9. Only 12 students can be in the next school play.
Let t represent the number of students who tried
out for the play. The number of students who tried
out but did not get a role is 42.

Answer:

0.13 cm per second

Step-by-step explanation:

Lets convert the minutes to seconds:

3/4 minutes = 3/4(60) = 45 seconds

The snail traveled 5.85 cm in 45 seconds

To find out the speed per second, we set up a proportion:

\(\frac{5.85}{45} = \frac{x}{1}\)      where 45 and 1 represent the number of seconds, and 5.85 and x represent the distance in that set of time

Let's solve for x, or the distance in 1 second:

\(\frac{5.85}{45}=\frac{x}{1}\\\\\\\frac{5.85*1}{45x}\\\\\\x = \frac{5.85}{45}\\\\\\\\\\x = 0.13\)

The snail travels 0.13 cm per second.

-Chetan K

Answer:MN

Step-by-step explanation:

I just did it lol

The vector  \(\vec {MN}\) that would map point A to its image T (A).

A vector is a quantity that possesses magnitude, direction, and adheres to the law of vector addition.

Given:

Two vectors \(\vec {PQ}\) and \(\vec {MN}\).

To map point A to its image T (A):

The translated map would be,

\(\vec {MN}\).

Therefore,  \(\vec {MN}\) is the vector.

To learn more about the vectors;

brainly.com/question/13188123

#SPJ2

I don't know the correct answer but I know its not 0.60 watts

Answer:

it is 3.6 watts

Step-by-step explanation:

there is no explanation but if needed proof i will try to post a picture of it

The coordinates of point D in the parallelogram ABCD are (15, 10).

To find the coordinates of point D, we can use the properties of a parallelogram. In a parallelogram, opposite sides are parallel and congruent. Therefore, we can use this information to determine the coordinates of point D.

Let's consider the given points:

A(-3, 5)

B(7, 12)

C(5, 3)

Since opposite sides of a parallelogram are parallel, the vector connecting points A and B should be equal to the vector connecting points C and D. We can express this as:

AB = CD

To find the vector AB, we subtract the coordinates of point A from the coordinates of point B:

AB = (7 - (-3), 12 - 5)

= (10, 7)

Now, we can express the vector CD using the coordinates of point C and the vector AB:

CD = (5, 3) + (10, 7)

= (15, 10)

Therefore, the coordinates of point D are (15, 10).

for such more question on coordinates

https://brainly.com/question/30107320

#SPJ8

(a) derivative of the given function is f'(x) = O + (d/dxZ)O (b) Slope of the tangent line at x=4 is f'(4) = O + (d/dxZ)O (c) equation of the tangent line to the graph at x = 4 is y = f'(4) * x + (f(4) - 4f'(4)).

Given the function: f(x) = zVOTo find: a) Derivative of the function, b) Slope of the tangent line to the graph at x = 4, c) Equation of the tangent line to the graph at x = 4.

a) The derivative of the given function f(x) = zVO is given by;f(x) = zVO ∴ f'(x) = (zVO)'

Differentiating both sides w.r.t x= d/dx (zVO) [using the chain rule]=

\(zV(d/dxO) + O(d/dxV) + (d/dxZ)O (using the product rule)= z(0) + O(1) + (d/dxZ)O\)(using the derivative of O, which is 0) ∴

\(f'(x) = O + (d/dxZ)O= O + O(d/dxZ) [using the product rule]= O + (d/dxZ)O= O + (d/dxZ)O [as (d/dxZ)\) is the derivative of Z w.r.t x]

Thus, the derivative of the given function is f'(x) = O + \((d/dxZ)O\)

b) Slope of the tangent line to the graph at x = 4= f'(4) [as we need the slope of the tangent line at x=4]= O + (d/dxZ)O [putting x = 4]∴ Slope of the tangent line at x=4 is f'(4) = O + (d/dxZ)O

c) Equation of the tangent line to the graph at x = 4The point is (4, f(4)) on the curve whose tangent we need to find. The slope of the tangent we have already found in part

(b).Let the equation of the tangent line be given by: y = mx + c, where m is the slope of the tangent, and c is the y-intercept of the tangent.To find c, we need to substitute the values of (x, y) and m in the equation of the tangent.∴ y = mx + c... (1)Putting x=4, y= f(4) and m=f'(4) in (1), we get:\(f(4) = f'(4) * 4 + c∴ c = f(4) - 4f'(4)\)

Hence, the equation of the tangent line to the graph at x = 4 is:\(y = f'(4) * x + (f(4) - 4f'(4))\)

Thus, the derivative of the function f(x) = zVO is O + (d/dxZ)O. The slope of the tangent line to the graph at x = 4 is f'(4) = O + (d/dxZ)O. And, the equation of the tangent line to the graph at x = 4 is y = f'(4) * x + (f(4) - 4f'(4)).

Learn more about derivative here:

https://brainly.com/question/29166048

#SPJ11

Answer:The slope represents ur mom

Step-by-step explanation:

Answer:

It's in Spanish I didn't know it and I used the application

Answer:

Answer Of this question is 1000

Answer:

19 hours

Step-by-step explanation:

Issac shovels driveways to earn money. He can shovel 14 driveways in 8 hours. Earns $25.00 for each driveway. Issac is saving up to buy a new computer that costs $831.25. How many hours does Issac need to work to earn enough money to purchase the computer?

Step 1 find the number of driveways to shovel

25x = $831.25

x = $831.25/25

= 33.25 driveways

Step 2

He can shovel

14 driveways = 8 hours

33.25 driveways = x

Cross Multiply

14x = 8 × 33.25

x = 8 × 33.25/14

x = 19 hours

The rate of the plane in still air is 550 mph, and the rate of the wind is 50 mph.

Let's denote the rate of the plane in still air as "p" and the rate of the wind as "w".

When the plane flies into the wind, its effective speed is reduced by the speed of the wind.

So, the speed of the plane relative to the ground is:

p - w

Similarly, when the plane flies with the wind, its effective speed is increased by the speed of the wind, so its speed relative to the ground is:

p + w

We know that the distance traveled by the plane is 3000 miles in both cases, so we can set up two equations based on the formula:

distance = rate x time

When the plane flies into the wind:

3000 = (p - w) x 6

And when the plane flies with the wind:

3000 = (p + w) x 5

Now we have two equations with two unknowns, which we can solve for "p" and "w".

Let's start by simplifying both equations:

Equation 1: 3000 = 6p - 6w

Equation 2: 3000 = 5p + 5w

We can then solve for one of the variables in terms of the other. For example, we can solve for "p" in terms of "w" by rearranging Equation 2:

5p = 3000 - 5w

p = (3000 - 5w) / 5

We can then substitute this expression for "p" into Equation 1 and solve for "w":

3000 = 6[(3000 - 5w) / 5] - 6w

Multiplying both sides by 5:

15000 = 6(3000 - 5w) - 30w

Distributing the 6:

15000 = 18000 - 30w - 30w

Combining like terms:

15000 = 18000 - 60w

Subtracting 18000 from both sides:

-3000 = -60w

Dividing both sides by -60:

w = 50

Now that we know the rate of the wind is 50 mph, we can substitute this value into either Equation 1 or Equation 2 to solve for "p".

Let's use Equation 2:

3000 = 5p + 5(50)

3000 = 5p + 250

2750 = 5p

p = 550.

For similar question on effective speed.

https://brainly.com/question/28605842

#SPJ11

To calculate a 95% confidence interval for the mean weight per apple based on the given data, we need to determine which test should be used and then calculate the interval.

The appropriate test depends on the sample size and whether the population standard deviation is known.

5. Test selection: Since the population standard deviation is known in this case and the sample size is large (n=49), the appropriate test to use is the one sample z-test for means.

Confidence interval calculation: To calculate the confidence interval, we can use the formula:

Confidence interval = sample mean ± (z-value * (standard deviation / √sample size))

In this case, the sample mean is 122.5 grams, the standard deviation is 12 grams, and the sample size is 49. The z-value for a 95% confidence level is approximately 1.96 (obtained from a standard normal distribution table).

Calculating the confidence interval:

Confidence interval = 122.5 ± (1.96 * (12 / √49))

Confidence interval = 122.5 ± (1.96 * 1.714)

Confidence interval ≈ [119.68, 125.32]

Therefore, the correct answers are B (One sample z-test for means), A ([119.68, 125.32]), and D (We are 95% certain that the population mean falls within the interval) for problems 4, 5, and 6, respectively.

To learn more about mean click here:

brainly.com/question/31101410

#SPJ11

If they work together, they will take 14.3 min to shovel the parking lot.

Provided to us :

time taken by Sebastian to shovel the parking lot = 50 min

time taken by Clair to shovel the parking lot = 20 min

both are doing the same work , so we take work as 1

Now , rate of doing work = work / time

Sebastian's rate of doing work = 1 /50

Clair's rate of doing work =  1/20

If they work together , the rate of doing work will

become = 1/50 + 1/20 = 7/100

So, the time for both to do the same work together will be

time = work / rate

time = 1 / (7/100)

time = 100/7

time = 14.3 minutes

So the time taken by both to work together and clear the parking lot will be 14.3 minutes.

learn more about work-time problems here :

https://brainly.com/question/19382734

#SPJ4

Answer:

b. angles 1 and 8

Step-by-step explanation:

alternate exterior angles theorm

33

Since it is parallel, that means that the line will have the same slope. Just simplify and add the x values in the first equation to get 33x.

The quadratic equation that represents the solution is F: p(x) = x² - 49.

The term "quadratic" refers to functions where the highest degree of the variable (in this example, x) is 2. A quadratic function's graph is a parabola, which, depending on the sign of the leading coefficient a, can either have a "U" shape or an inverted "U" shape.

Algebra, geometry, physics, engineering, and many other branches of mathematics and science all depend on quadratic functions. They are used to simulate a wide range of phenomena, including population dynamics, projectile motion, and optimisation issues.

Given that the solution of the quadratic function are x = -7 and x = 7 thus we have:

p(x) = (x + 7)(x - 7)

Solving the parentheses we have:

p(x) = x² - 7x + 7x - 49

Cancelling the same terms with opposite sign we have:

p(x) = x² - 49

Hence, the quadratic equation that represents the solution is F: p(x) = x² - 49.

Learn more about quadratic equation here:

https://brainly.com/question/30098550

#SPJ1

Point D's coordinates are mathematically given as: ( -0.5, 0.25 ).

The meaning of coordinate geometry.

What are the coordinates of D if n=5?

A coordinate plane is a flat, two-dimensional surface formed by the intersection of the x- and y-axes. The use of a collection of numbers to precisely locate points is called a "coordinate system" in geometry.

From C(2.5, 1.25) to E(5, 15), with n = 5, point D is 1/n of the way.

Point D will have these coordinates:

D = (1 / n) C

= ( 1 / n ) ( -2.5 , 1.25 )

= (1 / 5) ( -2.5 , 1.25 )

= ( -0.5 , 0.25 )

In conclusion, point D coordinates are ( -0.5, 0.25 ).

Read more about Coordinate geometry

brainly.com/question/18269861

#SPJ1

To check the if a table represents a linear function we have to find the rate of change between the first two ordered pairs can be compared to the rate of change between the first and last ordered pairs to see if they are the same.

Well, a straight line is proportional to a linear function (on a graph). And the answers to the numbers can't be the same. If the X input is 5, for instance, and the Y output is 7, then Another non-linear X input of 5 and Y output of 8 follows.

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

To know more about Straight line click on below link:

https://brainly.com/question/29223887#

#SPJ4

Answer:

The population of the world is 200 times of the population of Canada.

Step-by-step explanation:

Given that,

Canada's population = \(3.5\times 10^7\)

The population of world =  \(7.0\times 10^9\)

We need to find how many times larger is the population of the world compared to Canada's population. It can be solved as follows :

\(\dfrac{W}{C}=\dfrac{7.0\times 10^9}{3.5\times 10^7}\\\\\dfrac{W}{C}=200\\\\W=200C\)

So, the population of the world is 200 times of the population of Canada.

Considering the probabilities of each outcome, it is much more likely that Janet wins than David, hence this is not a fair method.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The 36 total outcomes for the roll of two dice are given as follows:

The number of outcomes in which the sum is less than 6 is:

10.

Hence the probability that David wins is:

p = 10/36.

Janet winning is complementary to David, hence the probability she wins is:

p = 26/36.

From the probabilities, it is much more likely that Janet wins than David, hence this is not a fair method.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

The correct answer is D: A and B ( Accounts receivable and cost goods )

Accounts receivable represents the amount of money owed to a company by its customers for goods or services that have been delivered but not yet paid for. As sales increase, the amount of accounts receivable also tends to increase since more customers will have outstanding balances.

Cost of goods sold (COGS) represents the direct costs associated with producing or purchasing the goods that are sold by a company. It includes the cost of raw materials, labor, and other direct expenses. As sales increase, the COGS also tends to increase since more goods are being produced or purchased for sale.

COGS is directly influenced by the level of sales because it is tied to the inventory turnover. When goods are sold, their associated costs are transferred from the inventory account to the COGS account. As sales increase, more goods are sold, and therefore, more costs are transferred to COGS.

COGS is calculated by subtracting the ending inventory value from the sum of the beginning inventory and the purchases made during a specific period. It is a key component in determining a company's gross profit and gross profit margin, which are important indicators of profitability.

On the other hand, administrative salaries (option c) typically do not vary directly with sales. Administrative salaries are usually fixed expenses that are paid to employees for their administrative roles regardless of the level of sales.

Therefore, the correct answer is option d. A and B, as both accounts receivable and cost of goods sold vary with sales.

To know more about gross profit margin, refer here :

https://brainly.com/question/32124148#

#SPJ11

Using the substitution u = sinh^2 x, the integral ∫^[infinity]_0 sinh^αx / cosh^βx dx evaluates to 1/2 B(α+1/2, β α/2), where -1 < α < β.

The integral ∫^[infinity]_0 sinh^αx / cosh^βx dx can be evaluated using the substitution u = sinh^2 x. This substitution helps us transform the integral into a form that can be expressed in terms of the Beta function.

By substituting u = sinh^2 x, we obtain the new integral ∫^[infinity]_0 u^(α/2 - 1/2) / (1 + u)^(β/2) du. This substitution allows us to work with the variable u instead of x.

Next, we recognize that the integral can be expressed using the Beta function, which is defined as B(p, q) = ∫_0^1 t^(p-1) (1-t)^(q-1) dt. To achieve this, we make the substitution t = u/(1+u), which gives us dt = du/(1+u)^2.

Substituting these new variables, the integral becomes ∫_0^1 (u/(1+u))^(α/2 - 1/2) (1/(1+u))^((β/2) - 1) du.

Simplifying further, we have ∫_0^1 u^(α/2 - 1/2) (1+u)^(-α/2 - β/2) du. This expression can be expressed as B(α/2 + 1/2, -α/2 - β/2) using the properties of the Beta function.

Finally, using the property of the Beta function B(p, q) = B(q, p), we can rewrite B(α/2 + 1/2, -α/2 - β/2) as 1/2 B(α + 1/2, β α/2), which gives us the final result.

In conclusion, the integral ∫^[infinity]_0 sinh^αx / cosh^βx dx evaluates to 1/2 B(α + 1/2, β α/2), where -1 < α < β. This result is obtained by applying the substitution u = sinh^2 x, rewriting the integral in terms of u, and utilizing the properties of the Beta function.

Know more about the Beta function click here:

https://brainly.com/question/31693416

#SPJ11

Answer:

15.925

Step-by-step explanation:

Answer:

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

D)

hope this helped

Step-by-step explanation:

Step-by-step explanation:

the answer is 3.142

\(3.142 \times 20 \times 18 \\ 2 = 1131.2 \times 3.142 \times 10^{2} = 628.4 \\ \\ = 1759.52\)

Answer:

point-slope form: y - 6 = -1/3(x + 6)

slope-intercept form: y = -1/3x + 4

Step-by-step explanation:

Work shown in attachment

The given two-way Frequency table, there are 33 left-handed students who are not in the music program.

The number of left-handed students who are not in the music program, we need to examine the data presented in the two-way frequency table.

From the table, we can see that the number of left-handed students in the music program is 15, and the total number of left-handed students is 48.

the number of left-handed students not in the music program, we subtract the number of left-handed students in the music program from the total number of left-handed students.

Number of left-handed students not in the music program = Total number of left-handed students - Number of left-handed students in the music program

Number of left-handed students not in the music program = 48 - 15

Calculating this, we find that the number of left-handed students not in the music program is 33.

Therefore, there are 33 left-handed students who are not in the music program, based on the data provided in the two-way frequency table.

In conclusion, based on the given two-way frequency table, there are 33 left-handed students who are not in the music program.

To know more about Frequency .

https://brainly.com/question/28821602

#SPJ8

A pond contains 100 fish, of which 30 are carp. if 20 fish are caught, what are the mean and variance of the number of carp among the 20. This Statement is based on the assumption that : X follows hyper-geometric distribution with the given information.

According to the Question:

Total fish = 100

Carp = 30

Number of fish caught = 20

Now,

The random variable X follows hyper-geometric distribution.

Mean = 30 *20 / 100

         = 600/100 = 6

Therefore,

Variance = 30*20/100 * ((20-1)*(30-1)/100-1 + 1-30*20/100)

⇒ Variance = 600/100 * 56/99

⇒ Variance = 112/33

⇒ variance = 3.1111 ≈ 3.12

Assumptions:

Is that X follows hyper-geometric distribution with the given information.

Hyper - Geometric Distribution:

In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that yields n draws without replacement for k successes (if the drawn object has a particular property). random draw). From a finite population of size N containing exactly K objects with this property, each draw either succeeds or fails. In contrast, the binomial distribution describes the probability of k successes in n draws with replacement.

Learn More about Variance:

https://brainly.com/question/29505178

#SPJ4

SOLUTION:

One can afford $1,100 per month mortgage payment and one has found a 30-year loan at 3.45% interest.

(a)

(b) The total money he would be paying

(c) $The amount of the money that is interest i;

The test statistic for the hypothesis would be 1.413.

Given that the participants in its new diet program lose, on average, more than 13 pounds and the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds.

The objective is to text the advertisement's claim that participants in new diet program lose weight, on average, more than 13 pounds.

Hypothesis:

Null hypothesis:H₀:μ=13

Alternative hypothesis:Hₐ:μ>13

Here, μ be the mean weight loss of all participants.

n=30,

Degree of freedom n-1=30-1=29

\(\bar{x}\)=13.8 and s=3.1

To test the null hypothesis H₀, the value of test static would be calculated as follows:

\(\begin{aligned}t&=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\\ t_{29}&=\frac{13.8- 13}{\frac{3.1}{\sqrt{30}}}\\ &=\frac{0.8}{0.566}\\ &=1.413\end\)

Hence, the value of the test static for the hypothesis with the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds is 1.413.

Learn more about hypothesis from here brainly.com/question/14783359

#SPJ4