A recent study conducted by a health statistics center found that 25% of households in a certain country had no landline service. This raises concerns about the accuracy of certain surveys, as they depend on random-digit dialing to houeholds via landlines. Pick five households form this country at random. Complete parts a) through c).
a) what is the probability that all five of them have a landline?
b) what is the probability that at least one of them does not have a landline?
c) what is the probability that at least one of them does have a landline?
Answers
Answer:
a) 23.73% probability that all five of them have a landline
b) 76.27% probability that at least one of them does not have a landline
c) 99.90% probability that at least one of them does have a landline
Step-by-step explanation:
For each household, there are only two possible outcomes. Either it has landline service, or it does not. The probability of a household having landline service is independent of other households. So we use the binomial probability distribution 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.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
25% of households in a certain country had no landline service.
This means that 100-25 = 75% have, so \(p = 0.75\)
Pick five households form this country at random.
This means that \(n = 5\)
a) what is the probability that all five of them have a landline?
This is P(X = 5).
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 5) = C_{5,5}.(0.75)^{5}.(0.25)^{0} = 0.2373\)
23.73% probability that all five of them have a landline
b) what is the probability that at least one of them does not have a landline?
Either all have, or at least one does not have. The sum of the probabilities of these events is 100%.
From a), 23.73% probability that all five of them have a landline
100 - 23.73 = 76.27
76.27% probability that at least one of them does not have a landline
c) what is the probability that at least one of them does have a landline?
Either none have a landline, or at least one has. The sum of the probabilities of these events is 1. So
\(P(X = 0) + P(X \geq 1) = 1\)
We want \(P(X \geq 1)\)
Then
\(P(X \geq 1) = 1 - P(X = 0)\)
In which
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 0) = C_{5,0}.(0.75)^{0}.(0.25)^{5} = 0.0010\)
So
\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0010 = 0.9990\)
99.90% probability that at least one of them does have a landline
Related Questions
Lines l and m are parallel. Which of the following pairs of angles are alternate interior angles?
Answers
The pairs of angles that are alternate interior angles will be angle 6 and angle 8.
What are alternate interior angles?When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairings of that transversal. Alternate interior angles are what they are termed.
Angles that are exterior to the lines, have different vertices, and sit on different sides of the transversal are referred to as alternate exterior angles. In other words, eight angles are created when a transversal intersects two parallel lines.
These van be illustrated in angle 6 and 8
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Lines l and m are parallel. Which of the following pairs of angles are alternate interior angles? ∠1 and ∠4 ∠2 and ∠3 ∠6 and ∠8
radius of a coin is 3cm then calculate its surface area
Answers
Elizabeth bought a cheese pizza. It was served on a metal tray with a diameter of 22 centimeters. What is the tray's area?
Answers
The Area of the tray ≈380 cm
Solution:We are given the diameter of the tray, which is equivalent to 22 cm.We are asked to find the area of the tray.Remember the formula:Area of a circle = πr²Whereπ -> pi (3.14...)r -> radiusNotice that we aren't given the radius. We're given the diameter only.No reason to panic. We can easily find the radius by dividing the diameter by 2.The radius is equal to 11 cm.Now, plug the values into the formula:A=π(11)²A=121πA≈380 cmHope it helps.
Do comment if you have any query.
Does the expression x^3-1 divided by x^2 -1 simplify to x?
Answers
No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.
To simplify the expression, let's first factorize both the numerator and denominator.
The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).
The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).
Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:
[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]
The (x - 1) terms cancel out, leaving us with:
x^2 + x + 1 / (x + 1)
So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.
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What is the shape of the cross section of a sliced cylinder
Answers
A sliced cylinder's cross section can be any shape that can be formed by intersecting a cylinder with a plane.
How to determine the shape?The shape of a sliced cylinder's cross section is determined by the angle and position of the slice.
If the slice is made parallel to the cylinder's base, the cross section is a circle.
If the slice is made at an angle to the cylinder's base, the cross section is an ellipse.
If the slice is made perpendicular to the cylinder's base, the cross section is a rectangle.
In general, a sliced cylinder's cross section can be any shape formed by intersecting a cylinder with a plane.
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Identify the expressions that correctly model the distance between a point located at (-2,3) and the point (x,y). Select all the apply
Answers
The distance between the two points is
d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².
What is distance between two points?Distance between two points is the length of the line segment that connects the two points in a plane.
The distance between two points is expressed as;
d = √ (X-x )² + (Y-y)²
X = -2
x = x
Y = 3
y = y
Therefore the distance between the two points is
d = √( -2-x)² + (3 -y)²
or it can also be written in this form
d = √ x-(-2)² + (y-3)²
d = √ x+2)² + (y-3)²
therefore the model of the distance between the two points can be
d = √( -2-x)² + (3 -y)² OR d = √ (x+2)² + (y-3)².
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The measures of the angles of the triangle are 32°, 53º,
950. Based on the side lengths, what are the measures
of each angle?
m2A = 95°, mZB = 53º, mZC = 32°
MZA= 32º, mzB = 53º, mZC = 95°
MZA= 43º, mZB = 32°, m2C = 95°
OmZA= 53º, m B = 95°, m2C = 32°
Answers
Answer:
m∠A = 32°
Step-by-step explanation:
8^2 = 12^2 + 15^2 - 2*12*15*cosA
Answer:
B
Step-by-step explanation:
did it on edge
A positive integer is 6 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(5,9), then find the two integers.
Answers
The two integers are equal to 1 and 7 respectively.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Let x represent the smaller number. Then the given relationships say ...
1/x + 2/(x+6) = 9/7
Multiplying by 7x(x+6), we have ...
7(x+6) +14x = 9x(x+6)
9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides
9x² +33x = 42 . . . . . . . . ...subtract 21x
3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3
(3x +14)(x -1) = 0 . . . . . . . . factor
Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.
Therefore, the two integers are equal to 1 and 7 respectively.
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In an orchard, there are 15 apple trees, 26 orange trees, and a cherry tree. What is the ratio of apple trees to cherry trees?
A: 41:1
B: 15:14
C: 1:15
D:15:1
NO LINKS
Answers
Answer:
D 15:1
Step-by-step explanation:
15 apple trees
26 orange trees
1 cherry tree
apple trees : cherry trees
15 : 1
Answer: D 15:1
Reuben bought 20 pounds of rice for $11. How many pounds of rice did he get per dollar?
Answers
20/11= 1.8
1.8 x 11 = 19.8
Round that up it’s 20
Answer:
Step-by-step explanation:
You can use a ratio and cross multiply to get your answer.
20 pounds 1 pound
---------------- = ----------------
$11 $ X
Forget about the units of measurement for now and just do the cross multiplying with the numbers to solve for X.
(20) x (X) = (1) x 11 then divide both sides of the equal sign by 20
20X 11
------- = ---------- the 20 on top and bottom on the left side cancel out.
20 20
So you are left with X = 11/20 which is $ 0.55
A quiz consists of multiple choice questions. each question has 4 possible answers (a-d) and only one answer is correct. if the student guesses the answer to each question, then what is the probability that the student answer correctly for that question?
Answers
Answer:
Answers - 4
Correct Answer - 1
Probability - 1/4
Question 10 of 25 What is the recursive formula for this geometric sequence? -2,-16, -128, -1024,... A. ○ B. C. (a, D. 3₁ = :-2 an = 2n-1 = = -2 an = an-1.8 • a₁ = 8 an = an-1• (-2) (a₁ = -8 30 = 20-1.2 SUBMIT
Answers
Answer:
\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2
Step-by-step explanation:
a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r
here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then
\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2
So desperate giving all of my points for this. Please show work and I'll give Brainliest. Please god please god please god
Answers
here you go someone already has answered this question before <3
HELP ASAP!!!
is the graph a function shown in the graph below one-to-one? why?
Answers
9514 1404 393
Answer:
(d) one output for every input
Step-by-step explanation:
A function is 1-to-1 if its graph passes the horizontal line test: a horizontal line may intersect the graph in only one place.
Which statement about the location of √7 on the number line is true?
A= It is located at the number 7 on the number line.
B= It is located at the number 3.5 on the number line.
C= It is located between the numbers 2 and 3 on the number line.
D=It is located between the numbers 4 and 9 on the number line
Answers
Explanation
The square root of a number is “what number times itself”
2 x 2 = 4
3 x 3 = 9
7 is between 4 and 9 so C is the correct answer
evaluate the expression (-6) squared
Answers
\( \huge \boxed{\mathfrak{Question} \downarrow}\)
Evaluate the expression ⇨ (-6) squared.\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)
\( \sf (-6) \: squared\)
This will be equal to..
\( \sf( - 6 ) ^ { 2 }\)
Multiply -6 by itself (squaring a number means to multiply the number by itself twice)
\( \sf- 6 \times - 6 \\ \)
-6 multiplied by-6 will get you 36 as the answer.
\( = \boxed{\boxed{\bf \: 36}}\)
100 point!!!
Nazim is planning to cook curries and sell them. He will take orders for parties. He will cook the curry and rice beforehand, then put the cooked food in serving dishes that will keep it hot. Nazim will pay his friend Raj, who has a van, to make deliveries and to fetch the serving dishes back after the party.Nazim’s first order is for a party of 27 people. He has a recipe using vegetables, chick peas, onions and tomatoes. He is now trying to work out the right quantities of spices. For 15 people he would normally use 100 g of spices, made up of ginger (20%), turmeric (25%), coriander (35%), and cumin seeds (20%). What weight of turmeric must Nazim put in a curry for 27 people?
Answers
Answer:
45 grams
Step-by-step explanation:
1st order: 27 people
15 people:
100 g
Ginger: 20 g
Turmeric: 25 g
Coriander: 35 g
Cumin Seeds: 20 g
20+25+35+20=60+40=100
For 1 person:
Ginger: 1 1/3 g
Turmeric: 1 2/3 g
Coriander: 2 1/3 g
Cumin Seeds: 1 1/3 g
Multiply all that by 27
For 27 people:
Ginger: 36 g
Turmeric: 45 g
Coriander: 63 g
Cumin Seeds: 36 g
45 g for Turmeric
The length of a rectangle is 4 yd longer than its width. If the perimeter of the rectangle is 40 yd, find its area.
Answers
Answer:
96
Step-by-step explanation:
sum n=3 ^ infty 6 ( 2 3 )^ n-3
Answers
We need to evaluate this:
Let me attach the work:
You can see that the series is infinite geometric series.
The first term (a) would be:
\(\frac{2}{3}^3=\frac{8}{27}\)The common ratio r is 2/3
So, sum to inifnity would be:
\(\text{Sum}=\frac{a}{1-r}=\frac{\frac{8}{27}}{1-\frac{2}{3}}=\frac{8}{9}\)Therefore:
\(\frac{81\times(\frac{8}{9})}{4}\)\(=18\)Answer is 18
list those numbers in order from least to greatest
-4,-9/4,1/2,3.7, √5
Answers
Answer:
-4, -9/4, 0.5, 2.2 (the last one) , 3.7
Step-by-step explanation:
I hope you have a great day and LEAVE ME ALONE! <3
What is -5 5/8+3 1/2?
Answers
Answer: -2 1/8
Step-by-step explanation:
3 1/2 = 3 4/8
5 5/8 - 3 4/8 = 2 1/8
Add the negative sign back to get -2 1/8
Determine which postulate or theorem can be used to prove that
ALMN=ANOL.
M
A. SAS
B. ASA
C. AAS
D. SSS
Answers
The answer is A. SAS.
If a parallelogram is given and we want to prove that ALMN is congruent to ANOL, we can use the SAS (Side-Angle-Side) postulate.
The SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In the case of the parallelogram, we know that AL is congruent to NO (opposite sides of a parallelogram are congruent) and LM is congruent to OL (opposite sides of a parallelogram are congruent). Additionally, angle LAM is congruent to angle LAO (opposite angles of a parallelogram are congruent).
By using the SAS postulate, we have two sides and the included angle that are congruent in both triangles. Therefore, we can conclude that triangle ALMN is congruent to triangle ANOL.
So, the answer is A. SAS.
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The graph of the function f(x) = (x - 3)(x + 1) is shown.
Ty
-10-8-6
10
8
6
-6
8
-10-
6
10
X
Which describes all of the values for which the graph is
positive and decreasing?
O all real values of x where x < -1
O all real values of x where x < 1
O all real values of x where 1
O all real values of x where x > 3
Answers
Answer:
all real values of x where x < -1
The correct statement is all real values of x where x < -1.
Option A is the correct answer.
We have,
To determine the values for which the graph of the function
f(x) = (x - 3)(x + 1) is positive and decreasing, we need to analyze the behavior of the function.
Let's consider the factors individually:
(x - 3): This factor is positive for x > 3 and negative for x < 3.
(x + 1): This factor is positive for x > -1 and negative for x < -1.
To determine the overall sign of the function, we need to consider the signs of both factors together.
When both factors are positive or both factors are negative, the function is positive.
When the factors have opposite signs, the function is negative.
From the above analysis, we can conclude the following:
When x > 3, both factors are positive, so the function is positive.
When -1 < x < 3, the factor (x - 3) is negative, while the factor (x + 1) is positive. Therefore, the function is negative.
When x < -1, both factors are negative, so the function is positive again.
Since we are looking for values where the function is positive and decreasing, we can eliminate the options that include positive and increasing regions (such as x > 3).
Thus,
The correct statement is all real values of x where x < -1.
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how do i solve this Please give me a advise
Answers
The probability of spinning an even number, flipping tails, then spinning an odd number is:
1/9 (as fraction) or 11.11% (as percent)
How to find the probability of spinning an even number, flipping tails, then spinning an odd number?
To find the probability of spinning an even number, flipping tails, then spinning an odd number. We need to consider the individual probabilities. That is:
We have only one even number in the spinner, and that is 2. Thus,
P(even number) = 1/3
For a coin, the probability of head or tail is 1/2. Thus,
P(tail) = 1/2
We have two odd number in the spinner, and that is 1 and 3. Thus,
P(odd number) = 2/3
Therefore, the probability of spinning an even number, flipping tails, then spinning an odd number will be:
P(even, tail, odd) = 1/3 * 1/2 * 2/3
= 2/18
= 1/9 (as fraction)
In percent:
P(even, tail, odd) = 1/9 * 100
= 11.11%
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Kyle sold an antique through an online auction website. The website host charges kyle $15, plus 2.5% of the final selling price of the antique. After selling the antique, kyle had to pay the website host $32. What was the selling price?
Answers
The selling price of the antique through an online auction website is $680.
Given that,
Kyle sold an antique through an online auction website.
The website host charges Kyle $15, plus 2.5% of the final selling price of the antique.
After selling the antique, Kyle had to pay the website host $32.
Let x be the selling price of the antique.
We get an equation,
15 + (2.5% × x) = 32
15 + 0.025x = 32
0.025x = 17
x = $680
Hence the selling price is $680.
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Write the linear equation that gives the rule for this table.
Answers
Linear equations are two-variable equations that graph as a straight line.
What is meant by linear equation?An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Two-variable equations that graph as a straight line are said to be linear equations. The slope and y-intercept of a linear equation allow it to be graphed. Y = mx + b, where m is the slope and b is the y-intercept, is the formula used to represent a line. A graph's straight line can be represented by a linear equation.
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what does it mean to love your country?
I'm supposed to write an essay on it but I just don't understand lolz
Answers
Answer:
not my words... used quotes
“To love your country is to desire to see it become the best version of itself, to point out its failures, to recognize how we each have been complicit in allowing its worst to persist, to work together to create a community in which every resident has all that they need — love, food, shelter, health, peace, prosperity — and are truly treated as equals in every regard.”
‘Be proud of it, but not afraid to confront its problems’
To love your country is to be proud of it, but also to not be afraid to confront its problems and work to solve them. I love our blatant freedoms, despite all of the cries of “communism,” “social justice warriors” and “cancel culture.” We are still largely free to do what we want!
Step-by-step explanation:
A family buys a studio apartment for 240000. They pay a down payment of 36000
Answers
Answer: the answer is 236400
Step-by-step explanation:
umb
1 MP Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 1/8 pounds of soil
and a box with 1 3/4pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
Answers
No, she does not have enough soil as she needs 4 pounds of soil.
What is meant by soil?
A mixture of organic material, minerals, gases, liquids, and living things make up soil, often known as earth or dirt, and they work together to support life. Certain scientific definitions separate dirt from soil by limiting the former term to just displaced soil.The field of edaphology investigates how soils affect living beings.The study of how soils are formed, described (morphology), and categorized in their natural environments is known as pedology.In engineering, the term "soil" is used to refer to loose material that is present on the Moon and other celestial bodies, as well as other loose material that is found above the bedrock.she as = 2 1/8 + 1 3/4
= 17/8 + 7/4
= 17+ 7 × 2 / 8
= 17 + 14 / 8
= 31/8
= 3 7/8 pounds
≤ 4 pounds.
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Each side of a quilt square measures approximately 4.25 inches. If there are about 2.54 centimeters in 1 inch, how long is each side of the square in centimeters? Use complete sentences to explain your reasoning.
Answers
Answer: approximately 10.8 centimeters
Step-by-step explanation:
We have a square, where each side measures approx. 4.25 in
Now we know that 1in ≈ 2.54 cm
Then, in 4.25 in, we have 4.25 times 1 inch, so we have 4.25 times the length of 2.54 cm
So the approximate measure of the sides in centimeters is:
4.25*(2.54)cm = 10.8 cm
So we have that each side measures approximately 10.8 centimeters