Molly has a container shaped like a right prism. She knows that the area of the base of the container is 12 in² and the volume of the container is 312 in³.

What is the height of Molly's container?

21 in.

26 in.

31 in.

36 in.

Answer:

I think its 2 times the original volume, im so sorry if im wrong!!

Step-by-step explanation:

Edit: I thought it was two but i guess it was 4, heres the real answer for people who were wondering, im so sorry!!

Answer:

  $27

Step-by-step explanation:

Assuming this price list, ...

  4 toy cars cost 6 dollars

  6 toy cars cost 9 dollars

  8 toy cars cost 12 dollars

We recognize that 18 cars is 3 times 6 cars, so the cost will be ...

  cost of 18 cars = 3(cost of 6 cars) = 3($9) = $27

The cost of 18 toy cars is $27.

Answer:

JMK

Step-by-step explanation:

Answer:

\(-\frac{1}{5}\) is the slope of the line.

Step-by-step explanation:

(7 , 1) = (x1 , y1)

(-3 , 3) = (x2 , y2)

slope = y2 - y1/x2 - x1

=3 - 1/-3 - 7

=2/-10

=1/-5

=\(-\frac{1}{5}\)

The missing side of the right triangle is as follows:

a = 22.7 units

b = 10.6 units

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The sides a and b can be found using trigonometric ratios as follows:

Hence,

sin 25 = opposite / hypotenuse

sin 25° = b / 25

cross multiply

b = 25 sin 25

b = 25 × 0.42261826174

b = 10.5654565435

b = 10.6 units

cos 25 = adjacent / hypotenuse

cos 25 = a / 25

cross multiply

a = 25 cos 25

a = 22.6576946759

a = 22.7 units

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(a) log (2) = log₁(x)

By definition, log 2 is the exponent to which the base 10 must be raised to obtain the value 2.

This implies that \(10^{log2} = 2\). Let the \(log_{1}(x) = y\), then we can write the equation above as follows:

\(log 2 =log 10^y\)

\(y = \frac{log 2}{log 10}\)

\(= 0.3010x\)

\(= 10^{0.3010}\)

\(= 2.0000\)

(b) 10log(x) = 5

The equation above can be written as log x = 0.5 which implies that

\(x = 10^{0.5}\)

\(x=0.3162\)

(d) log₂ (In(x)) = 3The equation above implies that \(In(x) = 2^3 = 8\).

This means that\(x = e^8 = 2980.9580\)

(e) \(ex = 10^3\)

Take natural logarithm of both sides. This gives us:

\(x = \frac{ln(10^3)}{e} = {ln(1000)}{e} = 6.9078\)

(f) 52x

We can write the equation above as:

\(5^2x = (5^x)^2\)

Take the logarithm of both sides using logarithm base 5.

We obtain:

\(log 5 (5^2x) = log 5 ((5^x)^2)\)

\(2x = 2xlog 5 (5)\)

\(log 5 (5) = 1x = 0.0192\)

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Answer:

64

Step-by-step explanation:

2x-4y=3

x= (3 +4y)/2

substitute into the main equation

y= 0

x= 3/2

16^x /256^y

16^3/2 ÷ 256^0

√16^3 ÷1

= 64

Answer:

64

Step-by-step explanation:

2x - 4y = 3

2x = 4y + 3

x = 2y + 1.5

\( \dfrac{16^x}{256^y} = \)

\( = \dfrac{16^{2y + 1.5}}{256^y} \)

\( = \dfrac{16^{2y + 1.5}}{16^{2y}} \)

\( = 16^{2y + 1.5 - 2y} \)

\( = 16^\frac{3}{2} \)

\( = 4^3 \)

\( = 64 \)

There are 30 possible schedules for Bob to play basketball on Wednesday or Monday or both.

Define the event A as playing basketball on Wednesday, and the event B as playing basketball on Monday. Since Bob can play basketball on either day, we want to count the number of schedules that include at least one of these events, which is equivalent to finding the union of the events A and B.

By the inclusion-exclusion principle, we can compute the number of schedules that include either A or B or both as:

|A ∪ B| = |A| + |B| - |A ∩ B|

To find |A|, we note that Bob can play basketball on any 3 of the remaining 6 days, which gives us:

|A| = C(6,3) = 20

Similarly, |B| = C(6,3) = 20, since the choices for playing basketball on the other days are the same.

To find |A ∩ B|, we note that Bob can play basketball on any 2 of the remaining 5 days, since Monday and Wednesday are already occupied. This gives us:

|A ∩ B| = C(5,2) = 10

Substituting these values into the formula for |A ∪ B|, we get:

|A ∪ B| = 20 + 20 - 10 = 30

Therefore, there are 30 possible schedules for Bob to play basketball on Wednesday or Monday or both.

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Main Answer: If ab = 4, then (a – b)3 – 9(a – b) = 0.

Supporting Explanation :Given that ab = 4To prove that (a – b)3 – 9(a – b) = 0.(a – b)3 – 9(a – b) = 0 can be written as (a-b)[(a-b)²-9]=0(a-b)²-9=0(a-b)²=9a-b=3 or a-b=-3as ab=4Let's take a=4 and b=1So, a-b=3(a-b)³-9(a-b)=0So, (3)³-9(3)=0 Therefore, (a – b)³ – 9(a – b) = 0 when a=4 and b=1.

The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Integer examples include 1, 2, 5, 8, -9, -12, etc. "Z" stands for an integer.

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Answer:

9.7

Step-by-step explanation:

\(5.2^{2}\) + \(8.2^{2}\) = \(c^{2}\)

94.28 = \(c^{2}\)

\(\sqrt{94.28}\) = \(\sqrt{c^{2} }\)

9.7≈c  Rounded

The volume of the regular pentagonal prism is approximately 1285.5 cubic centimeters.

The formula for the volume of a regular pentagonal prism is:

V = (5/2) × apothem² × height × sin(72°)

Given that the required apothem is of 6.9 cm and the height is 8 cm, we can plug in these values into the formula:

V = (5/2) × (6.9)² × 8 × sin(72°)

V = (5/2) × 47.61 × 8 × 0.9511

V ≈ 1285.5 cubic centimeters

Therefore, we can say that the volume of the regular pentagonal prism is approximately 1285.5 cubic centimeters.

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Complete Question:

Find the volume of the following regular pentagonal prism, if the apothem is 6.9 cm and the height of the prism is 8 cm. Round your final answer to the nearest tenth if necessary.

your scientific notation will be 2.505 x 10^4

Answer:

Step-by-step

3

The problem asks for the number of different samples of size 2 that can be selected from a population of size 10. To solve this problem, we can use the formula for the number of combinations of n objects taken r at a time, which is given by nCr = n!/(r!(n-r)!), where n is the size of the population and r is the size of the sample.

In this case, we have n=10 and r=2, so the number of different samples of size 2 that can be selected from a population of size 10 is given by 10C2 = 10!/(2!(10-2)!) = 45. Therefore, there are 45 different samples of size 2 that can be selected from a population of size 10.

Another way to think about this problem is to consider that when selecting a sample of size 2 from a population of size 10, we can choose the first element from any of the 10 objects in the population, and then choose the second element from the remaining 9 objects in the population (since we can't choose the same object twice).

Therefore, the total number of different samples of size 2 that can be selected is 10 x 9 = 90. However, since the order in which we choose the elements of the sample doesn't matter, we need to divide by 2 (the number of ways to arrange 2 elements), giving us a total of 45 different samples of size 2.

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Complete question:

How many different samples of size 2 can be selected from a population of size 10?

The observed proportion of correct diagnoses in a random sample of mechanics is not necessarily the same as the MLE, as the MLE involves a more formal estimation procedure that considers the underlying probability distribution and maximizes the likelihood function based on the observed data.

The Maximum Likelihood Estimation (MLE) and the observed proportion of correct diagnoses in a random sample of mechanics are related concepts but not the same.

The MLE is a statistical method used to estimate the parameters of a probability distribution based on observed data. It seeks to find the parameter values that maximize the likelihood of observing the given data. In the case of a binomial distribution, which could be used to model the number of correct diagnoses, the parameter of interest is the probability of success (correct diagnosis) for each trial (mechanic).

In this context, if we have a random sample of 20 mechanics and observe that 15 of them made correct diagnoses, we can calculate the observed proportion of correct diagnoses as 15/20 = 0.75.

While the observed proportion can be considered an estimate of the underlying probability of success, it is not necessarily the same as the MLE. The MLE would involve maximizing the likelihood function, taking into account the specific assumptions and model chosen to represent the data. The MLE estimate may or may not coincide with the observed proportion, depending on the distributional assumptions and the specific form of the likelihood function.

In summary, the observed proportion of correct diagnoses in a random sample of mechanics is not necessarily the same as the MLE, as the MLE involves a more formal estimation procedure that considers the underlying probability distribution and maximizes the likelihood function based on the observed data.

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Purpose,Planning,Participation are the three important elements of group discussion.

Goal setting up a group conversation has a goal as one of its initial elements. To reach an acceptable conclusion during a group discussion is the goal. The best method for deciding the next step is typically a group discussion.

A key component is preparation. The discussion's goal is decided by its participants. There cannot be just any expression of views in a group debate that seeks to reach a decision. It is important to structure the conversation so that each move brings the group one step closer to the desired outcome. Participation.

Any group conversation is only as good as its participants' participation. It is necessary to bring out group participants. There shouldn't be a few people that control it. Nevertheless, most groups have this tendency.

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Answer:

I beleive Kasey can make 36 servings of gelatin. If you want you can check your answer by using the steps I provided.

Step-by-step explanation:

1. First we need to see how many times 1 1/3 can go into 8, or (how many gelatin molds can be filled. So, we will divide 8 divided by 1 1/3 to get (6.)

2. So, since we can fill 6 gelatin molds and each mold makes six servings, we will multiply 6 times 6 to get our answer 36.

Answer: A. The probability of drawing a red tile is 36% and the probability of NOT drawing a red tile is 64%

Step-by-step explanation:

Number of red tiles = 9

Number of blue files = 10

Number of green tiles = 6

Total number of tiles = 9 + 10 + 6 = 25

Probability of drawing red tile = 9/25 = 0.36 = 36%

Probability of drawing blue tile= 10/25 = 0.40 = 40%

Probability of drawing green tile = 6/25 = 0.24 = 24%

Based on the explanation above, the correct answe is option A "The probability of drawing a red tile is 36% and the probability of NOT drawing a red tile is 64%".

Answer:

D. be congruent

Step-by-step explanation:

vertical angles are angles that are across from each other on intersecting lines and they are always congruent

The roots of the equation x^3 - 7x^2 + 14x - 6 = 0 accurate to within 10^-2 on the interval [3.2, 4] are approximately 3.35, 4.00, and 4.65.

We can use the Bisection method to find the roots of the equation x^3 - 7x^2 + 14x - 6 = 0 on the interval [3.2, 4] accurate to within 10^-2 as follows:

Step 1: Calculate the value of f(a) and f(b), where a and b are the endpoints of the interval [3.2, 4].

f(a) = (3.2)^3 - 7(3.2)^2 + 14(3.2) - 6 = -0.448

f(b) = (4)^3 - 7(4)^2 + 14(4) - 6 = 10

Step 2: Calculate the midpoint c of the interval [3.2, 4].

c = (3.2 + 4)/2 = 3.6

Step 3: Calculate the value of f(c).

f(c) = (3.6)^3 - 7(3.6)^2 + 14(3.6) - 6 = 4.496

Step 4: Check whether the root is in the interval [3.2, 3.6] or [3.6, 4] based on the signs of f(a), f(b), and f(c). Since f(a) < 0 and f(c) > 0, the root is in the interval [3.6, 4].

Step 5: Repeat steps 2 to 4 using the interval [3.6, 4] as the new interval.

c = (3.6 + 4)/2 = 3.8

f(c) = (3.8)^3 - 7(3.8)^2 + 14(3.8) - 6 = 1.088

Since f(a) < 0 and f(c) > 0, the root is in the interval [3.8, 4].

Step 6: Repeat steps 2 to 4 using the interval [3.8, 4] as the new interval.

c = (3.8 + 4)/2 = 3.9

f(c) = (3.9)^3 - 7(3.9)^2 + 14(3.9) - 6 = -0.624

Since f(c) < 0, the root is in the interval [3.9, 4].

Step 7: Repeat steps 2 to 4 using the interval [3.9, 4] as the new interval.

c = (3.9 + 4)/2 = 3.95

f(c) = (3.95)^3 - 7(3.95)^2 + 14(3.95) - 6 = 0.227

Since f(c) > 0, the root is in the interval [3.9, 3.95].

Step 8: Repeat steps 2 to 4 using the interval [3.9, 3.95] as the new interval.

c = (3.9 + 3.95)/2 = 3.925

f(c) = (3.925)^3 - 7(3.925)^2 + 14(3.925)

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Answer:

statement: segment HA is parallel to seg HD and seg HD is parallel to seg AN.

Reason: given

statement: angle 1 is congurent to angle 3.

reason: alternate interior angles are congruent.

statement: angles 2 and 4 are congruent

reason: alternate interior angles are congruent.

statement: Seg DA is congruent to seg DA

reason: reflexive property

statement: angle AHD is congruent to angle AND

reason: since angles 1 and 3 are congruent, and 2 and 4 are congruent, and HDA is a triangle, same with AND, the last angle must be congruent.

statement: seg HD is congruent to seg NA and HA is cong to ND.

reason: ASA angle side angle theorem states that if 2 angles and a side is congruent to the corresponding parts of another triangle, then it is congruent.

Step-by-step explanation:

The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.

∫3e^x dx = 3∫e^x dx = 3e^x + C₁

∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂

∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃

∫1 dx = x + C₄

Now, we can combine these results to obtain the final answer:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

where C is the constant of integration.

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Answer:

answer easy a

Step-by-step explanation:

6 is  bye 50

Answer:

total=4.5+9=13.5

Step-by-step explanation:

0.5×3=1.5. 3×3=9

1.5×3=4.5 A=4.5. A=9. 4.5+9=13.5

Answer:

Correct answer is option D

Answer:

Angle NQR congruent to Angle MRQ because it is given

Side QR is congruent to side QR because they are the same side

Angle NRQ is congruent to angle MQR because they are the equal angles of an isosceles triangle

Triangle QNR is congruent to Triangle RMQ by ASA

Step-by-step explanation:

It's actually pretty simple.  first you should be able to know angles NRQ and  MQR are congruent because triangle PQR is isosceles .  So now if you look at the two other triangles you can say angle NQR is congruent to angle MRQ, because of the information given, and with wht I just explained angles NRQ and MQR are congruent.  So now you can say the two triangles are similar by the angle angle postulate.  

To Say they are congruent since QR is the same for both triangles you can use the ASA postulate

Solve for dy/dx:   dy/dx = (-2x) / (2y) = -x / y which gives the slope of tangent line using implicit differentiation

To find the slope of a tangent line using implicit differentiation, follow these steps:

1. Start with the given equation that represents the relationship between x and y in the form of an equation involving both variables, for example: F(x, y) = 0.

2. Differentiate both sides of the equation with respect to x using the chain rule whenever necessary. Treat y as a function of x and apply the derivative rules accordingly.

3. After differentiating, have a resulting equation involving both x, y, and their derivatives (dy/dx). Rearrange the equation if necessary to isolate dy/dx on one side.

4. Solve for dy/dx to find the derivative of y with respect to x. This will give the slope of the tangent line at any given point on the curve defined by the implicit equation.

Note: The resulting expression for dy/dx may involve both x and y variables. To find the slope of the tangent line at a specific point, substitute the coordinates of that point into the expression for dy/dx.

Here's an example to illustrate the process:

Given the implicit equation: \(x^2 + y^2 = 25\)

1. Start with the equation: \(x^2 + y^2 = 25.\)

2. Differentiate both sides with respect to x:

  2x + 2y * (dy/dx) = 0

3. Rearrange the equation to isolate dy/dx:

  2y * (dy/dx) = -2x

4. Solve for dy/dx:

  dy/dx = (-2x) / (2y)

         = -x / y

Now, have the expression for the slope of the tangent line in terms of x and y. To find the slope at a specific point, substitute the coordinates of that point into the expression.

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Answer: I think it's B

Step-by-step explanation: You can use the answer if you want.

Answer:

Yup correct

Step-by-step explanation:

Step-by-step explanation:

32 seems to be the tangent on the circle with radius 24.

so, 32 and 24 are right-angled to each other (90°).

therefore, we can use Pythagoras to calculate x.

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle).

in our case

x² = 24² + 32² = 576 + 1024 = 1600

x = 40

GD DAY AND NIGHT EMMANUEL MUDIAY