Ask question

Ask question

All categories

photoshop1234 [79]

2 years ago

8

To prepare for a triathlon, Amanda starts from position A and rides her bike along a straight road for 12 miles to reach positio

n B. At B, she turns left and rides along another straight road for 15 miles to reach position C. At C, she turns left again and rides 20 miles along a straight road to return to A. In , what are m∠A, m∠B, and m∠C, respectively?

2 answers:

Dominik [7]2 years ago

6 0

Answer:

48.35°, 94.94°, 36.71°

Step-by-step explanation:

Sergio [31]2 years ago

3 0

Answer:

Step-by-step explanation:

Let's draw the given information first for better understanding . Check the image attached.

We can use cosine rule to find the angles .

for angle A ,

$Cos A =\frac{b^2+c^2-a^2}{2bc}$

$Cos A =\frac{20^2+12^2-15^2}{2*20*12}$

$Cos A =\frac{319}{480}$

m∠A = 48.35 degrees

Similarly for angle B

$Cos B =\frac{a^2+c^2-b^2}{2bc}$

$Cos B =\frac{15^2+12^2-20^2}{2*15*12}$

$Cos B =\frac{-31}{360}$

m∠B = 94.94 degrees

Now use A+B+C=180 degrees

48.35+94.94+C=180

C=180-48.35-94.94

m∠C = 36.71 degrees

You might be interested in

For a few months, Dexter recorded the amounts, in fluid ounces, of laundry detergent remaining y after he and his family washed

BigorU [14]

Definitely it's B: The amt of detergent left after x loads have been washed is y = (-$1.60/load)x + 50.

3 0

2 years ago

Evaluate 10m +\dfrac {n^2}410m+ 4 n 2 10, m, plus, start fraction, n, squared, divided by, 4, end fraction when m=5m=5m, equal

Readme [11.4K]

Answer: $54$

Step-by-step explanation:

Given the following expresion provided in the exercise:

$10m+\frac{n^2}{4}$

You can follow these steps in order to evaluate it when $m=5$ and $n=4$ :

1. You need to substitute $m=5$ and $n=4$ into the given expression:

$10(5)+\frac{(4)^2}{4}$

2. Now you can solve the mutiplication:

$=50+\frac{(4)^2}{4}$

3. Since $4^2=4*4$ , you get:

$=50+\frac{16}{4}$

4. You must solve the division. Divide the numerator 16 by the denominator 4. Then:

$=50+4$

5. And finally, you must solve the addition. So, you get this result:

$=54$

3 0

2 years ago

A web-based company has a goal of processing 90 percent of its orders on the same day they are received. If 434 out of the next

Kamila [148]

Answer:

We conclude that a web-based company are not exceeding their goal of 90%.

Step-by-step explanation:

We are given that a web-based company has a goal of processing 90 percent of its orders on the same day they are received.

434 out of the next 471 orders are processed on the same day.

Let p = <u><em>proportion of orders processing on the same day they are received.</em></u>

SO, Null Hypothesis, $H_0$ : p $\leq$ 0.90 {means that they are not exceeding their goal of 90%}

Alternate Hypothesis, $H_0$ : p > 0.90 {means that they are exceeding their goal of 90%}

The test statistics that would be used here <u>One-sample z test for</u> <u>proportions</u>;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of orders that are processed on the same day = $\frac{434}{471}$ = 0.92

n = sample of orders = 471

So, <u><em>the test statistics</em></u> = $\frac{0.92-0.90}{\sqrt{\frac{0.92(1-0.92)}{471} } }$

= 1.599

The value of z test statistics is 1.599.

<u>Now, at 0.025 significance level the z table gives critical value of 1.96 for right-tailed test.</u>

Since our test statistic is less than the critical value of z as 1.599 < 1.96, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u><em>we fail to reject our null hypothesis</em></u>.

Therefore, we conclude that a web-based company are not exceeding their goal of 90%.

8 0

1 year ago

You are in a bike race. When you get to the first checkpoint, you are 25 of the distance to the second checkpoint. When you get

Rom4ik [11]

Question:

You are in a bike race. When you get to the first checkpoint, you are 2/5 of the distance to the second checkpoint. When you get to the second check point, you are 1/4 of the distance to the finish. If the entire race is 40 miles, what is the distance between the start and the first check point?

Answer: 4 miles

Step-by-step explanation:

Let distance between start to first checkpoint = x

First checkpoint to second checkpoint = 2/5 of x

Distance of start to checkpoint 1 = ( 2/5 of start to checkpoint 2)

Distance of start to checkpoint 2 = (1/4 of start to finish)

If start to checkpoint 2 = 1/4 of start to finish

Then,

Distance of start to checkpoint 1 = ( 2/5 * 1/4 of start to finish)

Distance of start to checkpoint 1 = 2/20 of start to finish = 1/10 of start to finish

Entire race = 40 miles = distance from start to finish

1/ 10 of 40

= ( 1/10) × 40

= 4 miles

6 0

2 years ago

How do you write 4540 million in standard form?

vovangra [49]

For this case what we should do is take into account the following conversion:
$million = 10 ^ 6
$
We then have the following number:
$4540 million
$
Applying the given conversion we have:
$4540 * 10 ^ 6
$
By doing the corresponding calculation we have that the standard form is given by:
$4540 * 10 ^ 6 = 4,540,000,000
$
Answer:
4540 million in standard form is:
$4,540,000,000$

8 0

1 year ago

Read 2 more answers