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3 years ago

The area of a parallelogram in which b = (3x + 5) ft and h = (7x - 1) ft

1 answer:

6 0

The area of a parallelogram is equal to the base multiplied by the height. So in this instance it would be (3x+5)*(7x-1). Foil out the binomials. 21x^2+35x-3x-5 Combine like terms. 21x^2+32x-5
The area is 21x^2+32x-5

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Given: ABCD ∥gram, BK ⊥ AD , AB ⊥ BD AB=6, AK=3 Find: m∠A, BK, A

Masteriza [31]

Given: ABCD ∥gram,

BK ⊥ AD , AB ⊥ BD

AB=6, AK=3

Find: m∠A, BK

To proof

as given BK ⊥ AD

thus ΔABK is a right triangle.

thus by using the pythagoras theorem

we have

AB² = BK² + AK²

BK² = AB ²- AK²

= 6² - 3²

= 36 - 9

= 27

Hence

BK = <u> $3\sqrt{3}$ unit</u>

Now find the value m∠A

by using the trignometric function

FORMULA

cosA = $\frac{BASE}{HYPOTENUSE}$

cosA = $\frac{3}{6}$

= $\frac{1}{2}$

m∠A = 60°

hence proved

3 0

3 years ago

Water flows through a pipe at a rate of 91 fluid ounces every 2.5 weeks. Express this rate of flow in cups per hour. Round your

Ulleksa [173]

Answer:

Step-by-step explanation:

First, we convert:

ounces to cups
weeks to hours

Result of conversion:

91 fluid ounces = 11.375 cups (1 cup = 8 ounces)
2.5 weeks = 420 hours (1 week = 168 hours)

To get the rate, we must divide the number of cups by number of hours

11.375 cups / 420 hours = 0.027 cups per hour = 0.03 cups per hour (approximated)

Hope that helps!

7 0

3 years ago

A bank is trying to determine which model of safe to install. The bank manager believes that each model is equally resistant to

alexandr402 [8]

Answer:

So on this case the 95% confidence interval would be given by (-1.152;5.152).

$-1.152 < \mu_{safe1}-\mu_{safe2}$

Should we conclude that the average time it takes experts to crack the safes does not differ by model at the 5% significance level?

A) Yes, the 95% confidence interval for ?D contains 0.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution

Let put some notation

x=value for Safe 1 , y = value for Safe 2

x: 103, 90, 64, 120, 104, 92, 145, 106, 76

y: 101, 94, 58, 112, 103, 90, 140, 110, 74

The first step is calculate the difference $d_i=x_i-y_i$ and we obtain this:

d: 2, -4, 6, 8, 1, 2, 5, -4, 2

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{18}{9}=2$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =4.093$

The next step is calculate the degrees of freedom given by:

$df=n-1=9-1=8$

Now we need to calculate the critical value on the t distribution with 8 degrees of freedom. The value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , so we need a quantile that accumulates on each tail of the t distribution 0.025 of the area.