A survey of 100 high school students provided thisfrequency table on how students get to school:Drive toTake theGradeWalkSchoolbusSophomore2253Junior13202Senior2555Find the probability that a randomly selected studenteither takes the bus or walks.[?P(Take the bus U Walk)
Answers
Let's call the event of a student taking the bus as event A, and the event of a student walking as event B. The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes. We have a total of 100 students, where 50 of them take the bus and 10 of them walk. This gives to us the following informations:
[tex]\begin{gathered} P(A)=\frac{50}{100} \\ P(B)=\frac{10}{100} \end{gathered}[/tex]The additive property of probability tells us that:
[tex]P(A\:or\:B)=P(A)+P(B)-P(A\:and\:B)[/tex]Since our events are mutually exclusive(the student either walks or takes the bus), we have:
[tex]P(A\:and\:B)=0[/tex]Then, our probability is:
[tex]P(A\cup B)=\frac{50}{100}+\frac{10}{100}-0=\frac{60}{100}=\frac{3}{5}[/tex]The answer is:
[tex]P(Take\:the\:bus\cup Walk)=\frac{3}{5}[/tex]Related Questions
List the elements in the set
{x 1 x is a negative multiple of 5}
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S={-5,-10,-15,-20,-25......}; these are few negative multiples of 5 as stated in the set builder form of set theory {x :x is a negative multiple of 5}.
What is set?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things.
What is set builder form?Set builder notation is a type of mathematical notation used to describe sets by listing their components or highlighting the requirements that each member of the set must meet. We write sets in the form of in the set-builder notation.
{y | (properties of y)} OR {y : (properties of y)}
Here,
{x :x is a negative multiple of 5}
S={-5,-10,-15,-20,-25.....}
According to the set builder form of set theory, {x:x is a negative multiple of 5} S={-5,-10,-15,-20,-25...}; these are a few negative multiples of 5.
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(Score for Question 1: ___ of 5 points)1. Wendy wants to find the width, AB, of a river. She walks along the edge of the river 300 ft and markspoint C. Then she walks 80 ft further and marks point D. She turns 90° and walks until her location,point A, and point C are collinear. She marks point E at this location, as shown.AriverAD 80 ft300 ftBE(a) Can Wendy conclude that AABC and AEDC are similar? Why or why not?(b) Suppose DE = 50 ft Calculate the width of the river, AB. Show all your work.Answer
Answers
We know that two triangles are similar if two pairs of corresponding angles are equal.
In this case, we have:
• Angles EDC and ABC are right angles. Then, these angles are equal.
,• Angles DCE and ACB are ,vertical angles,. In other words, they are opposite angles made by two intersecting lines. Vertical angles are ,congruent,, then these angles are equal.
AnswerSince the above condition is fulfilled, triangles ABC and EDC are similar.
Part b)When two triangles are similar, their corresponding sides are in the same ratio.
[tex]\frac{a}{e}=\frac{b}{d}=\frac{c}{c^{\prime}}[/tex]Then, we can write and solve the following equation:
[tex]\begin{gathered} \frac{300ft}{80ft}=\frac{c}{50ft} \\ 3.75=\frac{c}{50ft} \\ \text{ Multiply by 50ft from both sides} \\ 3.75*50ft=\frac{c}{50ft}*50ft \\ 187.5ft=c \end{gathered}[/tex]AnswerThe width of the river is 187.5 feet.
Determine the x-intercept for 3x + 2y = 14.A) (7,0) B) (0,7) C) (14/3,0) D) (0,14/3)
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By definition, when the line intersects the x-axis, the value of "y" is:
[tex]y=0[/tex]Knowing this, you can substitute that value of "y" into ithe equation given in the exercise:
[tex]\begin{gathered} 3x+2y=14 \\ 3x+2(0)=14 \end{gathered}[/tex]Now you must solve for the variable "x" in order to find the x-intercept. This is:
[tex]\begin{gathered} 3x+0=14 \\ 3x=14 \\ x=\frac{14}{3} \end{gathered}[/tex]Then, you get this point:
[tex](\frac{14}{3},0)[/tex]The answer is: Option C.
what is 5/8 out of 100
Answers
5/8 of 100 can be obtained by applying the rule of three:
[tex]\begin{gathered} 1\text{ ----- 100} \\ 5/8\text{ ----x} \end{gathered}[/tex]then, x is given by
[tex]\begin{gathered} x=\frac{\frac{5}{8}\cdot100}{1} \\ x=62.5 \end{gathered}[/tex]then, the answer is 62.5.
The numerator of the sum 1+1/3+2 is (a) 1 (b) 2 (c) 5 (d) 6.
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The expression is given as,
[tex]\frac{1}{2}+\frac{1}{3}[/tex]Note that the denominator of both the fractions are prime numbers. So their lowest common multiple, LCM(2,3) will be the product of the numbers,
[tex]undefined[/tex]Suppose that you earn $15
Answers
Answer: 800 hours
Step-by-step explanation:
3x - 7 = 3(x - 3) + 2
Answers
3x - 7 = 3x - 7
3x - 3x = -7 + 7
0 = 0
This is obviously always true!
Any value of x will satisfy the original equation.
shows four types of polygons which type of polygon shown has no pairs of parallel sides
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Accoring to the given figures, the pentagon is the one without parallel sides.
Hence, the answer is Pentagon.1. ¿Qué expresiones a continuación se pueden usar para encontrar el área del prisma rectangular de abajo? ¡ELIJA TODOS LOS QUE SE APLIQUEN! Nota: Puede probarlos todos para asegurarse de que sean iguales. * 15 (5x2x3) + (2x3x3) (5x2) + (5x2) + (5x2) + (5x2) 5x2x2 2 (5x2) + 2 (5x2) + 2 (2x2)
Answers
We need to find the area of the prism given in the following image:
You need to add the surfaces of ALL rectangles in the image (recall that the area of a rectangle is : Base x Height)
So for this prism we have:
FOUR rectangles that measure 5 x 2
and also TWO small squares of area 2 x 2
So we need to select all the formulas they give you that read like the addition of the two above:
(5x2) + (5x2) + (5x2) + (5x2) + (2x2) + (2x2)
It can also be written as:
2 (5x2) + 2 (5x2) + 2 (2x2)
simplify the rational expression. 18x3y5 45x5y9
Answers
8y+63x+9
Assuming a fixed hourly pay rate, how much would an employee earn for working 4 hours based on this wage table? Hourly Pay Table Hours Worked 2 Money Earned $12.00 $24.00 $36.00 ? A. $36.00 B. $45.00 C. $64.00 D. $48.00
Answers
We have the following table
hour pay
1 12
2 24
3 36
4 ?
It seems that for each hour we work, we end up earning $12. Then, we know that if we work 3 hours we earn 36. So, if we work one more hour (4) we should add 12 to what we earn for working 3 hours. That is
[tex]12+36\text{ = 48 }[/tex]So we aren 48 for working 4 hours.
Samantha started with $25 in her account. she saves $7 per week. Australia has no money in his account, but adds $15 per week. for how many weeks will Australia have more money in his account than Samantha
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In this problem we can made a function to calculate the total amount for Samantha (S) and total amound of Australia (A) fon any time:
[tex]\begin{gathered} S=25+7t \\ A=0+15t \end{gathered}[/tex]when t is the number of weeks. if we made equal the ecuation we will have the time when they would have the same amound:
[tex]\begin{gathered} S=A \\ 25+7t=15t \end{gathered}[/tex]and we solve for t
[tex]\begin{gathered} 25=15t-7t \\ 25=8t \\ \frac{25}{8}=t \\ 3.125=t \end{gathered}[/tex]This means that in the next full number Australia will have more money than Samantha, so in 4 weeks this is going to happen.
This is matching:#1 If solving a problem with population growth compounding CONTINUOUSLY, which of the following formulas would you use?#2 If solving a problem with population growth compounding ANNUALLY, which of the following formulas would you use?#3 If solving a problem with population growth compounding QUARTERLY, which of the following formulas would you use?#4 If solving a problem with continuously compounding interest, which of the following formulas would you use?A: A(t)=P(1+r÷n)^ntB: A(t)=Pe^rtC: P(t)=P0(1+r)^tD: P(t)=P0^e^rt
Answers
#1
The formula for continuous compounding is:
[tex]A(t)=P_{}e^{r\cdot t}[/tex]#2
Since the population grows compounding annually, we have that:
[tex]P(t)=P_0(1+r)^t[/tex]#3
For a problem with population growth compounding quarterly, we have to divide the rate between n=4, therefore:
[tex]A(t)=P(1+\frac{r}{n})^{n\cdot t^{}}[/tex]#4
Finally, for continuously compounded interest we have the formula:
[tex]P(t)=P_0e^{r\cdot t}[/tex]Which of the following correctly identifies the vertices that lie on the major axis of the conic section shown below? (x - 2) 3-2*) (y+5) = 1 4 9 O A. (2,-2) and (2,-8) O B. (-5,5) and (-5,-1) O C. (5,5) and (-1,-5) O D. (0,-5) and (4,-5)
Answers
General equation of an ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]where (h,k) is the center, and a and b are some constants.
If b² is greater than a², then the y-axis is the major axis.
In this case, the ellipse is defined by the next equation:
[tex]\frac{(x-2)^2}{4}+\frac{(y+5)^2}{9}=1[/tex]This means that:
[tex]\begin{gathered} b^2=9 \\ b=\sqrt[]{9} \\ b=3 \end{gathered}[/tex]And, h = 2, k = -5
The vertices on the major axis are computed as follows:
(h, k+b) and (h, k-b)
Substituting with h = 2, k = -5, and b = 3, the vertices are:
(2, -5+3) and (2, -5-3)
(2, -2) and (2, -8)
Need help with this review question. I need to know how to find the measurements from the cyclic quadrilateral
Answers
Given a quadrilateral ABCD
A cyclic quadrilateral has all its vertices on the circumference of the circle
Also cyclic quadrilateral
has the opposites angles add up to 180°
then
[tex]\angle a+\angle c=180[/tex][tex]\angle b+\angle d=180[/tex]then
Option A
A=90
B=90
C=90
D=90
since A+C= 180
and B+D = 180
measures from Option A could come from a cyclic quadrilateral
Option B
A=80
B=80
C=100
D=100
Since A+C = 80+100 = 180
and B+D = 80 + 100 = 180
measures from Option B could come from a cyclic quadrilateral
Option C
A=70
B=110
C=70
D=110
Since A+C=70+70 = 140
And B+D =110+110=220
measures from Option C could NOT come from a cyclic quadrilateral
Option D
A=60
B=50
C=120
D=130
A+C= 60+120 = 180
B+D= 50+130 = 180
measures from Option D could come from a cyclic quadrilateral
Option E
A=50
B=40
C=120
D=150
A+C=50+120= 170
B+D=40+150 = 190
measures from Option E could NOT come from a cyclic quadrilateral
Then correct options are
Options
A,B and D
Classify each set of measures as AAS, ASA, SSA, SAS, or SSS. Then find the indicated length or angle measure (to the nearest tenth).
Answers
Hello there. To solve this question, we'll have to remember some properties about triangles.
Given the triangle:
Notice in this case we have two consecutive angles and a side between them. This is a case of ASA (angle-side-angle).
With respect to the side with measure x, we have two consecutive angles then the side, hence AAS.
To find x, we'll have to apply the law of sines:
[tex]\dfrac{A}{\sin(\alpha)}=\dfrac{B}{\sin(\beta)}=\dfrac{C}{\sin(\gamma)}=2R[/tex]In this case, the angle opposite to x measures 73º and the angle opposite to 4 measures 85º, hence:
[tex]\dfrac{x}{\sin(73^{\circ})}=\dfrac{4}{\sin(85^{\circ})}[/tex]Multiply both sides by a factor of sin(73º)
[tex]x=\dfrac{4\sin(73^{\circ})}{\sin(85^{\circ})}[/tex]Using a calculator, we get the following approximation (rounding to the nearest tenth):
[tex]x\approx3.8[/tex]This is the measure of x we're looking for.
Use the Distributive Property to solve the equation 2/3 (9a + 6) = 23.8
Answers
Distributive property tell us how to solve expressions in the form a(b+c), it says:
a(b+c)=ab+ac
Then,
[tex]\begin{gathered} \frac{2}{3}(9a+6)=23.8 \\ \frac{18a}{3}+\frac{12}{3}=23.8 \\ 6a+4=23.8 \\ 6a=23.8-4 \\ a=\frac{19.8}{6}=3.3 \end{gathered}[/tex]Select the polynomial functions for which (x+3) is a factor. Select all that apply.
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If x+3 is a factor, then the result of replacing x=-3 in each equation would be 0.
Replacing x=-3 in the polynomials, we have:
Option A
[tex]\begin{gathered} f(-3)=(-3)^4-12(-3)^3+54(-3)^2-108(-3)+81=1296\text{ } \\ \text{ We see that option A is incorrect.} \end{gathered}[/tex]Option B
[tex]\begin{gathered} f(-3)=(-3)^4-3(-3)^3-(-3)+3=168\text{ } \\ \text{We see that option B is incorrect.} \end{gathered}[/tex]Option C
[tex]\begin{gathered} f(-3)=(-3)^5+2(-3)^4-23(-3)^3-60(-3)^2=0\text{ } \\ \text{We see that option C is correct.} \end{gathered}[/tex]Option D
[tex]\begin{gathered} f(-3)=(-3)^5+5(-3)^4-3(-3)^3-29(-3)^2+2(-3)+24=0\text{ } \\ \text{We see that option D is correct.} \end{gathered}[/tex]The answers are options C and D.
given that the measure of arc AD=(17×+2), measure of arc AC=(7×-10),and measure of angle ABC=(4×+15) find the measure of angle ABC
Answers
In the given figure, angle ABC is formed by a tangent and a secant.
The angle formed by tangent and secant is given by
[tex]m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC})[/tex]Where mAD and mAC are the intercepted arcs.
For the given case,
[tex]\begin{gathered} m\angle ABC=(4x+15)\degree \\ m\bar{AD}=(17x+2)\degree \\ m\bar{AC}=(7x-10)\degree \end{gathered}[/tex]Let us substitute the given values into the above formula and solve for x
[tex]\begin{gathered} m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC}) \\ (4x+15)\degree=\frac{1}{2}\lbrack(17x+2)\degree-(7x-10)\degree\rbrack \\ 2\cdot(4x+15)\degree=(17x+2)\degree-(7x-10)\degree \\ 8x+30=17x+2-7x+10 \\ 8x-17x+7x=2+10-30 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}[/tex]The value of x is 9
So, the measure of angle ABC is
[tex]\begin{gathered} m\angle ABC=4x+15 \\ m\angle ABC=4(9)+15 \\ m\angle ABC=36+15 \\ m\angle ABC=51\degree \end{gathered}[/tex]Therefore, the measure of angle ABC is 51°
10 × 1/3
make sure the answer is a fraction and that u explain
Answers
multiply the top and bottom ----> 10*1 and 1*3
10/3 would be your answer
12 is what percent of 18
Answers
We have that
[tex]12\cdot\text{ }\frac{100}{18}=\text{ }\frac{1200}{18}\text{ = 66.6666}[/tex]So the answer is: 66.6666 .
A trapezoid has a height of 16 miles. The lengths of the bases are 20 miles and 35miles. What is the area, in square miles, of the trapezoid?
Answers
Given:
A trapezoid has a height of 16 miles.
The lengths of the bases are 20 miles and 35 miles.
To find:
The area of the trapezoid.
Explanation:
Using the area formula of the trapezoid,
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]On substitution we get,
[tex]\begin{gathered} A=\frac{1}{2}(20+35)\times16 \\ =\frac{1}{2}\times55\times16 \\ =440\text{ square miles} \end{gathered}[/tex]Therefore the area of the trapezoid is 440 square miles.
Final answer:
The area of the trapezoid is 440 square miles.
is H less than 9?[tex]h \leqslant 9[/tex]
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3) The given inequality is
[tex]h\text{ }\leq\text{ 9}[/tex]The inequality symbol is that of less than. Since it has an equal to sign attached, then, the meaning is h is less than or equal to 9. In words, h is at most 9, no more than 9.
Suppose you are completely locked out outside of your house. You remember that you left your bedroom window, which is 12 feet above the ground, unlocked from the inside (meaning you can climb up the window if you have a ladder, which you do!). You go to your garage, grab the 20 ft ladder and place it so that it reaches exactly to your bedroom window. What is the angle of elevation needed to reach your window? How far away will the bottom of the ladder be from your house?
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A diagram of the situation is shown below:
In order to determine the angle of elevation x, use the sine function, as follow:
sin x = opposite side/hypotenuse
the opposite side is the distance from the ground to the wi
Today, October 20, 2022, seven friends ate lunch together at Chipotle.
Friend #1 eats there every day - including weekends.
Friend #2 eats there every other day - including weekends
Friend #3 eats there every third day - including weekends
Friend #4 eats there every fourth day - including weekends
Friend #5 eats there every fifth day - including weekends
Friend #6 eats there every sixth day - including weekends
Friend #7 eats there every seventh day - including weekends
Assuming that none of them catch Covid or miss any days, what will be the date when the friends again all eat lunch together at Chipotle?
Answers
The most appropriate choice for LCM of two numbers will be given by -
All the friends together can eat lunch on 14th December 2023.
What is LCM?
LCM means Lowest Common Multiple. LCM of two numbers a and b is the least number that is divisible by both a and b.
Friend 1 eats lunch together at Chipotle everyday including weekends
Friend 2 eats lunch together at Chipotle every other day including weekends
Friend 3 eats lunch together at Chipotle every third day including weekends
Friend 4 eats lunch together at Chipotle every fourth day including weekends
Friend 5 eats lunch together at Chipotle every fifth day including weekends
Friend 6 eats lunch together at Chipotle every sixth day including weekends
Friend 7 eats lunch together at Chipotle every seventh day including weekends
Number of days after which all the friends together can eat lunch
= LCM of 1, 2, 3, 4, 5, 6, 7 = 420 days
All the friends together can eat lunch after 420 days
All the friends together can eat lunch on =
(31 - 20) + 30 + 31 + 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 +14 = 14th December 2023
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ill take a pic of it
Answers
The line passes through the points given.
Select any two points from the table, (-4,2) and (-3,5).
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Hence the slope is:
[tex]\begin{gathered} m=\frac{5-2}{-3-(-4)} \\ m=\frac{3}{1} \\ m=3 \end{gathered}[/tex]The slope is 3.
y+2=−3(x−4)y, plus, 2, equals, minus, 3, left parenthesis, x, minus, 4, right parenthesis Complete the missing value in the solution to the equation.
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The required equation is 11y = 3x + 2.
What is 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.
Given y+2=−3(x−4)y .....................(1)
Simplifying (1) and we get
y+2=−3x + 12y
=> 3x + y - 12y + 2 = 0
=> 3x -11y + 2 = 0
=> 3x - 11y = -2
=> 11y - 3x = 2
=> 11y = 3x + 2
Therefore, the required equation is 11y = 3x + 2.
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If a rectangle has a perimeter of 70, a length of x and a width of x-9, find the value of the length of the rectangle040 3113O 22
Answers
The formula for the perimeter of rectangle is,
[tex]P=2(l+w)[/tex]Substitute 70 for P, x for l and (x - 9) for w in the formula to determine the value of x.
[tex]\begin{gathered} 70=2(x+x-9) \\ 35=2x-9 \\ 2x=35+9 \\ x=\frac{44}{2} \\ =22 \end{gathered}[/tex]So value of x is 22.
How long can you lease the car before the amount of the lease is more than the cost of the car
Answers
ANSWER:
48 months
STEP-BY-STEP EXPLANATION:
According to the statement we can propose the following equation, where the price of the car is more than or equal to the amount of the lease. Just like this:
Let x be the number of months
[tex]16920\ge600+340x[/tex]We solve for x, just like this:
[tex]\begin{gathered} 600+340x-600\le16920-600 \\ \frac{340x}{340}\le\frac{16320}{340} \\ x\le48 \end{gathered}[/tex]Therefore, for 48 months, the car rental will be lower
Given points C(-3,-8) and D(-6.5,-4.5), find the coordinate of the point that is 2/3 of the way from C to D.
Answers
Answer:
(-16/3,-17/3)
Explanation:
Let the point which is 2/3 of the way from C to D = X
It means that point X divides the line segment CD internally in the ratio 2:1.
To determine the coordinate of point X, we use the section formula for internal division of a line segment:
[tex](x,y)=\left\{ \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right\} [/tex][tex]\begin{gathered} (x_{1,}y_1)=(-3,-8) \\ (x_2,y_2)=(-6.5,-4.5) \\ m\colon n=2\colon1 \end{gathered}[/tex]Substituting these values into the formula above, we have:
[tex]X(x,y)=\left\{ \frac{2(-6.5)+1(-3)}{2+1},\frac{2(-4.5)+1(-8)}{2+1}\right\} [/tex]We then simplify:
[tex]\begin{gathered} X(x,y)=\left\{ \frac{-13-3}{3},\frac{-9-8}{3}\right\} \\ =\left\{ \frac{-16}{3},\frac{-17}{3}\right\} \end{gathered}[/tex]Therefore, the exact coordinate of the point that is 2/3 of the way from C to D is (-16/3,-17/3).
