A survey asked students whether they have any siblings and pets. The survey
data are shown in the relative frequency table.
Pets
No pets
Total
Siblings
0.3
0.45
0.75
OA. 30%
OB. About 67%
O C. 75%
D. 40%
Given that a student has a sibling, what is the likelihood that he or she also
has a pet?
Answers
The likelihood that he or she has a pet given that a student does not have a sibling is 60%. Therefore, the correct option is option D.
Let A denote the event that a student does not have a sibling.
Let B denote the event that a student has a pet.
Then A∩B will denote the event that the student does not have a sibling but he has a pet.
Let P denote the probability of an event in this question.
Then, we have to find the conditional probability of event B which means the likelihood of event B occurring based on the occurrence of event A.
P(B|A)
We know that:
\(P(B|A) = \frac{P(A\cap B)}{P(A)}\)
Also from the table, we have:
P(A)=0.25
and P(A∩B)=0.15
Hence,
\(P(B|A) = \frac{0.15}{0.25}\)
\(P(B|A) = \frac{3}{5}\)
\(P(B|A) = 0.6\)
which in percentage is:
0.6 * 100 = 60 %
Therefore, the likelihood that he or she has a pet too is 60% and the correct option is option D.
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Related Questions
simplify pls do fast
Answers
The sum of the decimal values given is 0.93
Simplifying the decimal values can be done thus :
0.36 + 0.57Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .
0.36*100 = 36
0.57*100 = 57
Adding the whole numbers :
__36
+_57
_____
__93
Dividing the sum by 100 to convert to an equivalent decimal value,
93/100 = 0.93Therefore, the required value is 0.93
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Derive the first three (non-zero) terms of Taylor's series expansion for the function
(a) f(x)=sin(x)f(x)=sin(x) about the origin and thereby estimate sin(0.2)=
Answers
Answer:
We want to find the first 3 terms of the Taylor's series expansion for f(x) = sin(x) around x = 0.
Remember that a Taylor's series expansion of a function f(x) around the point x₀ is given by:
\(f(x) = f(x_0) + \frac{1}{2!}f'(x_0)*(x - x_0) + \frac{1}{3!}*f''(x_0)*(x - x0)^2 + ...\)
Where in the formula we have the first 3 terms of the expansion (but there are a lot more).
So, if:
f(x) = sin(x)
x₀ = 0
The terms are:
\(f(x_0) = sin(0) = 0\)
\(\frac{1}{2!}*f(x_0)'*(x - x_0) = \frac{1}{2} cos(0)*(x - 0) = x/2\)
\(\frac{1}{3!}*f(x_0)''*(x - x_0)^2 = \frac{1}{6}*-sin(0)*(x - 0)^2 = 0\)
\(\frac{1}{4!}*f(x_0)'''*(x - x_0)^3 = \frac{1}{24}*-cos(0)*(x- 0)^3 = -\frac{x^3}{24}\)
We already can see that the next term is zero (because when we derive the cos part, we will get a sin() that is zero when evaluated in x = 0), then the next non zero term is:
\(\frac{1}{6!}*f(x_0)''''*(x - x_0)^5 = \frac{1}{2*3*4*5*6} *(x - 0)^5 = \frac{x^5}{720}\)
Then we can write:
\(sin(x) = \frac{x}{2} - \frac{x^3}{24} + \frac{x^5}{720}\)
Evaluating this in x = 0.2, we get:
\(sin(0.2) = \frac{0.2}{2} - \frac{0.2^3}{24} + \frac{0.2^5}{720} = 0.099667\)
there are 538 jelly beans in a bowl hector and Michael decided to share the jelly beans how many jelly beans do Michael and hector get? Their mom tells them they can not eat all the jelly beans at once. They can each eat an equal amount of jelly beans for four days. How many jelly beans do hector and Michael eat each day for four days
Answers
Answer:
67.25
Step-by-step explanation:
Since they can each get 1/2 the jelly beans but need to eat it over 4 days they will be eating 1/2*1/4 jelly beans per day. This is equal to 1/8x where x is the total jelly beans. We know the total so we can plug 538 in for x and divide 538 by 8 to get 67.25
Stained glass slope graphing linear equation Description: Identify the slope and y-intercept of the linear equation. Then, graph the linear equations on the same coordinate plane. Make sure to extend the lines to the edge of the graph paper! Darken each line when finished. Color however YOU want to create a stained glass effect
Answers
Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
What is meant by slope-intercept?When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation. Given the slope of the line and the intercept it forms with the y-axis, the slope intercept form in mathematics is one of the forms used to determine the equation of a straight line. Y = mx + b is the slope intercept form, where m is the slope of the straight line and b is the y-intercept.To learn more about slope-intercept, refer to:
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Circle Project 1. Draw a point at (1, -2) 2. Draw an 8-unit long radius 3. Using a compass, Draw a circle with your point from step one as your center and the point from step two as the side. 4. Using a protractor, draw a 70 degree arc 5. Draw a central angle which intercepts your arc 6. Draw an inscribed angle which intercepts a 40 degree arc 7. Draw a tangent line 8. Draw a secant line 9. Write the equation of your circle.
Answers
Answer:
I can explain how to complete each of the steps you have provided.
1. Draw a point at (1, -2)
This is a simple step. Just mark a dot on your paper at the coordinates (1, -2).
2.
Draw an 8-unit long radius
Using your compass, set the radius to 8 units. Place the compass on the point you drew in step 1 and draw a circle around it, making sure that the radius is 8 units long.
3. Using a compass
Draw a circle with your point from step one as your center and the point from step two as the side: This step is already completed in step 2.
4. Using a protractor draw a 70 degree arc
Place your protractor on the center of the circle (the point you drew in step 1) and draw a 70 degree arc on the circle.
5. Draw a central angle which intercepts your arc
Use a straight edge to draw a line from the center of the circle to each endpoint of the arc you drew in step 4. This creates a central angle, which is an angle whose vertex is at the center of the circle and whose sides intercept the circle.
6. Draw an inscribed angle which intercepts a 40 degree arc
Use a straight edge to draw a line from one endpoint of the 70 degree arc to the other endpoint. Then, draw a perpendicular bisector of this line, which intersects the center of the circle. This creates a 40 degree arc on the circle. Draw a line from the center of the circle to one endpoint of the 40 degree arc, and draw a line from that endpoint to the other endpoint of the 40 degree arc. This creates an inscribed angle, which is an angle whose vertex is on the circle and whose sides intercept the circle.
7. Draw a tangent line
Choose a point on the circle that is not on the 70 degree arc. Draw a line from that point tangent to the circle.
8. Draw a secant line
Choose two points on the circle that are not on the 70 degree arc. Draw a line through those points, which intersects the circle at two points.
9. Equation of your circle
The equation of a circle with center (a,b) and radius r is (x-a)^2 + (y-b)^2 = r^2. Using the coordinates of the center from step 1 and the radius from step 2, the equation of the circle is (x-1)^2 + (y+2)^2 = 64.
Find the equation of the line passing through (-4,-2) and having a slope of 0.
Answers
Using the point-slope form:
⇒ \((y-y0) = m(x-x0)\)
Which require one point (x0,y0) on the line and the slope (m)
(x0,y0) --> (-4,-2)m --> 0Thus let us plug int the value
\((y + 2) = 0(x + 4)\\y + 2 = 0\\y = -2\)
Thus the equation of the line is y = -2
Hope that helps!
The heights of the starting players on each of two basketball teams are shown in the table below. Heights of Starters on Team A and Team B Team A 70 in. 72 in. 75 in. 68 in. 70 in. Team B 71 in. 73 in. 71 in. 72 in. 73 in. Jacob found that the mean height of Team A is 71 and the mean height of Team B is 72. He believes that because Team B has a greater mean, it also has a greater mean absolute deviation. Which explains Jacob’s error?
Answers
Answer:
The correct answer should be A
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Review: Jen sells flowers. She charges $2 per flower plug a $3 flat delivery fee. How many flowers did she deliver if she made $21?
Answers
Answer:
she delivers 9 flower plugs.
Step-by-step explanation:
in a standard equation the equation would be 21 = 2x + 3 and if you isolate the x you would have to first subtract the 3 from both sides and that would leave you with 18 = 2x and then you have to divide both sides by 2 and get 9=x
A study that looked at beverage consumption used sample sizes that were much smaller than previous national surveys. One part of this study compared 20 children who were 7 to 10 years old with 5 who were 11 to 13. The younger children consumed an average of 8.2 oz of sweetened drinks per day while the older ones averaged 14.1 oz. The standard deviations were 10.8 oz and 8.2 oz respectively.
Required:
Do you think that it is reasonable to assume that these data are Normally distributed? Explain why or why not?
Answers
Answer:
Step-by-step explanation:
In statistics, about 68 percent of values come in one standard deviation of the mean by using a standard normal model. Approximately 95% of the data were all within two standard deviations from the mean. Almost all of the data are in the range of three standard deviations of the mean (roughly 99.7%).
The 68-95-99.7 law, also known as the Empirical Rule, is based on this evidence. 68 percent of the data values of a naturally distributed data collection of small children with a mean of 8.2 and a standard deviation of 10.8 would be between -2.2 and 19.0.
Within a mean of 14.1 as well as a standard deviation of 8.2, 68 percent of the data values in a usually distributed data collection of older children would be between 5.9 and 22.3.
However, we cannot conclude that the data is naturally distributed since the real actual data vary from the usual normal curve computed above.
Hence, various measures like either goodness of fit or theory testing, would be used for this.
Can You please help me
Answers
Amelia has a music box that is shaped like a right rectangular
prism. She wants to pack the music box into a container,
with 1 in. of packing material between each face of the
music box and the container. A bag contains 200 in.3 of
packing material. How many bags of packing material will
Amelia need? Show your work.
Answers
The number of packing materials the Amelia will need = 2.4
How to calculate the quantity of packing materials Amelia will need?From the diagram given above, the formula for the volume of a right rectangular prism = Length×width ×height.
Where;
Length = 10in
Width = 6 in
Height = 8 in
The volume = 10×6×8 = 480 in³
But one bag = 200in³
The amount of bag that the music box can contain = 480/200 = 2.4
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need help writing a function
Answers
n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.
What is a linear equation in mathematics?
A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.
A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.
Roots : -3(mult . 2), 4(mult.2)
the function is given as
f(n) = (n + 3)² (n - 4)²
= (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)
= (n² + 6n + 9) (n² - 8n + 16 )
= n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1
collecting like term,
f(n) = n⁴ - 2n³ - 23n² + 24n + 144
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What is the slope of the line that passes
through (7,3) and (-2,4)?
O 7
02
- 9
0-
OS
Answers
\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)
Let's calculate the slope ~
\(\qquad \sf \dashrightarrow \: \dfrac{y_2 - y_1}{x_2 - x_1} \)
\(\qquad \sf \dashrightarrow \: \dfrac{3 - 4}{7 - ( - 2)} \)
\(\qquad \sf \dashrightarrow \: \dfrac{ - 1}{9} \)
That's the required slope, I hope it helps~
Which relationships have the same constant of proportionality between yyy and xxx as the following graph?
Answers
Answer:
Y=1 and X=4
Step-by-step explanation:
They have the same ratio as the point given
Dividing by a Monomial
What is (9x^3-6x^2+15x) ÷ 3x^2?
Answers
Answer:
\(3x-2+\frac{5}{x}\)
Step-by-step explanation:
To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:
(9x^3 - 6x^2 + 15x) ÷ (3x^2)
To simplify the division, we divide each term of the polynomial by 3x^2:
(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)
To divide monomials with the same base, we subtract the exponents. So:
9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x
(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2
15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x
Putting it all together, we have:
(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x
Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.
Method 1 Table of Values
Please help, I’ll mark brainlest
Answers
The graph of the quadratic function g(x) = - (x - 2)² + 4 on Cartesian plane is shown in the image attached below.
How to analyze and graph a quadratic equation
In this question we find the case of a quadratic equation in vertex form, whose definition is shown below:
y - k = a · (x - h)²
Where:
(h, k) - Coordinates of the vertex.a - Vertex constantThe equation of the axis of symmetry is shown below:
x = h
We can graph by using the coordinates of the vertex and two other points and understanding the vertex constant. Please notice that the parabola has an absolute minimum when vertex constant is positive, otherwise it is an absolute maximum.
First, find the coordinates of the vertex of the parabola:
(h, k) = (2, 4)
Second, determine the nature of the absolute extreme by interpretating the sign of vertex constant:
a = - 1 (The vertex is an absolute maximum)
Third, evaluate the function at two distinct points:
x = 0
g(0) = - (0 - 2)² + 4
g(0) = - (- 2)² + 4
g(0) = 0
x = 4
g(4) = - (4 - 2)² + 4
g(4) = - 2² + 4
g(4) = - 4 + 4
g(4) = 0
Fourth, graph the parabola on Cartesian plane. (Image is done with the help of a graphing tool)
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consider the equation 7x + 4 = ax + b.
for each pair of values for a and b, determine the number of solutions that the equation has.
select no solution, one solution, or infinitely many solutions for each pair of values.
1. a = 7, b = -4
2. a = 4, b = 7
3. a = 7, b = 4
4. a = -7, b = 4
Answers
Answer:
a = 7, b = -4:
This equation can be rewritten as 7x = ax + b - 4.
Since the coefficients of x on both sides are equal, the equation becomes 7x = ax - 4, we can see that the equation has only one solution.
a = 4, b = 7:
This equation can be rewritten as 7x = ax + b - 7.
Since the coefficients of x on both sides are different, the equation becomes 7x = 4x + 7, we can see that the equation has no solution.
a = 7, b = 4:
This equation can be rewritten as 7x = ax + b - 4.
Since the coefficients of x on both sides are equal, the equation becomes 7x = 7x + 4, we can see that the equation has infinitely many solutions.
a = -7, b = 4:
This equation can be rewritten as 7x = ax + b - 4.
Since the coefficients of x on both sides are different, the equation becomes 7x = -7x + 4, we can see that the equation has no solution.
Step-by-step explanation:
Given regular pentagon ABCDE, what are the coordinates of vertex C?
a) (b, c)
b) (b, -c)
c) (-b, c)
d) (-b, -c)
Answers
Answer: a
Step-by-step explanation: C is in quadrant 1 and quadrant 1 is (+,+)
The coordinate of the point C will be (b, c). Then the correct option is A.
What is regular pentagon?The polygon which is having five sides and each side are congruent. And each internal angle of the Pentagon will be of 108 degrees.
The pentagon ABCDE with the coordinate of A, B, C, D, and E are given below.
If a line intersect the shape and the shape look identical on both sides of line, then the line is known as axis of symmetry.
In a regular pentagon, there are five line of symmetry.
In the figure, the y-axis is the axis of symmetry and the axis of symmetry is passing through the point D.
The point C is in the first coordinate, then the abscissa and ordinate will be positive.
Then the coordinate of the C will be (b, c).
Then the correct option is A.
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Which of the following numbers is divisible by 2,3,5,6,9 and 10?
Answers
Answer: 15
Step-by-step explanation: 15 ÷ 5 = 3
I need help on solving.
Answers
Answer:
\(x = - 1 \\ - 2 + 0.4y = 0.4 \\ 0.4y = 0.4 + 2 = 2.4 \\ y = 2.4 \div 0.4 = 6 \\ y = 1 \\ 2x + 0.4 = 0.4 \\ 2x = 0.4 - 0.4 = 0 \\ x = 0\)
Answer:
\(2x + 0.4y = 0.4 \\ 2( - 1) + 0.4y = 0.4 \\ 0.4 y = 2.4 \\ y = \frac{2.4}{0.6} \\ \therefore \: y = 6 \\ 2x + 0.4(1) = 0.4 \\ \therefore \: x = 0\)
Write the following powers of 6 exponential form: 6 x 6
Answers
The exponential form of 6 × 6, is written as: 6².
How to Write an Expression in Exponential Form?Repeated multiplication involving base exponents and base can be written in exponential form, such as: a × a × a = a³.
Given the expression, 6 × 6, the number 6 will be the base while 2 will be the exponent if we want to express it in exponential form. Therefore:
6 × 6 = 6².
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26. Tyler has been saving his winning lottery tickets. He has 23 tickets that are worth a total of $175. If each ticket is worth either $5 or $10, how many of each does he have?
Answers
Work out the size of angle x
Answers
Answer:
53
Step-by-step explanation:
because triangle is equal to 180
the first one is 35 and there is 90 u will add them the u substraction 127 from 180 it equal to 53
hope it help
Plssssss answer thjs quet
Answers
Answer:
I’m. Not really good at math but I think its b
Step-by-step explanation:
if 25 worker need 3 days to build a house how long will 10 worker need
Answers
Answer:
3 x 10 = 30 man-days per house
Answer:
7.5 days
Step-by-step explanation:
Find length of rectangle of its area and breadth are 280m² and 40m
respectively.
Answers
Answer:
7
Step-by-step explanation:
Area= length times(x) width
280= L x 40
280 divided 40 =7
Answer:
Length=7
Step-by-step explanation:
Length=?
Area=280m^2
Breadth=40m
Area =LxB
so,Divide
280/40
=7
If every 2 cm on a scale drawing is equal to 7 feet in real life, which lines on the drawing would be greater than 21 feet in real life? Select all that apply. A) 7 cm B) 5 cm C) 9 cm D) 12 cm
Answers
The correct answers are A) 7cm, C) 9cm and D) 12cm
Define the Conversion of units?The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.
If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.
Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:
⇒ \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)
where y is the length of the line in real life. Solving for y, we get:
⇒ \(y = \frac{7 feet} {2cm} *x\)
⇒ \(y = 3.5 x feet\)
If we put x = 2cm (given) then, y = 7 feet
For y = 21 feet, the value of x = 6cm.
Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.
So, the lines on the drawing that are greater than 21 feet in real life are:
A) 7cm, C) 9cm, D) 12cm
Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm
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A salesman who uses his car extensively finds that his gasoline bills average $125.32 per month with a standard deviation of $49.51. Assume monthly gasoline bill amounts are normally distributed. The probability that his bill will be less than $50 a month or more than $150 for a single month is:
Answers
Answer:
The probability that his bill will be less than $50 a month or more than $150 for a single month is 0.3728 = 37.28%.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A salesman who uses his car extensively finds that his gasoline bills average $125.32 per month with a standard deviation of $49.51.
This means that \(\mu = 125.32, \sigma = 49.51\)
Less than 50:
p-value of Z when X = 50. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{50 - 125.32}{49.51}\)
\(Z = -1.52\)
\(Z = -1.52\) has a p-value of 0.0643
More than 150
1 subtracted by the p-value of Z when X = 150. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{150 - 125.32}{49.51}\)
\(Z = 0.5\)
\(Z = 0.5\) has a p-value of 0.6915
1 - 0.6915 = 0.3085
The probability that his bill will be less than $50 a month or more than $150 for a single month is:
0.0643 + 0.3085 = 0.3728
The probability that his bill will be less than $50 a month or more than $150 for a single month is 0.3728 = 37.28%.
Janice earns 4% commission on sales. One week she sold goods worth
$ 489, $568, $891, $922, and $631. How much commission did she earn?
a. $3,501
b. $140.04
c. $19.56
d. $22.72
Answers
Answer:
140.04
Step-by-step explanation:
(4.89+5.68+8.91+9.22+6.31)*4 = 140.04
Now you try on your own.
Kelly wants to build a new wardrobe for herself with only clothing pieces she loves, fit her well, and coordinate together. She already has most of the pieces she will use, but needs to save up to go shopping for the remaining items. She has already saved some money from her job, and she decides to set aside money weekly from her tips. The expression $25w+$65
represents the amount of money Kelly will have saved after some amount of weeks. What does each part of this expression represent?
$25=
Answer
w=
Answer
$65=
Answer
For this specific expression, would it make sense to plug in a negative number for w
? Answer
For this specific expression, would you ever expect to get a number less than 65
for your total amount saved?
Answers
The Interpretatiom of the equation is that;
w represents number of weeks she will have saved for the remaining items
$25 represents the amount she saves per week
$65 represents the amount she has already saved
How to solve algebra word problems?The algebra word problem can be solved by using variables to denote certain parameters I'm the question.
The general form of equation of a line in slope intercept form is;
y = mx + c
Where;
m is slope
c is y-intercept
We are given the equation:
$25w + $65
This equation represents the amount of money Kelly will have saved after some amount of weeks.
Thus;
w represents number of weeks she will have saved for the remaining items
$25 represents the amount she saves per week
$65 represents the amount she has already saved
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