In circle L, arc NOP is 90° and the radius is 5 units. Which statement best describes the length of arc NOP?

Answer:

(a) P (U and V) = 0.

(b) P (U|V) = 0.

(c) P (U or V) = 0.83.

Step-by-step explanation:

Mutually exclusive events are those events that cannot occur at the same time. That is, if events A and B are mutually exclusive then,

                                         [tex]P (A\cap B) = 0[/tex]

Given:

Events U and V are mutually exclusive.

P (U) = 0.27 and P (V) = 0.56

(a)

As events U and V are mutually exclusive, the probability of their intersection will be 0.

That is,

[tex]P(U\ and\ V) = P (U\cap V) = 0[/tex]

Thus, the value of P (U and V) is 0.

(b)

The conditional probability of event B given A is:

[tex]P(B|A) =\frac{P(A\cap B)}{P(B)}[/tex]

Compute the value of P (U|V) as follows:

[tex]P(U|V) =\frac{P(U\cap V)}{P(V)}\\=\frac{0}{0.56}\\ =0[/tex]

Thus, the value of P (U|V) is 0.

(c)

The probability of the union of two events, say A and B, is

[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Compute the value of P (U or V) as follows:

[tex]P(U\ or\ V)=P(U\cup V)\\=P(U)+P(V)-P(U\cap V)\\=0.27+0.56-0\\=0.83[/tex]

Thus, the value of P (U or V) is 0.83.

The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.

Given :

A) P(U and V)

P(U and V) = P(U [tex]\cap[/tex] V) = 0

Because U and V are mutually exclusive events.

B) P(U|V)

[tex]\rm P(U|V) = \dfrac{P(U\cap V)}{P(V)}[/tex]

[tex]\rm P(U|V) = \dfrac{0}{0.56}[/tex]

P(U|V) = 0

C) P(U or V)

[tex]\rm P(U \;or\;V) = P(U\cup V)[/tex]

[tex]\rm P(U \;or\;V) = P(U)+P(V)-P(U\cap V)[/tex]

P(U or V) = 0.27 + 0.56 - 0

P(U or V) = 0.83

The events U and V are mutually exclusive. So, the value of P(U and V) is 0, the value of P(U|V) is 0, and the value of P(U or V) is 0.83 and this can be determined by using the given data.

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Answer:

I'm assuming you meant 27 and not 2.7 sooo... 5/28 were pepperoni

Step-by-step explanation:

Answer:49

Step-by-step explanation:

294/6

=49

Answer:

See Explanation Below

Step-by-step explanation:

Question is incomplete.

(The height of the prism is missing and no attachment is provide)

However, I'll solve on a general rule.

Given

Volume of prism, V = 294in³

The volume of a prism is calculated multiplying the base area by the height of the prism.

Let's represent the base area by B and the height by H.

Mathematically,

V = B * H.

Make B the subject of formula

B = V/H

Substitute 294 for V.

The expression becomes

B = 294/H

Now, let's assume the height is 6 inches.

The expression for base area becomes

B = 294/6

B = 49 in²

Answer:

Option C: (2, 1, 0)

Step-by-step explanation:

We are given a system of three equations. Usually, we eliminate a variable from the equations. Solve for the remaining two equations and determine the value of the third equation later.

Here, we are given the choices. So, we can readily substitute each option in the equations. The solution should satisfy all the three equations.

Option A: (3, 1, 0)

Equation (1): 3x + 3y + 6z = 9

⇒ 3(3) + 3(1) + 6(0) = 9 + 3 ≠ 9

Option A does not satisfy the first equation. So, it is eliminated.

Option B: (0, 1, 0)

Substituting in the first equation: 3x + 3y + 6z = 9

⇒ 3(0) + 3(1) + 6(0) = 3 ≠ 9

Option B does not satisfy as well. Hence, it is eliminated.

Option C: (2, 1, 0)

Substituting in 3x + 3y + 6z = 9

⇒ 3(2) + 3(1) + 6(0) = 9

It satisfies Equation 1. For this to be a solution, it should satisfy all the three equations. So, we check for equation 2 and 3.

Equation 2: x + 3y + 2z = 5

2 + 3(1) + 2(0) = 2 + 3 = 5

Equation 3: 3x + 12y + 12z = 18

3(2) + 12(1) + 12(0) = 6 + 12 = 18

Option C satisfies all the equations. So, it is the solution to the system.

On simple substitution, Option D can be eliminated as well.

Hence, the answer.

Answer:

All Real Answers / Infinite Solutions

Step-by-step explanation:

Distribute: 5x-2x = 4x-x

Simplify: 3x=3x

Subtract 3x from each side: 0=0

Answer:

The length of rectangle is 14.25 inches and the width of rectangle is 8.25 inches

Step-by-step explanation:

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

[tex]P=45\ in[/tex]

so

[tex]45=2(L+W)[/tex]

simplify

[tex]22.5=L+W[/tex] -----> equation A

The length of a rectangle is 6 inches more than its width

so

[tex]L=W+6[/tex] ----> equation B

Solve the system by substitution

substitute equation B in equation a

[tex]22.5=(W+6)+W[/tex]

solve for W

[tex]22.5=2W+6\\2W=22.5-6\\2W=16.5\\W=8.25\ in[/tex]

Find the value of L

[tex]L=W+6[/tex]

substitute the value of W

[tex]L=8.25+6=14.25\ in[/tex]

therefore

The length of rectangle is 14.25 inches and the width of rectangle is 8.25 inches

Answer:-16

Step-by-step explanation:

You want to isolate the variables (in this case it's m)

-80=5m

divide both sides by 5

-16=m

Answer:

[tex]A=64.95\ in^2[/tex]

Step-by-step explanation:

we know that

A regular hexagon can be divided into six equilateral triangles

so

The area of a regular hexagon is the same that the area of six congruent equilateral triangles

The area of one equilateral triangle in the regular hexagon is equal to

[tex]A=\frac{1}{2}(b)(h)[/tex]

where

b is the base of triangle (the length of the regular hexagon)

h is the height of triangle (the apothem of the regular hexagon)

so

[tex]b=5\ in\\h=4.33\ in[/tex]

substitute

[tex]A=\frac{1}{2}(5)(4.33)=10.825\ in^2[/tex]

Multiply the area of one triangle by 6 to obtain the area of the regular hexagon

[tex]A=10.825(6)=64.95\ in^2[/tex]

Answer:

  y = -10/3x -23

Step-by-step explanation:

The 2-point form of the equation of a line is useful for this.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Using your points, we have ...

  y = (-3 -7)/(-6 -(-9))(x -(-9)) +7

  y = (-10/3)(x +9) +7

  y = -10/3x -23 . . . . . . . simplify

The equation of the line passing through the points (-9,7) and (-6, -3) is y = -10/3x -14.

In mathematics, the equation of a line can be given as y = mx + c, where m is the slope of the line and c is the y-intercept. Firstly, we need to calculate the slope (m) which is (y2 - y1) / (x2 - x1). If we substitute the points (-9,7) and (-6, -3) we get (-3 - 7) / (-6 + 9) = -10 / 3, so m = -10/3. Next, to get the y-intercept (c) we can substitute the slope and one of the points into the equation: 7 = -(10/3)*(-9) + c, and we get c = -14. Therefore the equation of the line is y = -10/3x -14.

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Answer:

That is math.

Answer:

When only solving for b you would multiple by the reciprocal of 1/18*b so you multiply 18 to both sides and b is equal to -108

Step-by-step explanation:

Step-by-step explanation:

[tex]50 \geqslant 15x \\ \\ \implies \: \frac{50}{15} \geqslant x\\ \\ \implies \: \frac{10}{3} \geqslant x \\ \\ \therefore \: x \leqslant \frac{10}{3} \\ thus \: \{x \: | \: x \leqslant \frac{10}{3} \} \: is \: the \: correct \: \\ solution \: set.[/tex]

The correct solution set of 50 ≥ 15x is {x | x ≤ 10/3 }.\

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given that the expression;

50 ≥ 15x

We can add subtract the 15x - 50 of both sides,

⇒50 - 15x - 50  ≥  15x -15x - 50

⇒50 - 15x - 50 ≥  15x -15x - 50

⇒ - 15x  ≥ - 50

Now we multiply by -1 ,after this process inequality symbol must be reversed

⇒ 15x  ≤  50

Divide by 50 on both sides,

⇒ 15x / 50  ≤  50 / 50

⇒ 3x/10  ≤ 1

⇒ x  ≤  10 /3

Therefore, the solution set is {x | x ≤ 10/3 }

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The system of equations is solved by setting the two equations equal to each other and solving for x followed by solving for y using the obtained x value. The solution is x = -15.6 and y = 0.2.

The student is asking to solve a system of two linear equations:

To find the solution, we need to set the two equations equal to each other since they both equal y:

47 + 3x = 8 + 0.5x

Now, let's solve for x:

Now that we have x, we can solve for y using either of the original equations:

y = 8 + 0.5(-15.6)

Calculate y:

y = 8 - 7.8

y = 0.2

Therefore, the solution to the system of equations is x = -15.6 and y = 0.2.

Answer:

4×(x² - 4x + 2)

Step-by-step explanation:

4x2 - 16x + 8 = 4×x² - 4×4×x + 4×2 = 4×(x² - 4×x + 2)

Answer:

270 units³

Step-by-step explanation:

l×w×h = 10

lwh = 10

New Volume = (3l)×(3w)×(3h)

= 27×lwh

= 27×10

= 270 units³

Alternately,

Since the sides are increased in the same ratio,

The two prisms are similar figures

For similar figures,

volume1/volume2 = (side1/side2)³

New Volume/10 = (3/1)³ = 27

New Volume = 270 units³

Final answer:

The new volume of a rectangular prism, whose dimensions are tripled, is calculated by cubing the factor of increase (3) and multiplying it by the original volume. The new volume will be 270 cubic units.

Explanation:

If the original volume of a rectangular prism is 10 cubic units and the length, width, and height are all made three times as long, the new volume can be calculated using the principle that volume is proportional to the cube of the linear dimensions of the prism. This is often represented as V  imes L³ where V is volume and L is the linear dimension.

To find the new volume, you would multiply each dimension by 3 so the new length (L'), width (W'), and height (H') would be three times the original dimensions. The new volume would then be calculated as:

V' = L' times W' times H' = (3L) times (3W) times (3H)

Since the original volume (V = L  imes W  imes H) is given as 10 cubic units, and you've multiplied each dimension by 3, you would cube the factor of increase (3³ = 27) and multiply it by the original volume:

V' = 27  imes V = 27  imes 10 = 270 cubic units

Therefore, the new volume of the rectangular prism would be 270 cubic units.

Answer:

a = 9√10

b=3√10

Step-by-step explanation:

see attached for reference for any right triangle

in our case

c is the hypotenuse

hence

c² = a² + b²

we are given that c = 30

also that a is 3 times as long as b or,

a = 3b    

substituting these into the pytharogrean formula.

c² = a² + b²

30² = (3b)² + b²

900 = 9b²+b²

10b² = 900

b² = 90

b = √90 = √9 √10 = 3√10

earlier we found that a = 3b,

hence

a = 3(3√10)

a = 9√10

Answer:

-7

12

10.54

-8

Step-by-step explanation:

Answer:

18, 21

Step-by-step explanation:

There is a difference of 3 between any two consecutive term ( succeeding - preceding)

Hence 15 + 3 = 18

& 18 + 3 = 21 are the required terms.

Answer: C.) 18, 21

Step-by-step explanation:

Answer:

367.25 dollars

Step-by-step explanation:

To calculate 35 percent of 565 you would first

35% is 197.75 the question says 35% off so you would have to take the 35% off the 565

(565-197.75 = 367.25)

Answer:

96 cubic feet

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I just had the same paper last night

Answer:

Ans: (-5, 5)

-5 < x < 5

Step-by-step explanation:

Standard form: f(x) = x^2 - 25 < 0.

First solve x^2 - 25 = 0 --> x = +- 5

Use the algebraic method to solve f(x) < 0. Between the 2 real roots (-5) and (5), f(x) < 0, as opposite in sign to a = 1.

Answer by open interval: (-5, 5)

First off, write the inequality as 2x>25

Divide both sides by 2 to get x>12.5

Hope this helped

Answer:

x-1=0 x=1

x+1=0 x= -1

x+5=0 x= -5

Step-by-step explanation:

Answer:

it is C

Step-by-step explanation:

40% of 20 is 8

so 15% of 20 is 3

Answer: dividing

Step-by-step explanation:

Final answer:

To convert a fraction to a percent, divide the numerator by the denominator to get a decimal, multiply the decimal by 100, and then add the percent symbol (%).

Explanation:

To convert a fraction to a percent, you start by converting the fraction into a decimal. To do this, divide the numerator (the top number) by the denominator (the bottom number). Once you have the decimal, you multiply it by 100 to get the percent value. Finally, append the percent symbol (%) to the number.

Example:

For the fraction 3/4, first convert it to decimal:

Another way to convert fractions to percent is by finding an equivalent fraction that has 100 as its denominator. Then, simply use the numerator as the percent. If the fraction's denominator is not easily scalable to 100, it is easier to use the decimal method described previously.

Final answer:

The division of 29r2 by 17 simplifies down to approximately 1.7059r^2, where r is a variable representing a real number.

Explanation:

The student is asking about a division of algebraic expressions, specifically 29r^2 divided by 17. The notation 29r^2 suggests that we have the variable r squared, multiplied by 29, and we need to divide this entire expression by 17. This is a straightforward division operation where each term in the numerator is divided by the denominator.

To find the solution, you divide 29 by 17 and keep r^2 (r squared) as part of the expression. Therefore, the simplified form of 29r^2 divided by 17 would be approximately 1.7059r^2, assuming that r represents a real number.

Answer:

The Answer Is C

Step-by-step explanation:

I took the test

Step-by-step explanation:

Given,

The diameter of small pizza = 8 inches,

The diameter of medium pizza  = 10 inches and

The diameter of large pizza (d) = 11 inches

To find, the circumference of each size of pizza = ?

We know that,

The circumference of the circle = [tex]2\pi r= \pi d[/tex]

∴ The circumference of small size of pizza = 3.14 × 8 = 25.12 inches

The circumference of medium size of pizza = 3.14 × 10 = 31.4 inches

Also,

The circumference of large size of pizza = 3.14 × 12 = 37.68 inches

Thus, the circumference of small size, medium size and large size of pizzas are  25.12 inches, 31.4 inches and 37.68 inches.

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Answer:

-75 ercent

Step-by-step explanation:

Answer:

2 quarters and 5 dimes

Step-by-step explanation:

(2) 25 cent coins = 50 cents

(5) 10 cent coins = 50 cents

equals $1

Answer:

Median and IQR

Step-by-step explanation:

If we are to accurately compare two data sets, the best measure of central tendency is median and best measure of variability is the MAD.

The reason is that:

1. Median is not affected by outlier or extreme value. Due to this, if we use the mean, it can be misleading if there is any case of outlier(s) in the data sets.

2. The interquartile range (IQR) is the middle half of the data. It uses the concept of median to operate - think about the median value that splits the dataset in half. Similarly, you can divide the data into quarters. This also is not affected by outlier(s) or extreme value(s).

NB: When we say middle half or middle number, we assumed you have sorted the data sets either in ascending order or descending order. This will put the data sets in order of their sizes. E.g., 1 < 2 < 3, etc.

Answer:

Median and IQR

Step-by-step explanation: