Air bag manufactured by Aces(A)=57%
So, Probability [tex]P(A)=\frac{57}{100}[/tex]
Air bag manufactured by Best (B) =26%
So, Probability [tex]P(B)=\frac{26}{100}[/tex]
Airbag manufactured by Cool(C)=17%
So, Probability [tex]P(C)=\frac{17}{100}[/tex]
Airbags made by Aces, Best, and Cool do not kill people at rates of 99%, 96%, and 87%, respectively.
Let K be the event which kill people.
Probability of Air bag made by A which kill people [tex]P(K/A)=\frac{1}{100}[/tex]
Probability of Air bag made by B which kill people [tex]P(K/B)=\frac{4}{100}[/tex]
Probability of Air bag made by C which kill people [tex]P(K/A)=\frac{13}{100}[/tex]
If an airbag kills a passenger, calculate the probability that the airbag was manufactured by Cool
Using Baye's theorem:
[tex]P(C/K)=\frac{P(K/C)P(C)}{P(K/A)P(A)+P(K/B)P(B)+P(K/C)P(C)}[/tex]
Substitute the values of probabilities into formula
We get,
[tex]P(C/K)=\frac{0.17\times 0.13}{0.57\times 0.01+0.26\times 0.04+0.17\times 0.13}[/tex]
Now we calculate it and get probability
So, [tex]P(C/K)=0.5785[/tex]
So, 57.85% of passenger kills if the airbag was manufactured by Cool.
A football team won 9 out of 12 games what percentage of games has the football team won
Can someone work out bomdas for me 32-7×4+42÷6×3
HELP ME I NEED TO ANSWER THIS BEFORE OCTOBER 26!!
For each table, identify the independent and dependent variables. Represent the relationship using words, an equation, and a graph.
Number of Chairs Painted, p | Paint Left (oz), L
0 | 128
1 | 98
2 | 68
3 | 38
Number of Snacks Purchases,s | Total Cost ,C
0 | $18
1 | $21
2 | $24
3 | $27
Number of Flights of Stairs Climbed,n| 0 | 1 | 2| 3 |
Elevation(ft above sea level),E |311|326|341|256|
Please Help Me
&
Thank You
ANSWER TO QUESTION 7
Independent Variable: Number of Chairs Painted(p)
Dependent Variable: Paint Left(L)
To represent the relationship using a graph, we draw two perpendicular axis, wth Number of Chairs Painted(p) on the horizontal axis, and Paint Left(L) on the vertical axis.
Then we plot the points
[tex](0,\:\:128)[/tex], [tex](1,\:\:98)[/tex], [tex](2,\:\:68)[/tex], [tex](3,\:\:38)[/tex].
Using a straight edge, we draw a straight line through the points as shown in the diagram attached.
From the graph the slope is given by
[tex]Slope=\frac{60}{-2}=-30[/tex]
and the y-intercept is
[tex]c=128[/tex]
The equation is given by
[tex]L=mp +c[/tex]
That is
[tex]L=-30p +128[/tex]
In words, Paint level is reducing at a rate of [tex]30[/tex]oz
ANSWER TO QUESTION 8
Independent Variable: Number of snacks purchased(s)
Dependent Variable: Total Cost(c)
To represent the relationship using a graph, we draw two perpendicular axis, with Number of snacks purchased(s) on the horizontal axis, and Total Cost(c) on the vertical axis.
Then we plot the points
[tex](0,\:\:18)[/tex], [tex](1,\:\:21)[/tex], [tex](2,\:\:24)[/tex], [tex](3,\:\:27)[/tex].
Using a straight edge, we draw a straight line through the points as shown in the diagram attached.
From the graph the slope is given by
[tex]Slope=\frac{3}{1}=3[/tex]
and the y-intercept is
[tex]c=18[/tex]
The equation is given by
[tex]C(s)=ms +c[/tex]
That is
[tex]C(s)=3s +18[/tex]
In words, the Total cost increases is reducing at a unit rate of [tex]3[/tex]
ANSWER TO QUESTION 9
Independent Variable: Number of flight of stairs climbed(n)
Dependent Variable:Elevation (ft above sea level),E
To represent the relationship using a graph, we draw two perpendicular axis, with Number of flight of stairs climbed(n) on the horizontal axis, and Elevation (ft above sea level),(E) on the vertical axis.
Then we plot the points
[tex](0,\:\:311)[/tex], [tex](1,\:\:326)[/tex], [tex](2,\:\:341)[/tex], [tex](3,\:\:356)[/tex].
Using a straight edge, we draw a straight line through the points as shown in the diagram attached.
From the graph the slope is given by
[tex]Slope=\frac{15}{1}=15[/tex]
and the y-intercept is
[tex]c=311[/tex]
The equation is given by
[tex]E(n)=mn +c[/tex]
That is
[tex]E(n)=15n +311[/tex]
In words, the unit rate of rising above sea level is [tex]15[/tex]
Please Help!!!
Which statement represents the biconditional statement of the conditional statements?
If the measures of two angles have a sum of 180º, then the angles are supplements.
If two angles are supplements, then their measures have a sum of 180º.
A. The measures of two angles have a sum of 180º if and only if the angles are supplements.
B. The measures of two angles do not have a sum of 180º if and only if the angles are supplements.
C. The measures of two angles do not have a sum of 180º if and only if the angles are not supplements.
D. The measures of two angles have a sum of 180º if and only if the angles are not supplements.
A. The measures of two angles have a sum of 180º if and only if the angles are supplements.
the angles must be supplementary to equal 180
help please? .....................
[tex]2x^2+6x-10=x^2+6\qquad\text{subtract}\ x^2\ \text{and 6 from both sides}\\\\x^2+6x-16=0\\\\x^2+8x-2x-16=0\\\\x(x+8)-2(x+8)=0\\\\(x+8)(x-2)=0\iff x+8=0\ \vee\ x-2=0\\\\x+8=0\qquad\text{subtract 8 from both sides}\\\boxed{x=-8}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}\\\\Answer:\ \boxed{B.\ -8\ and\ C.\ 2}[/tex]
If EF = 5w + 20, FG = 7w + 28, and EG = 72, find the value of w. Find EF and FG
Answer:
w = 2, EF = 30 , FG = 42
Explanation:
We have EF = 5w + 20 and FG = 7w + 28
Since these points E, F and G are col-linear points we have.
EG = EF + FG
And given that EG = 72
So, EF+EG = 72
5w + 20 + 7w + 28 = 72
12w + 48 = 72
12 w = 24
w = 2
So EF = 5w + 20 = 5x2 + 20 = 30
FG = 7w + 28 = 7x2 + 28 = 42
solve the world problem. the formula d = rt gives the distance traveled in time t at rate r. if a bicyclist rides for 2.3 hours and travels 41 miles, what was her average speed.
A.9.43 miles per hour
B.38.7 miles per hour
C.5.6 miles per hour
D.17.83 miles per hour
Solve the equation. Check your answer.
-11=5+8x
x=?
Answer:
x=-2
Step-by-step explanation:
Consider equation -11=5+8x
Collecting the like terms
-8x=11+5, -8x=16
Dividing through by -8 ob both sides of the equation
(-8x)-/8=16/-8
x=-2
Nick works two jobs to pay for college. He tutors for $15 per hour and also works as a bag boy for $8 per hour. Due to his class and study schedule, Nick is only able to work up to 20 hours per week but must earn at least $150 per week. If t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy, which system of inequalities represents this scenario?
A.) t + b greater than or equal to 20 15t + 8b = 150
B.) t + b less than or equal to 20 15t + 8b greater than or equal to 150
C.) t + b less than or equal to 20 15t + 8b less than or equal to 150
D.) None of the systems shown represent this scenario.
Answer:
Option B is the correct answer.
Step-by-step explanation:
Earning for tutoring per hour = 15$
Earning for bag boy per hour = 8$
We have Nick is only able to work up to 20 hours per week but must earn at least $150 per week and t represents the number of hours Nick tutors and b represents the number of hours he works as a bag boy.
Nick is only able to work up to 20 hours per week
t + b ≤ 20
But must earn at least $150 per week
15 t + 8 b ≥ 150
Option B is the correct answer.
Jackson bought 5 ounces of raisins for $,4. How many ounces of raisins can he buy with $1
Answer:
1.25 ounces
Step-by-step explanation:
Answer: The required number of ounces that he can buy with $1 is 1.25.
Step-by-step explanation: Given that Jackson bought 5 ounces of raisins for $4.
We are to find the number of ounces of raisins that he can buy with $1.
We will be using the UNITARY method to solve the problem.
We have
Number of ounces of raisins that can be bought with $4 = 5.
Therefore, the number of ounces of raisins that can be bought with $1 is given by
[tex]\dfrac{5}{4}=1.25.[/tex]
Thus, the required number of ounces that he can buy with $1 is 1.25.
To lose one pound of fat, a 200-pound person must burn 3,500 calories. If that person burns 180 calories by walking for 30 minutes, how many hours and minutes does the person have to walk to lose two pounds? Round your answer to the nearest minute. A. 53 hours 38 minutes B. 38 hours 53 minutes C. 19 hours 27 minutes D. 39 hours
For this case we have:
You lose 180 calories by walking 30min, that is:
180cal ---------> 30min
If to lose 1 pound of fat, the person should burn 3500 calories, to lose 2 pounds should burn twice the calories, that is, 7000 calories.
You want to know how long it takes to burn 7000 calories, knowing that they burn 180 in 30min. So:
180cal ---------> 30min
7000cal -------> x
Where x represents the time that must be used to burn the 7000 calories.
Resolving we have:
[tex]x = \frac{(7000cal * 30min)}{180cal}\\[/tex]
[tex]x = 1166.7min\\[/tex]
If 1h has 60min, then:
[tex]x = \frac{ (1166.7min * 1h)}{60min}\\[/tex]
[tex]x = 19.44h\\\\x = (19h + 0.44h)\\[/tex]
0.44h equals [tex]0.44 * 60min = 26.4min\\[/tex]
Thus, for the person to burn 7000 calories and lose 2 pounds, he must walk [tex]x = 19h + 26.4min[/tex].
Answer:
[tex]x = 19h + 26.4min\\[/tex]
Option C.
519 divided by 6 and 915 divided by 7 and 439 divided by 7 and 812 divided by 9 which one does not have a two digit quotient.
519/6=86.5
915/7=130.7142
439/7=62.7142
812/9=90.2222
so i think its the 1st on but i may be wrong.
In the given sets of divisions, 812 divided by 9 is the one that does not yield a three-digit quotient when considering only whole numbers. All other division operations yield a three-digit quotient.
Explanation:Let's start by dividing each number step by step. When we divide 519 by 6, we get 86.5, and when we divide 915 by 7, we get 130.71428571428572. Next, when we divide 439 by 7, we get 62.714285714285715, and finally when we divide 812 by 9, we get 90.22222222222223.
In this case, a quotient is the result obtained from division. We're asked to identify the operation which does not yield a two-digit quotient. Here, all the separate division operations give us a quotient that is a numerical value with more than two digits. However, when you consider whole numbers only, 812 divided by 9 gives us a two-digit quotient (90), while all other division operation results are three-digit numbers.
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A team of scientists estimate the current number of butterflies in a park to be 20 thousand. The butterfly population is expected to increase at a rate of 4% per year. Which equation models the number of butterflies, in thousands, in the park after n years? A. 0.04(20)n B. 20(1.04)n C. 1.04(20)n D. 20(0.04)n
Answer:
Option B is the correct answer.
Explanation:
Current number of butterflies in the park = 20 thousand.
Rate of increase of butterfly population = 4% = 0.04
The population of butterfly after 1 year = 20+0.04*20 = 20*1.04
The population of butterfly after 2 years = 20*1.04 + 20*1.04*0.04 = 20*1.04*1.04
The population of butterfly after 3 years = 20*1.04*1.04 + 20*1.04*1.04*0.04 = 20*1.04*1.04*1.04
So, population of butterfly after n years = 20*(1.04*1.04*1.04* .... n times)
[tex]= 20*1.04^n[/tex]
Option B is the correct answer.
Answer:
The answer is C
Step-by-step explanation:
If a movie starts at 7:10 and ended at 9:05 how long was it
1 hour 55 minutes
break the time down into hours and minutes
7 : 10 → 8 : 00 = 50 minutes
8 : 00 → 9 : 00 = 1 hour
9 : 00 → 9 : 05 = 5 minutes
adding 1 hour + 50 minutes + 5 minutes = 1 hour 55 minutes
The movie lasted for a total of 115 minutes, which is calculated by adding the one hour between 7:10 and 8:10 to the additional 55 minutes between 8:10 and 9:05.
To calculate the duration of a movie that starts at 7:10 and ends at 9:05, you would subtract the start time from the end time. Starting at 7:10 and going up to 8:10 is one hour. From 8:10 to 9:05 is an additional 55 minutes. Therefore, adding these two parts together, the movie lasted for 1 hour plus 55 minutes, which is a total of 115 minutes.
Step-by-step, the calculation is as follows:
Calculate elapsed time from 7:10 to 8:10 (1 hour).Add the additional minutes from 8:10 to 9:05 (55 minutes).Combine both to find the total duration (1 hour + 55 minutes = 115 minutes).
Solve the following multiplication problems.
a. 9 kg 3 hg 1 cg × 9 =
b. 11 dg 4 cg × 12 =
c. 10 g 5 dg × 6 =
d. 5 g 3 dg 4 cg × 8 =
a.9 kg 3hg 1cg x 9 =243^3hc
b. 11dg 4cg x 12=528dg^2c
c. 10g 5dg x 6= 300g^2
d. 480g^3dc
-i hope this helps
Answer:
a. 8370009 cg
b. 1368 cg
c. 630 dg
d. 4272 cg
Step-by-step explanation:
Since, 1 kg = 100000 cg,
1 hg = 10,000 cg,
1 dg = 10 cg,
1 g = 10 dg,
1 g = 100 cg,
a. So, 9kg 3hg 1cg × 9 = (900000+30000+1) × 9 = 930001 × 9 = 8370009 cg,
b. 11dg 4cg × 12 = (110 + 4) × 12 = 114 × 12 = 1368 cg,
c. 10g 5dg × 6 = ( 100 + 5 ) × 6 = 105 × 6 = 630 dg,
d. 5g 3dg 4cg × 8 = ( 500 + 30 + 4) × 8 = 534 × 8 = 4272 cg
Three friends each have some ribbon. Carol has 90 inches of ribbon, tino has 13.5 feet of ribbon, and baxter has 1.5 yards of ribbon. Express the total length of ribbon the three friends have in inches, feet, and yards.
To find the total length of ribbon Carol, Tino, and Baxter have, first convert each length into the same unit. The total length of ribbon is 306 inches, 25.5 feet, or 8.5 yards when combining all their ribbons.
The lengths of ribbon that Carol, Tino, and Baxter have must be expressed in the same unit to find the total length. We will convert all lengths into inches, feet, and yards.
Carol's ribbon: 90 inches
Tino's ribbon: 13.5 feet × 12 inches/foot = 162 inches
Baxter's ribbon: 1.5 yards × 3 feet/yard = 4.5 feet then 4.5 feet × 12 inches/foot = 54 inches
Total Length in Inches:
90 + 162 + 54 = 306 inches
Total Length in Feet:
306 inches ÷ 12 inches/foot = 25.5 feet
Total Length in Yards:
25.5 feet ÷ 3 feet/yard = 8.5 yards
Now we have the total length of ribbon in all three units: inches, feet, and yards.
A spider ate 2 5 % 25%25, percent more bugs this month than last month. The spider ate 8 88 bugs last month. How many bugs did the spider eat this month? Bugs
bugs eaten this month = bugs eaten last month plus 25% of last month
x = 88 + .25 x 88
x = 88 + 88(.25)
= 88 + 22
= 110
Answer: 110 bugs
50 yards of tape is needed to pack and ship 100 packages. You have a roll of tape that is 2000 inches long. About how many yards do you have? A) 28 yards B) 50 yards C) 56 yards D) 67 yards
Find out how many feet are in a yard.
3 feet = 1 yard
Find out how many inches are in a yard
3×12=36
Find out how many yards are in 2000 inches.
2000÷36=55.5
55.5 ≈ 56
The answer would be C) 56 yards
Graph the function with the given description. A linear function h models a relationship in which the dependent variable increases 1 unit for every 5 units the independent variable decreases. The value of the function at 0 is 3.
The function is an illustration of a linear function.
See attachment for the graph of [tex]\mathbf{h(x) =-\frac{1}{5}x + 3}[/tex]
Let the independent variable be x
The highlights are given as:
The value of the function at 0 is 3. i.e. h(0) = 3When the independent variable decreases by 5 (i.e. -5), the independent variable increases by 1. So, the slope (m) is -1/5From the above highlights, we have:
[tex]\mathbf{m = -\frac{1}{5}}[/tex] --- the slope
[tex]\mathbf{b = 3}[/tex] --- the y-intercept
A linear equation is represented as:
[tex]\mathbf{h(x) =mx + b}[/tex]
So, we have:
[tex]\mathbf{h(x) =-\frac{1}{5}x + 3}[/tex]
See attachment for the graph of [tex]\mathbf{h(x) =-\frac{1}{5}x + 3}[/tex]
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Help me on this someone please
In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC =
The angles in the triangle ABC total 120 degrees, verifying it as a correct triangle. Given it is an isosceles triangle with AB and AC being the equal sides of length 6, and by applying the law of cosines, the length of side AC can be calculated.
Explanation:Given the angles of the triangle ABC as m
We can use the Law of Cosines to find the length of the side AC. The Law of Cosines states that c² = a² + b² - 2ab * cos(y). By substituting the given values into this formula, we find AC = sqrt[4² + 6² - 2*4*6*cos(50°)] which gives us the length of side AC.
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Which conversions from scientific notation to standard notation are true? Check all that apply.
For this case we have the following expressions:
a) [tex]1.71 * 10 ^ 3[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 3 times. So, we have:
[tex]1.71 * 10 ^ 3 = 1,710[/tex]
b) [tex]8.05 * 10 ^ 5[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 5 times. So, we have:
[tex]8.05 * 10 ^ 5 = 805,000[/tex]
c)[tex]2.4 * 10 ^ 4[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 4 times. So, we have:
[tex]2.4 * 10 ^ 4 = 24,000[/tex]
d) [tex]8.25 * 10^{-3}[/tex], in this case we have a negative exponent, therefore we move the decimal point as many times to the left as indicated by the exponent, that is, 3 times. So, we have:
[tex]8.25 * 10^{-3} =0.00825[/tex]
e) [tex]7.09 * 10^{-6}[/tex], in this case we have a negative exponent, therefore we move the decimal point as many times to the left as indicated by the exponent, that is, 6 times. So, we have:
[tex]7.09 * 10^{-6} = 0.00000709[/tex]
f) [tex]3.99 * 10 ^ 5[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 5 times. So, we have:
[tex]3.99 * 10 ^ 5 = 399,000[/tex]
g) [tex]8 * 10 ^ 7[/tex], in this case we have a positive exponent, therefore we move the decimal point as many times to the right as indicated by the exponent, that is, 7 times. So, we have:
[tex]8 * 10 ^ 7 = 80,000,000[/tex]
h) [tex]1.03 * 10^{-4}[/tex], in this case we have a negative exponent, therefore we move the decimal point as many times to the left as indicated by the exponent, that is, 4 times. So, we have:
[tex]1.03 * 10^{-4}= 0.000103[/tex]
Answer:
The correct options are: b, e, g and h
Emma had some apples in her basket. Then, she picked 9 more apples. She gave 14 apples to Klara. She had 10 apples left. How many apples did Emma have in her basket to start?
Janelle buys 4 cases of water. Each case of water contains 12 bottles. Janelle drinks 3 bottles of water. Veronica writes a numerical expression to represent the situation. Her expression (12 - 3) x 4 has a mistake.
: student council is selling tickets to the fall ball dance. Tickets cost $6.00 per person , or $10 per couple. To cover the expenses required, they need to make at least $1,450. Let x represent the number of individual ticket sold, and y represent the number of couple tickets sold. Write a linear inequality to model the situation
To model the situation with a linear inequality, represent the number of individual tickets sold as x and the number of couple tickets as y. The inequality is 6x + 10y >= 1450, signifying that the revenue from individual and couple ticket sales needs to be at least $1,450.
Explanation:To write a linear inequality to model the student council ticket sales, let x represent the number of individual tickets sold, and y represent the number of couple tickets sold. The tickets cost $6.00 per individual and $10.00 per couple. The council needs to make at least $1,450 to cover the expenses of the fall ball dance.
To derive the inequality, we consider the revenue generated from selling individual tickets (x tickets × $6.00 per ticket) plus the revenue generated from selling couple tickets (y tickets × $10.00 per ticket) should be at least $1,450:
6x + 10y ≥ 1450
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Last year there were 1,435 8th grade students enrolled at your sc hool. This year there are 1,220. What is the percent change in the number of 8th grade students?
1.2% of 8th grade students is the percentage change.
Using synthetic division what is the quotient of (2x^3-3x-10) divided by (x-2)
|-67.05 – 42.98| – (29.80 + 45.83)
A.
30.04
B.
34.04
C.
34.40
D.
44.04
Answer:
its d 44.04
Step-by-step explanation:
(9 – 23) + |47 – 16|
A.
15
B.
17
C.
19
D.
25
You answer is: 17
Or otherwise B. is your correct answer.
(9 - 23) = -(14)
| 47 - 16| = 31
31 + (-14) = 17
Answer:
B: 17
Step-by-step explanation:
What is y greater Than or equal to 1/3x-2
Answer:
The given equation is
⇒y≥[tex]\frac{1}{3x-2}[/tex]
As domain of the function is 3 x-2≠0
x≠2/3
⇒For different values of x we get different values of y.
When, x>2/3 , we get positive values of y.
So , y≥ 0
and when x< 2/3 , we get values of y which are negative.
i.e y≤0
At x=2/3, function is not defined.So at that point there does not exist any value of y.