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3 years ago

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The sum of three certain consecutive numbers is 240. Find the three numbers. [Hint: Let x stand for the smallest number. Since t

he numbers are consecutive, add 1 to get the second number (x + 1) and add 2 to get the third number (x + 2).]

1 answer:

Verdich [7]3 years ago

8 0

The numbers are 79, 80, and 81.

79+80+81=240.

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PLEASE HELP!!! 15 PTS!!

kherson [118]

Answer:

$\large\boxed{C.\ (2,\ -45^o)}$

Step-by-step explanation:

Regular coordinates (x, y)

Polar coordinates (r, φ)

$r=\sqrt{x^2+y^2}\\\\\psi=\arctan\frac{y}{x}$

We have the point

$(\sqrt2,\ -\sqrt2)$

Substitute:

$r=\sqrt{(\sqrt2)^2+(-\sqrt2)^2}=\sqrt{2+2}=\sqrt4=2\\\\\psi=\arctan\left(\frac{-\sqrt2}{\sqrt2}\right)=\arctan(-1)=-45^o$

6 0

3 years ago

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.725.72 millimeters and a standard de

suter [353]

Answer:

Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 5.72, \sigma = 0.07$

Top 5%:

X when Z has a pvalue of 0.95. So X when Z = 1.645

$Z = \frac{X - \mu}{\sigma}$

$1.645 = \frac{X - 5.72}{0.07}$

$X - 5.72 = 1.645*0.07$

$X = 5.84$

Bottom 5%:

X when Z has a pvalue of 0.05. So X when Z = -1.645

$Z = \frac{X - \mu}{\sigma}$

$-1.645 = \frac{X - 5.72}{0.07}$

$X - 5.72 = -1.645*0.07$

$X = 5.60$

Top 5% is 5.84 milliters and the bottom 5% is 5.60 millimeters.

7 0

3 years ago

Read 2 more answers

Rhian sat a math test and an english test.In the maths test she scored 14 out of 17.In the english test she scored 31 out of 39.

Dvinal [7]

Answer:

The maths test

Step-by-step explanation:

If you convert both of the results to percentage,

Maths:

$\frac{14}{17} \times 100 = 82\%$

English:

$\frac{31}{39} \times 100 = 79\%$

You'll see that she scored better in the maths test.

4 0

3 years ago

Can somebody solve this system equation using addition please?

givi [52]

-4x - 5y = 7

3x + 5y = -14

You can add these two equations together straightaway since the y-terms have opposite coefficients.

-4x - 5y = 7

3x + 5y = -14

+___________

-x - 0 = -7

-x = -7

x = 7

Substitute 7 for x into either of the original equations and solve algebraically to find y.

3x + 5y = -14

3(7) + 5y = -14

21 + 5y = -14

21 = -14 - 5y

35 = -5y

-7 = y

Finally, check work by substituting both x- and y-values into both original equations.

-4x - 5y = 7

-4(7) - 5(-7) = 7

-28 + 35 = 7

7 = 7

3x + 5y = -14

3(7) + 5(-7) = -14

21 - 35 = -14

-14 = -14

Answer:

x = 7 and y = -7; (7, -7).

7 0

3 years ago

In the interval 0 x 360 find the values of x for which cos x =0.7252

Sergeeva-Olga [200]

Answer:

$x_1 = 43.5145\°$

$x_2 = 316.4855\°$

Step-by-step explanation:

We have a positive value for the cosine of x, so we know that the value of x should be in the first quadrant (0 ≤ x ≤ 90) or in the fourth quadrant (270 ≤ x ≤ 360).

Now, let's find the value of x that gives cos(x) = 0.7252 using the inverse function of the cosine, that is, the arc cosine function.

The value of x can be calculated using:

$x = arccos(0.7252)$

Using this function in a calculator (you may find it as: $cos^{-1}(x)$ ), we have that:

$x_1 = 43.5145\°$

So this is the value of x in the first quadrant. To find the other value of x, in the fourth quadrant, that gives the same result, we just need to calculate 360° minus the value we found:

$x_2 = 360\° - 43.5145\° = 316.4855\°$

So the values of x are:

$x_1 = 43.5145\°$

$x_2 = 316.4855\°$

7 0

3 years ago