Answer:
A. A data set is a collection of similar data.
D. A data set contains data all of which have some common characteristic.
Suppose that the Blood Alcohol Content (BAC) of students who drink five beers varies from student to student according to a Normal distribution with mean 0.07 ans standard deviation 0.01.
1. The middle 95% of students who drink five beers have a BAC between
a. 0.06 and 0.08 b. 0.05 and 0.09 c. 0.04 and 0.10 d. 0.03 and 0.11
2. What percent of students who drink five beers have a BAC above 0.08 (the legal limit for driving in most states)?
a. 0.15% b. 0.3% c. 2.5% d. 16% e. 32%
3. What percent of students who drink five beers have a BAC above 0.10 (the legal limit for driving in most states)?
a. 0.15% b. 0.3% c. 2.5% d. 16% e. 32%
Answer:
1. b. 0.05 and 0.09
2. d. 16%
3. a. 0.15%
Step-by-step explanation:
Given that :
mean = 0.07
standard deviation = 0.01
Confidence interval = 95%
The level of significance ∝= 1 - 0.95 = 0.05
At 0.05 level of significance,
critical value for [tex]z_{\alpha/2} = z_{0.05/2}[/tex]
critical value for [tex]z_{0.025}[/tex] = 1.96
Confidence interval = [tex]\mathtt{\mu \pm ( {z} \times{\sigma})}[/tex]
Lower limit = [tex]\mathtt{\mu -( {z} \times{\sigma})}[/tex]
Upper Limit = [tex]\mathtt{\mu +( {z} \times{\sigma})}[/tex]
Lower limit = [tex]\mathtt{0.07 - ({1.96} \times {0.01})}[/tex]
Upper limit = [tex]\mathtt{0.07 + ({1.96} \times {0.01})}[/tex]
Lower limit = 0.07 - 0.0196
Upper limit = 0.07 + 0.0196
Lower limit = 0.0504 [tex]\simeq[/tex] 0.05
Upper limit = 0.0896 [tex]\simeq[/tex] 0.09
The confidence interval of 95% is ( 0.05, 0.09)
2. What percent of students who drink five beers have a BAC above 0.08 (the legal limit for driving in most states)?
[tex]P(X> 0.08) = P(\dfrac{0.08 - \mu}{\sigma} > \dfrac{X - \mu}{\sigma} )[/tex]
[tex]P(X > 0.08) = P(z > \dfrac{0.08 - 0.07}{0.01} )[/tex]
[tex]P(X > 0.08) = P(z > \dfrac{0.01}{0.01} )[/tex]
[tex]P(X > 0.08) = P(z > 1 )[/tex]
[tex]P(X> 0.08) = 1- P(z < 1 )[/tex]
P(X > 0.08) = 1 - 0.8413
P(X > 0.08) = 0.1587
P(X > 0.08) [tex]\simeq[/tex] 16%
3. What percent of students who drink five beers have a BAC above 0.10 (the legal limit for driving in most states)?
[tex]P(X> 0.10) = P(\dfrac{0.10 - \mu}{\sigma} > \dfrac{X - \mu}{\sigma} )[/tex]
[tex]P(X > 0.10) = P(z > \dfrac{0.10 - 0.07}{0.01} )[/tex]
[tex]P(X > 0.10) = P(z > \dfrac{0.03}{0.01} )[/tex]
[tex]P(X > 0.10) = P(z > 3)[/tex]
[tex]P(X> 0.10) = 1- P(z < 3 )[/tex]
P(X > 0.10) = 1 - 0.9987
P(X > 0.08) = 0.0013
P(X > 0.08) [tex]\simeq[/tex] 0.15% which is the closet value to 0.0013
If √2x - 1 + 2=5, then x is equal to?
Answer:
x = 5
Step-by-step explanation:
Remove the radical by raising each side to the index of the radical.
x = 5
This was done assuming that 2x-1 was under the radical and that +2 wasn't.
Need Assitance
*Show Work*
Answer:
66 2/3 %
Step-by-step explanation:
First find the students not in the 8th grade
24 - 8 = 16
16 students are not in the 8th grade
Take the fraction of the students not in the 8th grade over the total
16/24 = 2/3
Change to a decimal
.66666666666
Multiply by 100 to change to a percent
66.666666%
66 2/3 %
Answer:
66.67% of students are not in eighth grade
Step-by-step explanation:
8/24=1/3
1/3=0.33333333333
1-0.33333333333=0.66666666667
0.66666666667=66.67%
A clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30, while 3,000 shirts can be sold at a price of $10. Find a linear equation in the form p(n)=mn+b that gives the price p they can charge for n shirts.
Answer:
p(n) = -1/100 n 40
Step-by-step explanation:
Use the two points (n, p): (1000, 30) and (3000, 10).
Now we find the equation of the line that passes through these two points.
m = (10 - 30)/(3000 - 1000)
m = -20/2000
m = -1/100
p(n) = mn + b
30 = -1/100 * 1000 + b
30 = -10 + b
b = 40
The equation is:
p(n) = -1/100 n 40
If a faucet drips 2ml of water every second, how much water will it spill waste in 2 days?
Answer:
[tex]\boxed{345,600 mL}[/tex]
Step-by-step explanation:
Hey there!
Well first we need to find the amount of seconds in a day,
24hrs in a day * 60 min in an hour
= 1440 minutes in a day
1440 min • 60 secs in a minute
= 86,400 seconds in a day
So now we do 2*86400 = 172800
172800 mL in a day
172800 * 2
= 345600 mL in 2 days
Hope this helps :)
g If the events A and B are independent with P( A) = 0.35 and P( B) = 0.45, then the probability that both events will occur simultaneously is:
Answer:
0.1575.
Step-by-step explanation:
Here, as they are independent, we multiply the probabilities:
P( A and B) = 0.35*0.45
= 0.1575.
The probability that both events will occur simultaneously is 0.1575.
Given that, the events A and B are independent with P( A) = 0.35 and P( B) = 0.45.
What is independent probability?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).
Since, the events A and B are independent
We have P(A and B)
= P(A) × P(B)
= 0.35 × 0.45
= 0.1575
Hence, the probability that both events will occur simultaneously is 0.1575.
Learn more about the independent probability here:
https://brainly.com/question/27987662.
#SPJ5
Hi everyone how to solve this question
$2x+7$
according to the flow chart,
1. multiply [tex] x[/tex] by $2$, so $2x$
and then add seven to it so $2x+7$
note, if the order was reverse, i.e. first add seven ($x+7$). then multiply by two ($2(x+7)$)
the answer would be $2x+14$
find the product 538 x 100=
Answer:
Answer=53,800
Step-by-step explanation:
just add the two zero behind the number
Two sides of a triangle are equal length. The length of the third side exceeds the length of one of the other sides by 3 centimeters. The perimeter of the triangle is 93 centimeters. Find the length of each of the shorter sides of the triangle
Answer:
30 cm
Step-by-step explanation:
let x be the lenght of the two sides of equal lenghts, so the other is x+3
and the perimeter is x+x +x +3
P=3x+3
P=3(x+1)
93=3(x+1)
31=x+1
x=30
so the shorter sides are of 30 centimeters and the longest is 33
(A LOT OF POINTS) Given the linear equation 2x + y = 6, perform the necessary operations to put the equation into the proper general form. Explain in complete sentences how you knew that the equation was in the proper general form. Complete your work in the space provided or upload a file that can display math symbols if your work requires it. Include the entire process for establishing the general form of the equation and the general form.
Answer:
[tex]\huge\boxed{2x + y - 6 = 0}[/tex]
Step-by-step explanation:
2x + y = 6
Subtracting both sides by 6
2x + y - 6 = 0
Comparing it with the general form of equation [tex]\sf Ax+By +C = 0[/tex] , we get:
A = 2, B = 1 and C = -6.
So, the equation is in proper general form.
Answer:
[tex]\boxed{2x+y-6=0}[/tex]
Step-by-step explanation:
[tex]\sf The \ general \ form \ for \ the \ equation \ of \ a \ line \ is \ given \ as \ Ax+By+C=0.[/tex]
[tex]2x+y=6[/tex]
[tex]\sf Subtract \ 6 \ from \ both \ sides.[/tex]
[tex]2x+y-6=6-6[/tex]
[tex]2x+y-6=0[/tex]
[tex]\sf A=2 \ \ \ B = 1 \ \ \ C=-6[/tex]
[tex]\sf The \ equation \ is \ in \ general \ form.[/tex]
[tex]\sf Graph \ equation:[/tex]
Lennox owns a big apple orchard. She ships her apples to various markets using a fleet of trucks. Every week, each truck goes on 3 trips, and for each trip Lennox gets 300 dollars. On a single trip, a truck delivers 50 packs, and each pack contains 12 kilograms of apples. Overall, Lennox sells 4500 dollars worth of apples in a week. How much does Lennox get for a single kilogram of apples?
Answer:
$0.50
Step-by-step explanation:
Each trip transports 50 packs at 12 kg each, for a total of 600 kg. That trip nets $300 in income.
Lennox gets paid ($300)/(600 kg) = $0.50/kg, or 50¢ for 1 kg of apples
Answer:5 trucks
Step-by-step explanation: in kahn it’s 4500 divided by 900 because she makes 300 a trip which makes 900$ a truck
Find the missing probability.
P(A) = 23,P(An B)= P(B|A) =?
Answer:
the formular is
p(B/A)=P(AnB)/P(A)
so the missing probability is:-
P(AnB)=P(B/A)×23
And the other missing probablility is:-
p(B/A)=P(AnB)/23
An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses. H0: The product does not change the height of the plant. Ha: The product makes the plant grow taller. Is the following an example of a type I or type II error? The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.
Answer:
hi
Step-by-step explanation:
hji
You make 85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary.
Answer:
The question is incomplete, below is a possible match for the complete question:
You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary. Complete parts (a) through (c) below.
(a) If you contribute $200 every month to your 401k, what will your company contribute each month?
The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)
(b) If you contribute $830 every month to your 401k, what will your company contribute each month?
The company will contribute $ (Type an integer or a decimal rounded to two decimal places as needed.)
(c) What is the maximum amount of money the company will contribute to your 401k each year?
The maximum amount that the company will contribute each year is $
(Type an integer or a decimal rounded to two decimal places as needed.)
Answer:
a.) The company will contribute $100
b.) The company will contribute $415
c.) maximum amount the company will be willing to contribute = $6,800 per year
Step-by-step explanation:
First, let us calculate the maximum amount the company will be willing to pay into the 401k plan yearly:
Annual salary = $85,000
Monthly salary = $7083.3333
maximum amount = 8% = 8/100 = 0.08 of salary
maximum amount = 0.08 × 7083.3333 = $566.67
a.) If you contribute $200 every month.
Since $200 is less than the maximum amount that the company will be willing to contribute, let us calculate how much the company is willing to contribute:
Company matches 50 cents for every dollar you deposit
1 dollar deposited = 50 cents from company
but 1 cent = $0.01
∴ 50 cents = 0.01 × 50 = $0.5
$1 deposited = $0.5 from company
∴ $200 deposited = 0.5 × 200 = $100 contributed by company
Therefore, if you contribute $200 every month, your company will contribute $100 each month.
from this example, we can see that the company is willing to contribute half of every amount you deposit every month ($100 = half of $200), hence, subsequently, we will use this for calculations.
b.) If you contribute $830 every month, the company will be willing to contribute half this amount, which is:
half of $830 = 830 ÷ 2 = $415
Therefore, if you contribute $830 per month, your company will contribute $415 per month.
c.) The maximum amount the company will be willing to contribute each year = 8% of salary per year
= [tex]= \frac{8}{100}\times 85,000 \\ =0.08\ \times\ 85,000 = \$6,800[/tex]
Therefore, the company will be willing to contribute $6,800 per year.
Factor the expression completely. 6×3- 4×2 – 16x A. 0 B. 2x(3×2 – 2x – 8) C. 2x(3x + 4)(x – 2) D. 4x(2x + 1)(x – 4) E. 2x(2×2 + 7x – 4) ill give brainliest
Answer:
The answer is option CStep-by-step explanation:
6x³ - 4x² - 16x
To factorize the expression first factor out the GCF out
The GCF in the expression is 2x
That's
2x( 3x² - 2x - 8)
Next Factorize the terms in the bracket
To factorize write - 2x as a difference
that's
2x( 3x² + 4x - 6x - 8)
Factor out x from the expression
2x [ x( 3x + 4) - 6x - 8 ]
Next factor out - 2 from the expression
2x [ x ( 3x + 4) - 2( 3x + 4) ]
Factor out 3x + 4 from the expression
We have the final answer as
2x( 3x + 4)( x - 2)Hope this helps you
In Triangle A B C, what is the value of x? Triangle A B C. Angle A is (10 x minus 10) degrees, angle B is (8 x) degrees, angle C is (10 x + 8) degrees.
Answer:
6.5
Step-by-step explanation:
The sum of all angles in a triangle are 180 degrees.
=> 10x -10 + 8x + 10x + 8 = 180
=> 28x -2 = 180
=> 28x = 182
=> x = 6.5
So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees
Angle B = 8 x 6.5 = 52 degrees
Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.
55 + 52 + 73 = 55 + 125 = 180 degrees
A cylindrical grain silo, with a flat top, is 30 feet tall and has a radius of 12 feet. It is full to the top with shelled corn. If the density of shelled corn averages 45 pounds/cubic foot, what does the corn in the silo weigh to the nearest pound
Answer:
610805 pounds
Step-by-step explanation:
The volume of grain in the silo will be calculated as equal to the volume of the cylinder formed by the silo
Height of the silo [tex]l[/tex] = 30 ft
radius of the silo r = 12 ft
volume of a cylinder = [tex]\pi r^{2} l[/tex]
substituting, we have
V = 3.142 x [tex]12^{2}[/tex] x 30 = 13573.44 cubic feet
We know that density ρ = weight/volume
density of the grains in the silo = 45 pound/cubic feet
therefore,
weight of grains = density x volume
weight of grains = 45 x 13573.44 = 610804.8 ≅ 610805 pounds
Identify the terms, constants, coefficient, factor of the algebraic expression -7x+9.
Answer:
Term is something that is being added together. Factor is something that is being multiplied together. Coefficient is a number that is being multiplied by the variable. 2x+6x+14. The 2x, 6x, and 14 are terms because they are being added together.
Step-by-step explanation:
!2,19,26 what comes nxt
Answer:
12 , 19 , 26 , 33
Explaination:Here, n+7
12+7=19
19+7=26
So,
26+7=33
Hope you understand ❣
Step-by-step explanation:
12 , 19 , 26 , ?
Given
___________
a1= 12
a2= 19
a3 = 26
d= ?
a4 = ?
––——————
we can solve this by using formula from Ap .
But for this we have to find d
As we know that
common difference(d) = a2-a1 = 19 -12
= 7
so difference after every no is 7 so
a4 = a3 + d
= 26 +7
= 33
So 33 is ur answer mate
Hope it helps
One ingot contains 10 kg of pure silver and 2 kg of league. What quantity of silver, whose grade is 0.700; is it necessary to melt to obtain silver with a grade of 0.750?
a) 20
b) 22
c) 16
d) 24
e) 19
Answer:
a) 20
Step-by-step explanation:
If x is the kg of 0.700 grade silver, then:
Silver in ingot + silver in 0.700 alloy = silver in 0.750 alloy
10 + 0.7x = 0.75(x + 12)
10 + 0.7x = 0.75x + 9
1 = 0.05x
x = 20
Choose the correct simplification of 9x^2(4x + 2x^2 − 1)
━━━━━━━☆☆━━━━━━━
▹ Answer
18x⁴ + 36x³ - 9x²
▹ Step-by-Step Explanation
9x²(4x + 2x² - 1)
36x³ + 18x⁴ - 9x²
18x⁴ + 36x³ - 9x²
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
What is the simplest fraction whose value is equal to the number (red heart) depicted on this number line. (Give your answer as a fraction, not a mixed number. "Simplest fraction" means the numerator and denominator should have no common divisor greater than 1. : Look closely at the numbers on the number line. (red heart) is between 2 and 3. There are 6 tick marks between 2 and 3. How many regions do those tick marks split the number line into?
Answer:
simplest fraction: 2 1/3 the tick marks split the number into 7 regions
Step-by-step explanation:
The red heart is on the 2 tick mark of the 6 ticks between 2 and 3. The answer is 2 2/6 which after simplifying if equal to 2 1/3.
Answer:
16/7
Step-by-step explanation:
2-3 is devided into 7 segments if you make 2 14/7 and 3 21/7 then you have 16/7 with no common devisor other than 1
.... i repost bec brainly would not allow me to make it lager
that is all i can do
Answer:
Hey there!
Richard has 480 dollars.
Giving 1/4 of the money to his brother would mean giving 120 dollars to his brother.
Richard has 480-120, or 360 dollars left.
Giving 1/3 of the money left would be giving 120 dollars to his sister.
His sister and brother both got 120 dollars from Richard.
Hope this helps, and let me know if you need more help. :)
Question
Consider these functions.
f(x) = -9x + 14
g(x)=-3x2
Select the correct answer from each drop-down menu.i
If x = 6, then f(6)
If g(x) -48, then x =
and x =
Submit
Answer:
[tex]\large \boxed{-40, \ 4, \ -4}[/tex]
Step-by-step explanation:
[tex]f(x)=-9x+14[/tex]
[tex]\sf Put \ x \ as \ 6.[/tex]
[tex]f(6)=-9(6)+14[/tex]
[tex]f(6)=-54+14[/tex]
[tex]f(6)=-40[/tex]
[tex]g(x)=-3x^2[/tex]
[tex]\sf Put \ g(x) \ as \ -48.[/tex]
[tex]-48=-3x^2[/tex]
[tex]\displaystyle \frac{-48}{-3} =\frac{-3x^2 }{-3}[/tex]
[tex]16=x^2[/tex]
[tex]\sqrt{16} =\sqrt{x^2 }[/tex]
[tex]x= \pm 4[/tex]
Answer:
F(6) = -9(6) + 14 = -54 + 14. f(6) = -40
G(x) = -48 / g(x) = -3(16) / g(4) = -48
Step-by-step explanation:
For the first one the drop answer is -40
For the second one its 4 then 16
I think because that whats im seeing but these are the right answers :)
In the diagram, XY bisects ZWXZ.
Z
Y
2
w
(5x + 3)
(7X - 70°
Х
x=
type your answer...
Answer:
x = 5
Step-by-step explanation:
Angle Bisector Theorem: When a ray bisects an angle, we get 2 congruent smaller angles
Step 1: Set equation equal to each other (Angle Bisector Theorem)
5x + 3 = 7x - 7
Step 2: Subtract 5x on both sides
3 = 2x - 7
Step 3: Isolate x term (Add 7 to both sides)
10 = 2x
Step 4: Isolate x (Divide both sides by 2)
x = 5
If 2x + 5 = 8x, then 12x = ?
A 5
B
10
C
15
D 20
Answer:
10
Step-by-step explanation:
2x + 5 = 8x
Subtract 2x from each side
2x-2x + 5 = 8x-2x
5 = 6x
We want 12x so multiply each side by 2
2*5 = 6x*2
10 = 12x
Answer:
B. 10
Step-by-step explanation:
To find 12x, you first need to find the value of x using the first equation:
[tex]2x+5=8x[/tex]
You need to get the variables (x) on the same side of the equation in order to simplify them. To do this, use reverse operations. Subtract 2x from both sides to keep the equation balanced:
[tex]2x-2x+5=8x-2x\\\\5=6x[/tex]
Now isolate the variable (x) by dividing both sides of the equation by 6 (using reverse operations):
[tex]\frac{5}{6}=\frac{6x}{6} \\\\\frac{5}{6}=x[/tex]
Now insert the given value of x into 12x:
[tex]12(\frac{5}{6})[/tex]
Simplify:
[tex]12*\frac{5}{6} \\\\\frac{12}{1}*\frac{5}{6}\\\\\frac{60}{6}=10[/tex]
12x equals 10.
:Done
Billy has x marbles. Write an
expression for the number of
marbles the following have…
a) Charlie has 5 more than Billy
b) Danny has 8 fewer than Billy
c) Eric has three times as many as
Billy
Answer:
[tex]Charlie = 5 + x[/tex]
[tex]Danny = x - 8[/tex]
[tex]Eric = 3x[/tex]
Step-by-step explanation:
Given
Billy's Marble = x
Required
Determine a,b and c
a. Charlie's Marble
"5 more" means 5 + or + 5
Since Billy's Marble is represented with x, then Charlie's Marbles will be
[tex]Charlie = 5 + x[/tex]
b. Danny's Marbles
Having "8 fewer" means we have to subtract 8 from Billy's marble;
Since Billy's Marble is represented with x, then Danny's Marbles will be
[tex]Danny = x - 8[/tex]
c. Eric Marbles
Having "three times as " means we have to multiply Bill's marble by 3;
Since Billy's Marble is represented with x, then Danny's Marbles will be
[tex]Eric = 3 * x[/tex]
[tex]Eric = 3x[/tex]
When Jason was 16 years old, he deposited $200 in an account that earned 223% interest compounded daily. If he makes no other deposits or withdrawals, what is Jason’s balance at age 20?
Answer:
Balance at the age of 20 will be $1455966.46
Step-by-step explanation:
Formula to calculate the final amount is,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount or amount invested
A = Final amount
r = Rate of interest
n = Number of compounding in a year
If Jason invested $200 in an account for 4 years with rate of interest 223%.
P = $200
r = 223%
n = 365
t = 4 years
A = [tex]200(1+\frac{2.23}{365})^{(4\times 365)}[/tex]
A = [tex]200(1.0061096)^{1460}[/tex]
A = $1455966.46
Therefore, balance amount in Jason's account at the age of 20 will be $1455966.46.
Which paper folding method can be used to form a perpendicular line segment
Answer:
Begin with a line segment on the paper and fold the paper so that the segment's endpoints lie on top of each other
URGENT, PLEASE HELP! (4/5) -50 POINTS- ! please no wrong answers for the points.! A) y = -3x + 2 B) y = -x + 2 C) y = 3x + 2 D) y = x + 1
Answer:
D y= x+1
Step-by-step explanation:
The line has a positive slope since it goes up from left to right
We can eliminate A and B
3 is a fairly steep slope for line C
Lets check with point x=7
y = 3*7 +2 = 21+2 = 23
Way too steep
Lets check 2
y = 3*2+2 = 6+2 = 8
Still above the points
Checking D
y = x+1
x=7
y = 7+1 =8 A little high
x=2
y = 2+1 =3 A little low but much better than C
Answer:
[tex]\huge \boxed{y=x+1}[/tex]
Step-by-step explanation:
Using a graph,
we can see the line y=x+1 is best fit for the data.
