PLEASE HELP!!!! ILL MARK BRAINLIEST WITH 10O POINTS!!!!!!! WITH EXLANATION!!
Use the diagram below to create a paragraph proof for the statement: "The sine and cosine of complementary angles are equal"
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Answer:
Complemenraty angles are two angles with sum of 90°. In the given triangle ∠A and ∠B are complementary.
Now, the sine and cosine
sine = opposite side/hypotenusecosine = adjacent side/hypotenuseFind the sine of ∠A and cosine of ∠B
sin A = BC/ABcos B = BC/ABSince right sides are equal, left sides are equal too
sin A = cos BSimilarly, we can show that
sin B = cos AProved
Related Questions
I. Elena wants to estimate what proportion of computers produced at a factory have a certain defect. A random sample of 200 computers shows that 12 computers have the defect. She is willing to assume independence between computers in the sample. Based on this sample, construct a 95% confidence interval for the proportion of computers that have the defect.
a
(0.4529, 0.5871)
b
(0.02709, 0.09291)
c
(0.02131, 0.09869)
d
(0.0309, 0.0691)
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Beryllium-li decomposes into boron-li with a half-life of
13.8 seconds. How long will it take 2400 g of beryllium-il
to decompose into 75 g of beryllium-il? (3 marks)
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[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &75\\ P=\textit{initial amount}\dotfill &2400\\ t=seconds\\ h=\textit{half-life}\dotfill &13.8 \end{cases} \\\\\\ 75=2400\left( \frac{1}{2} \right)^{\frac{t}{13.8}}\implies \cfrac{75}{2400}=\left( \frac{1}{2} \right)^{\frac{t}{13.8}}\implies \cfrac{1}{32}=\left( \frac{1}{2} \right)^{\frac{1}{13.8} t}[/tex]
[tex]\log\left( \cfrac{1}{32} \right)=\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8} t} \right]\implies \log\left( \cfrac{1}{32} \right)=t\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8}} \right] \\\\\\ \cfrac{\log\left( \frac{1}{32} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8}} \right]}=t\implies \cfrac{\log\left( \frac{1}{32} \right)}{\log\left[ \sqrt[13.8]{\frac{1}{2}} \ \right]}=t\implies 69\approx t[/tex]
Question The population of North Dakota was about 672,000 in 2010. The population is projected to be about 630,000 in 2020. Find the percent decrease of the population of North Dakota. (Round to the nearest tenth of a percent.)
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Answer: 6.25%
Step-by-step explanation:
Percent Decrease = ( ( Starting Value - Final Value ) / Starting Value ) * 100
So 672,000-630000 = 42,000
42,000 / 672,00 = 0.0625
Finally multiply by 100 soooooo 0.0625 * 100 = 6.25%
Please help me thank you!
10 points !
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Answer:
A = 120 C = 45
Step-by-step explanation:
180 - 15 = 165
(12x + 12) + (3x + 18) = 165
15x + 30 = 165
15x = 135
135 ÷ 15 = 9
x = 9
A = (12x + 12) = 108 + 12 = 120
C = (3x + 18) = 27 + 18 = 45
please help me.. no links pls
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Answer:
The Answer is 108 units.
It's number 2.
10.A water tank has strps inside it. A monkeyis sitting on topmost floor(i.e.,the first step).The water level is at ninth step. (i) He jumps 3 steps down and then jumps back 2 strps up.In gow many jumps will he reach the water level? Ch-integers class-7
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Answer:
7 steps.
Step-by-step explanation:
Since the monkey is sitting on the first step already you can subtract 9 by 1 to find the amount of steps left.
9-1 = 8 steps left
The monkey jumps 3 steps down
8-3= 5 steps
Then jumps 2 steps up
5 + 2 = 7 steps
The monkey has 7 more steps until he reaches the water level.
the total deposist made over a time of periode
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bro what.... finish the question...
Help me in math pls ty
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Answer:
See below ↓↓↓↓↓↓
Step-by-step explanation:
5.
12 2/3 - 5/738/3 - 5/7266/21 - 15/21251/21 or 11 20/216.
11 1/3 - 3/534/3 - 3/5170/15 - 9/15161/15 or 10 11/157.
9 1/6 - 2 3/455/6 - 11/4110/12 - 33/1277/12 or 6 5/128.
25 1/4 - 3/525.25 - 0.624.6524 13/25 or 613/259.
4 1/2 - 1 4/64 1/2 - 1 2/39/2 - 5/327/6 - 10/617/6 or 2 5/610.
6 1/8 - 2 2/349/8 - 8/3147/24 - 64/2483/24 or 3 11/24PLEASE HELP PLEASE HELP
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Answer:
I think line C and L since Jenna's numbers are the same
how do i do this? im confused
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Answer:
θ ≈ 64.62°
Step-by-step explanation:
In this problem we will use trig: SOH CAH TOA. Since we are given hypotenuse (line AB) and adjacent (line ) to the missing angle θ, we will use cosine.
cosθ = adjacent/hypotenuse
cosθ = 3/7
Now take inverse cosine of both sides to cancel out cosine and find the missing angle:
cos⁻¹(cosθ) = cos⁻¹(3/7)
θ = cos⁻¹(3/7) ----> Plug into calculator
θ ≈ 1.128 radians · 180°/π rad ------>. Convert from radians to degrees
θ ≈ 64.62°
Hope this helps!
Answer: The measure of angle ? is approximately 64.62 degrees.
Step-by-step explanation:
The given value 3 is adjacent to angle ? and 7 is the hypotenuse. Remembering SOH CAH TOA, that means 3/7 = cos(?). To solve, use a calculator to find the inverse cosine of 3/7, which is about 64.62. Look at https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/trig-solve-for-an-angle/a/inverse-trig-functions-intro to get a better understanding if needed.
2. Mississippi covers a total of 47,691 square
miles. The total population of the state in
2000 was 2,844,658. What was the population
per square mile?
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Answer:
60 people per square mile
Step-by-step explanation:
Given :
Population of Mississippi = 2,844,658Area of Mississippi = 47,691 square milesPopulation density is the rough calculation of people (population) per square milePopulation Density
Population / No. of square miles2,844,658 / 47,691⇒ 59.6476903 (approx.)⇒ 60 people per square milePopulation density:-
TOTAL population/Total area2844658/4769159.64Persons or 60(Rounded) persons per square mileA copy machine prints 10 copies per minute.
At what rate, in copies per minute, does the copy machine print?
Enter your answer in the space provided.
Answers
The rate in copies per minute the copy machine print is 10 copies per minutes.
What is rate?Rate is the ratio between two related quantities in different units.
In other word rate is a quotient of two measurements with different units.
In our case we were asked to find the rate at which the machine prints per minutes.
The two related quantities are amount printed and the time in minutes.
Since, the copy machine prints 10 copies in one minutes, the rate at which the copy machine print per minute is 10 copies per minutes.
learn more on rate here: https://brainly.com/question/14199541
Determine the area of the following shapes.
a. 144 in
b. 154 in
c. 164 in
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A) 144 in
is your answer. good luck
a how much will he have in 4. At the age of 30, Jasmine started a retirement account with $50,000 which compounded interest semi-annually with an APR of 4%. She made no further deposits. After 25 years, she decided to withdraw 50% of what had accumulated in the account so that she could con- tribute towards her grandchild's college education. She had to pay a 10% penalty on the early withdrawal. What was her penalty?
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Answer:
6795.70
Step-by-step explanation:
smart people
After paying 10% penalty on the early withdrawal, Jasmine's penalty for the early withdrawal was calculated to be $5,352.24.
What is the compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
here, we have,
We can use the formula for compound interest in ordr to solve this problem.
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (starting amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have the following values,
P = $50,000
r = 1.75% = 0.0175 (since it is compounded semi-annually, n = 2)
t = 25 years
So the final amount after 25 years can be calculated as under
A = 50000(1 + 0.0175/2)^(2×25) = $107,044.84
Jasmine has withdrawn 50% of this amount, which is:
$107,044.84 × 0.5 = $53,522.42
She had to pay a 10% penalty on the early withdrawal, so her penalty would be:
$53,522.42 × 0.1 = $5,352.24
Therefore, the penalty of Jasmine penalty for the early withdrawal was $5,352.24.
Learn more about compound interest :
brainly.com/question/19903178
#SPJ2
You need 120 pieces of chalk for art day. your teacher gar 6 boxes of chalk. Each box he's 18 pieces of chalk. Is that enough chalk for art day if there is 24 students
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Answer:
No
Step-by-step explanation:
6 time 180 is only 108
108<120
There is not enough chalk.
PLEASE HELP PLEASE I WILL GIVE BRAINLIEST
Answers
a tree diagram represents an experiment consisting of two trails.
P(A and D) = [?]
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Answer:
0.3
Step-by-step explanation:
Start at the beginning, follow the branch to A and then the branch to D (see attached annotated diagram).
When calculating the probability of an event AND another event, multiply the probabilities.
P(A and D) = 0.5 x 0.6 = 0.3
Line AB contains points A (8, −4) and B (1, −5). The slope of line AB is (1 point) a −7 b negative 1 over 7 c 1 over 7 d 7
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Heya !
Given two points A ( 8 , -4 ) and B ( 1 , - 5 )
To find - slope of line AB
Solution -
[tex] Slope = \frac{y_{2}-y_{1}}{x_{2} - x_{1}} \\ \\ \dashrightarrow \frac{ -5 - (-4 )}{ 1 - 8 } \\ \\ \dashrightarrow \frac{ - 5 + 4 }{ 1 - 8 } \\ \\ \dashrightarrow \frac{-1}{-7} \\ \\ \dashrightarrow \frac{1}{7}[/tex]
Hence ,
Option ( c ) is correct.
Hope helpful ~
The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. The perimeter of the rectangle is equal to 56cm. Find the lengths of each side of the rectangle
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Answer:
smaller side: 10 cmlarger side: 18 cmStep-by-step explanation:
The given relationships can be translated to equations using L and W for the length and width of the rectangle. The distance from the center to the short side is L/2, and the distance from the center to the long side is W/2.
SetupP = 2(L +W) . . . . . formula for the perimeter
56 = 2(L +W) . . . . . the perimeter is 56 cm
L/2 = 4 + W/2 . . . . . distance to short side is 4 cm longer
__
SolutionDividing the first equation by 2 gives ...
28 = L +W
Multiplying the second equation by 2 gives ...
L = 8 + W
Substituting for L in the first equation, we have ...
28 = (8 +W) +W . . . . . . use L=8+W
20 = 2W . . . . . . . . .subtract 8
10 = W . . . . . . . . divide by 2
L = 8 +10 = 18 . . . . . find the length
__
The smaller side is 10 cm; the larger side is 18 cm.
Ann has some dimes and quarters. If she has 11 coins worth a total of $2.00, how many of each type of coin does she have?
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Answer:
5.5 maybe i guess its fun
find the number that must be added to 40% of 225 to give 200
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Answer:
x = 110
Step-by-step explanation:
find the number : x
that must be added : +
to :
40/100 * 225 + x = 200
2/5 * 225 + x = 200
90 + x = 200
x = 200 - 90
x = 110
Zoe wants to buy two pairs of jeans. The jeans at the mall cost $35 and are on special for buy one pair, get the second pair half off. The same jeans are on sale at a local boutique for 20% off the regular price of $38 plus an additional $10 off purchases over $50. Which is the better buy?
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at 8 the temp in the city was -8. at noon the same day the temp was 2. what was the difference in temp between 8 and noon
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-8 to 0 = 8
0 to 2 = 2
total change = 8 + 2 = 10 degrees
Fill in the blanks below with the correct units. (a) Carmen saw an elephant at the zoo. The elephant's mass was about 5000 ? . (b) Deandre drank about 300 ? of juice with lunch. (c) Martina's family went on a hike that was about 9 ? .
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Answer:
a. 5000 kg
b. 300 ml
c. 9 hours
Looking for good answer on this
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[tex]\dfrac{6x-24}{16-x^2}\\\\=\dfrac{6(x-4)}{4^2 -x^2}\\\\=\dfrac{6(x-4)}{(4+x)(4-x)}\\\\=-\dfrac{6(x-4)}{(x+4)(x-4)}\\\\=-\dfrac{6}{x+4}[/tex]
Martinez and grouse swimming pool is finally finished and all this left to do is fill it with water
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Answer:
The aswer is 88
Step-by-step explanation:
Hope this helps
The number of jelly beans placed in jars by a class of kindergarteners is normally distributed with an unknown population
mean and standard deviation. A random sample of 20 jars is taken and results in a sample mean of 43 jelly beans and
sample standard deviation of 6 jelly beans.
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Using the t-distribution, the 80% confidence interval for the mean number of jelly beans is (41.22, 44.78).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 80% confidence interval, with 20 - 1 = 19 df, is t = 1.3277.
The other parameters are given as follows.
[tex]\overline{x} = 43, s = 6, n = 20[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 43 - 1.3277\frac{6}{\sqrt{20}} = 41.22[/tex]
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 43 + 1.3277\frac{6}{\sqrt{20}} = 44.78[/tex]
The 80% confidence interval for the mean number of jelly beans is (41.22, 44.78).
More can be learned about the t-distribution at https://brainly.com/question/16162795
I NEED help ASAP!!!!!!!
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Step-by-step explanation:
Step 1: Plot the points
L(1,2)
M(0,-1)
J(1,-2)
K(2,-1)
Step 2: Multiply each point by 5.
and record thise points so we have
L(5,10)
M(0,-5)
J(5,-10)
K(10,-5)
Step 3: Plot those points.
Answer:
Graph attached below.
Step-by-step explanation:
After dilation of 5, the new coordinates follow the rule :
(x, y) ⇒ (5x, 5y)The points are :J' = (1 x 5, -2 x 5) = (5, -10)K' = (2 x 5, -1 x 5) = (10, -5)L' = (1 x 5, 2 x 5) = (5, 10)M' = (0 x 5, -1 x 5) = (0, -5)Which circle is the graph of the equation (x + 4)2 + (y – 5)2 = 4?
Circle C
Circle B
Circle D
Circle A
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Answer: CIRCLE C
Step-by-step explanation:
8 less than the product of 3 and j
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Answer:
3j - 8
Step-by-step explanation:
8 less than the product of 3 and j
3×j - 8
3j - 8