Answers
Answer:
200√3
Step-by-step explanation:
The triangle given here is a special right triangle, one with angles measuring 30-60-90 degrees. The rule for triangles like these are that the side opposite the 30° angle can be considered x, and the side opposite the 60° angle is x√3, while the hypotenuse, or side opposite the right angle, is 2x. All we need to know here are the two legs to find the area.
Since b is opposite the 30° angle, it is x, while side RS is opposite the 60° angle, meaning it is equal to x√3, meaning that the area of the triangle is 1/2*x*x√3. We can substitute in 20 for x, making our area 1/2*20*20√3. Multiplying we get 10*20√3, or 200√3.
Related Questions
whats 1/2 + 2/4 - 5/8?
Answers
Answer:
3/8
Step-by-step explanation:
Step 1: Find common denominators
1/2 = 4/8
2/4 = 4/8
Step 2: Evaluate
4/8 + 4/8 - 5/8
8/8 - 5/8
3/8
Alternatively, you can just plug this into a calc to evaluate and get your answer.
Answer:
3/8
Step-by-step explanation:
Look at the denominator:
2, 4, 8. The LCM (Lowest Common Multiple) is 8.
So this equation becomes
4/8+4/8-5/8=3/8
Simple linear equations
Check Whether the value given in the brackets is the root of the given equation or not (nessessary steps is needed)
a) 4x = -4 [x=-1]
b) 2(x-3) =-12 [x=3]
c) 8x - 4x = 24 [x = 1/2]
d) 9x - 4x = 24 [x=18]
Answers
Answer: Evaluate the Function, right?
Hello!
~~~~~~~~~~~~~~~~~~
A) 4x = -4 [x=-1] =
4x = -4 =
x = -1 = x = -1
( The steps : Substitute the given value into the function and evaluate.)
B) 2(x-3) =-12 [x=3] =
2 ( x - 3) = -12 = x = -3
x = 3 = x = 3
( The steps : Substitute the given value into the function and evaluate.)
C) 8x - 4x = 24 [x = 1/2] =
8x - 4x = 24 = x = 6
x = 1/2 = x = 1/2
( The steps : Substitute the given value into the function and evaluate.)
D) 9x - 4x = 24 [x=18] =
9x - 4x = 24 = x = 24/5
x = 18 = x = 18
( The steps : Substitute the given value into the function and evaluate.)
~~~~~~~~~~~~~~~~~~
Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.
Hope this helped you!
Find the slope-intercept form of the line through (6, – 3) and perpendicular to the line y = 3x – 5.
Answers
Answer:
y=-1/3x-1
Step-by-step explanation:
We have the information y=3x-5, the lines are perpendicular, and the new line passes through (6,-3). The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 3, so flip it to 1/3 and multiply by -1, we get the slope of the new line as -1/3. So far we have the equation y=-1/3x+b. We are given a point on the line, (6,-3), so we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as -3=-1/3(6)+b. First you multiply to get -3=-2+b, then you add 2 to both sides to isolate the variable and you get b=-1. Then you can use b to complete your equation with y=-1/3x-1.
Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Answers
Answer:
paper = $4 and stapler = $7
Step-by-step explanation:
let p represent paper and s represent stapler, then
3p + 4s = 40 → (1)
5p + 6s = 62 → (2)
Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p
15p + 20s = 200 → (3)
- 15p - 18s = - 186 → (4)
Add (3) and (4) term by term to eliminate p
2s = 14 ( divide both sides by 2 )
s = 7
Substitute s = 7 into either of the 2 equations and evaluate for p
Substituting into (1)
3p + 4(7) = 40
3p + 28 = 40 ( subtract 28 from both sides )
3p = 12 ( divide both sides by 3 )
p = 4
Thus package of paper costs $4 and stapler costs $7
3
Select the correct answer.
What are the solutions to this equation?
16x² + 9 = 25
Answers
Answer:
Step-by-step explanation:
16x^2 + 9 = 25
16x^2 = 16
x^2 = 1
x = 1, -1
A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed.
a. Write a mathematical model representing the store's constraints.
b. Suppose the profit on sofas is $200 and on chairs is $100. On a given day, the probability that a displayed sofa will be sold is 0.03 and that a displayed chair will be sold is 0.05. Mathematically model each of the following objectives:
1. Maximize the total pieces of furniture displayed.
2. Maximize the total expected number of daily sales.
3. Maximize the total expected daily profit.
Answers
Answer:
a) 50S + 30C ≤ 800
b) 1) MAX = S + C
2) Max = 0.03S + 0.05C
3) Max = 6S + 5C
Step-by-step explanation:
Given:
Total space = 800 square feet
Each sofa = 50 square feet
Each chair = 30 square feet
At least 5 sofas and 5 chairs are to be displayed.
a) Write a mathematical model representing the store's constraints:
Let S denote number of sofas displayed and C denote number of chairs displayed.
The mathematical model will be:
50S + 30C ≤ 800
At least 5 sofas are to be dispayed: S ≥ 5
At least 5 chairs are to be displayed: C ≥ 5
b)
1) Maximize the total pieces of furniture displayed:
S + C = MAX
2) Maximize the total expected number of daily sales:
MAX = 0.03S + 0.05C
3) Maximize the total expected daily profit:
Given:
Profit on sofas = $200
Profit on chairs = $100
Max Expected daily profit =
Max = (200S * 0.03) + (100C * 0.05)
Max = 6S + 5C
Find the vector x determined by the given coordinate vector [x]B and the given basis B.
B = {[1 -3 1], [-3 8 3],[8 -2 3]}, [x]_B = [-3 -2 3]
a. [9 -13 0]
b. [0 -6 21]
c. [13 -24 -2]
d. [3 -13 16]
Answers
3. A 12 % discount on a pair of washer and dryer that Gayle purchased, amounted to $156.00.
Calculate the net price.
Answers
Answer:
For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:
[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]
Where x represent the net price. And if we solve for the value of x we got:
[tex] x= 100 *\frac{156}{88}= 177.273[/tex]
So then the net price for this case would be $ 177.273
Step-by-step explanation:
For this case we know that the price after the 12% of discount is 156 and we want to findd the net price so then we can use the following proportional rule:
[tex] \frac{x}{100} = \frac{156}{100-12}[/tex]
Where x represent the net price. And if we solve for the value of x we got:
[tex] x= 100 *\frac{156}{88}= 177.273[/tex]
So then the net price for this case would be $ 177.273
Christopher collected data from a random sample of 800 voters in his state asking whether or not they would vote to reelect the current governor. Based on the results, he reports that 54% of the voters in his city would vote to reelect the current governor. Why is this statistic misleading?
Answers
Answer:
The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).
Step-by-step explanation:
The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).
He should make inferences about the population that is well represented by his sample (voters in his state), or take a sample only from voters from his city to make inferences about them.
Is (0,-2) a solution of 3x - y = 2?
Answers
Answer:
yes, (0,-2) is the answer when graphing this equation.
Step-by-step explanation:
Answer:
yes.
Step-by-step explanation:
You just purchased two coins at a price of $1,030 each. Because one of the coins is more collectible, you believe that its value will increase at a rate of 7.7 percent per year, while you believe the second coin will only increase at 7.1 percent per year. If you are correct, how much more will the first coin be worth in 20 years
Answers
Answer:4541(Rounded) 4541.99779(Unrounded)
Step-by-step explanation:
A= P(1 + r)^T
A= answer
P=principle(amount of money)
r=Rate(percent / 100)
T=Time(Annually)
1030(1 + .077)^20
Brainliest would be appericiated!
. The client was hoping for a likability score of at least 5.2. Use your sample mean and standard deviation identified in the answer to question 1 to complete the following table for the margins of error and confidence intervals at different confidence levels. Note: No further calculations are needed for the sample mean. (6 points: 2 points for each completed row) Confidence Level | Margin of error | Center interval | upper interval | Lower interval 68 95 99.7
Answers
Answer:
The 68% confidence interval is (6.3, 6.7).
The 95% confidence interval is (6.1, 6.9).
The 99.7% confidence interval is (5.9, 7.1).
Step-by-step explanation:
The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\bar x[/tex]
And the standard deviation of the sample means (also known as the standard error)is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]
As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.
(a)
Compute the 68% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]
The 68% confidence interval is (6.3, 6.7).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]
(b)
Compute the 95% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]
The 95% confidence interval is (6.1, 6.9).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]
(c)
Compute the 99.7% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]
The 99.7% confidence interval is (5.9, 7.1).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]
Given that (0,0) is on the graph of f(x), find the
corresponding point for the function
f(x) – 5.
Answers
Answer:
(0, -5)
Step-by-step explanation:
You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).
That would be ...
(x, f(x) -5) = (0, 0 -5) = (0, -5)
1. Which of these is a Pythagorean triple?
(a) (3, 4, 5)
(b) (5, 6, 7)
(c) (10, 11, 12)
(d) (15, 16, 17)
2. If y2 = 172 – 82. What is the value of y?
(a) 10
(b) 25
(c) 15
(d) 16
3. How many kilograms are there in 5 tonnes?
(a) 500 kg
(b) 50 000 kg
(c) 5, 000 kg
(d) 50 kg
4. If the probability that a girl win a race is 0.6. What is the probability that that the girl loses the race?
(a) 0.4
(b) 1
(c) 4
(d) 6
5. The distance from Lagos to Ibadan can be measured using which of the following units of measurement?
(a) centimeter
(b) Millimeter
(c) Kilograms
(d) Kilometer
6. The longest side of a right-angled triangle is called?
(a) right side
(b) Opposite
(c) Hypotenuse
(d) None of the above
7. The mass/weight of your pen can be measured using………
(a) Grams
(b) Kilometer
(c) Centimetre
(d) Tonne
8. There 5 blue balls, 8 red balls and 2 black balls in a basket. One ball is picked at random. Find the probability that the ball picked is red.
(a) 58
(b) 815
(c) 215
(d) 13
9. The mass of a lorry can be measured using which of the following?
(a) liter
(b) Kilometer
(c) Tonne
(d) Milligram
10. How many tonnes are there in 15 000 kg?
(a) 150 tonnes
(b) 15 tonnes
(c) 1500 tonnes
(d) 1.5 tonnes
11. What is 20% of #38 000?
(a) #7 600
(b) #3 800
(c) #2 800
(d) #760
12. Express 17:30 hours as a.m. or p.m. time.
(a) 7:30 pm
(b) 7:30 a.m.
(c) 5:30 p.m.
(d) 5:30 a.m.
13. Angle 900 is also called?
(a) left angle
(b) quarter angle
(c) right angle
(d) middle angle
14. “Kilo” is a Greek word from the word “khilioi” meaning what?
(a) Million
(b) Thousand
C) Billion
D) Hundred
15. Which is the most widely used system of measurement in the world?
(a) tape rule system
(b) counter system
(c) metric system
(d) none of the above
PART B
ANSWER ALL QUESTIONS
1. The largest unit of measurement for distance/length is kilometer. True or false …………………….
2. The probability that a student fails an examination is 0.2. What is the probability that the student passes the examination? .................
The members of a village cooperative agree to contribute time and money towards a one year village improvement programme (VIP). Below is the table of activities of the programme.
Activity
Time (hour)
Money(#)
Planting/ watering trees
300
20 000
Collecting/burning rubbish
200
0
Clearing storm ditches
80
5 000
Making speed bumps
20
5 000
3. How much is the total money pledged? …………..
4. Which activity takes more money? ………………..
5. Which activity cost no money? ……………………….
Answers
Answer
1. (a) (3,4,5)--3^2 +4^2=9+16=25=5^2
2. (b) 25--172-82=50/2=25
3. (c) 5,000 kg--1,000 kg in 1 tonne
4. (a) 0.4--1-0.6=0.4
5. (d) kilometer
6. (c) hypotenuse
7. (a) grams
8. i think it is (a) 58--5+8+2=15~~8/15 =0.53~closest answer is 58
9. (c) tonne
10. (b) 15 tonnes--1000 kg in 1 tonne
11. (a) #7,600--38000*20%, or 0.20, =7,600
12. (a) 7:30 pm
13. (c) right angle
(c) metric system
Part B
1. True
2. 0.8
3. 30,000 dollars--20,000 +0+5,000+5,000=30,000
4. Planting/watering trees--20 dollars
5. Collecting/burning rubbish--0 dollars
You wish to accumulate $14,580 in 6 years. Payments are made at the end of every six-month period into an account earning 7.2% compounded semi-annually. Find the required payment amount to accomplish your goal.
Answers
an • 1.072^n = 14,580
Where a = payment every half year and n = number of half years
There are 12 half years in 6 years.
Therefore n = 12, substitute this.
12a • 1.072^12 = 14,580
12a = 14,580 / 1.072^12
12a = 6,330~
a = 527.5 ~
An adult has a total of about 22.5 square feet (ft2) of skin. Use the fact that 1 m is approximately equal to 3.281 feet to convert this measurement to square meters (m2). Round your answer to the nearest hundredth. Do not type the units in the space below.
Answers
Answer:
There are about 3.281 * 3.281 = 10.764 square feet in one square meter. Therefore, 22.5 square feet is 22.5 / 10.764 = 2.09 square meters.
Past studies have indicated that the percentage of smokers is estimated to be about 35%. Given the new smoking cessation programs that have been implemented, you now believe that the percentage of smokers has reduced. a) If you going to test this claim at the 0.05 significance level, what would be your null and alternative hypotheses
Answers
Answer:
H0: p = 3.5
H1: p < 3.5
Step-by-step explanation:
We are told that past studies have indicated that the percentage of smokers is estimated to be about 35%, but with the new smoking cessation programs that have been implemented, it is believed that the percentage of smokers has been reduced, we must propose our null and alternative hypotheses, which would be the following:
Null hypothesis: H0: p = 3.5
Alternative hypothesis: H1: p < 3.5
Arrange in ascending order. 8/13, 2/9,28/29
Answers
Step-by-step explanation:
he operation of sorting fractions in ascending order: 18/46, 28/41, 29/38, 29/44, 32/30 ... terms equivalents: 18/46=(2×3^2)/(2×23)=((2×3^2)÷2)/((2×23)÷2)=9/23; 28/41 already reduced to ... by the largest exponents: LCM (9, 28, 29)=2^2×3^2× 7×29=7308 Calculate LCM, the least ... /10 </13 </19
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.05 for the estimation of a population proportion
Answers
Answer:
A sample of 385 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How large a sample:
We need a sample of n.
n is found when M = 0.05.
We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]
[tex]n = 384.16[/tex]
Rounding up
A sample of 385 is needed.
Find the values of x and y in these equations. (x + yi) + (4 + 6i) = 7 − 2i (equation A) (x + yi) − (-8 + 11i) = 5 + 9i (equation B)
Answers
Answer:
Step-by-step explanation:
(x+yi)+4+6i=7-2i
x+yi=7-2i-4-6i
x+yi=3-8i
equating real and imaginary parts
x=3,y=-8
B.
x+yi=5+9i+(-8+11i)
x+yi=5+9i-8-11i
x+yi=-3-2i
equating real ,and imaginary parts
x=-3
y=-2
The value of x and y for equation A is
[tex]x=3, y=-8[/tex]
The value of x and y for equation B is
[tex]x=-3 , y=20[/tex]
Given :
[tex](x + yi) + (4 + 6i) = 7 - 2i[/tex]
find the value of x and y in the given equation
Lets open the parenthesis and combine like terms
Equate the real and imaginary part to solve for x and y
[tex]\left(x+4\right)+\left(y+6\right)i=7-2i\\x+4=7\\x=3\\\\y+6=-2\\y=-2-6\\y=-8[/tex]
The value of x=3 and y=-8
Now we do the same with second equation
[tex](x + yi) - (-8 + 11i) = 5 + 9i\\\\x+8+yi-11i=5+9i\\\left(x+8\right)+\left(y-11\right)i=5+9i\\x+8=5\\x=-3\\\\y-11=9\\y=9+11\\y=20[/tex]
The value of x and y is x=-3 and y=20
Learn more : brainly.com/question/18552411
A simple random sample of 20 items resulted in a sample mean of 10. The population standard deviation is = 3. Round your answers to two decimal places.
a. What is the standard error of the mean, ?
b. At 95% confidence, what is the margin of error?
Answers
Answer:
a. 0.67
b. 1.31
Step-by-step explanation:
We have the following information n = 20, mean (m) = 10 and standard deviation (sd) = 3
a.
SE (m) = sd / n ^ (1/2)
replacing we have:
SE (m) = 3/20 ^ (1/2) = 0.67
Therefore the standard error of the mean is 0.67
b.
the critical value is obtained as shown below:
the level of sifnificance is alfa = 1 - 0.95 = 0.05
the critical value with level of significance alfa / 2 = 0.05 / 2 = 0.025
and to this value corresponds z = 1.96 (z table)
The margin of error with 95 confidence is calculated as follows:
E = z * SE
E = 1.96 * 0.67
E = 1.31
Therefore the margin of error is 1.31
(a) The standard error will be "0.67".
(b) The margin of error will be "1.31".
According to the question,
Standard deviation,
sd = 3Sample size,
n = 20(a)
As we know,
→ The Standard error,
= [tex]\frac{sd}{\sqrt{n} }[/tex]
= [tex]\frac{3}{\sqrt{20} }[/tex]
= [tex]0.67[/tex]
(b)
As we know,
→ The margin of error,
= [tex]Z_{a/2}\times \frac{sd}{\sqrt{n} }[/tex]
By substituting the values, we get
= [tex]Z_{a/2}\times \frac{3}{\sqrt{20} }[/tex]
= [tex]1.96\times 0.67[/tex]
= [tex]1.31[/tex]
Thus the above response is right.
Learn more:
https://brainly.com/question/10501147
Use ￢, →, ∧ and ∨ to express the following declarative sentences in propositional logic; in each case state what your respective propositional atoms p, q, etc. a) If interest rates go up, share prices go down. b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. c) Today it will rain or shine, but not both. d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. e) My sister wants a black and white cat.
Answers
Answer:
a) If interest rates go up, share prices go down : this will be assigned p→q
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r)
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q)
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r)
e) My sister wants a black and white cat. p∧q
Step-by-step explanation:
A statement is said to be propositionally logical if the statement that can be assigned either true or false.
∧and
∨or
¬not
→implies
a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur
e) My sister wants a black and white cat. p∧q : both events can only occur together
Find the percent of increase. Original Price: $200 Retail Price: $250
Answers
Answer:
The percent of increase is 25%
Step-by-step explanation:
Percentage increase = increase in price/original price × 100 = ($250 - $200)/$200 × 100 = $50/$200 × 100 = 25%
calculate find the area f a rectangle measuring 25 feet long by 8 feet wide
Answers
Answer: 200 ft²
Step-by-step explanation:
The area of a rectangle is length times width
So, simply do 25 * 8 = 200
Hey there! :)
Answer:
A = 200 ft².
Step-by-step explanation:
Use the formula A = l × w to determine the area of a rectangle:
A = 25 × 8
Multiply:
A = 200 ft².
Write a two column proof Given: AB || DC; BC || AE Prove: BC/EA = BD/EB
Answers
Answer:
Step-by-step explanation:
Given:
AB║DC and BC║AE
To prove:
[tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex]
Statements Reasons
1). ∠ABE ≅ ∠CDB 1). Alternate interior angles
2). ∠AEB ≅ ∠CBD 2). Alternate interior angles
3). ΔCBD ~ ΔAEB 3). AA property of similarity
4). [tex]\frac{\text{BC}}{\text{EA}}=\frac{\text{BD}}{\text{EB}}[/tex] 4). Property of similarity [Corresponding sides of two similar triangles are proportional]
help with this I don't know how to solve
Answers
Answer:
86.53
Step-by-step explanation:
Area of Triangle Formula: A = 1/2bh
Pythagorean Theorem: a² + b² = c²
Step 1: Draw altitude and label numbers
If we draw a line down the middle, we can see that we get a perpendicular bisector and that we get 2 right triangles with a hypotenuse of 29 and a leg of 3. We need to find h using Pythagorean Theorem in order to use area formula:
3² + b² = 29²
b² = 29² - 3²
b = √832 = h
Step 2: Plug in known variables into area formula:
A = 1/2(√832)(6)
A = 3√832
A = 86.5332
The mean weight of an adult is 6767 kilograms with a variance of 121121. If 164164 adults are randomly selected, what is the probability that the sample mean would be greater than 64.864.8 kilograms
Answers
Answer:
99.48% probability that the sample mean would be greater than 64.8 kilograms.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 67, \sigma = \sqrt{121} = 11, n = 164, s = \frac{11}{\sqrt{164}} = 0.86[/tex]
What is the probability that the sample mean would be greater than 64.8 kilograms?
This is 1 subtracted by the pvalue of Z when X = 64.8.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.8 - 67}{0.86}[/tex]
[tex]Z = -2.56[/tex]
[tex]Z = -2.56[/tex] has a pvalue of 0.0052
1 - 0.0052 = 0.9948
99.48% probability that the sample mean would be greater than 64.8 kilograms.
HELP PLEASE!!!! I NEED HELP ASAP Which statement best describes the expression 3 + y ÷ 2? The quotient of 2 and the sum of 3 and y The quotient of the sum of 3 and y, and 2 The sum of 3 and the quotient of 2 and y The sum of 3 and the quotient of y and 2
Answers
Answer:
I believe it is D
Answer:
The sum of 3 and the quotient of y and 2.
Step-by-step explanation:
The order of operations requires that you evaluate the expression ...
3 + y ÷ 2
by first performing the division, then the addition. So, the addition gives you the sum of 3 and a quotient, because the quotient must be evaluated first.
The quotient is of y and 2 (not 2 and y), because the wording "the quotient of a and b" is always interpreted to mean a÷b.
So, the expression can be described as ...
the sum of 3 and the quotient of y and 2.
help help help help pls
Answers
Hi !!
For f(x) = 3/x + 4 , B is correct.
• f(-3) = 3/(-3) + 4
f(-3) = - 1 + 4
f(-3) = 3
• f(-2) = 3/(-2) + 4
f(-2) = -1,5 + 4
f(-2) = 2,5
• f(1) = 3/(1) + 4
f(1) = 3 + 4
f(1) = 7
• f(2) = 3/(2) + 4
f(2) = 1,5 + 4
f(2) = 5,5
• f(3) = 3/(3) + 4
f(3) = 1 + 4
f(3) = 5
Suppose a random variable X is best described by a uniform probability distribution with range 1 to 5. Find the value of that makes the following probability statements true.
a) P(X <-a)= 0.95
b) P(X
c) P(X
d) P(X ->a)= 0.89
e) P(X >a)= 0.31
Answers
Answer:
a) 4.8
b) 2.96
c) 4.4
d) 1.44
e) 3.76
Step-by-step explanation:
What we will do is solve point by point, knowing the following:
Fx (x) = P (X <= x) = (x - 1) / 4
a) P (X <-a) = 0.95
Fx (a) = 0.95
(a -1) / 4 = 0.95
a = 1 + 0.95 * 4
a = 4.8
b) P (X <a) = 0.49
Fx (a) = 0.49
(a -1) / 4 = 0.49
a = 1 + 0.49 * 4
a = 2.96
c) P (X <a) = 0.85
Fx (a) = 0.85
(a -1) / 4 = 0.55
a = 1 + 0.85 * 4
a = 4.4
d) P (X> a) = 0.89
P (X <a) = 1 - 0.89 = 0.11
Fx (a) = 0.11
(a -1) / 4 = 0.11
a = 1 + 0.11 * 4
a = 1.44
e) P (X> a) = 0.31
P (X <a) = 1 - 0.31 = 0.69
Fx (a) = 0.69
(a -1) / 4 = 0.69
a = 1 + 0.69 * 4
a = 3.76