Explain using models why a common denominator is required when adding fractions in 1/3 plus 3/4 but not when multiplying them as 1/3 * 3/4

The probability that the risk event will occur during the fourth month of the project is 0.2.

If a risk has a 20% chance of happening in any given month, then the probability of it not happening in any given month is 1 - 0.2 = 0.8.

Assuming the risk event is independent from month to month, the probability that the risk does not happen in the first three months is:

P(not happening in 1st month) × P(not happening in 2nd month) × P(not happening in 3rd month) = 0.8 × 0.8 × 0.8 = 0.512

The probability that the risk occurs in the fourth month, given that it has not occurred in the first three months, is:

P(happening in 4th month | not happening in 1st, 2nd, and 3rd months) = P(happening in 4th month) = 0.2

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The correct option is: c. treatment

The IV (Independent Variable) in an experiment refers to the variable that is systematically manipulated or varied by the researcher to observe its effect on the dependent variable.

In the given experiment, the IVs are "Gender" and "GSR" (Galvanic Skin Response), indicating that these variables are systematically manipulated or varied to observe their effect on the dependent variable.

Therefore, "Gender" and "GSR" are not dummy, extraneous, or classification variables.

They can be considered as treatment variables as they are manipulated to observe their effect on the dependent variable.

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The sample in this example is a small group of local college students selected for observation.

In this example, the researcher is working with a specific group of interest, which is college students.

She narrows down her focus to local college students and selects a small group to be observed.

The sample in this case would be the small group of local college students chosen for observation.

This sample is a subset of the larger population (all college students) that the researcher is interested in studying to test her hypothesis.

The sample in this example is the small group of local college students who were selected to be observed.

A sample is a subset of the population that is being studied in order to make inferences about the entire population.

In this case, the population of interest is college students, and the researcher is observing a sample of that population. It is important that the sample is representative of the population in order for the findings to be generalizable to the population as a whole.

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The ellipse in a scatterplot becomes thinner, the correlation coefficient (r) between the variables x and y will increase.

The correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables.

It ranges from -1 to 1, where values close to -1 or 1 indicate a strong linear relationship, and values close to 0 indicate a weak or no linear relationship.

When the scatterplot forms an ellipse, it indicates that there is some degree of correlation between the variables x and y.

If the ellipse is elongated, it suggests that the correlation is weak, while if the ellipse is more circular, it suggests that the correlation is stronger.

As the ellipse becomes thinner, it means that the spread of the data along one of the variables is becoming smaller, while the spread along the other variable is remaining the same.

This indicates that there is a stronger linear relationship between the variables, and as a result, the correlation coefficient (r) will increase.

Therefore, we can conclude that as the ellipse becomes thinner, the correlation coefficient (r) between the variables x and y will increase.

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To find the P(Z>0.93) using Appendix C-2, we first need to find the row containing 0.9 in the far left column. Next, we find the column containing 0.03 in the top row. The intersection of the row and column is 1.546. Therefore, the probability of Z being greater than 0.93 is 1 - 0.8289 = 0.1711 (rounded to four decimal places).

The values in Appendix C-2 represent the area to the left of a standard normal distribution. Since the total area under the curve is equal to 1, we can find the area to the right of a certain value by subtracting the area to the left from 1.

In this case, we want to find the area to the right of 0.93, which is equivalent to finding the area to the left of -0.93 (since the standard normal distribution is symmetric). By finding the corresponding value in Appendix C-2 and subtracting from 1, we get the probability of Z being greater than 0.93.

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The volume of the hemisphere is 301.44mm²

Any circle drawn around the Earth that divides it into two equal halves is called a hemisphere. Examples is a ball cut into two part. Each part will be an hemisphere.

The volume of an hemisphere is expressed as;

V = 2/3πr³

where v is the volume and r is the radius

Here, r = 12mm

Therefore;

V = 2/3 × ×3.14 × 12²

V = 904.32/3

V = 301.44mm²

therefore the volume of the hemisphere is 301.44mm²

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The horse's average speed for the race in units of kilometers per hour will be 178.06.

The winning horse in a recent race covered the 5.50-furlong distance in 22.37 seconds.

The distance covered by the particle or the body in an hour is called the average speed. It is a scalar quantity. It is the ratio of the total distance to the total time.

We know that the average speed formula is given as,

Average speed = Total distance / Total time

The conversion is given as,

1 furlong = 0.201168 km

5.50-furlong = 0.201168 x 5.5 km

5.50-furlong = 1.10642 km

1 second = 1/3600 hour

22.37 seconds = 22.37/3600 hour

22.37 seconds = 0.0062 hour

The average speed is calculated as,

Average speed = 1.10642 / 0.0062

Average speed = 178.06 km per hour

The horse's average speed for the race in units of kilometers per hour will be 178.06.

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The value of v in the given inequality 9v - 8 ≥ 8v + 2 is v≥10.

The given inequality is 9v - 8 ≥ 8v + 2

Now, we have to solve the value for v in the above inequality.

9v - 8 ≥ 8v + 2

Now, we subtract 8v on both sides.

9v - 8 - 8v ≥ 8v + 2 - 8v.

v - 8 ≥ 2.

Now, we add 8 on both sides

v - 8 + 8 ≥ 2 + 8

v ≥ 10.

Therefore, the value for v is v ≥ 10, which means all the values greater than 10 satisfy the given inequality.

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x is rational, because it can be expressed as the ratio of two integers (d-b) and (a-c).

Let's multiply both sides of the given equation by cx+d to eliminate the denominator:

ax + b = cx + d

ax - cx = d - b

x(a-c) = d - b

x = (d - b)/(a - c)

Since a, b, c, and d are integers and a ≠ c, (a-c) is also an integer. Therefore, x is rational, because it can be expressed as the ratio of two integers (d-b) and (a-c).

Note that this is a special case of the more general result that if p(x) and q(x) are polynomials with integer coefficients and q(x) ≠ 0 for some real number x, and if p(x)/q(x) is an integer, then p(x) is divisible by q(x).

In this case, q(x) = cx + d, which is nonzero because a ≠ c, and p(x) = ax + b - (cx + d) = (a-c)x + (b-d). Since p(x) is an integer and q(x) is an integer except possibly at x = -d/c, it follows that p(x) must be divisible by q(x), and hence x = (d-b)/(a-c) is rational.

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Answer:

30 lbs

Step-by-step explanation:

40/4=10

10 lbs per leg

10x3=30

Answer:

30

Step-by-step explanation:

Answer:

35%

Step-by-step explanation:

1. Add all the participants that attended

20 - 0-19yrs

40 - 20-39yrs

60 - 40-59yrs

50 - 60-79yrs

170 total

2. Divide the age group 40 - 59 by the total amount of participants to get the answer.

60/170 = about .35 = 35%

The scale of the blueprint is 1.5 inches : 4.5 feet, which means that every 1.5 inches on the blueprint represents 4.5 feet in the actual house. To find the length and width of the room on the blueprint, we need to convert the actual dimensions from feet to inches using the scale. The length of the room on the blueprint is (45 ft / 4.5 ft) * 1.5 in = 15 in. The width of the room on the blueprint is (60 ft / 4.5 ft) * 1.5 in = 20 in. The perimeter of the room on the blueprint is 2 * (15 in + 20 in) = 70 in.

It is explained how to obtain the four measures in this problem.

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Answer: The LCD is x(x-3)(x+1) the answer is c

Step-by-step explanation:

Answer:

Step-by-step explanation:

338.33 ft

The length of one drama is 47.4 minutes.

Given that a drama club is showing two videos from 4:00pm to 6:05pm having a 1/2 hours of break in between two of them,

We need to find the length of the dramas,

So,

Total time = 4:00 to 6:05 = 2 hours and 5 minutes.

Subtracting the break length = 2.083 hours - 0.5 hours = 1.58 hours.

Now the length of one drama = 1.58/2 = 0.79 hours.

= 47.4 minutes

Hence the length of one drama is 47.4 minutes.

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Answer:

Step-by-step explanation: 3

The correct answer is d  is used to test the effect of the IV on the variability of the DV.

The correct answer is d. The "stand alone F test" is used to test the effect of the independent variable (IV) on the variability of the dependent variable (DV). It is an inferential test commonly used in analysis of variance (ANOVA) to determine if there is a significant difference among the means of three or more groups.

Option a is incorrect because the "stand alone F test" is an inferential test that involves making a conclusion about a population based on sample data.

Option b is incorrect because the "stand alone F test" is used to test the assumption of equal variances, not homogeneity of variance.

Option c is incorrect because the "stand alone F test" can be directional or non-directional, depending on the research question and hypothesis being tested.

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The minimum amount monthly credit card payment be in order to pay off his debt in 14 months is $244.15, the correct option is C.

We are given that;

Out of savings=  $2,300

Credit card debt = $5,390

Rate=16.5%

Now,

We need to know the percentage rate that Alex’s issuer uses to calculate the minimum payment, and the interest charge and fees for each month. Assuming that Alex’s issuer uses a 2% rate, and that there are no fees or past-due amounts, we can use this formula:

Credit Card Minimum Payment = (A * P) + I

Where A is the statement balance, P is the percentage rate, and I is the interest charge.

The interest charge can be calculated by multiplying the balance by the APR and dividing by 123. For example, the interest charge for the first month is:

I = ($5,390 - $2,300) * 0.165 / 12 I = $42.74

The minimum payment for the first month is:

Credit Card Minimum Payment = ($5,390 - $2,300) * 0.02 + $42.74 Credit Card Minimum Payment = $104.54

To pay off the debt in 14 months, Alex needs to pay more than the minimum payment every month. We can use an online calculator4 to find out how much he needs to pay monthly to achieve this goal.

Therefore, by percentage the answer will be $244.15.

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The Bass diffusion model is a forecasting model that uses nonlinear optimization to predict the adoption of innovative and new technologies in the marketplace.

It was developed by Frank Bass in 1969 and has since become a widely used method for predicting the spread of new products in the market.

The Bass model assumes that the adoption of a new technology is driven by two factors: the innovative individuals who are the first to adopt, and the imitative individuals who adopt based on the influence of others. The model uses a combination of these two factors to predict the rate of adoption over time.

The Bass model takes into account the potential market size, the rate of innovation, and the rate of imitation. It is based on the assumption that the number of potential adopters is finite and that the rate of adoption will slow down as the market becomes saturated. The model also assumes that the rate of innovation will decrease over time as the technology becomes more established in the market.

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From the given triangle, the statement that julie says "sinA/cosA = tan A and sinB/cosB = tan B" is true.

To prove whether Julie's statement is true or false, we need to use the triangle and the definitions of the trigonometric ratios.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. And, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Using the definitions of sine and cosine, we can write:

sin A = b/c

cos A = a/c

sin B = a/c

cos B = b/c

Dividing sin A by cos A, we get:

sin A / cos A = (b/c) / (a/c) = b/a

Similarly, dividing sin B by cos B, we get:

sin B / cos B = (a/c) / (b/c) = a/b

We can see that sin A/cos A and sin B/cos B equals to tan A or tan B respectively. Therefore, Julie's statement is true.

In conclusion, we can prove whether a trigonometric statement is true or false by using the definitions of the ratios and the triangle. In this case, Julie's statement was proved to be true.

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The correct statement is:

B. If -2/5r = -20, then r = 50

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

To solve the equation, we can isolate the variable by multiplying both sides of the equation by the reciprocal of -2/5, which is -5/2:

(-2/5r) * (-5/2) = (-20) * (-5/2)

r = 50

Therefore, if -2/5r = -20, then r = 50.

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Answer:

Step-by-step explanation:

I thing number 5 the answer is 125 degrees

Answer:

yes

Step-by-step explanation:

cause as i see u if it is acute angle it must be <90

and for obtuse angle the angle is 90<x<180 ( between 90 and 180)

The soccer ball reaches a maximum height of approximately 34.8 feet.

The parametric equations for the motion of the soccer ball are:

x(t) = 39*cos(44°)t ≈ 26.9t

y(t) = [tex]39\sin(44)*t - 16t^2[/tex] ≈ [tex]22.7t - 16t^2[/tex]

where t is the time elapsed since the ball was kicked.

To find the maximum height of the ball, we need to find the vertex of the parabolic trajectory given by y(t).

The maximum height occurs at the vertex, which is at the time t = -b/2a, where a = -16 and b = 39*sin(44°).

So, t = -b/2a ≈ 1.1 seconds.

Substituting this value of t into the equation for y(t), we get the maximum height:

y(max) = [tex]39*\sin(44)1.1 - 16(1.1)^2 = 34.8 feet.[/tex]

Therefore, the soccer ball reaches a maximum height of approximately 34.8 feet.

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For strain 1 the average rate of change is 20, while for strain 2 it is 16.7, then Strain 1 has the larger one.

For a function y = f(x), we define the average rate of change on an interval [a, b] as:

R = (f(b) - f(a))/(b - a)

For the table, the average rate of change will be:

R = (85 - 25)/(4 - 1)

R = 60/3 = 20

For the graph, it will be:

R' = (70 - 20)/(4 - 1) = 50/3 = 16.7

Then we can see that the table (Strain 1) has a greater rate of change.

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The game awards 2.5 points for 10 minutes of play.

Part A:

Let's use the given information to find the constant of proportionality. For every 2 minutes of play, the game awards one-half point. Therefore,

1 min of play  = 0.5/2 = 0.25 points

6 min of play = 0.25 x 6 = 1.5 points

The constant of proportionality is 0.25

Part B:

We can use the formula for a proportional relationship,

y = kx

where

y = number of points awarded,

x = amount of time played (in minutes), and

k = constant of proportionality.

Substituting k = 0.25, we get:

y = 0.25x

Part C:

To graph this relationship, let x be the independent variable (amount of time played) and y be the dependent variable (number of points awarded). Then, we can choose several values for x, compute the corresponding values of y using the equation above, and plot the ordered pairs (x, y).

Part D: To find the number of points awarded for 10 minutes of play, we can simply substitute x = 10 into the equation we found in Part B:

y = 0.25x = 0.25(10) = 2.5

Therefore, 2.5 points are awarded for 10 minutes of play.

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Answer: 3/16 - 3/9 = -7/48

Step-by-step:

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD(3/16, 3/9) = 144

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

(3/16×9/9)−(3/9×16/16)=?

Complete the multiplication and the equation becomes

27/144−48/144=?

The two fractions now have like denominators so you can subtract the numerators.

Then:

27−48=−21

144=144

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 21 and 144 using

GCF(21,144) = 3

−21÷3=-7

144÷3=48

Therefore:

3/16−3/9=−7/48

The functions in this problem are classified as follows:

A linear function has the graph in the format of a line, hence function A is classified as a linear function.

A quadratic function has the graph in the format of a parabola, hence function B is classified as a quadratic function.

An exponential function has the graph that either increases or decreases very fast, hence function C is classified as an exponential function.

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The value of quadratic equation is,

⇒ y = x² + 10x + 22

Let the value of quadratic equation is,

⇒ y = ax² + bx + c

Now, Let the points from tables as;

⇒ (- 6, 2) (- 5, - 1) (- 4, - 2)

Substitute all the values in equation as;

⇒ y = ax² + bx + c

⇒ 2 = a(- 6)² + b(-6) + c

⇒ 2 = 36a - 6b + c

⇒ - 1 = a (- 5)² + b (- 5) + c

⇒ - 1 = 25a - 5b + c

⇒ - 2 = a (- 4)² + b (- 4) + c

⇒ - 2 = 16a - 4b + c

Solve expression for the values of a, b and c as;

a = 1

b = 10

c = 22

Thus, the value of quadratic equation is,

⇒ y = x² + 10x + 22

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