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4 years ago

Y=2/3(x-5)^2

Mathematics

1 answer:

Anvisha [2.4K]4 years ago

8 0

Answer:

see below

Step-by-step explanation:

The graph opens upward if the sign of the squared term is positive. If that sign is negative, the graph opens downward. The first three equations open upward; the last opens downward.

The line of symmetry is the value of x that makes the squared term zero. Here, that is x=5 for all equations.

y=2/3(x-5)^2: A, D

y=1/2(x-5)^2: A, D

y=3/4(x-5)^2: A, D

y=-4(x-5)^2: B, D

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Orlov [11]

11.667 c is the answer. :D

6 0

3 years ago

A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N. A new batch of yarn was made, usin

AlexFokin [52]

Answer:

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of normal variables:

When we subtract two normal variables, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N.

This means that $\mu_1 = 6.1, s_1 = \frac{0.7}{\sqrt{125}} = 0.0626$

In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.

This means that $\mu_2 = 5.8, s_2 = \frac{1}{\sqrt{75}} = 0.1155$

Distribution of the difference:

$\mu = \mu_1 - \mu_2 = 6.1 - 5.8 = 0.3$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0626^2+0.1155^2} = 0.1314$

Confidence interval:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = zs$

$M = 1.645*0.1314 = 0.22$

The lower end of the interval is the sample mean subtracted by M. So it is 0.3 - 0.22 = 0.08N

The upper end of the interval is the sample mean added to M. So it is 0.3 + 0.22 = 0.52N

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

3 0

3 years ago

1+2+2²+2³+...+2^x=1023

mrs_skeptik [129]

$1 + 2 + 2^{2} + 2^{3} + 2^{x} = 1023 \\3 + 4 + 8 + 2^{x} = 1023 \\7 + 8 + 2^{x} = 1023 \\15 + 2^{x} = 1023 \\2^{x} = 1023 - 15 \\2^{x} = 1008 \ln(2^{x}) = ln(1008) \\xln(2) = ln(16 * 8 * 7) \\xln(2) = ln(2^{4} * 2^{3} * 7) \\\frac{xln(2)}{ln(2)} = \frac{4ln(2) + 2ln(3) + ln(7)}{ln(2)} \\x = 4 + \frac{2ln(3)}{ln(2)} + \frac{ln(7)}{ln(2)}$