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adelina 88 [10]
2 years ago
11

Factor the expression completely. 40x^2+70 40x 2 +70

Mathematics
1 answer:
bogdanovich [222]2 years ago
8 0

Answer:

Are you sure you wrote it right?

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The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate, a,
omeli [17]
<span>f = v + at

Subtract v from both sides.

f - v = at

Divide both sides by a.

(f - v)/a = t

Switch sides.

t = (f - v)/a

t = \dfrac{f - v}{a}</span>
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1) mean: 7. median: 6. mode: 10
2) mean: 83.8. median: 84. mode: none
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A spherical water balloon is filled such that it has a diameter of 9 inches. Water is then released from the balloon until it ha
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A manufacturer uses production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standar
Arisa [49]

Answer:

\chi^2 =\frac{17-1}{12.15} 22.09 =15.87

Traditional method

We can find a critical value in the chi square distribution with df =16 who accumulates \alpha/2 =0.05 of the area on each tail and we got:

\chi^2_{crit}= 7.962

\chi^2_{crit}=26.296

Since the calculated value is between the two critical values we don't have enough evidence to conclude that the true deviation is NOT significantly different from 3.5 cm

Confidence level method

We can find the p value like this

p_v =2*P(\chi^2 >15.87)=0.92

Since the p value is higher then the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is NOT significantly different from 3.5 cm

Step-by-step explanation:

Data provided

n=17 represent the sample selected

\alpha=0.1 represent the significance

s^2 =4.7^2 =22.09 represent the sample variance

\sigma^2_0 =3.5^2 =12.15 represent the value to check

Null and alternative hypothesis

We want to verify if the new production method has lengths with a standard deviation different from 3.5 cm, so the system of hypothesis would be:

Null Hypothesis: \sigma^2 = 12.15

Alternative hypothesis: \sigma^2 \neq 12.15

The statistic for this case is given by:

\chi^2 =\frac{n-1}{\sigma^2_0} s^2

The degrees of freedom are:

df =n-1= 17-1=16

\chi^2 =\frac{17-1}{12.15} 22.09 =15.87

Traditional method

We can find a critical value in the chi square distribution with df =16 who accumulates \alpha/2 =0.05 of the area on each tail and we got:

\chi^2_{crit}= 7.962

\chi^2_{crit}=26.296

Since the calculated value is between the two critical values we don't have enough evidence to conclude that the true deviation is significantly different from 3.5 cm

Confidence level method

We can find the p value like this

p_v =2*P(\chi^2 >15.87)=0.92

Since the p value is higher then the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is significantly different from 3.5 cm

7 0
3 years ago
A boat can travel at an average speed of 10 miles per hour in still water. Traveling with the current, it can travel 6 miles in
oksano4ka [1.4K]

Answer: The speed of the current is 2 miles per hour.

Step-by-step explanation:

We know that the speed of the boat is:

S = 10 mph.

When the boat travels with the current, the speed will be:

S = 10mph + x

where x = speed of the current.

When the boat travels against the current, the speed will be:

S = 10mph - x

Now, for a given amount of time T, when the boat travels with the current, it moves a distance of 6 miles.

Then we have the equation:

(10mph + x)*T = 6mi

And against the current, in the same time the boat moves 4 mi, then:

(10 mph - x)*T = 4mi

Then we have the system of equations:

(10mph + x)*T = 6mi

(10 mph - x)*T = 4mi

Now, we can take the quotient of these two equations and get:

((10mph + x)*T)/((10 mph - x)*T) = (6mi/4mi)

(10mph + x)/(10 mph - x) = 3/2

Now we can solve this for x.

(10mph + x) = (3/2)*(10 mph - x)

10mph + x = (3/2)*10mph - (3/2)*x

x + (3/2)*x = (3/2)*10mph - 10mph

(5/2)*x = (1/2)*10mph = 5mph

x = (2/5)*5mph = 2mph.

The speed of the current is 2 miles per hour.

6 0
3 years ago
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