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2 years ago

Use the basic proportion = -to solve the following problem for the unknown quantity. Round your answer to the

Mathematics

1 answer:

Digiron [165]2 years ago

5 0

Answer:

154.34%

Step-by-step explanation:

We are asked to determine what percentage of 357 is 551.

Let us assume that x% of 357 is 551.

So, $\frac{357 \times x}{100} = 551$

⇒ $\frac{x}{100} = \frac{551}{357}$

⇒ $x = \frac{551}{357} \times 100$ ......... (1)

⇒ x = 154.34%

So, it is clear from the step (1) that when we take the basic ratio then multiply with 100, then we will get the percentage. (Answer)

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A roller coaster at XTRA Fun Rides goes into an underground tunnel during the first descent of the

gregori [183]

Answer:

y-intercept: (0, 75) ⇒ y = 75

x-intercepts: (3, 0) and (5, 0) ⇒ x = 3 and x = 5

vertex: (4, -5)

Step-by-step explanation:

Let the x-axis be the ground (when y = 0). Therefore underground when y < 0 and overground when y > 0

The function is a quadratic: f(x) = ax² + bx + c

If the coaster enters the tunnel three seconds after the first descent starts and stays in the tunnel for a total of 2 seconds, then y = 0 when x = 3 and x = 5

Also, when x = 1, y = 40

f(3) = 0
⇒ 9a + 3b + c = 0

f(5) = 0
⇒ 25a + 5b + c = 0

f(1) = 40
⇒ a + b + c = 40

Solve 2 equations simultaneously:

9a + 3b + c = 0
25a + 5b + c = 0
a + b + c = 40

⇒ a = 5 b = -40 c = 75

⇒ f(x) = 5x² - 40x + 75

y-intercept

when x = 0

⇒ f(0) = 5(0²) - 40(0) + 75 = 75

⇒ y-intercept = (0, 75)

x-intercepts

x = 3 and x = 5

Vertex

If the x-intercepts are when x = 3 and x = 5, then vertex is when x = 4

⇒ f(4) = 5(4²) - 40(4) + 75 = -5

⇒ vertex = (4, -5)

5 0

2 years ago

Construct a 95% confidence interval for the population standard deviation sigma of a random sample of 15 crates which have a me

Ad libitum [116K]

Answer:

There is a 95% confidence that the sample has a mean between 158.92 pounds and 171.48 pounds

Step-by-step explanation:

Given that mean (μ) = 165.2 pounds, standard deviation (σ) = 12.4 pounds, sample size (n) = 15 crates. Confidence (C) = 95% = 0.95

α = 1 - C = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

The z score of α/2 corresponds to the z score of 0.475 (0.5 - 0.025) which is 1.96. $z_{\frac{\alpha}{2} }=1.96$

The margin of error (E) is given by:

$E=z_{\frac{\alpha}{2} }\frac{\sigma}{\sqrt{n} } =1.96*\frac{12.4}{\sqrt{15} }= 6.28$

The confidence interval = μ ± E = 165.2 ± 6.28 = (158.92, 171.48)

The confidence interval is between 158.92 pounds and 171.48 pounds. There is a 95% confidence that the sample has a mean between 158.92 pounds and 171.48 pounds

4 0

2 years ago

0.00000000005 in scientific notation

marta [7]

It can be written as 5 x 10^ -11 or 0.5 x 10^ -10

Hope it helps.

4 0

3 years ago

Venla is 5 years older than her cousin Kora. How old is Kora when Venla is 18 years old?

krek1111 [17]

Answer:

kora is 13