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PIT_PIT [208]
1 year ago
15

2( 10 - a^2 ) + 7a If ( a = 4 )Evaluate each expression

Mathematics
1 answer:
Lostsunrise [7]1 year ago
6 0

Solution:

Given:

2(10-a^2)+7a

when a = 4, substitute for a in the expression;

\begin{gathered} 2(10-a^2)+7a=2(10-4^2)+7(4) \\ =2(10-16)+28 \\ =2(-6)+28 \\ =-12+28 \\ =16 \end{gathered}

Therefore, if (a = 4), then

2(10-a^2)+7a=16

Hence, the answer is 16.

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How many times does 6 go into 98
dmitriy555 [2]
16 times but the answer is 16.3(repeating)
5 0
3 years ago
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Find an equation of the plane consisting of all points that are equidistant from (-3, 5, -4) and (-5, 0, 4), and having -2 as th
Firdavs [7]

Answer:

-2x-5y+8z+4.5=0

Step-by-step explanation:

Let (x,y,z) be the coordinates of the point lying on the needed plane. This point is equidistant from the points (-3, 5, -4) and (-5, 0, 4), so

d_1=\sqrt{(x-(-3))^2+(y-5)^2+(z-(-4))^2}=\sqrt{(x+3)^2+(y-5)^2+(z+4)^2}\\ \\d_2=\sqrt{(x-(-5))^2+(y-0)^2+(z-4)^2}=\sqrt{(x+5)^2+y^2+(z-4)^2}\\ \\d_1=d_2\Rightarrow \sqrt{(x+3)^2+(y-5)^2+(z+4)^2}=\sqrt{(x+5)^2+y^2+(z-4)^2}\\ \\(x+3)^2+(y-5)^2+(z+4)^2=(x+5)^2+y^2+(z-4)^2\\ \\x^2+6x+9+y^2-10y+25+z^2+8z+16=x^2+10x+25+y^2+z^2-8z+16\\ \\-4x-10y+16z+9=0\\ \\-2x-5y+8z+4.5=0

5 0
3 years ago
Read 2 more answers
At a cell phone assembly plant, 77% of the cell phone keypads pass inspection. A random sample of 111 keypads is analyzed. Find
Serggg [28]

Answer:

The probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 \mu_{\hat p}=p

The standard deviation of this sampling distribution of sample proportion is:

\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}

Let <em>p</em> = the proportion of keypads that pass inspection at a cell phone assembly plant.

The probability that a randomly selected cell phone keypad passes the inspection is, <em>p</em> = 0.77.

A random sample of <em>n</em> = 111 keypads is analyzed.

Then the sampling distribution of \hat p is:

\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})\\\Rightarrow \hat p\sim N (0.77, 0.04)

Compute the probability that the proportion of passed keypads is between 0.72 and 0.80 as follows:

P(0.72

                             =P(-1.25

Thus, the probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.

8 0
3 years ago
The following system of equations can be used to find the roots of the equation x^3+72=5x^2+18x
Ivan
A graph shows the roots to be {-4, 3, 6}.

5 0
3 years ago
Back Next
emmasim [6.3K]

Answer:

C

Step-by-step explanation:

✔️First, solve for r:

r/2 ≤ 3

Multiply both sides by 2

r/2 × 2 ≤ 3 × 2

r ≤ 6

This implies that possible value of r is equal to 6 or less than 6.

Graphing this on a number line, the line with a shaded circle, indicating that 6 is included, starts at 6 and points to the left.

This indicates that value of r ranges from 6 and below.

The graph is C.

7 0
3 years ago
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