The velocity-time graph for a cycle is shown

I think the answer should be b, since y=3 when x=0, according to the option B.

y = x + 3, B

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

x+1/2=21/14

x = ?

Step 02:

14 (x + 1 ) = 2 * 21

14x + 14 = 42

14x = 42 - 14

x = 28 / 14

x = 2

The answer is:

The value of x is 2

Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

I'm not sure sorry ask anything else

The area of the region enclosed by one loop of the curve r = 8 sin 3θ is \(\frac{\pi a^{2} }{12}\)

given that

r = 8sin3θ

The radius of the curve will only be altered by changing the value of a.

Set r = 0 since this is where the curve is at its origin to determine where the curve starts and where it finishes.

if asin3θ = 0 then sin3θ = 0 since sinθ =0 at θ = 0,\(\pi\),2\(\pi\),....... we see that for sin3θ ,it will be 0 at 0,\(\pi\)/3,2\(\pi\)/3.......

So, the curve in the first quadrant varies from θ=0 to \(\pi\)/3

The expression for the area of any polar equation r from θ=α to θ = β

is given by

\(\frac{1}{2}\)\(\int\limits^\beta _\alpha\)\(r^{2}\) dθ

For one loop of the given equation, the corresponding integral is then

\(\frac{1}{2}\)\(\int\limits^\frac{\pi }{3} _0\)(asin3θ)^2 dθ

Working this integral:

\(\frac{1}{2}\)\(\int\limits^\frac{\pi }{3} _0\)(asin3θ)^2 dθ

= \(\frac{1}{2}\)\(\int\limits^\frac{\pi }{3} _0\)\(a^{2}\)(sin3θ)^2 dθ

we know that cos2θ = 1-2((sinθ)^2) we can rewrite it as (sinθ)^2 = 1/2(1-cos2θ)

we can write (sin3θ)^2 = 1/2(1-cos6θ)

then the integration is:

= \(\frac{1}{2}\)\(\int\limits^\frac{\pi }{3} _0\)\(a^{2}\)( 1/2(1-cos6θ))dθ

=\(\frac{a^{2} }{4}\)\(\int\limits^\frac{\pi }{3} _0\)(1-cos6θ)dθ

we need to integrate that

=\(\frac{a^{2} }{4}\)(θ - \(\frac{1}{6}\)sin6θ)with θ = \(\pi\)/3 to 0

=\(\frac{a^{2} }{4}\)[\(\frac{\pi }{3}\) - \(\frac{1}{6}\)sin2\(\pi\) - (0 - \(\frac{1}{6}\)sin0)]

=\(\frac{a^{2} }{4}\)(\(\frac{\pi }{3}\))

=\(\frac{\pi a^{2} }{12}\)

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The first constraint is a linear equation that relates the variables x1, x2, and x3, and the second constraint is an inequality constraint involving x1 and x2The given problem is a linear programming problem in its primal form.

The objective is to maximize the expression z = 7x1 - 5x2 - 2x3, subject to two constraints.. The goal is to find the values of x1, x2, and x3 that maximize the objective function while satisfying the given constraints.

In the primal problem, the objective is to maximize the expression z, which is a linear combination of the decision variables x1, x2, and x3. The coefficients 7, -5, and -2 represent the weights assigned to each variable in the objective function. The constraints represent the relationships and limitations imposed on the variables. The first constraint is an equality constraint, which means that the left-hand side of the equation must equal the right-hand side. The second constraint is an inequality constraint, indicating that the value of the expression 2x1 + x2 must be less than or equal to a certain value.

To solve this linear programming problem, various optimization techniques such as the simplex method or interior point methods can be applied. These methods iteratively adjust the values of the decision variables to find the optimal solution that maximizes the objective function while satisfying the given constraints. By solving the primal problem, the values of x1, x2, and x3 can be determined, leading to the maximum value of the objective function z.

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Answer:

x = -2, y = -4

Step-by-step explanation:

Take the first equation-   -2y = 2 - 3x
Arrange it first-
-3x + 2y = -2

Multiply is by 5 on both sides
5(-3x + 2y) = 5(-2)
-15x + 10y = -10

Take the second equation-    -5y = 10 - 5x
Arrange it-
-5x + 5y = -10

Multiply is by 2 on both sides
2(-5x + 5y) = 2(-10)
-10x + 10y = -20

Subtract second equation from the first one-

  -15x + 10y = -10
-  -10x + 10y = -20
= -5x = 10

-5x = 10
x = 10/(-5)
x = -2

Substitute the value of x in Equation 1
-2y = 2 - 3(-2)
-2y = 2 + 6
-2y = 8
y = 8/(-2)
y = -4

Hope it helps ;)

Answer:(0,-1)

Step-by-step explanation:

Use the distance formula to solve for the direct distance from (4,-4) up to (-14,8)

Since 1 grid is equal to 0.125 miles. Multiply the distance in units and we get

Rounding to 2 decimal places, the direct distance is 2.70 miles.

A) The stated the null and alternative hypotheses are defined as

H₀ : μItalian = μSeafood = μsteakhouse

Hₐ : Not all the population means are equal. So, correct answer is option (a).

B) The value of the test statistic is equals to the 6.70. The p-value is equals to the 0.0056.

C) Conclusion : The null hypothesis H0 is rejected, so there is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

We have a consumer reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains. The above table data show the meal prices ($) obtained for the 24 restaurants sampled ( 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses). So, sample size , n = 24

Significance level = 0.05

A) For Hypothesis testing, the null and alternative hypothesis are defined as

H₀ : μItalian = μSeafood = μsteakhouse

Hₐ : Not all the population means are equal. So, correct answer is option (a).

B) We have more than two groups for analysis so we use ANOVA test to compare the means among three or more groups. Using the Excel the above second table is made which represents the mean, standard deviations and standard error for data. It also contains ANOVA table. So,

Mean value of Italian = 17

Mean value of Seafood = 19

Mean value of steakhouse = 24

Uding all the above details or Excel command, The value of the F test- statistic value = 6.70

Using the distribution table, the p-value for test-static value 6.70 is 0.0056.

C)Now, we see P-value = 0.0056 < 0.05, which implies the null hypothesis is rejected. Thus, There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

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Complete question:

You may need to use the appropriate technology to answer this question. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains. † One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for a local newspaper thought that it would be of interest to her readers to conduct a similar study for restaurants located in her city. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices ($) obtained for the 24 restaurants sampled.

Italian Seafood Steakhouse

$12 $17 $23

13 18 18

16 18 24

16 27 25

18 23 21

19 15 23

18 20 28

24 14 30

Use α = 0. 05 to test whether there is a significant difference among the mean meal price for the three types of restaurants. State the null and alternative hypotheses.

a) H0: μItalian = μSeafood = μSteakhouse

Ha: Not all the population means are equal.

b)H0: μItalian ≠ μSeafood ≠ μSteakhouse

Ha: μItalian = μSeafood = μSteakhouse

c) H0: At least two of the population means are equal.

Ha: At least two of the population means are different.

d)H0: Not all the population means are equal.

Ha: μItalian = μSeafood = μSteakhouse

e) H0: μItalian = μSeafood = μSteakhouse

Ha: μItalian ≠ μSeafood ≠ μSteakhouse

B) Find the value of the test statistic. (Round your answer to two decimal places. )

test statistic=___

Find the p-value. (Round your answer to four decimal places. )p-value =____

V)What is your conclusion?

a)Do not reject H0. There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

b)Reject H0. There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

c)Do not reject H0. There is sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants.

d)Reject H0. There is not sufficient evidence to conclude that the mean meal prices are not all the same for the three types of restaurants

Answer:

Step-by-step explanation:

area circle = πr²   or  π(d/2)²  but how to find the diameter?

The only angles I can see to calculate is in the small right triangle

The smaller angle on the right is ...

        sin Ф = opp/hyp = 6/10    Ф = 36.87°

This angle is the same as the small angle on the LARGE right triangle

So now I want to calculate the side (diameter) opposite the smaller angle

      sin Ф = opp/hyp = diameter/300 = sin 36.87°    

                  diameter = 300 sin 36.87°

                                  = 300 (6/10)

                                  = 180 ft

area circle = πr²   or  π(d/2)²

area circle =  π(180/2)²

area circle = 25446 ft²  which is close to answer A  25434 ft²

There is actual no need to find the sin Ф wasted step      

just use 6/10  small triangle     is similar to diameter/300   the large triangle

  opp / hyp small  6/10  = diameter/300    diameter = 180

  area circle =  π(180/2)²  = 25446

Answer:

Solution given:

length [l]=h

for triangle

base[b]=4.8m

height [H]=6.1m

Now

area of triangular face=½{b*H)=½(4.8*6.1)=14.64m²

Volume of triangular prism =80.52m³

area of triangular faces×length=80.52

14.64*h=80.52

h=80.52/14.64

h=5.5m

height=5.5m

Area of base

Now

Answer:

-4

Step-by-step explanation:

(-6/7) / (3/14)

-0.8571428571 / 0.2142857143

-4

\(\huge\pink{\mathbb{Answer:}}\)

The simplest form of

\( \frac{ - 6}{7} \: \div \frac{3}{4} \)

is

\(-4\)

\(\huge\color{purple}{ \colorbox{orange}{\colorbox{white} {ChaEunWoo2009}}}\)

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Answer:-12x

Step-by-step explanation:

just trust me on this

Answer: (n + 5)(n - 5)

Explanation: In this problem, we have a binomial that's the difference of two squares because n² and 25 are both perfect squares and we are subtracting or taking the difference of these two squares.

Since the difference of two squares factors as the product of two binomials, we can setup our parenthses and in the first position, we use the factors of n² that are the same which are n · n.

In the second position, we use +5 and -5 as our factors of -25.

So our answer is (n + 5)(n - 5).

Answer:

b.

\( {4}^{15} \times {5}^{10} \)

Step-by-step explanation:

In the given expression u can bring the 5^-2 in the neumerator making it 5^2.

Then multiply both powers by 5.

You must explicitly state that the null hypothesis is demonstrated to be true in cases where there is insufficient evidence to disprove it.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H₀

Even though we are unable to rule out the null hypothesis, this does not always imply that it is accurate. The reason for this is that a hypothesis test cannot tell which hypothesis is true or even which is more likely. It just evaluates whether there is sufficient evidence to disprove the null hypothesis.

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Answer:

taco is 80 cents burrito is 1.50

Step-by-step explanation:

If you make two equations, multiply one of them by two so burritos have the same constant, subtract and find b. Then, substitute b into one of the equations to find t. Hope it helps.   :)

The average rate of change of the given function is 10π.

Given function

a = πx^2

Where a is the area of a circle with radius x

The radius changes from x = 4 to x = 6.

Calculating the average rate of change of function:

The method of finding the average rate between the function value over a certain interval is called the average rate of change.

The formula is given by :

Average = \(\frac{f(b)-f(a)}{b-a}\)

Where f(a) and f(b) are the function value over the limit a and b.

Average = \(\frac{f(6)-f(4)}{6-4}\)

= \(\frac{\pi (6)^{2} -\pi (4)^{2} }{6-4}\)

= \(\frac{\pi (36-16)}{2}\)

= \(\frac{20\pi }{2}\)

= 10π

The average rate of change of the given function is 10π.

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In the given problem, there are multiple scenarios related to combinations, permutations, and queuing theory.

1. The number of combinations of seasoning agents can be calculated using the formula for combinations: C(n, r) = n! / (r!(n-r)!). In this case, selecting 5 out of 8 brands gives C(8, 5) = 8! / (5!(8-5)!) = 56 combinations.

2. The number of displays the salesperson can make when the order of display is important can be calculated using the formula for permutations: P(n, r) = n! / (n-r)!. In this case, selecting 4 out of 9 products gives P(9, 4) = 9! / (9-4)! = 9! / 5! = 9 * 8 * 7 * 6 = 3,024 displays.

3. To determine the arrival rate (λ) and service rate (μ), we need to convert the given time parameters. The arrival rate λ can be calculated by dividing the average rate of 10 clients every 4 hours by the time duration in hours. Therefore, λ = 10 clients / 4 hours = 2.5 clients per hour. The service rate μ can be calculated by taking the reciprocal of the mean service time, which is 1/20 minutes = 3 clients per hour.

4. The time a client waits in the queue can be calculated using Little's Law, which states that the average number of customers in a system (L) is equal to the arrival rate (λ) multiplied by the average waiting time (W). Since the average number of customers in the system is not provided, this part cannot be answered.

5. The average waiting time for a client in the entire system can be calculated using Little's Law. Assuming a stable system, the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average waiting time in the system (W). Therefore, W = L / λ. Since the average number of customers in the system is not provided, this part cannot be answered.

6. The probability that the system is idle (P(idle)) can be calculated using the formula P(idle) = 1 - (λ / μ). Substituting the values, P(idle) = 1 - (2.5 clients per hour / 3 clients per hour) = 1 - 0.8333 = 0.1667, or approximately 16.67%.

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The probability that at least one of the numbers appears exactly 10 times in the sequence of spinning the spinner 30 times is approximately 0.4218 or 42.18%. This is computed using the binomial distribution.

To calculate the probability, we can consider the complementary event, which is the probability that none of the numbers appears exactly 10 times in the sequence.

Let's calculate the probability of each number not appearing exactly 10 times. The probability of any number appearing exactly 10 times is \((1/3)^10\), and the probability of it not appearing exactly 10 times is 1 -\((1/3)^10\). Since there are three equally-likely regions, the probability for each number not appearing exactly 10 times is\((1 - (1/3)^10)^3\).

Since these events are independent, the probability that none of the numbers appears exactly 10 times is the product of the probabilities for each number. Therefore, the probability that none of the numbers appears exactly 10 times in the sequence is \(((1 - (1/3)^10)^3)^30\).

Finally, the probability that at least one of the numbers appears exactly 10 times is 1 minus the probability that none of the numbers appears exactly 10 times. So the probability is 1 - \(((1 - (1/3)^10)^3)^30\), which is approximately 0.4218 or 42.18%.

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For the options C, D, and E, (where the 3 sides are given) result in the construction of unique triangles.

We will have unique triangles only if the length of the 3 sides are completely determined, so we need to know the 3 sides, or two sides and one angle.

With that in mind, for options C, D, and E (in the 3 cases the 3 sides of the triangles are given). Then for these 3 options, we can make a unique triangle.

While for the first two options, where we only know the angles, we can make infinite triangles.

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Sarah's score of 85 puts her at the 40th percentile in her class.

This means that 40% of the students in her class got a score equal to or below her score, and 60% of the students got a score above her score.

Percentile is a statistical measure that indicates the percentage of a population that is below or equal to a certain score or value.

If a student scores in the 90th percentile, it means that they have performed better than 90% of the other students in their class.

To calculate the percentile rank of a student, you need to follow these steps:

Determine the total number of scores in the class, including the student's score.

Sort the scores in ascending order.

Count the number of scores that are below the student's score.

This is called the student's rank.

Divide the student's rank by the total number of scores and multiply the result by 100.

This gives you the student's percentile rank.

Let's say that a class of 30 students took a math test, and one student, Sarah, received a score of 85.

To determine Sarah's percentile rank, you would follow these steps:

The total number of scores in the class is 30.

Sorting the scores in ascending order, Sarah's score of 85 falls between the 21st and 22nd scores.

There are 20 scores below Sarah's score of 85.

Her rank is 21.

Dividing Sarah's rank (21) by the total number of scores (30) and multiplying by 100 gives us her percentile rank:

(21/30) × 100 = 70.

This means that Sarah scored higher than 70% of the other students in the class.

Percentile rank is a useful measure for comparing individual scores to a larger group or population.

Percentile rank, you can easily determine a student's score falls in comparison to their peers.

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Answer: x+-2 and x+-1

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

m angle A and m angle C are equal sine two of those sides are equal. You would do 3x + 40 = x +50

You subtract x, leaving it to be 2x + 40 = 50

Subtract the 40, leaving it be 2x = 10

Divide both sides by 2, which leaves x = 5

and then you would do 3(5) + 40, which is 55

Answer:

distance of his partner from the base of the tower ≈ 53.6 ft(nearest tenth)

Step-by-step explanation:

The forest ranger is on top of a fire tower and he sees his partner on the ground at the angle of depression of 40°. The tower is 45 ft tall.  

The illustration forms a right angle triangle.

The adjacent side of the triangle is the distance from the partner to the base of the tower.

Using tangential ratio

tan 40° = opposite/adjacent

tan 40° = 45/adjacent

cross multiply

adjacent tan 40° = 45

divide both sides by tan 40°

adjacent =45/tan 40°

adjacent = 45/0.83909963117

adjacent = 53.6289116667

distance of his partner from the base of the tower ≈ 53.6 ft

Answer:

it will be n=4

Step-by-step explanation:

12,000 1-n/5 =2,400n

12000-12000=2,400

2,400-12000=-9600

                      -2400  n=4

Answer:

29/45 ≈ 0.644

Step-by-step explanation:

There are 450 students in total

110-60=50 students are only in the choir

240-60=180 students are only in the band

60 students are in both

160 students are neither in the band nor in the choir

So the chance of being in either is (50+60+180)/450 = 29/45 ≈ 0.644

Answer:

D. 2200 ft.lb/s

Explanation:

First, recall the standard conversion between horsepower and foot-pounds per second.

Therefore:

The correct choice is D.