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In this 45-46-90 triangle , I have been given the length of a leg . How do I find the length of the hypotenuse

Answers

Answer 1

Answer:

Answer:

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Answer 2

Answer:

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Sum of the interior angles of any triangle equal 180° .

Thus ;

The angle which facing to the side 4 is 45°.

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Hint:

In a right triangle, the side facing the 45° angle is √2 / 2 times the hypothenuse .

Thus ;

$( √(2) )/(2) x = 4 \n$

Multiply sides by 2

$2 * ( √(2) )/(2) x = 2 * 4 \n$

$√(2) x = 8 \n$

Divide sides by √2

$( √(2)x )/( √(2) ) = (8)/( √(2) ) \n$

$x = (4 * 2)/( √(2) ) \n$

$x = (4 * √(2) * √(2) )/( √(2) ) \n$

$x = 4 √(2) \n$

$x = hypothenuse = 4 √(2)$

Done...

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QuestionAlice drove from the town of Everett to the town of Gage at an average speed of 45 miles per hour. If she Grove for 40 minutes, how far did she travel? (1 hour = 60 minutes)

The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean and the standard deviation were 110 mg and 7.1 mg respectively. Use the data to construct a 98% confidence interval for the mean caffeine content for cups dispensed by the machine. Interpret the interval!

Answers

Answer:

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .

Step-by-step explanation:

Given -

The sample size is large then we can use central limit theorem

n = 50 ,

Standard deviation $(\sigma)$ = 7.1

Mean $\overline{(y)}$ = 110

$\alpha =$ 1 - confidence interval = 1 - .98 = .02

$z_{(\alpha)/(2)}$ = 2.33

98% confidence interval for the mean caffeine content for cups dispensed by the machine = $\overline{(y)}\pm z_{(\alpha)/(2)}\frac{\sigma}√(n)$

= $110\pm z_(.01)\frac{7.1}√(50)$

= $110\pm 2.33\frac{7.1}√(50)$

First we take + sign

$110 + 2.33\frac{7.1}√(50)$ = 112.34

now we take - sign

$110 - 2.33\frac{7.1}√(50)$ = 107.66

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .

The board of a large company is made up of 7 women and 9 men. 6 of them will go as a delegation to a national conference. a) How many delegations are possible?

b) How many of these delegations have all men?

c) How many of these delegations have at least one woman?

Answers

Answer:

a) 5765760

b) 60480

c) 5705280

Step-by-step explanation:

Assuming that order is not important:

Number of women = 7

Number of men = 9

Members of the delegation = 6

a) How many delegations are possible?

$n=(16!)/((16-6)!)=16*15*14*13*12*11\n n= 5765760$

b) How many of these delegations have all men?

$n_(men) = (9!)/((9-6)!)=9*8*7*6*5*4 \nn_(men) = 60480$

c) How many of these delegations have at least one woman?

$n_(women >0)=n-n_(men)\nn_(women >0) =5765760-60480\nn_(women >0) =5705280$

A. Use your calculator to approximate ∫^ b_0 e^-0.00001x dx for b=10, 50, 100 and 1000.b. Based on your answers to part a, does ∫^[infinity]_0 e^-0.00001 dx appear to be convergent or divergent?
c. To what value does the integral actually converge?

Answers

Answer:

Step-by-step explanation:

We are to integrate the function

$e^-0.00001x$ from 0 to b for different ascending values of x.

$\int e^-0.00001x = -10^5 e^-0.00001x$

Now we substitute the limits

When b =10

I = integral value = $-10^5 e^-0.00001*10$

b =50, I = $-10^5(e^-0.00001*50-1)$

b =100, I = $-10^5( e^-0.00001*100-1)$

b =1000 I= $-10^5 (e^-0.00001*1000-1)$

b) As b increases exponent increases in negative, or denominator increases hence when b becomes large this will be a decreasing sequence hence converges

c) Converges to $-10^5 (0-1)$ =10^5

Examine the work shown. Explain the error and find the correct result. 2(4 - 16) - (-30)2-12) - (-30)
24 - (-30)
54

Answers

Answer:

-54

Step-by-step explanation:

When you solve any equation always remember to use PEMDAS (Parentheses Exponents, Multiplication, Division, Addition and Subtraction) use also move left to right. The correct way to solve this is

2(4-16)-30

2(-12)-30

-24-30

-54

Hope this helped

Answer:

Step-by-step explanation:

Third line. "24 - (-30)" has to multiply 2 with -12, so it would be "-24" and not "24".

2(4 - 16) - (-30)

2(-12) + 30

-24 + 30 = 6

WILL MARK BRAINLIEST List all of the number sets that contain the number 15.
A. rational numbers and integers
B. rational numbers, integers, and natural numbers
C. rational numbers, integers, and whole numbers
D. rational numbers, integers, natural numbers, and whole numbers

Answers

Answer: D

Step-by-step explanation:

1. Suppose you have a fair 6-sided die with the numbers 1 through 6 on the sides and a fair 5-sided die with the numbers 1 through 5 on the sides. What is the probability that a roll of the six-sided die will produce a value larger than the roll of the five-sided die? 2. What is the expected number of rolls until a fair five-sided die rolls a 3?

Answers

Answer:

a. 0.5 or 50%

b. 5 rolls.

Step-by-step explanation:

a. There are 30 possible outcomes for this experiment, the sample space for the outcomes in which the six-sided die produces a value larger than the roll of the five-sided die is:

S={6,1; 6,2; 6,3; 6,4; 6,5; 5,1; 5,2; 5,3; 5,4; 4,1; 4,2; 4,3; 3,2; 3,1; 2,1}

There are five outcomes when rolling a 6, four when rolling a 5, three when rolling a 4, two when rolling a 3 and one when rolling a two.

The probability is:

$P = (5+4+3+2+1)/(5*6)=0.5$

b. The probability of rolling a 3 on the five-sided die is 1 in 5 or 0.20. The expected number of rolls until a fair five-sided die rolls a 3 is:

$E(x=1) = (1)/(p(x))=(1)/(0.2)= 5\ rolls$

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