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Nata [24]
3 years ago
14

Find f(4) when f(x)=4x^2 - 2 x - 4

Mathematics
1 answer:
prisoha [69]3 years ago
8 0

Answer:

52

Step-by-step explanation:

f(x)=4x^2-2x-4

f(4)=4(4)^2-2(4)-4 (I replaced x with (4) since we are to find f(4).)

f(4)=4(16)-2(4)-4    (By the order of operations, we take care of the exponents before whatever else we have here.)

f(4)=64-8-4           (By the order of operations, we take care of the multiplication as we see if left to right.)

f(4)=56-4              (By the order of operations, we perform addition/subtraction as we see it left to right.)

f(4)=52                 (This completes the simplification.)

We could have also put this in our calculator as:

4(4)^2 -  2(4)  -  4

This would have returned 52.

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The weights of a certain brand of candies are normally distributed with a mean weight of 0.8544 g and a standard deviation of 0.
aleksandr82 [10.1K]

Answer:

The probability is 0.508 = 50.8%.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean weight of 0.8544 g and a standard deviation of 0.0525 g.

This means that \mu = 0.8544, \sigma = 0.0525

If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8535 g.

This is 1 subtracted by the pvalue of Z when X = 0.8535. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{0.8535 - 0.8544}{0.0525}

Z = -0.02

Z = -0.02 has a pvalue of 0.492

1 - 0.492 = 0.508

The probability is 0.508 = 50.8%.

8 0
3 years ago
Tom has a gift box that is 3 units long, 6 units wide, and 12 units tall. What is the volume of the gift?
Kryger [21]

Answer:

216

Step-by-step explanation:

LxWxH fill it in 3x6x12=216

5 0
3 years ago
The regular price of a tv is x dollars during a sale ,$39 is subtracted from this price the sale price is $215
klemol [59]

Answer:

254

Step-by-step explanation:

x-39=215

215+39=x

215+39=254

6 0
3 years ago
Read 2 more answers
The equation for the ellipse given is 4x^2+9y^2-16x+18y-11​
natita [175]

Answer:

a. a = 3, b = 2

b. The coordinate of the center is (2, -1)

c. The eccentricity of the ellipse is √5/3

d. Please see attached graph of the ellipse created with MS Excel

Step-by-step explanation:

7. a. The given equation of the ellipse is presented as follows;

4·x² + 9·y² - 16·x + 18·y - 11

The general equation of an ellipse

\dfrac{(x - h)^2}{a^2}  + \dfrac{(y - k)^2}{b^2} = 1

We can write;

4·x² - 16·x + 9·y² + 18·y - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) - 25 - 11

4·(x² - 4·x + 4) + 9·(y² + 2·y + 1) =  25 + 11 = 36

4·(x - 2)² + 9·(y + 1)² = 36

\dfrac{4\cdot (x - 2)^2}{36}  + \dfrac{9 \cdot (y + 1)^2}{36} = \dfrac{36}{36}

\therefore \dfrac{ (x - 2)^2}{9}  + \dfrac{  (y + 1)^2}{4} =  \dfrac{ (x - 2)^2}{3^2}  + \dfrac{  (y + 1)^2}{2^2}  = 1

By comparison, a = 3, b = 2, h = 2, k = -1

b. The coordinate of the center, (h, k) = (2, -1)

c. The eccentricity of the ellipse = c/a

c² = a² - b²

∴ c² = 3² - 2² = 5

c = √5

Eccentricity = √5/3

d. Please find attached the graph of the ellipse created with MS Excel

8 0
3 years ago
Molly used 1-inch cubes to build the structure shown.she left a 3 inch by 1-inch opening in both layers of the structure.what to
Sergio [31]

Answer:i think a ruler

Step-by-step explanation:

7 0
3 years ago
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