A red die and a blue die are thrown. Both dice are loaded (that is, not all sides are equally likely). Rolling a 1 with the red die is twice as likely as rolling each of the other five numbers and rolling a 3 with the blue die is twice as likely as rolling each of the other five numbers. a. (2.5 pt.) What is the probability of each outcome of the red die

Answer: 1/2

Step-by-step explanation:

g(x) = ⅞x - ½

g(7) = ⅞(7) - ½

= 49/8 - ½

= 49/8 - 4/8

= 45/8

= 5 ⅝

So, the value of g(7) for that function is 5 ⅝

Hope it helpful and useful :)

The value of the given function for g(7) is 45/8.

The given function is [tex]g(x)=\frac{7}{8}x-\frac{1}{2}[/tex].

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

We need to find the value of g(7)

Substitute x=7 in the given function and simplify, we get

[tex]g(7)=\frac{7}{8}(7)-\frac{1}{2}[/tex]

= 49/8 - 1/2

= 49/8 - 4/8

= 45/8

Hence, the value of the given function for g(7) is 45/8.

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The number at the end of the equation shifts the graph up or down.

Changing the 1/2 to a -2 would shift the graph down which would change the y-intercept.

The answer is D.

Answer:

Jo : μ ≤ 64.

Jo : μ > 64.

Step-by-step explanation:

From the question, the Important information to solve this question is that; ''the speed limit on this portion of Interstate 95 is 64 mph''.

The question wants us to find the fact that the average speed is greater or more than the speed limit.

Therefore, In order to solve this question, the formula to use is the ''null and alternative" hypothesis. It states that;

Jo : μ ≤ 64.

Jo : μ > 64.

The above expression is the competing hypotheses in order to determine if the average speed is greater than the speed limit.

Answer:

it is 6,358.2. hope this helps

Answer:

 0 days 3 hours 40 minutes 0 seconds

- 0 days 1 hours 55 minutes 0 seconds

= 0 days 1 hours 45 minutes 0 seconds

= 0.0729167 days

= 1.75 hours

= 105 minutes

= 6,300 seconds

Step-by-step explanation:

Final answer:

To calculate the difference between given times, convert them into minutes and subtract. The result will be the time difference in minutes.

Explanation:

Compute: 3:40 - 1:55

To compute the difference between 3:40 and 1:55, you need to subtract the two times. First, convert both times into minutes: 3:40 = 3 x 60 + 40 = 180 + 40 = 220 minutes, and 1:55 = 1 x 60 + 55 = 60 + 55 = 115 minutes. Then, subtract 115 from 220 to get the result.

The difference between 3:40 and 1:55 is 105 minutes.

Answer:

V = (10*6*12)/3

V = 720/3

V = 240 cm^3

Step-by-step explanation:

V = LWH/3

L = base length

W = base width

H = pyramid height

Answer:

His salary after 20 years is $48892

Step-by-step explanation:

Kevin started his new job with a salary of $26,550.

We are also given that every year, he receives a 3.1% increase in his salary

So, rate of increase = 3.1%

Formula : [tex]y(t)=y_0(1+r)^t[/tex]

Where y(t)= Amount after t years

[tex]y_0[/tex] = initial amount = 26550

r = rate of increase in decimals = [tex]\frac{3.1}{100}[/tex]

t = time =20

we are supposed to find his salary after 20 years

Substitute the values in the formula :

Salary after 20 years = [tex]26500(1+\frac{3.1}{100})^{20}=48892.00[/tex]

Hence His salary after 20 years is $48892

Answer:

$676

Step-by-step explanation:

26 percent of 2600 is 676.

2600 x .26

Answer:

5

Step-by-step explanation:

2 log₃(x + 4) − log₃9 = 2

2 log₃(x + 4) − log₃3² = 2

2 log₃(x + 4) − 2 = 2

2 log₃(x + 4) = 4

log₃(x + 4) = 2

3^(log₃(x + 4)) = 3^2

x + 4 = 9

x = 5

The solutions to the logarithmic equation 2 log₃(x + 4) - log₃(9) = 2 are x = 5 and x = -13.

To solve the logarithmic equation 2 log₃(x + 4) - log₃(9) = 2, we can use logarithmic properties to simplify the equation and then solve for x.

First, let's apply the properties of logarithms:

2 log₃(x + 4) - log₃(9) = 2

Using the power rule of logarithms, we can rewrite 2 log₃(x + 4) as log₃((x + 4)²):

log₃((x + 4)²) - log₃(9) = 2

Next, we can combine the logarithms using the quotient rule:

log₃((x + 4)² / 9) = 2

Now, we can eliminate the logarithm by rewriting the equation in exponential form:

3² = (x + 4)² / 9

9 = (x + 4)² / 9

Multiplying both sides of the equation by 9:

81 = (x + 4)²

Taking the square root of both sides:

±√81 = ±√((x + 4)²)

±9 = x + 4

Solving for x, we have two possible solutions:

x + 4 = 9

x = 9 - 4

x = 5

or,

x + 4 = -9

x = -9 - 4

x = -13

Therefore, the solutions to the logarithmic equation 2 log₃(x + 4) - log₃(9) = 2 are x = 5 and x = -13.

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Answer: D

H0: μ=522

H1: μ>522

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

So, for this case;

The null hypothesis is that the mean score equals to 522

H0: μ=522

The alternative hypothesis is that the mean score is greater than 522.

H1: μ>522

The correct answer is D. [tex]Upper H_0: = 522, Upper H_1 > 522[/tex].

In this scenario, the math teacher is claiming that her review course increases the scores of students on the math portion of a college entrance exam. Therefore, the null hypothesis [tex](H_0)[/tex]  should represent the claim that there is no increase in the mean score, which would be that the mean score is equal to the population mean of 522. The alternative hypothesis [tex](H_1)[/tex]   should represent the teacher's claim that the mean score has increased, which would be that the mean score is greater than 522.The null hypothesis is a statement of no effect or no difference and serves as the baseline for testing. The alternative hypothesis is what we aim to support; it is a statement that there is an effect or a difference. In this case, we are testing whether the mean score of students after taking the review course is greater than the population mean.Therefore, the correct hypotheses are:- Null Hypothesis [tex](H_0): = 522[/tex] , indicating no increase in the mean score.- Alternative Hypothesis [tex](H_1): > 522[/tex] , indicating an increase in the mean score.This is a one-tailed test because we are only interested in whether the mean score has increased, not whether it has changed at all (which would require a two-tailed test).

Complete Question

The line plot shows the amount of green ooze (in cup) carried by ten contestants. Find the amount each contestant would carry if the total amount carried (5 cups) was redistributed equally among all the contestants.

Answer:

1/2 Cup

Step-by-step explanation:

This is a Line Plot in which:

Total

[tex]=(\frac{1}{4}X2) +(\frac{3}{8}X2) +(\frac{1}{2}X2) +(\frac{5}{8}X3) +(\frac{7}{8}X1) \\\\=\frac{2}{4} +\frac{6}{8} +1 +\frac{15}{8} +\frac{7}{8}\\\\$=5 Cups[/tex]

If this amount was redistributed equally among the ten contestants:

Each contestant would carry (5/10) cups =1/2 cup.

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: Systolic blood pressure of a U.S. adult. (mmHg)

X~N(μ;σ²)

μ= 122 mmHg

σ= 20 mmHg

For all calculations you have to work under the standard normal distribution, because it is tabulated. It is easier and faster to standardize or "translate" all values of X into values of Z and look for the corresponding probabilities in the table than to manually calculate them using the density function of the normal distribution.

The standard normal distribution is derived from the normal distribution. Considering a random variable X with normal distribution, mean μ and variance δ², the variable Z =(X-μ)/δ ~N(0;1) is determined.

Any value of any random variable X with normal distribution can be "converted" by subtracting the variable from its mean and dividing it by its standard deviation.

Since the distribution is centered in zero, there are two entries for its table, the left entry shows the cumulated probabilities corresponding to negative values of Z: P(Z≤z)=α and the right entry show the cumulated probabilities corresponding to positive values of Z: P(Z≤z)= 1 - α

a)

You need to calculate the percentage/ proportion of U.S. adults that have a systolic pressure greater than 142 mmHg, symbolically:

P(X>142) = 1 - P(X≤142)

To standardize this value od the variable you have to do the following calculation:

Z =(X-μ)/δ= (142-122)/20= 1

Now you look in the right entry for the cumulative probability until z= 1.00

(Remember, the first column of the table shows you the integer and first digit, the first row of the table shows you the second integer of the z value)

P(Z≤1)= 0.84134

Now you calculate the asked value:

P(X>142) = 1 - P(X≤142)= 1 - P(Z≤1)= 1 - 0.84134= 0.15866

b)

The sample mean is derived from a random variable with a normal distribution it shares that distribution with the exception that its variance is directly affected by the sample size:

X[bar]~N(μ;σ²/n)

μ= 122 mmHg

σ/√n= 20/√29= 3.71 mmHg

c)

The claim is that the mean systolic pressure of the employees is higher than the national average, symbolically μ> 122

The statistical hypotheses are:

H₀: μ≤ 122

H₁: μ> 122

d)

t= 5.495 p-value: 0.000003591

In this example the test statistic depends on the mean and the p-value is 3.591*10⁻⁶. This value indicates that 0.0003591% of the samples with size n=29 taken from a population with mean 122 mmHg, will produce a mean that provides evidence as (or stronger) than the current sample that μ is not at most 122 mmHg.

e)

The type II error is the scenario when you fail to reject the null hypothesis when the hypothesis is false. In this case, it is to fail to reject that the average systolic pressure of the company's employees is at most as the national average.

f)

The variable "X: Age of an employee" was recorded and linear regression of the systolic blood pressure as a function of the employee's ages estimated.

^Y= 97.0771 + 0.9493Xi

0.9493mmHg/years is the modification of the estimated average systolic blood pressure of the company's employees when their age increases one year.

g)

To determine the type of linear regression between the two variables, you have to analyze the slope of the equation:

As you can see in the graphic, the slope of the regression is positive, which means there is a positive regression between the systolic pressure and the age of the employees. I.e. each time the age of the employee increases, his systolic pressure also increases.

To determine the strength of the regression between these two variables you have to analyze the coefficient of determination R²:

The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variables under the estimated regression. It takes values between 0 to 1 or 0 to 100% if expressed in percentage. The closer the coefficient is to zero, the weaker the relationship between these two variables.

The closer the coefficient is to 100%, the stronger the relationship between these two variables.

R²= 0.712

71.2% of the variability of the systolic pressure is explained by the age fo the employees under this estimated model ^Y= 97.0771 + 0.9493Xi

The relationship between these variables is strong enough to consider the regression.

I hope this helps!

Answer:

Probability of even = 0.5

Step-by-step explanation:

Probability of even = total number of even numbers/ total number

Total number of Eve number = [ 2,4,6] = 3

Total numbers = [ 1,2,3,4,5,6] = 6

Probability of even = 3/6

Probability of even = 1/2

Probability of even = 0.5

Answer:(x-5)^2+(y-4)^2=49

Step-by-step explanation:

equation of a circle is:

(x-h)^2+(y-k)^2=r^2

(x-5)^2+(y-4)^2=7^2

(x-5)^2+(y-4)^2=7x7

(x-5)^2+(y-4)^2=49

The equation of the circle of center (5, 4) and radius 7, is:

(x - 5)^2 + (y - 4)^2  = 49

The general equation for a circle of radius R centered at the point (a, b) is:

(x - a)^2 + (y - b)^2 = R^2

In this case, the center is (5, 4) and the radius is 7, so we need to replace:

a = 5

b = 4

R = 7

Then the equation is:

(x - 5)^2 + (y - 4)^2 = 7^2 = 49

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Answer:

$159075.84

Step-by-step explanation:

100-7.6=92.4

1721.60*92.4=$159075.84

The 95% confidence interval for the number of hours students at the college study weekly, given a sample size of 49, mean of 12.2 hours, and standard deviation of 1.6, is from 11.62 hours to 12.78 hours.

In statistics, the 95% confidence interval for the mean number of hours students study in a week can be calculated using the collected data and the t-distribution. Given that the sample size is 49 (n=49), the sample mean(x) is 12.2 hours, and the standard deviation(s) is 1.6 hours, we need to apply the formula for the confidence interval which is x ± t∗(s/√n). The t-value for 95% confidence with 48 degrees of freedom (49-1) can be found using the t-distribution Inverse Calculator applet, which is about 2.01 (it varies slightly depending on the calculator used).

Now, plug in the given values into the formula: 12.2 ± 2.01 * (1.6 / √49), it simplifies to 12.2 ± 0.58. So, the 95% confidence interval for the number of hours students in the college study each week is from 11.62 hours to 12.78 hours.

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Final answer:

The desired exponential function that goes through the points (0,18) and (2,288) is y=18 × 4^x.

Explanation:

To write an exponential function in the form y = ab^x that passes through the points (0,18) and (2,288), we first use the given points to find the values of a and b.

When x = 0, the equation simplifies to y = a because b0 equals 1. Therefore, from the point (0,18), we can conclude that a equals 18.

Next, substituting x = 2 and y = 288 into the equation and using the value of a, we have 288 = 18 × b^2. To find b, divide both sides by 18 to get b^2 = 16, which means b = 4 since b is positive in the growth of an exponential function.

So the desired exponential function is y = 18 × 4^x.

Answer:

2.5 or 5/2

Step-by-step explanation:

The formula for the area of a triangle is \dfrac{bh}{2}, where b represents the length of the base and h represents the length of the height. With this in mind, you can set up the following equation:

[tex]\dfrac{15}{8}=\dfrac{1.5b}{2}[/tex]

[tex]\dfrac{15}{4}=1.5b[/tex]

b=2.5 or [tex]\frac{5}{2}[/tex]

Hope this helps!

Answer:585 cubic inch

Step-by-step explanation:

volume=15 x 10 x 3 + 9 x 3 x 5

Volume=450 + 135

Volume=585

Answer:it’s strong the person under me is slow

Step-by-step explanation: cause I said so

Answer:

The committee can be formed in 31,752 ways.

Step-by-step explanation:

Every committee position has the same duties and voting rights. This means that the order in which the members are chosen is not important to solve this question. So the combinations formula is used.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In how many ways can the committee be formed

4 faculty members from a set of 9

5 students from a set of 10.

Then

[tex]T = C_{9,4} \times C_{10,5} = \frac{9!}{4!(9-4)!} \times \frac{10!}{5!(10-5)!} = 31752[/tex]

The committee can be formed in 31,752 ways.

Answer:

C -9a - 15

Step-by-step explanation:

bionomial means two terms

Answer:

The test statistic value is 1.474.

Step-by-step explanation:

In this case we need to determine whether the plant is making a higher than expected number of irregular t-shirts.

If more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process..

The hypothesis for this test can be defined as follows:

H₀: The proportion of irregular t-shirts is 8%, i.e. p = 0.08.

Hₐ: The proportion of irregular t-shirts is more than 8%, i.e. p > 0.08.

The information provided is:

n = 100

X = number of irregular t-shirts = 12

Compute the sample proportion as follows:

[tex]\hat p=\frac{X}{n}=\frac{12}{100}=0.12[/tex]

Compute the test statistic as follows:

[tex]t=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

  [tex]=\frac{0.12-0.08}{\sqrt{\frac{0.08(1-0.08)}{100}}}\\\\=1.47441\\\\\approx 1.474[/tex]

Thus, the test statistic value is 1.474.

Answer:

D. This scenario should be analysed using paired data because the groups are dependent and have a natural pairing.

Step-by-step explanation:

Paired Data can be defined as data set, when sample units of one data set are related to sample units in other data set.

Research Study about spouses number of hours of sleep each night is paired data. As, each man in the male sample group is related to a corresponding woman (his wife) in the female sample group. So, they have a natural paring & they, their sleep schedules are dependent on each other.

Based on the information given, this scenario should be analyzed using paired data because the groups are dependent and have a natural pairing.

In conclusion, the correct option is D.

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Answer:

(4, -1)

Step-by-step explanation:

The point of intersection of two lines is also the solution to the system of equations of the two lines

Step-by-step explanation:

The answer to this question is where both of the lines intersect.  For this problem, the answer is (4, -1)

Look at the attachment for clarification:

Answer: The answer is C (about 47%) because the total amount of Mountain View residents is 0.38, 0.18 people chose Olunloyo, which is about 47 percent of residents.

To find out what percentage of the Mountain View polled supported Olunloyo, divide the number of Olunloyo supporters by the total number of poll participants, and multiply by 100. This reflects the views of the polled sample, not the entire population.

To determine what percentage of the Mountain View polled supported Olunloyo, you would first need to know the total number of people who participated in the poll from Mountain View. Then, find out the number of these participants who indicated their support for Olunloyo. Divide the number of supporters by the total number of participants, and multiply the result by 100. This will give you the percentage of Mountain View residents in the poll who supported Olunloyo. Remember that this only applies to the sample of the population that participated in the poll and may not reflect the entire population of Mountain View.

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Answer:

Step-by-step explanation:

You can write the linear system model as follows. Let t, l, c represent acres of tomatoes, lettuce, and carrots, respectively. The we have ...

  t + l + c ≤ 120 . . . . . constraint on available land

  5t +4l +2c ≥ 480 . . requirement for spending on fertilizer

  4t +2l +2c ≤ 600 . . constraint on available labor

  t ≥ 0; l ≥ 0; c ≥ 0 . .  requirement for non-negative acres

Then the objective function (profit) is ...

  p = 3000t +1400l +400c

The linear programming problem is to maximize p subject to the above constraints.

__

Any of a variety of solvers can find the solution to this problem. That solution is ...

  (t, l, c) = (120, 0, 0) and p = 360,000

In summary ...

  tomatoes acre(s) = 120 (all available acres are used)

  lettuce acre(s) = 0

  carrots acre(s) = 0

  profit $ = $360,000

_____

Additional comments

This solution suggests that it can be found simply by examining the profit associated with each unit of resource.

  profit per acre is maximized for tomatoes, at $3000 per acre

  profit per fertilizer dollar is maximized for tomatoes, at $600 per dollar

  profit per labor hour is maximized for tomatoes, at $750 per hour

That is, the profit per acre is maximized for tomatoes, regardless of the resource being considered. Thus it make sense to put all of the acreage in tomatoes. At $5 per acre for fertilizer, we use $600 worth of fertilizer. At 4 hours per week per acre, we use 480 hours of labor, so not all available labor is used.

To maximize profits, use linear programming to find the number of acres for each crop. The total farm acres used depends on the constraints.

To maximize total profits, the number of acres of each crop should be determined. Let's assign the variables t, l, and c to represent the number of acres of tomatoes, lettuce, and carrots, respectively. We have the following constraints:

The objective is to find the values of t, l, and c that satisfy the constraints and maximize the profit. This is a linear programming problem that can be solved using methods such as the simplex method or graphical method.

To determine if all 120 acres will be used, we need to check if t + l + c = 120 under the constraints.

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