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Tpy6a [65]
3 years ago
15

A staircase handrail is made from congruent parallelograms. in parallelogrampqrs, pq = 17.5, st = 18, and m∠ qrs = 110° . find m

∠ pqr.
Mathematics
1 answer:
liubo4ka [24]3 years ago
7 0
<span>Answer: Consec. angles of PRQS are supplementary, so mâ PQR = 70°.</span>
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weqwewe [10]

Answer:

y =14

11x = 11*3.5 =38.5

3x+2y = 11x = 38.5

Step-by-step explanation:

The perimeter of a triangle is the sum of all three sides

3x+2y + 11x+y = 91

Combine like terms

14x +3y = 91

The lines mean the sides are equal

3x+2y = 11x

Simplify

Subtract 3x from each side

3x-3x+2y = 11x-3x

2y = 8x

Divide by 2

2y/2 = 8x/2

y = 4x

Substitute 4x in the first equation every time you see y

14x +3y = 91

14x +3(4x) = 91

14x+12x=91

26x = 91

Divide by 26

26x/26 =91/26

x = 3.5

Now we can find y

y = 4x

y = 4(3.5)

y = 14

We know x and y we can find the length of each of the sides

y =14

11x = 11*3.5 =38.5

3x+2y = 11x = 38.5

8 0
3 years ago
The degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. Two random samples from
Vinvika [58]

Answer:

t=\frac{(810-770)-0}{\sqrt{\frac{67^2}{13}+\frac{56^2}{19}}}}=1.771  

df=n_1 +n_2 -2=13+19-2=30  

Since is a right tailed test the p value would be:  

p_v =P(t_{30}>1.771)=0.0434  

Comparing the p value with the significance level \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the mean for group 1 is significantly higher than the mean for the group 2

Step-by-step explanation:

Data given

\bar X_{1}=810 represent the mean for sample 1  

\bar X_{2}=770 represent the mean for sample 2  

s_{1}=67 represent the sample standard deviation for 1  

s_{2}=56 represent the sample standard deviation for 2  

n_{1}=13 sample size for the group 2  

n_{2}=19 sample size for the group 2  

\alpha=0.05 Significance level provided

t would represent the statistic (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the mean for category 1 is higher than the mean for category 2, the system of hypothesis would be:  

Null hypothesis:\mu_{1}-\mu_{2}\leq 0  

Alternative hypothesis:\mu_{1} - \mu_{2}> 0  

We don't have the population standard deviation's, so for this case is better apply a t test to compare means, and the statistic is given by:  

t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}} (1)  

And the degrees of freedom are given by df=n_1 +n_2 -2=13+19-2=30  

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

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

t=\frac{(810-770)-0}{\sqrt{\frac{67^2}{13}+\frac{56^2}{19}}}}=1.771  

P value  

Since is a right tailed test the p value would be:  

p_v =P(t_{30}>1.771)=0.0434  

Comparing the p value with the significance level \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the mean for group 1 is significantly higher than the mean for the group 2

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Solve x:<br><br> 3x + 99x= 1224<br><br> 10 pts
Masja [62]
Answer is 12
Reason
Combine like terms
3x + 99 x = 1224
102x = 1224
Now solve for x
Divide both sides by 102
x= 12
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Step-by-step explanation:

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Answer:

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