A candy bar box is in the shape of a triangular prism. The volume of the box is 1,200 cubic centimeters.

A triangular prism is shown with base of triangle labeled 10 cm, sides of the triangles labeled 13 cm, and length of the box equal to 20 cm.

Part A: What is the height of the base? Show your work. (5 points)

Part B: What is the approximate amount of cardboard used to make the candy box? Explain how you got your answer. (5 points)

Answer:

yes, after 7 weeks they will have the same amount of money. 46 dollars.

Step-by-step explanation:

First start of by writing an expression to represent this problem

11 + 5x = 60 - 2x

combine like terms. and find value of x.

subtract 11 from the 60

5x = 49 - 2x

move the 2x over to the other side. So + 2x

7x = 49

divide 7 from 49

49/7

x = 7

x=7 amount of weeks they will have the same amount of money

Answer:

90 and 80 degrees

Step-by-step explanation:

Answer:

Length of side QR is 16 units.

Step-by-step explanation:

Given that dimensions of \(\triangle PQR\) are as follows:

\(\angle QPR =90^\circ\)

Side QP \(= 8 \sqrt3\ units\)

Side PR = 8 units

To find, side QR = ? units

Please refer to the attached figure for the representation of the given dimensions.

Base is side QP,

Perpendicular is side PR and

Hypotenuse is side QR.

In a right angled triangle, Pythagorean theorem holds true i.e.

Accoring to pythagoras theorem:

\(\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\)

\(\Rightarrow QR^{2} = QP^{2} + PR^{2}\)

Putting the values of QP and PR:

\(\Rightarrow QR^{2} = (8\sqrt3)^{2} + 8^{2}\\\Rightarrow QR^{2} = 64 \times 3+ 64\\\Rightarrow QR^{2} = 64 \times 4\\\Rightarrow QR = 8 \times 2\\\Rightarrow QR = 16\ units\)

So, the value of length of side QR is 16 units.  

Answer:

it's C

Step-by-step explanation:

: 0

Answer:

30 × 24 = 720 inches

since there are 12 inches in a foot

720 ÷ 12 = 60

60 feet converted to yards is 20 yards

50 - 20 = 30

they should have 30 yards of string left over

Answer:

Dog years will not print an output is the answer

Step-by-step explanation:

Answer:

human_years = 3 should be assigned first

Step-by-step explanation:

I am not sure, sorry if wrong

No explanation, but...

hope this helps and have a great day!

Answer:

74.4%

Step-by-step explanation:

Given data

Initial price=$1.25

Final price= $2.18

Required

The percent increase

%increase= FInal-initial/ initial*100

substitute

%increase= 2.18-1.25/ 1.25*100

%increase= 0.93/ 1.25*100

%increase= 0.744*100

%increase= 74.4%

Hence the percent increase is 74.4%

Answer:

There are 2 hours and 30 minutes in 150 minutes.

Step-by-step explanation:

Answer:

Step-by-step explanation:

150 ÷ 60

Quotient will be the hours and remainder will be the minutes

2 hours 30 minutes

The formula to calculate the future value of an investment with compound interest is:

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

where:

A = future value

P = principal (initial investment)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = time (in years)

In this case, we have:

P = $200 (initial investment)

r = 20% = 0.20

n = 1 (compounded annually)

t = 6 (6 years)

So, we can plug these values into the formula:

A = 200(1 + 0.20/1)^(1*6)

A = 200(1.20)^6

A = $766.97 (rounded to the nearest cent)

Therefore, Robert will have approximately $766.97 in his retirement account after 6 years.

Algebraic rule

As

here the polynomial has degree 6

6 can be all negative or positive

Answer:

Both positive (or) negative

Step-by-step explanation:

The polynomial's degree is 6 and so the polynomial has 6 zeroes. These zeroes can be either positive or negative.

Answer: x is greater than or equal to 18

Step-by-step explanation:

Answer:

x ≤ - 2

Step-by-step explanation:

- x/6 ≤ 3

- x/2 ≤ 1

- x ≤ 2

x ≤ - 2

If a > 3, then a, a + 2, and a + 4 cannot all be primes, and they can't all be powers of primes either.


1. Let's first analyze the numbers a, a + 2, and a + 4. Notice that at least one of these numbers must be divisible by 3 since they are consecutive even numbers.
2. If a is divisible by 3, then it cannot be prime as a > 3.
3. If a is not divisible by 3, then either a + 2 or a + 4 must be divisible by 3.
4. Since a + 2 and a + 4 are consecutive even numbers, one of them is divisible by 2, and thus, not prime.
5. Now, let's consider the possibility of them being powers of primes.
6. If a is a power of a prime, then it must be divisible by the prime it's raised to. Since a > 3, it cannot be a power of 3 or a power of 2, as it would then be divisible by 2 or 3.
7. If a + 2 or a + 4 are powers of primes, they must also be divisible by their respective prime bases, which contradicts the fact that they are consecutive even numbers and not prime themselves.

Therefore, if a > 3, it is impossible for a, a + 2, and a + 4 to all be primes or powers of primes.

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The indefinite integral of ∫x√(9 - x²) dx is (1/3)(9 - x²)\(^(3/2)\)+ C.

To evaluate the indefinite integral ∫x√(9 - x²) dx, we can use the substitution method. Let u = 9 - x². Taking the derivative of both sides, du = -2x dx. Rearranging, we have dx = -(1/2x) du.

Substituting these values into the integral, we get ∫x√(9 - x²) dx = ∫-x(1/2x)√(u) du = -1/2 ∫√(u) du.

Now we integrate with respect to u: -1/2 ∫√(u) du = -(1/2)(2/3)(u\(^(3/2)\)) + C = -(1/3)(9 - x²)\(^(3/2)\) + C.

Therefore, the indefinite integral of ∫x√(9 - x²) dx is given by (1/3)(9 - x²)\(^(3/2)\) + C.

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If the distance from trough to crest is 4, then the amplitude is half of that distance. Therefore, the amplitude is 2. So the correct option is 2.

The amplitude of a wave is the measure of its maximum displacement from its equilibrium or resting position. The distance from the trough (lowest point) to the crest (highest point) is called the "peak-to-peak" distance or "trough-to-crest" distance.

In this case, the trough-to-crest distance is 4, which means the maximum displacement from the equilibrium position is 2 units in either direction (half of 4). Therefore, the amplitude of the wave is 2.

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Step-by-step explanation:

the sum of all angles in a triangle is always 180 degrees.

so,

x + 12 + 2x - 29 + x + 5 = 180

4x - 12 = 180

4x = 192

x = 48

Answer:

Step-by-step explanation:

We have that

A = 51°, b = 14, c = 6

step 1

find the value of a

Applying the law of cosines

a²=c²+b²-2*c*b*cos A

a²=6²+14²-2*6*14*cos 51-------> 126.27

a=11.2

we know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

we have

a=11.2

b=14

c=6

so

(a+b) > c-------------> (11.2+14)=25.2

25.2 > 6-----> is not correct

therefore

the answer is the option

a. No triangles possible

I don't know if i am right sorry if this is wrong

Answer:

Step-by-step explanation:

2ft

Therefore, on average, Crunch Code has approximately 4 uncompleted projects in the system at any given time.

To calculate the average number of uncompleted projects in the system at any given time, we need to use Little's Law, which states that the average number of entities (in this case, projects) in a stable system is equal to the average arrival rate multiplied by the average time spent in the system.

Given:

Average arrival rate (λ) = 1 project every 4.8 hours

Average time spent in the system (W) = 19.2 hours

Using Little's Law, the average number of uncompleted projects (L) is given by:

L = λ * W

Substituting the values:

L = (1/4.8) * 19.2

= 0.208 * 19.2

≈ 3.9936

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Answer:

(x ÷ 2) + 7

Step-by-step explanation:

A quotient is the answer to a division problem...

So.... Let's say "a number" is x

(x ÷ 2) + 7 = Seven more than the quotient of a number and 2

That should be the answer!

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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\(40(x )+6( 1.5x) = 612.5\)

So C.

B:

49x=612.5

x=12.5$

Geometric series is convergent if the |r|<1 where r is the common ratio.

Let Sn=∑ni=0(−3/4)i then

Sn=(−3/4)n+1−1(−3/4)−1

Now take n→∞ then

Sn→0−1(−3/4)−1=4/7

because |−3/4|<1 and so (−3/4)n→0. Now note that your sum is

lim ∑i=1n+1(−3)i−14i=lim 14∑i=1n+1(−3)i−14i−1=1/4.lim Sn=1/7.

Geometric series: A geometric series is the result of adding together geometric sequences indefinitely. Depending on the sequence given to us, such infinite sums can either be finite or infinite. A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series frequently reach, reach, or avoid a particular number.

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Therefore, the value of y at t = 0.4 is 5.To find the value of y at t = 0.4, we can use the Euler's method. Here are the steps to solve the given differential equation.

1. Given the differential equation y' + 0.2y = 0, we need to find the value of y at t = 0.4.

2. Start with the initial condition y(0) = 5. This gives us the starting point for our approximation.

3. Let's choose a step size h = 0.2. This means we will approximate the value of y at t = 0.4 using the values of y at t = 0, t = 0.2, and t = 0.4.

4. To approximate y at t = 0.2, we use the formula:
  y(0.2) = y(0) + h * (dy/dt)(0)
         = 5 + 0.2 * [y'(0) + 0.2 * y(0)]

5. Substitute the values into the formula:
  y(0.2) = 5 + 0.2 * [y'(0) + 0.2 * 5]

6. Now, let's find the value of y'(0):
  Given the differential equation, y' + 0.2y = 0, we can rearrange it to find y':
  y' = -0.2y

7. Substitute this value into the formula:
  y(0.2) = 5 + 0.2 * [-0.2 * 5 + 0.2 * 5]

8. Simplify the equation:
  y(0.2) = 5 + 0.2 * [0]
         = 5

9. Now, to find y at t = 0.4, we repeat the process using the values of y at t = 0.2 and t = 0.4:
  y(0.4) = y(0.2) + h * (dy/dt)(0.2)
         = 5 + 0.2 * [y'(0.2) + 0.2 * y(0.2)]

10. Substitute the values into the formula:
   y(0.4) = 5 + 0.2 * [(-0.2 * 5) + 0.2 * 5]

11. Simplify the equation:
   y(0.4) = 5 + 0.2 * [0]
          = 5.

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Answer:

Vertical Angles

x = 21

Step-by-step explanation:

Vertical Angles

4x + 3 = 87

4x = 84

x = 21

To form a parallelogram, the opposite sides of the quadrilateral should be parallel. Let's find the coordinates of point D such that AB is parallel to DC.

The slope of line AB = (yB - yA) / (xB - xA) = (6 - 1) / (-2 - 3) = -1

Therefore, the slope of line DC should also be -1.

Let's assume the x-coordinate of point D is xD.

The slope of line CD = (yD - yC) / (xD - xC)

Since the slope of CD is -1, we can write:

(yD - yC) / (xD - xC) = -1

yD - yC = -(xD - xC)

yD = -(xD - xC) + yC

Substituting the coordinates of points C and A, we get:

yD = -(xD - 6) + 4

yD = -xD + 10

Therefore, the coordinates of point D are (xD, -xD + 10).

To find the x-coordinate of point D, we can use the fact that BC is parallel to AD.

The slope of line BC = (yC - yB) / (xC - xB) = (4 - 6) / (6 + 2) = -1/4

Therefore, the slope of line AD should also be -1/4.

The slope of line AD = (yD - yA) / (xD - xA)

Substituting the coordinates of points A and D, we get:

(yD - 1) / (xD - 3) = -1/4

yD - 1 = -(xD - 3) / 4

yD = -(xD - 3) / 4 + 1

yD = -xD/4 + 5/4

Substituting the equation we found for yD in terms of xD, we get:

-xD/4 + 5/4 = -xD + 10

3/4 xD = 35/4

xD = 35/3

Therefore, the coordinates of point D are (35/3, -35/3 + 10) = (35/3, 5/3).

We can now plot the points A, B, C, and D on the coordinate axes, and verify that they form a parallelogram.

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Answer:

77

Step-by-step explanation:

To find the median marks, we first need to arrange the scores in ascending order:

55, 60, 65, 77, 80, 82, 85

Since there are 8 students, the middle value will be the 4th value in the ordered set. In this case, the median marks will be 77

Therefore, the median marks for the 8 students in maths is 77.

The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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