The triangle is formed by using the diameter as its base, so angle opposite to the diameter, i.e., ∠QRS = 90°
Given that QR and SR are equal, so it is an isosceles triangle. Hence, ∠RQS and ∠RSQ are equal. Hence, ∠RSQ = x + 6° because given that ∠RQS = x + 6°.
We know that all angles of a triangle adds up to 180°.
So, (x+6°) + (x+6°) + 90° = 180°
=> 2(x+6°) + 90° = 180°
=> 2(x+6°) = 180° - 90°
=> 2(x+6°) = 90°
=> 2x + 12° = 90°
=> 2x = 90° - 12°
=> 2x = 78°
=> x = 78°/2
=> x = 39°
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within with % confidence if (a) she uses a previous estimate of ? (b) she does not use any prior estimates?
Answer:
732 samples ;
752 samples
Step-by-step explanation:
Given :
α = 90% ; M.E = 0.03 ; p = 0.58 ; 1 - p = 1 - 0.58 = 0.42
Using the relation :
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.58 * 0.42) / 0.03²
n = 0.65918769 / 0.0009
n = 732.43076
n = 732 samples
B.)
If no prior estimate is given, then p = 0.5 ; 1 - p = 1 - 0.5 = 0.5
n = (Z² * p * (1 - p)) / M.E²
Zcritical at 90% = 1.645
n = (1.645² * 0.5 * 0.5) / 0.03²
n = 0.67650625 / 0.0009
n = 751.67361
n = 752 samples
Your help is very much appreciated and I will mark you brainliest:)
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Answer:
(c) Yes, SSS
Step-by-step explanation:
The three pairs of corresponding sides have the same ratio:
12/8 = 15/10 = 21/14 = 3/2
The triangles are similar by SSS.
_____
No angles are shown, so SAS and AAA cannot apply.
Accidents on highways are one of the main causes of death or injury in developing countries and the weather conditions have an impact on the rates of death and injury. In foggy, rainy, and sunny conditions, 1/6, 1/12, and 1/21 of the accidents result in death, respectively. Sunny conditions occur 64% of the time, while rainy and foggy conditions each occur 18% of the time.
What is the probability that an accident results in a death? Round your answer to three decimal places (e.g. 98.765).
shining dnkxdvsuxnxkjdndnx
You think that $39,500 is a good salary and are interested in a job with Fast Pax. What other information might you want to know about Fast Pax salaries, and why?
The credit department of Lion's Department Store in Anaheim, California, reported that 30% of their sales are cash, 30% are paid with a credit card, and 40% with a debit card. Twenty percent of the cash purchases, 90% of the credit card purchases, and 60% of the debit card purchases are for more than $50. Ms. Tina Stevens just purchased a new dress that cost $120. What is the probability that she paid cash?
Answer:
Hence the probability that she paid cash is 0.105
Step-by-step explanation:
P(cash) = 0.3
P(credit card ) = 0.3
P(debit card ) = 0.4
P ( more than $50 | cash ) = 0.2
P (more than $50 | credit card ) =0.9
P (more than $ 50 |debit card ) = 0.6
P ( more than $50) = P ( more than $50 | cash )* P (cash) + P (more than $50 credit card ) * P(credit card ) + P (more than $ 50 |debit card )* P(debit card )
= 0.2 * 0.3 + 0.9 * 0.3 + 0.6* 0.4
= 0.57
P ( more than $50) = P ( more than $50 | cash )* P (cash) / P ( more than $50)
= 0.2* 0.3 / 0.57
= 0.105
Sand, gravel and cement are mixed in a ratio of 5 : 10 : 3 to make concrete. If 35 shovels of sand are used, how many shovels of gravel, and how many shovels of cement are used?
Answer:
70 shovels of gravel, and 21 shovels of cement.
Step-by-step explanation:
35/5 = 7.
10 x 7 = 70, which is the number of shovels for gravel.
3 x 7 = 21, which is the number of shovels for cement.
Sheri surveyed eighty students and then generated three random samples of twenty-five student responses. The means of the samples are shown below. Looking at the table of samples means, which value is the best estimate of the mean of the population?
Answer:
Where is the table cant help unless shown
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
12< average >16
14 is the only one in between 12 and 16.
or.....................................................................................................
12 + 16 + 13 = 41.
41/3 = 13 2/3.
13 2/3 rounds to 14 and it's the closest to it.
Dave's favorite recipe (spaghetti pie) calls for 20 ounces of ground sausage. Since it's awesome, everybody wants some, so he decided to make five pies and pass them out to the select few in his inner circle. The sausage comes in one-pound tubes. How many tubes did Dave need, and how many grams of delicious sausage were left over for his omelet the next morning
Answer:
hi
Step-by-step explanation:
Find the probability of obtaining exactly one tail when flipping 3 coins. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. Please help me figure this out
Answer:
3/8
or
.375
Step-by-step explanation:
This is a binomial distribution
[tex]{3\choose1}*.5*(1-.5)^2=.375[/tex] or 3/8
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 35113511 grams and a variance of 253,009253,009. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 46174617 grams. Round your answer to four decimal places.
Answer:
The answer is "0.1397".
Step-by-step explanation:
[tex]\mu=3511\\\\[/tex]
variance [tex]\ S^2= 253,009\\\\[/tex]
standard deviation [tex]\sigma =\sqrt{253,009}=503\\\\[/tex]
Finding the probability in which the weight will be less than [tex]4617 \ grams\\\\[/tex]
[tex]P(X<4617)=p[z<\frac{4617-3511}{503}]\\\\[/tex]
[tex]=p[z<\frac{1106}{503}]\\\\=p[z< 2.198]\\\\= .013975\approx 0.1397[/tex]
The probability that a school wins their first game in the national college basketball tournament is related to the rank they have going into the tournament. This can be expressed by the equation y=−6.39x+104 where x is their rank (out of 16) and y is the percent chance they have of winning their first game
According to the model, a school ranked #3 has what probability of winning their first game? Round your answer to the nearest percent.
A. 76%
B. 85%
C. 105%
D. 93%
Answer:
According to the model, a school ranked #3 has 85% probability of winning their first game.
What is the area of parallelogram ABCD?
A)13 square units
B)14 square units
C)15 square units
D)16 square units
Answer:
c 15 square units
Step-by-step explanation:
it is very easy
fine x and y alpha ln trigonometry ln triangles
Step-by-step explanation:
it is easy to get a answer go to web
Find cos(2x) from the given information. tan(x)= 9/8, x in quadrant I
Answer:
cos2x=-17/145
Step-by-step explanation:
Recall cos2x=cos^2x-sin^2x
Or cos2x=cos^2x-(1-cos^2x)*
Or cos2x=2cos^2x-1**
*By a Pythagorean Identity
**Combined like terms
I'm going to use third identity from above because I only have to find cosx or cos^2x to get requested answer for cos2x.
Recall Pythagorean identity 1+tan^2x=sec^2x.
Plug in our tangent valuem...
1+(9/8)^2=sec^2x
1+81/64=sec^2x
145/64=sec^2x
Cosine and secant are reciprocals of each other.
64/145=cos^2x
Now we are ready to plug in and get final answer:
cos2x=2cos^2x-1
cos2x=2(64/145)-1
cos2x=128/145-1
cos2x=-17/145
if a circle’s circumference is decreased by12% what percent is the diameter decreased by?
A) 2√3 %
b) 6 %
C) 12 %
D)24%
Answer:
A) 12%
Step-by-step explanation:
Lets assume a random diameter to work with. I will use a diameter of 10.
Circumference = πD
Circumference = π * 10
Circumference = 31.415
Decreasing the circumference by 12%
31.415 * 0.12 = 3.769
31.415 - 3.769 = 27.64
To find out what percent the diameter is reduced by we will find out the new diameter with the new circumference
Circumference = πD
27.64 = π * D
D = 27.64 / π
New Diameter = 8.8
OldD - NewD
10 - 8.8 = 1.2
1.2/10 = 0.12
The diameter decreased by 12%
The diameter of the circle decreased by 12% due to decrease of circles circumference by 12%.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The diameter is the longest line that can be drawn inside a circle.
Area of circle = πr² and the perimeter of circle = 2πr where r is the radius of the circle.
Let's say the diameter of the circle is D
Circumference of circle = πD
12% of Circumference = (12/100) × πD
⇒ 0.12πD
So new circumference will be
πD - 0.12πD = 0.88πD
Now let say new diameter after decreasing circumference is d
Circumference of new circle will be
πd = 0.88πD
d = 0.88D
% decrement = (change/original) × 100
diameter decrease = (D - 0.88D)/D × 100
⇒ 12% hence it will be correct answer.
To learn more about the circle,
https://brainly.com/question/266951
#SPJ2
What is the area of xyz pleae help?
Step-by-step explanation:
here's the answer to your question
Answer:
A = 14 in²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 7 and h = 4 , then
A = [tex]\frac{1}{2}[/tex] × 7 × 4 = [tex]\frac{1}{2}[/tex] × 28 = 14 in²
Express the confidence interval in the form of .
Answer:
0.075 - 0.022 < p < 0.075 + 0.022
Do not evaluate each of the math expressions above.
===========================================================
Explanation:
The given confidence interval is in the form (L, U)
L = lower bound = 0.053U = upper bound = 0.097Find the midpoint of L and U to get
(L+U)/2 = (0.053+0.097)/2 = 0.075
This is the value of [tex]\hat{p}[/tex] which is the symbol p-hat or phat (both pronounced the same). It's the sample proportion.
To get the margin of error E, we could do either of the following
E = (U-L)/2 = (0.097-0.053)/2 = 0.022E = U - phat = 0.097 - 0.075 = 0.022E = phat - L = 0.075 - 0.053 = 0.022This value of E represents half the width of the confidence interval. The full width being U-L.
he radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?
Answer:
The bones were 12,485 years old at the time they were discovered.
Step-by-step explanation:
Amount of the element:
The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:
[tex]A(t) = A(0)e^{-kt}[/tex]
In which A(0) is the initial amount and k is the decay rate, as a decimal.
The radioactive element carbon-14 has a half-life of 5750 years.
This means that [tex]A(5750) = 0.5A(0)[/tex], and we use this to find k. So
[tex]A(t) = A(0)e^{-kt}[/tex]
[tex]0.5A(0) = A(0)e^{-5750k}[/tex]
[tex]e^{-5750k} = 0.5[/tex]
[tex]\ln{e^{-5750k}} = \ln{0.5}[/tex]
[tex]-5750k = \ln{0.5}[/tex]
[tex]k = -\frac{\ln{0.5}}{5750}[/tex]
[tex]k = 0.00012054733[/tex]
So
[tex]A(t) = A(0)e^{-0.00012054733t}[/tex]
A scientist determined that the bones from a mastodon had lost 77.8 % of their carbon-14. How old were the bones at the time they were discovered?
Had 100 - 77.8 = 22.2% remaining, so this is t for which:
[tex]A(t) = 0.222A(0)[/tex]
Then
[tex]0.222A(0) = A(0)e^{-0.00012054733t}[/tex]
[tex]e^{-0.00012054733t} = 0.222[/tex]
[tex]\ln{e^{-0.00012054733t}} = \ln{0.222}[/tex]
[tex]-0.00012054733t = \ln{0.222}[/tex]
[tex]t = -\frac{\ln{0.222}}{0.00012054733}[/tex]
[tex]t = 12485[/tex]
The bones were 12,485 years old at the time they were discovered.
13 A traffic roundabout has a circular garden
in the centre and two lanes for traffic
encircling the garden. The diameter of the
garden is 16 metres and each lane is 3 metres
wide. Each lane is to be resurfaced. Calculate
the area to be resurfaced. Answer in square
metres to the nearest whole number.
Answer:
Step-by-step explanation:
The area to be resurfaced is the area of the
whole circle including garden and lanes minus
the area of the garden.
Area of a circle is (pi)r2
radius of garden is (1/2)diameter = 8 m
Garden area: (pi)82 = 64(pi) m2
Diameter of garden plus traffic lanes is
16 + 2(6) because we add 6 m to both sides
of the diameter of the garden.
Full diameter = 16+12 = 28 m
Full radius = 28/2 = 14 m
Full area: (pi)142 = 196(pi) m2
Area to be resurfaced:
196(pi) - 64(pi) = 132(pi) m2 ≅ 415 m2
Write a word description of the set.
{−9, −8, −7, −6, −5, −4, −3, −2, −1}
the set of which one whole numbers,natural numbers, negative integers or integers
greater than__________________.
Answer: negative integers greater than -10
This is because stuff on the number line to the right is larger than stuff on the left. We can say 2 < 7 since 7 is to the right of 2.
Also, -7 < -2 for similar reasoning.
Saying integers greater than -10 excludes this endpoint. We stop once we reach -1 because 0 and anything larger aren't negative integers.
The probability that it will rain on a given day during the rainy season in Miami is 70%. If there are 140 days in the rainy season. On how many days should you except it to rain?
If you can please answer this! Thanks
Answer:
98 days.
Step-by-step explanation:
140 * 0.70
A sequence is defined recursively by the formula f(n+1)=-2f(n). The first term of the sequence is -1.5. What is the next term in the sequence ?
Answer:
next term is 3
Step-by-step explanation:
[tex]f(n+1)=-2f(n)\\\\f(1)=-1.5=-\frac{3}{2}f(2)=-2f(1)=-2*(-\frac{3}{2})=3[/tex]
Answer:
3
Step-by-step explanation:
Took the test and got this right.
A drinking container is shaped like a cone and must hold at least 10 ounces of fluid. The radius of the top of the container is 2.25 inches. The steps for determining the height of the cone-shaped container are shown below.
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Answer:
C. h ≥ 1.9 in
Step-by-step explanation:
As the final step, divide both sides of the inequality by 5.3:
(5.3h)/5.3 ≥ 10/5.3
h ≥ 1.9
4 pts
John makes $2,800 per month and has an opportunity to invest $150 per month at an APR of 4.5% in a 401K plan through work. He plans to retire in 30 years.
Type in the EXACT formula you would use in excel (no spaces) to find the amount in the account after he has invested for 30 years.
Using excel, what is the answer to the formula from the previous part?
How much money will he deposit into the 401K over the 30 years?
How much total interest will he earn on his 401K over the 30 years?
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Answer:
=FV(4.5%/12,30*12,-150,0)$113,907.92$54,000$59,907.92Step-by-step explanation:
We have used the formula shown in Go.ogle Sheets to give the results shown. (We presume Excel has a similar function.)
The result is that the future value of the investment is $113,907.92.
The amount deposited is ($150/mo)(12 mo/yr)(30 yr) = $54,000.
The interest earned is the difference: $113,907.92 -54,000 = $59,907.92.
Use a table of values to graph the function ƒ(x) = x−−√. Choose the correct graph from the options below.
Answer:
B
Step-by-step explanation:
The square root function's graph is graph (b). This makes logical sense, because, when taking the square root (the principal root in particular), a general rule is that both the input and the output must be positive. Moreover, if one were to create a table of values to find points on the graph of the function, each of the points can be found on graph (b).
[tex]f(x)=\sqrt{x}[/tex]
x y
1 1
4 2
9 3
16 4
Therefore graph (B) is the correct answer.
Find the expression that is equivalent to 7(x2 – 5x + 1).
Answer:
7x^2 -35x +7
Step-by-step explanation:
7(x^2 – 5x + 1)
Distribute
7x^2 -7*5x +7*1
7x^2 -35x +7
Tristen is packing lunch boxes for the school trip. Each lunch box consists of 1 sandwich, 1 fruit, and 1 drink. Tristen can choose from 3 types of sandwiches, 4 types of fruit, and 2 types of drinks. How many different lunch boxes can Tristen pack?
(question: is this a combination or a permutation?)
Answer:
2
Step-by-step explanation:
Write an equation for a function y=square root of x then shifted up 8 units
Answer:
y= x^2 + 8
Step-by-step explanation:
x square rooted is x^2 and shifted up 8 unit probably means that it wants the y-intercept to be 8.
help me please, i don't know this
its full form is portable document format
can someone help with these? ik the answers i just don’t know how to show work
Step-by-step explanation:
use trigonometry ratios
