Answer:
Step-by-step explanation:
Charlotte starts at 19 years old.
Rachel starts at 24 years old.
Then two years later, Rachel is 26 and Charlotte is 21. This is not 3 times Charlotte's age.
Do you have all the right info?
Find the length of BC, last one
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the given angle, we know the opposite side and want to know the adjacent side. Therefore, we should use the tangent function.
tan(54) = 16/BC
BC = 16/tan(54)
BC = 11.62 units
Hope this helps!
A 90% confidence interval is found to be (120,140). What is the margin of error?
Answer:
There is 10% error in both minimum and extreme values i.e. 120 & 140 , Error in 120 is 10% i.e. = 12, Since value can be more or less in error ∴ Error in 120 is ±12.
help fast!! i need this asap! thank youu
5/3 is farthest according to me
Answered by Gauthmath must click thanks and mark brainliest
Answer:
0.27, 1.1, - 1/4, 5/3
Change all to decimal:-
0.27, 1.1, -.2.5, 1.67
So, 1.67 is farthest from zero
D) 5/3 is your answer
~OAmalOHopeO
A ladder leans against the side of the a house. The ladder is 19 feet long and forms an angle of elevation of 75 degree when leaned against the house. How far away from the house is the ladder? Round your answer to the nearest tenth.
Answer: 18.35259
Hope it helps!
You need 675 mL of a 90% alcohol solution. On hand, you have a 25% alcohol mixture. How much of the 25% alcohol mixture and pure alcohol will you need to obtain the desired solution?
Answer:
90 ml of the 25 percent mixture and 585 of pure alcohol
Step-by-step explanation:
Firstly, you should find the quantity of alcohol in the desired mixture.
675:100*90= 675*0.9= 607.5
Firstly, define all the 25 percents mixure as x, the pure alcohol weight is y.
1. x+y= 675 (because the first and the second liquid form a desired liquid).
Then find the equation for spirit
The first mixture contains 25 percents. It is x/100*25= 0.25x
When the second one consists of pure alcohol, it contains 100 percents of spirit, so it is x.
2. 0.25x+y=607.5
Then you have a system of equations ( 1.x+y= 675 and 2. 0.25x+y= 607.5)
try 2-1 to get rid of y
x+y- (0.25x+y)= 675-607.5
0.75x= 67.5
x= 90
y= 675-x= 675-90= 585
It means that you need90 ml of the 25percents mixture and 585 0f pure alcohol
A student-faculty committee consisting of 6 members is to be chosen from a pool of candidates consisting of 5 students and 7 faculty members. The committee must have at least 2 student members and at least 1 faculty member. How many possibilities are there
Answer:
[tex]T=812[/tex]
Step-by-step explanation:
From the question we are told that:
No. Committee Members [tex]n=6[/tex]
Pool of : 5 students and 7 faculty members
At least 2 student members and at least 1 faculty member
Generally the committee is mathematically given by
The Total Events are
[tex]T=(^5C_2*^7C_4)+(^5C_3)*(^7C_3)+(^5C_4)*(^7C_2)+(^5C_5)*(^7C_1)[/tex]
[tex]T=350+350+105+7[/tex]
[tex]T=812[/tex]
The mathematics department of a college has 6 male professors, 12 female professors, 14 male teaching assistants, and 11 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female.
The probability is ___.
(Type an integer or a fraction. Simplify your answer.)
Answer:
37/43
Step-by-step explanation:
6+12+14+11=43
Males: 6+14=20
Females: 11+12=23
If the selected person is a teaching assistant or a female, then the probability is 11+12+14=37. 37/43
It is claimed that the average child has no time to go to school. For the child spends 8 hours per day,or one third of his/her time sleeping. Based on a 365 day year, that’s 121.67days sleeping. Also the child spends three hours per day eating. That’s a total of 45 days in the year spent eating. Also the child spends 90 days taking summer vacation. Also the child spends 21 days on Christmas and Easter holiday. Finally, the child has each Saturday and Sunday off. That’s a total of 104 days. In short, we (rounding to whole days accounted for 122+45+90+21+104=382 days of the year taken up by ordinary child inlike activities. This is already more than the 365 days that are known to comprise a year. We conclude that there is certainly no time for the child to attend school. What is wrong with this reasoning?
Answer:
See below.
Step-by-step explanation:
Sleeping:
8/24 * 365 = 121.76 days
Eating:
3/24 * 365 = 45.63 days
Total sleeping and eating: 167 days
Summer Vacation & Holidays:
90 + 21 = 111 days
Saturdays and Sundays: 52 + 52 = 104 days
Vacation + Holidays Saturdays + Sundays = 111 + 104 = 215 days
It may be true that all days of vacation, holiday, Saturdays, and Sundays combined are a total of 215 days, but these 215 days cannot be added to the 167 days above because these 215 days include time for sleeping and eating which was already included in the sleeping and eating times for the entire year. The mistake in the reasoning is counting twice the time of sleeping and eating on the 215 days in which there is no school.
state and prove Bayes Theorem
Answer:
Bayes’ Theorem describes the probability of occurrence of an event related to any condition. It is also considered for the case of conditional probability.
For prove refer to the attachment.
Hope this helps you^_^
Consider this equation. √x - 1 - 5 = x - 8 The equation has(two valid solutions, one valid solution) and(one extraneous solution, no extraneous solutions) A valid solution for x is(0, 4, 2, 5)
The equation has 2 valid solutions; no extraneous solutions
The given equation is:
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
First, we determine the solutions
[tex]\sqrt{x - 1} - 5= x - 8[/tex]
Add 5 to both sides
[tex]\sqrt{x - 1} = x - 8 + 5[/tex]
[tex]\sqrt{x - 1} = x - 3[/tex]
Square both sides
[tex]x - 1 = (x - 3)^2[/tex]
Expand
[tex]x - 1 = x^2- 3x - 3x + 9[/tex]
[tex]x - 1 = x^2- 6x + 9[/tex]
Collect like terms
[tex]x^2 - 6x - x + 9 + 1 = 0[/tex]
[tex]x^2 - 7x + 10 = 0[/tex]
Expand again
[tex]x^2 - 2x-5x + 10 = 0[/tex]
Factorize
[tex]x(x - 2) -5(x -2)= 0[/tex]
Factor out x - 2
[tex](x - 5)(x -2)= 0[/tex]
Split
[tex]x - 5=0[/tex] or [tex]x - 2 = 0[/tex]
[tex]x= 5[/tex] or [tex]x = 2[/tex]
The above values are valid values of x.
Hence, the equation has 2 valid solutions; no extraneous solutions
Read more about equations at:
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Answer:
That person is wrong, First blank is : one valid solution , Second blank is : one extraneous solution, and I'm not sure what the 3rd blank is but I think It's 4.
Step-by-step explanation:
for plato users
find the missing length indicated
Answer:
192
Step-by-step explanation:
geometric mean theorem :
with p and q being the segments of the Hypotenuse, then
h = x = sqrt(p×q)
p = 144
q = 400-144 = 256
h = x = sqrt(144×256) = 12×16 = 192
A vending machine dispenses coffee into a twelve ounce cup he amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.006 ounce. You can allow the cup to overfill 4â% of the time. What amount should you set as the mean amount of coffee to beâ dispensed?
Answer:
this mean amount of coffee to be dispensed would be 11.99, approximately 12
Step-by-step explanation:
first of all we have this information available to answer this question.
standard deviation σ = 0.006 ounces
prob(x > 12) = 0.04
we use this formular to find the mean
z = x - μ/σ
the value of the z score at 4% is equal to 1.7507
such that
[tex]1.7507 = \frac{12-u}{0.006}[/tex]
we cross multiply from this stage
1.7507*0.006 = 12-μ
0.0105042 = 12-μ
μ = 12 - 0.0105042
herefore, the mean amount μ = 11.99 this can be approximated to 12
A hexagonal pyramid is located ontop of a hexagonal prism. How many faces are there?
A. 15
B. 24
C. 6
D. 13
Answer:
15
Step-by-step explanation:
The figure has total 15 faces, the correct option is A.
What is a Hexagon?A hexagon is a polygon with six sides.
A hexagonal pyramid has 8 faces
From (2 hexagonal base + 6 lateral surfaces)
A hexagonal prism has 7 faces
From ( A hexagonal base + 6 lateral faces)
Total faces the figure has is 8 +7 = 15
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Ba sinh viên A, B, C cùng làm bài thi một cách độc lập. Xác suất làm được bài thi của sinh viên A, B, C tương ứng là 0,6; 0,7 và 0,9. Tính xác suất để có ít nhất 1 sinh viên làm được bài.
Answer:
2 sinh viên sẽ làm đc 0,452
in how many ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies?
Answer:
5880 ways
Step-by-step explanation:
For selections like this, we solve using the combination theory. Recall that
nCr = n!/(n-r)!r!
Hence given to find the number of ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies,
= 10C6 * 8C4
= 10!/(10-6)!6! * 8!/(8-6)!6!
= 10 * 9 * 8 * 7 * 6!/4 *3 *2 * 6! * 8 * 7 * 6!/2 * 6!
= 210 * 28
= 5880 ways
The arrangement can be done in 5880 ways
Find the APR, rounded to the nearest tenth of a percent (one decimal place) for the loan. Purchase a living room set for $4,900 at 8% add-on interest for 4 years. Enter only the number without % sign.
9514 1404 393
Answer:
14.3%
Step-by-step explanation:
We assume this question is asking for the annual interest rate for an amortized loan that would produce the same total repayment amount as if 8% simple interest were added to the $4900 loan amount. There is no formula for that, but there are a number of apps and spreadsheets that can calculate it. In the attached, we have use a graphing calculator.
The APR is about 14.3%.
_____
The amount to be repaid is calculated using the simple interest formula:
A = P(1 +rt) = $4900(1 +0.08·4) = $6468
Then the required monthly payment (for 48 months) is ...
$6468/48 = $134.75
__
The payment amount for a 48-payment loan at rate r on a principal of $4900 will be ...
A = 4900(r/12)/(1 -(1 +r/12)^-48)
In the attachment, we show the value of r (in percent) that would make the payment amount A be $134.75. We have done this by casting the problem in the form f(r) = 0 and looking for the x-intercept of f(r).
_____
Additional comment
The second attachment uses a spreadsheet for the same purpose. Here, we have used Go.ogle Sheets with a "Goal Seek" add-on to adjust the value in cell B5 so that the computed payment on the loan (cell B6) is the same as the value we calculated in cell B4.
We found the graphing calculator solution to be much quicker, though in that case we actually had to know the formula to use to calculate the payment. The payment formula is built into the spreadsheet.
What is the domain of the following function?
Answer:
the domain is all real numbers except x=3
Step-by-step explanation:
The domain is the values that x can take
X can be all real number except when the denominators equal zero
x-3 ≠ 0
x≠3
the domain is all real numbers except 3
Suppose that the distribution of snake lengths in a certain park is not assumed to be symmetric. According to Chebyshev's Theorem, at least what percentage of snake lengths are within k =2.9 standard deviations of the mean?
According to Chebyshev,
P(|X - µ| ≤ 2.9σ) ≥ 1 - 1/2.9² ≈ 0.8811
The distribution of widgets from a production line is known to be approximately normal with mean 2.7 inches and standard deviation 0.25 inches. About 95% of the distribution lies between what two values?
A. 2.45 inches and 3.2 inches
B. 2.45 inches and 2.95 inches
C. 2.2 inches and 3.2 inches
D. 1.95 inches and 3.45 inches
Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.
To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81
The formula for calculating the z-score is expressed as;
[tex]z=\frac{x-\overline x}{s}[/tex] where:
[tex]\overline x[/tex] is the mean
s is the standard deviation
z is the z-scores
Given the following
[tex]\overline x[/tex]=2.7 in
s = 0.25
if z = -2.81
[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]
Similarly:
[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]
Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.
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The perimeter of a rectangular parking lot is 318m. If the width of the parking lot is 61m what is the length
Answer:
98 meters
Step-by-step explanation:
Simplify each side of the equation:
318 = 2(61+x)
318= (2)(61) + (2)(x)
318= 122 + 2x
Flip the equation:
2x + 122 = 318
Subtract 122 from each side:
2x + 122 − 122 = 318 − 122
2x = 196
Divide both sides by 2:
2x/2 = 196/2
x = 98
A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 101.8 pounds and a standard deviation of 3.76 pounds.
Required:
a. What is the probability that a drum meets the guarantee? Give your answer to four decimal places.
b. What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99?
Answer:
The answer is "0.6368 and 0.773".
Step-by-step explanation:
The manufacturer of organic compounds guarantees that its clients have at least 100 lbs. of solvent in every fluid drum they deliver. [tex]X\ is\ N(101.8, 3.76)\\\\P(X>100) =P(Z> \frac{100-101.8}{3.76}=P(Z>-0.47))[/tex]
For point a:
Therefore the Probability =0.6368
For point b:
[tex]P(Z\geq \frac{100-101.8}{\sigma})=0.99\\\\P(Z\geq \frac{-1.8}{\sigma})=0.99\\\\1-P(Z< \frac{-1.8}{\sigma})=0.99\\\\P(Z< \frac{-1.8}{\sigma})=0.01\\\\z-value =0.01\\\\area=-2.33\\\\ \frac{-1.8}{\sigma}=-2.33\\\\ \sigma= \frac{-1.8}{-2.33}=0.773[/tex]
If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω), is given by 1/R = 1/R1 + 1/R2 . If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast is R changing when R1 = 60 Ω and R2 = 80 Ω? (Round your answer to three decimal places.)
The rate of change of R with time in the given equation is 0.004 ohm/s
Given parameters:
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{dR_1}{dt} = 0.3 \ ohm/s\\\\\frac{dR_2}{dt} = 0.2 \ ohm/s\\\\R_1 = 60 \ ohms\\\\R_2 = 80 \ ohms[/tex]
To find:
The rate of change of R with time in the given equation.First determine the value of R from the given equation;
[tex]\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} \\\\\frac{1}{R} = \frac{1}{60} + \frac{1}{80} \\\\\frac{1}{R} = \frac{4 + 3}{240} \\\\\frac{1}{R} = \frac{7}{240} \\\\R = \frac{240}{7} = 34.286 \ ohms[/tex]
Finally, to determine the rate of change of R, differentiate the given equation.
[tex]\frac{-1}{R^2} \frac{dR}{dt} = \frac{-1}{R_1^2} \frac{dR_1}{dt} - \frac{1}{R_2^2} \frac{dR_2}{dt} \\\\\frac{1}{R^2} \frac{dR}{dt} = \frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt}\\\\\frac{dR}{dt} = R^2(\frac{1}{R_1^2} \frac{dR_1}{dt} + \frac{1}{R_2^2} \frac{dR_2}{dt})[/tex]
[tex]\frac{dR}{dt} = 34.286(\frac{1}{(60)^2} \times 0.3 \ \ \ + \ \ \ \frac{1}{(80)^2} \times 0.2)\\\\\frac{dR}{dt} = 34.286(8.333 \times 10^{-5} \ \ \ + \ \ \ 3.125 \times 10^{-5})\\\\\frac{dR}{dt} = 34.286(11.458 \times 10^{-5})\\\\\frac{dR}{dt} = 0.00393\\\\\frac{dR}{dt} \approx 0.004 \ ohm/s[/tex]
Thus, from the given equation the rate of change of R with time is 0.004 ohm/s
Learn more here: https://brainly.com/question/14796851
Answer:
the verified answer is wrong.
Step-by-step explanation:
OP forgot to square R (34.286)
In how many ways can a committee of 3 men and 2 women can be formed from 7 men and 5 women?
Answer:
in five (5) ways a committee can be formed from 7 men and 5 women
If A={2,3,5,7} and B={2,4,6,8} then what is AnB?
Answer:
A∩B = {2}Step-by-step explanation:
It asks for the common set of A and B.
There only one element common to both the given sets:
A={2,3,5,7} and B={2,4,6,8} ⇒ A∩B = {2}Answer:
A ∩ B = {2}Step-by-step explanation:
∩ == this symbol stands for the common element/set
So according to this question you have to find the element which is common for both A and B sets.
A = { 2,3,5,7}B = {2,4,6,8}So now you can see that only number 2 is common for both.
So, the answer is,
A ∩ B = {2}PLEASE ANSWER!!!!!!!
Graph the line with x - intercept of -2 and has a slope of 3
Answer:
The graph is given below.
Step-by-step explanation:
X intercept = - 2
slope, m = 3
The point t which the line intersects the X axis is (-2 , 0) .
The equation of line passing through a point and the slope is given
y - y' = m (x - x')
y - 0 = 3 (x + 2)
y = 3 x + 6
So, the graph is given below.
Compare by y = m x + c .
here y intercept is 6 .
investing $12,000 in a savings account at 6% annual interest compounded monthly will result in approximately how much money after five years? use formula A 0 P(1 + r/m) ^mt
Answer:
$16186.20
Step-by-step explanation:
Assuming that P represents the initial amount, A represents the end amount, r represents the annual interest rate, m represents the amount of times compounded per year, and t represents the amount of years, we can write this as
A = P(1+r/m)^(mt)
Since 12,000 is invested, that is the initial amount. To find the interest rate as a decimal from a percent (as we need it in decimal form for this formula), we can divide the percent by 100 to get 6%/100 = 0.06 as our interest rate. Because there are 12 months in a year, the interest is compounded 12 times a year, and since it takes 5 years, t=5. Our formula is now
A = 12000 * (1+0.06/12)^(12 * 5)
A = 12000 * (1+0.06/12) ^(60)
A = 16186.20 rounded to the nearest cent
What is the value of 3x^2 + 4y^2 if x = 2 y = 1
Answer:
16 is answer
Step-by-step explanation:
3(2)^2+4(1)^2= 3(4)+4(1)=12+4=16
6 less than six times a number is 42 what is the number
Answer:
x = 8
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
6x - 6 = 42
Step 2: Solve for x
[Addition Property of Equality] Add 6 on both sides: 6x = 48[Division Property of Equality] Divide 6 on both sides: x = 8Answer: -6
Step-by-step explanation:
We can create an equation based on the info given.
6-6x=42 Now you solve for x, the unknown number.
-6 -6 Subtract 6 on both sides
-6x=36
/-6 /-6 Divide by -6 on both sides
x=-6
The number is -6.
Solve the system.
x-y =-1
x+z=-5
y-z=2
Answer:
x= -2
y= -1
z= -3
Step-by-step explanation:
x-y= -1 (1)
x+z= -5 (2)
y-z= 2 (3)
(1)+(3)==> x-z= 1 (4)
(4)+(2)==> 2x= -4 ==> x= -2
we replace x by its value in equation (2):
-2+z= -5 ==> z= -3
we replace z by its value in equation (3):
y-(-3)= 2 ==> y+3=2 ==> y= -1
If you deposit $500 dollars “Each Month!” Into an account paying 3% interest, compounded monthly, how much would be in said account after 4 years.
Please show proper work and give a good explanation in regards as to how you got your answer
Answer:
26029.26
Step-by-step explanation:
Assuming we are investing the 500 at the end of the period and starting with 500 in the account
[ P(1+r/n)^(nt) ]+PMT × {[(1 + r/n)^(nt) - 1] / (r/n)}
PMT = the monthly payment
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time in years
[ 500(1 + .03/12)^(4*12) ]+500 × {[(1 + .03/12)^(4*12) - 1] / .03/12)}
[ 500(1 + .0025)^(48) ]+500 × {[(1 + .0025)^(48) - 1] / .0025)}
563.66 +25465.60
