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A motorcycle shop maintains an inventory of four times as many new bikes. If there are 80 new bikes, how many used bikes are now

Ghella [55]

Answer: There are 20 used bikes

Explanation: If there are 4 times the used bikes then you would have to do 80 divided by 4 and there’s the answer

7 0

3 years ago

Read 2 more answers

The sum of four consecutive odd number is 8o. Find the number

yarga [219]

Answer:

The sum of 4 consecutive odd number is 80

Let X be the first of these numbers

Then the next odd number is X+2

The third is X+4The fourth is X+6

All of these add up to 80

(X) + (X+2) + (X+4) + (X+6) = 80

Using the commutative and associative laws, let's transform this equation into

(X + X + X + X) + (2 + 4 + 6) = 804X + 12 = 80

Subtract 12 from both sides of the equation gives4X = 68

Divide both sides by 4 gives

X = 17

Going back to the original question:What are the 4 consecutive odd numbers: 17, 19, 21, 23Checking our answer:17 + 19 + 21 + 23 = 80 Correct!

5 0

3 years ago

M angle PQS= 3x; m angle SQR=5x-20 Find x

Dahasolnce [82]

Let as consider the complete ques is : Ray QS bisects ∠PQR. Solve for x and find m∠PQR. m∠PQS = 3x ; m∠SQR = 5x-20.

Given:

Ray QS bisects ∠PQR.

m∠PQS = 3x

m∠SQR = 5x-20

To find:

The value of x and m∠PQR

Solution:

Ray QS bisects ∠PQR. So,

$m\angle PQS=m\angle SQR$

$3x=5x-20$

$3x-5x=-20$

$-2x=-20$

$x=10$

The value of x is 10.

Now,

$m\angle PQR=m\angle PQS+m\angle SQR$

$m\angle PQR=3x+5x-20$

$m\angle PQR=8x-20$

Put x=10,

$m\angle PQR=8(10)-20$

$m\angle PQR=80-20$

$m\angle PQR=60$

Therefore, the m∠PQR is 60 degrees.

5 0

4 years ago

What is the simplest form of x²+5x-6/x²+9x+18

Lyrx [107]

Answer:

(x - 1) / (x + 3).

Step-by-step explanation:

x²+5x-6/x²+9x+18

Factoring top and bottom:

= (x + 6)(x - 1) / (x + 6)(x + 3) (x + 6) is common, so:

= (x - 1) / (x + 3) (answer).

4 0

3 years ago

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found t

Wittaler [7]

Answer:

$a=30 +1.04*8=38.32$

So the value of height that separates the bottom 85% of data from the top 15% is 38.32.

C) 38.32

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Solution to the problem

Let X the random variable that represent the waiting time in minutes of a population, and for this case we know the distribution for X is given by:

$X \sim N(30,8)$

Where $\mu=30$ and $\sigma=8$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

We want to find a value a, such that we satisfy this condition:

$P(X>a)=0.15$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=1.04$

And if we solve for a we got

$a=30 +1.04*8=38.32$

So the value of height that separates the bottom 85% of data from the top 15% is 38.32.

C) 38.32

7 0

4 years ago