Mary signed up for a 5K race. It is called a 5K because it is 5 kilometers long. Mary doesn’t know how far a kilometer is and wants to visualize this distance in miles. How many miles will she have to run for the race?

Answer:

The required probability is option [tex]C)\ \dfrac{1}{9}[/tex]

Step-by-step explanation:

There are a total of 9 cards.

Total number of cases = 9

Let A be the event of choosing 1, 2 or 3.

Total number of favorable cases for event A = 3

Let B be the event of choosing 7, 8 or 9.

Total number of favorable cases for event B = 3

Formula for finding probability of an event E is:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Finding P(A), using the formula:

[tex]P(A) = \dfrac{3}{9}\\\Rightarrow \dfrac{1}{3}[/tex]

Now, it is given that the card is replaced, so again total number of cases are 9.

For finding P(B), using the formula:

[tex]P(B) = \dfrac{3}{9}\\\Rightarrow \dfrac{1}{3}[/tex]

To find the probability that events A and B both happen, we can simply multiply P(A) and P(B) because these are independent events.

[tex]\text{Required probability = }P(A) \times P(B)\\\Rightarrow \dfrac{1}{3} \times \dfrac{1}{3} \\\dfrac{1}{9}[/tex]

Answer:

CBD = 82°

Step-by-step explanation:

From the chords relations in a circle, we have that when two chords intersects, we have the following angles:

CBF = DBE =  (1/2) * (arc(CF) + arc(DE))

CBD = FBE = (1/2) * (arc(CD) + arc(EF))

So, using the second equation to find the value of the angle CBD, we have that:

CBD = (1/2) * (100 + 64)

CBD = (1/2) * 164

CBD = 82°

Answer:

x=5

Step-by-step explanation:

2^x=32 , solve for x, so x=5

Answer:

2(4a + 7)

Step-by-step explanation:

2 to the 4 and 7

This would give you 8a + 14 because 2 times 4 is 8,  and 2 times 7 is 14.

Hope this helps.

Answer:

2(4a + 7)

Step-by-step explanation:

Multiply 2x 4 to make 8a. Then multiply 2 x 7 to make 14. 8a + 14.

THANKS FOR THE POINTS BTW

Answer:

The first step is to expand it to get rid of brackets .

Step-by-step explanation:

The first step, you have to eliminate brackets by expanding :

[tex]2(3k + 1) = 4k + 32[/tex]

[tex]2(3k) + 2(1) = 4k + 32[/tex]

[tex]6k + 2 = 4k + 32[/tex]

Next you have to collect like terms by making the same variable to one side and lastly, solve it :

[tex]6k - 4k = 32 - 2[/tex]

[tex]2k = 30[/tex]

[tex]k = 30 \div 2[/tex]

[tex]k = 15[/tex]

Answer:

Use the distributive Law on the left side of the equation.

Step-by-step explanation:

The first step is to distribute the 2 over the parentheses:

2(3k + 1) = 4k + 32 Distributing:

2*3k + 2*1  = 4k + 3

6k + 2 = 4k + 3

2k = 1

k = 1/2.

Answer:

x=2 x=-4

Step-by-step explanation:

x2+2x−8=0

Step 1: Factor left side of equation.

(x−2)(x+4)=0

Step 2: Set factors equal to 0.

x−2=0 or x+4=0

x=2 or x=−4

Answer:

x=2 or x=−4

Answer:

x=2 or x=-4

Step-by-step explanation:

ax^2+bx+c=0

when solving this equation you should find two numbers that if we multiply them we get c and when we subtract them we get b so in this equation we get 2 and -4

Answer:

The value of x is 12

Step-by-step explanation:

4x3=12

7x3=21

Therefore 12/21

To explain further:

If you divide 12 by 3 you get 4

If you divide 21 by 3 you get 7

Therefore resulting to 4/7

(I found out that the number three goes in both numbers to begin with)

Is this clearer?

Answer:

56 pack

Step-by-step explanation:

To find the number of packs of seed needed, we will first find the area of the rectangular backyard. We're given that the length is 32 feet and the width is 21 feet.

We get the following. Area =length × width =×3221 =672 square feet So the area of the backyard is 672 square feet. Each pack of seed covers 12 square feet. So we can find the number of packs of seed needed as follows. =÷6721256 packs Thus, Justin will need 56 packs of seed.

Answer: 25°

Step-by-step explanation:

From the question, Toothy the crocodile wants to eat a delicious chicken and his mouth is open to an angle of 30 degrees but he needs to open his mouth to the angle of 55 degrees for the chicken to fit.

The additional angle that Toothy's mouth needs to be open so he can eat the chicken will be:

= 55° - 30°

= 25°

Answer:

25

Step-by-step explanation:

did it on khan academy

Answer:

b

Step-by-step explanation:

Answer:

24 ft^3

Step-by-step explanation:

Cylinder:

Volume = (pi)r^2h

Cone:

Volume = (1/3)(pi)r^2h

When using r and h for both a cylinder and a cone, the only difference is the factor of 1/3 for the volume of the cone.

A cone with the same radius and height as a cylinder has 1/3 the volume of the cylinder.

volume of cylinder = 72 ft^3

volume of cone = (1/3) * 72 ft^3 = 24 ft^3

Answer:

The volume of cone is 24 ft³

Step-by-step explanation:

Given that volume of cylinder = 72 ft³

Volume of cylinder = πr²h

Volume of cone = [tex]\frac{1}{3}[/tex][tex]\pi[/tex]r²h

Volume of cone = volume of cylinder/3

= 72/3

= 24 ft³

Answer:

The interval with the most amount of dots has the greatest number of boxes.

Step-by-step explanation:

Because each dot represents equal number of box(es), the interval with the most number of dots has the greatest number of boxes.

Answer:18

Step-by-step explanation:

i'd say it would be 4 over 1         4/1    so you go up 4 and to the right 1 if they were negative then it would be the oposite way around.

Answer:

For y=x-3. (0,2) the equation is y=x+2

For y=3-x. (0,2) the equation is y=2-x

For y=3x+1. (0,3) the equation is y=3x+3

For y=-1/2x+4. (0,1) the equation is y=-1/2x+1

Step-by-step explanation:

How I got my answers:

For y=x-3: the gradient is 1 because we do not have anything before x.

For the points given for example (0,2) x is zero  and y-intercept is 2. same for the rest of the points.

Now you can write your equation in the form y=mx+b

where m is your gradient, and b is the y point. So you say y=1x+2 for the first one. Do the same for the rest. Remember 1x is the same as x so you can leave out 1.

You can comment if you did not understand my explanation because this explained how you can do it.

Answer:

he played around 20 games

Answer:20

Step-by-step explanation:

N\A

Answer:

a fixed point equidistant from all points on the surface of the sphere

Step-by-step explanation:

I assume you are taking the test, so that's the answer

Answer:

d. g36

Step-by-step explanation:

The solution is, g^36 power is equivalent to the expression (g-12)-3.

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

given expression is,

g^(-12)(-3)

=g^(12*3)

=g^36

Hence, The solution is, g^36 power is equivalent to the expression (g-12)-3.

To learn more on exponent number click:

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Firstly let's find hypotenuse(let it will be "n" of smaller triangle

Let use Pythagorean theorem

[tex]a^{2} + {b}^{2} = {n}^{2} \\ {20}^{2} + {10}^{2} = {n}^{2} \\ n = \sqrt{500} [/tex]

Now we need to find hypotenuse(x) of bigger triangle

[tex] {c}^{2} + {n}^{2} = {x}^{2} \\ {9}^{2} + { \sqrt{500} }^{2} = {x}^{2} \\ x = \sqrt{581} [/tex]

The value of x must be rounded to 1 DP, so

[tex] \sqrt{581} = 24.1039... \\ \sqrt{581} \simeq \: 24.1[/tex]

Answer: x=24.1

Answer:

6pi or 18.84

Step-by-step explanation:

120/360 times 2 pi 9

120/360 = 1/3

2 times 9 = 18

18 times 1/3 equals 6

Answer:

x^3+8

The polynomial given may be: x^3 + 8. One choice

Step-by-step explanation:

The polynomial given may be: x^3 + 8. One choice

x^3+8

Answer is above

Hope this helps.

Answer:

This is a right triangle

Step-by-step explanation:

We can check if this is a right triangle by using the Pythagorean theorem

a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse

3^2+4^2 = 5^2

9+16 = 25

25=25

This is true so it is a right triangle

Answer:

see explanation

Step-by-step explanation:

cos F = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{FD}{EF}[/tex] = [tex]\frac{5}{13}[/tex]

sin F = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{ED}{EF}[/tex] = [tex]\frac{12}{13}[/tex]

tan F = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{ED}{FD}[/tex] = [tex]\frac{12}{5}[/tex]

====================================================

Work Shown:

5% = 5/100 = 0.05

5% of 42 = 0.05*42 = 2.10

tax = $2.10

total cost including tax = $42 + $2.10 = $44.10

----------

An alternative is to multiply 42 by 1.05 to get

1.05*42 = 44.10

We get the same answer. The 1.05 refers to 1 + 0.05 where the "1" is 100% and the 0.05 is 5%, so the two combine to 105%, meaning the total cost is 105% of the cost before tax is considered.

The values for a and b in the given exponential function are a = 4 and b = 1/2

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

For example, exponential functions can be used to calculate changes in population, loan interest charges, bacterial growth, radioactive decay or the spread of disease.

Given that,

The exponential function is given as, y = abˣ, we need to find the value of a and b,

When x = 0, ab⁰ = 4

a=4 (since, b⁰ = 1)

When x = 1, ab¹ = 2

4b = 2

b = 1/2

Hence, The values of a and b are a = 4 and b = 1/2

Learn more about exponential function, click;

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Answer:

1,253 inches cubed

Step-by-step explanation:

This is easy, just find the separate volumes of both and add.

Figure 1: 7x5x5= 175 inches cubed

Figure 2: 11x14x7= 1,078 inches cubed

Added together: 1,253 inches cubed

Therefore it's C

:))))))

Answer:

[tex]\frac{4}{3} \\1.333333[/tex]

Step-by-step explanation:

Answer:

acute acute obtuse right

Step-by-step explanation:

if it is less than 90° it will be acute. it is exactly 90° it is right. it is more than 90° it is obtuse.

good luck