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Robin's teacher asked her to find a box that would hold some small
1 inch cubes that the kindergartners used for counting. Robin
found three boxes with the following dimensions: Box A: 4" x 6" x
8" Box B: 6" x 3" x 12" Box C: 6" x 6" x 4" Which box would be
able to hold all the cubes if Robin's teacher had 200 cubes? Box
Volume of Box A =
cu.in.
Volume of Box C =
cu.in. Volume of Box B =
30 pts
cu.in.

Answer:

True

Step-by-step explanation:

40oz = 2.5 lb

10 = 0.625

Based on the sample response given, the statements included in the explanation on the horizontal line test are:

The horizontal line test is used to not only find out if a graph has an inverse function, but also if that inverse is also a function itself.

To pass the horizontal line test, the function has to be one-to-one which means that a horizontal line can intersect the graphed function at one point in all places. If this happens, then there is an inverse and the inverse itself is a function.

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Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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Answer:

(x+3)(x+7)

Step-by-step explanation:

x²+10x+21

x²+3x+7x+21

x(x+3)+7(x+3)

(x+3)(x+7)

The factorization of the following trinomial are; (x+3)(x+7)

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given the expression

x²+10x+21

x²+3x+7x+21

x(x+3)+7(x+3)

Therefore, the factor are; (x+3)(x+7)

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Answer:

26/93

Step-by-step explanation:

3/31=9/93

9/93 +17/93=26/93

the answer is 15 because it is in the middle

Answer:

Step-by-step explanation:

Median is the middle term of the data set.

Median = 15

13 , 13 , 13 , 15 , 15 , 16 , 16 , 17 , 17

Using the derivative of the velocity, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.

Given:

Acceleration function, a(t) = 2sin(t) + 1

Initial velocity, v(0) = 0

Initial position, s(0) = 3

To find:

Velocity function, v(t)

Position function, s(t)

Average value of the position function from t = 2 seconds to t = 5 seconds

Solution:

We know that acceleration is the derivative of velocity, and velocity is the derivative of position. So we can find the velocity and position functions by integrating the acceleration function.

Velocity function:

\(v(t) = \int a(t) dt\\v(t) = \int (2sin(t) + 1) dt\\v(t) = -2cos(t) + t + C1\)

We know that the initial velocity, v(0) = 0. Substituting this value in the above equation, we get:

\(0 = -2cos(0) + 0 + C1\\C1 = 2\)

Therefore, the velocity function is:

\(v(t) = -2cos(t) + t + 2\)

Position function:

\(s(t) = \int v(t) dt\\s(t) = \int (-2cos(t) + t + 2) dt\\s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + C2\)

We know that the initial position, s(0) = 3. Substituting this value in the above equation, we get:

\(3 = 2sin(0) + 0 + 0 + C2\\C2 = 3\\\)

Therefore, the position function is:

\(s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + 3\)

Average value of the position function from t = 2 seconds to t = 5 seconds:

We can find the average value of the position function using the following formula:

\(Avg = (1/(b-a)) * \int(a,b) f(t) dt\)

Here, a = 2 and b = 5. So, substituting the values in the above formula, we get:

\(Avg = (1/(5-2)) * \int(2,5) (2sin(t) + \frac{1}{2} t^2 + 2t + 3) dt\\Avg = \frac{1}{3} * [ -2cos(t) + 1/6 t^3 + t^2 + 2t ] \eval(2,5)\\\)

\(Avg = \frac{1}{3} * [ (-2cos(5) + 1/6 (5^3) + 5^2 + 25) - (-2cos(2) + 1/6 (2^3) + 2^2 + 22) ]\\Avg = 14.5\)

Therefore, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.

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Clara can reach a height of 2.57 meters when she jumps.

Given information:

The ceiling in Clara’s basement is 2.75 meters high.

When Clara jumps she is 18 centimeters short of being able to touch the ceiling.

We can start by converting the height of the ceiling and Clara's jump to the same units, either meters or centimeters. Let's convert Clara's jump to meters:

18 centimeters = 0.18 meters

Now we can subtract Clara's jump from the height of the ceiling to find how high she can reach:

2.75 meters - 0.18 meters = 2.57 meters

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The value of c on the normal distribution such that P(Z > c) = 0.1446 is given as follows:

c = 1.06.

The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

Considering the second bullet point, the value of c is the z-score with a p-value of 1 - 0.1446 = 0.8554, hence it is given as follows:

c = 1.06.

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The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.

The population parameter is the true value of the statistic for the entire population. The probability that the statistic is obtained is the probability that it will be obtained in a single sample from the population. The variance of the values is the amount of variation among the values of the statistic in the sample. The formula for calculating the variance is the sum of the squared deviations from the mean, divided by the number of values in the sample. This can be written mathematically as: Variance = Σ (x - X)2/ n, where x is each value in the sample, X is the mean value, and n is the number of values in the sample.

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Answer: 0.05t ==> 1st blank

1 ==> 2nd blank

-0.1t+6 ==> 3rd blank

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

(x^2+3)(x-5)

That's the answer

Answer:

$52.50

Step-by-step explanation:

210 divided by 4 equals 52.50

Answer:

value of x is y to the nearest tenth. is 6.0 is equal to 8.3 to 5.8. 6.2

Note that the estimated time it will take to cause hearing loss at 106 decibels is 0.0625 hours or 3 minutes, 75 seconds.

The formula used is:


Exposure Time = 8/ 2^((dBA-85)/3)

Since the decibel (dBA) given is 106


Exposure Time = 8/ 2^((106-85)/3)

= 8/2^1
= 8/ 128

= 0.0625 hours or 3 minutes, 75 seconds.

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Answer:

16x^9/9+9 should be the answer

Step-by-step explanation:

Answer:

quneotentendeiporoqenouteetendxdin

Step-by-step explanation:

Answer:100,000

Step-by-step explanation:

The total materials handling cost allocated to the modular homes is $246,372.84.

The total materials handling cost allocated to the Prefab Barns is closest to $108,000.

To allocate materials handling cost based on material moves, we must determine proportion of material moves for each product and then apply that proportion to the total materials handling cost.

Proportion of material moves for Modular Homes:

= (Total expected material moves for Modular Homes) / (Total expected material moves for both products)

= 590 / (590 + 190)

= 0.756

Total materials handling cost allocated to Modular Homes:

= Proportion of material moves for Modular Homes * Total materials handling cost

= 0.756 * $325,890

= 246 372.84

= $246,372.84.

To allocate the materials handling cost based on direct labor-hours, we need to determine proportion of direct labor-hours for each product.

For Modular Homes:

Total direct labor-hours for Modular Homes:

= 6,000 units * 800 hours/unit

= 4,800,000 hours

For Prefab Barns:

Total direct labor-hours for Prefab Barns:

= 9,000 units * 300 hours/unit

= 2,700,000 hours

Total direct labor-hours for both products:

= 4,800,000 hours + 2,700,000 hours

= 7,500,000 hours

Proportion of direct labor-hours for Prefab Barns:

= 2,700,000 hours / 7,500,000 hours

= 0.36

Allocated materials handling cost for Prefab Barns:

= Proportion of direct labor-hours for Prefab Barns * Total materials handling cost

= 0.36 * $300,000

= $108,000.

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Answer:

24/7

Step-by-step explanation:

tan A = opp/adj

For angle Z, the adjacent leg is 14, and the opposite leg is 48.

tan Z = 48/14

tan Z = 24/7

Answer:

6

Step-by-step explanation:

Speed = Distance/time

Therefore time must = distance/speed

Since the two students are running apart from eachother, we can add their speeds together.

Also we can subtract 10 feet from our goal of 1870 since they're already 10 feet apart.

1860 feet/(150+1650) feet per minute

We can cancel out the feet since it's a common term.

And we're left with 6 minutes.

The  time before they are 1870 feet apart is mathematically given as

X=6min

Question Parameters:

Two old RSM students were standing 10 feet apart

at the speeds of 150 feet per minute

they are 1870

feet apart

Generally, the time they are apart is mathematically given as

X=final distance apart/speeds of run

Therefore

X=1870/(150+160)

X=6min

In conclusion,time before they are 1870 feet apart

X=6min

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Answer: 12.25 or Approximately 12.3

Step-by-step explanation:

To solve this problem, we first need to solve for x. We are given with 2ˣ=7.

To get x alone, we want to use natural log, or ln.

\(xln(2)=ln(7)\)         [once you find ln of both sides, you bring the x to the front]

\(x=\frac{ln(7)}{ln(2)}\)                 [divide both sides by ln(2)]

\(x=2.81\)

We now know that x is approximately 2.81. We can plug that in to find 4ˣ⁻¹.

\(4^(^x^-^1^)\)                     [plug in x]

\(4^(^2^.^8^1^-^1^)\)                 [parenthesis]

\(4^{1.81}\)                        [exponent]

\(12.3\)

The answer is approximately 12.3. To get a more exact answer, you would plug in \(\frac{ln(7)}{ln(2)}\) into x.

\(4^{\frac{ln(7)}{ln(2)}-1 }\)

\(12.25\)

The exact answer would be 12.25. This is close to 12.3 since it is rounded up to one decimal place.

Answer: 3^3 Square root 3

Step-by-step explanation:

A, percentages

You would see percentages on a circle graph, because it's how many parts of the whole that they take up.

Happy to help, have a great day! :)

Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer:

1. 9 bounds of carbon dioxide

2.  27 bounds of carbon dioxide

Step-by-step explanation:

So let's find a unit rate: 1 to 9

"Why is it 1:9?"

If I can find divide 72 pounds into 8 hours? What would I find? You would find the pounds for each other

Example: 72/8=9. So If 9 carbon dioxide per hour. I can do 3 hours is 27 pounds of carbon dioxide.

So to sum it up, 72/8=9 so 1:9 can be used to figure out any amount of pounds used in a certain number of hours. So If 3 hours, then 27 pounds.

Answer:

1. 9 pounds of carbon dioxide

2. 27 pounds of carbon dioxide

Step-by-step explanation:

Well, I just know it.

The number of M&M's that were in the bowl before Amelia arrived is; 12

Let the original amount in the bowl be x. Thus;

If Amelia grabbed 50%, then amount left = (100% - 50%)x = 50%x = 0.5x

Now, we are told that domicick took 50% of what was keft after amelia. Thus; New amount left = 100%x - (0.5x + 0.25x) = 0.25x

Now, we are told that there were finally 3 left after all the deductions. Thus;

0.25x = 3

x = 3/0.25

x = 12

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1521=1521 therefore a triangle has sides with lengths of 15 inches, 36 inches, and 39 inches  form a right triangle.

What is Right traingle?

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

When we enter the values of the triangle's legs (15 and 36) and hypotenuse (39),

assuming it is a right triangle, into the Pythagoras theorem, the values of each side of the equation will be equal;

The Pythagoras Theorem is:

\(a^2+b^2=c^2\)

Making substitutions and applying the math results in:

\(15^2 + 36^2= 39^2\)

225 + 1296 = 1521

1521 = 1521

Therefore, it is a right traingle.

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