Answer:
157.8
Step-by-step explanation:
Add them all up to get 789 and divide them by 5 as there are five numbers to get the answer:)
It is estimated that 75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.
(a) On average, how many young adults do not own a landline in a random sample of 100?
(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?
(c) What is the proportion of young adults who do not own a landline?
(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?
(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?
(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?
(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?
Answer:
a) 75
b) 4.33
c) 0.75
d) [tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline
e) [tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.
f) Binomial, with [tex]n = 100, p = 0.75[/tex]
g) [tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.
Step-by-step explanation:
For each young adult, there are only two possible outcomes. Either they do not own a landline, or they do. The probability of an young adult not having a landline is independent of any other adult, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
75% of all young adults between the ages of 18-35 do not have a landline in their homes and only use a cell phone at home.
This means that [tex]p = 0.75[/tex]
(a) On average, how many young adults do not own a landline in a random sample of 100?
Sample of 100, so [tex]n = 100[/tex]
[tex]E(X) = np = 100(0.75) = 75[/tex]
(b) What is the standard deviation of probability of young adults who do not own a landline in a simple random sample of 100?
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100(0.75)(0.25)} = 4.33[/tex]
(c) What is the proportion of young adults who do not own a landline?
The estimation, of 75% = 0.75.
(d) What is the probability that no one in a simple random sample of 100 young adults owns a landline?
This is P(X = 100), that is, all do not own. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 100) = C_{100,100}.(0.75)^{100}.(0.25)^{0} = 3.2 \times 10^{-13}[/tex]
[tex]3.2 \times 10^{-13}[/tex] probability that no one in a simple random sample of 100 young adults owns a landline.
(e) What is the probability that everyone in a simple random sample of 100 young adults owns a landline?
This is P(X = 0), that is, all own. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.75)^{0}.(0.25)^{100} = 6.2 \times 10^{-61}[/tex]
[tex]6.2 \times 10^{-61}[/tex] probability that everyone in a simple random sample of 100 young adults owns a landline.
(f) What is the distribution of the number of young adults in a sample of 100 who do not own a landline?
Binomial, with [tex]n = 100, p = 0.75[/tex]
(g) What is the probability that exactly half the young adults in a simple random sample of 100 do not own a landline?
This is P(X = 50). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 50) = C_{100,50}.(0.75)^{50}.(0.25)^{50} = 4.5 \times 10^{-8}[/tex]
[tex]4.5 \times 10^{-8}[/tex] probability that exactly half the young adults in a simple random sample of 100 do not own a landline.
The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 5 inches more than 2 times the perimeter. Find the length and width of the rectangle
Answer:
Step-by-step explanation:
L = 4 + w
A = 2P - 4
lw = 2(2l +2w) - 4
lw = 4(l + w) - 4
(w+4)w = 4 ( w+4+w) -4
(w +4)w = 4(2w + 4) - 4
w^2 + 4w = 8w + 16 - 4
w^2 + 4w = 8w + 12
w^2 - 4w - 12 = 0
( w - 6 )( w + 2 ) = 0
w - 6 = 0 ----> w = 6 ----> L=10 ---> P = 32 and A = 60
w + 2 = 0 ---> w = -2 <--- width cannot be negative; disqualified/rejected
What is the difference between these two linear equations?
Y=3x - y=-3x
Place the labels in the chart
If you can draw this out for me or describe were they are that will be very helpful:)
Answer:
Check the image
Peaches cost $5 a dozen. Use a table to determine the following:
A. The cost of 3dozen peaches.
B. The cost of 60peaches.
C. The number of peaches you can buy for $35
Answer:
A. $15
B. $25
C. 84 peaches
Answer:
a)3dozenx$5=$15
b)60=5 dozen 5x$5=$25
c)35/5=7,7 dozen, 7 x 12= 84
Step-by-step explanation:
SOMEONE PLS HELP ME!!!
Answer:
No
Step-by-step explanation: Bye
help it's due in 20 minutes
Answer:
Its the first one | -9 | < | 9 |
Step-by-step explanation:
its false because both sides are identical
Hope this helps!
Answer:
Choice AStep-by-step explanation:
|-9| = |9| = 9, not true-2² = -4 < 3, true-7≤-5, true|-1| = 1 ≥ 0, trueWhat is the first step to solve the equation 16x-21 = 52?
1 Add 52 to both sides
2 Add 21 to both sides
3 Subtract 21 from both sides
4 Subtract 52 from both sides
Answer:
2) Add 21 to both sides
Step-by-step explanation:
When solving [tex]16x-21=52[/tex] for [tex]x[/tex], our goal to isolate [tex]x[/tex] such that we have [tex]x[/tex] set equal to something.
Therefore, we want to start by adding 21 to both sides. This leaves us with [tex]16x=73[/tex] and we are one step closer to isolating [tex]x[/tex].
Consider an x distribution with standard deviation o = 34.
(a) If specifications for a research project require the standard error of the corresponding distribution to be 2, how
large does the sample size need to be?
B) If specifications for a research project require the standard error of the corresponding x distribution to be 1, how large does the sample size need to be?
Part (a)
The standard error (SE) formula is
[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\[/tex]
where n is the sample size. We're given SE = 2 and sigma = 34, so,
[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\2 = \frac{34}{\sqrt{n}}\\\\2\sqrt{n} = 34\\\\\sqrt{n} = \frac{34}{2}\\\\\sqrt{n} = 17\\\\n = 17^2\\\\n = 289\\\\[/tex]
So we need a sample size of n = 289 to have an SE value of 2.
Answer: 289========================================================
Part (b)
We'll use SE = 1 this time
[tex]\text{SE} = \frac{\sigma}{\sqrt{n}}\\\\1 = \frac{34}{\sqrt{n}}\\\\1*\sqrt{n} = 34\\\\\sqrt{n} = 34\\\\n = 34^2\\\\n = 1156\\\\[/tex]
Because we require greater precision (i.e. a smaller SE value), the sample size must be larger to account for this. In other words, as SE goes down, then n must go up, and vice versa.
Answer: 1156Slope 0; through (-5, -1)
Answer:
y = -1
Step-by-step explanation:
(03.04) Use the graph below for this question: What is the average rate of change from x = −3 to x = 5? (1 point)
A.−1
B.0
C.1
D.8
Answer:
B. 0
Step-by-step explanation:
Rate of change from x = -3 to x = 5
Rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]
where, from the graph, we have:
a = -3, f(a) = -1,
b = 5, f(b) = -1,
Plug in the values
Rate of change = [tex] \frac{-1 -(-1)}{5 - (-3)} [/tex]
Rate of change = [tex] \frac{0}{8} [/tex]
Rate of change = 0
[tex] \frac{3x - 2}{7} - \frac{5x - 8}{4} = \frac{1}{14} [/tex]
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
[tex]\frac{3x-2}{7}-\frac{5x-8}{4}=\frac{1}{14}[/tex]
In order to factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5.
The number of times that each prime divides the original integer becomes its exponent in the final result.
In here, Prime number 2 to the power of 2 equals 4.
[tex]\frac{3x-2}{7}-\frac{5x-8}{2^{2} }=\frac{1}{14}[/tex]
First, We need to add fractions-
Rule:-
[tex]\frac{A}{B} +\frac{C}{D} =\frac{\frac{LCD}{B}+\frac{LCD}{D}C }{LCD}[/tex]
LCD = [tex]7 \cdot 2^{2}[/tex]
[tex]\frac{4(3x-2)+7(-(5x-8))}{7*2^{2} } =\frac{1}{14}[/tex]
[tex]x=2[/tex]
OAmalOHopeO
1. MATHEMATICS The sum of ages of Bola, Dada and Ayo is 32 years. After sharing a sum of money in ratio of their ages, if Bola gets N400, Dada get-A400 and Ayo get N800. How old is Bola?
Bola will be 8 years old.
Let Bola's age be x
Dada's age be y
Ayo's age be z
If the sum of ages of Bola, Dada, and Ayo is 32 years, then;
x + y + z = 32
If they share a sum of money in the ratio of their ages, then the ratio of their ages will be x: y: z
Also if Bola gets N400, Dada get-N400 and Ayo get N800, then the total amount of money shared will be expressed as:
T = 400 + 400 + 800
T = N1600
Next is to get the age of Bola
[tex]\frac{age \ of \ bola}{32}* Total \ amount \ shared = Bola's \ Share[/tex]
Substitute the required variables and values into the formula;
[tex]\frac{x}{32}*1600= 400\\50x=400\\x=\frac{400}{50}\\x=8[/tex]
This shows that Bola is 8 years old
Learn more on ratio here: https://brainly.com/question/19473677
A 12 ounce bag of rice costs $4.08. A 16-ounce bag of the same rice costs $5.76. Which bag is the better by
and by how much
Answer:
16 once is the better one.
Answer: 12-ounce bag is better by $0.02 per ounce
Concept:
When coming across questions that ask for a comparison between prices, we should make the final unit [price per object].
In finding [price per object], simply do [Total price / number of objects].
Solve:
A 12-ounce bag of rice costs $4.08
Total price / number of objects = 4.08 / 12 = $0.34 per ounce
A 16-ounce bag of rice costs $5.76
Total price / number of objects = 5.76 / 16 = $0.36 per ounce
$0.36 - $0.34 = $0.02
$0.34 < $0.36, therefore, 12-ounce bag is better by $0.02 per ounce.
Hope this helps!! :)
Please let me know if you have any questions
Find the length of FV
Answer:
72.47
Step-by-step explanation:
FV cos 43 = TV
FV (0.73135370161 ) = 53
FV = 72.468 = 72.47
Answer:
A
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos43° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{TV}{FV}[/tex] = [tex]\frac{53}{FV}[/tex] ( multiply both sides by FV )
FV × cos43° = 53 ( divide both sides by cos43° )
FV = [tex]\frac{53}{cos43}[/tex] ≈ 72.47 ( to 2 dec. places )
what is the volume of a cube with a length of a 10cm,
a width of 8cm and a height of 8cm
Answer:
640
Step-by-step explanation:
muntiply all the number length width height
the ages of two students are in the ratio of 3:5,if the older is 40yrs. How old is the younger student
The ratio/proportion is young / old = young / old.
We know that one ratio is 3 / 5, so we need to complete the other.
3 / 5 = young / 40
5 goes into 40, 8 times, therefore we need to multiply the numerator by 8 also.
3 x 8 = 24
The younger student is 24 years old.
Hope this helps!
Answer:
24
Step-by-step explanation:
younger : older
3 :5
The older is 40
40/5 = 8
Multiply each by 8
younger : older
3 *8 :5 *8
24 : 40
The younger is 24
ANSWER NOW IM TIMED Louie uses 10 feet of wood, 16 wheels and one can of paint for every 4 skateboards he builds.
A 4-column table with 3 rows. Column 1 is labeled Skateboards with entries 1, 4, 10. Column 2 is labeled Wood with entries blank, 10 feet, blank. Column 3 is labeled Wheels with entries blank, 16, blank. Column 4 is labeled paint with entries blank, 1 can, blank.
Use the table to find how much of each item Louie needs to build 10 skateboards.
Louie needs
feet of wood,
wheels, and
cans of paint.
Answer: 25 feet of wood
40 wheels and 2.5 cans of paints
Step-by-step explanation:
Answer:
25 feet of wood
40 wheels and
2.5 cans of paints
Step-by-step explanation: I did this before Also can i get brainlyist please
Question
(X-5y/y3)-1=
Answer:
[tex]x = y^3+5y[/tex]
Step-by-step explanation:
Complete question
[tex]\frac{x - 5y}{y^3} - 1=0\\[/tex]
Required
Solve for x
We have:
[tex]\frac{x - 5y}{y^3} - 1=0[/tex]
Collect like terms
[tex]\frac{x - 5y}{y^3} = 1[/tex]
Multiply through by [tex]y^3[/tex]
[tex]x - 5y = y^3[/tex]
Make x the subject
[tex]x = y^3+5y[/tex]
A computer parts company wants to make a rectangular memory board that has a perimeter of 14 cm and a diagonal of length 5 cm. What are the dimensions of the board?
Answer:
A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.: Call the two sides L & W: the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution
Step-by-step explanation:
==========================================================
Explanation:
x = width
y = length
both x and y are positive real numbers, and the units of which are in cm.
The perimeter of any rectangle is found by saying
P = 2*(length+width)
P = 2*(x+y)
Plugging in P = 14 leads us to
P = 2*(x+y)
14 = 2*(x+y)
14/2 = x+y
7 = x+y
Solve for one of the variables. Let's say we solve for y. That should get us y = 7-x which we'll use a bit later.
--------------
Notice how the diagonal forms two identical right triangles. The legs of which are x and y as defined earlier. The hypotenuse is 5, which is the diagonal length.
Use the pythagorean theorem to help solve for x
a^2 + b^2 = c^2
x^2 + y^2 = 5^2
x^2 + (7-x)^2 = 25 ... plug in y = 7-x
x^2 + 49 - 14x + x^2 = 25 ... use FOIL rule
2x^2-14x+49 = 25
2x^2-14x+49-25 = 0
2x^2-14x+24 = 0
2(x^2-7x+12) = 0
x^2-7x+12 = 0
(x-3)(x-4) = 0
x-3 = 0 or x-4 = 0
x = 3 or x = 4
If x = 3, then y = 7-x = 7-3 = 4
If x = 4, then y = 7-x = 7-4 = 3
We have this symmetry going on. If x is one of 3 or 4, then y is the other of those values. Because x = 3 and y = 4, or vice versa, this means we have a 3-4-5 right triangle (well to be fair we have two identical copies of such a triangle to form the rectangle).
Therefore, the dimensions of the rectangular board is 3 cm by 4 cm. The order doesn't matter so you could easily say "4 cm by 3 cm" to mean the same thing.
--------------
Check:
P = perimeter
P = 2*(length+width)
P = 2*(x+y)
P = 2*(3+4)
P = 2*7
P = 14
That helps confirm the answer.
The sum of three numbers is 124
The first number is 10 more than the third.
The second number is 4 times the third. What are the numbers?
Answer:
182/3,3 8/3, 152/3
Step-by-step explanation:
a+b+c=124
a trừ c= 10
4b=c
Answer:
a=29,b=79,c=19
Step-by-step explanation:
a=c+10
b=4c
=> a+b+c=c+10+4c+c=124
=> c=19
=> a= 29, b=79
The legend on a map states that 1 inch is 20 miles. If you measure 5 inches on the map, how many miles would the actual distance be? Actual distance = [ ? ] miles
Answer:
1 inch= 20 miles. 5*20=100 miles. The answer is 100 miles.
Step-by-step explanation:
On these types of questions just do that every time, then you don't need to ask, for example:
1 foot = 50 miles
If it measures 3 feet.
3*50=150 miles.
If you have any questions regarding my answer, tell me in the comments, and I will answer them.
on the same graph draw line 2y-x=10 and y=3x
Answer:
Step-by-step explanation:
Convert 15,000 meters to centimeters.
15,000 centimeters
150,000 centimeters
15,000,000 centimeters
1,500,000 centimeters
Answer:
1500000
Step-by-step explanation:
1 metre = 100 cm
15000metre =15000*100
=1500000
Find the value of a.
A. 58
B. 130
C. 86
D. 65
Answer:
[tex]C. \ \ \ 86[/tex]°
Step-by-step explanation:
1. Approach
In order to solve this problem, one must first find a relationship between arc (a) and arc (c). This can be done using the congruent arcs cut congruent segments theorem. After doing so, one can then use the secants interior angle to find the precise measurement of arc (a).
2. Arc (a) and arc (c)
A secant is a line or line segment that intersects a circle in two places. The congruent segments cut congruent arcs theorem states that when two secants are congruent, meaning the part of the secant that is within the circle is congruent to another part of a secant that is within that same circle, the arcs surrounding the congruent secants are congruent. Applying this theorem to the given situation, one can state the following:
[tex]a = c[/tex]
3. Finding the degree measure of arc (a),
The secants interior angle theorem states that when two secants intersect inside of a circle, the measure of any of the angles formed is equal to half of the sum of the arcs surrounding the angles. One can apply this here by stating the following:
[tex]86=\frac{a+c}{2}[/tex]
Substitute,
[tex]86=\frac{a+c}{2}[/tex]
[tex]86=\frac{a+a}{2}[/tex]
Simplify,
[tex]86=\frac{a+a}{2}[/tex]
[tex]86=\frac{2a}{2}[/tex]
[tex]86=a[/tex]
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 is the GCF of the expression 5x2y + 10xy2?
Answer:
[tex]5xy[/tex]
Step-by-step explanation:
[tex]\mathrm{Factor\:}:5x^2y[/tex]
[tex]5\cdot \:x\cdot \:x\cdot \:y[/tex]
[tex]\mathrm{Factor\:}:10xy^2[/tex]
[tex]2\cdot \:5\cdot \:x\cdot \:y\cdot \:y[/tex]
Common factor:-
[tex]5\cdot \:x\cdot \:y[/tex]
OAmalOHopeO
Differentiate y=2x+200/x with respect to x
Answer:
Hello,
[tex]\boxed{y'=2-\dfrac{200}{x^2} }\\[/tex]
Step-by-step explanation:
[tex](f(x)+g(x))'=f'(x)+g'(x)\\\\(2x)'=2*(x)'=2*1=2\\\\(\dfrac{200}{x} )'=200*(x^{-1})'=200*(-1)*x^{-1-1})=-\dfrac{200}{x^2} \\\\\\\boxed{y'=2-\dfrac{200}{x^2} }\\[/tex]
Answer:
[tex] \frac{dy}{dx } = 2 - \frac{200}{ {x}^{2} } [/tex]
Step-by-step explanation:
[tex]the \: equation \: can \: be \: rewriten \: as \\ y = 2x + 200 {x}^{ - 1} \\ \\ now \: differentiate \: the \: equation\ \\ \frac{dy}{dx} = 2 - 200 {x}^{ - 2} \\ \frac{dy}{dx} = 2 - \frac{200}{ {x}^{2} } [/tex]
Evaluate the expression when x=6 and y=-3.
-x+7y
Answer:
-27
Step-by-step explanation:
Let x = 6 and y = -3
[tex]-(6)+7(-3)\\-6-21\\-27[/tex]
Which figure always has exactly one line of symmetry?
A. rectangle
B. trapezoid
C. isosceles right triangle
D. circle
A shape of a trapezoid has exactly one line of symmetry. The correct option is B.
What is a trapezoid?An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium.
A balanced and proportionate likeness between an object's two halves is referred to as symmetry in geometry. It implies that one half is the other's mirror image.
A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel. The parallel sides may be vertical, horizontal, or angled.
Therefore, the shape of a trapezoid has exactly one line of symmetry. The correct option is B.
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