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3 years ago

9

Omar rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 78 cents for each mile dr

iven. Omar had to pay $165.63 when he returned the truck. For how many miles did he drive the truck?

1 answer:

natulia [17]3 years ago

6 0

165.63-$18.99= $146.64

$146.64 / .78€ per mi= 188miles

188 miles is your answer

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Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8 + x^2 + 7 ?

Ad libitum [116K]

Answer:

The function translated 4 units right and 9 units down

The third answer

Step-by-step explanation:

* To solve the problem you must know how to find the vertex

of the quadratic function

- In the quadratic function f(x) = ax² + bx + c, the vertex will

be (h , k)

- h = -b/2a and k = f(-b/2a)

* in our problem

∵ f(x) = x²

∴ a = 1 , b = 0 , c = 0

∵ h = -b/2a

∴ h = 0/2(1) = 0

∵ k = f(h)

∴ k = f(0) = (0)² = 0

* The vertex of f(x) is (0 , 0)

∵ g(x) = -8x + x² + 7 ⇒ arrange the terms

∴ g(x) = x² - 8x + 7

∵ a = 1 , b = -8 , c = 7

∴ h = -(-8)/2(1) = 8/2 = 4

∵ k = g(h)

∴ k = g(4) = (4²) - 8(4) + 7 = 16 - 32 + 7 = -9

∴ The vertex of g(x) = (4 , -9)

* the x-coordinate moves from 0 to 4

∴ The function translated 4 units to the right

* The y-coordinate moves from 0 to -9

∴ The function translated 9 units down

* The function translated 4 units right and 9 units down

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3 years ago

The number of fruit tarts that a baker makes each day is 40% of the total number of desserts she makes. On Monday, the baker mak

Harrizon [31]

225 to get this answer you should do this 90/40%=225

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3 years ago

Read 2 more answers

A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 7

SCORPION-xisa [38]

Answer:

The probability that exactly eight of them take more than 93.6 minutes is 5.6015 $\times 10^{-6}$ .

Step-by-step explanation:

We are given that it is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes.

A random sample of twelve service calls is taken.

So, firstly we will find the probability that service calls take more than 93.6 minutes.

Let X = <u><em>times for service calls.</em></u>

So, X ~ Normal( $\mu=75,\sigma^{2} =15^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 75 minutes

$\sigma$ = standard deviation = 15 minutes

Now, the probability that service calls take more than 93.6 minutes is given by = P(X > 93.6 minutes)

P(X > 93.6 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{93.6-75}{15}$ ) = P(Z > 1.24) = 1 - P(Z $\leq$ 1.24)

= 1 - 0.8925 = <u>0.1075</u>

The above probability is calculated by looking at the value of x = 1.24 in the z table which has an area of 0.8925.

Now, we will use the binomial distribution to find the probability that exactly eight of them take more than 93.6 minutes, that is;

$P(Y = y) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; y = 0,1,2,3,.........$

where, n = number of trials (samples) taken = 12 service calls

r = number of success = exactly 8

p = probability of success which in our question is probability that

it takes more than 93.6 minutes, i.e. p = 0.1075.

Let Y = <u><em>Number of service calls which takes more than 93.6 minutes</em></u>

So, Y ~ Binom(n = 12, p = 0.1075)

Now, the probability that exactly eight of them take more than 93.6 minutes is given by = P(Y = 8)

P(Y = 8) = $\binom{12}{8}\times 0.1075^{8} \times (1-0.1075)^{12-8}$

= $495 \times 0.1075^{8} \times 0.8925^{4}$

= 5.6015 $\times 10^{-6}$ .

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It is approximately a thousand times larger

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10 times the square root of 5

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Answer:

22.36

or 559/25

or 22 9/25

Step-by-step explanation:

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