Answer:
Probability that 24 or more of those drivers were involved in accidents is 0.15625.
Step-by-step explanation:
We are given that an insurance agent research suggested that first year drivers had roughly an 13% chance of being involved in an automobile accident while driving.
The insurance agent provided insurance to 152 first year drivers last year.
Let [tex]\hat p[/tex] = sample proportion of drivers who were involved in accidents
The z score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt\frac{\hat p(1-\hat p)}{n} {} }[/tex] ~ N(0,1)
where, p = population proportion of first year drivers involved in an automobile accident while driving = 13%
n = sample of first year drivers = 152
Now, probability that 24 or more of those drivers were involved in accidents is given by = P([tex]\hat p[/tex] [tex]\geq[/tex] [tex]\frac{24}{152}[/tex])
P([tex]\hat p[/tex] [tex]\geq[/tex] 0.16) = P( [tex]\frac{\hat p-p}{\sqrt\frac{\hat p(1-\hat p)}{n} {} }[/tex] [tex]\geq[/tex] [tex]\frac{0.16-0.13}{\sqrt\frac{0.16(1-0.16)}{152} {} }[/tex] ) = P(Z [tex]\geq[/tex] 1.01) = 1 - P(Z < 1.01)
= 1 - 0.84375 = 0.15625
The above probability is calculated by looking at the value of x = 1.01 in the z table which has an area of 0.84375.
Hence, the required probability is 0.15625.
Jeff collected 100 baseball cards. Thirty-three of the cards are Cincinnati Reds players, and 22 of them are Cleveland Indians. Part B What decimal represents the part of the cards that are neither Cincinnati Reds nor Cleveland Indians?
Answer:
0.45.
Step-by-step explanation:
To find the solution to this question, we will first need to determine how many cards are neither Cincinnati Reds and Cleveland Indians. We can do this by:
100 - 22 - 33 = 45. This is the number of cards that are neither the two teams.
To convert this to a decimal, simply divide by 100, giving us:
45 ÷ 100 = 0.45.
A soccer player uses her head to hit a ball up in the air from a height of 1 meters with an initial vertical velocity of 5 meters per second. The height h in meters of the ball is given by h = −4.9t2 + 5t + 1, where t is the time elapsed in seconds. How long will it take the ball to hit the ground if no other players touch it? Enter the time to two decimal places.
Answer:
It will take 1.19 seconds for the ball to hit the ground if no other players touch it
Step-by-step explanation:
The height of the ball after t seconds is given by the following equation:
[tex]h(t) = -4.9t^{2} + 5t + 1[/tex]
How long will it take the ball to hit the ground if no other players touch it?
This is t when h(t) = 0. So
[tex]-4.9t^{2} + 5t + 1 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]-4.9t^{2} + 5t + 1 = 0[/tex]
So [tex]a = -4.9, b = 5, c = 1[/tex]
So
[tex]\bigtriangleup = 5^{2} - 4*4.9*1 = 44.6[/tex]
[tex]t_{1} = \frac{-5 + \sqrt{44.6}}{2*(-4.9)} = -0.17[/tex]
[tex]t_{2} = \frac{-5 - \sqrt{44.6}{2*(-4.9)} = 1.19[/tex]
Since we want a time measure, the answer cannot be negative.
It will take 1.19 seconds for the ball to hit the ground if no other players touch it
a circle has a center located at 2 5 and passes through the point 10 3 answer
Determine the equation of the circle. Show how you arrived at your answer.
Write the equation of the tangent line to the circle at the point . Show how you determined your answer.
Answer:
[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]
Step-by-step explanation:
Givens
The center of the circle is at (2,5).A point on the circumference is at (10,3).First, we need to find the radius, which is the distance between the given points.
[tex]d=\sqrt{(3-5)^{2} +(10-2)^{2} } =\sqrt{4+64}=\sqrt{68}[/tex]
Therefore, the radius of the circle is
[tex]r \approx 8.25[/tex]
The explicit form of the equation of the circle would be
[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]
Note: The monthly loan payment was calculated at 119 payments of $330.38 plus a final payment of $329.73. Loan Balance: $25,000.00 Loan Interest Rate: 10.0% Monthly Loan Payment: $330.38 Number of Payments: 120 Cumulative Payments: $39,644.95 Total Interest Paid: $14,644.95 On average, what dollar amount of each monthly payment is interest? $ What percent of the total payments is total interest? %
Answer:
Average monthly interest = $ 122.04
% total interest =36.94 %
Step-by-step explanation:
There are 120 cumulative payments and the total interest paid was $ 14,644.95.
Hence, the average monthly interest is :
Average monthly interest = $ 14,644.95 / 120
Average monthly interest = $ 122.04
% total interest
= ($ 14,644.95) / $ 39,644.95 x 100
% total interest =36.94 %
Find the number of digits in the square root of 61504.
Answer:
3
Explanation
There are 3 digits in the number 248 which is the square root of 61504.
√61504 = 248 --- 3 digits in 248
For every pound a company spends on advertising, it spends £0.59 on its website. Express the
amount spent on advertising to its website as a ratio in its simplest form.
Answer:
100:59
Step-by-step explanation:
For every pound a company spends on advertising, it spends £0.59 on its website.
Amount Spent on Advertising = £1
Amount Spent on Website = £0.59
Therefore:
Amount Spent on Advertising : Amount Spent on Website
= 1 : 0.59
Multiply both sides by 100
= 100: 59
The ratio of the amount spent on advertising to its website as a ratio in its simplest form is 100:59 in its simplest form.
Answer:
£100 : £59
Step-by-step explanation:
The said company spends £0.59 on its website for every pound spent on advertisement. This implies that out of £1.00 spent on advertisement by the company, £0.59 is for website placements.
Thus, the rate of the amount spent on advertisement to amount spent on website is given as:
£1.00 : £0.59
To convert this to the nearest whole number, multiply through by 100, so that the ratio becomes;
£100.00 : £59.00
Therefore, the ratio expressed in its simplest form is £100 : £59
(3/5)/2=(1/4)/x solve for x
Answer:
[tex]x=\frac{6}{5}[/tex]
Step-by-step explanation:
[tex]\frac{3}{5} / 2=\frac{3}{10}[/tex]
[tex]\frac{3}{10} =\frac{1}{4} x[/tex]
[tex]x=\frac{6}{5}[/tex]
Answer:
x=
[tex] \frac{5}{6} [/tex]
Step-by-step explanation:
(3/5)/2=(1/4)x
3/10=1/4x
12x=10
x=10/12=5/6
What is the slope of the line perpendicular to the segment with endpoints (2,0) and (-6,3)?
A. 8/3
B. 3/4
C. -4/3
D. -3/8
Answer:
A line that passes (2, 0) and (-6, 3) has slope:
S1 = (-6 -2)/(3 - 0) = -4/3
Another line that is perpendicular with above line has slope:
S2 = -1/S1 = -1/(-4/3) = 3/4
=> Option B is correct
Hope this helps
:)
The segment with endpoints (2,0) and (-6,3) has a line perpendicular to it with a slope of 4/3.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
From the general formula of the slope:
slope = (change in y) / (change in x)
The change in y is 3 - 0 = 3, and the change in x is -6 - 2 = -8. So the slope of the segment is:
slope = (3 - 0) / (-6 - 2) = -3/4
To find the slope of the line perpendicular to the segment, we know that it must have the opposite reciprocal slope. That is:
the slope of perpendicular line = -1 / slope of segment
slope of perpendicular line = -1 / (-3/4) = 4/3
Therefore, the slope of the line perpendicular to the segment with endpoints (2,0) and (-6,3) is 4/3.
Learn more about Linear equations here:
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Rewrite the function by completing the square.
h(x)=4x^2-36x+81
Answer:
y = 4 (x - 9/2) +0
Step-by-step explanation:
hope ot helps you
Answer:
here
Step-by-step explanation:
Andrea brought $54.00 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was one-sixths as much as the sketchbook, and the sketchbook cost three-fourths the cost of the paint set. Andrea had $1.50 left over after buying these items.
Answer:
See explanation below
Step-by-step explanation:
In this case, I'm assuming you want to know the price of all items purchased by Andrea.
Let's gather all the data.
Andrea has initially 54$. From that she got a Brush (B), a sketchbook (S) and a paint set (P). At the end, she has a left over of 1.5$, so she actually spends 52.5$, and our first equation would be:
B + S + P = 52.5 (1)
Now, the B cost 1/6 as the S, and S was 3/4 the paint set, so oru equations here would be:
B = 1/6S (2)
S = 3/4P (3)
Now, according to this we can write the (1) expression in function of (2) and (3).
Replacing (3) in (2):
B = 1/6 (3/4P)
B = 3/24P
B = 1/8P (4)
And replacing (3) and(4) in (1) we have:
1/8P + 3/4P + P = 52.5
From here we can solve for P:
15/8P = 52.5
P = 52.5 * 8 / 15
P = 28.16$
Now we can replace this value to get the Sketchbook, and then, the brush:
S = 3/4 * 28.16
S = 21.12$
B = 1/6 * 21.12
B = 3.52$
These values would be the price of all items.
All the ice cream sold has exactly one flavor and one treat. If a chocolate ice cream is picked at random, what is the probabilitly that it will have blue swirls
Answer:
Zero
Step-by-step explanation:
Since all the ice cream sold has exactly one flavor and one treat, a chocolate ice cream can't have a blue swirl. This means that the number of chocolate ice cream with blue swirl is zero. Therefor the probability is zero.
Megan, Sally and Tom share £180 in the ratio 1:3:2 how much more does Sally recieve than Megan?
Answer: Sally recieves £60 more than Megan
Step-by-step explanation:
Add the ratio together 1+3+2=6
£180 divided by 6 = 30
Megan gets 30
Sally gets 30x3=90
Tom gets 30x2=60 30:90:69
Which is the correct first step in finding the area of the base of a cylinder with a volume of 140pi cubic meters and a height of 12 meters?
Answer:
CCCC
Step-by-step explanation:
100) 4030
What’s the greatest common factor
Answer: 10
Step-by-step explanation:
100/10=10
4030/10=403
What is the inverse function of f(x) equals X over X -2
Answer:
(2x)/(x-1)
x = y/(y-2)
(y-2)x = y
yx - 2x =y
yx-y = 2x
y(x-1) = 2x
y= 2x/(x-1)
The volume of a cylinder with base radius 3 cm and height 6 cm is
_______ π cubic centimeters.
Answer:
54 π cubic centimeters
Step-by-step explanation:
Formula for the volume of a cylinder: πr²h
π×3²×6=
9×6×π=
54π cm³
I need help with question 9 please
Answer:
The population is everyone listed in the city phone directoy; the sample is the 75 people selected
Step-by-step explanation:
Use the unit circle to evaluate the six trigonometric functions of θ = -π.
Sin θ=
Cos θ=
Tan θ=
Csc θ=
Sec θ=
Cot θ=
Answer:
sin=0
cos=-1
tan=0
csc=undefined
sec=-1
cot=undefined
Step-by-step explanation:
On the unit circle, [tex]-\pi=\pi[/tex]. The sin of theta is therefore 0, the cosine is -1, and the tangent is 0/-1=0. Since the following functions are just the reciprocals of the previous ones, the cosecant is 1/0=undefined, the secant is 1/-1=-1, and the cotangent is 1/0= undefined. Hope this helps!
All six trigonometric ratios were calculated using a unit circle and comes out to be
[tex]sin(-\pi )= -sin\pi =0\\cos(-\pi )= cos\pi =-1\\tan(-\pi )= -tan\pi=0 \\cosec(-\pi )= -cosec\pi =infinity\\sec(\pi )= sec\pi =-1\\cot(-\pi )=-cot\pi=infinity[/tex]
I have attached a unit circle diagram.
What is a unit circle in trigonometry?In this unit circle corresponding values of sine and cosine have been written near the angle 'α' in form (cosα,sinα)
x-coordinate is cosα
y-coordinate is sinα
now,
one can find other trigonometric ratios
[tex]tan\alpha =\frac{sin\alpha }{cos\alpha } \\\\cot\alpha =\frac{1}{tan\alpha } \\\\cosec\alpha =\frac{1}{sin\alpha } \\\\sec\alpha =\frac{1}{cos} \\[/tex]
Hence, we can find the rest of the trigonometric ratios by using the coordinates (cosα,sinα) for a particular angle 'α'.
to get more about unit circle refer to the link,
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What is the greatest common factor of 9 and 14?
Answer:
1
Step-by-step explanation:
The factors of 9 are 9, 3, 1The factors of 14 are 14, 7, 2, 11 is the only number that can be divided into 9 and 14 without a remainder.The greatest common factor GCF of 9 and 14 is 1.
What is the greatest common factor of the given numbers?Given the numbers in the question:
9 and 14
To find the greatest common factor of two numbers, we need to identify all the factors of each number and then determine the greatest number they have in common.
First:
Factors of 9 are 1, 3, and 9, as these are the whole numbers that divide 9 without leaving a remainder.
Next,
Factors of 14 are 1, 2, 7, and 14, as these are the whole numbers that divide 14 without leaving a remainder.
The common factors of 9 and 14 are 1 since it is the only number that divides both 9 and 14.
Therefore, the greatest common factor of 9 and 14 is 1.
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Anne Deno purchased a house to fix up and use as a rental property. The house sold for $123,400. Anne made a $23,400 down payment and mortgaged the rest. Her annual expenses for mortgage interest, taxes, repairs, insurance, and depreciation totaled $8,750. Anne rented the house for $960 per month. What is the annual net income?
Answer:
The annual net income is $2770
Step-by-step explanation:
The annual net income on the rental property is the yearly rental minus the yearly annual expenses which consist mortgage interest,taxes, repairs,insurance as well as annual depreciation totaling $8,750
Annual rental =monthly rental* 12 months=$960*12=$ 11,520.00
Annual net income=$ 11,520.00-$8,750.00=$2,770
The annual net income is the gain that accrues to Anne Deno for purchasing the rental property and the subsequent letting to tenants
Here is a probability scale:
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
There are 3 white counters and 2 black counters in a bag.
I take one of the counters at random.
Put a cross on the probability scale to show the probability
that I have chosen one of the white counters.
Answer:
see below
Step-by-step explanation:
You have 3 chances in 5 of drawing a white counter, so the probability is ...
3/5 = 0.6
Your mark will go at 0.6 on the probability scale.
use the rules of significant figures to simplify the following expression: 31.5 x 10.51
Answer:
31.5×10.51
315/10×1051/100
331065/1000
331.065
A copy machine makes 32 copies per minute.how many copies does it make in 5 minutes and 15 seconds
Answer:
168
Step-by-step explanation:
You do 5 times 32 then divided 60 by 15 to figure out how much of 1 min is 15 sec its 1/4 so u do 1/4 of 32, 8 and add that to 5 times 32
Let point C be on circle A. If ∠BAC 5 radians and segment BC is 12cm, what is the length of the radius
Answer:
2.4 cm
Step-by-step explanation:
The formula we would use
S = rθ
Where S = Arc length
θ = central angle in radians
r = radius of the circle or length of the radius.
From the question, we can see that if
If C = a point on circle A
The Segment BC = The arc length of the circle = 12cm
∠BAC = central angle in radians = 5 radians.
Since, S = rθ,
Length of the radius = S/θ
= 12cm/5 radians
Length of the radius = 2.4 cm
18 - 3 x 2/ 5-1 squared
Answer:-3/5x(squared)+17
Step-by-step explanation:
Simplify and combine like terms
A university's freshman class has 5000 students. 90% of those
students are majoring in Economics. How many students in the
freshman class are Economics majors?
Answer:
4,500
Step-by-step explanation:
To find the number of students majoring in economics, you must turn 90% into a decimal making it .9.
Then you multiply the decimal to how many students there are (5000x.9) and that gives you 4,500.
Can someone help me please
Answer:
Step-by-step explanation:
At an amusement park john wants to ride a rollercoaster that costs 19 tickets, a bumper car that costs 3 tickets, and a merry-go-round that costs 33 tickets. John had 31 tickets but lost 10 of them on a ride. How many more tickets does he need?
Answer:
John will need 34 more tickets to be able to go on all the rides he wants
Step-by-step explanation:
To solve this, we need to first of all know the total cost in terms of tickets of all the rides that john wants to have.
This will be
cost of roller coaster ride = 19 tickets
cost of bumper car ride = 3 tickets
cost of merry-go-round ride = 33 tickets
Total cost of rides = 19 + 3 + 33 =55 tickets
Next, we will need to find the number of tickets that John has left after losing 10 of them.
This will be 31 - 10 = 21 tickets left
To find the number of more tickets that John needs , we will subtract the number of tickets he has left from total ride ticket cost.
This will be 55-21 = 34 tickets.
Hence, John will need 34 more tickets to be able to go on all the rides he wants
A sector with a radius of 6 cm has a central angle measure of 4pi/9 in radians. What is the area of the sector?
Answer:
8πcm² = 8pi cm²
Step-by-step explanation:
The formula for area of a sector = ½r²θ
Where r = radius = 6cm
θ = central angle = 4pi/9 in radians = 4π/9
Area of the sector = 1/2 × 6² × 4π/9
Area of the sector = (144π/18)cm²
Area of the sector = 8πcm²
Therefore, Area of the sector =
8πcm² = 8pi cm²
Answer:
8πcm² = 8pi cm²
Step-by-step explanation:
trust
-13=-18+w/4 two step equation
Answer:
w = 20
Step-by-step explanation:
Add 18 on both sides:
[tex]\frac{w}{4} =5[/tex]
Multiply by 4 on both sides:
w = 20
Answer:
20
Step-by-step explanation:
Let's solve your equation step-by-step.
−13=−18+ w/ 4
Step 1: Simplify both sides of the equation.
−13=−18+ w/ 4
−13=−18+ 1/ 4 w
−13= 1/ 4 w−18
Step 2: Flip the equation.
1/ 4 w−18=−13
Step 3: Add 18 to both sides.
1/ 4 w−18+18=−13+18
1/ 4 w=5
Step 4: Multiply both sides by 4.
4*( 1/ 4 w)=(4)*(5)
w=20