On the most recent math test, Ashley

0 of 10

Aleksandr-060686 [28]

Answer:

1038

Step-by-step explanation:

you add 308 and 730

4 0

3 years ago

A circle has a circumference of 6. It has an arc of length 17/3. What is the central angle of the arc, in degrees?

zepelin [54]

Answer:

340 degrees

Step-by-step explanation:

So the key thing here is to notice that we are given the circumference which will allow us to find a value for the radius of the circle and hence the angle subtended by the arc (the central angle).

So the circumference of a circle = 2pi(r)

This means:

6 = 2pi(r)

Which means that

r = 6/2pi or r = 3/pi

Now we can use this value of r to find our angle in conjunction with the value of the arc length. So:

Arc length is defined by: length = θr

Where θ is our angle value.

So lets plug in:

$\frac{17}{3} = (angle)\frac{3}{\pi }$

Multiply by pi to get:

$\frac{17\pi }{3} = 3(angle)$

Divide by 3 to get that:

θ = 17pi/9

So if we convert that from radians to degrees we get 340 degrees.

7 0

2 years ago

A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience i

s344n2d4d5 [400]

Answer:

5.3%

Step-by-step explanation:

The final probability is calculated by means of the quotient of the specific combinations and the total of total combinations

Let's start with the specific ones,

First the number of combinations of 4 of the 30 students getting a spot, i.e .:

A combinations are equal to:

nCx = n! / x! * (n-x)!

Replacing:

30C4 = 30! / (4! * 26!) = 27405

Segundo the number of combinations of the other audience members filling the other 4 (8-4) spots n = 110, 140 - 30

110C4 = 110! / (4! * 106!) = 5773185

Now the total combinations of possible 8 contestants from the audience

140C8 = 140! / (8! * 132!) = 2.98 * 10 ^ 12

Finally, the probability is equal to:

P = (30C4 * 110C4) / 140C8

replacing:

P = 27405 * 5773185 / 2.98 * 10 ^ 12

P = 0.053

Therefore the probability is 5.3%

4 0

3 years ago

Match the numerical expressions to their simplest forms.

Aloiza [94]

Answer:

$(a^6b^1^2)^\frac{1}{3}$ = $a^2b^4$

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$ = $a^3b^2$

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$ = $a^2b$

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$ = $ab^3$

Step-by-step explanation:

Simplify each of the expressions:

1

$(a^6b^1^2)^\frac{1}{3}$

Distribute the exponent. Multiply the exponent of the term outside of the parenthesis by the exponents of the variable.

$(a^6b^1^2)^\frac{1}{3}$

$a^6^*^\frac{1}{3}b^1^2^*^\frac{1}{3}$

Simplify,

$a^2b^4$

2

Use a similar technique to solve this problem. Remember, a fractional exponent is the same as a radical, if the denominator is (2), then the operation is taking the square root of the number.

$\frac{(a^5b^3)^\frac{1}{2}}{(ab)^-^\frac{1}{2}}$

Rewrite as square roots:

$\frac{\sqrt{a^5b^3}}{\sqrt{(ab)}^-^1}$

A negative exponent indicates one needs to take the reciprocal of the number. Apply this here:

$\frac{\sqrt{a^5b^3}}{\frac{1}{\sqrt{ab}}}$

Simplify,

$\sqrt{a^5b^3}*\sqrt{ab}$

Since both numbers are under a radical, one can rewrite them such that they are under the same radical,

$\sqrt{a^5b^3*ab}$

Simplify,

$\sqrt{a^6b^4}$

Since this operation is taking the square root, divide the exponents in half to do this operation:

$a^3b^2$

3

$(\frac{a^5}{a^-^3b^-^4})^\frac{1}{4}$

Simplify, to simplify the expression in the numerator and the denominator, the base must be the same. Remember, the base is the number that is being raised to the exponent. One subtracts the exponent of the number in the denominator from the exponent of the like base in the numerator. This only works if all terms in both the numerator and the denominator have the operation of multiplication between them:

$(\frac{a^8}{b^-^4})^\frac{1}{4}$

Bring the negative exponent to the numerator. Change the sign of the exponent and rewrite it in the numerator,

$(a^8b^4)^\frac{1}{4}$

This expression to the power of the one forth. This is the same as taking the quartic root of the expression. Rewrite the expression with such,

$\sqrt[4]{a^8b^4}$

SImplify, divide the exponents by (4) to simulate taking the quartic root,

$a^2b$

4

$(\frac{a^3}{ab^-^6})^\frac{1}{2}$

Using all of the rules mentioned above, simplify the fraction. The only operation happening between the numbers in both the numerator and the denominator is multiplication. Therefore, one can subtract the exponents of the terms with the like base. The term in the denomaintor can be rewritten in the numerator with its exponent times negative (1).

$(a^3^-^1b^(^-^6^*^(^-^1^)^))^\frac{1}{2}$

$(a^2b^6)^\frac{1}{2}$

Rewrite to the half-power as a square root,

$\sqrt{a^2b^6}$

Simplify, divide all of the exponents by (2),

$ab^3$

7 0

3 years ago

Carolyn has been contributing to a pre-tax retirement account. Her youngest child is ready to start college, and Carolyn wants t

Flauer [41]

Answer: 77,089.64 or 83,256.81

Step-by-step explanation:

Either or because it doesnt specify is she has to pay 10% and 25% or 10% early and 15% later on. If you know then the lower answer is 10% now and 15% later on. GL!

6 0

2 years ago