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3 years ago

5

55 POINTS!!! The hypotenuse of a right triangle is 5cm more than 4 times the length of the shortest leg. The longer leg and the

hypotenuse are consecutive integers. Find all lengths.

1 answer:

max2010maxim [7]3 years ago

7 0

Answer:

Short leg is 9.

Hypotenuse is 41.

Long leg is 40.

Step-by-step explanation:

Shortest leg is x.

Hypotenuse is (4x + 5).

Longer leg is shorter than hypotenuse, and they are consecutive numbers,

so longer leg is (4x + 5 - 1) = (4x + 4).

Using Pythagorean theorem

x² + (4x + 4)² = (4x + 5)²

x² + 16x² + 2*4x*4 + 4² = 16x² + 2*4x*5 + 5²

x² + 32x + 16 = 40x + 25

(x - 4)² = 5²

x - 4 = 5 or x - 4 = - 5

x = 9 , or x = - 1

Leg cannot be negative.

So, short leg is 9.

Hypotenuse (4x+5) = (4*9 + 5) = 41

Long leg is 41 - 1 = 40

Check:

9² + 40² = 41²

1681 = 1681 True

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The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. Th

e-lub [12.9K]

Answer:

95% of monthly food expenditures are between $110 and $190.

Step-by-step explanation:

Given : The monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical, normal distribution. The sample mean is $150 and the standard deviation is $20.

To find : Using the Empirical rule, about 95% of the monthly food expenditures are between which of the following two amounts?

Solution :

At 95% of the data is between two standard deviation to left and right of the mean is given by,

To the left side, $\bar{x}-2\sigma$

To the right side, $\bar{x}+2\sigma$

We have given,

The sample mean $\bar{x}=\$150$

The standard deviation $\sigma=\$20$

Substitute in the formula,

$\bar{x}-2\sigma$

$=150-2(20)$

$=150-40$

$=110$

$\bar{x}+2\sigma$

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Therefore, 95% of monthly food expenditures are between $110 and $190.

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3 years ago

A study sampled 350 upperclassmen (Group 1) and 250 underclassmen (Group 2) at high schools around the city of Houston. The stud

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Answer:

$-0.048$

Do not reject $H_0:P_1-P_2=0$

Step-by-step explanation:

From the question we are told that

Sample size $n_1=350$

Sample size $n_2=250$

Sample proportion 1 $\hat P= \frac{25}{350} =>0.07$

Sample proportion 2 $\hat P= \frac{19}{250} =>0.076$

95% confidence interval

Generally for 95% confidence level

Level of significance

$\alpha = 1-0.95=>0.05$

$\alpha /2=\frac{0.05}{2} =>0.025$

Therefore

$Z_a_/_2=1.96$

Generally the equation for confidence interval between $P_1 - P_2$ is mathematically given as

$(\hat P_1-\hat P_2)\pm Z_a_/_2\sqrt{\frac{\hat P_1(1-\hat P_1)}{n_1}+\frac{\hat P_2(1-\hat P_2)}{n_2} }$

$(0.07-0.076)\pm 1.96\sqrt{\frac{0.07(1-0.07)}{350}+\frac{0.076(1-0.076)}{250} }$

$(0.07-0.076)\pm 1.96\sqrt{4.66896*10^-^4 }$

$(-0.006)\pm 0.042$

$(-0.006)- 0.042=>-0.048$

$(-0.006)+ 0.042=>0.036$

Therefore

Confidence interval is

$-0.048$

Conclusion

Given the confidence interval has zero

Therefore do not reject $H_0:P_1-P_2=0$

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