Find the volume of rectangular prism. (You should have at least 2 steps shows in your work!)(show all decimal places or a fraction)

The multiplicative inverse of 5/6 as required to be determined in the given task content is 6/5.

It follows from the task content that the multiplicative inverse of the given number; 5/6 is required to be determined.

By definition; it follows that the Multiplicative inverse of an expression refers to its reciprocal. It is the value that, when multiplied by the original, give a product of 1 (the multiplicative identity element).

So,

5/6 × 6/5

= 30/30

= 1

Hence, 6/5 is the multiplicative inverse of 5/6

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It should be noted that 81.85% of the scores are between 72 and 87.

The probability that a score is greater than 77 is approximately 0.8413.

a) The z-score for 72 is calculated as:

z = (72 - 82) / 5 = -2

The z-score for 87 is calculated as:

z = (87 - 82) / 5 = 1

0.8413 - 0.0228 = 0.8185

So, approximately 81.85% of the scores are between 72 and 87.

b) The z-score for 77 is calculated as:

z = (77 - 82) / 5 = -1

1 - 0.1587 = 0.8413

Therefore, the probability that a score is greater than 77 is approximately 0.8413 (or 84.13%).

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The slope of the line perpendicular to the line is m = ( 7/2 )

Given data ,

The equation of the given line is y = -2/7x + 3/7.

Now , it is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The slope of the given line is -2/7, which means that for any line perpendicular to this line, the slope would be the negative reciprocal of -2/7.

So , m = ( 7/2 )

Hence , the slope of the perpendicular line is = 7/2

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Answer:

m = 3 + 2√3 or m = 3 - 2√3

Step-by-step explanation:

The given equation is:

m^2 - 6m = 3

We can rewrite the equation in standard quadratic form as:

m^2 - 6m - 3 = 0

We can use the quadratic formula to solve for m:

m = [-b ± √(b^2 - 4ac)] / 2a

where a = 1, b = -6, and c = -3.

Substituting these values, we get:

m = [-(-6) ± √((-6)^2 - 4(1)(-3))] / 2(1)

m = [6 ± √(36 + 12)] / 2

m = [6 ± √48] / 2

m = [6 ± 4√3] / 2

Simplifying the expression, we get:

m = 3 ± 2√3

Therefore, the solutions to the equation are:

m = 3 + 2√3 or m = 3 - 2√3

If this helps, please mark my answer as brainliest so i can help you more!:)

Answer:

[tex]x=3+2\sqrt{3}\\\\ x=3-2\sqrt{3}[/tex]

Step-by-step explanation:

The quadratic formula is:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore, to solve the given equation using the quadratic formula, first subtract 3 from both sides of the equation so that it is in the required form.

[tex]m^2-6m-3=3-3[/tex]

[tex]m^2-6m-3=0[/tex]

Comparing the coefficients:

Substitute the values of a, b and c into the formula and solve for x:

[tex]\implies x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(-3)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{36-4(-3)}}{2}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{36+12}}{2}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{48}}{2}[/tex]

Rewrite 48 as a 4² · 3:

[tex]\implies x=\dfrac{6 \pm \sqrt{4^2 \cdot 3}}{2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{4^2} \sqrt{3}}{2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies x=\dfrac{6 \pm 4 \sqrt{3}}{2}[/tex]

Simplify:

[tex]\implies x=\dfrac{6}{2}\pm\dfrac{4 \sqrt{3}}{2}[/tex]

[tex]\implies x=3\pm2 \sqrt{3}[/tex]

Therefore, the values of x are:

[tex]x=3+2\sqrt{3}\\\\ x=3-2\sqrt{3}[/tex]

Answer:

Step-by-step explanation:

a. Using the formula p(t) = 1 - e^(-kt), where k = 0.28:

Probability of mastering the dance's steps in 1 trial: p(1) = 1 - e^(-0.28*1) ≈ 0.243

Probability of mastering the dance's steps in 2 trials: p(2) = 1 - e^(-0.28*2) ≈ 0.446

Probability of mastering the dance's steps in 5 trials: p(5) = 1 - e^(-0.28*5) ≈ 0.846

Probability of mastering the dance's steps in 11 trials: p(11) = 1 - e^(-0.28*11) ≈ 0.981

Probability of mastering the dance's steps in 16 trials: p(16) = 1 - e^(-0.28*16) ≈ 0.997

Probability of mastering the dance's steps in 20 trials: p(20) = 1 - e^(-0.28*20) ≈ 0.999

b. The rate of change, p'(t), can be found by taking the derivative of the function p(t):

p'(t) = k * e^(-kt)

c. Here's a graph of the function p(t):

I apologize for the technical issue, but the graph doesnt load, so here's a description of the graph:

The graph of p(t) should be an increasing curve that starts at 0 and approaches 1 asymptotically. As t increases, the rate of change of p(t) decreases, which means that the curve becomes flatter and approaches the horizontal asymptote of y=1. The curve is concave down, meaning that its rate of change is decreasing. At t=0, the rate of change is k, which is the steepest point of the curve.

_______________________

graph of p(t) = 1 - e^(-0.28*t)

The x-axis represents the number of learning trials, and the y-axis represents the probability of mastering the dance's steps. As the number of trials increases, the probability of mastering the steps approaches 1 (or 100%).

The likelihood that Mia and Lia place in 1st or 2nd is unlikely

From the question, we have the following parameters that can be used in our computation:

People = 50

Positions = 1st, 2nd, and 3rd place

The probabilities are

P(1st) = 1/50

P(2nd) = 1/49

Using the above as a guide, we have the following:

P = 1/50 * 1/49

Evaluate

P = 0.00040816326

This value is less than 50%

So, the likelihood is unlikely or less likely

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Answer:

53

Step-by-step explanation:

20+8=28

90-28=62

62-9=53

90 angle!

Answer:

18

Step-by-step explanation:

AC=AB

BC^2=AB^2+AC^2

162+162=324

Square root of 324 is 18.

(a) Sum of values = Mean × Number of values = 64 × 5 = 320

(b) Sum of values = Mean × Number of values = 8.2 × 5 = 41

Fifth value = Sum of values - sum of known values = 41 - (6 + 10 + 7 + 12) = 41 - 35 = 6

(c) The resulting middle number when computing 10, 20, 30, 40, 50;that is (10 + 20 + 30 + 40 + 50)/5, totals up to 150 and dividing that number by 5 reflects a mean of 30.

i) Forming an average of 20, 30, 40, 50, 60;that is (20 + 30 + 40 + 50 + 60)/5 provides an outcome of 200 and divided by 5 reveals a mean of 40.

ii) With 0, 10, 20, 30, 40 used, (0 + 10 + 20 + 30 + 40)/5 practices calculation yielding a total of 100 which, split into five parties, imparts a mean of 20.

iii) Taking into consideration the input of 100, 200, 300, 400, 500;whereby (100 + 200 + 300 + 400 + 500)/5 develops a collective of 1500, cut in half produces a mean of 300.

iv) Calculating 1, 2, 3, 4, 5's mean; namely (1 + 2 + 3 + 4 + 5)/5 ascertains a collective amount of 15, divide that figure by five culminates with a mean of 3.

v) Accordingly, the following general assumptions can be made:

i) Introducing a constant to each value augments the mean by that very same constant.

ii) Extracting a constant from all values decrements the mean by such said constant.

iii) Multiplying every value by one constant multiplies the mean by the same specific constant.

iv) Dividing all values by a particular constant divides the mean by that given constant.

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Answer:14

Step-by-step explanation:

2 pants can only go with the different shirts once. So it should be 14

Answer:

First, we need to calculate the volume of the rectangular fish tank. The volume of a rectangular solid is given by the formula:

volume = length x width x height

Plugging in the values we have, we get:

volume = 35 cm x 30 cm x 25 cm = 26,250 cubic cm

Next, we need to find the volume of water in the fish tank. The volume of water is equal to the volume of the space the water occupies, which is a rectangular solid with length 35 cm, width 30 cm, and height 20 cm. The volume of this rectangular solid is:

volume = length x width x height = 35 cm x 30 cm x 20 cm = 21,000 cubic cm

To convert cubic centimeters (cm^3) to liters (L), we need to divide by 1000:

volume = 21,000 cm^3 ÷ 1000 = 21 L

Therefore, the volume of water in the fish tank is 21 liters.

Step-by-step explanation:

The variables to the parallelogram OPQR are;

1. coordinates of points M is (1, 2.5)

2. The length of PQ is 4

3. The length of QR is 5.4

4. The length of PM is 3.9

5. The length of OM is 2.7

6. The perimeter of the parallelogram OPQR is approximately  18.8

7. if m ∠QMR = 120° m ∠ QMP = 60°

8. If m ∠ QRO = 80°  m ∠ROP =  100°

To calculate for every listed length of parallelogram OPQR it will be helpful to list all the coordinate for this diagram and they are;

O (0, 0)

p (-2, 5)

R (4, 0)

Q (2, 5)

To find for M, we could just get it from the diagram by looking at the points for x and then y. This is (1, 2.5). You can also calculate it like this

Mx = (Px + Rx)/2 = (-2 + 4)/ 2 = 2/2 = 1

My = (Py + Ry)/2 = ( 5 + 0)/2 = 2.5

To calculate for the length of any side, we say

LPQ = √(Qx -Px)² + (Qy - Py)² = √(2 - -2)² + (5-5)² = √8 = 4

LQR = √(Rx -Qx)² + (Ry - Qy)²

LPM = √(Mx -Px)² + (My - Py)²

LOM = √(Mx -Mx)² + (Oy - My)²

if m∠QMP = 180° - m∠QMR = 180° - 120° = 60°

The question below is as seen in the pictures provided.

The diagonals of parallelogram OPQR intersect at point M.

What are the coordinates of points M?

Find PQ

Find QR

Find PM

Find OM

Find permeter of parallelogram OPQR

if m ∠QMR = 120° what is m ∠ QMP

If m ∠ QRO = 80°  what is m ∠ROP

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Answer: $34.01

Step-by-step explanation:

To get the answer, we must first add up the entire amount of money saved after four weeks of mowing the neighbor's lawn, then subtract the bike's price.

Since we get $40 a week, after 4 weeks we will have saved the following:

40 × 4 = 160

We will therefore have $160 to spend on the bike. The bike costs $125.99, so we will have the following amount of money after purchasing the bike:

160 - 125.99 = 34.01

Therefore, after purchasing the bike, we will have $34.01 leftover.

a)

The investment cost for replacing the 800 fixtures is $240,000.

b)

Annual utility cost savings is $57,600/year.

c)

Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.

We have,

a.

The investment cost for replacing the 800 fixtures is given as $300 per fixture, so the total investment cost would be:

Total Investment Cost = Number of fixtures x Investment cost per fixture

Total Investment Cost = 800 x $300

Total Investment Cost = $240,000

b.

To calculate the annual utility cost savings, we need to find the difference in the watt-hour consumption per fixture between HID and LED lighting, and multiply it by the number of fixtures, operating hours per day, operating days per year, and the metered utility rate per kilowatt-hour:

Energy consumption savings per fixture per hour = HID watt hour consumption - LED watt hour consumption

Energy consumption savings per fixture per hour = 500 watts/hr - 300 watts/hr

Energy consumption savings per fixture per hour = 200 watts/hr

Total energy consumption savings per hour for 800 fixtures:

= Energy consumption savings per fixture per hour x Number of fixtures

Total energy consumption savings per hour for 800 fixtures.

= 200 watts/hr x 800

Total energy consumption savings per hour for 800 fixtures.

= 160,000 watts/hr

Total energy consumption savings per year = Total energy consumption savings per hour x Operating hours per day x Operating days per year

Total energy consumption savings per year = 160,000 watts/hr x 10 hrs/day x 300 days/year

Total energy consumption savings per year = 480,000,000 watt-hours/year

Total energy consumption savings per year in kilowatt-hours (kWh):

= Total energy consumption savings per year / 1,000

Total energy consumption savings per year in kWh = 480,000,000 / 1,000

Total energy consumption savings per year in kWh = 480,000 kWh/year

Annual utility cost savings:

= Total energy consumption savings per year in kWh x Metered utility rate per kWh

Annual utility cost savings = 480,000 kWh/year x $0.12/kWh

Annual utility cost savings = $57,600/year

c.

To evaluate the proposal using net present value (NPV), we need to calculate the present value of the investment cost and the present value of the annual utility cost savings over a 15-year period.

Using the Present Value of the Ordinary Annuity formula with a 15-year life and 8% minimum rate of return, we get:

PV of Investment Cost = -$240,000 (negative because it's a cash outflow)

PV of Annual Utility Cost Savings = $514,883.81

NPV = PV of Annual Utility Cost Savings - PV of Investment Cost

NPV = $514,883.81 - (-$240,000)

NPV = $754,883.81

Therefore,

The investment cost for replacing the 800 fixtures is $240,000.

Annual utility cost savings is $57,600/year.

Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.

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Answer:5.08

4.34 are correct

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

6u^2 - 3u - 8 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 6, b = -3, and c = -8. Substituting these values, we get:

u = (3 ± sqrt(9 + 192)) / 12

u = (3 ± sqrt(201)) / 12

Therefore, either:

Answer:

A) [tex]x = \dfrac{\log_6(46) + 6}{4}[/tex]

B) [tex]x = \dfrac{\ln(11)}{2}[/tex]

C) [tex]x = \dfrac{11}{5}[/tex]

Step-by-step explanation:

A) We can solve for x by taking log base 6 of both sides.

[tex]\log_6(6^{4x-6}) = \log_6(46)[/tex]

[tex]4x - 6 = \log_6(46)[/tex]

[tex]4x = \log_6(46) + 6[/tex]

[tex]\boxed{x = \dfrac{\log_6(46) + 6}{4}}[/tex]

B) First, we have to divide both sides by 2.

[tex]2e^{2x} / 2= 22 / 2[/tex]

[tex]e^{2x} = 11[/tex]

Then, we can solve for x by taking the natural log (log base e) of both sides.

[tex]\ln(e^{2x})= \ln(11)[/tex]

[tex]2x= \ln(11)[/tex]

[tex]\boxed{x = \dfrac{\ln(11)}{2}}[/tex]

C) We can solve for x by raising 2 to the power of each side.

[tex]2^{\log_2(5x + 5)} = 2^4[/tex]

This cancels the log base 2 on the left.

[tex]5x + 5 = 16[/tex]

[tex]5x = 11[/tex]

[tex]\boxed{x = \dfrac{11}{5}}[/tex]

Answer:

  cylinder

Step-by-step explanation:

You want to know which of two popcorn containers is a better value:

The volume formulas for the two shapes are ...

  V = 1/3πr²h . . . . . cone

  V = r²h . . . . . . . . . cylinder

For r = d/2, the ratio of these two volumes is ...

  [tex]\dfrac{V_{con}}{V_{cyl}}=\dfrac{\dfrac{1}{3}\pi\left(\dfrac{d_{con}}{2}\right)^2h_{con}}{\pi\left(\dfrac{d_{cyl}}{2}\right)^2h_{cyl}}=\dfrac{d_{con}^2\cdot h_{con}}{3\cdot d_{cyl}^2\cdot h_{cyl}}=\dfrac{12^2\cdot19}{3\cdot 8^2\cdot 15}=\dfrac{2736}{2880}=0.95[/tex]

The cone has less volume and costs more, so the cylindrical container is the better value.

Check the picture below.

bearing in mind that a vertical line always has that slope.

a) An equation that represents the amount of money that Gilberto

receives during a school year:  y = 5 + (0.5) x

b) The number of correct answers Gilberto needs to buy a new shirt that costs $25 = 40

Let us assume that y represents the amount of money and x represents the number of correct answers.

We know that One dollar = 100 cents.

so, 50¢ = 0.5 dollars

From the described informtaion, we can write the equation that represents the amount of money that Gilberto receives during a school year as: y = 5 + (0.5) x

Now we need to find the number of correct answers Gilberto needs to buy a new shirt that costs $25

i.e., for y = 25, we need to find the value of x.

Substitute y = 25 in above equation.

25 = 5 + (0.5) x

We solve this equation for x

(0.5) x = 20

x = 20 / (0.5)

x = 40

This means that he needs to give 40 correct answers.

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The complete question is:

Gilberto's  grandfather gives Gilberto $5 and then 50¢ for each math question he answers correctly on his math exams for the year.

a. Write an equation that represents the amount of money that Gilberto

receives during a school year. Explain what the variables and numbers mean.

b. Use the equation to find the number of correct answers Gilberto needs to buy a new shirt that costs $25. Show your work.

The value of p in the equation 7p - 4 = 8 is p = 12/7

From the question, we have the following parameters that can be used in our computation:

7p - 4 = 8

Add 4 to both sides

So, we have

7p = 12

Divide both sides by 7

So, we have

p = 12/7

Hence, the solution is p = 12/7

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The requried, perimeter and area of the parallelogram are 18.4 centimeters and 18 square centimeters respectively.

To find the perimeter of parallelogram EFGH, we need to find the length of all four sides and add them up. The distance formula is used to find the length of each side:

EF = √((2-(-1))² + (8-5)²) = √(3² + 3²) = √(18)

FG =√(20)

GH = √(18)

HE = √(20)

Therefore, the perimeter is:

Perimeter = EF + FG + GH + HE = √(18) + √(20) + √(18) + √(20) ≈ 18.4

Similarly,
The area of the parallelogram is given as,
= 18 square centimeters

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The correct statement regarding whether the graph represents a function is given as follows:

No, it is not a function.

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

In the graph, we have that at x = 0 = y-axis, the function has three numeric values, which is a case of vertically aligned points, hence the graph does not represent a function.

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Answer: The brother is 16 and she is 19.

Step-by-step explanation:

35 - 3 = 32

32 / 2 = 16

16 + 3 = 19

Answer:

H

Step-by-step explanation:

Firstly, G and J cannot be the answers because the beginning numbers are too big. If you look at the fractions, you can see 2 and 7/8 because 2 is the smallest of all of them. Now the answer is between F and H.

In F, the second number is 3 and 1/2.

In H, the second number is 3 and 1/4.

If you want to make it an improper fraction to visualize better, it would be 7/2 and 12/4=6/2. Or you can just compare to see which is smaller, 1/2 or 1/4. In this case, 3 and 1/4 is smaller. Therefore the answer is H.

The area of the semicircle is 157. 00 cm

To determine the area of the semi-circle, we need to consider the formua.

the formula for calculating the area of a semi-circle is expressed with the equation;

A = 1/2π²

Such that the parameters of the formula are;

It is important to note that

Formula for diameter is expressed as

Diameter = 2radius

Radius = 10cm

Substitute the values

Area = 1/2× 3.14 × 100

Multiply the values

Area = 157 cm²

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The price at the point of equilibrium is 105

From the question, we have the following parameters that can be used in our computation:

The supply/demand graph

The price at the point of equilibrium is the price where the lines/curves of the supply and the demand functions intersect

Using the above and the graph as a guide, we have the following:

Price = 105 when demand = supply

Hence, the price at the point of equilibrium is 105

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Question

Using the above supply/demand graph, what is the price at the point of equilibrium? a. 105 b. 100 c. 95 d. 80

The height from the ground to the top of the ladder is 61. 28 feet

First, we need to know that their are six different trigonometric identities.

These identities includes;

From the information given, we have that;

the height of the ladder that is leaning against the house = 80 feet

This the hypotenuse side

The angle of elevation is 50 degrees

Then, the opposite side is the height from the ladder = x

Using the sine identity, we have;

sin 50 = x/80

cross multiply the values

x = 61. 28 feet

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Answer:

2700

Step-by-step explanation:

20 inches x 15 inches x 9 inches! <3

also get some sleep lol