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3 years ago

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Two buses leave a station at the same time and travel in opposite directions. One bus travels 17 mi/h slower than the other. If

the two buses are 345 miles apart after 3 hours, what is the rate of each bus? Please help!

2 answers:

Anon25 [30]3 years ago

5 0

Answer:

one bus travels at 66mi/hr and the other bus at 49mi/hr

Step-by-step explanation:

Let's assume one bus, A is traveling at x mi/hr and the other bus, B at x+17 mi/hr

after 3hrs, bus A will have covered 3x miles and bus B will have covered 3(x+17) miles.

the buses are 345 mils apart but from the same origin,

meaning Distance of A + Distance of B =345 miles

3x+3(x+17)=345

x=49

for bus A

and x+17=66 for bus B

yarga [219]3 years ago

3 0

Answer:

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ryzh [129]

Answer:

b

Step-by-step explanation:

8 0

3 years ago

Trudy borrowed $560.00 from a friend and agreed that for several years she would make equal monthly payments to pay only the int

likoan [24]

Answer:

$54.6

Step-by-step explanation:

Amount borrowed = $560

Interest paid in the 12-month period = 6.5% of 560 =$36.4

The amount of interest Trudy pays in 18 months is worked out as

Monthly interest = $36.4/12

Interest payable in 18 months

= ($36.4/12) x 18

= $54.6

5 0

3 years ago

If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

1. A given binomial distribution has a mean of 153.1 and a standard deviation of 18.2. Would a value of 187 be considered usual

Triss [41]

Answer:

Usual, because the result is between the minimum and maximum usual values.

Step-by-step explanation:

To identify if the value is usual or unusual we're going to use the Range rule of thumbs which states that most values should lie within 2 standard deviations of the mean. If the value lies outside those limits, we can tell that it's an unusual value.

Therefore:

Maximum usual value: μ + 2σ

Minimum usual value: μ - 2σ

In this case:

μ = 153.1

σ = 18.2

Therefore:

Maximum usual value: 189.5

Minimum usual value: 116.7

Therefore, the value of 187 lies within the limits. Therefore, the correct option is D. Usual, because the result is between the minimum and maximum usual values.

8 0

3 years ago

|x+5|+20=4 Needs to show work on how you came up with the answer.

arlik [135]

Answer:

No solution

Step-by-step explanation:

So we have the equation:

$|x+5|+20=4$

First, subtract 20 from both sides:

$|x+5|=-16$

Now, we can stop. Recall that absolute value will always <em>always</em> give a positive answer.

Since this equals -16, this means that there is no solution.

And we're done!

5 0

3 years ago