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3 years ago

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Mathematics

1 answer:

Evgesh-ka [11]3 years ago

8 0

Answer:

The shortest walking route is through the diagonal AC: 102.89m

Step-by-step explanation:

One can go from A to C using 2 paths:

- ADC or ABC

- using diagonal AC and half of that inner circle.

We need to compute the length of each path.

1) ADC=AD+DC=80+50=130m

2) AC²=AD²+DC²=80²+50⁵=6400+2500= 8900m²

AC=sqrt(8900)=94.34m.

Note that the diagonal AC has a missing segment, whose length is the diameter of the inner circle. So the straight line has a length of: AC-d=94.34-15=79.34m.

Perimeter of half the circle=pi×r= 3.14×(15/2)= 3.14×7.5=23.55m

So, if one is using the diagonal to go from A to C, then he has to walk:

79.34+23.55=102.89m

Comparing the two routes: 130m vs 102.89m, we notice that the route using the diagonal AC is shorter.

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What is the greatest common factor for 9x^2 6x and show work

VMariaS [17]

Answer:

Step-by-step explanation:

9x^2 ?6x

9x? 6x

÷3x. ÷3x

=3x and 2x

highest number is 3x

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3 years ago

Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches.

Maurinko [17]

Answer:

Q3 = 65.7825.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 63.6, \sigma = 2.5$

Find the value of the quartile Q3. (Hint: Q3 has an area of 0.75 to its left.)

This is the value of X when Z has a pvalue of 0.75. So it is X when Z = 0.675.

$Z = \frac{X - \mu}{\sigma}$

$0.675 = \frac{X - 63.6}{2.5}$

$X - 63.6 = 0.675*2.5$

$X = 65.7825$

Q3 = 65.7825.

3 0

3 years ago

James is applying for a new job at a game design company. Job A offers $40,000 starting salary with a $1000 raise each year. Job

Ad libitum [116K]

Job B because every year he gets a $2800 every year and if he continues for 5 years he will get a total of $14000 but if he works at job A he gets $5000 after 5 years

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3 years ago

Read 2 more answers

2/7 (4+c)=6 plz help me I need to get it right

choli [55]

Problem: 2/7 (4+c)=6

1. 7/2 x 2/7 x (4+c)=7/2 x 6

2. 4+c=7 x 3

3. 4+c=21

4. c=21-4

Answer: c=17

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3 years ago

What are the two possible answers for the equation Ix/5I = 3?

bagirrra123 [75]

Answer:

Either $x = -15$ or $x = 15$ .

Step-by-step explanation:

$|x| = \left\lbrace \begin{aligned} & x && \text{if $x \ge 0$} \\ & -x && \text{if $x < 0$}\end{aligned}\right.$ .

Hence, there are two possibilities to consider:

Either $(x / 5) \ge 0$ ,
Or $(x / 5) < 0$ .

If $(x / 5) \ge 0$ , then $|x / 5| = x / 5$ .

Substitute into the original equation: $x/ 5= 3$ . Solve for $x$ : $x = 15$ .

Important: verify that the solution $x = 15$ meet the assumption $(x / 5) \ge 0$ . Indeed, $(x / 5) = (15 / 5) = 3$ and is indeed non-negative. Hence, the solution $x = 15\!$ is valid.

On the other hand, if $(x / 5) < 0$ , then $|x / 5| = - x / 5$ .

Substitute into the original equation: $(-x / 5) = 3$ . Solve for $x$ : $x = -15$ .

Similarly, verify that the solution $x= - 15$ satisfies the current assumption that $(x / 5) < 0$ . Indeed, this assumption is met, and $x = -15$ is also a valid solution.

5 0

3 years ago