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3 years ago

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NEED HELP ASAP! Triangle PQR has vertices at the following coordinates: P(0, 1), Q(3, 2), and R(5, -4). Determine wether or not

triangle PQR is a right triangle. Show all calculations for full credit.

1 answer:

puteri [66]3 years ago

6 0

We will apply the formula:
AB = rad((Xb-Xa)^2+(Yb-Ya)^2)

PQ = rad((3-0)^2+(2-1)^2) = rad(9+1) = rad(10)
PR = rad((5-0)^2+(-4-1)^2) = rad(25+25) = rad(50)
QR = rad((5-3)^2+(-4-2)^2) = rad(4+36)=rad(40)

We can apply the reverse of the Pythagorean Theorem(If a triangle has sides of lengths a, b, and c where c is the longest length and c^2 = a^2 + b^2, then the triangle is a right triangle)

PQ^2+QR^2=PR^2
10+40=50 TRUE

The final statement is that <span>PQR is a right triangle with <PQR as a right angle.</span>

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they are 15 entrees available at a restaurant. from these, Archie is to choose 6 for his party. how many groups of 6 entrees can

Goshia [24]

In this item, we are informed that the order of the entries does not matter in determination the number of ways in which the Archie can choose for his party. Because the arrangement or order is not important, this type of problem uses the concept of COMBINATION.

The equation for combination is,
nCr = n!/((n - r)!(r!))

nCr is read as "combination of n taken r".

Substituting the known values to the equation,
15C6 = 15! / ((15 - 6)!(6!))
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3 years ago

Solve the equation -5(s+30)=-17

zzz [600]

Answer:

s = -133/5 = -26.600 ⬇️

Step-by-step explanation:

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(0 - 5 • (s + 30)) - -17 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

-5s - 133 = -1 • (5s + 133)

Equation at the end of step 3 :

-5s - 133 = 0

Step 4 :

Solving a Single Variable Equation :

4.1 Solve : -5s-133 = 0

Add 133 to both sides of the equation :

-5s = 133

Multiply both sides of the equation by (-1) : 5s = -133

Divide both sides of the equation by 5:

s = -133/5 = -26.600

One solution was found :

s = -133/5 = -26.600

7 0

3 years ago

A recent study of two vendors of desktop personal computers reported that out of 836 units sold by Brand A, 111 required repair,

iris [78.8K]

Answer:

Step-by-step explanation:

Hello!

The study variables are:

$X_A$ : The number of Brand A units sold that required repair.

$n_A= 836$

$x_A= 111$

$X_B$ : THe number of Brand B units sold that required repair.

$n_B= 739$

$x_B= 111$

1. Calculate the difference in the sample proportion for the two brands of computers, p^BrandA−p^BrandB =?.

The sample proportion of each sample is equal to the number of "success" observed xi divided by the sample size n:

^p $_A$ = $\frac{x_A}{n_A}= \frac{111}{836}= 0.1328$

^p $_B$ = $\frac{x_B}{n_B}= \frac{111}{739} =0.1502$

^p $_A$ - ^p $_B$ = 0.1328 - 0.1502= -0.0174

Note: proportions take numbers from 0 to 1, meaning they are always positive. But this time what you have to calculate is a difference between the two proportions so it is absolutely correct to reach a negative number it just means that one sample proportion is greater than the other.

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of computers needing repairs is different for the two brands?

A. H0:pA−pB=0 , HA:pA−pB<0

B. H0:pA−pB=0 , HA:pA−pB>0

C. H0:pA−pB=0 , HA:pA−pB≠0

If you want to test whether the proportion of computers of both brands is different, you have to do a two-tailed test, the correct option is C.

3. Calculate the pooled estimate of the sample proportion, ^p= ?

To calculate the pooled sample proportion you have to use the following formula:

^p= $\frac{x_A+x_B}{n_A+n_B}= \frac{111+111}{836+739}= 0.14095 = 0.1410$

4. Is the success-failure condition met for this scenario?

A. Yes

B. No

The conditions that have to be met are:

$n_A\geq 30$ ⇒ Met

$n_A*p_A\geq 5$ ⇒ 836 * 0.1328= 111.4192; Met

$n_A*(1-p_A)\geq 5$ ⇒ 836 * (1 - 0.1328)= 727.5808; Met

$n_B\geq 30$ ⇒ Met

$n_B*p_B\geq 5$ ⇒ 739 * 0.1502= 110.9978; Met

$n_B*(1-p_B)\geq 5$ ⇒ 739 * (1-0.1502)= 628.0022; Met

All conditions are met.

5. Calculate the test statistic for this hypothesis test. ? =

$Z_{H_0}= \frac{(p'_A-p'_B)-(p_A-p_B)}{\sqrt{p'(1-p')[\frac{1}{n_A} +\frac{1}{n_B} ]} } = \frac{-0.0174-0}{\sqrt{0.1410*0.859*[\frac{1}{836} +\frac{1}{739} ]} }= -0.9902$

6. Calculate the p-value for this hypothesis test, p-value = .

This hypothesis test is two-tailed and so is the p-value, since it has two tails you have to calculate it as:

P(Z≤-0.9902) + P(Z≥0.9902)= P(Z≤-0.9902) + ( 1 - P(Z≤0.9902))= 0.161 + (1 - 0.839) = 0.322

7. What is your conclusion using α = 0.05?

A. Do not reject H0

B. Reject H0

The decision rule using th ep-value is:

If p-value > α, the decision is to not reject the null hypothesis.

If p-value ≤ α, the decision is to reject the null hypothesis.

The p-value= 0.322 is greater than α = 0.05, so the decision is to not reject the null hypothesis.

8. Compute a 95 % confidence interval for the difference p^BrandA−p^BrandB = ( , )

The formula to calculate the Confidence interval is a little different, because instead of the pooled sample proportion you have to use the sample proportion of each sample to calculate the standard deviation of the distribution:

( $p'_A-p'_B$ ) ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'_A(1-p'_A)}{n_A} +\frac{p'_B(1-p'_B)}{n_B} }$

-0.0174 ± 1.965 * $\sqrt{\frac{0.1328*0.8672}{836} +\frac{0.1502*0.8498}{739} }$

[-0.0520; 0.0172]

I hope it helps!

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3 years ago

In the equation<br> (x-3)2+(y-2)2=16, the center of the circle is...

valkas [14]

Answer:

The center circle of this question is (2,3)

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3 years ago

Consider the system of equations:

vodka [1.7K]

Answer:

(x, y) = (5, 1)

Step-by-step explanation:

To <em>eliminate</em> x, you can double the second equation and subtract the first.

... 2(x +4y) -(2x -3y) = 2(9) -(7)

...11y = 11 . . . . . simplify

... y = 1 . . . . . . divide by 11

Using the second equation to find x, we have ...

... x + 4·1 = 9

... x = 5 . . . . . subtract 4

_____

<u>Check</u>

2·5 -3·1 = 10 -3 = 7 . . . . agrees with the first equation

(Since we used the second equation to find x, we know it will check.)

5 0

4 years ago

Read 2 more answers