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3 years ago

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If , f(x)= 3/(x+2) minus the square root of x-3, complete the following statement: f(19) = _____ (need help as soon as possible

not sure if the answer is just 19?)

2 answers:

Svet_ta [14]3 years ago

4 0

All you need to do is plug 19 in for x and solve.

f(19) = 3/(19+2) - sqrt(19-3) = 1/7 - sqrt(16)= 1/7 - 4

The answer is -3.8571 or as a fraction -27/7

Natasha_Volkova [10]3 years ago

4 0

Answer:

$f(x)= \frac{3}{x+2}- \sqrt{x-3}$

the given function has domain

x+2≠0

x≠ -2

x-3≥0

x≥3

That is , x ∈ [3,∞]

Now, calculating ,f (19)

$f(19)= \frac{3}{19+2}-\sqrt{19-3}\\\\ = \frac{3}{21} - \sqrt{16}\\\\ f(19)=\frac{1}{7}-4\\\\=\frac{1-28}{7}\\\\=\frac{-27}{7}$

$f(19)=-[3\frac{6}{7}]$

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Which equation is y = â€""6x2 3x 2 rewritten in vertex form?.

Ber [7]

The vertex form needed is :

$-6(x-0.25)^2 +2.375$

Given the equation:

$-6x^2 + 3x + 2\\$

The vertex form of $f(x) = ax^2 + b(x) + c$ is given by:

$f(x) = a(x-h)^2 + k$

Here, (h,k) is the vertex of the parabola equation given.

Conversion will go like this:

$-6x^2 + 3x + 2\\= -6(x^2 - 0.5x) + 2\\= -6(x^2 -0.5x + 0.0625 - 0.0625) + 2\\= -6(x^2 -0.5x + 0.0625) + 2 +0.375\\= -6(x-0.25)^2 + 2.375\\\\$

This is the resultant vertex form.

Thus the vertex form needed is :

$-6(x-0.25)^2 +2.375$

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2 years ago

∠F and ∠G are supplementary angles. If m∠F is two less than six times the measure of ∠G, find the measures of both angles

Mnenie [13.5K]

Answer:

∠ G = 26°, ∠ F = 154°

Step-by-step explanation:

Express ∠ F in terms of ∠ G, that is

F = 6G - 2

and since the angles are supplementary, then

G + 6G - 2 = 180, that is

7G - 2 = 180 ( add 2 to both sides )

7G = 182 ( divide both sides by 7 )

G = 26

Thus

∠ G = 26° and ∠ F = 6(26) - 2 = 156 - 2 = 154°

4 0

3 years ago

The stock market dropped 220 points on Monday. It lost another 48 points on Tuesday, and on Wednesday, it gained 96 points. What

MissTica

48 points gained in those 3 days.

Subtract 220 with 48, then add 96. Last step would be subtracting 220 with the amount they have now in those 3 days to find how much points the stock market gained in those 3 days.

Subtract 220-48.It‘ll be 172.

Add 172 with 96. 172+96=268.

Subtract 268 with how much points the stock market had 3 days ago. 268-220.

Sot eh stock market gained 48 points in 3 days.

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3 years ago

Simplify to create an equivalent expression 2-6(-5t+1)

Mariulka [41]

Answer:

30t - 4

Step-by-step explanation:

Remember to follow PEMDAS. First, distribute -6 to all terms within the parenthesis:

2 -6(-5t + 1) = 2 + (-6 * -5t) + (-6 * 1)

2 + (30t) + (-6) = 2 + 30t - 6

Simplify. Combine like terms:

2 + 30t - 6 = 30t + (-6 + 2) = 30t - 4

30t - 4 is your answer.

~

6 0

3 years ago

Read 2 more answers

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 oun

sveticcg [70]

Answer:

a. $f_X(x) = \dfrac{1}{3.5}8.5$

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. 86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

$f_X(x) = \dfrac{1}{B-A}A$

where A and B are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x) = \dfrac{1}{12-8.5}8.5$

$f_X(x) = \dfrac{1}{3.5}8.5$

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

$F(x) = \dfrac{x-A}{B-A}$

$F(10) = \dfrac{10-8.5}{12-8.5}$

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

$P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx$

$P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}$

$P(X\geq11) = {\dfrac{1}{3.5}} (12-11)$

$P(X\geq11) = {\dfrac{1}{3.5}} (1)$

$P(X\geq11) = 0.2857$

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)$

$P(9.5 \leq X\leq11.5) =0.2857* (2)$

$P(9.5 \leq X\leq11.5) =0.5714$

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

$P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx$

$P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}$

$P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)$

$P(X \geq 9) = {\dfrac{1}{3.5}}(3)$

$P(X \geq 9) = 0.2857*}(3)$

$P(X \geq 9) = 0.8571$

NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

3 0

3 years ago