x = 7

By using  Fundamental Theorem of Calculus, we find the derivative of the function g(x) = In { sqrt( t + t^3)dt } limit from x to 0 is  ln(sqrt(x + x^3)).  The derivative of the function g(x) = { In (1+t^2) dt} where limit are from x to 1 is  ln(1 + x^2).

The Fundamental Theorem of Calculus, which states that if a function is defined as the definite integral of another function, then its derivative is equal to the integrand evaluated at the upper limit of integration.

So, applying this theorem, we have:

g'(x) = d/dx [∫x_0 ln(sqrt(t + t^3)) dt]

= ln(sqrt(x + x^3)) * d/dx (x) - ln(sqrt(0 + 0^3)) * d/dx (0)

= ln(sqrt(x + x^3))

Therefore, g'(x) = ln(sqrt(x + x^3)).

Using the Fundamental Theorem of Calculus, we have:

g'(x) = d/dx [∫1_x ln(1 + t^2) dt]

= ln(1 + x^2) * d/dx (x) - ln(1 + 1^2) * d/dx (1)

= ln(1 + x^2)

Therefore, g'(x) = ln(1 + x^2).

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____The given question is incomplete, the complete question is given below:

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. 7 g(x) = In { sqrt( t + t^3)dt } limit from x to 0.  8. g(x) = { In (1+t^2) dt} where limit are from x to 1.

Answer:

3 and 8

Step-by-step explanation:

3 and 8 are the only numbers that have a variable, or the letter beside it

The probability of 0.0475 is less than 0.05, so it is unlikely to happen. Hence, it would be unusual if less than 30% of the sampled teenagers owned smartphones.

a) Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45b) Find the probability that less than 45% of sampled teenagers own smartphonesc) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?a)Find the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45We know that the proportion of teenagers aged 12-17 who own smartphones is 0.38. Now, we need to find the probability that the proportion of sampled teenagers who own smartphones is between 0.35 and 0.45.The sample size is 120.Let P be the probability that a teenager has a smartphone. The population mean is P = 0.38, while the standard deviation is σ =√((P (1 - P)) /n).P (0.38) and n (120) are given, so σ is calculated as follows:σ=√((P (1 - P)) /n) =√((0.38 (1 - 0.38)) /120) =√((0.38 × 0.62) /120) =0.048Now, let us define the Z scores for both sides, i.e. for 0.35 and 0.45.z1 = (0.35 - 0.38) /0.048 = -0.625z2 = (0.45 - 0.38) /0.048 = 1.458Hence, P(0.35 < p < 0.45) is equal to P(-0.625 < z < 1.458).The probability can be calculated using standard normal tables, which gives 0.5763. Therefore, the probability that the proportion of the sampled teenagers who own a smartphone is between 0.35 and 0.45 is 0.5763.b) Find the probability that less than 45% of sampled teenagers own smartphonesLet P be the probability that a teenager has a smartphone. The population mean is P = 0.38, while the standard deviation is σ =√((P (1 - P)) /n).P (0.38) and n (120) are given, so σ is calculated as follows:σ=√((P (1 - P)) /n) =√((0.38 (1 - 0.38)) /120) =√((0.38 × 0.62) /120) =0.048Now, let us define the Z score as follows:z = (0.45 - 0.38) /0.048 = 1.458We must find the probability that a randomly selected teenager from the sample has less than 0.45 probability of owning a smartphone. This probability can be calculated using a standard normal table. P(z < 1.458) = 0.9265, thus, the probability that less than 45% of sampled teenagers own smartphones is 0.9265.c) Would it be unusual if less than 30% of the sampled teenagers owned smartphones?For this, we need to find the Z-score of 0.30.z = (0.30 - 0.38) /0.048 = -1.667The probability is obtained using a standard normal table. The probability is 0.0475. The probability of 0.0475 is less than 0.05, so it is unlikely to happen. Hence, it would be unusual if less than 30% of the sampled teenagers owned smartphones.

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Where h is the number of hours Melanie can rent the bike, and the solution is h < 5.5.

Let's first determine the cost of renting a bike for h hours:

Cost = 8h + 6

Since Melanie wants to rent a bike for less than $50, we can set up the following inequality:

8h + 6 < 50

Now we can solve for h:

8h < 44

h < 5.5

Since Melanie cannot rent a bike for a fraction of an hour, the maximum number of hours she can rent the bike is 5 hours.

Therefore, the inequality that will help Melanie find the maximum number of hours she can rent the bike is:

8h + 6 < 50

Where h is the number of hours Melanie can rent the bike, and the solution is h < 5.5.

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Answer:

The identity tan(A+B) is given and so is used again for tan(x+x)/tan(2x)

There are 3 cases to consider when determining horizontal asymptotes:

1) Case 1: if: degree of numerator < degree of denominator. then: horizontal asymptote: y = 0 (x-axis)

2) Case 2: if: degree of numerator = degree of denominator.

3) Case 3: if: degree of numerator > degree of denominator.

Answer:

Identifying and moving the base is the key to changing from logarithmic form into exponential form. Identifying the base of the logarithmic equation and moving the base to the other side of the equal sign is how to change a logarithmic equation into and exponential equation.

Example- log 8 base 2=3

then 2^3=8

The opposite of a logarithmic function is an exponential equation, and vice versa

As a general rule, we have the following equation to convert a log function to an exponential.

\(\log_ba = x \to a = b^x\)

Take for instance, we have the following logarithmic function

\(\log_216 = x\)

The equivalent exponential equation is:

\(16 = 2^x\)

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The values of x and y in the system of equations is given as y = 8x and y = 10x - 4 are 2 and 16

The system of equations is given as

y = 8x

y = 10x - 4

Substitute 8x for y in the second equation i.e. y = 10x - 4

So, we have

8x = 10x - 4

Collect the like terms

8x -10x = -4

Evaluate the like terms

-2x = -4

Divide both sides of the equation by -2

x = 2

Substitute 2 for x in the equation y = 8x

y = 8 * 2

Evaluate the product

y = 16

Hence, the values of x and y in the system of equations is given as y = 8x and y = 10x - 4 are 2 and 16

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The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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