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3 years ago

The expression 2x² + ax is equivalent to x (2x + 7) for some constant a. What is the value of a ?

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

7 0

2x^2 + ax = x(2x+ 7)
2x^2 + ax = 2x^2 + 7x
Subtract 2x^2 from both sides
ax = 7x
a = 7

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The administrator of a nursing home would like to do a time-and-motion study of staff time spend per day performing nonemergency

WINSTONCH [101]

Answer:

32 days must be sampled to test the proposed hypothesis.

Step-by-step explanation:

Consider the provided information.

The average number of person-hours per day spent on these task was $\mu_0=16$ .

The actual value of μ is 12 hours or less i.e μ=12

She wants a test having α=0.05

The probability of a type II error of at most β=0.10 and σ=7.64.

δ = μ-μ0

= 12-16

= -4

Now use the formula for calculating the sample size:

$N=\frac{(Z_{\alpha}+Z_{\beta})^2\sigma^2}{\delta^2}$

Substitute the respective values.

$N=\frac{(Z_{0.05}+Z_{0.1})^2(7.64)^2}{(-4)^2}$

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$N=31.2437958482\approx 32$

Hence, 32 days must be sampled to test the proposed hypothesis.

5 0

3 years ago

Graph m=3 b=-1 m=-2 b=4

Fittoniya [83]

Answer:

y= 3x − 4

Step-by-step explanation:

The slope-intercept form for a linear equation is

y= mx + b, where m = the slope, and b = the y-intercept.

Given:

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6 0

3 years ago

4.3 to the 3rd power simplified

zhuklara [117]

Answer:

4.3 to the 3rd power is exactly<em> 79.507 </em>. That number may be rounded, but not simplified.

Step-by-step explanation:

4.3 to the 3rd power means (4.3 x 4.3 x 4.3) . Perform the indicated multiplications to arrive at the solution.

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3 years ago

Read 2 more answers

A go-cart racetrack has 100-meter straightaways and semicircular ends with diameters of 40 meters. Calculate the average speed i

emmainna [20.7K]

Answer:

Average speed of go cart is 217.07 meters per minute.

Step-by-step explanation:

We are given the following in the question:

Length of straightway racetrack = 100 m

Diameter of semicircular end = 40 m

Radius =

$r = \dfrac{d}{2} = \dfrac{40}{2} = 20\text{ m}$

Perimeter of racetrack =

Perimeter of semicircle + 2(Length of straightway) + Perimeter of semicircle

$=\pi r + 2(100) + \pi r\\=2\pi r + 2(200)\\=(2\times 3.14\times 20) + 200\\=325.6\text{ m}$

Speed =

$s = \dfrac{\text{Distance}}{\text{Time}}\\\\s = \dfrac{4\times \text{Perimeter of track}}{6}\\\\s = \dfrac{4\times 325.6}{6}\\\\s = 217.06\text{ meter per minute}$

Thus, average speed of go cart is 217.07 meters per minute.

4 0

3 years ago

ishmal invested £3500 for 3 years at 2.5% per annum simple interest. Work out the total amount of interest Ishmal earned.

Jlenok [28]

Answer:

Interest Earned is $262.5

Step-by-step explanation:

Interest=PRT/100

When P=Principal, R=Rate, T=Time

Interest earn =( 3500 x 3 x 2.5)/ 100

I=$26,250 / 100

I=$262.5

6 0

4 years ago