Answer: 10
Step-by-step explanation:
Given : Total number of coins tossed = 10
Possible outcomes to toss a coin = Head or tail
Number of possible outcomes = [tex]2^{10}=1024[/tex]
Number of ways of obtaining exactly 1 heads = [tex]{10}C_1=\dfrac{10!}{1!9!}[/tex] [using combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex] ]
=10
Hence, the numbers of ways of obtaining exactly 1 heads= 10
The Ambell Company uses batteries from two different manufacturers. Historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours. Only 75% of the batteries from manufacturer 2 last for over 40 hours. A battery in a critical tool fails at 32 hours. What is the probability it was from manufacturer 2?
Answer:
The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625
Step-by-step explanation:
Given that:
60% of the batteries are from manufacturer 1
90% of these batteries last for over 40 hours
Let the number of the battery duration be n = 0.90
Therefore n' = 1 - 0.90 = 0.10
Let p = manufacturer 1 and q = manufacturer 2
q = 1 - p
q = 1 = 0.6
q = 0.4
Thus ; 40% of the batteries are from manufacturer 2
However;
Only 75% of the batteries from manufacturer 2 last for over 40 hours.
Let number of battery duration be m = 0.75
Therefore ; m' = 1 - 0.75 = 0.25
A battery in a critical tool fails at 32 hours.
Thus; the that the battery in a critical tool fails at 32 hours was from manufacturer 2 is:
[tex]= \dfrac{q \times m' }{ p \times n' + q \times m' }[/tex]
[tex]= \dfrac{0.4 \times0.25 }{ (0.6 \times 0.1) + (0.4 \times 0.25 ) }[/tex]
[tex]=\dfrac{0.1}{0.06+ 0.1}[/tex]
[tex]=\dfrac{0.1}{0.16}[/tex]
= 0.625
The probability that the battery in a critical tool fails at 32 hours was from manufacturer 2 is 0.625
The probability that the battery was from manufacturer 2 is 62.5%.
Since the Ambell Company uses batteries from two different manufacturers, and historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours, while only 75% of the batteries from manufacturer 2 last for over 40 hours, if a battery in a critical tool fails at 32 hours, to determine what is the probability it was from manufacturer 2 the following calculation must be performed:
You must establish the percentage of failure of the total batteries, and determine what percentage of failures corresponds to each manufacturer. Manufacturer 1 = 60 x 0.1 = 6 Manufacturer 2 = 40 x 0.25 = 10 Total = 16 16 = 100 10 = X 100 x 10/16 = X 62.5 = X
Therefore, the probability that the battery was from manufacturer 2 is 62.5%.
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The function ƒ(x) = 2x is vertically translated 5 units down and then reflected across the y-axis. What's the new function of g(x)?
Answer:
g(x) = -2x - 5
2x becomes -2x as a reflection across the y-axis
add on -5 to shift the function 5 units down
g Given p, q, and r three propositional variables, how many different ways are for the propositional logic formula (p -> q) ^ (q -> r) ^ p to be evaluated to FALSE
Answer:
There are 7 ways in which the formula can be evaluated to False.
Step-by-step explanation:
In order to solve this problem we will need to build a truth table. In order to build the truth table, we must start by setting the possible truth values combinations. In total there must be 8 rows, which you can see on the first three columns of the attached table.
Next, it is advisable that you divide the formula in little chunks of information that will be easier to evaluate. One column can be (p->q).
Let's evaluate that first column. In general, that column can only be false if p=T -> q=F. Which happens only on the 3dr and 4th rows of the table. The rest of the statements are true.
The next column will be (q->r). The same condition is met here, but this time you take into account the values given on the q and r columns. The false values will happen only on the 2nd and 6th rows. The rest of the rows for that collumn should be true.
Finally you can test for the whole formula. the first, 4th and 5th columns must be true for the formula to be true as well, which will happen only on the first row. The rest of the rows will have at least one false statement which makes the whole row false. So the rest of the rows are false.
(see attached picture for the whole truth table)
Which graph shows the solution to the equation below? log Subscript 3 Baseline (x + 3) = log Subscript 0.3 (x minus 1)
Answer:
The answer is 20
Step-by-step explanation:
(Edge2020)
Answer:
Its A on edge
Step-by-step explanation:
i took the test. good luck guys!
Change Y = 3X to the standard form of the equation of a line.
Answer:
-3x+y=0
Step-by-step explanation:
Standard form= Ax+Bx=C
Add -3x both sides, answer -3x+1y=0
what is the ratios 3/4 in it simplest form
Answer:
3/4
Step-by-step explanation:
3/4 is already in it's simplest form as you already know that consecutive numbers don't have anything in common to multiply.So, it is in it's simplest form.
Hope it helps u : )
The equivalent and the percentage form of 3/4 are 12/16 and 75% respectively.
What is the ratio?
The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, the ratio of 3/4
Percentage of 3:4 = 34×100%=75%
the equivalent ratio of 3:4 is 12:16.
A ratio is a fraction that may compare part to whole or part to part. For example, suppose in a class, the ratio of boys to girls is 3 to 4. It means that the number of boys divided by the number of girls is a fraction that, in its simplest form, equals 3 over 4.
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Which inequality is represented by the graph?
Answer:
Step-by-step explanation:
the inequality represented by the graph is B
Plot the points
2x - 4/5y ≥ 3
y ≤ 2/5x - 3/2
x y
0 -3/2
15/4 0
Classify the triangle with angles measuring 1130, 47°, and 20°.
A. Straight
B. Right
C. Acute
D. Obtuse
Answer:
D. Obtuse
Step-by-step explanation:
Answer:
You typed that incorrectly. That first angle should be 113 degrees.
It would be an obtuse triangle.
Step-by-step explanation:
Andreas wants to estimate how many fish there are in a lake. One day he catches 20 fish,marks them,and returns them to the lake. The next day he catches 10 fish of which four are marked. Estimate the number of fish in the lake.
Answer:
50
Step-by-step explanation:
The ratio of marked fish to caught fish is 4:10, we need to solve for x in 20:x, since 4 * 5 = 20, 10 * 5 = x so x = 50 fish.
The assistant principal set up chairs in the auditorum for graduation. She placed
the chairs in 24 rows with 28 chairs in each row. How many chairs are set up in
the auditorium
Answer:
672 chairs
Step-by-step explanation:
24 × 28 = 672
hope this helps
j/2 +7=-12 solve for j
Answer:
j/2+7= -12
(j+14)/2= -12
cross-multiply
j+14= -24
j= -38
Answer:
[tex]\boxed{j=-38}[/tex]
Step-by-step explanation:
[tex]\frac{j}{2} +7=-12[/tex]
Subtract 7 on both sides.
[tex]\frac{j}{2} +7-7=-12-7[/tex]
[tex]\frac{j}{2}=-19[/tex]
Multiply both sides by 2.
[tex]\frac{j}{2}(2)=-19(2)[/tex]
[tex]j=-38[/tex]
There were females and males present at the high school pep rally. Find the ratio of males to the total number of people present. Express as a simplified ratio.
Answer: 4:9
Step-by-step explanation:
The complete question is provide in the attachment below.
Given, Number of females = 125
Number of males = 100
Total people = 120+100=225
Now, the ratio of males to the total number of people present = [tex]\dfrac{\text{Total number of males}}{\text{Total people}}[/tex]
[tex]=\dfrac{100}{225}[/tex]
Divide numerator and denominator by 25 , we get
Ratio of males to the total number of people present =[tex]\dfrac{4}{9}[/tex]
Hence, the ratio of males to the total number of people present = 4:9
given that H0: μ=40 against H1: μ < 40 if mice have an average life of 38 months with a standard deviation of 5.8 months. If the distribution of life spans is approximately normal, how large a sample is required in order that the probability of committing a type II error be 0.1 when the true mean is 35.9 months? Assume that level of significance 0.05.
Answer: sample required n = 18
Step-by-step explanation:
Given that the value under under null hypothesis is 40 while the value under the alternative is less than 40, specifically 35.9
∴ H₀ : u = 40
H₁ : u = 35.9
therefore β = ( 35.9 - 40 ) = -4.1
The level of significance ∝ = 0.05
Probability of committing type 11 error P = 0.1
standard deviation α = 5.8
Therefore our z-vales (z table)
Z₀.₅ = 1.645
Z₀.₁ = 1.282
NOW let n be sample size
n = {( Z₀.₅ + Z₀.₁ )² × α²} / β²
n = {( 1.645 + 1.282 )² × 5.8²} / (- 4.1)²
n = 17.14485
Since we are talking about sample size; it has to be a whole number
therefore
sample required n = 18
among the following, an incorrect statement is a) the volume of the hollow sphere =4/3π (r^3—r^3), where r is the radius of the outer sphere and r is the radius of the inner sphere. b) the volume of the hemisphere of radius(r) is 2πr^3 c) the surface area sphere = 4πr^2 d) the surface area of a spherical shell = 4π (r^2—r^2), where r = external radius and r= internal radius
please can someone say which one is incorrect
Answer:
fncjcnj jcj jcj jcj jd. d. c. dn. d. c. c. x. c. c. c.
water drips from a faucet at a rate of 41 drops/ minute. Assuming there are 15,000 drops in gallon, how many minutes would it take for the dripping faucet to fill a 1 gallon bucket? Round your answer to the nearest whole number
Answer:
366 Minutes
Step-by-step explanation:
Investment: Suppose you receive a gift of $1,000 and decide to open a CD (certificate of
deposit) as a low risk investment. The best CD rate you could find is 2.25%, which means that
your original investment will grow at a rate of 2.25% each year.
Assuming the rate of increase does not change, which of the following statements is TRUE
about your CD account balance?
It will no longer grow after several years.
It will triple in approximately 3 years.
O 4 years after the original investment, it is approximately $1,093.
O It will double in approximately 10 years.
Answer: 4 years after the original investment, it is approximately $1,093.
Step-by-step explanation:
Hi, to answer this question we have to apply the simple interest formula:
I = p x r x t
Where:
I = interest
P = Principal Amount
r = Interest Rate (decimal form)
t= years
Replacing with the values given
I = 1000x (2.25/100) x t
It will triple in approximately 3 years. FALSEI = 1000x (2.25/100) x 3 =67.5
1000+67.5 = 1067.5
It will no longer grow after several years: False, it will grow because it has a growth rate.4 years after the original investment, it is approximately $1,093. TRUEI = 1000x (2.25/100) x 4 =90
1000+90 = $1090
It will double in approximately 10 years.I = 1000x (2.25/100) x 10 =225
1000+90 = $1225
Feel free to ask for more if needed or if you did not understand something.
HELP ASAP I NEED THIS RIGHTNOW 30 points
Answer:
Pretty sure it is c
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
She will be painting the outsides of the table, so we need to find the surface area of the table.
There is the flat part of the table, which is a rectangular prism. There are also four legs, which are rectangular prism.
So, she will paint C. the surface area of 6 rectangular prisms.
Hope this helps!
Suppose you start at the origin, move along the x-axis a distance of 4 units in the positive direction, and then move downward along the z-axis a distance of 7 units. What are the coordinates of your position
Answer:
(4,0,-7)
Step-by-step explanation:
The initial position was (0,0,0) since it was the origin
Now, we have a movement of positive x at a distance of 4 units, with a distance of z a total of 7 units(negative since downward)
The current position is thus;
(4,0,-7)
Thus correlates to (x,y,z) and our y has remained zero as there is no movement along the y-axis
Solve for x.
a) 5√12
b) 12√5
c) 33
d) 6√5
Answer:
b
Step-by-step explanation:
Altitude- 0n- hypotenuse theorem
(leg of big Δ )² = ( part of hypotenuse below it ) × ( whole hypotenuse ), that is
x² = (30 - 6) × 30 = 24 × 30 = 720 ( take square root of both sides )
x = [tex]\sqrt{720}[/tex]
= [tex]\sqrt{144(5)}[/tex] = [tex]\sqrt{144}[/tex] × [tex]\sqrt{5}[/tex] = 12[tex]\sqrt{5}[/tex] → b
Find the x-value of the removable discontinuity of the function.
Answer:
x=2
Step-by-step explanation:
[tex]f(x)=\frac{x^2-4}{x^2-12x+20}[/tex]
Factor the numerator and denominator:
[tex]f(x)=\frac{(x-2)(x+2)}{(x-2)(x-10)}[/tex]
We can remove (x-2) from the function:
[tex]f(x)=\frac{x+2}{x-10}[/tex]
(x-2) is a removable discontinuity.
The x-value of x-2 is x=2.
If four times the brother's age is subtracted from three times the sister's age, the difference is 17. Give an equation that represents this statement using bbb as the age of the brother and s as the age of the sister.
Answer:
3s-4bbb=17
Step-by-step explanation:
brother=4bbb
sister=3s
3s-4bbb=17
which point is a solution tot eh linear inequality y < -1/2x + 2?
(2,3)
(2,1)
(3,-2)
(-1,3)
Answer:
Step-by-step explanation:
(3,-2)
plug in 3 for x and -2 for y
-2< -1/2x3+2
-2<-1.5+2
-2<0.5
50 Points. Select all correct graphs. Choose the graph that indicate equation with no solutions.
Concepts:
Graph equationsAnswer:
First option and fifth option
-2x-1=3^(-x) and 2^(-x)+2= -5^x + 3 don't intersect.
Therefore, the graphs have no solution.
Which of the following
examples have a constant rate of change?
A : You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles.
B : The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year.
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
D : The amount bacteria double every hour.
Answer:
C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.
Step-by-step explanation:
If a salesperson earns $50 plus $10 for every $100 of merchandise he sells, the rate of change is 100. The linear equation is T = 50 + 100h, where T is the total amount he earns and h is the number of $100 in merchandise he sells.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Let's check all the options, then we have
A: You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles. It is an example of a linear function but the slope gets changed after 2 hours.
B: The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year. It is an example of the exponential function.
C: A salesperson earns $50 plus $10 for every $100 of merchandise he sells. It is an example of a linear function.
D: The number of bacteria doubles every hour. It is an example of the exponential function.
The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.
More about the average rate change link is given below.
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Please answer this correctly without making mistakes
Answer:
B)Gift shop
pls mark me as BRAINLIEST
hope the answer helped you
In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to:
Answer:
[tex]Mean = 344[/tex]
Step-by-step explanation:
Given
[tex]Population = 1013[/tex]
Let p represents the proportion of those who worry about identity theft;
[tex]p = 66\%[/tex]
Required
Mean of those who do not worry about identity theft
First, the proportion of those who do not worry, has to be calculated;
Represent this with q
In probability;
[tex]p + q = 1[/tex]
Make q the subject of formula
[tex]q = 1 - p[/tex]
Substitute [tex]p = 66\%[/tex]
[tex]q = 1 - 66\%[/tex]
Convert percentage to fraction
[tex]q = 1 - 0.66[/tex]
[tex]q = 0.34[/tex]
Now, the mean can be calculated using:
[tex]Mean = nq[/tex]
Where n represents the population
[tex]Mean = 1013 * 0.34[/tex]
[tex]Mean = 344.42[/tex]
[tex]Mean = 344[/tex] (Approximated)
limit xtens to 0 x^2logx^2 what is the ans of interminate forms?
Rewrite the limit as
[tex]\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}[/tex]
Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get
[tex]\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}[/tex]
James determined that these two expressions were equivalent expressions using the values of x - 4 and x-6.
Which statements are true? Check all that apply.
7x+4 and 3x+5+4x-1
When x-2, both expressions have a value of 18.
The expressions are only equivalent for x = 4 and x-6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When x-0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if x - 8.
Answer:
1 - Correct
2 - incorrect
3- incorrect
4 - incorrect
5 - Correct
Step-by-step explanation:
Notice that
3x + 5 + 4x -1 = 3x + 4x + 5 -1 = 7x + 4
therefore the two expressions are equivalent for ANY number, specially x = 4 and x = 6 therefore
1 - Correct
Since that is true for all numbers
2 - incorrect
3- incorrect
4 - incorrect
The expressions are equivalent for all numbers therefore
5 - Correct
Complete the following questions on the picture
Answer:
Step-by-step explanation:
Hello!
For this particular organism population the growth rate is so that is doubled every 20 years. Using the starting population of 9 billion individuals by year 2000 you have to calculate the expected population values every 20 years.
All you have to do is multiply the original population by 2 to obtain the next value.
Year 2000:
Population: 9*10⁹ or 9 000 000 000 x 2= 18 000 000 000
To express 18 billion in scientific notation you have to add a "comma" after the first digit and then count the number of digits behind it:
1, 8 000 000 000 there are 10 digits behind the first digit. This notation summarizes the number in base 10 exponents so 18 billion in scientific notation is:
1.8 * ten "exponent the number of digits behind the comma"
1,8*10¹⁰So the population for year 2020 will be 1,8*10¹⁰
Next for year 2040 you have to multiply the population of year 2020 by 2
1,8*10¹⁰ x 2= 3,6*10¹⁰
And so on:
2060: 3,6*10¹⁰ x 2)= 7.2*10¹⁰
2080: 7.2*10¹⁰ x2= 1.44*10¹¹
2100: 1.44*10¹¹ x2= 2.88*10¹¹
2120: 2.88*10¹¹x2= 5.76*10¹¹
2140: 5.76*10¹¹x2= 1.152*10¹²
2160: 1.152*10¹²x2= 2.304*10¹²
2180: 2.304*10¹²x2= 4.608*10¹²
2200: 4.608*10¹² x2= 9.216*10¹²
2220: 9.216*10¹²x2= 1.8432*10¹³
2240: 1.8432*10¹³x2= 3.6864*10¹³
2260: 3.6864*10¹³x2= 7.3728*10¹³
2280: 7.3728*10¹³x2= 1.47456*10¹⁴
2300: 1.47456*10¹⁴x2= 2.94912*10¹⁴
2320: 2.94912*10¹⁴x2= 5.89824*10¹⁴
2340: 5.89824*10¹⁴x2= 1.179648*10¹⁵
2360: 1.179648*10¹⁵x2= 2.359296*10¹⁵
2380: 2.359296*10¹⁵x2= 4.718592*10¹⁵
2400: 4.718592*10¹⁵x2= 9.437184*10¹⁵
So for year 2400 the expected population will be 9.437184*10¹⁵, writen in common notation that is:
9 437 184 000 000 000 individuals
I hope this helps!
WHY CAN'T ANYONE HELP ME PLEASE? THANKS! A student at a university makes money by buying and selling used cars. Charles bought a used car and later sold it for a 15% profit. If he sold it for $4669, how much did Charles pay for the car?
Step-by-step explanation:
Given,
a student (Charles) bought a car and sold it in 15 % profit for $4669.
we have the formula,
[tex]cp = \frac{sp \times 100}{100 + p\%} [/tex]
so,
[tex]cp = \frac{4669 \times 100}{100 + 15} [/tex]
by simplifying it we get,
CP is $4060.
Therefore, the cp was $4060.
Hope it helps...