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katen-ka-za [31]
3 years ago
15

Find the quadratic function y=ax^(2)+c with a graph that includes (0,1/2) (-3,73/2).

Mathematics
1 answer:
Aloiza [94]3 years ago
6 0
The answer is B.  The way you find it is through substitution. First use the coordinate (0, 1/2) in y = ax^2 + c to solve for c: 1/2=a(0)^2 + c--> 1/2=c. Now use that c value in the same y = ax^2 + c equation with the other coordinate to solve for a: 73/2 = a(-3)^2 + 1/2. Subtract 1/2 from both sides to get 72/2=9a. 72/2 is 36. So 36 = 9a...a = 4. Now fill in your a and your c to get y = 4x^2 + 1/2
You might be interested in
What happens to the volume of a rectangular prism when its length is tripled?
earnstyle [38]

The volume of a rectangular prism is represented by the following equation:

V=wlh

where w is the width , l is the length, and h is the height

Replace l with 3l since the length is tripled

V_0=w(3l)h

=3(wlh)

From this, we see that this new volume is 3x larger than the original. Thus, the volume is tripled when its length is tripled.

Let me know if you need any clarifications, thanks!

3 0
2 years ago
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 139 millimeters,
FinnZ [79.3K]

Answer:

0.4010 = 40.10% probability that the sample mean would differ from the population mean by more than 0.8 millimeters

Step-by-step explanation:

To solve this question, we need to understan the normal probability distribution and the central limit theorem.

Normal probability distribution:

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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 139, \sigma = 6, n = 40, s = \frac{6}{\sqrt{40}} = 0.9487

Either the sample mean differs by 0.8 mm or less from the population mean, or it differs by more. The sum of these probabilities is decimal 1.

Probability it differs by less than 0.8mm

pvalue of Z when X = 139 + 0.8 = 139.8mm subtracted by the pvalue of Z when X = 139 - 0.8 = 138.2 mm

X = 139.8

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{139.8 - 139}{0.9487}

Z = 0.84

Z = 0.84 has a pvalue of 0.7995

X = 138.2

Z = \frac{X - \mu}{s}

Z = \frac{138.2 - 139}{0.9487}

Z = -0.84

Z = -0.84 has a pvalue of 0.2005

0.7995 - 0.2005 = 0.5990

What is the probability that the sample mean would differ from the population mean by more than 0.8 millimeters?

p + 0.5990 = 0.4010

0.4010 = 40.10% probability that the sample mean would differ from the population mean by more than 0.8 millimeters

7 0
3 years ago
What’s the answer to the question down below
levacccp [35]

Any linear equation can be written as

y = mx+b

where m is the slope and b is the y intercept

m = 1/2 in this case. It represents the idea that the snow fell at a rate of 1/2 inch per hour. In other words, the snow level went up 1/2 an inch each time an hour passed by.

b = 8 is the y intercept. It's the starting amount of snow. We start off with 8 inches of snow already.

The info "snow fell for 9 hours" doesn't appear to be relevant here.

3 0
2 years ago
in toby's yard there are 4 petunias for every 7 rhododendrons toby counts a total of 28 rhododendrons in his yard how many petun
mamaluj [8]

Answer:

16 petunias

Step-by-step explanation:

28/7  =  x/4

7x=28*4

7x= 112

x=112/7

x=16

3 0
3 years ago
#1: Simplify the expression below. Type your answer as an integer.<br> 7 + 1 - 18 : 6
myrzilka [38]

Answer:

5

Step-by-step explanation:

<u>Steps of calculation:</u>

  • 7 + 1 - 18 : 6 =
  • 7 + 1 - 3 =
  • 8 - 3 =
  • 5

Answer is 5

8 0
3 years ago
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