cosine = adjacent / hypotenuse
So that means the adjacent side = 15 and the hypotenuse = 17
By Pythagorean Theorem, we know that
opposite^2 = hypotenuse^2 - adjacent^2
opposite^2 = 17^2 - 15^2
opposite^2 = 289 - 225
opposite^2 = 64
opposite side = 8
sine = opposite / hypotenuse
So,
sine A = 8 / 17
A simple random sample of electronic components wil be selected to test for the mean lifetime in hours. Assume that component lifetimes are normally distributed with population standard deviation of 16 hours. How many components must be sampled so that a 99% confidence interval will have margin of error of 3 hours
Answer:
189 components must be sampled.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
Assume that component lifetimes are normally distributed with population standard deviation of 16 hours.
This means that [tex]\sigma = 16[/tex]
How many components must be sampled so that a 99% confidence interval will have margin of error of 3 hours?
n components must be sampled.
n is found when M = 3. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]3 = 2.575\frac{16}{\sqrt{n}}[/tex]
[tex]3\sqrt{n} = 2.575*16[/tex]
[tex]\sqrt{n} = \frac{2.575*16}{3}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575*16}{3})^2[/tex]
[tex]n = 188.6[/tex]
Rounding up:
189 components must be sampled.
Winston typically spends about $200 per year playing the lottery. If he took that same
amount of money, for 30 years, and invested it in an index fund earning an average of
6%, approximately how much money would Winston have?
A. More than $12,000, because the investment will grow faster over time as the interest
compounds.
B. Less than $6000, because inflation would make his money less valuable.
C. Exactly $6000.
D. Approximately $6360, because he earns almost $400 in interest.
Answer:
point!!!!!!!
Step-by-step explanation:
Winston would have A. More than $12,000, because the investment will grow faster over time as the interest compounds.
If Winston invested $200 every year at 6% for 30 years, the $200 would be an annuity and the future value of an Annuity is calculated as:
= Annuity x ( (1 + rate) ^ number of years - 1) / rate
= 200 x ( ( 1 + 6%) ³⁰ - 1) / 6%
= $15,811.64
Winston would have $15,811.64 which is more than $12,000 because compounded interest makes investments grow faster.
Find out more at https://brainly.com/question/14761171.
Which angle had a positive measure?
Answer:
the second angle
sorry if wrong
Step-by-step explanation:
I need help with six and seven plz
Answer:
6) 102
7) 58
NOTE: Supplementary add to 180° and Complementary add to 90°
Please mark as brainliest if answer is right
Have a great day, be safe and healthy
Thank u
XD
what is the effect on the graph of f(x)=x^2 when it is transformed to h(x)=1/8x^2-13?
a.the graph of f(x) is vertically compressed by a factor of 8 and shifted 13 units to the right
b. the graph of f(x) is vertically compressed by a factor of 8and shifted 13 units down
c. the graph of f(x) is horizontally compressed by a factor of 8 and shifted 13 units down
d. the graph or f(x) is horizontally stretched by a factor of 8 and shifted 13 units to the right
please help!
The transformation of a function may involve any change. The correct option is D.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)Right shift by c units: y=f(x-c)(same output, but c units late)Vertical shift:
Up by d units: y = f(x) + d Down by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k \times f(x)Horizontal stretch by a factor k: y = f\left(\dfrac{x}{k}\right)The given function f(x)=x² is transformed to h(x)=(1/8)x^2-13, therefore, the graph or f(x) is horizontally stretched by a factor of 8 and shifted 13 units to the right.
Hence, the correct option is D.
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Answer:
A.the graph of f(x) is vertically compressed by a factor of 8 and shifted 13 units to the right
Miguel draws a square on a coordinate plane. One vertex is located at (5,4). The length of each side is 3 units. Circle the letter by all the ordered pairs that could be another vertex. A. (5,1) B. (5,7) C. (7,8) D. (2,6) E. (2,1)
I will give brainliest if you answer both questions!
Answer:
A, B, and E.
Step-by-step explanation:
We know that one vertex is at (5, 4), and each side of our square is 3 units long.
Then the distance between the known vertex and another vertex is 3 units (if those vertexes are connected by a side of the square) or (√2)*3 units (if those vertexes are connected by the diagonal of the square).
Also remember that the distance between two points (a, b) and (b, c) is:
distance = √( (a - c)^2 + (b - d)^2)
So we need to find the distance between our point and all the ones given in the options:
A) the distance between (5, 4) and (5, 1) is:
distance = √( (5 - 5)^2 + (4 - 1)^2) = 3
Then point (5, 1) can be a vertex.
B) The distance between (5, 4) and (5, 7) is:
distance = √( (5 - 5)^2 + (4 - 7)^2) = 3
Then (5, 7) can be a vertex.
C) The distance between (5, 4) and (7, 8) is:
distance = √( (5 - 7)^2 + (4 - 8)^2) = √( 2^2 + 4^2) = √20
Point (7, 8) can not be a vertex.
D) The distance between (5, 4) and (2, 6) is:
distance = √( (5 - 2)^2 + (4 - 6)^2) = √( 3^2 + 2^2) = √13
Point (2, 6) can not be a vertex.
E) The distance between (5, 4) and (2, 1) is:
distance = √( (5 - 2)^2 + (4 - 1)^2) = √( 3^2 + 3^2) = √18 = √(2*9) = √2*√9 = √2*3
Then point (2, 1) can be a vertex.
13) 7x - 4x
A) 2 - 3x
B) -X
C) 8x
D) 3x
Pam flips a coin 12 times. The coin lands on heads 8 times. What is the theoretical
probability of landing on heads on the next flip?
Answer:
If a coin is tossed 12 times, the maximum probability of getting heads is 12. But, 12 coin tosses leads to 212 , i.e. 4096 number of possible sequences of heads & tails.
Step-by-step explanation:
Answer:
8/13
Step-by-step explanation:
Pam flips a coin 12 times. The coin lands on heads 8 times. What is the theoretical
probability of landing on heads on the next flip?
well it would be 8 and 13
Determine the value of x in the diagram.
Answer:
Hello! answer: x = 68
Hope this helps!
Answer:
x = 68⁰
Step-by-step explanation:
112+112+68+x = 360 (Theorem - The sum of the internal angles of a square is 360.)
292⁰+x = 360⁰
x = 360⁰ - 292⁰
x = 68⁰
A bike travels 24 miles in 3 hours. At this rate, how many miles will the bike travel in 10 hours?
A 129 miles
B 80 miles
C 32 miles
D 124 miles
Answer:
B) 80 miles
Step-by-step explanation:
Answer:
80 mlies,
Step-by-step explanation:
how I got it. 24÷3 hours is 8miles per hour multiple by 10=80miles
I need help on ( NUMBER 10 )!!
Answer:
Box 1 = -2 and Box 2=+1.......
Answer:
-2.5 if you have to write as a decimal and not a fraction.
cathi scored 6 baskets in each of her last 3 basketball games. Each basket was worth 2 points. how many points did cathi score in all her games? Write an expression and solve.
Answer:
p=36
Step-by-step explanation:
3(6*2)=p
3(12)=p
36=p
Sorry if its hard to understand I'm new to anwering questions on brainly
i need solution to these two questions please
Answer:
Step-by-step explanation:
4). Given functions are,
[tex]f(x)=\frac{1}{3x}[/tex]
For [tex]x=\frac{1}{12}[/tex]
[tex]f(\frac{1}{12})=\frac{1}{3(\frac{1}{12})}[/tex]
[tex]=\frac{1}{\frac{1}{4}}[/tex]
[tex]=1\times\frac{4}{1}[/tex]
[tex]=4[/tex]
[tex]g(x)=\frac{1}{x^2}[/tex]
For [tex]x=\frac{1}{5}[/tex],
[tex]g(\frac{1}{5})=\frac{1}{(\frac{1}{5})^2}[/tex]
[tex]=\frac{1}{\frac{1}{25}}[/tex]
[tex]=25[/tex]
[tex]f(\frac{1}{12})-g(\frac{1}{5})=4-25[/tex]
[tex]=-21[/tex]
5). f(x) = -2x² + 3x - 8
f(k + 4) = -2(k + 4)² + 3(k + 4) - 8
= -2(k² + 8k + 16) + 3(k + 4) - 8
= -2k² - 16k - 32 + 3k + 12 - 8
= -2k² - 13k - 28
A woman standing on a hill sees a flagpole that she knows is 55 ft tall. The angle of depression to the bottom of the pole is 14°, and the angle of elevation to the top of the pole is 18°. Find her distance x from the pole. (Round your answer to one decimal place.)
Answer:
Round to one decimal place: x=78.4ft
Step-by-step explanation:
I searched it up : )
What is the P(A and B) given that P(A) = 0.53, P(B) = 0.39, and P(A or B) = 0.48
Answer:
P(A and B) = 0.44
Step-by-step explanation:
Venn probabilities:
Suppose that we have two events, A and B. The probability of A and B is:
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]
In which [tex]P(A \cup B)[/tex] is P(A or B).
In this question:
[tex]P(A) = 0.53, P(B) = 0.39, P(A \cup B) = 0.48[/tex]
Then
[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.53 + 0.39 - 0.48 = 0.44[/tex]
So
P(A and B) = 0.44
Jennys room is 13 feet long and 12 feet wide, Ruth's room is 14 feet long and 11 feet wide, whose room has the greater area?
Answer:
Jenny's room
Step-by-step explanation:
13x12 = 156 and 14x11 = 154
Therefore Jenny's room is bigger.
Answer please and explain
Evaluate ab-c, if a = 7,b = 8, and c = 12
Answer:
44
Step-by-step explanation:
axb=56
56-c=44
what will come in the following series 20 25 23 28 26 31 29 34 _? answer is 31. please explain how?? urgent pls
The series of numbers is adding 5 and then subtracting 2
20+5=25
25-2=23
23+5=28
28-2=26
and so on. Do you understand?
What is the perimeter of parallelogram RSTU, rounded to the nearest whole number?
Given:
The vertices of the parallelogram RSTU are R(-4,4), S(2,6), T(6,2) and U(0,0).
To find:
The perimeter of parallelogram RSTU, rounded to the nearest whole number.
Solution:
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the distance formula, we get
[tex]RS=\sqrt{(2-(-4))^2+(6-4)^2}[/tex]
[tex]RS=\sqrt{(6)^2+(2)^2}[/tex]
[tex]RS=\sqrt{36+4}[/tex]
[tex]RS=\sqrt{40}[/tex]
[tex]RS=6.32[/tex]
Similarly,
[tex]ST=\sqrt{\left(6-2\right)^2+\left(2-6\right)^2}[/tex]
[tex]ST\approx 5.66[/tex]
[tex]TU=\sqrt{\left(0-6\right)^2+\left(0-2\right)^2}[/tex]
[tex]TU\approx 6.32[/tex]
[tex]RU=\sqrt{\left(0-\left(-4\right)\right)^2+\left(0-4\right)^2}[/tex]
[tex]RU\approx 5.66[/tex]
Now, the perimeter of the parabola is:
[tex]P=RS+ST+TU+RU[/tex]
[tex]P=6.32+5.66+6.32+5.66[/tex]
[tex]P=23.96[/tex]
[tex]P\approx 24[/tex]
The perimeter of the parallelogram RSTU is 24 units.
Therefore, the correct option is C.
Note: Unit of perimeter cannot be in square.
Sharon buys fabric that costs $6 per yard. She wants to find the number of yards of fabric she can buy for $20. She finds the answer using the problem. 3 r2 6 120 -18 2 Sharon can buy 3 yards of fabric. What does the remainder mean? A. She will have $2 left over. B. She can buy 2 more yards of fabric. O C. She will have 2 yards of fabric left over. D. She needs $2 more to buy another yard of fabric.
Answer:
A. She will have $2 left over
Step-by-step explanation:
I know this because 3 yards of fabric cost $18 dollars so there would be $2 left
-7x+2y =18 in slope intercept
and 6x+6y =0
Answer:
y=3.5x+9
and
y=x
The amount that Gretchen charges for babysitting is proportional to the number of hours she babysits. She charges $18 to babysit for
1.5 hours
Which equation relates the amount Gretchen charges in dollars, c, and the amount of time in hours that she babysits, h?
Answer:
Gretchen charges $12 dollars per hour
Step-by-step explanation:
$18/1.5=$12
30 POINTS! HELP!!
The table shows the probability distribution of siblings of students in a high school with 1500 students. What is the expected value for the number of siblings of a randomly chosen student?
A. 2.5
B. 1.29
C. 1.08
D. 1.11
The expected value for the number of siblings of a randomly chosen student is 1.11.
What is expected value mean?"In a probability distribution, the weighted average of possible values of a random variable, with weights given by their respective theoretical probabilities, is known as the expected value".
For the given situation,
The table shows the probability distribution of siblings of students in a high school with 1500 students.
For number of siblings = 0, Probability = 0.18.
For number of siblings = 1, Probability = 0.65.
For number of siblings = 2, Probability = 0.09.
For number of siblings = 3, Probability = 0.05.
For number of siblings = 4, Probability = 0.02.
For number of siblings = 5, Probability = 0.01.
The formula for expected value mean, E(x) = ΣxP(x)
[tex]E(x)=(0)(0.18)+(1)(0.65)+(2)(0.09)+(3)(0.05)+(4)(0.02)+(5)(0.01)[/tex]
⇒ [tex]E(x)=1.11[/tex]
Hence we can conclude that the expected value for the number of siblings of a randomly chosen student is 1.11.
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Help please i have no idea where to even start???
Answer:
Actually, all of them!
Hope that helps! :)
-Aphrodite
Step-by-step explanation:
Jason Is vacationing on the beach and wants to rent an ATV. The table below shows the cost of renting an ATV Including the helmet. What would be the cost of the helmet?
A. $15
B. $20
C. $25
D. $30
Solve the system of equations.
y= x + 3
y= x2 - 2x-1
Please help :)
9514 1404 393
Answer:
C. (-1, 2) and (4, 7)
Step-by-step explanation:
It may be simplest just to try the answer choices.
We notice that y = x+3 is not satisfied by the points in choices A or D, so those can be eliminated.
__
The second equation can be written in vertex form as ...
y = (x -1)^2 -2
This equation is not satisfied by the points of choice B.
Using (-1, 4) (from choice B), we get 4 = (-1-1)^2 -2 = 4-2 = 2 . . . FALSE.
However it is a good match for the points of choice C.
Using (-1, 2) (from choice C), we get 2 = (-1-1)^2 -2 = 4 -2 = 2 . . . True
The appropriate choice is ...
(-1, 2) and (4, 7)
Who jointly built the International Space Station?
A
NASA, Roscosmos, JAXA, ESA, and CSA
B.
NASA, ESA, and JAXA
C.
ESA, CSA, and Roscosyjs
D.
CSA. NASA. ESA, and Roscosmos
Step-by-step explanation:
This assembly required more than 40 missions. A partnership between European countries (represented by ESA), the United States (NASA), Japan (JAXA), Canada (CSA) and Russia (Roscosmos), the International Space Station is the world's largest international cooperative programme in science and technology.
Answer:
the answer is option D csa nasa esa and roscosmos
I am a two digit number above 50. the sum of my digits is twelve and the difference of my digits is 4. who am I?
Answer:
The answer should be 84
Step-by-step explanation:
12 - 4 = 8
8 + 4 = 12
8 - 4 = 4
Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
3/4 + (1/3 • 1/6) - ( - 1/2) = ?
A) 3 1/4
B) 2 1/4
C) 1 3/4
D) 3/4
9514 1404 393
Answer:
A) 3 1/4
Step-by-step explanation:
Your calculator can help with this.
__
3/4 + ((1/3)/(1/6)) -(-1/2)
= 3/4 + ((2/6)/(1/6)) + 2/4
= 5/4 + 2/1
= 3 1/4
Q) 3/4 + {(1/3) ÷ (1/6)} - ( - 1/2) = ?
→ 3/4 + {(1/3) ÷ (1/6)} - ( - 1/2)
→ 3/4 + {(1/3) × (6/1)} - ( - 1/2)
→ 3/4 + 6/3 - ( - 1/2)
→ {(3/4) + (6/3)} + 1/2
→ 11/4 + 1/2
→ (11 + 2)/4 = 13/4
→ 3 1/4
Hence, option (A) is the answer.