Answer: LCM = 1320
Step-by-step explanation:
2 | 220, 440, 660
2 | 110, 220, 330
2 | 55, 110, 165
3 | 55, 55,165
5 | 55, 55 , 55
11 | 11, 11, 11
| 1, 1, 1
= 2 × 2 × 2 × 3 × 5 × 11
= 1320
Therefore the LCM is 1320
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solve each question please thank you
Answer:
SURE
Step-by-step explanation:
A principal P is to be invested at continuous compound interest of 1.9% to yield $50,000 in 20 years. What is the approximate value of P to be invested?
You may need to delete the dollar sign and/or the comma when typing in the answer.
=======================================================
Work Shown:
[tex]A = P*e^{rt}\\\\50,000 = P*e^{0.019*20}\\\\50,000 = P*e^{0.38}\\\\P = \frac{50,000}{e^{0.38}}\\\\P \approx 34,193.0704606\\\\P \approx 34,193.07\\\\[/tex]
Side note: the 'e' is a special constant roughly equal to 2.71828...
Julio has a net pay of $ 537.00 each paycheck. He pays $ 142.00 in pre-tax deductions and taxes each paycheck. What is Julio's gross income before the tax deductions?
Answer:
Julio's gross income before the tax deductions is $ 405.
Step-by-step explanation:
Given that Julio has a net pay of $ 537.00 each paycheck, and he pays $ 142.00 in pre-tax deductions and taxes each paycheck, to determine what is Julio's gross income before the tax deductions the following calculation must be performed:
547 - 142 = X
405 = X
Therefore, Julio's gross income before the tax deductions is $ 405.
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
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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.
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.
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:
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.
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
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
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
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
Which of the following expressions are equivalent to -3x- 6/10
Choose all that apply:
A=3/6x1/10
b=- 3/10x-6
c= none of the above
Answer:
c= none of the above
Step-by-step explanation:
-3x- 6/10
This has two separate terms, a term with a variable
-3x and a term with a constant -6/10
A=3/6x1/10 This has only one term
b=- 3/10x-6 This has a different x term -3/10 which is not -3
c= none of the above
twelve people enter a contest. prizes will be given for first second and third place. how many ways can the prizes be given
Answer:
1320 ways
Step-by-step explanation:
Number of contestants = 12
Positions that are n be awarded = First, Second, Third
Number of contestants who could be first = 12 (all 12 contestants)
Number of contestants who could be second = 11 (all 12 contestants - first)
Number of contestants who could be third = 10 (all 12 contestants - first and second )
The number of ways prices can be given :
(1st * 2nd * 3rd) = 12 * 11 * 10 = 1320 ways
Find the area of the shaded region.
A. 112.5 in²
B. 73.5 in²
C. 122.5 in²
D. 147 in²
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Answer:
B. 73.5 in²
Step-by-step explanation:
The triangle area is half the rectangle area, so the shaded area is also half the rectangle area:
A = 1/2LW = 1/2(21 in)(7 in) = 73.5 in²
Answer:
B.) 73.5 in2
Step-by-step explanation:
I got it correct on founders edtell
What is the value of Z? Z =2^3
the value of Zis 8.
Z =2^3=8
Now we have to,
find the required value of Z.
→ Z = 2^3
→ [Z = 8]
Therefore, value of Z is 8.
Use the figure to find x
Answer:
The value of x is [tex]\frac{7\sqrt{6}}{2}[/tex]
Solution given:
AB=7
BD=x
<BAC=60°
<DBC=45°
In right angled triangle ABC
Tan 60°=opposite/adjacent
Tan 60°=BC/AB
Substitute value
[tex]\sqrt{3}[/tex]=[tex]\frac{BC}{7}[/tex]
BC=[tex]7\sqrt{3}[/tex]
again
In right angled triangle BCD
Using Cos angle
Cos 45=adjacent/hypotenuse
Cos45°=BD/BC
Substituting value
[tex]\frac{\sqrt{2}}{2}=\frac{x}{7\sqrt{3}}[/tex]
Doing criss cross multiplication
[tex]\frac{\sqrt{2}}{2}*7\sqrt{3}=x[/tex]
x=[tex]\frac{7\sqrt{6}}{2}[/tex]
Billy's heart rate is 13 beats every 10 seconds. What is his heart rate in beats per MINUTE (bpm)?
Reminder: 1 Minute=60 Seconds
(A)23 bpm
(B)63 bpm
(C)78 bpm
(D)130 bpm
write an expression to represent the sum of 3 and the quotient of a number divided by 6
A box of tangerines that weighs 5 pounds costs $4.25.
What is the cost per pound?
Answer:
$0.85
Step-by-step explanation:
$4.25 divided by 5 pounds equals $0.85 per pound.
Answer:
$0.85
Step-by-step explanation:
Find the unit rate.
4.25/5=x/1
Solve for x. X= 4.25/5=0.85
So 1 lb of tangerines costs $0.85.
An office manager booked 55 airline tickets. He booked 6 more tickets on Airline A than Airline B. On Airline C, he booked 5 more than twice as many tickets as on Airline B. How many tickets did he book on each Airline?
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Answer:
A: 17B: 11C: 27Step-by-step explanation:
If we let a, b, c represent tickets booked on airlines A, B, C, respectively, then we have ...
a + b + c = 55
a - b = 6
-2b + c = 5
Using the last two equations to write expressions for a and c, we have ...
a = b +6
c = 5 +2b
These can be substituted into the first equation to give ...
(b +6) +b +(5 +2b) = 55
4b +11 = 55
4b = 44
b = 11
a = b+6 = 17
c = 5 +2b = 27
He booked 17 tickets on Airline A, 11 tickets on Airline B, and 27 tickets on Airline C.
