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2 years ago

Given: ABCD is a parallelogram m∠A = 60º ; BK ⊥ AD AK = KD; Perimeter of ABCD = 24 Find: BD.

1 answer:

3 0

Since AK = KD, then the triangle ABD is isosceles,
Then BD = AB. Denote AB by x and AK by y.
Then,
2x+4y=24 (the perimeter)
cos 60=y/x.
From the second equation we get $y=0.5x$
Plug in the first equation we get:
$2x+4(0.5x)=24\\2x+2x=24\\4x=24\\x=6$
We deduce that $BD=6.$

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Zenaida is shopping and wants to purchase a $320 stereo system. The store is offering an incentive of 10 to 30 percent off when

lesantik [10]

The stereo system costs $256.

Step-by-step explanation:

Given:

Cost of the stereo system = $320.

The discount Zenaida received = 20%.

To Find:

Cost of the stereo system after the discount=?

Solution:

Step1: Finding the discount amount:

Discount percentage =20

Discount amount = original cost × discount percent

Substituting the values,

$\text { Discount amount }=320 \times 20 \%$

$\text { Discount amount }=320 \times \frac{20}{100}$

$\text { Discount amount }=320 \times \frac{1}{5}$

$\text { Discount amount }=320 \times 0.2$

$\text { Discount amount }=64$

Step 2: Removing the discounted amount from the original price

Final cost of the stereo system =original cost of the stereo system –discount amount

Substituting the values we get,

Final cost=320-64

Final cost=256

Result:

Thus the cost of the stereo system after discount is $256

7 0

2 years ago

Read 2 more answers

"Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A r

sergiy2304 [10]

Answer:

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

(b) We conclude that there is a statistical difference in these two proportions measured initially and then one year later.

Step-by-step explanation:

We are given that a random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured.

A different random sample of 1,100 drivers found 96.9% compliance."

Let $p_1$ = proportion of drivers that were in compliance initially

$p_2$ = proportion of drivers that were in compliance one year later

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$ {means that there is not any statistical difference in these two proportions measured initially and then one year later}

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that there is a statistical difference in these two proportions measured initially and then one year later}

The test statistics that will be used here is Two-sample z proportion statistics;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{ \frac{\hat p_1(1-\hat p_1)}{n_1} + \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of drivers in compliance initially = 98.9%

$\hat p_2$ = sample proportion of drivers in compliance one year later = 96.9%

$n_1$ = sample of drivers initially = 1,250

$n_2$ = sample of drivers one year later = 1,100

(b) So, the test statistics = $\frac{(0.989-0.969)-(0)}{\sqrt{ \frac{0.989(1-0.989)}{1,250} + \frac{0.969(1-0.969)}{1,100}} }$

= 3.33

Now, P-value of the test statistics is given by;

P-value = P(Z > 3.33) = 1 - P(Z $\leq$ 3.33)

= 1 - 0.99957 = 0.00043

Since in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test.

Since our test statistics does not lies within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a statistical difference in these two proportions measured initially and then one year later.

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2 years ago

A recipe for a dessert for 6 people requires 120g of sugar. How much sugar would I need for a dessert 9 people?

zzz [600]

Answer:

180g of sugar

Step-by-step explanation:

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2 years ago

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Anna and Hannah have \$80$80dollar sign, 80 each. Their friend offered to invest their money, promising to return a sum rrr time

sergey [27]

9514 1404 393

Answer:

2r(20r +60) = 80r^2

Step-by-step explanation:

Anna's first investment:

Anna's first return:

20r

Anna's second investment:

20r +60

Anna's second return:

r(20r +60)

Hannah's first investment:

Hannah's first return, and her second investment:

80r

Hannah's second return:

80r^2

Twice Anna's return was equal to Hannah's return:

2r(20r +60) = 80r^2

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2 years ago

Last Sunday, the average temperature was 8\%8%8, percent higher than the average temperature two Sundays ago. The average temper

SVETLANKA909090 [29]

Answer: The two answers are 1.08T and (1 + $\frac{8}{100}$ )T.

Step-by-step explanation:

Try multiplying 1.08 times any random number. If you use 5, 1.08 times 5 gives you 5.4. This makes sense. Solve the other other expression as well and substitute T with the SAME number that you used before (5). Hope that helps!

5 0

2 years ago