Answer:
Hello,
Step-by-step explanation:
[tex]Let\ (u_n)\ the\ geometric\ progression.\\\\r\ is\ the\ common\ ratio.\\\\u_3=u_0*r^3\\u_6=u_0*r^6\\\\\dfrac{u_6}{u_3} =r^3=\dfrac{\frac{243}{16} }{\frac{9}{2} } =\dfrac{27}{8} =(\frac{3}{2} )^3\\\\\boxed{r=\dfrac{3}{2} }\\\\\\u_3=u_1*r^2 \Longrightarrow\ u_1=\dfrac{u_3}{r^2} =\dfrac{\frac{9}{2} }{(\frac{3}{2^2}) } =2\\\\\\u_7=u_6*\dfrac{3}{2} =\dfrac{729}{32}[/tex]
A television and DVD player cost a total of $1230. The cost of the television is two times the cost of the DVD player. Find the cost of each item
Answer:
Television = 820
DVD Player = 410
Step-by-step explanation: Imagine the television as 2, and the DVD player as 1. If you’re were to draw it out with boxes, you’d see that the tv has two boxes and the DVD player has 1 box. All are exactly the same amount, and there are a total of three boxes. So divided 1230 by 3 and you get 410. Using the idea of the boxes, the DVD player get’s one 410, and the tv gets two 410s, or 820.
find the missing side length in the image below
Let missing side be x
Using basic proportionality theorem
[tex]\\ \sf\longmapsto \dfrac{18}{14}=\dfrac{27}{x}[/tex]
[tex]\\ \sf\longmapsto \dfrac{9}{7}=\dfrac{27}{x}[/tex]
[tex]\\ \sf\longmapsto 9x=7(27)[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{7(27)}{9}[/tex]
[tex]\\ \sf\longmapsto x=21[/tex]
What does union mean in a statistics problem?
Step-by-step explanation:
The union of two sets is the set of elements that belong to one or both sets.
Symbolically, the union of X and Y is denoted by X ∪ Y. As an example, suppose set A = {1, 2, 3} and set B = {1, 3, 5}.
Then, the union of sets A and B would be {1, 2, 3, 5}.
Find area of shaded region
Answer:
ayyyy i go to RSM too? Which location r u at? ANyways the answer is
According to Zimmels (1983), the sizes of particles used in sedimentation experiments often have a uniform distribution. In sedimentation involving mixtures of particles of various sizes, the larger particles hinder the movements of the smaller ones. Thus, it is important to study both the mean and the variance of particle sizes. Suppose that spherical particles have diameters that are uniformly distributed between 0.02 and 0.08 centimeters. Find the mean and variance of the volumes of these particles. (Recall that the volume of a sphere is (4/3) πr3) Round your answers to four decimal places.
E(Y)= ___ x10−5 cm3
V(Y) = ___ x10−9
The expected value of a normal distribution is the mean of the distribution, while the variance measures the squared deviation of a value from the expected value. The expected value and the variance are: [tex]13.6190 \times 10^{-5}[/tex] and [tex]580.8000 \times 10^{-9}[/tex]
Given that, the diameters are:
[tex]d_1 = 0.02[/tex]
[tex]d_2 = 0.08[/tex]
The radius is:
[tex]r = \frac{d}{2}[/tex]
So, we have:
[tex]r_1 = \frac{0.02}{2} = 0.01[/tex]
[tex]r_2 = \frac{0.08}{2} = 0.04[/tex]
The volume of the sphere is:
[tex]V = \frac{4}{3} \times \pi \times r^3[/tex]
For [tex]r_1 = 0.01[/tex], the volume is:
[tex]V_1 = \frac{4}{3} \times \frac{22}{7} \times 0.01^3 = 0.419047 \times 10^{-5}[/tex]
For [tex]r_2 = 0.04[/tex], the volume is
[tex]V_2 = \frac{4}{3} \times \frac{22}{7} \times 0.04^3 = 26.819047 \times 10^{-5}[/tex]
The mean of a uniform distribution is:
[tex]E(y) = \frac{a + b}{2}[/tex]
In this case, the mean is:
[tex]E(y) = \frac{V_1 + V_2}{2}[/tex]
So, we have:
[tex]E(y) = \frac{0.419047 \times 10^{-5} + 26.819047 \times 10^{-5}}{2}[/tex]
[tex]E(y) = \frac{27.238094\times 10^{-5} }{2}[/tex]
[tex]E(y) = 13.619047 \times 10^{-5}[/tex]
Approximate
[tex]E(y) = 13.6190 \times 10^{-5}[/tex]
The variance of a uniform distribution is:
[tex]V(y) = \frac{(b-a)^2}{12}[/tex]
In this case, the volume is:
[tex]V(y) = \frac{(V_2-V_1)^2}{12}[/tex]
So, we have:
[tex]V(y) = \frac{(26.819047 \times 10^{-5}- 0.419047 \times 10^{-5})^2}{12}[/tex]
[tex]V(y) = \frac{(26.4 \times 10^{-5})^2}{12}[/tex]
[tex]V(y) = \frac{(696.96 \times 10^{-10})}{12}[/tex]
[tex]V(y) = 58.08000 \times 10^{-10}[/tex]
Rewrite as:
[tex]V(y) = 580.8000 \times 10^{-9}[/tex]
Hence, the expected value and the variance of the sphere are:[tex]13.6190 \times 10^{-5}[/tex] and [tex]580.8000 \times 10^{-9}[/tex]
Learn more about expected values and variance at:
https://brainly.com/question/4470015
Given the directrix of y = 4 and focus of (0, 2), which is the equation of the parabola?
Answer:
The equation of the parabola is,
x²+4y-12=0
PLEASE HELP AND BE RIGHT PLEASE AND THANK YOU
Answer:
4 units
Step-by-step explanation:
A'B' = 2 × AB
8 = 2×AB
AB = 8/2 = 4
Answer:
16 units
Step-by-step explanation:
The triangle will get bigger because it has a scale factor that is greater than 1.
k=scale factor
k<1=reduction
k>1=enlargement
What is the inverse of the function ? f(x)=x+1 over x?
plato
Answer:
[tex]f { - 1}^{} = \frac{1 - x}{x - 1} [/tex]
Step-by-step explanation:
bxhrrrhi5u44ftj7gttjoy
Answer:
x = (y+1)/y
xy = (y+1)
xy -y = 1
y(x-1)=1
y = 1/(x-1)
Step-by-step explanation:
Which polynomial is prime?
a. x³+3x²+2x+6
b. x³+3x²-2x-6
c. 10x²-4x+3x+6
d. 10x²-10x+6x-6
How does sample size affect determinations of statistical significance? The smaller the sample size, the more confident one can be in one's decision to reject or retain the null hypothesis. The smaller the sample size, the greater the probability that the variable has an effect. The larger the sample size, the more accurate the estimation of the true population value. The larger the sample size, the greater the probability that the variable has an effect.
Answer:
The larger the sample size, the more accurate the estimation of the true population value.
Step-by-step explanation:
As large will be the sample size more data will be shown and more are the c c changes of it being an estimate of a true population. The sample size can be determined on the basis of use of experience, target variance, confidence level, and target for power.The height of the triangle is 4 meters longer than twice its base. find the height if the area of the triangle is 80 square meters. The height must be ___meters
Answer:
The height is 20 meters
Step-by-step explanation:
First set up the equation (Area)80=bh/2 then set up another equation, (height) h=4+2b (base). After this you can substitute h in the equation to end up with 80=(b(2b+4))/2 simplify it to get 80=b^2+2b then solve. The base is 8 meters, plug into the formula that we made before and you find the height is 20 meters.
There are 9 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommitteeses are possible?
Answer:
126
Step-by-step explanation:
9 choose 4 (Order does not matter)
9 nCr 4 = 126
How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol. Write as an expression.
Answer:
13/9l or 1 4/9 l
Step-by-step explanation:
Answer:
quantity of alcohol = l liters
we need to make a solution of having 45% alcohol by adding water.
45% alcohol means whatever id the total quantity of solution there is 45% alcohol.
Let the total quantity of solution be x.(
then
quantity of alcohol in terms of x = 45% of x = 45/100 x
but we know that quantity of alcohol = l liters
45/100 x = l
x = 100/45 l
Thus, total quantity of solution is 100/45 l,
but in it, there are l liters of alcohol.
to find the quantity of water we need to subtract the quantity of alcohol from the total quantity of solution
quantity of water in the solution = 100l/45 - l = (100l - 45l)/45 = 65l/45
quantity of water in the solution = 13/9l = 1 4/9 l -------->answer.
Thus, 1 4/9 liters of water needs to be added to l liters of alcohol to make a solution of 45% alcohol.
PLEASE MARK THIS AS BRAINLIST
A plumber had two pipes. The ratio of the length of the longer pipe to the
shorter pipe was 9 : 2. When he
cut 1.65 m from the longer pipe, the
remaining length was 3 times that of the shorter
pipe. Find the length of
the shorter pipe in metres.
Answer:
4.95m
Step-by-step explanation:
Let the length of longer and shorter pipe be x and y respectively..
given,
x/y=9/2...(i)
x-1.65=3y ...(ii)
in eqn ii..
x-1.65=3y
or, x/y - 1.65/y = 3
or, 9/2-1.65/y =3
or, 4.5-3 = 1.65/y
or, y=1.65/1.5
•°• y = 1.1m
now,
x/y = 9/2
or, x/1.1 = 4.5
x= 4.5×1.1
•°• x= 4.95m
thus, the length of the longer pipe is 4.95m
Insurance companies are interested in knowing the population percentage of drivers who always buckle up before riding in a car. When designing a study to determine this population proportion, what is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.04
Answer:
The minimum number of drivers you would need to survey is 601.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
What is the minimum number of drivers you would need to survey to be 95% confident that the population proportion is estimated to within 0.04?
The number is n for which M = 0.04.
We don't have an estimate for the proportion, so we use [tex]\pi = 0.5[/tex]. Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2[/tex]
[tex]n = 600.25[/tex]
Rounding up:
The minimum number of drivers you would need to survey is 601.
Let f(x)= [x/3] (where f(x) is the ceiling function). We learned that the floor and the ceiling functions are NOT invertible, but we also learned about the set of preimages of any value in the Range, the set of images. Keeping that in mind, give your answer in interval notation if necessary.
a. Find f-1({5})
b. Find f-1({-2})
c. Find f-1({x | 5 = x = 9 })
d. Find f-1({x | -6 = x = -2})
(a) We have ⌊x⌋ = 5 if 5 ≤ x < 6, and similarly ⌊x/3⌋ = 5 if
5 ≤ x/3 < 6 ==> 15 ≤ x < 18
(b) ⌊x⌋ = -2 if -2 ≤ x < -1, so ⌊x/3⌋ = -2 if
-2 ≤ x/3 < -1 ==> -6 ≤ x < -3
In general, ⌊x⌋ = n if n ≤ x < n + 1, where n is any integer.
I do not understand what is being asked in (c) and (d), so you'll have to clarify...
HELP ME PLEASE I NEED HELP
Answer:
1. 3-5
2. 5-3
3. 3-5
4. 5-3
Step-by-step explanation:
This is simple! Just get rid of the parenthesis for each of the expressions shown.
3 + (-5)
the plus sign is next to the negative which is in the parenthesis. Negative times positive is equal to negative. The expression then becomes
3 - 5
Now do the same for the rest!
For things like 3 and 4, you can just flip it like 3-5 and 5-3 because it will all equal the same :]
Hope this helps !!
-Ketifa
An equal number of juniors and seniors are trying out for six spots in this year's decathlon
team. If the team must consist of four seniors and two juniors, then how many different
possible decathlon teams could result if five juniors try out?
50
55
75
100
There are 50 different possible debating teams that could be selected as obtained using COMBINATION.
Since there are EQUAL number of juniors and seniors ;
Then we have 5 of each.
Here, the order of arrangement DOES NOT matter, Hence, we use COMBINATION
since the team MUST contain 4 SENIORS and 2 JUNIORS
4 Seniors from 5 = 5C4 = 5
2 Juniors from 5 = 5C2 = 10
Hence, (5C4 * 5C2) = 5 * 10 = 50
Hence, there are 50 different possible debating teams that could be selected.
Learn more about COMBINATION :
https://brainly.com/question/8018593
How would the following triangle be classified?
O scalene acute
O scalene obtuse
O isosceles acute
O isosceles obtuse
Answer:
isosceles acute
Step-by-step explanation:
We have two sides that are equal so the triangle is isosceles
None of the angles are larger than 90 degrees so non of the angles are obtuse, and none of the angles are 90 degrees, so the triangle is acute ( which means the angles are all less than 90 degrees)
Which statement is true about the value of Start Absolute Value negative 5 End Absolute Value?
Statements? At least look for one that says it is equivalent to positive 5.
Find the missing side of the triangle
Answer:
x = 4[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Pytago:
x[tex]x^{2} +7^{2} = 9^{2} \\\\x = \sqrt{9^{2} - 7^{2} } x = 4\sqrt{2}[/tex]
What is the slope of the points (-2,7) and (2,-5)?
4
-3
-12
3
Answer:
The slope of a line that goes through both [tex](-2,\, 7)[/tex] and [tex](2,\, -5)[/tex] would be [tex](-3)[/tex].
Step-by-step explanation:
The slope of a line is the ratio between rise and run between these two points.
The rise between two points is the change to the corresponding [tex]y[/tex] coordinates. Between [tex](-2,\, 7)[/tex] and [tex](2,\, -5)[/tex], the rise would be [tex](-5) - 7 = (-12)[/tex] (subtract the first [tex]y\![/tex]-coordinate from the second.)
The run between two points is the change to the corresponding [tex]y[/tex] coordinates. Between [tex](-2,\, 7)[/tex] and [tex](2,\, -5)[/tex], the rise would be [tex]2 - (-2) = 4[/tex] (likewise, subtract the first [tex]x[/tex]-coordinate from the second.)
Hence, the slope of this line would be:
[tex]\begin{aligned} \frac{\text{rise}}{\text{run}} &= \frac{-12}{4} = -3\end{aligned}[/tex].
Please help me with 9 I really need it
Answer:
605 boys.
Step-by-step explanation:
5:7 means 5 parts consists of boys and 7 parts consist of girls.
Since 7 parts = 847, 1 part = 121 and 5 parts = 605
Hence there are 605 boys.
Hope you have a nice day :)
A plumber can do a job in 4 hours. When he and his 2 helpers do the job, they can finish it in 2 hours. If both helpers work at the same rate, how many hours would each helper take to do the job alone?
A car rental agency rents 480 cars per day at a rate of $20 per day. For each $1 increase in rate, 10 fewer cars are rented. At what rate should the cars be rented to produce the maximum income? What is the maximum income?
Answer:
340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.
Step-by-step explanation:
Given that a car rental agency rents 480 cars per day at a rate of $ 20 per day, and for each $ 1 increase in rate, 10 fewer cars are rented, to determine at what rate should the cars be rented to produce the maximum income and what is the maximum income, the following calculations must be performed:
480 x 20 = 9600
400 x 28 = 11200
350 x 33 = 11550
300 x 38 = 11400
310 x 37 = 11470
320 x 36 = 11520
330 x 35 = 11550
340 x 34 = 11560
Therefore, 340 cars at $ 34 should be rented to produce the maximum income of $ 11,560.
Please help me with the question?
Answer:
<a=55° ,< b=55° and <c=70°
A football team has a probability of 0.76 of winning when playing any of the other four teams in its conference. If the games are independent, what is the probability the team wins all its conference games
Answer:
0.33362176
Step-by-step explanation:
Probability is the ratio of the number of possible outcomes to the number of total outcomes.
Given that a football team has a probability of 0.76 of winning when playing any of the other four teams in its conference, the probability that the team wins all its conference games
= 0.76 * 0.76 * 0.76 * 0.76
= 0.33362176
This is the probability that the teams wins the 4 matches played against the other teams in the conference.
Please help me with this question
In a class of 30 students, 4 received a grade of A. What fraction of the class did not receive an A? Reduce to the lowest terms.
Answer: 13/15
Step-by-step explanation:
Given:
Total number of students = 30
Number of students received an A = 4
Solve:
STEP ONE: Find the number of students who did not receive an A
No A = Total - Yes A
No A = 30 - 4
No A = 26
STEP TWO: Find the fraction of the class that didn't receive an A
Fraction = No A / Total
Fraction = 26 / 30
Fraction = 13 / 15
Hope this helps!! :)
Please let me know if you have any questions
Write a 6-digit number that fits the description.
1. The value of its thousands digit is 5,000.
2. The value of its hundreds digit is 700.
3. Its tens digit is 2 less than the thousands digit.
4. Its hundred thousands digit is the same as the hundreds digit.
The number is?
Answer:
175731 is one of the answers of the 6 digit number
some others are:
275732
375733
475734
575735
675735
775734
875732
The 6-digit number is 175731.
What is the place value strategy?The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.
Let the number would be ABCDEF
Given the condition that the value of its thousands of digits is 5,000.
So C = 5
Given the condition that the value of its hundreds of digits is 700.
So D = 7
Given the condition that Its tens digit is 2 less than the thousand digits.
So E = 5-2 = 3
Given the condition that Its hundred thousand digits is the same as the hundred digits.
So B = 7
Therefore, all possible answers:
275732
375733
475734
575735
675735
775734
875732
Hence, the 6-digit number is 175731
Learn more about the place value strategy here:
brainly.com/question/654419
#SPJ2
Charlie has an annual salary of $75,000.00. He is paid every two weeks. What is the gross income amount for each paycheck?
Answer:
$2884.62
Step-by-step explanation:
A year has 52 weeks
The number of times Charlie will receive a paycheck will be 52w ÷ 2w = 26 times
Charlie's gross income each paycheck will be 7500÷26 = $2884.62 every two weeks
75000 ÷ (52 ÷2)
7500 ÷ 26
$2884.62
