The figure below is made of 2 rectangular prism.
What is the volume of this figure?

triangle C

Step-by-step explanation:

If you draw it out, it looks unique

The average rate of change of f(x) from x = -3 to x = 6 is 7.

What is meant by average?

The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.

To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.

For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:

[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]

The value of the function at [tex]x = 6[/tex] is:

[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]

The difference in the function values is:

[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]

The difference in the input values is:

6 - (-3) = 9

Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:

average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]

So, the average rate of change of f(x) from x = -3 to x = 6 is 7.

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Answer:

Step-by-step explanation:

We can use the standard normal distribution to solve this problem by standardizing the score.

z = (x - mu) / sigma

Where:

x = 70 (score we are interested in)

mu = 60 (mean score)

sigma = 7 (standard deviation)

z = (70 - 60) / 7 = 1.43

Using a standard normal distribution table or calculator, we can find the probability that z is greater than 1.43. The probability is approximately 0.0764.

Therefore, the probability that a randomly selected student scored more than 70 on the exam is 0.0764 (or about 7.64%).

Answer:

20$

Step-by-step explanation:

since there is a discount we first find the discount allowed which is 40$. After we also use the coupon which is 50% off. then you get 20$ as your answer

The probability that it rains at least one day this weekend is [tex]$\frac{a}{b}$[/tex],  so the value of a+b is given as 107.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

Let x be the probability that it rains on Sunday given that it doesn't rain on Saturday then we have,

3/5x + 2/5(2x) = 3/10

7/5x = 3/10

x = 3/14.

Therefore, the probability that it doesn't rain on either day is,

[tex]$\left(1-\dfrac{3}{14}\right)\left(\dfrac{3}{5}\right)=\dfrac{33}{70}$[/tex]

Therefore, the probability that rains on at least one of the days is

[tex]$1-\dfrac{33}{70}=\dfrac{37}{70}$[/tex],

so adding up the 2 numbers, we have,

37 + 70 = 107.

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Complete question;

There is a 40% chance of rain on Saturday and a 30% chance of rain on Sunday. However, it is twice as likely to rain on Sunday if it rains on Saturday than if it does not rain on Saturday. The probability that it rains at least one day this weekend is [tex]$\frac{a}{b}$[/tex], where a and b are relatively prime positive integers. Find a+b.

On average, 50% of athletes are able to begin activity 90 days after a knee operation, with a standard deviation of 15 days.

This means that the median time for 50% of athletes to be able to participate is 75 days, rounded to the nearest day.

The average time for an athlete to begin activity after a knee operation is 90 days, and the standard deviation is 15 days.

Standard deviation is a measure of how spread out the data points are in a data set; a larger standard deviation means that the data points are more spread out.

In this case, 50% of athletes can begin activity within 75 days, which is the median. By rounding to the nearest day, this would be 75 days. Therefore, 50% of athletes are able to participate within 75 days, rounded to the nearest day.

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Answer:

area=36.5

Step-by-step explanation:

8×4=32

8-5=3 for the base of the triangle

7-4=3 for the height of the triangle

3×3=9

9÷2=4.5

4.5+32=36.5

area=36.5

Your longitude in DMS is 135 degree. So the option D is correct.

This is because there are 12 hours left in the local time ( i.e. 12 hours noontime or mid-day).

As UT (or GMT) time is 9 p.m., there are 9 hours between GMT time and local time.

9 hours = 9 × 60 minutes = 540 minutes

Now, we know that:

Every four minutes, the Earth turns one degree.

Thus, 1-degree longitude difference = 4 minutes

Or, 4 minutes of time difference = 1 degree of longitude

Or, 1 minute of time difference = 1/4 degree of longitude

Or, 540 minutes of time difference = (1/4) × 540 degrees of longitude

540 minutes of time difference = 135 degrees of longitude

Also, we can infer that the current location is in the Western hemisphere because we know that it is 9 hours behind GMT (or UT) time.

Hence, the longitude of the current location = 135⁰

So the option 4 is correct.

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The complete question is:

Your chronometer is set for Greenwich Mean Time (GMT or Universal Tim, UT). High noon at your present location is 9 pm UT. What is your longitude in DMS (not decimal degrees)?

1. 30° 18'W

2. 30° 16'W

3. 30° 17'W

4. none of the above

Answer:

For problem a: 0,4 0,5 0,6

For Problem B: 1,0 2,0 3,0

Step-by-step explanation:

Graph each equation on a graph Figure out either solid or dotted line. Then depending on <=,<,>,>= is whre you shade on your graph. The spot where both lines meet when shaded is your solution area and you pick any spot on that. You can check your answer by plugging in ordered pairs for your X,Y values in the system.

As per integration, the height of the water in the barrel at time = 2 hours is 1.672 feet (option C).

The formula is r(t) = 47-15, where t is the time in hours since the rain began. This formula tells us how fast the water level is changing at any given time t.

In this case, we're asked to find the height of the water in the barrel at t = 2 hours, given that the height at t = 1 hour is 0.75 feet. To solve this problem, we'll integrate the rate formula from t = 1 to t = 2, and add the starting height of 0.75 feet.

∫(47-15)dt from t=1 to t=2 = [47t-15t] from t=1 to t=2 = 0.922

So the total increase in height from t=1 to t=2 is 0.922 feet. Adding this to the starting height of 0.75 feet, we get the height of the water at t=2:

0.75 + 0.922 = 1.672 feet

Therefore, the correct option is (C).

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The given equation 3x + 7y = 11 is equal to (1,-2).

The given equation is 3x + 7y = 11.

To find the solution of the equation, we need to consider the given options:

(6,-1)(1,-2)(0,4)

Now substitute each value of x and y in the given equation, we get,

If x = 6 and y = -13(3 × 6) + (7 × -1) = 18 - 7 = 11 ≠ 11

If x = 1 and y = -2(3 × 1) + (7 × -2) = 3 - 14 = -11 ≠ 11

If x = 0 and y = 4(3 × 0) + (7 × 4) = 0 + 28 = 28 ≠ 11

Therefore, the given equation 3x + 7y = 11 is equal to (1,-2).

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The function f(x) = x² - 7 is an example of a function that is neither even nor odd, as it does not exhibit either type of symmetry.

To determine whether a function is even, odd, or neither, we need to examine its algebraic form and look for a particular type of symmetry.

Let's apply this concept to the given function, f(x) = x² - 7. To determine whether f(x) is even or odd, we need to evaluate f(-x) and compare it to f(x).

f(-x) = (-x)² - 7 // substitute -x for x

= x² - 7 // simplify

Comparing f(-x) to f(x), we can see that they are not equal:

f(-x) = x² - 7

f(x) = x² - 7

Since f(-x) is not equal to f(x), the function is not even. To determine whether it is odd, we need to evaluate f(-x) + f(x) and see if the result is zero.

f(-x) + f(x) = (x² - 7) + (x² - 7) // substitute -x for x in the second term

= 2x² - 14

Since f(-x) + f(x) is not equal to zero for all values of x, the function is not odd either.

Therefore, we can conclude that the given function, f(x) = x² - 7, is neither even nor odd.

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There are 100,947 ways to assign the tasks to the 7 people.

This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.

Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,

The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is

(17 + 6) choose 6 = 23 choose 6 = 100947

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Answer:

153

Step-by-step explanation:

The relationship in the row is below

4³ +2³ +1³ =64 + 8 +1 = 72

1³ + 2³ +6³= 1 + 8 + 216

3³ + 1³ + 5³ = 27 +1 +125 = 153

All numbers below the first level are raised to power 3 and added together

Probability that exactly four workers carpool to work is 0.214990847, or approximately 21.5%.

We must apply the binomial distribution formula to resolve this issue. The number of successes in a certain number of independent trials that all have the same chance of success are described by the binomial distribution, which is a type of probability distribution. In this scenario, the number of successes is the number of workers who carpool, and the probability of success is 0.1.

The binomial distribution's formula is:

[tex]P(X=k) = to (n pick k) * p*k*1-p (n-k)[/tex]

Where n is the total number of trials (in this case, 8), p is the success probability (0.1), and (n choose k) is the binomial coefficient, which is equal to [tex]n! / (k! * (n-k)![/tex] and P(X=k) is the probability of obtaining exactly k successes.

This formula can be used to determine the likelihood that four employees will carpool to work:

[tex]P(X=4) = (8 pick 4) * 0.14 * 0.94 * 0.214 = 0.214990847.[/tex]

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Answer:

10 + 2x

also,

2x + 10

Step-by-step explanation:

"a number value" is the unknown, so use a variable (letter) I used x, but could be almost any letter (avoid e and i, they have other math meanings)

"10 more than" means to add on 10. You can do that up front or at the end. Order is way more important for subtracting, so no worries here.

"product" means multiplying. So the "product of 2 and a number" is 2x.

So to translate this word phrase into an algebraic expression, you get:

10 + 2x

but also 2x + 10 is the same thing.

Answer:

To find the probability of the next customer ordering peanut butter cup, we need to determine the total number of ice cream cones and the number of cones that are peanut butter cup.

The total number of cones is:

4 + 5 + 2 + 3 + 2 = 16

The number of cones that are peanut butter cup is 2.

Therefore, the probability of the next customer ordering peanut butter cup is:

2/16 = 0.125

So, the probability of the next customer ordering peanut butter cup is 0.125 or 12.5%.

Answer:

The answer to your problem is, [tex]16cm^{2}[/tex]

Step-by-step explanation:

Sophie has a small cube shaped box.

Volume of the box is [tex]64cm^{3}[/tex]

We have to find the area of one face of the box.

Let one side of the box is x

Then volume = [tex]x^{3}[/tex] = 64

x³ = 4³

= 4

Now area of one face of the cube = x²

then area = 4² = 16 cm²

Thus the answer to your problem is, [tex]16cm^{2}[/tex]

The value of angle x in the right triangle KJI is approximately 63.4 degrees.

What is trigonometric ratios ?

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

These ratios are defined as follows:

Sine (sin) of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the angle to the length of the hypotenuse.

Tangent (tan) of an angle is the ratio of the length of the side opposite to the angle to the length of the adjacent side.

Finding the value of x :

We can use the trigonometric ratios to find the value of angle x in the right triangle KJI.

First, we can use the Pythagorean theorem to find the length of the hypotenuse KI:

[tex]KI^2 = KJ^2 + JI^2[/tex]

[tex]KI^2 = 27^2 + 48^2[/tex]

[tex]KI^2 = 729 + 2304[/tex]

[tex]KI^2 = 3033[/tex]

[tex]KI =\sqrt{3033}[/tex]

Next, we can use the sine function to find the value of angle I:

[tex]sin(I) = JI / KI[/tex]

[tex]sin(I) = 48 / \sqrt{3033}[/tex]

[tex]I = sin^-1(48 / \sqrt{3033})[/tex]

[tex]I = 63.4[/tex] degrees

Therefore, the value of angle x in the right triangle KJI is approximately 63.4 degrees.

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The probability that the number of phone calls between 2:00 pm and 2:10 pm is exactly 25 is 1/110,592,893.

To calculate this probability, use the Poisson distribution formula: P(x) = (e^-λ * λ^x) / x!, where λ = 3 x 10 = 30. Therefore, P(25) = (e^-30 * 30^25) / 25! = 1/110,592,893.

The probability that the number of phone calls between 2:00 pm and 2:10 pm is more than 25 is the sum of probabilities of all calls more than 25. That is, the probability is 1 - (e^-30 * (30^0 + 30^1 + 30^2 + ... + 30^25)) / (0! + 1! + 2! + ... + 25!).

By using the same Poisson distribution formula, the probability is 1 - 0.99988822 = 0.00011178.

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Answer:

slope of 3/4 = line C

undefined slope = line A

Step-by-step explanation:

remember that slope is [tex]\frac{rise}{run}[/tex]. Pick any two points on the graph and count up and over to find the rise/run.

OR

use the slope formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] to plug the two points into and find the slope.

- vertical lines are always undefined.

- horizontal lines have a slope of 0

To estimate the number of new subscribers in Charlottesville and Albemarle County, we'll use the given joint probability density function (pdf) f(x,y).

Here's a step-by-step explanation:
1. Identify the random variables: In this case, X represents the number of new subscribers (in thousands) in Charlottesville, and Y represents the number of new subscribers (in thousands) in Albemarle County outside of Charlottesville.
2. Understand the joint probability density function (pdf): The function f(x,y) describes the probability of having a specific number of new subscribers in both areas. The joint pdf is used to find the probability of a particular combination of X and Y values.
3. Determine the desired outcome: In this case, you want to estimate the number of new subscribers in both Charlottesville (X) and Albemarle County (Y) next year.
4. Calculate the probabilities: To find the probability of a specific combination of X and Y values, you'll need to evaluate the joint pdf f(x,y) at those values.
5. Analyze the results: Based on the probabilities you've calculated using the joint pdf, you can make informed estimates about the number of new subscribers in both areas next year.
By following these steps and using the joint probability density function f(x,y), you can estimate the number of new subscribers for F XYZ finity Cable in Charlottesville and Albemarle County next year.

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Answer:

y = -2/3x + 1/3

Step-by-step explanation:

2x + 3y = 1

3y = -2x + 1

y = -2/3x + 1/3

To sketch:

Pretend x is 3. y would be -1 2/3.

Now that you have this point, draw through the point (0, 1/3).

There ya go

Using the given values, the values of the expression and equations are:

25. -0.8

28. S ≈ 137.22

29. V ≈ 50.94

From the question, we are to evaluate each of the expressions for the given values

25.

[-b + √(b² -4ac)]/2a

a = 2, b = 8, c = 5

Substituting the values into the expression

[-b + √(b² -4ac)]/2a

= [-8 + √((8)² - 4(2)(5))]/2(2)

= [-8 + √(64 - 40)]/4

= [-8 + √(24)]/4

= [-8 + 2√6]/4

= -2 + 1/2(√6)

= -0.775

≈ -0.8

28.

S = 2πrh + 2πr²

r = 2.3, h = 7.1 (Take π = 3.14)

Thus,

S = 2(3.14)(2.3)(7.2) + 2(3.14)(2.3)²

S = 103.9968 + 33.2212

S = 137.218

S ≈ 137.22

29.

V = 4/3 πr³

r = 2.3(Take π = 3.14)

V = 4/3 × 3.14 × (2.3)³

V = 50.939

V ≈ 50.94

Hence, the value of V is 50.94

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The expression or equation that correctly represents the situation given is y = 2x.

Based on the table, for each package of cashews 2 cans of peanuts are required. Here are some examples:

Based on this relationship and assuming y represents the cans of peanuts and x represents the packages of cashews a possible equation to represent this situation would be y = 2x.

Note: This question is incomplete; below I attach the missing information:

Write an equation to represent this relationship:

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it takes Sheela to run the second leg of the race: Ascertain the total or contrast: x = 13.83.

In view of the given circumstances, plan:: 14.06+ x = 27.89

Modify variables to the left half of the situation: x = 27.89 - 14.06

Ascertain the total or contrast: x = 13.83

Speed = Distance/Time - This lets us know how slow or quick an article moves. It portrays the distance voyaged partitioned when taken to cover the distance.

Speed is straightforwardly Relative to Distance and Conversely corresponding to Time. Thus,

Distance = Speed X Time, and

Time = Distance/Speed, as the speed builds the time taken will diminish as well as the other way around.

Utilizing these recipes any fundamental issues can be settled. Nonetheless, the right utilization of units is additionally something essential to consider while utilizing equations.

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Answer: D) -20.99

Step-by-step explanation:

-4.97-2.36+-5.19-8.47 = -20.99

b + 2p = 10 ,we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. if Evelyn buys two purses, she also buys six bracelets.

Let's start by defining our variables. We'll let "b" represent the number of bracelets that Evelyn buys and "p" represent the number of purses she buys.

We know that each bracelet costs $6 and each purse costs $12. We also know that her total purchase is $60.

Using this information, we can create an equation:

6b + 12p = 60

Now we want to solve for "b", which represents the number of bracelets. To do this, we need to isolate "b" on one side of the equation. We can start by simplifying the equation by dividing both sides by 6:

b + 2p = 10

Now we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. We can use this equation to find the value of "b" given any value of "p". For example, if Evelyn buys two purses, we can substitute "p = 2" into the equation and solve for "b":

b + 2(2) = 10

b + 4 = 10

b = 6    

So if Evelyn buys two purses, she also buys six bracelets.

In general, we can see that the equation tells us that for every two purses that Evelyn buys, she buys one less bracelet. This makes sense because purses are more expensive than bracelets, so as she buys more purses, she can afford fewer bracelets.

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The sum of the first $20$ terms of the arithmetic sequence is $420$.

In an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. The sum of the first $20$ terms of this sequence can be calculated using the following formula:

Sum of the first $20$ terms = $20$/2($a_1 + a_{20})$, where $a_1$ is the first term of the sequence and $a_{20}$ is the twentieth term of the sequence.

Therefore, we need to find the first term of the sequence and the twentieth term of the sequence. To find the first term, we use the following equation:

$5 = a_2 + a_8$, where $a_2$ is the second term and $a_8$ is the eighth term.

To find the twentieth term, we use the following equation:

$5 = a_4 \times a_5$, where $a_4$ is the fourth term and $a_5$ is the fifth term.

Solving both equations, we get $a_2 = 1$ and $a_{20} = 40$. Then, we can calculate the sum of the first $20$ terms of the sequence:

Sum of the first $20$ terms = $20$/2($1 + 40$) = $420$.

Therefore, the sum of the first $20$ terms of the arithmetic sequence is $420$.

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The gorilla has a heart rate that is four times faster than the chimpanzee's when they are resting.

Expression in math is a combination of numbers, variables, operations and/or symbols that represent a value, quantity or an equation. It can either be a single term, or several terms connected by mathematical operations such as addition, subtraction, multiplication and division. Expressions are typically used in equations, formulas and problems to help solve them.

To calculate the heart rate of the gorilla, we use the power function given: H(m) = 240m. Substituting in m = 200, we get H(200) = 240(200) = 48,000 beats per minute.

To calculate the heart rate of the chimpanzee, we use the same power function: H(m) = 240m. Substituting in m = 50, we get H(50) = 240(50) = 12,000 beats per minute.

Therefore, the gorilla has a heart rate that is four times faster than the chimpanzees when they are resting.

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