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The angle between a diagonal and the longer base of the isosceles trapezoid MNFD is 45°. NK is an altitude to the longer base. I

Elanso [62]

Answer:

$NK \approx 7.001$ , $MK = 2$ , $MF \approx 7.001$ , $A_{AMNFD} = 49.007$

Step-by-step explanation:

According to the statement, we find the following inputs:

$\angle MDK = \angle DMF = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$MD = 9$

$NF = 5$

Given than longer base and shorter base are parallel to each other, we conclude that:

$\angle KND = 180^{\circ} -\angle NKD - \angle KDN$

$\angle KND = 180^{\circ}-90^{\circ}-45^{\circ}$

$\angle KND = 45^{\circ}$

$\angle FND = 90^{\circ}-\angle KND$

$\angle FND = 45^{\circ}$ (By definition of complementary angles)

$\angle FND = \angle NFM = 45^{\circ}$ (Due to the condition of isosceles trapezoid)

$\angle MDK = \angle DMF = \angle FND = \angle NFM = 45^{\circ}$

$\angle NOF = \angle MOD = \angle MOF = \angle FOD = 90^{\circ}$ (By definitions of complementary and vertical angles and the theorem that states that sum of internal angles within a triangle equals 180º)

$MO = DO = \frac{\sqrt{2}}{2}\cdot MD$ (By theorem for 45-45-90 Right Triangle)

$NO = OF = \frac{\sqrt{2}}{2}\cdot NF$ (By theorem for 45-45-90 Right Triangle)

If we know that $MD = 9$ and $NF = 5$ , then we find that:

$DO = MO \approx 6.364$

$NO = OF \approx 3.536$

The value of MK is obtained from the following relationship:

$MK = \frac{MD-NF}{2}$

$MK = \frac{9-5}{2}$

$MK = 2$

And the value of KD is calculated from this expression:

$KD = MD-MK$

$KD = 9-2$

$KD = 7$

Now by the Pythagorean Theorem we find that:

$NK = \sqrt{(NO+DO)^{2}-KD^{2}}$

$NK = \sqrt{9.9^{2}-7^{2}}$

$NK \approx 7.001$

And considering the symmetry characteristics of an isosceles trapezoid, we determine MF:

$MF = NO + DO \approx 7.001$

Lastly, the area of the isosceles trapezoid is determined by the following formula:

$A_{AMNFD} = NF\cdot NK + MK\cdot NK$

$A_{AMNFD} = NK\cdot (NF+MK)$

If we know that $NK \approx 7.001$ , $NF = 5$ and $MK = 2$ , then the area of the figure is:

$A_{AMNFD} = (7.001)\cdot (5+2)$

$A_{AMNFD} = 49.007$

8 0

3 years ago

Kit pays an annual premium of $1,575 for automobile insurance, including comprehensive coverage of up to $750,000. He pays this

Sonbull [250]

29850. 14 x 1575 is how much he paid. Subtract that from the cost of the car ($51900). 51900 -22050 = 29850

7 0

3 years ago

Is .8749 greater than or less than .05

Leto [7]

Answer:

it is greater than .05 because 8 is larger

6 0

3 years ago

Emily spent $55 from her savings on a new dress. explain how to descibe the change Emily's savings balance in 2 different ways

vodomira [7]

S=saving
X=amount left
S-55=x

Another way : x=s-55

4 0

3 years ago

A report on consumer financial literacy summarized data from a representative sample of 1,570 adult Americans. Based on data fro

alexgriva [62]

Answer:

a) 95% confidence interval for the proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance = (0.498, 0.547)

This means we are 95% confident that the true proportion all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is within the range 49.8% and 54.7%.

b) The confidence interval from part (a) is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B because the interval obtained contains proportions that are greater than 50% indicating that there is significant evidence that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is more than half of the total population.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = (820/1570) = 0.5223

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 95% confidence interval for sample size of 1570 is obtained from the z-tables.

Critical value = 1.960

Standard error of the mean = σₓ = √[p(1-p)/n]

p = sample proportion = 0.5223

n = sample size = 1570

σₓ = √(0.5223×0.4777/1570) = 0.0126063049 = 0.01261

95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.5223 ± (1.96 × 0.01261)

CI = 0.5223 ± 0.02471

95% CI = (0.4975916424, 0.5470083576)

95% Confidence interval = (0.4976, 0.5470)

We are 95% confident that the true proportion all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is within the range 49.8% and 54.7%.

b) The confidence interval from part (a) is consistent with the statement that a majority of adult Americans would give themselves a grade of A or B because the interval obtained contains proportions that are greater than 50% indicating that there is significant evidence that the true proportion of all adult Americans who would give themselves a grade of A or B on their financial knowledge of personal finance is more than half of the total population.

Hope this Helps!!!!

7 0

3 years ago