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Molodets [167]
3 years ago
14

A segment with endpoints A (3, 4) and C (5, 11) is partitioned by a point B such that AB and BC form a 2:3 ratio. Find B.

Mathematics
2 answers:
Dima020 [189]3 years ago
7 0

Answer:

(3.8, 6.8)

Step-by-step explanation:

Point B:

Has coordinates (x,y)

AB and BC form a 2:3 ratio.

This means that:

B - A = \frac{2}{2+3}(C - A)

B - A = \frac{2}{5}(C - A)

We apply this both for the x-coordinate and for the y-coordinate.

x-coordinate:

x-coordinate of A: 3

x-coordinate of C: 5

x-coordinate of B: x

B - A = \frac{2}{5}(C - A)

x - 3 = \frac{2}{5}(5 - 3)

x - 3 = \frac{4}{5}

x = 0.8 + 3 = 3.8

y-coordinate:

y-coordinate of A: 4

y-coordinate of C: 11

y-coordinate of B: y

B - A = \frac{2}{5}(C - A)

y - 4 = \frac{2}{5}(11 - 4)

y - 4 = \frac{14}{5}

y = 2.8 + 4 = 6.8

Thus the correct answer is:

(3.8, 6.8)

adoni [48]3 years ago
4 0

Answer:

(3.8, 6.8) is correct

Step-by-step explanation:

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Ziv's taxicab ride cost $33. He left a 15% tip.
sergiy2304 [10]

Answer:

Step-by-step explanation:

1. Find 15% of $33 to find the tip.

Find 1%  of $33 (move the decimal over 2 places to the left.        $0.33

2. Multiply the 1% tip by 15%

       33 * 15 =  $4.95  

3. Add $33 and $4.95

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3 years ago
Activity 2
Vsevolod [243]
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3 years ago
The inequality x + 2y ≥ 3 is satisfied by point (1, 1).<br> True<br> False
andre [41]
In the given statement above, in this case, the answer would be TRUE. It is true that the  inequality x + 2y ≥ 3 is satisfied by point (1, 1). In order to prove this, we just have to plug in the values. 1 + 2(1) <span> ≥ 3 
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7 0
3 years ago
Read 2 more answers
Big babies: The National Health Statistics Reports described a study in which a sample of 354 one-year-old baby boys were weighe
Vedmedyk [2.9K]

Answer:

Yes. The data provide enough evidence to support the claim that the mean weight of one-year-old boys is greater than 25 pounds.

P-value=P(t>2.84)=0.0024

Step-by-step explanation:

Hypothesis test on the population mean.

The claim is that the mean weight of one-year-old boys is greater than 25 pounds.

Then, the null and alternative hypothesis are:

H_0: \mu=25\\\\H_a:\mu>25

The significance level is α=0.05.

The sample size is n=354. The sample mean is 25.8 pounds and the sample standard deviation is 5.3 pounds. As the population standard deviation is estimated from the sample standard deviation, we will use a t-statistic.

The degrees of freedom are:

df=n-1=354-1=353

The t-statistic is:

t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{25.8-25}{5.3/\sqrt{354}}=\dfrac{0.8}{0.2817}=2.84

For a right tailed test and 353 degrees of freedom, the P-value is:

P-value=P(t>2.84)=0.0024

As the P-value is smaller than the significance level, the effect is significant and the null hypothesis is rejected.

There is enough evidence to support the claim that the mean weight of one-year-old boys is greater than 25 pounds.

7 0
3 years ago
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