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2 years ago

Fill in the blank to make the expression a perfect square.. . u^2-16u+?

Mathematics

1 answer:

hram777 [196]2 years ago

8 0

U² - 16 u + 64 = ( u - 8 )²
because: A² - 2 A B + B² = ( A - B )²
Answer: 64

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Certain tubes manufactured by a company have a mean lifetime of 800 hours and a standard deviation of 60 hours. Find the probabi

Anna71 [15]

Answer:

Step-by-step explanation:

given that certain tubes manufactured by a company have a mean lifetime of 800 hours and a standard deviation of 60 hours.

Sample size n =16

Std error of sample mean = $\frac{\sigma}{\sqrt{n} } \\= 15$

x bar follows N(800, 15)

the probability that a random sample of 16 tubes taken from the group will have a mean lifetime

(a) between 790 and 810 hours,

= $P(790$

(b) less than 785 hours

$=P(X$

, (c) more than 820 hours,

$=P(X>820)\\=p(Z>1.333)\\= 0.0913$

(d) between 770 and 830 hours

= $P(|Z|$

4 0

2 years ago

To play basketball with her friends, Evangeline needs to pump air in her ball, which is completely deflated. Before inflating it

Nadya [2.5K]

Answer:

ρ_air = 0.15544 kg/m^3

Step-by-step explanation:

Solution:-

- The deflated ball ( no air ) initially weighs:

m1 = 0.615 kg

- The air is pumped into the ball and weight again. The new reading of the ball's weight is:

m2 = 0.624 kg

- The amount of air ( mass of air ) pumped into the ball can be determined from simple arithmetic between inflated and deflated weights of the ball.

m_air = Δm = m2 - m1

m_air = 0.624 - 0.615

m_air = 0.009 kg

- We are to assume that the inflated ball takes a shape of a perfect sphere with radius r = 0.24 m. The volume of the inflated ( air filled ) ball can be determined using the volume of sphere formula:

V_air = 4*π*r^3 / 3

V_air = 4*π*0.24^3 / 3

V_air = 0.05790 m^3

- The density of air ( ρ_air ) is the ratio of mass of air and the volume occupied by air. Expressed as follows:

ρ_air = m_air / V_air

ρ_air = 0.009 / 0.05790

Answer: ρ_air = 0.15544 kg/m^3

4 0

2 years ago

Read 2 more answers

For a printing company, the cost of printing business cards is a linear function, C(x) = 0.05x + 20, where x is the number of ca

Svetllana [295]

Answer:

Step-by-step explanation:

You plug in 1200 for x.

C(1200)=0.05(1200) +20

Then solve. Multiply first then add.

60+20

5 0

2 years ago

What is the SLOPE of HI ? Justify your answer hurry PLEASE

PilotLPTM [1.2K]

Step-by-step explanation:

since it is in the same line as DE, both have the same slope.

the slope is the ratio of "y coordinate change / x coordinate change" when going from one point on the line to another.

and so by using the coordinates of D and E

x changes by +4 (from 8 to 12).

y changes by -8 (from 32 to 24).

the slope is therefore

-8/+4 = -2

8 0

2 years ago

8.46 If 100 is decreased by a% and the result is decreased by b%, then what is the total percent decrease (in terms of a and b)?

Marysya12 [62]

Answer:

The total percent decrease is $a+b-\frac{a b}{100}$

Step-by-step explanation:

We are given with a word problem
We are asked to find the total percentage decrease
We can do this in two steps

Step 1: Finding the two percentage decrease

Step 2: Finding their difference

Step 1 of 2

Let the decrease by a% be 100-a

Then b% decrease is

$\begin{aligned}\frac{b}{100} \times(100-a) &=\frac{100 b-a b}{100} \\\frac{100 b}{100}-\frac{a b}{100} &=b-\frac{a b}{100}\end{aligned}$

Step 2 of 2

The percentage difference between the two percentages is,

$\begin{aligned}&(100-a)-\left(b-\frac{a b}{100}\right)=100-a-b+\frac{a b}{100} \\&100-a-b+\frac{a b}{100}=100-\left(a+b-\frac{a b}{100}\right)\end{aligned}$

Since 100 is the total percent $a+b-\frac{a b}{100}$ is the percentage decrease.

3 0

1 year ago