Lorenzo went to the store with 20$. He bought some cans of soup for 2$ each and a gallon of milk for 3$. He had 1$ left over.

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Mars2501 [29]

The first one is 2x^2+2x-2
the second one is 2x^2-2x-2
the third one is 6h+6k

3 0

3 years ago

Given a polynomial f(x), if (x − 4) is a factor, what else must be true?

ollegr [7]

Answer:

$f(4)=0$

Step-by-step explanation:

The Remainder Theorem states that when you divide a polynomial $f(x)$ by a linear factor $(x-a)$ , where $a$ is a constant, the remainder is $f(x)$ evaluated at $x=a$

Moreover, according to the Factor Theorem, an extension of the Remainder Theorem, if the remainder of the function $f(x)$ is 0 when evaluated at $x=a$ , then $(x-a)$ is said to be a factor of the polynomial $f(x)$

Given the 2 theorems above, it follows that if $(x-4)$ is a factor of $f(x)$ , then the remainder is equal to 0 when $f(x)$ is evaluated at $x=4$

Which means $f(4)=0$

Third answer choice is correct.

3 0

3 years ago

Read 2 more answers

The area of a triangle is 1,4440 cm^2. The base of the triangle is 5 times the height. What is the height of the triangle?

DochEvi [55]

Answer:

h = 24 cm

Step-by-step explanation:

The formula for area of a triangle is

A = (1/2)bh where b is the base and h is the height.

We are told that the base is 5 times the height, this translates to

b = 5h, so we can rewrite our formula to

A = (1/2)(5h)(h) or

A = (1/2)5h²

We are given A = 1,440, so plug that in and solve for h...

1,440 = (1/2)5h²

2,880 = 5h² (multiply both sides by 2 to get rid of the fraction)

576 = h² (divide both sides by 5 to get the h value by itself)

24 = h (take the square root of both sides)

3 0

3 years ago

Becky swims 3/4 of a mile each day. How many miles does she swim in 5 days?

pav-90 [236]

The answer is C. 3 3/4 is the answer.

5 0

3 years ago

The service department of a luxury car dealership conducted research on the amount of time its service technicians spend on each

mart [117]

Answer:

Probability that the mean service time is between 1 and 2 hours is 0.96764.

Step-by-step explanation:

We are given that a systematic random sample of 100 service appointments has been collected.

The 100 appointments showed an average preparation time of 90 minutes with a standard deviation of 140 minutes.

Let $\bar X$ = sample mean service time

The z-score probability distribution for sample mean is given by;

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

where, $\mu$ = average preparation time = 90 minutes

$\sigma$ = standard deviation = 140 minutes

n = sample of appointments = 100

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, probability that the mean service time is between 60 and 120 minutes is given by = P(60 minutes < $\bar X$ < 120 minutes)

P(60 minutes < $\bar X$ < 120 minutes) = P( $\bar X$ < 120 min) - P( $\bar X$ $\leq$ 60 min)

P( $\bar X$ < 120 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{120-90}{\frac{140}{\sqrt{100} } }$ ) = P(Z < 2.14) = 0.98382

P( $\bar X$ $\leq$ 60 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{60-90}{\frac{140}{\sqrt{100} } }$ ) = P(Z $\leq$ -2.14) = 1 - P(Z < 2.14)

= 1 - 0.98382 = 0.01618

The above probability is calculated by looking at the value of x = 2.14 in the z table which has an area of 0.98382.

Therefore, P(60 min < $\bar X$ < 120 min) = 0.98382 - 0.01618 = 0.96764

7 0

3 years ago