Nine children and six adults bought tickets to the circus.
Which expression represents the total cost if c represents
the cost of a child's ticket and a represents the cost of an
adult's ticket?

Answer:

x= 2.4

Step-by-step explanation:

Answer:

2.4 or 12/5

Step-by-step explanation:

1.2/0.96=3/x

convert the decimal into a fraction---- 6/5 /0.96= 3/x

Simplify the complex fraction-----5/4 = 3/x

simplify the equation using cross-mulitpication----- 5 x = 12

divide both sides of the equation by 5--- x= 12/5

Check if the solution is in the defined range

Alternitive form:

x=2 2/5, x =2.4

Answer: one-sixth

Step-by-step explanation:

Noah drew the circle which is divided into six equal parts

This shows that cherries must be divided into six persons

each sector of the circle is  \(\frac{1}{6}^{th}\) of the whole circle

From this, we can conclude that each person receives  \(\frac{1}{6}\)  pound of cherries.

The total number of marbles present in the bag is 40.

Given the probability of finding a red marble in a bag containing red and blue marbles by randomly choosing is

                                                       \(P(r) =\)  \(\frac{5}{8}\)

Given the total number of red marbles are

                                                      \(N(r) = 25\)

Now the probability of selecting a specific color marble is given as

                                                        \(P = \frac{n}{N}\)

where, \(n\) = Number of a specific color marble

and      \(N\) = Total number of marbles

So from the given data for red marbles, we can get the total number of marbles(this is only possible as all red marbles are equally likely to be chosen)

                                                         \(\frac{5}{8} = \frac{25}{N}\)

Thus,                                            \(N = \frac{8}{5}*25 = 40\)

So we get the total number of marbles as 40.

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To find the probability of exactly 5 heads in 8 coin flips, we need to consider the total number of possible outcomes and the number of favorable outcomes.

In each coin flip, there are two possible outcomes: heads (H) or tails (T). Therefore, the total number of possible outcomes in 8 coin flips is 2^8 = 256.

To calculate the number of favorable outcomes, we need to determine the number of ways we can get exactly 5 heads in 8 coin flips. This can be calculated using the binomial coefficient, also known as "n choose k" (denoted as C(n, k)).

C(8, 5) = 8! / (5! * (8-5)!) = 56

The binomial coefficient tells us that there are 56 ways to choose 5 heads out of 8 coin flips.

So, the probability of getting exactly 5 heads in 8 coin flips is:

P(exactly 5 heads) = favorable outcomes / total outcomes

P(exactly 5 heads) = 56 / 256

P(exactly 5 heads) = 0.21875

Therefore, the probability of getting exactly 5 heads in 8 coin flips is approximately 0.21875 or 21.875%.

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The percent decrease in the high temperature from yesterday to today is 35%.

To calculate the percent decrease in temperature from yesterday to today, we first need to calculate the actual decrease in temperature:

Actual decrease = Yesterday's high temperature - Today's high temperature

Actual decrease = 80°F - 52°F

Actual decrease = 28°F

The percent decrease can be calculated using the formula:

Percent decrease = (Actual decrease / Yesterday's high temperature) x 100%

Substituting the values, we get:

Percent decrease = (28°F / 80°F) x 100%

Percent decrease = 0.35 x 100%

Percent decrease = 35%

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The complete question is below:

Yesterday, the high temperature was 80 degrees Fahrenheit. Today,  the high temperature was 52°F. What is the percent decrease in the high temperatures from yesterday to today?

Answer:

Option D.

Step-by-step explanation:

The given points are (-2,0), (0,1), (0,-4) and (3,0).

In each ordered pair first element is x-coordinate and second is y-coordinate.

For 4 points, the table must have 2 columns and 4 rows.

So, the required table of values is

x         y

-2        0

0       -4

0        1

3        0

Therefore, the correct option is D.

Answer:

13. 9.77 inches (rounded to 3 s.f.)

14. 249m² (rounded to 3 s.f.)

Step-by-step explanation:

13. To find the arc length, the formula is the angle of the arc out of 360° multiplied by the circumference of the full circle. Circumference of circle: pi × r × 2

\(\frac{80}{360}\) × pi × 7 × 2 = 3\(\frac{1}{9}\)pi

                       = 9.77 inches (rounded to 3 s.f.)

14. To find the sector area, the formula is the angle of the sector out of 360° multiplied by the area of the full circle. Area of circle: pi × r × r

\(\frac{285}{360}\) × pi × 10 × 10 = 79\(\frac{1}{6}\)pi

                          = 249m² (rounded to 3 s.f.)

Answer:

Each time, t, is associated with exactly one car value, y.

Step-by-step explanation:

The concept being tested is functions.

The graph describe is a vertical parabola that opens downwards.

All vertical parabolas are functions because the pass the vertical line test.

In other words, each time, t, is associated with exactly one car value, y.

The correct answer is the second option.

Step-by-step explanation:

here you go!

so basically x = 9 cars

Step-by-step explanation:

Answer:

Minimum Unit Cost = $14,362

Step-by-step explanation:

The standard form of a quadratic is given by:

ax^2 + bx + c

So for our function, we can say,

a = 0.6

b = -108

c = 19,222

We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a

So,

-(-108)/2(0.6) = 108/1.2 = 90

Plugging this value into original function would give us the minimum (unit cost):

The range of the function g(x) is given as follows:

[0, ∞).

From the graph of the function given in this problem, y assumes all real non-negative values, hence the interval notation representing the range of the function is given as follows:

[0, ∞).

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Answer:

r = - 9

Step-by-step explanation:

Given

4r + 10 = - 26 ( subtract 10 from both sides )

4r = - 36 ( divide both sides by 4 )

r = - 9

Answer:

m is 3 since it's the slope and b is -2 since its the y-intercept

Step-by-step explanation:

the formula is y=mx+b so 3 is in the m spot and -2 is in the b spot.

Answer:  m = 3 , b = -2

Step-by-step explanation:

y = 3x - 2, we found out m and b by using the form y = mx + b, where m is the number in front of x.

Therefore we found out that m is 3, b is -2.

The equation that describing how x and y are related is y = 2x + 7

From the given table we have to choose two points

The first point = (1, 9)

The second point = (2, 11)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line

The slope of the line = \(\frac{y_2-y_1}{x_2-x_1}\)

Substitute the values in the equation

The slope of the line = (11-9) / 2 - 1

= 2 / 1

= 2

From the table

At x = 0 the value of y = 7

Therefore the y intercept = 7

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Then,

y = 2x + 7

Hence, the equation that describing how x and y are related is y = 2x + 7

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Work Shown:

Use the compound interest formula

A = P*(1+r/n)^(n*t)

A = 10000(1+0.039/1)^(1*4)

A = 11,653.65589441

A = 11,653.66

That's the amount of money Tammy will have at the end of 4 years.

Subtract off the principal from this value to get the interest.

interest = A - P

interest = 11,653.66 - 10,000

interest = 1,653.66

We can say with 90% confidence that the proportion of pain reduction for the treatment group is between 0.28 and 0.46, while the proportion for the placebo group is between 0.13 and 0.29.

A. An appropriate design for the new study would be a randomized, double-blind, placebo-controlled clinical trial. The treatment group would receive vitamin A oil injections into the pain site in the cervical region of the back, while the control group would receive a placebo injection. The method of treatment assignment would be randomization, and neither the patients nor the researchers would know which group each patient is assigned to (double-blind). The variables that should be measured include the level of pain reduction, measured through self-reporting after each injection, as well as any adverse effects or complications that may arise from the injections.

B. If the study consisted of 100 young patients and 100 old patients instead of 200 patients aged 20–40, the study design may need to be modified. Age is an important factor that could influence the effectiveness of the treatment, so it would be important to ensure that the two groups are balanced in terms of age. One option would be to stratify the randomization process by age, so that half of the young patients and half of the old patients are assigned to the treatment group, and the other half are assigned to the control group.

C. To construct 90% confidence intervals for the proportion of pain reduction for each treatment group, we can use the following formula:

Confidence interval = proportion ± (z-value x standard error)

where z-value for a 90% confidence level is 1.645, and standard error is calculated as:

standard error = √(proportion x (1 - proportion) / sample size)

For the treatment group:

Proportion = 37/100 = 0.37

Standard error = √(0.37 x 0.63 / 100) = 0.049

Confidence interval = 0.37 ± (1.645 x 0.049) = (0.28, 0.46)

For the placebo group:

Proportion = 21/100 = 0.21

Standard error = √(0.21 x 0.79 / 100) = 0.044

Confidence interval = 0.21 ± (1.645 x 0.044) = (0.13, 0.29)

D. Based on the data collected, we can conclude that vitamin A oil injections are associated with a higher proportion of pain reduction compared to the placebo injections. The confidence interval for the treatment group does not overlap with the confidence interval for the placebo group, indicating a statistically significant difference between the two groups. However, further studies are needed to confirm these findings and to assess the safety and long-term effectiveness of the treatment.

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The value of the objective function at this point is Z = 840.  The solution (7, 7) is feasible.

a. Formulation of linear programming model:To solve this problem, the following linear programming model can be used:x1 = Activity 1 (in units)x2 = Activity 2 (in units)Maximize Z = 60x1 + 50x2 subject to30x1 + 126x2 ≤ 4,752 (Acceptable limit)60x1 + 126x2 ≤ 8,436 (Benefit 1)Step-by-step explanation is given below:Function: Linear Programming modelSolution:

a. Formulation of linear programming model:To solve this problem, the following linear programming model can be used:x1 = Activity 1 (in units)x2 = Activity 2 (in units)Maximize Z = 60x1 + 50x2 subject to30x1 + 126x2 ≤ 4,752 (Acceptable limit)60x1 + 126x2 ≤ 8,436 (Benefit 1)  

b. Checking for feasible solutionsWe need to check the following solutions:(x1, 32) (7, 7) (7, 8) (8, 7) (8, 8) (8, 9) (9, 8)Let us substitute the values in the linear programming model for each solution:Solution: (x1, 32)30x1 + 126(32) = 4,752 + 4,032 = 8,784 > 4,752 (Infeasible)Solution: (7, 7)30(7) + 126(7) = 966 < 4,752 (Feasible)60(7) + 126(7) = 1,092 < 8,436 (Feasible)Solution: (7, 8)30(7) + 126(8) = 5,070 > 4,752 (Infeasible)Solution: (8, 7)30(8) + 126(7) = 5,016 > 4,752 (Infeasible)Solution: (8, 8)30(8) + 126(8) = 5,196 > 4,752 (Infeasible)Solution: (8, 9)30(8) + 126(9) = 5,322 > 4,752 (Infeasible)Solution: (9, 8)30(9) + 126(8) = 5,358 > 4,752 (Infeasible)Therefore, only the solution (7, 7) is feasible.

c. Expressing the model in algebraic form:We have,x1 = Activity 1 (in units)x2 = Activity 2 (in units)Maximize Z = 60x1 + 50x2 subject to30x1 + 126x2 ≤ 4,752 (Acceptable limit)60x1 + 126x2 ≤ 8,436 (Benefit 1)The solution x = (7, 7) is feasible and optimal, with Z = 60(7) + 50(7) = 840.d. Using the graphical method:Below is the graph plotted for the above linear programming model:graph{(y-4752)/126<=-(3/2)x+316}The feasible region is given by the shaded region in the graph. The optimal solution is (7, 7), which is at the point of intersection of the two lines. The value of the objective function at this point is Z = 840.

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F(3) is equal to 9, based on the given table and the corresponding values of x and f(x). Option D.

To find the value of F(3) based on the given table, we look at the corresponding x-value of 3 and find its corresponding f(x) value.

From the table, we see that when x = 3, f(x) = 9. Therefore, F(3) = 9.

The table shows the values of x and their corresponding f(x) values. We can see that when x increases by 1, f(x) also increases by 3. This indicates that the function has a constant rate of change, where the change in f(x) is always 3 units for every 1 unit change in x.

Given that F(3) represents the value of the function when x = 3, we look at the x-values in the table and find the corresponding f(x) value. In this case, when x = 3, f(x) = 9.

Therefore, the value of F(3) is 9. Option D is correct.

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Answer:

Step-by-step explanation:

To find x:

1) Substitute 0 for y.

3x - 0 < 5

The zero doesn't really matter so you can get rid of it.

3x < 5

2) Divide by 3 to get x by itself

3x/3 < 5/3

x < 5/3

or

x < 1 2/3

To find y:

1) Substitute 0 for x.

3(0) - y < 5

3 times 0 equals zero so you can get rid of it.

-y < 5

2) There is an invisible 1 in front of the -y. So you divide by -1 to get y by itself.

-y/-1 < 5/-1

y < -5

Since the limit of f(x) is non-zero, the limit distributes over the quotient and

\(\displaystyle \lim_{x\to c} \frac{g(x)}{f(x)} = \frac{\displaystyle \lim_{x\to c}g(x)}{\displaystyle \lim_{x\to c}f(x)} = \frac{\dfrac15}{-4} = \boxed{-\frac1{20}}\)

The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

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If x = \(t^3\) - t and y = \(\sqrt{3t + 1}\), then dy/dx is 3/8 at t = 1.

To find dy/dx at t=1, we need to first find dx/dt and dy/dt, and then use the chain rule.
1. Find dx/dt:
x = \(t^3\) - t
Differentiate with respect to t:
dx/dt = \(3t^2\) - 1
2. Find dy/dt:
y = sqrt(3t + 1)
Differentiate with respect to t:
dy/dt = 1/2 * \((3t + 1)^{(-1/2)}\) * 3
dy/dt = 3/(2 * \(\sqrt{(3t + 1)}\))
3. Use the chain rule to find dy/dx:
dy/dx = (dy/dt) / (dx/dt)
4. Plug in the values at t = 1:
dx/dt (t=1) = \(3(1)^2\) - 1 = 2
dy/dt (t=1) = 3/(2 * \(\sqrt{(3(1) + 1)}\)) = 3/4
5. Calculate dy/dx at t = 1:
dy/dx = (3/4) / 2 = 3/8
So, the answer is 3/8.

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The values of the variables for the parallelogram include the following;

In Mathematics and Geometry, a parallelogram is a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

In this context, we can reasonably infer and logically deduce that this parallelogram has both pairs of opposite sides parallel to each other and the opposite angles (vertical angles) are equal and congruent.

By CPCTC, the variable x can be calculated as follows;

15x = 45°

x = 45°/15

x = 3

Since the diagonals of a parallelogram are perpendicular to each other, we have:

m<1 = 3y - 9 = 90

3y = 99

y = 33

15x = 18z

15(3) = 18z

45 = 18z

z = 45/18

z = 2.5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

2 ( 3x - 5 ) = 3x + 17

6x - 10 = 3x + 17

6x - 3x = 17 + 10

3x = 27

x = 27 /3

x= 9

Answer:

n = 9

Step-by-step explanation:

2n - 41 = - 23

2n = - 23 + 41

n = 18/2

Answer:

Dodecagon (12 sides)

Step-by-step explanation:

PLS GIVE BRAINLIEST

These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

Gregory most likely took an intelligence test, specifically the Wechsler Adult Intelligence Scale (WAIS). The WAIS is designed to measure an individual's cognitive abilities and is commonly used in psychological assessments. It consists of a full scale or total score, which is a combination of the verbal score and the performance score. The verbal score measures an individual's language and communication skills, while the performance score measures an individual's ability to solve problems and complete tasks. These scores are used to provide an overall measure of an individual's intelligence and cognitive abilities.

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Answer:

25.4 or 25 times

Step-by-step explanation:

137.25-10.25=127

127/5=25.4

Options a, b, d, and g are the correct conditions for a Binomial Distribution.

The four conditions necessary for X to have a Binomial Distribution are:

a. There are n set trials: In a binomial distribution, the number of trials, denoted as "n," must be predetermined and fixed. Each trial is independent and represents a discrete event.

b. The trials must be independent: The outcomes of each trial must be independent of each other. This means that the outcome of one trial does not influence or affect the outcome of any other trial. The independence assumption ensures that the probability of success remains constant across all trials.

d. There can only be two outcomes, a success and a failure: In a binomial distribution, each trial can have only two possible outcomes. These outcomes are typically labeled as "success" and "failure," although they can represent any two mutually exclusive events. The probability of success is denoted as "p," and the probability of failure is denoted as "q," where q = 1 - p.

g. The probability of success, p, is constant from trial to trial: In a binomial distribution, the probability of success (p) remains constant throughout all trials. This means that the likelihood of the desired outcome occurring remains the same for each trial. The constant probability ensures consistency in the distribution.

The remaining options, c, e, and f, are not conditions necessary for a binomial distribution. Option c, "Continue sampling until you get a success," suggests a different type of distribution where the number of trials is not predetermined. Options e and f, "You must have at least 10 successes and 10 failures" and "The population must be at least 10x larger than the sample," are not specific conditions for a binomial distribution. The number of successes or failures and the size of the population relative to the sample size are not inherent requirements for a binomial distribution.

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