Answer:
[tex]X \sim Hyp (N = 810, M=102, n=4)[/tex]
[tex] P(X=0) = \frac{(102C0)(810-102 C 4-0)}{810C4}[/tex]
And solving we got:
[tex] P(X=0)= \frac{(102C0) (708C4)}{810C4} = 0.583[/tex]
So then for the problem given the probability that the entire bath will be accepted (none is defective among the 4) is 0.583
Step-by-step explanation:
For this case we can model the variable of interest with the hypergeometric distribution. And with the info given we can do this:
[tex]X \sim Hyp (N = 810, M=102, n=4)[/tex]
[tex]P(X=k)= \frac{(MCk)(N-M C n-k)}{NCn}[/tex]
Where N is the population size, M is the number of success states in the population, n is the number of draws, k is the number of observed successes
And for this case we want to find the probability that none of the scales selected would be defective so we want to find this:
[tex] P(X=0)[/tex]
And using the probability mass function we got:
[tex] P(X=0) = \frac{(102C0)(810-102 C 4-0)}{810C4}[/tex]
And solving we got:
[tex] P(X=0)= \frac{(102C0) (708C4)}{810C4} = 0.583[/tex]
So then for the problem given the probability that the entire bath will be accepted (none is defective among the 4) is 0.583
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly. The relationship between the elapsed time,t, in seconds, and the number of bacteria, B(t), in the petri dish is modeled by the following function:
B(t)=9,300•(1/64)^t
Complete the following about the rate of change of the bacterial culture. Round your answer to two decimal places.
The bacterial culture loses 1/2 of its size every _________ seconds.
Answer:
0.17
Step-by-step explanation:
The function can be rewritten as ...
B(t) = 9300·((1/2)^6)^t = 9300·(1/2)^(6t)
In order to multiply the number of bacteria by 1/2, the value of the exponent 6t must be equal to 1:
6t = 1
t = 1/6 ≈ 0.166667 ≈ 0.17
The culture loses half its size every 0.17 seconds.
.17
Step-by-step explanation:
How to solve this problem?
g = number of goblins
w = number of wizards
There are 220 club members altogether, so
g + w = 220
There are 20% more goblins than wizards, so
g = 1.2 w
Substitute this into the first equation and solve for w, then for g.
1.2 w + w = 2.2 w = 220 ==> w = 100
g = 1.2 w ==> g = 120
9. The temperature at noon was 84° F and it began to drop 0.8° each hour. If the current temperature is 79.2° F, write and solve an equation to determine the number of hours that have passed.
Answer:6 hours have passed by.
Step-by-step explanation:
0.8x= 84-79.2 where x is the number of hours.
O.8x = 4.8
Divide both sides by 0.8
X= 6
Identify two Pythagorean triples using the known triple 9, 40 , 41. *
Your answer
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {9}^{2} + {40}^{2} = {41}^{2} \\ 81 + 1600 = 1681 \\ 1681 = 1681[/tex]
Compute 90, 91, 92, 93, 94, and 95. 90 = 1 91 = 9 92 = 81 93 = 729 94 = 6561 95 = 59049 Make a conjecture about the units digit of 9n, where n is a positive integer. If n is even, the units digit of 9n is 1 . If n is odd, the units digit of 9n is 9 . Use strong mathematical induction to prove your conjecture. Submit your proof as a free response. (Submit a file with a maximum size of 1 MB.)
Answer:
Step-by-step explanation:
First we compute [tex]9^n[/tex], for [tex]n = 0,1,2,3,4,5[/tex]
[tex]9^0=1,9^1=9,9^2=81,9^3=729,9^4=6561,9^5=59049[/tex]
We have the unit digit of [tex]9^n[/tex], is either 1 or 9
Therefore, the conjecture can be state as follows
Conjecture; the unit of digit of [tex]9^n[/tex], is 1, when n is even and 9 when n is odd
Let the property p(n) be the formula;
"The unit digit of [tex]9^n[/tex], is 1 when n is even and 9 when n is odd"↔ P(n)
To show p(n) is true , we will use strong mathematical inductive
Show tgat p(0) and p(1) are true
We have to show the unit digit of [tex]9^0[/tex] is 1 and [tex]9^1[/tex] is 9
Since any integer with zero power is one and hence
[tex]9^0=1[/tex] and [tex]9^1 = 9[/tex]
Therefore, p(0) and p(1) are true
Show that for al integer [tex]k\geq 1[/tex], if p(i) is true for all integer i from o through k, then p(k+1) is also true
let k be any integer with [tex]k \geq 1[/tex] and suppose that for all integer i with [tex]0 \leq i \leq \leq k[/tex]
the unit digit of [tex]9^i[/tex] is 1 when is even and 9 when n is odd
we must show that [tex]9^{k +1}[/tex] equals 1 when n is even and 9 when n is odd
Case I; (k +1 is odd)
in this case k is even and so, by inductive hypothesis, the unit digit of [tex]9^k[/tex] is 1 and hence there is some non negative integer q such that
[tex]9^k = 10q + 1[/tex]
now, [tex]9^{k+1}=9^k(9)[/tex]
= (10q + 1)9
= 90q + 9
= 10.9q + 9
Note that for any non negative integer q , 9q is also an integer and this implies the unit digit of [tex]9^{k+1}[/tex] is 9
Case II
(k +1 is even)
in this case k is odd and so, by inductive hypothesis, the unit digit of [tex]9^k[/tex] is 9 and hence there is some non negative integer q such that
[tex]9^k=10q+9[/tex]
Now,
[tex]9^{k+1}=9^k.9\\=(10q+9)9\\=90q+81\\=10(9q+8)+1[/tex]
Note that any non negative integer q, 9q + 8 is also an integer and this implies the unit of [tex]9^{k+1}[/tex] is 1
Since we have proved both the basis and the inductive step of the strong mathematical induction, we conclude that the given statement is true
The amounts of money Gillian earned each week from babysitting are $5, 10, $20, $10, $15, $5, $42, $5. How is the mean of the data set affected when the outlier is removed?
Answer:
The mean will increase, after the outlier is removed.
Please help if you can
Answer:
4
Step-by-step explanation:
We just have to find the corresponding d(t) value when t=2. From the graph, we can see that when t = 2, d(2) = 4. Hope this helps!
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
Answer:
plot the points (0, 2) and (π, 4)
Step-by-step explanation:
To use your sine plotting tool, you need two points on the graph. The midline point is given for you. It is the y-intercept, (0, 2).
The maximum amplitude point is 1/4 of a period from this midline point. The frequency is 1/(4π), and the period is the inverse of frequency:
T = 1/f = 4π
So, 1/4 of a period is ...
T/4 = (4π)/4 = π
The peak value of the function is the amplitude added to the midline, so is 2+2 = 4.
The second point you need to plot is the peak value, (π, 4).
Your points are (0, 2) and (π, 4).
I need the answer ASAP giving 20 points!
Answer: a makes the most sense
Step-by-step explanation:
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! CHECK ALL THAT PPLY
Answer:
F
Step-by-step explanation:
x = 26-9
Answer:
F. 17
Step-by-step explanation:
There would only be one answer choice, and to find this, all you can do is subtract 9 from both sides, like so:
x + 9 = 26
- 9 - 9
________
x = 17
This means that when you plug in 17 for x, the answer will come out to 26.
3) Write an equation of a circle satisfying the following conditions:
Center: (-2,5)
Radius: 23
a) (x - 2)2 + (v + 5)= 12
b) (x + 2)2 + (y – 5)2 = 12
c) (x - 2)2 + (y + 5)= 144
d) (x + 2)2 + (-5) = 154
Answer:
Ok :] ummmm report me i'm no help.
Step-by-step explanation:
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What’s the correct answer for this?
Answer:
A number, such as 10 is a composite number because it is even.
what is the mode following data set: 0.5, 0.3, 0.2, 0.9, 0.3, 0.5, 0.2, 0.3
Answer:
the mode is 0.3
Step-by-step explanation:
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!
hope this helps!!!!!!!!
A standard die is rolled two times. What is the probability that it lands on 5 both times?
I’m stuck between 1/18 and 1/36.
Answer:
1/36
Step-by-step explanation:
A die can roll a 1,2,3,4,5,6
P (5) = number of 5's / total
= 1/6
The 2nd roll is independent so the probability is the same
P (5) = number of 5's / total
= 1/6
P(5, 5) = 1/6*1/6 = 1/36
Zoe says an equilateral triangle is always an acute triangle, but an acute triangle is never an equilateral triangle. Which statement explains whether Zoe is correct or not?
Zoe is not correct because equilateral triangles are acute triangles with three sides of equal length. Acute triangles can sometimes be equilateral triangles.
Zoe is not correct because equilateral triangles have three acute angles. Acute triangles have three acute angles, so acute triangles are always equilateral triangles.
Zoe is correct because equilateral triangles have three sides of equal length, and acute triangles have three sides of different lengths.
Zoe is correct because equilateral triangles have three acute angles. Acute triangles have one acute angle, so an acute triangle cannot be an equilateral triangle PLEASE HELP ME
Answer:
Zoe is not correct because equilateral triangles are acute triangles with three sides of equal length. Acute triangles can sometimes be equilateral triangles.
Step-by-step explanation:
i need help with this problem x/56=7/8 Thank you
[tex] \dfrac{x}{56} = \dfrac{7}{8} \\ x = \dfrac{56 \times 7}{8} \\ x = 49[/tex]
The article “Heavy Drinking and Polydrug Use Among
College Students” (J. of Drug Issues, 2008: 445–466) stated
that 51 of the 462 college students in a sample had a lifetime
abstinence from alcohol. Does this provide strong evidence
for concluding that more than 10% of the population sam-
pled had completely abstained from alcohol use? Test the
appropriate hypotheses using the P-value method. [Note:
The article used more advanced statistical methods to study
the use of various drugs among students characterized as
light, moderate, and heavy drinkers.]
Answer:
Yes it does provide strong evidence
Step-by-step explanation:
please answer this correctly I have to finish this today as soon as possible
Estimate the measure of this angle within 10°.
Answer:
It seems like it is 110 degrees.
Step-by-step explanation:
In this geometric sequence, what is the common ratio?
104, -52, 26, -13, ...
2
-2
-
Answer:
-2
Step-by-step explanation:
Each value is divided by -2 to get to the next term
Answer:-1/2
Step-by-step explanation:
common ratio=(2nd term➗Ist term) or (3rd term➗2nd term)
first term=104
Second term=-52
Common ratio=-52 ➗ 104
Common ratio=-1/2
Describe a free market economy
Answer:
soviet russia
Step-by-step explanation:
just kidding
The free market is an economic system based on supply and demand with little or no government control. ... Based on its political and legal rules, a country's free market economy may range between very large or entirely black market
Countries that have a market economy are Mexico, United States, United Kingdom, Germany, and Canada . These countries have a market economy because the prices of goods and services are set by supply and demand
If 2 pounds of steak can serve 5 people how many pounds will serve 13 people
Step-by-step explanation:
wait sorry that was wrong
Answer:
5.2
Step-by-step explanation:
The answer is 5.2 pounds of meat. To find this just divide the number of people by what the information you have about servings. 13/5=2.6(number of sets), then you multiply that by how many pounds are in each set.
Fernanda is filling a cylindrical pot with cans of vegetable soup. The pot has a diameter of 15 in. and a height of 10 in. The soup can has a diameter of 4 in. and a height of 5 in. How many cans of soup will it take to fill up the pot?
Answer:
28.125 cans
Step-by-step explanation:
Step 1: Determine the Volume of the Pot
Diameter= 15 inches, therefore Radius=15/2=7.5 Inches
Height =10 Inch
Volume of a cylinder =[tex]\pi r^2h[/tex]
Volume of the Pot [tex]=\pi*7.5^2*10=562.5\pi[/tex] cubic inches.
Step 2: Determine the Volume of each can
Diameter= 4 inch, therefore Radius=4/2=2 Inches
Height =5 In.
Volume of a cylinder =[tex]\pi r^2h[/tex]
Volume of one can [tex]=\pi*2^2*5=20\pi[/tex] cubic inches.
Step 3: Divide the Volume of the Pot by the Volume of the can
To obtain the number of cans that will fill the pot, we divide the Volume of the Pot by the Volume of the can.
Volume of the Pot÷Volume of one can
[tex]=562.5\pi \div 20\pi\\=28.125 \:cans[/tex]
Therefore, we conclude that it takes 28.125 cans to fill up the cylindrical pot of soup.
The rectangle is 3 3⁄4 centimeters long and 2 1⁄2 centimeters wide. What is the area of this rectangle?
What is the value of x in the equation below? Negative 3 minus (negative 8) minus (negative 2) = x
Answer:7
Step-by-step explanation:
-3-(-8)-(-2)=x
-3+8+2=x
-3+10=x
7=x
x=7
Given: m = 1/2 and b = 4
The slope and y-intercept for a linear equation are given. Which graph matches this information?
Answer:
Graph C
Step-by-step explanation:
This graph had a slope of 1/2 and a y-intercept of 4.
If this answer is correct, please make me Brainliest!
Triangle CDE with vertices C(1, -1), D(2, 3), and E(3,-2) is reflected in line x= 4.
What are the coordinates of D’?
(7,-1)
(5,-2)
(6,7)
(6,3)
Answer:
(6,3)
Step-by-step explanation:
Two is two away from four and since it is on the left side, you add to get six as your x coordinate. The y coordinate stays the same.
Bette has a life insurance policy that will pay her family $40,000 per year if
she dies. Bette's insurance company expects that it would have to put
$2,500,000 into a bank account so that it could make the payments. What
does Bette's insurance company expect the interest rate to be?
Answer:
1.6%
Step-by-step explanation:
Solve for r
40,000=(2,500,000)(r/100)(1)
40,000=(25,000)r
r=40,000/25,000
r=1.6
a roll of dimes is 5. if the diameter of a dime is 18 millimeters and the height of each dime is 1.4 millimeters, what is the approximate volume of the roll of dimes?
Answer:
17.8 cm³
Step-by-step explanation:
The radius of the roll is half the diameter, so is 9 mm. The length of the roll of 50 dimes is 1.4·50 mm = 70 mm. With these dimensions, we can use the formula for the volume of a cylinder:
V = πr²h = π(9 mm)²(70 mm) = 5670π mm³ ≈ 17,812.8 mm³
Perhaps a more convenient unit of measure is cm³. Each cm³ is 1000 mm³, so the volume of a roll of dimes is approximately ...
V ≈ 17.8 cm³
Elliot is simplifying a radical. His work is shown
Which statement best applies to Elliot's mathematical work?
A. The equality V64 = 4.16 is incorrect or invalid.
B. Removing the 4 from under the radial in the second step is incorrect or invalid
C. The work shown above is correct; however, 2V16 can be simplified further.
D. The work shown above is correct; and 2V16 cannot be simplified further
Answer:
C. correct, but can be further simplified
Step-by-step explanation:
Elliot's work is correct, but he apparently failed to recognize that 64 = 8². The radical could be simplified to ...
√64 = 8
Answer:
c
Step-by-step explanation:
got it right
Mark wants a new car that costs $30000. He only has $500 in his savings account and $300 in his checking account. Which financing option should he chose
Answer: He should choose the savings account because he can earn more interest and the money in his savings account is more than the money in his checking account.
Step-by-step explanation:
