4. A 30-60-90 triangle has a hypotenuse of 16 and a short side of 8. Use special right angle formulas to find the third side. Explain your work. Does your answer match what you got on number 3?

Answer:

x=112

Step-by-step explanation:

First, let's get all of the fractions to a common denominator.

Based on the numbers given (8,56, and 7), let's make all of the denominators be 56

for \(\frac{-7}{8} x\), multiply the numerator and denominator by 7.

\(\frac{-7x}{8}\)×\(\frac{7}{7}\)= \(\frac{-49}{56} x\)

we can leave \(\frac{-5}{56}x\) as it is

and for \(\frac{1}{7} x\), we cam multiply the numerator and denominator by 8

\(\frac{1x}{7}\)×\(\frac{8}{8}\)=\(\frac{8x}{56}\)

Here's the equation now:

\(\frac{-49x}{56}\)-\(\frac{5x}{56}\)+\(\frac{8x}{56}\)=-92

now simlify the fractions

numerators:

-49x-5x+8x=-46x

here's the fraction now:

\(\frac{-46x}{56}\)=-92

We can simplify the fraction by 2 so it's \(\frac{-23x}{28}\)

\(\frac{-23x}{28}\)=-92

now multiply both sides by \(\frac{28}{-23}\), which is the reciprocal of \(\frac{-23}{28}\) (to isolate the variable)

\(\frac{28}{-23}\)×\(\frac{-23x}{28}\)=-92×\(\frac{28}{-23}\)

\(\frac{-92*28}{-23}\)

x=112

Hope this helps!

Answer:

x = 112

Step-by-step explanation:

The common denominator is 56 because 8*7 is 56

\(-\frac{7*7*x}{8*7} -\frac{5*x}{56}+\frac{8*x}{56} = - 92 \\-\frac{49*x}{56} -\frac{5*x}{56}+\frac{8*x}{56} = - 92 \\\frac{-46*x}{56}=-92\)

Multiply both sides by 56

-46*x = -92 * 56

-46*x = -5152

Divide by - 46

x = -5152/-46

x = 112

Answer:

1222222+1222222

Step-by-step explanation:

and then add doodod

Answer:

\(|z| = 27\) -- Modulus

\(\theta = \frac{\pi}{3}\) --- Argument

Step-by-step explanation:

Given

\(((\sqrt 3)(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18}))^6\)

Required

Determine the modulus and the argument

We have that:

\(z = ((\sqrt 3)(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18}))^6\)

Expand:

\(z = (\sqrt 3)^6(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6\)

\(z = 27(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6\)

A complex equation can be expressed as:

\(z = |z| e^{i\theta}\)

Where

\(|z| = modulus\)

\(\theta = argument\)

Where

\(e^{i\theta} = (cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})\)

So:

\(z = 27(cos\frac{\pi}{18} + i\ sin\frac{\pi}{18})^6\) becomes

\(z = 27(e^{i\frac{\pi}{18}})^6\)

By comparison:

\(e^{i\theta} = (e^{i\frac{\pi}{18}})^6\)

This gives:

\({i\theta} = i\frac{\pi}{18}}*6\)

\({i\theta} = i\frac{6\pi}{18}}\)

\({i\theta} = i\frac{\pi}{3}}\)

Divide through by i

\(\theta = \frac{\pi}{3}\)

Hence, the modulus, z is:

\(|z| = 27\)

And the argument \(\theta\) is

\(\theta = \frac{\pi}{3}\)

Answer: C. M=27 A=pi/3

Step-by-step explanation:

edge

(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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Answer:

We reject H₀, we find that the  current level of mercury uptake in the Everglades has decrease

Step-by-step explanation:

We need to test the current wading bird average 14,6 vs the 1995 average. As sample mean is 14,6 and population mean is 15 we are going to check test is of one tail (left tail test)

Test Hypothesis:

Null hypothesis             H₀          μ   =  μ₀

Alternative hypothesis Hₐ          μ   <  μ₀

Sample size 25             then n < 30 we will use t-student table

Population mean : μ₀ = 15 ppm

sample mean :  μ  = 14,6 ppm

sample standard deviation:   s = 1 ppm

Sample size n :  25

degrees of freedom   df = n - 1         df = 24

We will develop the test for CI 90%  then  α = 10%      α = 0,1   α/2 = 0,05

For that values in t student table we find:

t(c) = 1,711    by symmetry t(c) = - 1,711

To compute ts

t(s) =  ( μ - μ₀ ) / s/√n

t(s) = 14,6 - 15 / 1 /√25

t(s) = - 0,4*5 / 1

t(s) = - 2

Comparing t(c)and t(s)

|t(s)| > |t(c) |      and t(s) < t(c)         -2 < -1,711

Therefore t(s) in in the rejection region, we reject H₀  

the sum of the measures of the exterior angles of a 32-gon is d. 5400

Whenever we have "AND" in a probability question, it means "x" [multiplication].

When we have "OR" in a probability question, it means "+" [addition].

Here, we want Probability of Quarter [P(q)] OR Probability of Dime [P(d)].

So, we will add the individual probabilities.

Now,

Total Coins = 7 + 11 + 8 + 15 = 41

Number of Quarters = 7

Number of Dimes = 11

So, we find individual probabilities:

P(q) = 7/41

and

P(d) = 11/41

Now, we add them up:

To get percentage, we do the division and multiply by 100.

18 divided by 41 = 0.4390

Multiply by 100:

0.4390 * 100 = 43.90%

The sorter's error is 91 seconds. This means that the sorter miscalculated the time it would take for the water bottle to travel the length of the belt by 91 seconds.

When anything is referred to as being "long," it refers to its overall length. In other words, it is the larger of the third or upper two dimensions of a geometric object. An example of a shape with two dimensions is a rectangle.

To find out how many seconds it takes for the water bottle to travel the length of the belt, we can use the equation:

distance = rate x time

We know the distance (294 feet) and the rate (7 feet per 6 seconds). Let's solve for time:

294 feet = (7 feet/6 seconds) x time

294 feet x 6 seconds = 7 feet x time

1764 seconds = 7 feet x time

time = 1764 seconds / 7 feet

time = 252 seconds

So it takes 252 seconds for the water bottle to travel the length of the belt.

Now let's calculate the sorter's error:

343 seconds - 252 seconds = 91 seconds

The sorter's error is 91 seconds. This means that the sorter miscalculated the time it would take for the water bottle to travel the length of the belt by 91 seconds.

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Approximately 17.65% of Ana's salary is withheld for taxes.

To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.

Number of hours worked per week (H) = 25 hours

Hourly wage (W) = $10

Net salary (S) = $212.50

Calculate the total earnings before taxes:

Total earnings = Hours worked * Hourly wage

Total earnings = 25 hours * $10/hour

Total earnings = $250

Determine the amount of tax withheld:

Tax withheld = Total earnings - Net salary

Tax withheld = $250 - $212.50

Tax withheld = $37.50

Calculate the percentage of salary withheld for taxes:

Percentage withheld = (Tax withheld / Net salary) * 100

Percentage withheld = ($37.50 / $212.50) * 100

Percentage withheld ≈ 17.65%

Therefore, approximately 17.65% of Ana's salary is withheld for taxes.

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Answer:

The entire clock measures 360 degrees. As the clock is divided into 12 sections. The distance between each number is equivalent to 30 degrees (360/12)

I hope this helps you!

Answer:

100

Step-by-step explanation:

10 times 10 is 100

You can add10 ten times to get the answer.

Answer:

100

Step-by-step explanation:

Answer:

B (6,7)

Step-by-step explanation:

point x has moved 2 places left, so you move z to places left

Answer:

The width of the rectangle lies between 12 and 20.

Step-by-step explanation:

Let the width of the rectangle is w.

length of the rectangle,

L = 8 w + 20

116 < L < 180

So,

116 < 8 w + 20 < 180

96 < 8 w < 160

12 < w < 20

So, the width of the rectangle lies between 12 and 20.

The solutions of given equations are x = 0,b = -3,y = 2 and c = 5 respectively.

A formula known as an equation uses the same sign to denote the equality of two expressions.

The equation must be constrained by =,< or >.

Given the equations,

01) x/4 + 2x/3 - 4 = - 4 + 5x/2

(3x + 8x)/12 = 5x/2

x = 0

02) 3.2b + 10 = -1.7b - 4.7

2.2b + 1.7b = -4.7 - 10

b = -3

03) 6.6y + y + 6.5 = y - 6.7

5.5y = -6.7 - 6.5

y = 2

04) 2c - 7c + 8 = -17

-5c = -25

c = 5

Hence "The solutions of given equations are x = 0,b = -3,y = 2 and c = 5 respectively".

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On solving the provided question we can say that median from the vertex in an isosceles triangle is perpendicular to the base.

ƒ(x)=sin(x)

consider Asin(Bx + C) = y +D changes the amplitude of the function (how high or low it is).

if you want to

Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.

Let O be the circle's centre and P be the midpoint of BC. After that, OP LBC.

Let AP =x and PB = CP -y.

Applying Pythagoras theorem in As AP B and OP B, we have

AB2 = BP2 + AP2 and OB2 = OP2 +BP2

Y2 +x2 ... (i) and, 81 = (9 —x)2 + Y2

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Answer:

33

Step-by-step explanation:

The annual interest is $22.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

Given;

Amount invested= $550

Annual interest= 4%

SI= 550*4*1/100

=5.5*4

=22

Therefore, the simple interest will be $22.

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Probability is simply how likely something is to happen. There can be many probability of the same thing to occur in future. the probability that a box of cereal will be:

A. The probability that a box of cereal will be more than one ounce underweight is equivalent to the probability of getting a weight less than 15 ounces. Using a standard normal distribution table or calculator, we can find that this probability is approximately 0.0228 or 2.28%.

B. The probability that a box of cereal will not be underweight is equivalent to the probability of getting a weight greater than or equal to 16 ounces. Using a standard normal distribution table or calculator, we can find that this probability is approximately 0.5 or 50%.

C. The likelihood that a package of cereal will weigh less than or equal to 17 ounces is the same as the likelihood that it won't be more than 1 ounce overweight. This chance can be calculated using a typical normal distribution chart or calculator as 0.9772 or 97.72%.

D. Because weight is a continuous variable with an infinitesimally tiny chance of attaining any precise value, the likelihood of receiving exactly 16 ounces is very low. The area under the normal distribution curve between 15.5 and 16.5 ounces, or roughly 0.3829 or 38.29%, can be used to determine the chance.

Possibility or probability is all game of occurrence of the thing.

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Answer: a) The probability of matching the first five selected numbers to the later five numbers drawn is given by the formula:

P = (C(69,5) / C(69,5)) * (C(5,5) / C(26,1))

where C(n,r) is the number of combinations of n items taken r at a time. The first term in the product represents the number of ways to choose the first five numbers from the pool of 69, and the second term represents the probability of choosing the correct number from the second set of 26 numbers.

Simplifying the expression, we get:

P = (1) * (1/26) = 1/26

Therefore, the probability of matching the first five selected numbers to the later five numbers drawn is 1/26.

b) The probability of matching the sixth selected number to the later number drawn from the second set is given by:

P = C(1,1) / C(26,1) = 1/26

Therefore, the probability of matching the sixth selected number to the later number drawn is 1/26.

c) The probability of winning the jackpot is the product of the probabilities of matching the first five selected numbers to the later five numbers drawn and matching the sixth selected number to the later number drawn. Using the results from parts (a) and (b), we get:

P = (1/26) * (1/26) = 1/676

Therefore, the probability of winning the jackpot is 1 in 676.

Step-by-step explanation:

Check the picture below.

Answer:

5761

Step-by-step explanation:

First, let's find the digit in the tenths place. The quotient of 10 and 2 is 5 because 10/2 = 5. Next, the digit in the hundredths place is the product of 3.5 and 2. 3.5 * 2 = 7. The number in the thousandths place is the sum of the digit in the tenths place and the ten thousandths place, so we have to find the digit in the ten thousandths place first. It says that every number in the code is divisible by the digit in the ten thousands place. The factors of 5 are 1,5 and the factors of 7 are 1,7. The only number that is the same in both is 1, so the last digit must be 1. Knowing that information, we can add the digit in the tenths place (5) to the number in the ten thousandths place (1) to get the third digit (6). Now we place those digits in order: tens (5), hundredths (7), thousandths (6), and ten thousandths (1) to get 5761.

Answer:

(7/8 - 4/5)^2 = 9/

1600

= 0.005625

Answer:

length times width equals area LxW=Area

Step-by-step explanation:

so,

4 times 4= 26 yards

1=4 square yards

then 26X4 = 104 square yards

Answer:

Step-by-step explanation:

Answer:

y=4(9)x

Hope it helps

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Thank you

Step-by-step explanation:

70 ÷ 3 = 23  1/3