20 Points
The length of the shorter leg of a 30-60-90 Special Right Triangle is 6 cm long. How long is the hypotenuse of the triangle?

Question 2 options:

63–√ cm

6 cm

12 cm

62–√ cm

Answer:

Step-by-step explanation:

Answer:

It should be called A decic polynomial

Step-by-step explanation:

Applying the area of trapezium, the approximate area filled by water in the picture would be close to: about 48 in.²

Area of trapezium = 1/2(a + b)h.

The following are dimensions of the area of the trapezium filled with water:

Area = 1/2(6 + 8) × 6 = 42 in.²

Therefore, applying the area of trapezium, the approximate area filled by water in the picture would be close to: about 48 in.²

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Answer:

55a=

step-by-step explanation:

Answer:

-3125

Step-by-step explanation:

Got it right on delta

Answer:

J=118

L=62

M=62

Step-by-step explanation:

In an isoseles trapezoid, the top angles are congruent to each other and the bottom angles are congruent to each other. Opposite angles are supplementary, and all angles together add up to 360.

Multiplication of a positive number and negative number

   ⇒ is like any other multiplication

      30 * -20 = 30 * ((-1) * 20) = 30 * -1 * 20 = (-1) * 600 = -600

Hope that helped!

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The required equation is :

[tex] \qquad \sf  \dashrightarrow \:y = a \sin(bx) + k[/tex]

Now, let's find the required values :

period (p) = 4

[distance between any successive Crest or trough]

a = - 3 (flipped)

b = 2π/p = 2π/4 = π/2

k = 1

Distance of starting position from origin = k

Now, plug in the values ~

[tex]\qquad \sf  \dashrightarrow \: - 3 \sin( \frac{ \pi}{2}x ) + 1[/tex]

Answer:

95 is the answer I took the test

The correct answer would be: 6/5

Answer:

Ratio

Step-by-step explanation:

1. Your checking account number as a name for your account. Nominal (renaming)

2. Your checking account balance as a measure of the amount of money you have in that account. Ratio

3. Your checking account balance as a measure of your wealth. Interval

4. The number you get from a machine (32, 33,...) as a measure of the time you arrived in line. Ordinal

5. The order in which you were eliminated in a spelling bee as a measure of your spelling ability. Interval

6. Your score on the first statistics test as a measure of your knowledge of statistics. Ratio

7. Your score on an individual intelligence test as a measure of your intelligence. Nominal

8. The distance around your forehead measured with a tape measure as a measure of your intelligence. Interval

9. A response to the statement "Abortion is a woman's right" where Strongly Disagree = 1, Disagree = 2, No Opinion = 3, Agree = 4, and Strongly Agree = 5, as a measure of attitude toward abortion. Ordinal

hope it helps:)

Answer:

34 degrees

Step-by-step explanation:

Assuming that ADJ is a right angle, we can add 4x and 3x-8 and set equal to 90 degrees to simply to get get x.

7x-8=90

Add 8

7x = 98

 x= 14

Now that we know x, we can plug in the value to find angle CDJ.

3x-8

3(14)-8

34 degrees

Answer:

The answer is (n – 2) (3n + 2)

Step-by-step explanation:

3n² – 4n – 4

3n² – 6n + 2n – 4

3n(n – 2) + 2(n – 2)

(n – 2) (3n + 2)

Thus, (n – 2) (3n + 2) is a factored of

3n² - 4n - 4

Use L'Hopital's rule twice:

[tex]\displaystyle \lim_{x\to0^+} \frac1{\sin^2(x)} \int_{\frac x2}^x \sin^{-1}(t) \, dt = \lim_{x\to0^+} \frac1{\sin^2(x)} \left(\int_0^x \sin^{-1}(t) \, dt - \int_0^{\frac x2} \sin^{-1}(t) \, dt\right) \\\\ = \lim_{x\to0^+} \frac{\sin^{-1}(x) - \frac12 \sin^{-1}\left(\frac x2\right)}{2\sin(x)\cos(x)} ~~~~~~~~~~ (LHR) \\\\ = \lim_{x\to0^+} \frac{2\sin^{-1}(x) - \sin^{-1}\left(\frac x2\right)}{2\sin(2x)} \\\\ = \lim_{x\to0^+} \frac{\frac2{\sqrt{1-x^2}} - \frac1{2\sqrt{1-\frac{x^2}4}}}{4\cos(2x)}  ~~~~~~~~~~ (LHR) \\\\ = \lim_{x\to0^+} \frac{\frac2{\sqrt{1-x^2}} - \frac1{\sqrt{4-x^2}}}{4\cos(2x)}[/tex]

The remaining limand is continuous at x = 0, and the limit is

[tex]\displaystyle \lim_{x\to0^+} \frac1{\sin^2(x)} \int_{\frac x2}^x \sin^{-1}(t) \, dt = \frac{2-\frac12}4 = \boxed{\frac38}[/tex]

Answer:

1 chance in 123,396,455

Step-by-step explanation:

Number of permutations of 5 out of the 53 = 53*52*51*50*49 = 344362200

Number of permutations of 4 out of these 5 correct = 120

So number permuations for first 53  = 344362200/ 120 = 2869685

So for minimum prize there are 2869685 * 43 = 123396455 perms.

Answer:

1.c

2.a

3.d

4.b

5.b

Step-by-step explanation:

I found the answers on a web site.

Answer:

1.A

2.D

3.C

4.B

5.A

Step-by-step explanation:

Answer:

a₆ = 243

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

3 ÷ 1 = 9 ÷ 3 = 27 ÷ 9 = 3

this indicates the sequence is geometric with nth term

[tex]a_{n}[/tex] = a₁ × [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 1 and r = 3 , then

a₆ = 1 × [tex]3^{5}[/tex] = 243

243

Hope it helps.

Do comment if you have any query.

Answer:

O = 15

Step-by-step explanation:

.mean ' is the average

(12 + 16 + O + 14 + 8) / 5 = 13

50 + O = 65

O = 15

The net amount that will be saved by the Jones for the first year will be $814.32.

From the information given, the old mortgage yearly payment will be:

= Monthly payment × Months

= $259.32 × 12

= $3111.84

The new monthly yearly payment will be:

= Monthly payment × Months

= $327.18 × 12

= $3926.16

Therefore, the net amount that will be saved will be:

= $3926.16 - $3111.84

= $814.32

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Answer:

Step-by-step explanation:

11. identity property

12. associative property

13. commutative property

14. zero property

Answer:

The answer for this question is 2 ft

Step-by-step explanation:

12ft÷6ft=2

Answer:

4.32 Liters

Step-by-step explanation:

12*360 mL= 4320 mL

mL to L= mL/1000

4320/1000= 4.32

so for a height of 869 feet the time will be 21.725s

[tex]1s = 40ft \\ x = 869ft \\ x= \frac{869}{40} \\ x = 21.725ft[/tex]

Answer:

Step-by-step explanation:

[tex]-3x^2-7x-9=F(x)[/tex]

[tex]F(-5)=-75+40-9=-49[/tex]

[tex]F(2)=-12-14-9=-35[/tex]

[tex]f(-5)+f(2)=-49-35=-84[/tex]

Answer:

An unlimited number of lines are parallel to the line described by y = 5x + 2. The requirement is that it is in the form y = 5x + b, b ≠ 2.

Step-by-step explanation:

employed: 1,312,700 people

employed people:

Unemployed persons

Employed persons

Answer:

D

Step-by-step explanation:

Here's why I think it's D.

y = x + 44 is the equation the car wash owner uses

x represents the number of days

y represents the number of cars (washed)

so if we plug in one of the given numbers (from the chart)

example:

Day 2 Numbers of Cars Washed 44

2 will represent the "number of days" also known as x

44 will represent the "number of cars" also known as y

so if we plug in those values to the equation the car wash owner uses

y = x + 44, it doesn't match

__________________________________

(44) = 2 + (44)

44 [tex]\neq[/tex] 46

Therefore, I believe the answer is D

Answer:

D

Step-by-step explanation:

The f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain, and range

Linear equations are equations that has a degree of 1 while polynomial equations are equations that has a degree of 2 and above.

Given the following functions

f(x) = –4x + 5 and;

g(x) = x^3 + x^2 – 4x + 5

Since the f(x) has a degree of 1, hence it is linear in nature while g(x) is a polynomial function because of the third degree.

The key features that they have in common are the y-intercept, domain and range

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The amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx. The probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex])

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z tables, the p-value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

Let we take:

X = The balance of a person’s bank account in Superior, WI

Then, by the given data, we have:

[tex]X \sim N(\mu = 580, \sigma = 125)[/tex]

Let the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents be X = x dollars. This is the money, below which lie 80% of Superior, WI residents, and so as their income, or values of X.

Symbolically, we have:

[tex]P(X < x) = 80\% = 0.8[/tex]

Converting X to standard normal variate Z, we have:

[tex]Z = \dfrac{X - \mu}{\sigma} = \dfrac{X - 580}{125}\\[/tex]

Thus, the probability statement can be rewritten as:

[tex]P(X < x) =0.8\\P\left( Z < z = \dfrac{x -580}{125} \right) = 0.8[/tex]

From the z-tables, the value of Z for which the p-value comes out as between 0.84 and 0.85, let it be their average 0.845.

Thus, we get:

[tex]P(Z < z = 0.845) \approx 0.8[/tex]

Thus, we get:

[tex]z = \dfrac{x - 580}{125} \approx 0.8\\\\x \approx 0.8 \times 125 + 580 = 680[/tex]

Thus, the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx.

Now, for second question, we need:

The probability a random person from Superior has less than $400 or more than $1000 in their bank account.

So, income of a random person from Superior is a random value of X.

So, this probability is written as:

[tex]P(400 < X < 1000)[/tex]

Rewritting it, we get:

[tex]P(400 < X < 1000) = P(X < 1000) - P(X \leq 400)[/tex]

Converting X to Z (standard normal variate), we get:

[tex]P(400 < X < 1000) = P(X < 1000) - P(X \leq 400)\\\\P(400 < X < 1000) = P\left(Z < \dfrac{1000-580}{125} \right) - P\left(Z \leq \dfrac{400-580}{125} \right)\\\\P(400 < X < 1000) = P( Z \leq 3.36) - P(Z \leq -1.44)[/tex]

The p-value for Z = 3.36 is 0.9996

The p-value for Z = -1.44 is 0.0749

Thus, we get:

[tex]P(400 < X < 1000) = P( Z \leq 3.36) - P(Z \leq -1.44)\\\\P(400 < X < 1000) = 0.9996 - 0.0749 = 0.9247[/tex]

Thus, the probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247

Thus, the amount of money which would guarantee a person has more money in their account than 80% of Superior, WI residents is $680 approx. The probability a random person from Superior has less than $400 or more than $1000 in their bank account is 0.9247

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