find the length of AB. leave your answer in terms of pi. Please please help!!!!

Answer: D. Taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .

Step-by-step explanation:

We know that for dependent events A and B , the conditional probability of getting a given that B is given by :-

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

From the given table, if A represent taking French class and B represent taking Art class.

Then P(A)=0.6

and P(B)=0.55

[tex]P(\cap B)=0.2[/tex]

Now, [tex]P(A|B)=\dfrac{0.2}{0.55}=0.036363\approx0.036[/tex]

[tex]P(B|A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{0.2}{0.6}=0.33333\aprox0.333[/tex]

Clearly, [tex]P(A|B)\neq P(A)[/tex]

[tex]P(B|A)\neq P(B)[/tex]

Therefore taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B) .[ By definition of independent events]

The correct statement is D; Taking Art class and taking French class are not independent events.

Consider A represent taking a French class and B represents taking an Art class.

The formula to determine whether two events are independent or not is P(A and B) = P(A) x P(B),

where P(A and B) is the probability of both events happening together, P(A) is the probability of event A happening, and P(B) is the probability of event B happening.

D. Taking Art class and taking French class are not independent events because P(A|B)≠P(A) and P(B|A)≠P(B).

This statement is incorrect because the formula to determine whether two events are independent or not is;

P(A and B) = P(A) x P(B),

not P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

Using the values in the table:

P(A) = 0.6 (taking French class)

P(B) = 0.55 (taking Art class)

P(A and B) = 0.2 (taking both classes)

P(A and B) ≠ P(A) x P(B)

0.2 ≠ 0.6 x 0.55

The correct statement is option D.

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Answer:

The line which has slope 1/3 is a shallow line.

The line which has slope 2 is a steep line.

Both are increasing.

Step-by-step explanation:

Compare the lines by finding the slope between each pair of points.

Using the slope formula, substitute the points.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{4-2}{6-0} = \frac{2}{6} = \frac{1}{3}[/tex]

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{7-1}{5-2} = \frac{6}{3} = 2[/tex]

The line which has slope 1/3 is a shallow line.

The line which has slope 2 is a steep line.

Answer:

(3, -6)

Step-by-step explanation:

The formula for reflecting across the Y axis is that the X axis value will become opposite, so the -3 becomes positive 3.

Answer:

(3, -6)  

Step-by-step explanation:

When you reflect a point (x, y) in the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign. Thus,

(-3, -6)⟶ (3, -6)

The image below shows the point before and after the reflection.

Answer:

8:10

Step-by-step explanation:

If you add the amount of minutes it takes for her to get ready, then add them to 7:15 (55 minutes after 7:15) you get 8:10

The answer is d. I already did the math on the calculator

➷ The formula for surface area of a cylinder is:

[tex]2\pi rh + 2\pi r^2[/tex]

The radius is half the diameter

radius = 8/2 = 4

Substitute the values in:

[tex]2\pi (4)(18) + 2\pi (4)^2[/tex]

Solve it:

surface area = [tex]176\pi[/tex]

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

525.64 [tex]cm^{2}[/tex]

Step-by-step explanation:

The formula is S.A. =2[tex]\pi r^{2} + 2\pi rh[/tex]

write the equation out. *raduis is half of diameter, d=8. r=4)

2 x 3.14 x [tex]4^{2}[/tex] + 2 x 3.14 x 4 x 18 = S.A.

Solve

2 x 3.14 x 4^2 = 100.48

Rewrite

100.48 + 2 x 3.14 x 4 x 18 = S.A.

solve second halve

2 x 3.14 x 4 x 18 = 452.16

rewrite

100.48 + 425.16 = 525.64

525.64 [tex]cm^{2}[/tex]

Hope this helped! Please mark as brainliest! Thanks!

Answer:

[tex]f^{-1}(x) = 6(4-x) = 24-6x[/tex]

Step-by-step explanation:

Let [tex]y=f(x)[/tex] and swap x and y:

[tex]x = 4 - \frac{y}{6}[/tex]

Then, rearranging for y:

[tex]x+\frac{y}{6} = 4[/tex]

[tex]\frac{y}{6}= 4-x[/tex]

[tex]y= 6(4-x) = 24-6x[/tex]

Final answer:

Explaining the inverse function of a given function.

Explanation:

Inverse function of f(x) = 4 - x/6:

Replace f(x) with y: y = 4 - x/6.

Swap x and y: x = 4 - y/6.

Solve for y: y = 24 - 6x.

The given 3rd option is the viable answer.

Answer:

hello : (4, –2)

Step-by-step explanation:

because put : x = 4 and y = - 2  in the inequality    y+3 ≤ 2x  you have :

- 2 +3 ≤ 2(4)

1 ≤ 8 .... right

Answer:

#1: No #2: Yes #3: Yes #4: Yes

Unit conversion is a way of converting some common units into another without changing their real value. Only b and c are the correct statements.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

a.) 2,000 km = 2m

No, since 1 km is equal to 1000 m, therefore, 2 m will not be equal to 2,000 km.

b.) 2,000 mm= 2m

Yes, since 1 m is equal to 1000 mm, therefore, 2000 mm will be equal to 2 meters.

c.) 20 cm= 200 mm

Yes, since 1 cm is equal to 10 mm, therefore, the 20 cm will have 200 mm.

d.) 20m = 2,000 cm

No, since 1 meter is equal to 100 cm, therefore, 20 m will not be equal to 2,000 cm.

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Answer:

A

Step-by-step explanation:

2/3x-1=4

Add 1 to each side

2/3x = 5

Divide each side by 2/3

x = 7.5

Find the same value...

15/2 = 7.5

Answer:

36 cubic feet

Step-by-step explanation:

1. know that the equation for volume is l*w*h

2. plug in all the information that is shown in the question. (9*4*1)

3. 9*4*1 is 36 so your answer is 36 cubic feet

Answer: 36 ft³

Step-by-step explanation:

You must apply the formula for calculate the volume of a rectangular prism, which is show below:

[tex]V=l*w*h[/tex]

Where l is the lenght, w is the width and h is the height.

Given the dimensions shown in the problem, you can substitute values into the formula shown above.

Therefore, you obtain that the volume of the rectangular prims is:

[tex]V=(9ft)(1ft)(4ft)\\V=36ft^3[/tex]

Answer:

its D. 456 in

Step-by-step explanation:

if u multiply 10 x 10 then u get 100. that same square is there twice so if u add it u get 200. then the only one greater than 100 is 456.

Answer:

the answer is d 456^in2

Step-by-step explanation:

hope this helps

Answer:

pythag. theorem

100^2 +60^2 =c^2

10,000+3600= (take sq. root) 13,600

c= 116.62ft

Step-by-step explanation:

The length of the diagonal of the football field is 116.62 yards.

The Pythagorean theorem states that in a right-angled triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse.

A football field is rectangular in shape.

The diagonal of a rectangle divides it into two right-angled triangles.

Therefore, the diagonal becomes the hypotenuse of the right-angled triangles.

Therefore, diagonal² = length² + width²

⇒ diagonal² = 10,000 + 3600 yards²

⇒ diagonal² = 13,600 yards²

⇒ diagonal = 116.62 yards

Therefore, the length of the diagonal of the football field is 116.62 yards.

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Answer:

x = -14

Step-by-step explanation:

-3.5 = x/4

In the right side, the fraction x/4 means x divided by 4. We want x alone, so we multiply both sides by 4.

-3.5 * 4 = x/4 * 4

-14 = x

Answer: x = -14

The solution to the equation -3.5 = x/4for x using the multiplication property of equality is x = -14.

Multiplication property of equality is an equality property which states that if both the sides of an equation are multiplied by the same number, the expressions on the both sides of the equation are equal.

So,

-3.5 = x/4

multiply both sides by 4

-3.5 × 4 = x/4 × 4

-14 = x

Therefore, x equals negative 14.

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Answer:

3 hours

Step-by-step explanation:

Subtract the sale price from the original price:

200 - 150 = 50.

Now divide the difference by the original price and then multiply that by 100:

50 / 200 = 0.25 x 100 = 25%

The discount is 25%

Answer:

160 cups of lemonade and 80 packages of cookies.

Step-by-step explanation:

l = lemonade

c = cookies

l+1.5c=280

2c=l

Substitute.

3.5c=280

Simplify.

c=80

Substitute into the second equation.

l=160.

Plug it back into the equations to check.

Answer:

A. $240,000

Step-by-step explanation:

look at the chart - find $30,000 and find 35 year old / 75%.. go down and to the right of the chart and find 8.0.. multiply 30,000 by 8.0 = 240,000.

hope this helps!!

Answer:

CE = 12

Step-by-step explanation:

ΔCDB and ΔEAB are similar, hence the ratios of corresponding sides are equal

We require to find the length of BC to complete CE

[tex]\frac{BC}{BE}[/tex] = [tex]\frac{DB}{AB}[/tex], substitute values

[tex]\frac{BC}{8}[/tex] = [tex]\frac{5}{10}[/tex] ( cross- multiply )

10BC = 40 ( divide both sides by 10 )

BC = 4

CE = CB + BE =4 + 8 = 12

Answer:

B. [tex]g(x)=(x+4)^2-3(x+4)-2[/tex]

Step-by-step explanation:

The given function is

[tex]f(x)=x^2-3x-2[/tex]

If [tex]f(x)[/tex] is shifted to the left 4 units and the result is [tex]g(x)[/tex].

Then;

[tex]g(x)=f(x+4)[/tex]

We substitute [tex](x+4)[/tex] into [tex]f(x)=x^2-3x-2[/tex] to find the [tex]g(x)[/tex].

[tex]g(x)=(x+4)^2-3(x+4)-2[/tex]

The correct choice is B.

The spiciness of chili is determined by comparing the proportion of chili powder to tomato sauce. Jack consistently uses 222 teaspoons of chili powder per cup of sauce, whereas Marsha's ratio varies, but never exceeds 126.86 teaspoons per cup. Therefore, Jack's chili is spicier.

To determine whose chili is spicier, we must compare the ratio of chili powder to tomato sauce used by Jack and Marsha. Jack uses 222 teaspoons of chili powder for every 1 cup of tomato sauce. For Marsha, we'll have to establish the ratios based on her table.

Regardless of the quantity she makes, Marsha's ratio never goes below 115.43, which is less than Jack's ratio of 222. So, Jack's chili is spicier than Marsha's.

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Answer:

f

−

1

(

x

)

=

2

x

+

6

?

f^-1(x)=2x+6 is the answer i believe

Answer:

−2x−3

Step-by-step explanation:

I don't know if right

Answer:

10 km

Step-by-step explanation:

8^2+6^2=10^2

Answer:

Juan traveled 10 km.

Step-by-step explanation:

is also right on EDGEN.

Answer:

Option A. The ratio of the area to the circumference is equal to half the radius

Step-by-step explanation:

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

The ratio of the area to the circumference is equal to

[tex]\frac{A}{C}=\frac{\pi r^{2}}{2\pi r}[/tex]

Simplify

[tex]\frac{A}{C}=\frac{r}{2}[/tex]

Verify

In this problem

[tex]A=153.86\ units^{2}[/tex]

[tex]C=43.96\ units[/tex]

[tex]\frac{A}{C}=\frac{153.86}{43.96}=3.5\ units[/tex]

and [tex]3.5\ units[/tex] is equal to half the radius

therefore

The ratio of the area to the circumference is equal to half the radius

Answer:

A: The ratio of area of circle to the circumference is equal to half the radius.

Step-by-step explanation:

We are given that area of a circle=153.86 square units

Circumference of circle=43.96 units

Radius of circle=7 units

We have to find that the relation ship between area of circle and circumference of circle

Area of circle=[tex]\pi r^2[/tex]

Circumference of circle=[tex]2\pi r[/tex]

Ratio of area of circle to the circumference=[tex]\frac{\pi r^2}{2\pi r}[/tex]

Ratio of area of the circle to the circumference of the circumference=[tex]\frac{1}{2} r[/tex]

Ratio of area to the circumference=[tex]\frac{153.86}{43.96}=\frac{7}{2}=\frac{r}{2}[/tex]

Hence, option A is true.

Answer:A: The ratio of area of circle to the circumference is equal to half the radius.

we just have to locate these coordinates on graph and see which one lies on line .

you will find option 4 lies on line so it's the one of the solution of line

Answer:

(--3,2)

The only (x,y) that is on the line is (-3,2)

the rest don't fit on the line.

Answer:

83

Step-by-step explanation:

8 is one less than 3x3

Answer with explanation:

We have to describe the rational number in words

     [tex]=\frac{8}{21 n}[/tex]

Dividend =8

Divisor =21 n

Quotient

     [tex]=\frac{\text{Dividend}}{\text{Divisor}}\\\\=\frac{\text{Eight}}{\text{Twenty one} \times \text{A number}}[/tex]

Option C: → The quotient of eight and twenty-one times a number

Answer:

The son is 7 and the daughter is 21

Step-by-step explanation:

So, if they’re his kids they must be younger than him which means that both ages are more than 42. One number also has to be the other one times 3. 7*3 = 21 and they are also both less than 42. That means it’s your answer.

Brainliest please

After 10 years, the two siblings are 12 years and 36 years old.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

A father who is 42 years old has a son and a daughter.

The daughter is three times as old as the son.

Let x be the age of the son, then 3x be the age of the daughter.

After 10 years, the sum of all their ages will be 100 years.

That means,

x + 10 + 3x + 10 + 42 = 100

4x = 48

x = 12

Then 3x = 36.

Therefore, the ages of the siblings are 12 and 36.

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Answer:

it's already in simplest form, as a decimal it would be 8.875

Step-by-step explanation:

The problem involves adding mixed numbers. First, convert them to improper fractions, add them up, and convert back to mixed numbers if possible. The first equation results in [tex]5\frac{1}{2}[/tex] while the second results in [tex]8\frac{7}{8}[/tex].

The student is asking this question in the context of addition of fractions. To tackle these problems, the first thing to do is to switch both numbers into improper fractions.

In equation 1,

[tex]4\frac{1}{6} +1\frac{2}{6} \\= \frac{25}{6} + \frac{8}{6} \\=\frac{33}{6} \\=\frac{11}{2} \\=5\frac{1}{2}[/tex]

In equation 2,

[tex]7\frac{4}{8} + 1\frac{3}{8}\\ =\frac{60}{8} + \frac{11}{8}\\ =\frac{71}{8}\\ =8\frac{7}{8}[/tex]

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Answer:

1.20

Step-by-step explanation:

you multiply 0.02 by 60 usually 120 but 2 decimal points so move the decimal  2 to the left

Answer:

Fifty two thousand nine hundred forty

Step-by-step explanation:

Thank you!!

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