1. The probability distribution of a random variable X is given below. x -2 -1 1 4 Px (x) 5k 0.24 3k 0.2 • Restore the probability mass function. . Find the probability that X is less than 3 and gre

The number of independent variables that can be tested in a single experiment depends on various factors, including the research design, resources, and the complexity of the study. In general, it is best to limit the number of independent variables to maintain control over the experiment and facilitate clear interpretation of results.

In simpler experiments, researchers often focus on a single independent variable to study its effect on the dependent variable while controlling for other factors. This allows for a clear cause-and-effect relationship to be established.

However, in more complex experiments, researchers may introduce multiple independent variables to examine their combined effects or interactions. This can provide insights into how different factors influence the outcome simultaneously.

The exact number of independent variables that can be tested in a single experiment varies, but it is generally recommended to keep the number manageable and avoid excessive complexity. This ensures that the experiment remains feasible, interpretable, and effectively addresses the research question or hypothesis.

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The probability that a test revealed that Jared is a carrier but Lucia is not is 1/4

Mendel discovered that genes are inherited as separate, paired units, one from each parent. Its application of mathematics to illuminate observations of natural phenomena.

Given that lucia and jared each have a sibling with cystic fibrosis, but neither lucia nor jared nor their parents have the disease

Mendel theory is a technique used to estimate the probability of getting specific characteristics.

Lucia and Jared have a probability of both carrier and non carrier

If both of them are non carrier then the children born to their family have no chances of getting disease.

If any one of them is carier, then there is a chance of getting one child as a carrier. That is ¼ or the ratio is 1:4

If both of them are carriers then the ratio will be 1:2:1

If Jared is carrier then the probability will be ¼

Therefore the probability if a test revealed that jared is a carrier but lucia is not is ¼

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To find the measure of the central angle for the Human resources category, we need to calculate the percentage of the pie chart it represents in degrees.

The measure of the central angle can be calculated using the following formula: Central angle = Percentage of category / Total percentage of the pie chart * 360 degrees. In this case, the percentage of spending on Human resources is given as 17%. Assuming the pie chart represents 100% of the total spending, the total percentage of the pie chart is 100%.Substituting these values into the formula: Central angle = 17% / 100% * 360 degrees. Calculating the central angle: Central angle = 0.17 * 360 degrees. Central angle ≈ 61.20 degrees.

Therefore, the measure of the central angle for the Human resources category is approximately 61.20 degrees.

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Answer:

17.6 ft

Step-by-step explanation:

tan 37 = 130/x

x = 130/tan 37 = 130/0.7536 = 172.5 feet

tan 40 = 130/y

y = 130/tan 40 = 130/0.8391 = 154.9

172.5 - 154.9 = 17.6 ft

Answer:

17.6 Ft

Step-by-step explanation:

Geometry B E2020!! :3

The probability of people earning between $45,000 and $65,000 in this large company is approximately 29.46%.

We need to use the standard normal distribution formula, where we standardize the original distribution with mean and standard deviation to a standard normal distribution with mean 0 and standard deviation 1. We can then use a Z-table to find the probability.

First, we calculate the Z-scores for the lower and upper limits of the range of interest:

Z1 = (45,000 - 50,000) / 20,000 = -0.25

Z2 = (65,000 - 50,000) / 20,000 = 0.75

We can then look up the probabilities associated with these Z-scores in a standard normal distribution table. From the table, we find that the probability of a Z-score between -0.25 and 0.75 is 0.2946. To convert this back to the original units, we need to multiply the probability by 100 to get a percentage:0.2946 x 100 = 29.46%.

The normal distribution is a continuous probability distribution, so the probability of exact values is zero. We are calculating the probability of a range of values.

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Answer: 20

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Using the chain rule along with standard derivatives

Given

y = f(g(x)) , then

\(\frac{dy}{dx}\) = f'(g(x)) × g'(x)

\(\frac{d}{dx}\) (sinx) = cosx , \(\frac{d}{dx}\) (cosx) = - sinx

(a)

y = sin x²

\(\frac{dy}{dx}\) = cos x² × \(\frac{d}{dx}\) (x² )

   = cos x² × 2x

   = 2xcosx²

(b)

y = cos4x³

\(\frac{dy}{dx}\) = - sin4x³ × \(\frac{d}{dx}\) (4x³ )

   = - sin4x³ × 12x²

   = - 12x²sin4x³

The maximum number of major ideas that can be included in a specific purpose statement depends on several factors, but it is generally recommended that the statement include one to three major ideas. This helps the speaker to focus their ideas and organize their content in a way that effectively communicates their message to the audience

A specific purpose statement is a statement that defines the main objective or goal of a speech or presentation. It serves as a guide for the speaker, helping them to focus their ideas and organize their content in a way that effectively communicates their message to the audience.

The number of major ideas that can be included in a specific purpose statement depends on several factors, including the length of the speech or presentation, the complexity of the topic, and the speaker's ability to effectively communicate their message.

In general, it is recommended that a specific purpose statement include only one to three major ideas. This allows the speaker to focus their attention on a limited number of key points and ensures that the audience is not overwhelmed with too much information. Additionally, having a limited number of major ideas makes it easier for the speaker to organize their content and for the audience to understand and retain the information.

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A specific purpose statement should include one or two major ideas that are focused and directly relevant to the topic at hand.

Including too many ideas can make the statement confusing and difficult for the audience to understand, so it's important to be selective about which ideas to include.

The goal is to create a specific purpose statement that is clear, concise, and easy for the audience to understand, while effectively conveying the key ideas of the communication.

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Two unit vectors that make an angle of 60 degrees with v = (3, 4) are approximately (2.5000, 4.3301) and (-2.5000, -4.3301).

To find two unit vectors that make an angle of 60 degrees with vector v = (3, 4), we can use trigonometry and vector operations.

Step 1: Calculate the magnitude of vector v:

|v| = sqrt(3^2 + 4^2) = 5

Step 2: Convert the given angle of 60 degrees to radians:

θ = 60 degrees * (π/180) = π/3 radians

Step 3: Calculate the components of the unit vector in the same direction as v:

u1 = cos(θ) = cos(π/3) ≈ 0.5000

u2 = sin(θ) = sin(π/3) ≈ 0.8660

Step 4: Multiply the components by the magnitude of v to obtain the unit vectors:

u1 = u1 * |v| ≈ 0.5000 * 5 ≈ 2.5000

u2 = u2 * |v| ≈ 0.8660 * 5 ≈ 4.3301

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The maximum flow rate at the pumping station is 61.713.

A differential equation is an equation that contains one or more functions with its derivatives.

The flow rate at a water pumping station on a given day is given by the equation

R(t)=53+7sin( (πt)/6+3. 6 ) + 9cos( (πt/12)+8. 9 )

The total volume of water in one day is

V=53t+42/πcos(π+3. 6 ) + 108/πsin( 2π+8. 9 )

After applying the limits from 0 to 24

=53(24)-42/πcos(π+3. 6 )+ 108/π sin( 2π+8. 9 )+42/πcos(π+3. 6 )-108/π sin( 2π+8. 9 )

V=53(24)

V=1272

and R(t) has maximum value at t= 9.36

Hence, R(t)=61.713 from the graph

Hence, the maximum flow rate at the pumping station is 61.713.

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Answer:

8 balloons

Step-by-step explanation:

We want to find how many she kept for herself.

She brought 24 balloons to the picnic.

She gave 1/3 to Karen.

She will be left with 2/3 of the balloons:

2/3 * 24 = 16

She will be left with 16 balloons.

She gave 1/2 of what was left to Tim. She will be left with 1/2 of the balloons:

1/2 * 16 = 8

She will be left with 8 balloons.

Answer:

20 units squared

Step-by-step explanation:

Area = base times height

Area = 5 x 4 = 20

Answer:

Hyperbole

Step-by-step explanation:

because i did that test

Answer:

Both r hyperbole

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

if a = 7

7 +4 = 11

or

a + 4 = 11

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Answer:

One solution

Step-by-step explanation:

They have isolated y for you in both equations so you can plug either one into the other.

y = 3x - 1

2x + 7 = 3x - 1

isolate the x

7 = x - 1

x = 8

Go back to the original and plug 8 into x to get y.

y = 2 (8) + 7

y = 16 + 7

y = 23

This means at (8, 23) y = 2x+7 is equal to y = 3x-1. In other words they share a point at (8, 23). This is the only solution because for any other x and y they'd not be equal.

Answer:

Step-by-step explanation:

Answer:

1.) y > - 1/5

2.) y < -2

Step-by-step explanation:

-5y < 1

y > - 1/5

6y < -12

y < - 12/6

y < -2

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Answer:

( − ∞ , − 12 )

Step-by-step explanation:

The result can be shown in multiple forms.

Inequality Form:

−  5  <  1  and  6 y  <  − 12

Interval Notation:

( − ∞ , − 12 )

The equation of a line is in the form of y = mx + c

m = slope

c = y-intercept

The slope of the line y = 2/3x + 3/2 is 2/3.

Slope = m = 2/3

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

y = 2x + 3

The slope of the line is 2 and the y-intercept is 3.

We have,

y = 2/3x + 3/2 _____(1)

The equation of a line is in the form of y = mx + c

m = slope

c = y-intercept

From (1) we can see that,

The slope of the line is 2/3

Slope = m = 2/3

Thus,

The slope of the line y = 2/3x + 3/2 is 2/3.

Slope = m = 2/3

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Answer:

Its C

Step-by-step explanation:

Because when its 3 the output is 5 and if you look at 5 it is multiplies by 2 to get 10. so the formula is times 2

The solution of the quadratic equation is x = 2. Therefore, \(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)  or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

The quadratic formula can be use to solve the quadratic equation as follows:

x² - 4x + 4 = 0

Modelling it to quadratic equation, ax² + bx + c

Hence,

using quadratic formula,

\(\frac{-b+\sqrt{b^{2}-4ac } }{2a}\) or \(\frac{-b-\sqrt{b^{2}-4ac } }{2a}\)

where

Hence,

a = 1

b = -4

c = 4

Therefore,

\(\frac{4+\sqrt{-4^{2}-4(1)(4) } }{2(1)}\) or \(\frac{4-\sqrt{-4^{2}-4(1)(4) } }{2(1)}\)

Finally

x = 2

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The odds in favor of the event happening are 5 to 4.

We have,

To find the odds in favor of an event happening, we use the formula:

Odds in favor = Probability of the event happening / Probability of the event not happening

In this case,

The probability of the event happening is 5/9.

The probability of the event not happening is 1 - 5/9, which simplifies to 4/9. So the odds in favor of the event happening are:

Odds in favor

= 5/9 / 4/9

= 5/4

Therefore,

The odds in favor of the event happening are 5 to 4.

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Answer:

C (8,6)    A (2,14)

Step-by-step explanation:

(2+m)/2 = 5

2(2+m)/2 = 5 x 2

2+m = 10

m = 10 - 2

m = 8

(-6+n)/2 = 0

2(-6+n)/2 = 2 x 0

-6 + n = 0

n = 6

(-8+x)/2 = -3

2(-8+x)/2 = -3 * 2

-8 + x = -6

x = -6 + 8

x = 2

(-2+y)/2 = 6

2(-2+y)/2 = 6 * 2

-2 + y = 12

y = 12 + 2

y = 14

The best method to use to solve the system of equation will be Elimination method.

According to the description of the elimination approach, it involves removing a phrase that contains any of the variables from the equation in order to simplify the computations. To achieve this, multiply or divide a number by the equation(s) until all of the variable terms' coefficients are the same. The term is then eliminated or removed from the result by adding or subtracting from both equations. Because of this, the addition technique is another name for the elimination approach. For illustration, let's use the elimination approach to resolve two linear equations with two variables.

The two equations are:

3x+7y=-19

-3x+4y=12

From the above equations we can observe that the value of the coefficient of x is same, as well as, they have opposite sign.

Hence, the best method to use to solve the system of equation will be Elimination method.

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Answer:

2√6cm

Step-by-step explanation:

Area = L×L

A=L2

24 =L2

√24 =√L2

2√6= L

:.L =2√6.cm.

Answer:

x=(2×4)-(4×2)

Step-by-step explanation:

The difference will be a number so we call it x. Subtract is represented as - in an expression. Thus the answer x=(2×4)-(4×2)

The earnings in the simple interest and compound interest for a 5 year period is in the table below where S is for Suzanne and D is for Derrick

            S - annual interest  S - Balance   D - annual interest   D - Balance

Year 1                 147                   3147                      147                    3147

Year 2                294                  3294                     301.2                 3301.2

Year 3                441                   3441                      462.96              3462.96

Year 4                588                  3588                     632.65              3632.65

Year 5                735                   3735                     810.65               3810.65

Simple interest is calculated by the formula

principal x time x rate / 100

In the problem

Principal = $3000

rate = 4.9%

time is varying from 1 to 5

For the first year we have

= 3000 * 1 * 4.9 / 100

= 147

Compound interest the formula is

Principal(1 + rate)^(year) - 1)

For the first year, (the rate is already divided by 100 to get 0.049) we have

= 3000(1 + 0.049)^(1) - 1)

= 147

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Answer: Option (4)

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.