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notsponge [240]

1 year ago

7

An airplane flew at an average rate of 600 miles per hour from Tokyo to Seattle. Because of a strong headwind, the average rate

of the return trip was only 480 mph. The round trip took 18 hours. Which equation can be used to determine the time for each leg? 600t = 480t 600t = 18 – t 600t = 480 – t 600t = 480(18 – t)

2 answers:

Dvinal [7]1 year ago

5 0

600t = 480(18 – t) should be it

larisa [96]1 year ago

3 0

Answer:

Option D. 600t = 480( 18-t )

Step-by-step explanation:

An airplane flew at an average rate of 600 miles per hour fro Tokyo to Seattle.

Let the airplane travels for t hours so distance covered by the airplane will be = speed × time

= 600t miles

Similarly, average speed in return trip was 480 mile/hour. So distance covered in return trip = speed × time

= 480 ( 18-t ) [ since time taken by plane in round trip was 18. So time taken in return trip will be ( 18-t) ]

Therefore, distance traveled in one trip = distance covered in return trip

600t = 480( 18-t )

Option D is the answer.

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2 years ago

A. The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

erastovalidia [21]

Answer:

The average yearly salary of the architect is <u>$62,000</u> and the lawyer is <u>$100,000</u>.

Step-by-step explanation:

Given:

The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

Combined, an architect and a lawyer earn $ 210 thousand.

Now, to find the average yearly salary of an architect and a lawyer.

Let the average yearly salary of an architect be $x.$

So, the average yearly salary of the lawyer = $2x-24,000.$

Combined, architect and lawyer earn = $\$210,000.$

Now, to get the average salary of the architect and lawyer:

$x+(2x-24000)=210000$

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<em>Adding both sides 24000 we get:</em>

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<u>The average salary of architect = $62,000.</u>

Now, to get the average salary of lawyer by substituting the value of $x$ :

$2x-24000\\\\=2(62000)-24000\\\\=124000-24000\\\\=\$100,000.$

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2 years ago

COHEA 8th Grade Test 1

abruzzese [7]

Answer:d

Step-by-step explanation:

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2 years ago

A random sample of 35 undergraduate students who completed two years of college were asked to take a basic mathematics test. The

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Answer:

$(75.1 -72.1) -1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= -1.96$

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And the confidence interval would be given by:

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And since the confidence interval contains the value 0 we have enough evidence to conclude that we don't have significant differences between the two means at 10% of significance.

Step-by-step explanation:

For this case we have the following info given :

$\bar X_1= 75.1$ represent the sample mean for the scores of the undergraduate students

$s_1 = 12.8$ represent the standard deviation for the undergraduate students

$n_1 =35$ the sample size for the undergraduate

$\bar X_2= 72.1$ represent the sample mean for the scores of the high school students

$s_2 = 14.6$ represent the standard deviation for the high school students

$n_2 =50$ the sample size for the high school

The confidence interval for the true difference of means is given by:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}$

The degrees of freedom are given by:

$df=n_1 +n_2 -2= 35+50-2=83$

The confidence level is 90% and the significance level is $\alpha=0.1$ and $\alpha/2 =0.05$ then the critical value would be:

$t_{\alpha/2}= 1.99$

And replacing the info we got:

$(75.1 -72.1) -1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= -1.96$

$(75.1 -72.1) +1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= 7.96$

And the confidence interval would be given by:

$-1.96 \leq \mu_1 -\mu_2 \leq 7.96$

And since the confidence interval contains the value 0 we have enough evidence to conclude that we don't have significant differences between the two means at 10% of significance.

8 0

1 year ago

Andre and Diego were each trying to solve 2x+6=3x−8. Describe the first step they each make to the equation. The result of Andre

Oksi-84 [34.3K]

Answer:

Andre subtracted 3x from both sides
Diego subtracted 2x from both sides

Step-by-step explanation:

<u>Andre</u>

Comparing the result of Andre's work with the original, we see that the "3x" term on the right is missing, and the x-term on the left is 3x less than it was. It is clear that Andre subtracted 3x from both sides of the equation.

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<u>Diego</u>

Comparing the result of Diego's work with the original, we see that the "2x" term on the left is missing, and the x-term on the right is 2x less than it was. It is clear that Diego subtracted 2x from both sides of the equation.

_____

<em>Comment on their work</em>

IMO, Diego has the right idea, as his result leaves the x-term with a positive coefficient. He can add 8 and he's finished, having found that x=14.

Andre can subtract 6 to isolate the variable term, and that will give him -x=-14. This requires another step to get to x=14. Sometimes minus signs get lost, so this would not be my preferred sequence of steps.

As a rule, I like to add the opposite of the variable term with the least (most negative) coefficient. This results in the variable having a positive coefficient, making errors easier to avoid.

3 0

1 year ago