the volume of a rectangular prism is 36x6y8. the length of the prism is 4x3y5 and the width of the prism is 3xy2. what is the height of the prism?

Answer:

x = 3 and y = 1

Step-by-step explanation:

A) most efficient way is to multiply the first equation by 3 to eliminate the 'x' terms and get 9x - 15y = 12

if you add this to -9x + 3y = -24 you will get -12y = -12

y = 1

substitute 1 for 'y' to get 'x':  3x - 5 = 4

3x = 9

x = 3

Answer:

17

Step-by-step explanation:

Answer:

The answer is 17

Answer:

B and E

Step-by-step explanation:

Information we need to know:

Like terms - a set of number which variables are the same

In the question we can see that there are two numbers that have the variable y and two numbers that have the variable of 0 (meaning that they are regular numbers)

Hence our options would be B and E

Hope this helps, have a lovely day! :)

Slope intercept equation of the line parallel to \(y = -\frac{2}{3} x + 12\)  will be: \(y = -\frac{2}{3} x + 7\)

In the given question, we have a line \(y = -\frac{2}{3} x + 12\). We have to find out the equation of the line that is parallel and passes through points (6, 3). We know the standard slope-intercept form is: y = mx + b. By comparing this to the equation of line \(y = -\frac{2}{3} x + 12\) we get slope m = -2/3.

Also, we know parallel lines have the same slope m = -2/3. And the parallel line passes through (6, 3). We can find the equation of the line by using the point-slope form: y - y₁ = m(x - x₁).

Putting values of m, and (x₁,y₁), we get: \(y - 3 = -\frac{2}{3} (x - 6)\)

=> \(y - 3 = -\frac{2}{3}x + 4\)  

=> \(y = -\frac{2}{3}x + 7\)

Hence, the slope-intercept form of the line is \(y = -\frac{2}{3} x + 7\)

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The value of probabilities are,

P (1, 1) = 1 / 36 = 0.027

P (both odd) = 0.166

P (even, odd) = 0.25

P (2 anywhere) = 0.3055

P (sum 8) = 0.1389

P (sum 1) = 0

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one

Given that;

Two dice are rolled at the same time.

Hence, There are total number of possibilities = 36

Thus, The value of P (1, 1) is,

P (1, 1) = 1 / 36

Since, There are 6 possibilities when both dice have rolled to get odd.

Hence, The value of P (both odd) is,

P (both odd) = 6 / 36

                   = 1/ 6

Since, There are 9 possibilities to get first dice even and second odd.

Hence, The value of P (even, odd) is,

P (even, odd) = 9/36

                     = 1/4

Since, There are 11 possibilities when 2 is in anywhere.

Hence, The value of P (2 anywhere) is,

P (2 anywhere) = 11/36

Since, There are 5 possibilities to get sum 8.

Hence, Value of P (sum 8) is,

P (sum 8) = 5/36

Since, There are no possibilities to get sum 1.

Hence, P (sum 1) = 0

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in this case since it's a cylinder always have to do is multiply the two given measurements dancing that she gets all you need to do is run it off to the nearest two decimal places when you say to the nearest two decimal places while trying to say they are two numbers after the coma

Answer:

1. <

2. <

Step-by-step explanation:

Have a good day :)

Overall Equipment Effectiveness (OEE) is a performance measure that is commonly used to assess the effectiveness and efficiency of the equipment in a manufacturing process.

It calculates the percentage of time the equipment is available, the rate at which it produces good quality products, and the quality of the products produced. A machine produces an assembled unit every 4.75 seconds. It is unavailable for 45 minutes on average during a 12-hour shift due to start-up problems and preventative maintenance.

The number of good quality assembled units produced during the shift is 8,232, and the defect rate is 2%.

To calculate the OEE, we need to calculate three metrics: Availability, Performance, and Quality.

Availability:It is the percentage of time that the machine is available to produce good quality products. The formula to calculate the Availability is:

Availability = (Operating time − Downtime) / Operating time.

Downtime = 45 minutes = 2700 seconds.

Operating time = 12 hours − 45 minutes = 11.25 hours = 40500 seconds.

Availability = (40500 - 2700) / 40500 = 0.9333.

Performance:It is the ratio of actual production to the maximum production rate that can be achieved. The formula to calculate the Performance is:

Performance = Actual Production / Maximum Production.

Maximum Production = 1 / 4.75 * 60 * 60 * 11.25 = 9,720Actual Production = 8,232Performance = 8,232 / 9,720 = 0.8462.

Quality:It is the percentage of good quality products produced. The formula to calculate Quality is:

Quality = (Total Production − Defective Units) / Total Production.

Total Production = Actual Production = 8,232Defective Units = 2% of Total Production = 0.02 * 8,232 = 165.28Quality = (8,232 − 165.28) / 8,232 = 0.9800OEE:It is the product of Availability, Performance, and Quality.

The formula to calculate the OEE is:

OEE = Availability × Performance × Quality

OEE = 0.9333 × 0.8462 × 0.9800 = 0.7953 ≈ 79.53%.

The Overall Equipment Effectiveness (OEE) of the machine is 79.53%. The OEE indicates that the machine is performing well and efficiently during the 12-hour shift, despite the downtime and the 2% defect rate.

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Choosing the lump-sum option of $26.5M would result in receiving approximately $2.93M more in today's dollars compared to the annuity option.

To determine which option is more advantageous, we need to compare the present value of the annuity payments with the lump-sum amount. The present value is calculated by discounting future cash flows at the appropriate discount rate.

For the annuity option, we have equal payments for 25 years. Using the discount rate of 4.7%, we calculate the present value of the annuity payments.For the lump-sum option, we have a single payment of $26.5M.

By discounting the annuity payments and summing them up, we find that the present value of the annuity is lower than the lump-sum amount. The difference between the present value of the annuity and the lump-sum is approximately $2.93M.

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Answer:

Your answer is B

Step-by-step explanation:

6 x 13 +11 = 89

13 x 6 + 11 = 89

TRUE

Answer:

Anwer is B

Step-by-step explanation:

13×6+11=89

so 6×13+11=89

so the true answer is B

The maximum bending moment at 40 ft away from the left support is 135600 in-lb or 11300 ft-lb.

Given that, Length of the beam, L = 120 ft Distance of the point of interest from the left end of the beam, x = 40 ft Wheel loads, P1 = 15 kips, P2 = 10 kips, and P3 = 20 kips Wheel loads' distances from the left end of the beam, a1 = 30 ft, a2 = 50 ft, and a3 = 80 ft.

The bending moment at the point of interest can be calculated using the equation for bending moment at a point in a simply supported beam, M = (Pb - Wx) × (L - x)

Pb = Pa = (P1 + P2 + P3)/2W is the total load on the beam, which can be calculated as W\(= P1 + P2 + P3= 15 + 10 + 20 = 45\)kips For x = 40 ft, we have,

\(Pb = (P1 + P2 + P3)/2= (15 + 10 + 20)/2= 22.5 kip\)s

W = 45 kips

M = (Pb - Wx) × (L - x)

= \((22.5 - 45 × 40) × (120 - 40)\)

= (-\(1695) ×\) 80

= \(-135600 in-lb or -11300 ft-l\)b.

Therefore,

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Answer:

bottom right hand corner is false

Step-by-step explanation:

Key word perpendicular, it just needs to have relectional symmetry across the line that goes across the figure

The distance Chyna ran is 7 1 / 2 kilometres.

Ronaldo ran 9 / 10 fewer kilometres than Chyna ran. Ronaldo ran 6 3 / 5

kilometres

Therefore, the distance Chyna ran in kilometres can be calculated as follows:

Therefore,

Distance Ronaldo ran = 6 3 / 5  = 33 / 5 kilometres

Hence,

Distance Chyna ran = 33 / 5 + 9 / 10

Distance Chyna ran = 66 + 9 / 10

Distance Chyna ran = 75 / 10

Therefore,

Distance Chyna ran = 7 5 / 10

Distance Chyna ran = 7 1 / 2 kilometres

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The rounded potential volume of the tank is approximately 348,700.9 cubic feet, making the approximate volume of the tank 348,700.9 cubic feet.

To calculate the potential volume of the tank (cylinder), we need to know the radius of the base. However, the given information only provides the circumference of the tank and the height. We can use the circumference to find the radius, and then use the radius and height to calculate the volume of the cylinder.

Let's proceed with the calculations step by step:

Step 1: Find the radius of the tank's base

The formula for the circumference of a cylinder is given by:

C = 2πr, where C is the circumference and r is the radius.

Given that the circumference is approximately 295.3 feet, we can solve for the radius:

295.3 = 2πr

Divide both sides by 2π:

r = 295.3 / (2π)

Calculate the value of r using a calculator:

r ≈ 46.9 feet

Step 2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is given by:

V = π\(r^2h\), where V is the volume, r is the radius, and h is the height.

Substitute the values we have:

V = π(\(46.9^2)(40)\)

V = π(2202.61)(40)

Calculate the value using a calculator:

V ≈ 348,700.96 cubic feet

Step 3: Round the volume to the nearest tenth

The potential volume of the tank, rounded to the nearest tenth, is approximately 348,700.9 cubic feet.

Therefore, the potential volume of the tank is approximately 348,700.9 cubic feet.

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Answer: 16.75 milliliters

Step-by-step explanation:

I believe it is 16.75 because 0.35 + 16.4 is 16.75 why is it addition decimals? Because it says How many milliliters does the mixture contain. It is talking about both combined, I hope this helps you if not sorry this was rushed! I am also 3rd Grade this Year! :D

The total mixture is 16.75 ml

Mixture is a combination of two or more elements to form a third element.

Given here, Jada mixes 0.35 ml to 16.4 ml milk and therefore the total mixture is equal to 0.35 + 16.4 = 16.75 ml

Hence Jada's mixture contains 16.75 ml

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Answer:

Interior Angle - 144 degrees

Exterior Angle - 36 degrees

Step-by-step explanation:

180*8/10=18*8=144

180-144=36

Answer:

$17.10

Hope this helped!

The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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The correct statement is: 'A standard normal distribution has a mean of 0 and a standard deviation of 1 '

The correct answer is an option (b)

In this question, we need to complete given statement.

We know that the normal distribution is a symmetrical and bell-shaped distribution.

In standard normal distribution the mean, median and mode are all equal. Also, it always has a mean of zero and a standard deviation of one.

So,  A standard normal distribution has a mean of 0 and a standard deviation of 1 .

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Answer:

The answer should be either 2(p+10) or 2p + 20

Step-by-step explanation:

just simplify.

Answer:

p^2 +20p+100

Step-by-step explanation:

Use Foil Method

First: p*p=p^2

Outside: 10*p=10p

Inside: 10*p= 10p

Last: 10*10= 100

Simplify p^2+10p +10p +100

ANSWER: p^2 +20p+100

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Answer:

3.

Step-by-step explanation:

Factor: 5

Composite Number: 2

Prime Number: 6

Operation: 8

Integers: 3

Negative Number: 4

Positive Number: 7

Expression: 1

It will take Derrick 40 months or approximately 3 years and 4 months to save $2,000 for the down payment if he continues to add $50 every month.

A down payment is an initial payment made when purchasing an item or a property, typically used to cover a portion of the total cost. The size and frequency of down payment payments can vary depending on the item or property being purchased.

To determine how long it will take Derrick to save $2,000 for the down payment, we need to calculate how much he saves every month and divide the total amount he wants to save by the amount saved per month.

Given that Derrick adds $50 every month, the total amount he saves in a year can be calculated as:

$50 * 12 = $600

So, it would take Derrick to save $2,000 for the down payment is:

$2,000 / $600 = 3.33 years (approx. 4 years)

Therefore, It will take Derrick 40 months, or approximately 3 years and 4 months to save $2,000 for the down payment if he continues to add $50 every month.

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Let's say that the cost of each postcard is "p".

We can write the equation as follows:

7p + 15.89 = 19.32

If we solve for "p", we get:

7p = 19.32 - 15.89

p = 3.43 / 7

p = $<<3.43/7=0.49>>0.49

Therefore, each postcard costs $0.49.

Answer:

7619.04

In scientific notation, it's 7.62 * 10^3

Step-by-step explanation:

Approximately 84% of scores fall between the mean and z = -1 for normally distributed scores.

In a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean, both above and below. Z-scores are used to describe the location of a score relative to the mean, in terms of standard deviations.

A z-score of -1 indicates that a score is 1 standard deviation below the mean. So, if we consider all the scores that are 1 standard deviation below the mean or closer to the mean, then we would have a total of 68% of the scores, which includes the mean.

And, if we consider only the scores that are between the mean and 1 standard deviation below the mean, then we would have 84% of the scores. Hence, approximately 84% of scores would fall between the mean and z = -1 for normally distributed scores.

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