How do i solve for surface area on a rectangular prism

Answer:

11.7

Step-by-step explanation:

1111111938338388383828

Answer:

157.62

Step-by-step explanation:

I took the mass(g) of 34.932 and divided it by the volume of 4.1

\(\frac{34.932}{4.1} =8.52\)

To prove that this was correct I did the same thing for the next row

\(\frac{47.712}{5.6} =8.52\)

I took 8.52 and multiplied it by the volume of 18.5 to get the mass.

\(8.52*18.5=157.62\)

The mass is 157.62

hope this helps! :))

1. The given values, we have: n(AC ∩ B ∩ CC) = 35.

2. n(A' ∩ B ∩ C') = 0.

To answer the first question, we can use the inclusion-exclusion principle:

n(A ∩ B) = n(B) - n(B ∩ AC)         (1)

n(B ∩ AC) = n(A ∩ B ∩ C) + n(A ∩ B ∩ CC)       (2)

n(AC ∩ B ∩ C) = n(A ∩ B ∩ C)        (3)

Using equation (2) in equation (1), we get:

n(A ∩ B) = n(B) - (n(A ∩ B ∩ C) + n(A ∩ B ∩ CC))

Substituting the given values, we have:

n(A ∩ B) = 380 - (115 + 135) = 130

Now, to find n(AC ∩ B ∩ CC), we can use a similar approach:

n(B ∩ CC) = n(B) - n(B ∩ C)         (4)

n(B ∩ C) = n(A ∩ B ∩ C) + n(AC ∩ B ∩ C)       (5)

Substituting the given values, we have:

n(B ∩ C) = 115 + 95 = 210

Using equation (5) in equation (4), we get:

n(B ∩ CC) = 380 - 210 = 170

Finally, we can use the inclusion-exclusion principle again to find n(AC ∩ B ∩ CC):

n(AC ∩ B) = n(B) - n(A ∩ B)

n(AC ∩ B ∩ CC) = n(B ∩ CC) - n(A ∩ B ∩ CC)

Substituting the values we previously found, we have:

n(AC ∩ B ∩ CC) = 170 - 135 = 35

Therefore, n(AC ∩ B ∩ CC) = 35.

To answer the second question, we can use a similar approach:

n(B ∩ C) = n(A ∩ B ∩ C) + n(AC ∩ B ∩ C)       (6)

n(AC ∩ B ∩ C) = 95        (7)

Using equation (7) in equation (6), we get:

n(B ∩ C) = n(A ∩ B ∩ C) + 95

Substituting the given values, we have:

210 = 115 + 95 + n(A ∩ B ∩ CC)

Solving for n(A ∩ B ∩ CC), we get:

n(A ∩ B ∩ CC) = 210 - 115 - 95 = 0

Therefore, n(A' ∩ B ∩ C') = 0.

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Answer:

all real numbers.

Step-by-step explanation:

First, distribute 3 to all terms within the parenthesis:

3(x + 4) = 3(x) + 3(4) = 3x + 12

3x + 12 = 3x + 12

Because both sides are the same, your answer for x is "all real numbers".

~

The equation of the linear function is (d) y = 2/3x + 4

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

Points = (-3, 2), (0, 4), and (3, 6)

A linear function is represented as

y = mx + c

Where

Slope = m

c = the value of y when x = 0

This means that

c = 4

So, we have

y = mx + 4

For the point (3, 6), we have

3m + 4 = 6

So, we have

3m = 2

Divide by 3

m = 2/3

Recall that y = mx + 4

So, we have

y = 2/3x + 4

Hence, the equation is y = 2/3x + 4

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Answer:

3y−2

2y−3

Step-by-step explanation:

Answer:-3y2-3y-7

Step-by-step explanation:

If the "2" after the "y" is meant to be exponents

SOLUTION

Given:

Add two to the difference of seven and five​.

The answer is:

4 or 0

Answer:

The door is 7 feet x 3 feet

Step-by-step explanation:

AREA: 7 x 3 = 21

PERIMITER: 7 + 7 + 3 + 3 = 20

Answer:

Step-by-step explanation:

(1)

apple × apple × 2apple = 54

2apple³ = 54    divide both sides by 2

apple³ = 27 → apple = ∛27

apple = 3

(2)

apple + apple × green_apple = 24   substituite apple = 3

3 + 3 × green_apple = 24        subtract 3 from both sides

3 × green_apple = 21         divide both sides by 3

green_apple = 7

(3)

strawberry - bannana - banana = 0 → strawberry = 2banana

(4)

strawberry + banana + cherry = 24     substitute from (3)

2banana + banana + cherry = 24

3banana + cherry = 24

(5)

apple + banana - cherry = -1          substitute apple = 3

3 + banana - cherry = -1         subtr3 from both sides

banana - cherry = -4

Add both sides of (4) and (5)

 3banana + cherry = 24

+banana - cherry = -4      

4banana = 20       divide both sides by 4

banana = 5

Substitute it to (4):

3(5) + cherry = 24

15 + cherry = 24      subtract 15 from both sides

cherry = 9

Substitute to the last equation:

3 + 5 × 9 = 3 + 45 = 48

/USED PEMDAS/

For any positive numbers a, b and c other than 1, it is shown that Log_b(a) * Log_c(b) * Log_a(c) is equal to 1.

We need to show that the expression Log_b(a) * Log_c(b) * Log_a(c) equals 1, given that a, b, and c are positive numbers other than 1.

Let's start by using the logarithmic identities to simplify the expression.

Using the property Log_b(a) = 1 / Log_a(b), we can rewrite the expression as:

(1 / Log_a(b)) * (1 / Log_b(c)) * (1 / Log_c(a))

Now, let's simplify further by multiplying the three fractions:

1 / (Log_a(b) * Log_b(c) * Log_c(a))

Next, we can use the change of base formula, Log_a(b) = Log_c(b) / Log_c(a), to rewrite the expression as:

1 / ((Log_c(b) / Log_c(a)) * (Log_c(c) / Log_a(c)) * (Log_a(a) / Log_b(a)))

Simplifying, we get:

1 / (Log_c(b) * Log_a(c) * Log_b(a))

Now, we can observe that Log_c(b) * Log_a(c) * Log_b(a) is equal to 1 according to the multiplicative property of logarithms.

Therefore, the expression simplifies to:

1 / 1

which equals 1.

Hence, we have shown that Log_b(a) * Log_c(b) * Log_a(c) is equal to 1 for positive numbers a, b, and c other than 1.

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The probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

b) To find the probability that exactly 4 children would draw the nickel too small, we can use the binomial probability formula. The formula is: P(X = k) = (nCk) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.

In this case, n = 8 (as 8 children are chosen), k = 4 (as exactly 4 children drawing the nickel too small), p = 0.15 (as the probability of a child drawing the nickel too small), and q = 1 - p = 1 - 0.15 = 0.85.

So, the probability that exactly 4 children would draw the nickel too small is: P(X = 4) = (8C4) * (0.15^4) * (0.85^(8-4)).

c) To find the probability that at least one child would draw the nickel too small, we can use the complement rule. The probability of at least one success is equal to 1 minus the probability of no success.

The probability of no success (all children drawing the nickel of the right size) is given by: P(X = 0) = (8C0) * (0.15^0) * (0.85^8).

Therefore, the probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

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By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

From the given figure, KR=9 units, RL=15 units, MT=7.5 units and TL=12.5 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Consider ΔKML and ΔRTL, we get

RL/KL =15/(15+9)

= 15/24

= 5/8

TL/ML =12.5/(12.5+7.5)

= 12.5/20

= 5/8

Here, RL/KL=TL/ML

Here, ∠KLM≅∠RLT

By SAS similarity, ΔKML and ΔRTL are similar triangles

So, ∠KMT≅∠RTL

By SAS similarity, ΔKML and ΔRTL are similar triangles. Therefore, option A is the correct answer.

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Answer:

a

Step-by-step explanation:

got it right in edmentum

The area is equal to 324π square units.

To find the area of a circle with radius 18 units, we can use the formula for the area of a circle, which is given by A = πr^(2), where r is the radius.

Given that the radius is 18 units, we can plug this value into the formula:

A = π(18)^2

Now, square the radius:

A = π(324)

Next, multiply 324 by π:

A = 324π

Therefore, the area of the circle with radius 18 units is 324π square units.

Now, let's compare the options with the given options:

a) 18π units^(2)- This is incorrect, as we calculated the area to be 324π square units.

b) 36π units^(2)- This is also incorrect, as our calculated area is 324π square units.

c) 9π units^(2)- This is incorrect, as our calculated area is 324π square units.

d) 324π units^(2)- This is the correct option , as we calculated the area to be 324π square units.

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To find the steady-state probability vector for the given Markov process with transition matrix A, we need to solve the equation A * x = x, where A is the transition matrix and x is the probability vector.

The given transition matrix A is:

A = [1/2  1/5]

   [1/2  4/5]

Let's assume the probability vector as x = [p₁  p₂], where p₁ and p₂ are the probabilities.

Setting up the equation A * x = x, we have:

[1/2  1/5]   [p₁]   [p₁]

[1/2  4/5] * [p₂] = [p₂]

Expanding the matrix multiplication, we get:

(p₁/2 + p₂/2) = p₁

(p₁/5 + 4p₂/5) = p₂

Simplifying the equations, we have:

p₁/2 + p₂/2 = p₁

p₁/5 + 4p₂/5 = p₂

Multiplying both equations by 10 to eliminate the denominators, we get:

5p₁ + 5p₂ = 10p₁

2p₁ + 8p₂ = 10p₂

Simplifying further, we have:

5p₁ - 10p₂ = 0

2p₁ - 2p₂ = 0

Solving the equations, we find:

3p₁ = 5p₂

To find the steady-state probability vector, we normalize the probabilities by setting their sum to 1. Let's assume p₁ = 5 and p₂ = 3:

p₁ + p₂ = 5 + 3 = 8

Normalizing the probabilities, we divide each by 8:

p₁ = 5/8 ≈ 0.625

p₂ = 3/8 ≈ 0.375

Therefore, the steady-state probability vector for the given Markov process is approximately [0.625 0.375].

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Answer:

90

Step-by-step explanation:

its half

The outward flux of the given vector field across the surface S formed by planes x=0, x=5, y=0, y=25, z=0, and z=125 is 31(5⁸)/2.

The flux of a vector field F across a closed surface S is given by the surface integral of the dot product of F and the unit normal vector to S, which is oriented outward.

In this problem, we need to find the outward flux of the vector field F = 5(xyi + yzj + xzk) across the surface S formed by the planes x=0, x=5, y=0, y=25, z=0 and z=125 in the first octant.

To find the outward normal vector to each of the six surfaces of S, we can use the unit vectors i, j, and k.

For example, the outward normal vector to the plane x=0 is -i, since the plane is perpendicular to the x-axis and points in the negative x direction. Similarly, the outward normal vector to the plane x=5 is i, and so on.

Next, we need to compute the surface area of each of the six planes. The area of the plane

x=5 is (25)(125) = 3125,

and the area of each of the other planes is zero, since they lie on one of the coordinate planes. Therefore, the total surface area of S is

5(3125) = 15,625.

Using the dot product between F and the outward normal vector to each plane, we can find the flux through each plane. The flux through the planes x=0 and x=5 is zero, since the normal vectors are perpendicular to the x component of F.

The flux through the planes y=0 and y=25 is zero, since the normal vectors are perpendicular to the y component of F. The flux through the planes z=0 and z=125 is 5(125)(25), since the normal vectors point in the direction of the z component of F.

Finally, we can add up the flux through each of the six planes to find the total outward flux across S

flux = 2(5)(125)(25) = 31(5⁸)/2

Therefore, the answer is 31(5⁸)/2.The flux of a vector field F across a closed surface S is given by the surface integral of the dot product of F and the unit normal vector to S, which is oriented outward.

Therefore, the answer is 31(5⁸)/2. The correct option is A).

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Standard deviation is a measure of variation.

The degree of variance or dispersion in a set of data values is measured statistically using the standard deviation. It reveals how far the data values differ from the data set's average. Data points tend to be close to the mean when the standard deviation is low, and are dispersed over a larger range when the standard deviation is high.

While measurements of the centre, such as mean, median, and mode, are used to describe a data set's central tendency. The median is the midway value when a data set is ordered, and the mode is the value that appears in a data set the most frequently. The mean is the sum of the data divided by the number of observations.

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Hypothesis test used to test the batting average of the two given team national league and American league is given z-test.

As given in the question,

Given : Mean batting for American league is not equal to Mean batting for National league.

Therefore, hypothesis test used to test the batting average of the national league and American league is given z-test.

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As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution becomes smaller.

The standard deviation shows the average level of variability in your dataset. It provides the standard deviation of every statistic.

A low standard deviation indicates that values are frequently within a certain distance of the mean, whereas a high standard deviation indicates that values are frequently outside of this range.

The standard normal distribution is special case of normal distribution which centers at 0 thus the mean μ of standard normal distribution is zero and the dispersion from mean value is unity measured by standard deviation σ.

Thus, the mean of standard normal distribution is zero and standard deviation is unity.

Consider the numbers 2, 1, 3, 2, and 4. The deviations from the mean of the observations will be represented by the average and the sum of squares, which will be 2.4 and 5.2, respectively.

This indicates that the standard deviation will be (5.2/5) = 1.01.

Therefore,

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution becomes smaller.

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The expressions B, C, and D are true when the number 8 fills in the blank.

Let's check each expression to see if the number 8 fills in the blank to make the equation true:

A) 4(7 + 4) = 28 + 8

4(11) = 28 + 8

44 = 36

This is not true, so option A is incorrect.

B) 8(3 + 11) = 24 + 88

8(14) = 24 + 88

112 = 112

This is true, so option B is correct.

C) 7(8 + 12) = 56 + 84

7(20) = 56 + 84

140 = 140

This is true, so option C is correct.

D) 4(9 + 2) = 36 + 8

4(11) = 36 + 8

44 = 44

This is true, so option D is correct.

So, the expressions B, C, and D are true when the number 8 fills in the blank.

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Answer:

Step-by-step explanation:

Equation for the linear function has been given as,

y = 26 - 4x

For x = 1,

y = 26 - 4(1)

  = 26 - 4

  = 22

For x = 2,

y = 26 - 4(2)

  = 26 - 8

  = 18

For x = 3,

y = 26 - 4(3)

  = 26 - 12

  = 14

For x = 6,

y = 26 - 4(6)

  = 26 - 24

  = 2

Therefore, table for the function will be,

x               y

1              22  

2              18

3              14

6               2

The given system of equations has infinitely many solutions.

Explanation:

To determine the number of solutions for the given system of equations, we can analyze the system using various methods such as substitution, elimination, or matrix operations. Let's use the method of elimination to solve the system.

Given equations:

1) 2x + y = -1

2) x + y - z = -4

3) 3x + 3y + z = 0

We can start by manipulating the equations to eliminate variables. Multiplying equation 2 by 2 and adding it to equation 1 will cancel out the variable "y":

1) 2x + y = -1

2) 2(x + y - z) = 2(-4)    ->    2x + 2y - 2z = -8

Adding equation 1 and the modified equation 2 gives us:

4x - 2z = -9          (equation 4)

Next, let's multiply equation 3 by -2 and add it to equation 4 to eliminate the variable "z":

-6x - 6y - 2z = 0

4x - 2z = -9

Simplifying:

-6x - 6y - 2z + 4x - 2z = 0 - 9

-2x - 6y - 4z = -9

Dividing the equation by -2:

x + 3y + 2z = 4.5     (equation 5)

Now we have equations 4 and 5:

4x - 2z = -9

x + 3y + 2z = 4.5

Looking at the equations, we notice that the variable "x" can be eliminated by multiplying equation 5 by 4 and adding it to equation 4:

4(x + 3y + 2z) = 4(4.5)    ->    4x + 12y + 8z = 18

Adding equation 4 and the modified equation 5 gives us:

4x - 2z + 4x + 12y + 8z = -9 + 18          (equation 6)

Simplifying:

8x + 12y + 6z = 9          (equation 6)

From equations 6 and 5, we can see that both have the same coefficients for variables "x," "y," and "z." This indicates that the two equations are dependent and represent the same line in three-dimensional space.

Since the system has dependent equations, there are infinitely many solutions. In other words, any values of "x," "y," and "z" that satisfy the equation of the line represented by the system will be a solution.

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To construct a confidence interval to estimate the true average tip with 90% confidence, we can use the following formula:
Confidence Interval = mean ± (critical value * standard deviation / sqrt(sample size))

In this case, the sample mean is 11.6% and the standard deviation is 2.5%. The critical value for a 90% confidence level is 1.645 (obtained from the z-table).

Plugging in the values, we have:

Confidence Interval = 11.6 ± (1.645 * 2.5 / sqrt(sample size))

Since the sample size is not mentioned in the question, we cannot calculate the exact confidence interval. However, you can use the formula provided above and substitute the actual sample size to obtain the interval. Remember to round the endpoints to two decimal places, if necessary.

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Answer:

Let call the angle X

Its complement will be 90-x

Its supplement will be 180-x

(180-x)+15 = 4(90-x)

180-x+15 = 360-4x

4x-x = 360-180-15

3x = 165

x = 55

Prove

The complement of 55 is 35

And the supplement of 55 is 125

Now we must see if the relation stated holds

125+15 = 4(35)

125+15 = 140 The measure of the supplement of an angle is 15 degrees less than four times the measure of the complement.

140 = 140

Therefore the solution of the problem is given by an angle of 55 degrees.

Answer:

2.8

Step-by-step explanation:

Step 1:

7x + 3 = 10x - 5.4  Equation

Step 2:

3 = 3x - 5.4   Subtract 7x from both sides

Step 3:

8.4 = 3x   Add 5.4 to both sides

Step 4:

8.4 ÷ 3  Divide

Answer:

x = 2.8

Hope This Helps :)

Answer:

x=2.8

Step-by-step explanation:

7x + 3 = 10x - 5.4

(first, put x's on your left side, and normal numbers on right side, watch out for changing sign in front of the numbers)

7x - 10x = -3 -5.4

(subtract/add up the numbers)

-3x = - 8.4

(divide whole equation with -3 (which is in front of x)

x = 2.8

Answer:

81 levels

Step-by-step explanation:

Answer: 1

Step-by-step explanation:

5 * 9 = 45

9/9 = 1

Or

5/45 / 5/5 =1/9

Answer:

D

Step-by-step explanation: D

For an investment with completely certain returns, the return distribution would be a very tight, vertical line at the predetermined return. This is because the risk associated with the investment is zero, meaning the return will not vary regardless of market conditions.

For an investment with completely uncertain returns, the return distribution would be a flat line with no particular shape. This is because the risk associated with the investment is very high, meaning the return could be anything, as it is impossible to predict the returns with any degree of accuracy.

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The Laplace transform of the given function f(t) is (5 - 5e^(-4s))/s.

We can write the given function f(t) in terms of unit step functions as follows:

f(t) = 5u(t) - 5u(t-4)

This expression gives us the value of f(t) as 5 for 0 ≤ t < 4, and as -5 for t ≥ 4.

To find the Laplace transform of f(t), we use the linearity property of Laplace transforms and the fact that the Laplace transform of a unit step function u(t-a) is given by e^(-as)/s. Therefore, we have:

L{f(t)} = L{5u(t)} - L{5u(t-4)}

= 5L{u(t)} - 5L{u(t-4)}

= 5 * [1/s] - 5 * [e^(-4s)/s]

Simplifying this expression, we get:

L{f(t)} = (5 - 5e^(-4s))/s

Therefore, the Laplace transform of the given function f(t) is (5 - 5e^(-4s))/s.

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Answer:

34 = s

Step-by-step explanation:

To solve for s, add 21 to both sides of the equation.

13 = s - 21

21 + 13 = s - 21 + 21

34 = s

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