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nikdorinn [45]
3 years ago
6

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!
Mathematics
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
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