Answer:
(a)
Number of cars with defective turn signals = 65
Number of cars with no defective turn signals = 410 - 65 = 345
Required probability:
P = 345/410*100% ≈ 84.15%(b)
Number of cars with defects = 65 + 35 = 100
Number of cars with no defects = 410 - 100 = 310
Required probability:
P = 310/410*100% ≈ 75.61%What is the inverse of the function g (x) = 5 (x - 2)
Answer:
g − 1 ( x ) = x/ 5 + 2
Step-by-step explanation:
See the pic for solutions :)
The price of an item has been reduced by 70%. The original price was $30. What is the price of the item now?
Answer:
$9
Step-by-step explanation:
30*(100%-70%)=9
Answer:
9
Step-by-step explanation:
Take the original price
Multiply by the discount percent
30 *70%
30 *.70
21
The discount is 21 percent
Subtract this from the original amount
30-21
9
Jorge plans to paint a bedroom wall that is shaped like a trapezoid. The bottom edge of the wall is 22.5 feet long, and the top edge of the wall is 9.5 feet long. If the wall is 8 feet tall, what is the area of the wall? Round your answer to the nearest hundredth if necessary.
A building security code has 2 numeric
digits, O through 9, followed by 2 letters.
What is the probability that the first digit
is 9 and the last letter is A?
Answer:
Step-by-step explanation:
First number is 1/10
Last letter is 1/26
The second digit is 1/9
The first letter is 1/25
1/10 * 1/26 * 1/9 * 1/25
0.00001709
This assumes no duplication is allowed,
If there are duplications
then 1/10 * 1/10 * 1/26 * 1/26
0.000014782
*20 points*
A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.
Sample 1: 4
Sample 2: 1
Sample 3: 9
How do the sample statistics compare to the population mean and standard deviation?
There will be about 6.25 sheep on each acre.
250/40 = 6.25
Are the two triangles below similar?
U
ВО
56
No because there are not to pairs of congruent corresponding angles
Yes because there are two pairs of congruent corresponding angles
No because the corresponding sides are not proportional
Yes because the corresponding sides are proportional
Answer:
Yes, because there are two pairs of congruent corresponding angles
Step-by-step explanation:
Two triangles are similar if they have the same angles. For triangle UVT on the left, we know that the sum of angles in a triangle is 180 degrees. There is one missing angle there, so the sum of angles is
80 + 55 + missing angle = 180
subtract 80+55 = 135 from both sides
45 = missing angle
Therefore, the angles in UVT are 45, 55, and 80
Similar, for XWY,
missing angle + 45 + 55 = 180
subtract 45 + 55= 100 from both sides
missing angle = 80
The angles for XWY are 45, 55, and 80. The angles are the same for both triangles, and there are three pairs of congruent corresponding angles (45, 55, and 80). Therefore, the triangles are similar
first person answers this gets 25 points its khan academy algebra 1
a-7=3(b+2)
1. Simplify/Combine like terms
a-7=3b+6
2. Remove a variable
a-7-a=3b+6-a
7=2b+6
3. Isolate the variable
7-6=2b-6
1=2b
4. Divide
1/2=2b/2
b=1/2
1/2g?
Five hundred randomly selected adult residents in Sacramento are surveyed to determine whether they believe children should have limited smartphone access. Of the 500 people surveyed, 381 responded yes - they believe children should have limited smartphone access.
You wish to estimate a population mean y with a known population standard devi- ation o = 3.5. If you want the error bound E of a 95% confidence interval to be less than 0.001, how large must the sample size n be?
Answer:
The sample size must be of 47,059,600.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation:
[tex]\sigma = 3.5[/tex]
If you want the error bound E of a 95% confidence interval to be less than 0.001, how large must the sample size n be?
This is n for which M = 0.001. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.001 = 1.96\frac{3.5}{\sqrt{n}}[/tex]
[tex]0.001\sqrt{n} = 1.96*3.5[/tex]
[tex]\sqrt{n} = \frac{1.96*3.5}{0.001}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*3.5}{0.001})^2[/tex]
[tex]n = 47059600[/tex]
The sample size must be of 47,059,600.
Suppose you have 3 bags. Two of them contain a single $10 bill, and the third contains a single $5 bill. Suppose you pick one of these bags uniformly at random. You then add a $5 bill to the bag, so it now contains two bills. The bag is shaken, and you randomly draw a bill from the bag without looking into the bag. Suppose it turns out to be a $5 bill. If a you draw the remaining bill from the bag, what is the probability that it, too, is a $5 bill
Answer:
1/2
Step-by-step explanation:
Number of bags = 3
number of bags with $10 bill initially = 2
number of bags with $5 bill initially = 1
assume :
event you pick a $5 bill at first draw = A
event you pick a $5 bill at second draw = B
hence : P ( A n B ) = 1/3 * 1 = 1/3
P( A ) = ( 1/3 * 1 ) + ( 1/3 * 1/2 + 1/3 * 1/2 ) = 2/3
therefore P( that the second drawn bill is $5 )
P( B | A ) = P(A n B ) / P ( A )
= (1/3) / (2/3) = 1/2
The probability that it, too, is a $ 5 bill is 33.33%.
Since you have 3 bags, and two of them contain a single $ 10 bill, and the third contains a single $ 5 bill, supposing you pick one of these bags uniformly at random and you then add a $ 5 bill to the bag, so it now contains two bills, and the bag is shaken, and you randomly draw a bill from the bag without looking into the bag, supposing it turns out to be a $ 5 bill, if a you draw the remaining bill from the bag, to determine what is the probability that it, too, is a $ 5 bill, the following calculation must be performed:
3 bags = 2 with a 10 bill and 1 with a 5 bill 1/3 = 0.3333 0.3333 x 100 = 33.33
Therefore, the probability that it, too, is a $ 5 bill is 33.33%.
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Given f (x) = 4x-3, g(x) = x^3 +2x
Find (f-g) (4)
Answer:
[tex](f-g)(4) = -59[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=4x-3\text{ and } g(x) = x^3 +2x[/tex]
And we want to find the value of:
[tex](f-g)(4)[/tex]
Recall that this is equivalent to:
[tex](f-g)(4) = f(4) - g(4)[/tex]
Find f(4):
[tex]f(4) = 4(4)-3 = 13[/tex]
And find g(4):
[tex]g(4) = (4)^3 + 2(4) =72[/tex]
Substitute:
[tex](f-g)(4) = (13)-(72)[/tex]
And subtract. Hence:
[tex](f-g)(4) = -59[/tex]
Step-by-step explanation:
I love this question!
So there are a couple different ways of solving this. You feel free to ignore whichever one makes less sense.
Subtracting First
The first option is taking f(x) and g(x) and subtracting them, then introducing the number.
The calculation:
f(x) - g(x)
Substitute.
4x - 3 - (x^3 + 2x)
Multiply out the negative.
4x - 3 - x^3 - 2x
Rewrite.
-x^3 + 4x - 2x - 3
Simplify.
-x^3 + 2x - 3
Then, replace x with 4.
-(4)^3 + 2(4) - 3
Simplify.
-64 + 8 - 3
Add.
-59
Making x = 4 first
Here, we'll do what's on the tin. Find f(4) and g(4), then subtract them.
f(x) = 4x - 3
f(4) = 4(4) - 3
f(4) = 16 - 3
f(4) = 13
Then find g(4):
g(x) = x^3 + 2x
g(4) = (4)^3 + 2(4)
g(4) = 64 + 8
g(4) = 72
Then, subtract these two:
f(4) - g(4) = 13 - 72
f(4) - g(4) = -59
Answer:
Either way, the answer is -59
a. 6
b. 10
c. 7
d. 9
Answer:
6
Step-by-step explanation:
21-20 = 1
20-18 =2
18 -15 = 3
15-11 = 4
We are subtracting 1 more each time
11-5 = 6
Mike wants to buy a scooter worth R10000 but cannot afford so he opts for the hire purchase agreement which requires a 13% deposit and a 24 equal monthly installments at a rate of 15% per annum compounded monthly
A.How much will his deposit be?
B.calculate how much does he still need to pay after the deposit
C.calculate the monthly installment
Answer: I think the answer is A
Step-by-step explanation:
Cahrlotte is 19/5 YEARS YONGER THAN RACHEL. 2 YEARS LATER, RACHEL WILL BE THRICE AS OLD AS CHARLOTTE. FIND THEIR AGES SFTER 3 YEARS. (ESTAMATE THE AGE TO THE NEAREST WHOLE NUMBER).
Answer:
Step-by-step explanation:
Charlotte starts at 19 years old.
Rachel starts at 24 years old.
Then two years later, Rachel is 26 and Charlotte is 21. This is not 3 times Charlotte's age.
Do you have all the right info?
DVD Video Rentals (Refer to Example 3.) The func-
tion V computes the percent share of disc DVD rentals
accounted for by various companies. This function is
defined by V(R) = 37, V(N) = 30, and V(S) = 17,
where R is Redbox, N is Netflix, and S is rental stores.
(Source: Business Insider.)
(a) Write V as a set of ordered pairs.
(b) Give the domain and range of V.
T
Answer:
[tex](a)\ V = \{(N,30),(R,37),(S,17)\}[/tex]
[tex](b)[/tex]
[tex]Domain = \{N,R,S\}[/tex]
[tex]Range = \{37,30,17\}[/tex]
Step-by-step explanation:
Given
[tex]V(R) = 37,\ V(N) = 30,\ V(S) = 17[/tex]
Solving (a): Set of ordered pair
A function y = f(x) is represented as (x,y)
So, the ordered pair of V is:
[tex]V = \{(R,37),(N,30),(S,17)\}[/tex]
Order the alphabets in increasing order
[tex]V = \{(N,30),(R,37),(S,17)\}[/tex]
Solving (b): The domain and the range
In a function [tex]\{(x_1,y_1),...,(x_n,y_n)\}[/tex]
The domain and the range are represented as:
[tex]Domain = \{x_1,x_2....x_n\}[/tex]
[tex]Range = \{y_1,y_2....y_n\}[/tex]
So, we have:
[tex]Domain = \{N,R,S\}[/tex]
[tex]Range = \{37,30,17\}[/tex]
Shahril bought a CD, 2 T-shirts and a pair of jeans for $133. Each
T-shirt cost $13 more than the CD. The pair of jeans cost $30 more
than each T-shirt. Find the cost of the CD.
Step-by-step explanation:
Let the price of CD, tshirt and jeans be x,y and z respectively.
given:
x+2y+2z=133......(i)
y=x+13.......(ii)
2z=y+30....(iii)
in eqn (iii) ,
2z=y+30
or, 2z=x+13+30
or, z=(x+43)/2....(iv)
now in eqn (i),
x+2y+2z=133
or, x+2(x+13)+2((x+43)/2) =133
or, x+2x+26+x+43=133
or, 4x=133-69
or, x= 64/4
•°• x=$16
Question 1 of 10
The value of 9 is not-3 because
Answer:
It's a negative.
Step-by-step explanation:
The value of a positive number is still a positive number.
The function y=-16r^2+38 represents the height y (in feet) of a water droplet t seconds after falling from an icicle. After how many seconds does the water droplet hit the ground? Round your answer to two decimal places. A second water droplet falls from a height of 41 feet. After how many seconds does that water droplet hit the ground? Round your answer to one decimal place.
Answer:
The first droplet will hit the ground after about 1.54 seconds.
The second droplet will hit the ground after about 1.6 seconds.
Thus, the first hits the ground first.
Step-by-step explanation:
We are given the function:
[tex]y=-16r^2 + 38[/tex]
Which represents the height y in feet of a water droplet t seconds after falling from an icicle.
Part A)
We want to find the time it took for the water droplet to hit the ground.
When it hit the ground, its height y above ground will be zero. Therefore, we can let y = 0 and solve for r:
[tex]0=-16r^2+38[/tex]
Subtract 38 from both sides:
[tex]-38 = -16 r^2[/tex]
Divide:
[tex]\displaystyle r^2 = \frac{38}{16} = \frac{19}{8}[/tex]
And take the principal square root of both sides:
[tex]\displaystyle r= \sqrt{\frac{19}{8}} = \frac{\sqrt{38}}{4} \approx1.54\text{ seconds}[/tex]
So, the first water droplet hits the ground after about 1.54 seconds.
Part B)
We want to determine how long it will take for a water droplet to hit the ground from a height of 41 feet.
From the original equation, if r = 0, then y = 38. So, the initial height was 38 feet.
Then we can modify the function into:
[tex]y= -16r^2 + 41[/tex]
In this case, when r = 0, the starting height y is 41 feet.
Again, let y = 0 and solve for r:
[tex]0 = -16r^2 + 41[/tex]
Isolate:
[tex]\displaystyle r^2 = \frac{41}{16}[/tex]
And take the principal square root of both sides:
[tex]\displaystyle r = \sqrt{\frac{41}{16}} = \frac{\sqrt{41}}{4} \approx 1.6\text{ seconds}[/tex]
So, the second drop will hit the ground after approximately 1.6 seconds.
And in conclusion, the first drop will hit the ground sooner (as expected).
What's the dependent variable shown in the table?
A)
The amount of water given to the plant
B)
The color of the flowers
C)
The number of flowers on the plant
D)
The speed at which the plant grows
Answer:
The number of flowers on the plant
Step-by-step explanation:
Answer:
C: Number of flowers on the plant
Step-by-step explanation:
i got it right on my test
You take out a 60-day loan for $5000. At the end of the loan, you owe $73.97 in interest. What is the annual percentage rate? Round your answer to the nearest tenth of a percent.
The PERCENTAGE ANNUAL RATE is 9.0% to the nearest tenth using the SIMPLE INTEREST FORMULA
The question is related to a SIMPLE INTEREST problem:
Loan period = 60 days
using 365 days a year ;
converting to years , 60 days = (60 / 365) years
interest on loan = 73.97
principal = 5000
Using the formula:
interest = (principal * rate * time)
73.79 = (5000 * rate * (60/365)
Rate = 73.79/(5000 * (60/365)) =8.977%
rate = 9%
Therefore, PERCENTAGE ANNUAL RATE is 9.0%
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Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of three points. A random sample of 36 scores is taken and gives a sample mean of 68. Find a 85 % confidence interval estimate for the population mean exam score. Explain what the confidence interval means
this the answer of queastions
Step-by-step explanation:
67.18,68.82
Let mu be the true population mean of statistics exam scores. We have a large random samples of n=36 scores with a sample mean of 68.we know that the population standard deviation is sigma=3.A pivotal quantity is 3^sqrt(36)=(3/6)=68(1/2) which is approximately normally distributed. Therefore the 85%confidence interval is 68-(1/2)(1.6449), 68+(1/2)(1.6449) i.e (67.18,68.82)
3（6x+3）=63 How to do it
A concave polygon can never be classified as a regular polygon true or false??? Need answer ASAP please
Answer:
Regular Polygons are never concave by definition.
Step-by-step explanation:
The three sides of a triangle are n, 3n+3, and 3n−1. If the perimeter of the triangle is 72m, what is the length of each side?
Answer: 10m, 33m, and 29m
Step-by-step explanation:
n + 3n+3 + 3n-1 = 72m
7n+2=72m
7n = 72-2
n = 70/7
n = 10
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 0), (negative 1, 2).
A. (–2, 0)
B. (0, –2)
C. (5, –7)
D. (5, –2)
9514 1404 393
Answer:
B. (0, –2)
Step-by-step explanation:
Put the (x, y) values into the given formula.
(x, y) ⇒ (x +5, y -2)
B(-5, 0) ⇒ B'(-5+5, 0-2) = B'(0, -2)
Mua hàng hóa 10000kg về nhập kho,Đơn giá 200 000đ/kg,thuế gtgt là 10%,trả bằng chuyển khoản 50%,còn nợ người bán.Chi phí vận chuyển 2 100 000 bao gồm thueest gtgt 5% trả tiền mặt
If this fish tank is filled halfway, how much water will it hold?
96 cubic inches
768 cubic inches
48 cubic inches
384 cubic inches
Answer:
384 cubic inches
Step-by-step explanation:
first find the volume of the fish tank by multipying the length, width, and height.
v=lwh
=(16in)(4in)(12in)
= 768 cubic inches (This answer is equal to the volume of the entire fish tank, however we need to find how much water half the tank can hold. To figure this out, we need to divide 768 by 2. And you should get 384 cubic inches)
Answer:
384
Step-by-step explanation:
took the quiz
A family has a day of 7 activities planned: shopping, picnic, hiking, swimming, bike ride, video games, and movie. To make it more adventurous they decide to randomly pick the order of the activities out of a hat. Find the probability that bike ride and movie are chosen consecutively, in either order.
Answer:
[tex]Pr= \frac{1}{21}[/tex]
Step-by-step explanation:
Given
[tex]n(S) = 7[/tex] --- number of games
Required
Probability of bike and movie in consecutive order
This probability is represented as:
[tex]Pr = P(Bike\ and\ Movie) \ or\ P(Movie\ or\ Bike)[/tex]
So, we have:
[tex]Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)[/tex]
The probability is an illustration of selection without replacement;
So, we have:
[tex]P(Bike\ and\ Movie) = P(Bike) * P(Movie)[/tex]
[tex]P(Bike\ and\ Movie) = \frac{n(Bike)}{n(S)} * \frac{n(Movie)}{n(S) - 1}[/tex] ---- without replacement
Bike and Movie appear in the game list 1 time.
So, the equation becomes
[tex]P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{7 - 1}[/tex]
[tex]P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{6}[/tex]
[tex]P(Bike\ and\ Movie) = \frac{1}{42}[/tex]
Similarly,
[tex]P(Movie\ and\ Bike) = \frac{1}{42}[/tex]
So, we have:
[tex]Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)[/tex]
[tex]Pr= \frac{1}{42}+\frac{1}{42}[/tex]
Take LCM
[tex]Pr= \frac{1+1}{42}[/tex]
[tex]Pr= \frac{2}{42}[/tex]
[tex]Pr= \frac{1}{21}[/tex]
(x)=4log(x+2) Which interval has the smallest average rate of change in the given function? 1≤x≤3 5≤x≤7 3≤x≤5 −1≤x≤1
Answer:
5≤x≤7
Step-by-step explanation:
For a given function f(x), the average rate of change in a given interval:
a ≤ x ≤ b
is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Here we have:
f(x) = 4*log(x + 2)
And we want to see which interval has the smallest average rate of change, so we just need fo find the average rate of change for these 4 intervals.
1) 1≤x≤3
here we have:
[tex]r = \frac{f(3) - f(1)}{3 - 1} = \frac{4*log(3 + 2) - 4*log(1 + 2)}{2} = 0.44[/tex]
2) 5≤x≤7
[tex]r = \frac{f(7) - f(5)}{7 - 5} = \frac{4*log(7 + 2) - 4*log(5 + 2)}{2} = 0.22[/tex]
3) 3≤x≤5
[tex]r = \frac{f(5) - f(3)}{5 - 3} = \frac{4*log(5 + 2) - 4*log(3 + 2)}{2} = 0.29[/tex]
4) −1≤x≤1
[tex]r = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{4*log(1 + 2) - 4*log(-1 + 2)}{2} = 0.95[/tex]
So we can see that the smalles average rate of change is in 5≤x≤7
Samuel baked 81 cakes how many more cake does Samuel have to bake to have 123 cakes
Answer:
42 cakes
Step-by-step explanation:
123 - 81 = 42
.....
Samuel needs to bake 42 more cakes to have a total of 123 cakes.
To find out how many more cakes Samuel needs to bake to have a total of 123 cakes, we subtract the number of cakes he already baked from the desired total.
Total desired cakes: 123
Cakes already baked: 81
To find the remaining cakes, we subtract the number of cakes already baked from the desired total:
123 - 81 = 42
Therefore, Samuel needs to bake 42 more cakes to have a total of 123 cakes.
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The entrance ticket for a carnival costs $89.97, which includes a royal meal
that costs $10.85, 1 play station game, and 3 water rides (Each water ride
costs the same price). The cost of a water ride is twice as that of a play
station game. Find the cost of a water ride. Estimate to the nearest tenths.
Subtract the meal:
89.97- 10.85 = 79.12
Let the play station game = x
A water ride is twice that so a water ride is 2x
There is 3 water rides : 3 x 2x =6x
The PlayStation game and water rides = 79.12
6x + x = 79.12
Simplify:
7x = 79.12
Divide both sides by 7:
X = 11.30
The PlayStation game is 11.30
The water ride = 2 x 11.30 = 22.60
