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2 years ago

AC CE and D is the midpoint of CE. IF CE 10x + 18, DE =7x -1, and BC = 9x - 2, find AB, AB =

Mathematics

1 answer:

Anastasy [175]2 years ago

4 0

Answer:

<h3> If you mean: AC=CE, the answer is: AB = 24</h3>

Step-by-step explanation:

D is the midpoint of CE, then

CD = DE = 0.5CE = 0.5(10x+18) = 5x + 9

So: 5x + 9 = 7x - 1

-9 -9

5x = 7x - 8

-7x -7x

-2x = -8

÷(-2) ÷(-2)

x = 4

AC = CE = 10x + 18 = 40 + 18 = 58

BC = 9x - 2 = 36 - 2= 34

AB = AC - BC = 58 - 34 = 24

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Which expression is equivalent to the equation?

IrinaK [193]

Answer:

Option 1

Step-by-step explanation:

The given equation equals 3072, so find the other equation that equals 3072.

Option 1 = 3072 - correct

Option 2 = 432 - wrong

Option 3 = 2883 - wrong

Option 4 = 432 - wrong

I hope this helps!

4 0

1 year ago

Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of

Thepotemich [5.8K]

<h2>Answer with explanation:</h2>

As per given , we have

sample size : n= 65

degree of freedom : df=n-1=64

sample mean : $\overline{x}=19.5$

sample standard deviation : s= 5.2

Since , the population standard deviation is not given , so we apply t-test.

Significance level for 90% confidence : $\alpha=1-0.90=0.10$

t-critical value for significance level 0.10 and df = 64 would be :

$t_c=t_{\alpha/2, df}=t_{0.05,\ 64}=1.6690$

Formula for Confidence interval :

$\overline{x}\pm t_c\dfrac{s}{\sqrt{n}}$

Then , 90% confidence intervals for the population mean number of weekly customer contacts for the sales personnel would be :

$19.5\pm(1.669)\dfrac{5.2}{\sqrt{65}}$

$=19.5\pm1.076$

$(19.5-1.076,\ 19.5+1.076)=(18.424,\ 20.576)$

∴ 90% confidence intervals for the population mean number of weekly customer contacts for the sales personnel : (18.424, 20.576)

Significance level for 95% confidence : $\alpha=1-0.95=0.05$

t-critical value for significance level 0.05 and df = 64 would be :

$t_c=t_{\alpha/2, df}=t_{0.05,\ 64}=1.9977$

Then , 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel would be :

$19.5\pm(1.9977)\dfrac{5.2}{\sqrt{65}}$

$=19.5\pm1.288$

$(19.5-1.288,\ 19.5+1.288)=(18.212,\ 20.788)$

∴ 95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel : (18.212, 20.788)

4 0

2 years ago

The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches. Use the Empiric

maks197457 [2]

Answer: c)[50,60]

Step-by-step explanation:

The Empirical rule says that , About 68% of the population lies with the one standard deviation from the mean (For normally distribution).

We are given that , The heights of students in a class are normally distributed with mean 55 inches and standard deviation 5 inches.

Then by Empirical rule, about 68% of the heights of students lies between one standard deviation from mean.

i.e. about 68% of the heights of students lies between $\text{Mean}\pm\text{Standard deviation}$

i.e. about 68% of the heights of students lies between $55\pm5$

Here, $55\pm5=(55-5, 55+5)=(50,60)$

i.e. The required interval that contains the middle 68% of the heights. = [50,60]

Hence, the correct answer is c) (50,60)

4 0

2 years ago

Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 \text{ m}2.8 m2, point, 8, start text, space,

Karo-lina-s [1.5K]

Answer:

420 meters

Step-by-step explanation:

Q. Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 m, and the tire revolves 1.5 times per second. What is the distance Benjamin travels in 100 seconds?

Given:

Circumference of circular tire = 2.8 meters

Tire revolves per second = 1.5 times

Question asked:

What is the distance Benjamin travels in 100 seconds?

Solution:

Circumference of circular tire means distance covered by the unicycle's tire when it revolves 1 time that is 2.8 meters.

Now, by unitary method:

In 1 second, tire revolves = 1.5 times

In 100 seconds, tire revolves = 1.5 $\times$ 100

= 150 times

Distance covered by the tire when it revolves 1 time = 2.8 m

Distance covered by the tire when it revolves 150 times = 2.8 $\times$ 150

= 420 meters

Therefore, Benjamin travels 420 meters in 100 seconds.

8 0

2 years ago

Read 2 more answers

2.4 Backgammon. Backgammon is a board game for two players in which the playing pieces are moved according to the roll of two di

muminat

Answer:

The claim is not fair because:

Probability of roliing two 6s = Probability of rolling two 3s = 1/36

Step-by-step explanation:

The probaility of an event is defined as the number of favorable outcomes divided by the number of total possible events.

P (event E) = number of outcomes for event E / number of possible events

1. As first step, you may draw a table to find the sample space (set of all possible outcomes).

Sample space

The results of the rolling two dice are summarized in this table:

Second roll 1 2 3 4 5 6

First roll

1 (1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

2 (2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

3 (3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

4 (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

5 (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

6 (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

2.Now, in that table, you can observe:

The results (3,3) and (6,6) are highlited.

a) Total number of events: 6 × 6 = 36

b) Nnmber of outcomes for the event rolling two 6s (6,6): 1

c) Number of outcomes for the event rolling two 3s (3,3): 1

3) Next, you can calculate the probabilities:

a) Probability rolling two 6s = 1 / 36

b) Probability of rolling two 3s: 1 / 36

4. Conclusion: the probabilities prove that rolling two 6s is just as likely as rolling two 3s.

7 0

2 years ago