What is the volume of the triangular prism?

A) 12 cm3
B) 18 cm3
C) 24 cm3
D) 48 cm3

Answer:

P(E and F) = 0.123

P(E or F) = 0.677

P(E|F) = 0.189

Step-by-step explanation:

The formula for conditional probability is P(B|A) = P(A and B)/P(A)

The addition rule is P(A or B) = P(A) + P(B) - P(A and B)

∵ P(E) = 0.15

∵ P(F) = 0.65

∵ P(F|E) = 0.82

- Use the first rule above

∵ P(F|E) = P(E and F)/P(E)

- Substitute the values of P(F|E) and P(E) to find P(E and F)

∴ 0.82 = P(E and F)/0.15

- Multiply both sides by 0.15

∴ 0.123 = P(E and F)

- Switch the two sides

∴ P(E and F) = 0.123

Use the second rule to find P(E or F)

∵ P(E or F) = P(E) + P(F) - P(E and F)

∴ P(E or F) = 0.15 + 0.65 - 0.123

∴ P(E or F) = 0.677

Use the first rule to find P(E|F)

∵ P(E|F) = P(F and E)/P(F)

- P(F and E) is the same with P(E and F)

∴ P(E|F) = 0.123/0.65

∴ P(E|F) = 0.189

Answer:

If it was reflected over the y-axis, the x variable would be inverted, causing the coords to be M(2,8)

Answer:

313.3084 in3

Step-by-step explanation:

To find the final volume of the finished ball, we need to find the volume of the whole sphere and then decrease it by the volume of the three holes.

The volume of the sphere is given by this formula:

V = (4/3)*pi*r^3

Where r is the radius. In our case, the radius is 8.5 / 2 = 4.25 in, so the volume is:

V1 = (4/3)*pi*4.25^3 = 321.5551 in3

The volume of each cilindrical hole can be calculated as:

V = pi*r^2*h

Where r is the radius and h is the height. We have that the radius is 1/2 = 0.5 inches and the height is 3.5 inches, so:

V2 = pi*0.5^2*3.5 = 2.7489 in3

So the final volume is:

V = V1 - 3*V2 = 321.5551 - 3*2.7489 = 313.3084 in3

Answer:

313.313inches³

Step-by-step explanation:

A bowling ball is spherical in shape hence,

The Formula used to calculate the volume of sphere is

= 4/3 πr³

For the question, we were given diameter.

Diameter of the bowling ball = 8.5 inches

Radius = Diameter ÷ 2

Radius = 8.5 inches ÷ 2

Radius = 4.25 inches

Hence,

Volume of a Sphere =

4/3πr³

= 4/3 × π ÷ 4.25

= 321.55509806inches³

Approximately = 321.56inches³

From the question we can see that the bowling ball has 3 cylindrical holes in it

With a diameter of 1 inch and a depth of 3.5inches

Hence we find the volume of these holes

Volume of a cylinder = πr²h

Diameter = 1 inch,

Radius = Diameter /2 = 1/2 inches

Height(Depth) = 3.5 inches

Volume of the cylindrical holes = π ×(1/2) ² × 3.5

Volumes = 2.749inches³

Since we have 3 holes ,

Volumes of the 3 holes = 2.749inches³ × 3

= 8.247inches³

The Volume of the total Spherical bowling ball

= Volume of the total bowling ball without holes - Volume of the cylindrical holes on the bowling ball

= 321.56inches³ - 8.247inches³

= 313.313inches³

Hence, the best estimate of the volume of resin in the finished ball = 313.313inches³

Answer:

AB = 23.4 inches

Step-by-step explanation:

If the diameter of the wheel is 25 inches, we have that its radius is 25/2 = 12.5 inches.

If we draw a radius to the bottom of the wheel and a radius to point A, we have a triangle where we can use Pythagoras' formula:

(see image attached for better understanding)

r^2 = (r-8.1)^2 + (AB/2)^2

12.5^2 = 4.4^2 + AB^2/4

156.25 = 19.36 + AB^2/4

AB^2/4 = 136.89

AB^2 = 547.56

AB = 23.4 inches

Answer:

1. 336 in3

2. 384 cm3

3. 336 m3

Step-by-step explanation:

im not positive but i think you just multiply the numbers and put the label as cubed

Answer:

Alvin can't have more than 2 fishes on his tank.

Step-by-step explanation:

In order to calculate how many fish Alvin can have in his tank we first need to calculate the volume of the tank. A prism's volume is given by the following formula:

v = Abase*h

Therefore for Alvin's, we have:

v = 0.9*0.6 = 0.54 m³

Since he can't have more than 5 fish per cubic meter we can use a rule of three in a way that:

5 fish -> 1 m³

x fish -> 0.54 m³

5/x = 1/0.54

x = 0.54*5 = 2.7

Since he can't have a 0.7 fish and in order to mantain the density to the recommended level, he can't have more than 2 fishes.

Answer:

6 in.

Step-by-step explanation:

The Length of the large rectangle is 2 units.

It is required to find the length of the large rectangle.

A rectangle is a type of quadrilateral, whose opposite sides are equal and parallel. It is a four-sided polygon that has four angles, equal to 90 degrees. A rectangle is a two-dimensional shape.

Given:

A rectangle is 2 inches wide, and more than 2 inches long.

According to given question we have,

Ratio of width to length of known rectangle is 2:4 this simplifies to 1:2

The smaller similar rectangle will have the same ratio. .i.e. 1:2

Since the width is 1 then the length will be 2.

.This can also be looked at another way. the second value in the ratio is

2:1 of the first value in the ratio and the first value is 1:2 of the second value.

So, Length of the large rectangle is 2 units.

Width of the large rectangle is 1 units.

Therefore, the Length of the large rectangle is 2 units.

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Answer:

2(4+x)

Step-by-step explanation:

"Twice the sum of" tells us it will be the equation times two

"the sum of four and a number" is easy, thats 4 + x

The second number is x because the number is not specified so we need a place holder, x in this case, to tell us that the number is not given.

All this put together = twice the sum of four and a number, or 2(4+x)

The expression for "twice the sum of four and a number" is represented by 2(x + 4) or 2 * (x + 4), signifying that you first sum the number with four and then double the result.

The expression that correctly represents "twice the sum of four and a number" is 2(x + 4) or 2 * (x + 4), where x is the variable representing the unknown number. To arrive at this expression, you first find the sum of four and the number (x + 4) and then multiply the result by two to get twice this sum.

In this context, the word 'twice' is similar to triple as in triple the amount of money being three times as much. This operation is an example of simple addition, much like when two numbers are added in any order, such as 2 + 3 or 3 + 2, which illustrates the commutative property of addition.

Answer:

he saved $40

Step-by-step explanation:

The required money saved by spencer at the end of the summer sale is $40.98.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Spencer picked out a remote–control car on sale for 20% off the original price of $79.99.
He also picked out a robot for 25% off the original price of $99.99.

Money saved by spencer = 0.2 × 79.99 + 0.25 × 99.99
                                       = 15.99 + 24.99
                                       = $40.98

Thus, the required money saved by spencer at the end of the summer sale is $40.98.

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Answer:

The answer is n = 11

Explanation:

Divide both sides by 5

Move the constant to the right

Then add the numbers.

Answer:

n is 11

Step-by-step explanation:

because when you work backwards 45 divided by 5 is 9 so then 9 + 2 is 11 and that is N

Part(a): The value of the Z-score is -1.2

Part(b): The age of the winner is -1.2 standard deviation from the mean.

Part(c): Yes, the age is unusual.

Given,

[tex]\mu =27.2\\\sigma = 3.5[/tex]

Winner age, X = 23

Part(a):

The formula for the Z-score is,

[tex]Z=\frac{x-\mu }{\sigma } \\=\frac{23-27.2}{3.5}\\=-1.2[/tex]

Part(b): The age of the winner is -1.2 standard deviation from the mean which is equal to its Z-score value.

Part(c): Yes, the age is unusual.

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To calculate the z-score, subtract the mean age from the winner's age and divide by the standard deviation, resulting in -1.2. This indicates the winner is 1.2 standard deviations younger than the mean age. Since the z-score is not beyond -2, the age is not considered unusual.

The question requires us to calculate a z-score and interpret the results regarding a recent cycling tournament winner's age in context of a normal distribution.

Calculating the z-score

To calculate the z-score:

Subtract the mean age from the winner's age.

Divide by the standard deviation.

In our case:

The winner's age = 23 years

The mean age = 27.2 years

The standard deviation = 3.5 years

Thus, z = (23 - 27.2) / 3.5 = -1.2

Interpretation

This z-score means the winner's age was 1.2 standard deviations to the left of the mean. In other words, the winner is younger than the average.

Determining Unusual Age

If we consider ages that lie more than 2 standard deviations from the mean as unusual (which corresponds to roughly the outer 5% of data in a normal distribution), then a z-score of -1.2 does not qualify as unusual, since it is not beyond the 2 standard deviation threshold.

Answer:

c its the right answer

Step-by-step explanation: i just took it and got it right

Answer:

its C!!

Step-by-step explanation:

Answer:

Required equation of tangent plane is [tex]z=\frac{6}{5}(x-5y-11)[/tex].

Step-by-step explanation:

Given surface function is,

[tex]f(x,y)=6-\frac{6}{5}(x-y)[/tex]

To find tangent plane at the point (5,-1,1).

We know equation of tangent plane at the point $(x_0,y_0,z_0)[/tex] is,

[tex]z=f(x_0,y_0)+f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)\hfill (1)[/tex]

So that,

[tex]f(x_0,y_0)=6-\frac{6}{5}(5+1)=-\frac{6}{5}[/tex]

[tex]f_x=-\frac{6}{5}y\implies f_x(5,-1,1)=\frac{6}{5}[/tex]

[tex]f_y=-\frac{6}{5}x\implies f_y(5,-1,1)=-6[/tex]

Substitute all these values in (1) we get,

[tex]z=\frac{6}{5}(x-5)-6(y+1)-\frac{6}{5}[/tex]

[tex]\therefore z=\frac{6}{5}(x-5y-11)[/tex]

Which is the required euation of tangent plane.

Answer:

32

Step-by-step explanation:

Assuming they all complete it at the same rate,

896/28 = 32

To find the distance the diver needs to swim along the ocean floor to reach the treasure chest, we can use trigonometry. By using the angle of depression and the depth the diver is lowered, we can calculate the hypotenuse of the right triangle formed, which represents the distance the diver needs to swim. The diver needs to swim approximately 199 meters along the ocean floor to reach the treasure chest.

To find the distance the diver needs to swim along the ocean floor, we can use trigonometry. Let's consider the right triangle formed by the diver, the treasure chest, and the ship's sonar. The angle of depression is 12°, and the diver is lowered 40 meters. We need to find the hypotenuse of the triangle, which represents the distance the diver needs to swim.

Using the angle of depression and the opposite side of the triangle (the depth the diver is lowered), we can set up the following trigonometric equation:
tan(12°) = opposite/hypotenuse

Substituting the values:
tan(12°) = 40/hypotenuse

Solving for the hypotenuse, we get:
hypotenuse = 40/tan(12°)

Calculating this value gives us approximately 199.20 meters. Therefore, the diver needs to swim approximately 199 meters along the ocean floor to reach the treasure chest.

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Answer:

Step-by-step explanation:

Assume that you have two distinct and nonvertical lines, ℓ 1 {\ell _1} ℓ1 and ℓ 2 {\ell _2} ℓ2 in Slope-Intercept Form. They are parallel lines if their slopes are equal or the same. They are perpendicular lines if their slopes are opposite reciprocals of each other, or the product of their slopes equals −1.

Answer is y= -1

The equation will be y = -1/3x + 1 in slope-intercept form.

The general equation of a line is y = mx + c

where m is the slope of the line and c is the intercept.

A linear equation is defined as an equation in which the highest power of the variable is always one.

First, we need to determine the slope of the given line.

To do this, we convert the equation to the slope/intercept form:

y − 5 = -1/3(x+2)

y = -1/3x -2/3 + 5

y = -1/3x - 13/3

So the slope of the given line is -13.

The line passes through the point (6,−1)

Now we can use the point-slope form of a line to create the equation of the new line:

(y + 1) = (-1/3) (x - 6)

y = -1/3x + 2 -1

y = -1/3x + 1

Hence, the equation will be y = -1/3x + 1 in slope-intercept form.

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Answer:

Step-by-step explanation:

4 x pi = 12.57

Pi is approx. equal to 3.14

4 x 3 = 12

39.853

Step-by-step explanation:

He walked 39.853 miles on Monday, Wednesday

and Friday.

Answer:

2x + 3y

Step-by-step explanation:

Answer:

[tex]=18[/tex]

Step-by-step explanation:

[tex]\sum _{j=1}^33j[/tex]

Apply the constant multiplication rule:

[tex]=3\cdot \sum _{j=1}^3j[/tex]

[tex]\sum _{j=1}^3j[/tex]

Apply sum formula:

[tex]=\frac{1}{2}\cdot \:3\left(3+1\right)[/tex]

[tex]\frac{1}{2}\cdot \:3\left(3+1\right)[/tex]

[tex]=3\cdot \:4\cdot \frac{1}{2}\\[/tex]

[tex]=\frac{1\cdot \:3\cdot \:4}{2}[/tex]

[tex]=\frac{12}{2}[/tex]

[tex]=6[/tex]

[tex]=3\cdot \:6[/tex]

[tex]=18[/tex]

Answer:

345

Step-by-step explanation:

i know it not

Answer:

565$

Step-by-step explanation:

Y because he got more money

Answer:

The answer to your question is 56 gal

Step-by-step explanation:

Data

Percent filled = 95%

Total water can hold = 1120 gal

remaining water = ?

Process

1.- Calculate the 95% of 1120 gal

              1120 gal ------------------ 100%

                x           ------------------   95%

                      x = (95 x 1120) / 100

                      x = 106400 / 100

                      x = 1064 gal

2.- Calculate the remaining water by subtracting the previuos value to the total capacity.

Remaining water = 1120 - 1064

                             = 56 gal

Answer:

sgdggggggggggggsdfgfgfg

Step-by-step explanation:

Answer:

p = x * (3/8)

Where p is the amount of a box and x is the number of people.

For x=2 -> p = 2 * (3/8) = 3/4

Step-by-step explanation:

If Mark uses 3/8 of a box to make enough for one person, we can find the amount required (p) to be enough for 'x' people using a rule of three:

3/8 of a box -> 1 person

p -> 'x' people

(3/8)/p = 1/x

p/(3/8) = x

p = x * (3/8)

If we want the amount for 2 people, we use x = 2 in the equation:

p = 2 * (3/8) = 3/4

So Mark will need 3/4 of a box.

Answer: 15 tickets

Step-by-step explanation:

given that the cost of the bear = 30 tickets

He has paid $5 for 10 tokens to use to play games . And So far he's won 15 tickets and used 7 tokens for different games. Since he has won 15 tickets, then

He needs to will 30 -15 = 15 tickets

The best unit for the answer is ticket

Answer: c) [tex]3x^4-13y^4+x^3y+9xy^3-8x^2y^2[/tex]

Step-by-step explanation:

[tex]9xy^3-4y^4-10x^2y^2+x^3y+3x^4+2x^2y^2-9y^4[/tex]

Let's rearrange from the 4th power to 1.

[tex]3x^4-4y^4-9y^4+x^3y+9xy^3-10x^2y^2+2x^2y^2[/tex]

Combine like terms (check if they have the same variable raised to the same power.

[tex]3x^4+(-4y^4-9y^4)+x^3y+9xy^3+(-10x^2y^2+2x^2y^2)[/tex]

[tex]3x^4+(-13y^4)+x^3y+9xy^3+(-8x^2y^2)[/tex]

[tex]3x^4-13y^4+x^3y+9xy^3-8x^2y^2[/tex]

Answer:

Most people found the probability of just stopping at the first light and the probability of just stopping at the second light and added them together. I'm just going to show another valid way to solve this problem. You can solve these kinds of problems whichever way you prefer.

There are three possibilities we need to consider:

Being stopped at both lights

Being stopped at neither light

Being stopped at exactly one light

The sum of the probabilities of all of the events has to be 1 because there is a 100% chance that one of these possibilities has to occur, so the probability of being stopped at exactly one light is 1 minus the probability of being stopped at both lights minus the probability of being stopped at neither.

Because the lights are independent, the probability of being stopped at both lights is just the probability of being stopped at the first light times the probability of being stopped at the second light. (0.4)(0.7) = 0.28

The probability of being stopped at neither is the probability of not being stopped at the first light, which is 1-0.4 or 0.6, times the probability of not being stopped at the second light, which is 1-0.7 or 0.3. (0.6)(0.3) = 0.18

The probability at being stopped at exactly one light is 1-0.18-0.28=.54 or 54%.

Answer:

23

Step-by-step explanation:

29 minus 6 equals 23

Answer:

k = 23

29 = k + 6

Step-by-step explanation:

29 = k + 6

k = 29 - 6

k = 23

Answer:

142

Step-by-step explanation:

[tex]\frac{x+18}{5}=32[/tex]

Multiplying both sides by 5, you get:

x+18=160

Now, you can subtract 18 from both sides to get:

x=142

Hope this helps! Comment if this wasn't clear enough, or you need more explanation.

Answer: x=142

Step-by-step explanation:

x+18 / 5 = 32

first multiply both sides by 5

x + 18 = 160

then subtract 18 from both sides

x=142

Answer:

If you are asking for the equation, it is y= -(1/2)x -2