All categories

3 years ago

Pythagorean theorem

Mathematics

2 answers:

lilavasa [31]3 years ago

6 0

Answer:

b = 63

Step-by-step explanation:

In a right angled triangle, hypotenuse squared is equal to the sum of the square of the other sides.

c² = a² + b² (where c is the hypotenuse, and a and b are the other two sides)

c = 65 , a = 16 b = ?

65² = 16² + b²

4225 = 256 + b²

4225 - 256 = b²

b² = 3969

b = $\sqrt{3969}$

b = 63

check

c² = 16 ² + 63²

= 256 + 3969

= 4225

c = √4225

c = 65

ki77a [65]3 years ago

5 0

Answer:

hello

Step-by-step explanation:

a²+b²=c²

16²+b²=65²

256+b²=4225

b²=4225-256

b²=3969

$b = \sqrt{3969}$

b=63

b=63 mi

have a nice day

You might be interested in

2. A marketing firm is trying to estimate the proportion of potential car buyers that would consider

Maurinko [17]

Answer:

a. The number of people that should be in the pilot study are 600 people

b. The point estimate is 0.62 $\overline 6$

c. At 95% confidence level the true population proportion of potential car buyers of hybrid vehicle is between the confidence interval (0.588, 0.6654)

d. Two ways to reduce the margin of error are;

1) Reduce the confidence interval

2) Use a larger sample size

Step-by-step explanation:

a. The given parameters for the estimation of sample size is given as follows;

The margin of error for the confidence interval, E = 4% = 0.04

The confidence level = 95%

The sample size formula for a proportion as obtained from an online source is given as follows;

$n = \dfrac{Z^2 \times P \times (1 - P)}{E^2}$

Where, P is the estimated proportions of the desired statistic, therefore, we have for a new study, P = 0.5;

Z = The level of confidence at 95% = 1.96

n + The sample size

Therefore, we have;

$n = \dfrac{1.96^2 \times 0.5 \times (1 - 0.5)}{0.04^2} = 600.25$

Therefore, the number of people that should be in the pilot study in order to meet this goal at 95% confidence level is n = 600 people

b. The point estimate for the population proportion is the sample proportion given as follows;

$\hat p = \dfrac{x}{n}$

Where;

x = The number of the statistic in the sample

n = The sample size

From the question, we have;

The number of potential car buyers, n = 600

The number of respondent in the sample that indicated that they would consider purchasing a hybrid, x = 376

Therefore, the point estimate, for the proportion of potential car buyers that would consider buying a hybrid vehicle, $\hat p$ = 376/600 = 0.62 $\overline 6$

c. The confidence interval for a proportion is given as follows

$CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

Therefore, we get;

$CI=0.62 \overline 6\pm 1.96\times \sqrt{\dfrac{\hat{0.62 \overline 6}\cdot (1-\hat{0.62 \overline 6})}{600}}$

C.I. ≈ 0.6267 ± 0.0387

The 95% confidence interval for the true population proportion of potential buyers of hybrid vehicle, C.I. = (0.588, 0.6654)

d. The margin of error is given by the following formula;

$MOE_\gamma = z_\gamma \times \sqrt{\dfrac{\sigma ^2}{n} }$

Where;

$MOE_\gamma$ = Margin of error at a given level of confidence

$z_\gamma$ = z-score

σ = The standard deviation

n = The sample size

Therefore, the margin error can be reduced by the following two ways;

1) Reducing the confidence interval and therefore, the z-score

2) Increasing the sample size

6 0

3 years ago

The median of a set of three numbers is x. there at least three numbers in the set. Write an algebraic expression, in terms of x

LUCKY_DIMON [66]

The median of a set of three numbers is x. there at least three numbers in the set. Write an algebraic expression, in terms of x, to represent the median of the new set of numbers obtained by
a] adding 1/8 to every number in the set
Let the numbers be w,x,y
adding 1/8 to the number we get:
(w+1/8),(x+1/8),(y+1/8)
the new median will be:
(x+1/8)

b. subtracting 9 1/4 from every number in the set
Given our data set is w,x,y
adding 9 1/4 to each number we get:
(w+9 1/4),(x+9 1/4), (y+9 1/4)
thus the new median is:
(x+9 1/4)

c]multiplying -5.8 to every number in the set and then adding 3 to the resulting numbers
Multiplying each number by -5.8 we get:
(-5.8w),(-5.8x),(-5.8y)
adding 3 to these numbers we get:
(-5.8w+3),(-5.8x+3),(-5.8y+3)
thus the new median is:
(-5.8x+3)

d]dividing every number in the set by 0.5 and then subtracting 1 from the resulting numbers
dividing each number in our set by 0.5 we get:
(w/0.5),(x/0.5),(y/0.5)
this will give us:
(2w),(2x),(2y)
then subtracting 1 from the above we get:
(2w-1),(2x-1),(2y-1)
thus the median will be:
(2x-1)

e. adding 7.2 to the greatest number in the set
from our set:
w.x.y
the greatest number is y, then adding 7.2 to the greatest numbers gives us:
y+7.2
thus new series is:
w,x,y+7.2
thus the median is:
x
Conclusion
The median doesn't change

f. subtracting 4.2 from the least number in the set
from our set w,x,y; subtracting 4.2 from the least number gives us:
w-4.2
the new set is:
w-4.2, x, y
thus the new median is x
Conclusion
The median doesn't change

5 0

4 years ago

A triangle has two sides of lengths 7 and 9. What value could the length of the third side be?

Dominik [7]

X - length of the 3rd side

$7+9>x \wedge 7+x>9 \wedge 9+x>7\\
x2 \wedge x>-2\\
x\in(2,16)$