What is the exact area of the following circle?

Answer:

8 out of 20 or 2 out of 5(both anwsers are correct)

[tex]\\ \rm\Rrightarrow 2x+2y=28[/tex]

[tex]\\ \rm\Rrightarrow x+y=14[/tex]--(1)

And

[tex]\\ \rm\Rrightarrow (x-y)^2=(x+y)^2-4xy[/tex]

[tex]\\ \rm\Rrightarrow (x-y)^2=14^2-4(45)=196-180[/tex]

[tex]\\ \rm\Rrightarrow (x-y)^2=16[/tex]

[tex]\\ \rm\Rrightarrow x-y=4[/tex]--(2)

Adding (1) and (2)

And

Answer:

B) 9 in x 5 in

Step-by-step explanation:

Let W = width of rectangle

Let L = length of rectangle

Area of a rectangle = WL

Perimeter of a rectangle = 2W + 2L

Given area = 45 and perimeter = 28:

⇒ WL = 45

⇒ 28 = 2W + 2L

Rewrite 28 = 2W + 2L to make W the subject:

⇒ 2W = 28 - 2L

⇒ W = 14 - L

Substitute W = 14 - L into WL = 45 and solve for L:

⇒ (14 - L)L = 45

⇒ 14L - L² = 45

⇒ L² -14L + 45 = 0

⇒ (L - 9)(L - 5) = 0

⇒ L = 9, L = 5

Substitute found values of L into W = 14 - L and solve for W:

⇒ W = 14 - 9 = 5

⇒ W = 14 - 5 = 9

As width < length, length = 9 in and width = 5 in

the answer is: (7k−6)(4k²+7)

The known facts

Now, let's set up the equations where N is Natalie's age and F is Fred's age.

N + F = 36   ---- equation 1

N + 4F = 72 ---- equation 2

equation 2 minus equation 1 ---> 3F = 36 ---> F = 12, thus N = 24

Thus Fred is 12 years old, and Natalie is 24 years old.

Answer:

in this problem, we are going to translate our words into a mathematical equation, solve the equation and then answer the question. So we have, the father is three years older than the mother, so is three, is our answer there for this equation. So if we take the oldest minus the youngest, It would give us a difference of three. So since the father is older, we're going to say the father's age minus the mother's age is three, So we know that the mother is 42 years old, So the father minus the 42 would give us three. So to solve for F, we're going to use the addition property of equality and add 42 to both sides. So F -40 to plus 42 is F and Add 42 to both sides, and three plus 42 is 45. So this means that the father is 45 years old.

Step-by-step explanation:

Mark me brainliest!!

The probability that the combination starts with 2 is 1/3

Probability is the likelihood or chance that an event will occur.

Probability = expected/total outcome

The total outcome  = 3! = 6

The expected outcome if the combination starts with 2 is given as 2! = 2

Pr(the combination starts with 2) = 2/6 = 1/3

Hence the probability that the combination starts with 2 is 1/3

Learn more on probability here: https://brainly.com/question/25870256

Answer:

B. Caleb's experiment had 100 bacteria and Jenna's experiment had 2500 bacteria.

Step-by-step explanation:

[tex]\displaystyle Jenna \hookrightarrow 2500 = 50^2 \\ Caleb \hookrightarrow 100 = [2][50][/tex]

Take a clocer look at the keywourds next to each name. When you square a quantity, you duplicate and multiply it, but when you double a quantity, you multiply by two.

I am joyous to assist you at any time.

Answer:

Yes, the graph is proportional

Step-by-step explanation:

This graph is proportional because the origin (where the line starts) is at

(0, 0)

Hope this helps! Let me know if you still don't understand :)

The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 is given by: Option B: 0.284 approx.

Suppose two dimensions are there, viz X and Y. Some values of X are there as [tex]X_1, X_2, ... , X_n[/tex] and some values of Y are there as [tex]Y_1, Y_2, ... , Y_n[/tex]

List them in title of the rows and left to the columns. There will be [tex]n \times k[/tex] table of values will be formed(excluding titles and totals), such that:

Value(ith row, jth column) = Frequency for intersection of  [tex]X_i[/tex]  and [tex]Y_j[/tex]  (assuming X values are going in rows, and Y values are listed in columns).

Then totals for rows, columns, and whole table are written on bottom and right margin of the final table.

For n = 2, and k = 2, the table would look like:

[tex]\begin{array}{cccc}&Y_1&Y_2&\rm Total\\X_1&n(X_1 \cap Y_1)&n(X_1\cap Y_2)&n(X_1)\\X_2&n(X_2 \cap Y_1)&n(X_2 \cap Y_2)&n(X_2)\\\rm Total & n(Y_1) & n(Y_2) & S \end{array}[/tex]

where S denotes total of totals, also called total frequency.

n is showing the frequency of the bracketed quantity, and intersection sign in between is showing occurrence of both the categories together.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

The missing frequency table is attached below. If we name events as:

Then, the needed probability is P(B|A) (as it is already specified that the person would be older than 35 years.)

Using the table, we get:

[tex]P(A) = \dfrac{\text{Total person who are older than 35 years age}}{\text{Total person in survey}}\\\\P(A) = \dfrac{162}{429} \approx 0.3776[/tex]

Using the table, we get the value on the place where A and B both occur(when person selected is older than 35 years and have hemoglobin between 9 and 11 ) as:

[tex]n(A \cap B) = 162 - 40 - 76 = 46[/tex]

Thus, we get:

[tex]\\\\P(A\cap B) = \dfrac{\text{Total person older than 35 years age and have hemoglobin level between 9 and 11}}{\text{Total person in survey}}\\\\P(A \cap B) = \dfrac{46}{429} \approx 0.1072[/tex]

Using the chain rule, we get:

[tex]P(B|A)P(A) = P(A\cap B)\\\\P(B|A) = \dfrac{P(A \cap B)}{P(A)} = \dfrac{0.1072}{0.3776} \approx 0.284[/tex]

Thus, the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 is given by: Option B: 0.284 approx.

Learn more about probability here:

brainly.com/question/1210781

Answer:

first term :9=a

common difference: 2 =d

A6=a+5d

=9+5(2)

=19

no of terms =9

[tex]s{n} = \frac{n}{2} (a + an) \\ = \frac{6}{2} (9 + 19) \\ = 3(28) \\ = 84[/tex]

Answer:

No, because it has repeating domains (x-values) which is -2

Step-by-step explanation:

A function should not have repeating x-values.

Answer:

1. k = 240

2. [tex]y=\dfrac{240}{x}[/tex]

3. 30 hours

Step-by-step explanation:

1.  if y varies inversely:

[tex]\implies y=\dfrac{k}{x}[/tex]

[tex]\implies 40=\dfrac{k}{6}[/tex]

[tex]\implies k=240[/tex]

2.

[tex]\implies y=\dfrac{240}{x}[/tex]

3. If x = 8:

[tex]\implies y=\dfrac{240}{8}=30[/tex]

Answer:

312 people

Step-by-step explanation:

Hello!

Step 1:

First, we want to calculate what percentage of the random sample voted pretzels. To do that, we divide the number of pretzel voters depending on the total number of voters.

Calculate:

So, approximately 12% of the sample voted on pretzels.

Step 2:

Now that we know the average percentage of people that want pretzels, we can find the same percentage of the actual population of 2600 people.

We need to solve for 12% of 2600

Calculate:

Based on our percentages, we predict that 312 people favor pretzels.

Answer:

Option A

Step-by-step explanation:

Given the following question:

[tex]x < -1[/tex]

Keep a few things in mind when graphing the inequality:
. x value is less than -1 (which means the line will go in the direction of the x)
. < is a greater sign not greater than or equal (≤) so it would be a open dot.
. The number line starts at -1.

According to all this information your answer is indeed option A.

Hope this helps.

Answer:

45 is the answer I think I don't know

Answer:

Step-by-step explanation:

The answer is (B), because the rate of the function is 0.50 from 0 to 8 ounces, thus the line should have a slope of 1/2. But afterward, it levels off horizontally as every ounce above 8 ounces to 12 ounces is $4.

Hope that helps!

Answer:

B

Step-by-step explanation:

Since it is 0.5 per serving between 0 and 8 ounces the graph would intersect at (1, 0.5) and it does for B. And then it says $4 for any serving 8 oz and 12 oz. B shows that the line changes to 4 dollars when it reaches 8 oz. Sorry for the terrible explanation.

Answer: 61 degrees

Step-by-step explanation:

Answer:

x would equal 1/4

x = 1/4

Step by step:

1. Distribute the equation on the left 4(2x+2). That would equal 8x+8 when you multiply 4 · 2x and 4 · 2

2. Rearrange the terms for the equation on the left side 8(2-3x). It should be 8(-3x+2)

3. Now distribute the left side. 8(-3x+2) = -24x+16

4. Now subtract 8 from both sides of the equation ( 8x+8-8 ) = (-24x+16-8)

You should get 8x= -24x+8

5. Now add 24x to both sides ( 8x+24x = -24x+8+24x )

6. Combine the like terms (8x+24x = 32x = 8)

7. Divide both sides by 32. 32/32 and 8/32

And that should get you 1/4

Hope the explanation helped

Answer:

x = 0.25

Step-by-step explanation:

The first step for this problem is  to multiply (2x+2) by 4 and (2-3x) by 8:

4(2x+2) = 8x+8

8(2-3x) = 16-24x

The equation becomes: 8x+8 = 16-24x

The second step for this problem is to move the terms with x to one side of the equals sign, and to move the terms without x to the other side.

8x+8 = 16-24x

8x+24x = 16-8

The third step is to combine like terms.

8x+24x = 32x

16-8 = 8

The equation becomes 32x = 8

The final step is to divide 8 by 32 to isolate the x:

32x = 8

x = 8/32 = 1/4 = 0.25

Answer:

219.8

Step-by-step explanation:

you multiply 70 and 3.14 and get 219.8

Answer:

The answer is 219.8

Step-by-step explanation:

I took the test

Answer:

Step-by-step explanation:

A side of a square garden is represented by the expression 2s + 5. Which expression represents the area of the garden?

Area = s * s ( side x side or side²)

(2s + 5) * (2s + 5)

or

(2s + 5)²

Answer: 12

Step-by-step explanation: V of prism = S of triangle*Height of prism

height of prism is 30

S of triangle = a/2*h( a =18 cm)

3240=30*(18/2)*h

h=3240/(9*30)=12

Two ways are there

Make it simple, go through second way

[tex]\\ \rm\Rrightarrow h^2=15^2-9^2[/tex]

[tex]\\ \rm\Rrightarrow h^2=225-81[/tex]

[tex]\\ \rm\Rrightarrow h^2=144[/tex]

[tex]\\ \rm\Rrightarrow h=12cm[/tex]

Answer:

same

Step-by-step explanation:

since if a central angle measures 87 then its arc will measure the same because the length of the arc equals the radian measure of the angle

Answer: Hope this helps <3

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

x=13

x-6

replace x with 13

13-6

7

Answer:

should be C

Step-by-step explanation:

Answer:

C

Step-by-step explanation: took the test

Answer:

Step-by-step explanation:

To find the slope, we use the slope formula

m = (y2-y1)/(x2-x1)

   = ( 4-4)/( 5 - -3)

   = 0/ ( 5+3)

  = 0/8

 = 0

Answer:

1) first one is 7/12

the second one is 45

as the chance of getting a 3,9 or 11 is 3/12

So you do 3/12 x 180 = 540/12 which is simplified to 45.

Answer:

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

[tex]g(f^{-1}(x))=\dfrac{-1}{x-1}[/tex]

[tex]g^{-1}(x)=\dfrac{1}{1-x}[/tex]

Step-by-step explanation:

[tex]f(x)=\dfrac{1}{1-x} \ \ \textsf{and} \ \ g(x)=\dfrac{x-1}{x}[/tex]

[tex]f(g(x))=\dfrac{1}{1-(\frac{x-1}{x})}[/tex]

[tex]\implies f(g(x))=\dfrac{1}{\frac{x}{x}-\frac{(x-1)}{x}}[/tex]

[tex]\implies f(g(x))=\dfrac{1}{\frac{x-x+1}{x}}[/tex]

[tex]\implies f(g(x))=\dfrac{1}{\frac{1}{x}}[/tex]

[tex]\implies f(g(x))=x[/tex]

[tex]x=\dfrac{1}{1-y}[/tex]

[tex]\implies 1-y=\dfrac{1}{x}[/tex]

[tex]\implies y=1-\dfrac{1}{x}[/tex]

[tex]\implies f^{-1}(x)=1-\dfrac{1}{x}[/tex]

[tex]g(f^{-1}(x))=1-\dfrac{1}{1-\frac{1}{x}}[/tex]

[tex]\implies g(f^{-1}(x))=1-\dfrac{1}{\frac{x-1}{x}}[/tex]

[tex]\implies g(f^{-1}(x))=1-\dfrac{x}{x-1}[/tex]

[tex]\implies g(f^{-1}(x))=\dfrac{x-1-x}{x-1}[/tex]

[tex]\implies g(f^{-1}(x))=\dfrac{-1}{x-1}[/tex]

[tex]x=\dfrac{y-1}{y}[/tex]

[tex]\implies xy=y-1[/tex]

[tex]\implies 1=y-xy[/tex]

[tex]\implies 1=y(1-x)[/tex]

[tex]\implies y=\dfrac{1}{1-x}[/tex]

[tex]\implies g^{-1}(x)=\dfrac{1}{1-x}[/tex]