In the accompanying diagram PA is tangent to circle 0 at A if CN=12 and PB=4 what is the length of PA?

Talia has a square bedroom. Her family is moving and her bedroom in her new apartment will be 3 feet shorter in one direction an

djverab [1.8K]

Answer (x represents the first direction and the y represents the second direction):

(x - 3) × (y + 5)
New bedroom: 7 ft × 15 ft. Her new bedroom is 5 sq. ft larger than her old bedroom

I hope this helps!

3 0

2 years ago

Given equation x = 6 + i, w = -1 + 5i and z = 4 - 8i, determine each of the following in the form of a + bi

Temka [501]

Answer:

i) 28 - 30i

ii) 36 + 28i

Step-by-step explanation:

i) x = 6 + i ⇒2x = 2(6 + i) = 12 + 2i

z = 4 - 8i ⇒ 4z = 4(4 - 8i) = 16 - 32i

2x + 4z = (12 + 2i) + (16 - 32i) = 28 - 30i

ii) w = -1 + 5i and z = 4 - 8i

w × z = (-1 + 5i)(4 - 8i) = -4 + 8i + 20i - 40 $i^{2}$ ⇒collect like terms

w × z = -4 + 28i - 40 $i^{2}$

∵ $i^{2}=-1$

∴w × z = -4 + 28i - 40(-1) = -4 + 28i + 40 = 36 + 28i

3 0

2 years ago

Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

3 0

3 years ago

What is the lowest form of 32:28?

BartSMP [9]

Answer:

to lowest terms of 32:28 is 8/7 or 8:7

Step-by-step explanation:

5 0

3 years ago

help need to answer asap!!! a basketball team played 64 games. They won 20 more than they played; how many did they win?; how ma

melisa1 [442]

20 more than what they played or 20 more than what they lost?

7 0

2 years ago