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scZoUnD [109]
2 years ago
5

Eric made a scale drawing of the auditorium. The stage, which 15 35 feet wide in real life,

Mathematics
1 answer:
Molodets [167]2 years ago
7 0
Based on the given conditions, formulate: 5/35
Simplify by dividing by dividing the numerator and denominator by 5: 1/7

Therefore the scale of the drawing is 1/7
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Simplifying Complex fractions using any method
zloy xaker [14]

Answer:

3ab

-------------------

(b+a)

Step-by-step explanation:

3/a - 3/b

-------------------

1/a^2 - 1/b^2

Multiply the top and bottom by a^2 b^2/ a^2/b^2 to clear the fractions

(3/a - 3/b) a^2 b^2

-------------------

(1/a^2 - 1/b^2) a^2b^2

3ab^2 - 3 a^2 b

-------------------

b^2 -  a^2

Factor out 3ab on the top

3ab( b-a)

-------------------

b^2 -  a^2

The bottom is the difference of squares

3ab( b-a)

-------------------

(b-a) (b+a)

Cancel like terms from the top and bottom

3ab

-------------------

(b+a)

6 0
3 years ago
Read 2 more answers
Suppose a city with population 600,000 has been growing at a rate of 3​% per year. If this rate​ continues, find the population
andrezito [222]

Answer:

The answer should be around 1,149663 (Rounded off to the nearest whole number. Also if a population has a remainer you usually add it as 1. This is because these are people)

Step-by-step explanation:

First step involves listing the formulas being used:

600,000= population, 0.03= growth rate 22years= period

Therefore, we take the 600,000 and multiply by 1+0.03 ^22(to the power of 22 or period)

So, 600,000(1+0.03)^22

=1,149662.045 /1,149663

Hope this helps!

6 0
2 years ago
A genetic experiment involving peas yielded one sample of offspring consisting of 409 green peas and 171 yellow peas. Use a 0.05
grigory [225]
The usual expectation for this kind of experiment is that the peas would yield green and yellow peas in a 3:1 ratio, or 75% green to 25% yellow. So your null hypothesis is that the proportion of yellow peas is p=0.25.

You're testing the claim that 26% of the offspring will be yellow, which means the alternative hypothesis is that the proportion of yellow peas is actually 0.26, or more generally that the expected proportion is greater than 0.25, or p>0.25.

The test statistic in this case will be

Z=\dfrac{\hat p-p_0}{\sqrt{\dfrac{p_0(1-p_0)}n}}

where p_0 is the proportion assumed under the null hypothesis, \hat p is the measured proportion, and n is the sample size. You have p_0=0.25, \hat p=\dfrac{171}{171+409}\approx0.29, and n=409+171=580, so the test statistic is

Z=\dfrac{0.29-0.25}{\sqrt{\dfrac{0.25\times0.75}{580}}}\approx2.2247

Because you're testing p>p_0, this is a right-tailed test, so the P-value is

\mathbb P(Z>2.2247)\approx0.0131

The critical value for a right-tail test at a 0.05 significance level is Z_\alpha\approx1.6449, which means the rejection region is any test statistic that is larger than this critical value. Since Z>Z_\alpha in this case, we reject the null hypothesis.

So the conclusion for this test is that the sample proportion is indeed statistically significantly different from the proportion suggested by the null hypothesis.
8 0
3 years ago
Read 2 more answers
A runner has run 1.192 kilometers of a 10-kilometer race. How much farther does he need to run to finish the race? Show your rea
lesantik [10]

Answer: 8.808 kilometers

Step-by-step explanation: have a good night :)

7 0
2 years ago
(16x^2 - 25) ÷ (4x + 5)<br> DO NOT INCLUDE PARENTHESES IN YOUR ANSWER
Marina86 [1]
\cfrac{16x^2-25}{4x+5}=  \cfrac{(4x)^2-5^2}{4x+5}=  \cfrac{(4x-5)(4x+5)}{(4x+5)}= 4x-5
3 0
3 years ago
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