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1 year ago

6

brian filled 72 glasses with apple juice for a school party if each glass holds 1 cup of juice how many quarts of apple juice di

d brian use

1 answer:

GaryK [48]1 year ago

5 0

4 cups in a quart so you would have 72 cups divided by 4 and get 18

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Triangle H N K is shown. Angle H N K is 90 degrees. The length of hypotenuse H K is n, the length of H N is 12, and the length o

Mazyrski [523]

Answer:

13

Step-by-step explanation:

From the question, we are given a triangle HNK with an angle of 90°

The length of hypotenuse H K is n,

the length of HN is 12

the length of N K is 6.

From the above values, obtained in the question, we can see that this is a right angled triangle.

We are asked to find the length of the hypotenuse.

We can use Pythagoras Theorem of solve for this.

c² = a² + b²

where c = HK = n

a = NK = 6

b = HN = 12

c² = 6² + 12²

c² = 36 + 144

c² = 180

c = √180

c = 13.416407865

Approximately to the nearest whole number = 13

Therefore the value of HK = n = 13

We can also use Law of Cosines as given in the question to solve for this.

a² = b² + c² - 2ac × Cos A

where c = HK = n

a = NK = 6

b = HN = 12

Hence

c² = a² + b² - 2ab × Cos C

c = √ (a² + b² - 2ab × Cos C)

Where C = 90

c = √ 6² + 12² - 2 × 6 × 12 × Cos 90

c = 13.42

Approximately to the nearest whole number ≈ 13

Therefore the value of HK = n = 13

8 0

1 year ago

In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . If m∠ADE is with 34° smaller than m∠CAB, find the measures

Charra [1.4K]

Answer:

34°

Step-by-step explanation:

If m∠ADE is with 34° smaller than m∠CAB, then denote

m∠ADE=x°,

m∠CAB=(x+34)°.

Since DE ║ AB, then

m∠ADE=m∠DAB=x°.

AD is angle A bisector, then

m∠EAD=m∠DAB=x°.

Thus,

m∠CAB=m∠CAD+m∠DAB=(x+x)°=2x°.

On the other hand,

m∠CAB=(x+34)°,

then

2x°=(x+34)°,

m∠ADE=x°=34°.

7 0

1 year ago

in a random sample of 200 people, 154 said that they watched educational television. fine the 90% confidence interval of the tru

melisa1 [442]

Answer:

[0.7210,0.8189] = [72.10%, 81.89%]

Step-by-step explanation:

The sample size is

n = 200

the proportion is

p = 154/200 = 0.77

<em>Since both np ≥ 10 and n(1-p) ≥ 10 </em>

<em>We can approximate this discrete binomial distribution with the continuous Normal distribution. As the sample size is large enough, not applying the continuity correction factor makes no significant difference. </em>

The approximation would be to a Normal curve with this parameters:

<em>Mean </em>

p = 0.77

<em>Standard deviation </em>

$\bf s=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.77*0.23}{200}}=0.0298$

The 90% confidence interval for the proportion would be then

$\bf [0.77-z^*0.0298, 0.77+z^*0.0298]$

where $\bf z^*$ is the 10% critical value for the Normal N(0,1) distribution , this is a value such that the area under the N(0,1) curve outside the interval $\bf [-z^*,z^*]$ is 10%=0.1

We can either use a table, a calculator or a spreadsheet to get this value.

In Excel or OpenOffice Calc we use the function

<em>NORMSINV(0.95) and we get a value of 1.645 </em>

The 90% confidence interval for the proportion is then

$\bf [0.77-1.645^*0.0298, 0.77+1.645^*0.0298]=[0.7210,0.8189]$

This means there is a 90% probability that the proportion of people who watch educational television is between 72.10% and 81.89%

If the television company wanted to publicize the proportion of viewers, do you think it should use the 90% confidence interval?

Yes, I do.

5 0

2 years ago

Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real

adoni [48]

Step-by-step explanation

<h3>Prerequisites:</h3>

<u>You need to know: </u>

$b^2 - 4ac = 0 \Rightarrow 1 solution$

$b^2 - 4ac > 0 \Rightarrow 2 solutions$

$b^2 - 4ac < 0 \Rightarrow No\ real\ solutions$

----------------------------------------------------------------

$2x^2-7x-9 = 0$

$b^2 - 4ac$

$-7^2 - 4(2)(-9) = 121$

2 Solutions

---------------------------------------------------------------

$x^2-4x+4 = 0$

$b^2 - 4ac$

$-4^2 - 4(1)(4) = 0$

1 Solution

---------------------------------------------------------------

$4x^2-3x-1 = 0$

$b^2 - 4ac$

$-3^2 - 4(4)(-1) = 25$

2 Solutions

---------------------------------------------------------------

$x^2-2x-8 = 0$

$b^2 - 4ac$

$-2^2 - 4(1)(-8) = 36$

2 Solutions

---------------------------------------------------------------

$3x^2+5x+3 = 0$

$b^2 - 4ac$

$5^2 - 4(3)(3) = -11$

No Solutions

---------------------------------------------------------------

3 0

2 years ago

Read 2 more answers

Find the area, circumference =6pi yd

vitfil [10]

Circumference = 2πr

Given that circumference 0s 6π, find radius:
2πr = 6π
r = 6π ÷ 2π = 3

Now that we know that the radius is 3 yard, find area:
Area = πr²
Area = π(3)²
Area = 9π = 28.27 yd²

Answer: 28.27 yd²

7 0

2 years ago