Final answer:
The student's question is about finding the probability that at least two of the 11 balls drawn with replacement from a box of 80 uniquely numbered balls are the same. We use the complement rule to find the probability of all balls being unique and subtract this from 1 to find the desired probability.
Explanation:
The student is asking about the probability of drawing at least two balls with the same number when 11 balls are drawn with replacement from a box containing 80 uniquely numbered balls. To solve this, we can use the complement rule, which states that the probability of an event occurring is equal to one minus the probability of the event not occurring.
The probability of drawing 11 unique balls in a row with replacement from 80 can be calculated by multiplying the probabilities of drawing a unique ball at each draw after the first. For the first ball, the probability is 80/80 (since any ball can be drawn), for the second ball it's 79/80 as one unique ball is already drawn, for the third it's 78/80, and so on until the eleventh ball.
The probability of drawing 11 unique balls is therefore (80/80) * (79/80) * (78/80) *...* (70/80). The probability of at least two balls having the same number is 1 minus this product, which represents the probability of all balls being unique.
Which of the following groups has terms that can be used interchangeably with the others?1. Percentage, Probability, and Proportion2. Critical Value, Probability, and Proportion3. Critical Value, Percentage, and Probability4. Critical Value, Percentage, and Proportion
Answer: 1) Percentage, Probability, Proportion
Step-by-step explanation:
In statistics,
▪Proportion means a fraction of the total.
▪Percentage means a number or a ratio, expressed as a fraction of 100. Here, the total is 100.
▪Probability which may look slightly different from the other two means a number between 0 and 1, showing the exact likelihood of an event happening. Which in context can mean, a number showing a fraction of an event happening out of the whole (0 to 1).
▪Critical value means a point in hypothesis testing on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.
In the four definitions, the odd one out is Critical Value.
So the option without critical value in it is option 1) Percentage, Probability, Proportion since we can use the three interchangeable.
Answer:
1. Percentage, Probability, and Proportion
Step-by-step explanation:
Proportion means a portion of a whole e.g. 2/5
Percentage means a ratio of a number expressed as a fraction of 100 e.g 20/100
Probability- This means the likelihood of an event to occur e.g 1/2
All these three terms are usually expressed as a Fraction of a Number which makes them similar.
Find the product of all constants t such that the quadratic x^2 tx - 9 can be factored in the form (x a)(x b), where a and b are integers.
Answer:
product of the constants P will be
P = 12
Step-by-step explanation:
the quadratic equation
F= x² + t*x - 9
has as solution
a and b= [-t ± √( t² - 4*1*(-9)) ] /2]
then
a - b = -t/2
a= b - t/2
since b is an integer , then t/2 should be an integer , then t=2*n , where n is any integer
also
a and b= [-t ± √( t² - 4*1*(-9)) ] /2] = [-2*n ± √(4*n²+36 )] /2 = -n ± n √ (1+9/ n²]
since n are integers , then √ (1+9/ n²] should be and integer and therefore
9/ n² should be an integer. Then the possible values of n are
n=1 and n=3
therefore the possible values of t are
t₁=2*1 = 2
t₂=2*3 = 6
the product of the constants P will be
P=t₁*t₂ = 12
Answer:
729
Step-by-step explanation:
Arianna solved a fraction division problem using the rule "multiply by the reciprocal." Her work is shown below. Two-thirds divided by StartFraction 4 Over 5 EndFraction. Two-thirds times StartFraction 4 Over 5 EndFraction = StartFraction 8 Over 15 EndFraction Which is the most accurate description of Arianna's work? Arianna solved the problem correctly. Arianna multiplied the dividend by the divisor instead of finding the reciprocal. Arianna multiplied the denominators instead of finding a common denominator. Arianna multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.
Answer:
Arianna multiplied the dividend by the divisor instead of finding the reciprocal.
Step-by-step explanation:
The fraction division problem Arianna solved is [tex]\frac{2}{3}\div \frac{4}{5}[/tex]
Adrianna's next step is [tex]\frac{2}{3}\times \frac{4}{5}[/tex]
We are supposed to choose from the options the most accurate description of Arianna's work.
The mistake Arianna committed is that, she did not reciprocate the [tex]\frac{4}{5}[/tex] before multiplying.
Therefore the correct answer is:
Arianna multiplied the dividend by the divisor instead of finding the reciprocal.
In the first 2 hours after Meadow's self-service laundry opens, m large washing machines and n small washing machines are in continual use. Including the time for filling and emptying the washing machines, each load of laundry takes 30 minutes in a large washing machine and 20 minutes in a small washing machine. What is the total number of loads of laundry done at Meadow's self-service laundry during this 2-hour period?
Answer:
Nt=10 (m=4,n=6)
Step-by-step explanation:
we have that m = amount of time used by the large washing machine to wash a load of clothes and n = amount of time used by the small washing machine to wash a load of clothes, so
[tex]m=\frac{Tt}{Tpm}=\frac{2h}{\frac{1h}{2}}=4\\n=\frac{Tt}{Tpn}=\frac{2h}{\frac{1h}{3}}=6[/tex]
Nt=m+n=10
where Tt = time frame, Tpm= m' time frame, Tpn = n' time frame and Nt = total number of charges
Answer: Total laundry done in 2hours=110
Step-by-step explanation:
Let m be large washing machines
Let n be small washing machines
Load of laundry for large machine=30mins
Load of laundry in small machine=20 mins
2 hours laundry =2×60=120mins
For m in 2hrs=120/30=4
For n in 2hrs=120/20=6
m loads in 2hrs=4m
n loads in 2hrs=6n
1st statement:n=3m
Substituting
4m+6(3)=x
4m+18m=x
X=22m
Value of m cannot be determined because statement 1 is insufficient
From the 2nd statement: 2m+3n=55
Multiply both sides by2
4m+6n=110
Using drt what is the Answer to this question a car in a bus set out at 2 PM find the same point headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours the car is 20 miles ahead of the bus. Find the rate of the car
Answer: the rate of the car is 50mph
Step-by-step explanation:
Let x represent the average speed of the bus.
Let y represent the distance travelled by the bus.
The average speed of the car is 30 mph slower than twice the speed of the bus. This means that the average speed of the car would be
2x - 30
Distance = speed × time
Time = distance/speed
Therefore, In 2 hours time,
2 = y/x
2x = y
In two hours the car is 20 miles ahead of the bus. Therefore
2 = (y + 20)/(2x - 30)
2(2x - 30) = y + 20
4x - 60 = y + 20 - - - - - - - - -1
Substituting y = 2x into equation 1, it becomes
4x - 60 = 2x + 20
4x - 2x = 20 + 60
2x = 80
x = 80/2 = 40
The speed of the car would be
2x - 30 = 2 × 40 - 30
= 80 - 30 = 50 mph
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below.
A
manman
is selected by a marketing company to participate in a paid focus group. The company says that the
manman
was selected because
hehe
waswas
randomlyrandomly
chosenchosen
fromfrom
allall
adults.adults.
nothing
nothing
nothing
nothing
Answer: Random sampling
Step-by-step explanation:
A random sampling technique is the basic sampling technique in which the researcher randomly choose individuals from the whole population . This sampling method provides equal opportunity to each and every individual in the population to get selected for the sample.In the given situation , the population of interest is "all adults"
Since the man got selected randomly from entire population of adults by the marketing company, it means the type of sampling method was used is random sampling technique.
Hence, the correct answer is "random"
Luke wants to buy a $575 iPad. Luke has no money saved, but will be able to deposit $65 into a savings account when he receives his paycheck each Friday. However, before luke can buy the iPad, he must give his sister $55 that he owes her. For how many week will Luke need to deposit money into his savings account before he can pay back his sister and buy the iPad
Answer:Luke needs to deposit money into his savings account for 10 weeks before he can pay back his sister and buy the iPad.
Step-by-step explanation:
The cost of the iPad that Luke wants to buy is $575
before Luke can buy the iPad, he must give his sister $55 that he owes her. This means that the total amount of money that he must save would be 575 + 55 = $630
He will be able to deposit $65 into a savings account when he receives his paycheck each Friday.
Let x represent the number weeks it takes him to save enough money in his account. Therefore, the total amount that he saves for x weeks would be 65 × x = 65x
Therefore,
65x = 630
x = 630/65
x = 9.69
The vector product of vectors A and B has magnitude 12.0 m² and is in the +z-direction. Vector A has magnitude 8.0 m and is in the −x-direction. Vector B has no x-component.
Part A: What is the magnitude of vector B?
Part B: What is the direction angle θ of vector B measured from the +y-direction to the +z-direction?
Final answer:
The magnitude of vector B is 1. There is no valid direction angle theta for vector B.
Explanation:
Part A:
The magnitude of vector B can be found using the formula for the magnitude of the vector product:
|A x B| = |A||B|sin(theta)
Given |A x B| = 12, |A| = 8, and |B| = ?
Using the formula above, we can solve for |B|:
12 = 8 * |B| * sin(theta)
sin(theta) = 12 / (8 * |B|) = 1.5 / |B|
Sine of any angle lies between -1 and 1, therefore 1.5 / |B| should lie in this range
|-1| <= 1.5 / |B| <= |1|
1 <= 1.5 / |B| <= 1
1.5 <= |B| <= 1
The magnitude of vector B is 1.
Part B:
The direction angle theta can be found using the formula:
cos(theta) = Bz / |B|
Given Bz = |B| and sin(theta) = 1.5 / |B|
1.5 / |B| = sqrt(1 - sin^2(theta)) = sqrt(1 - 1) = sqrt(0) = 0
This implies that sin(theta) = 1.5 / |B| = 0, which is not possible
Hence, there is no valid direction angle theta for vector B.
Final answer:
The magnitude of vector B is 1.5 m. The direction angle θ of vector B measured from the +y-direction to the +z-direction is 90°.
Explanation:
Part A: To find the magnitude of vector B, we need to use the relationship between the magnitude of the vector product A x B and the magnitudes of vectors A and B. According to the given information, the magnitude of the vector product A x B is 12.0 m². Since the vector product is in the +z-direction, we can conclude that the magnitudes of vectors A and B multiplied by the sine of the angle between them equals 12.0 m².
Let's use this information to find the magnitude of vector B:
|A x B| = |A||B|sin(θ)
12.0 m² = 8.0 m * |B| * sin(90°)
|B| = 12.0 m² / (8.0 m * sin(90°))
|B| = 12.0 m² / 8.0 m = 1.5 m
Therefore, the magnitude of vector B is 1.5 m.
Part B: To find the direction angle θ of vector B measured from the +y-direction to the +z-direction, we can use the relationship between the components of vectors A and B and the direction angle θ:
tan(θ) = By / Bz
Substituting the given information into the equation:
tan(θ) = 0 / Bz
Since vector B has no x-component, we know that Bx = 0. Therefore, we only need to find the value of Bz to determine the direction angle θ.
Recall that |B| = 1.5 m. Using the Pythagorean theorem, we can find the value of Bz:
|B|² = Bx² + By² + Bz²
(1.5 m)² = (0)² + (0)² + Bz²
Bz² = (1.5 m)²
Bz = 1.5 m
Since Bz > 0, we know that the direction angle θ is in the positive range. In this case, the direction angle θ is 90° measured from the +y-direction to the +z-direction.
A line is a set of all points that:
A line is a set of all points that : C. are the same distance from two points.
Step-by-step explanation:
A line is defined as a set of all points that are the same distance from two given points. For a line to form, you must connect points, thus its correct to say a line is formed when you draw a locus of a given point.
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A proper rectangle has a lengh of 6 inches and a with of 8 inches. A square with a side lenght of 3 inches was cut of it. What is the area of the remaining paper?
Final answer:
To find the remaining area after cutting a 3-inch square from a 6x8 rectangle, subtract the area of the square (9 square inches) from the area of the rectangle (48 square inches), resulting in 39 square inches left.
Explanation:
Calculating the Remaining Area of a Rectangle
To determine the area of the remaining paper after a square is cut off, we must first know the area of the initial rectangle and the area of the square that was removed. The area of the rectangle is found by multiplying its length by its width. Rectangle area = length × width, so it is 6 inches × 8 inches = 48 square inches. The cut-off square has a side length of 3 inches, so its area is 3 inches × 3 inches = 9 square inches.
Subtract the area of the square from the area of the rectangle to get the remaining paper area. Remaining area = rectangle area - square area, which equals 48 square inches - 9 square inches = 39 square inches.
Terry bergolt bank granted him a single payment loan of $4,400 at an intreats rate of 6% exact interest. The term of the loan is 172 days what is the exact interest? what is the maturity of the loan?
Answer:
Step-by-step explanation:
We would apply the formula for determining simple interest which is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T =172 days = 172/365 = 0.47 years
P = $4400
R = 6%
Therefore
I = (4400 × 6 × 0.47)/100
I = 12408/100
I = $124.08
The maturity of the loan would be
4400 + 124.08 = $4524.08
Three consecutive natural numbers ae such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60
Answer:
The three consecutive natural numbers are 9,10,11
Step-by-step explanation:
Step 1 : -
Let x be the number
Given three consecutive natural numbers are x, x+1,x+2
Given data are three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60
that is [tex](x+1)^2 = (x+2)^2 - x^2 +60{\tex]
step 2:-
on simplification on both sides are , we get
by using [tex](a+b)^2 = a^2+2 a b+b^2[\tex]
[tex]x^2+2 x+1 = x^2+4 x+4-x^2+60[\tex]
cancelling x^2 terms and simplify
[tex] x^2 -2 x-63=0[\tex]
now finding factors of [tex] 63 = 9 X 7[\tex]
[tex] x^2 - 9 x+7 x -63=0 [\tex]
[tex] x(x-9)+7(x-90 =0 [\tex]
[tex]( x+7)(x-9) =0 [\tex]
here x= -7 is not an natural number
so we have to take x=9
therefore the three consecutive natural numbers are
x,x+1,x+2
The three consecutive natural numbers are 9 , 10, 11
Answer:
three consecutive natural numbers are
5,6,7
Step-by-step explanation:
Let x, x+1 and x+2 are the three consecutive natural numbers
middle number is x+1
square of middle number is [tex](x+1)^2=x^2+2x+1[/tex]
difference of square of other two numbers is
[tex]x^2-(x+2)^2= x^2-x^2-4x-4=-4x-4[/tex]
the square of the middle number exceeds the difference of the squares of the other two numbers by 60
So [tex]x^2+2x+1=-4x-4+60[/tex]
[tex]x^2+2x+1+4x+4-60=0[/tex]
[tex]x^2+6x-55=0[/tex]
[tex](x+11)(x-5)=0[/tex]
[tex]x+11=0, x=-11[/tex]
[tex]x-5=0, x=5[/tex]
we take only natural number so x=5
three consecutive natural numbers are
5,6,7
Sickle-cell disease is caused by a recessive allele. Roughly one out of every 500 African Americans (0.2%) is afflicted with sickle-cell disease. Use the Hardy-Weinberg equation to calculate the percentage of African Americans who are carriers of the sickle-cell allele. Hint: 0.002 = q2. Show your work.
Answer:
heterozygous (Aa) are 0.085 = or 8.54%
Step-by-step explanation:
The heterozygous individuals are carriers of the sickle cell trait. They have a genotype of Aa and are represented by the 2pq term
in the H-W equilibrium equations.
According to the question 0.2% of the population is affected with sickle cell anemia, thus q^2
= 0.2% = 0.002 in decimal. So, q =
sqr(q^2)
or sqr(0.002) =
0.04472
and p + q = 1, thus p = 1 – q = 1 – 0.04472 = 0.96
Thus, A allele has a frequency of 0.96 and the a allele has a frequency of 0.04472. Therefore, the
percentage of the population that is heterozygous (Aa) and are carriers is = 2pq = 2× 0.04472× 0.96 =0.085 = or 8.54%
Solve the system using elimination.
x plus 7 y
equals
22
4 x minus 7 y
equals
negative 17
The solution is
nothing.
(Simplify your answer. Type an ordered pair.)
Answer:
After simplifying we get (x,y) as (1,3).
Step-by-step explanation:
Given:
[tex]x+7y=22[/tex],
[tex]x-7y=-17[/tex]
We need to use elimination method to solve the and simplify the equations.
Solution;
Let [tex]x+7y=22[/tex] ⇒ equation 1
Also Let [tex]4x-7y=-17[/tex]⇒ equation 2
Now by solving the equation we get;
first we will Add equation 2 from equation 1 we get;
[tex](x+7y)+(4x-7y)=22+(-17)\\\\x+7y+4x-7y=22-17\\\\5x=5[/tex]
Now Dividing both side by 5 using division property of equality we get;
[tex]\frac{5x}{5}=\frac{5}{5}\\\\x=1[/tex]
Now Substituting the vale of x in equation 1 we get;
[tex]x+7y=22\\\\1+7y=22[/tex]
subtracting both side by 1 using subtraction property of equality we get;
[tex]1+7y-1=22-1\\\\7y=21[/tex]
Now Dividing both side by 7 using division property of equality we get;
[tex]\frac{7y}{7}=\frac{21}{7}\\\\y=3[/tex]
Hence we can say that, After simplifying we get (x,y) as (1,3).
A chef wants to make sure he uses all the eggs he bought he had 8 cartons with 36 eggs in each carton he uses 2/5 for Fridays breakfast and 3/8 of the remaining on Saturdays breakfast how many eggs did the chef use?
Answer:
Step-by-step explanation:
The Chef bought he had 8 cartons with 36 eggs in each carton. This means that the total number of eggs that the Chef bought is
36 × 8 = 288 eggs
He uses 2/5 for Fridays breakfast. This means that the number of eggs that he used on Friday is
2/5 × 8= 16/5 cartons
The remaining number of cartons would be
8 - 16/5 = 24/5 cartons
He used 3/8 of the remaining for Saturdays breakfast. This means that the number of eggs that he used on Saturday is
3/8 × 24/5 = 9/5 cartons
Total number of cartons that he used is
16/5 + 9/5 = 25/5 = 5 cartons
Since one carton contains 36 eggs, then the total number of eggs that the Chef used is
5 × 36 = 180 eggs
solve the equation, justify each step with an algebraic property.
-4+-17+x.
–21 + x
Explanation:
Step 1: Given expression: –4 + (–17) + x
Step 2: In the algebraic property, positive × negative = negative
So, –4 + (–17) + x = –4 – 17 + x
Step 3: Add two negative numbers, the result will be sum with minus sign
–4 – 17 + x = –21 + x
Hence, –21 + x is the required equation.
An insurance company claims that in the entire population of homeowners, the mean annual loss from fire is --$250 and the standard deviation of the loss is ơ-$1000. The distribution of losses is strongly right-skewed: many policies have $0 loss, but a few have large losses. An auditor examines a random sample of 10,000 of the company's policies. If the company's clairm is correct, what's the probability that the average loss from fire in the sample is no greater than $275?
Answer:
the probability that the average loss from fire in the sample is no greater than $275 is 0.9938
Step-by-step explanation:
given information:
mean, μ = $250
std deviation, σ = $1000
random sample, n = 10000
x = $275
P([tex]x[/tex] ∠_ 275) = P(z < (z ∠ (x - μ)/(σ/√n))
= P (z ∠ (275 - 250)/(1000/√10000)
= P(z ∠ 2.5)
= 0.9938
The probability that the average loss from fire in the sample is no greater than $275 is 99.38%.
Given to us,mean, μ = $250 standard deviation, σ = $1000 random sample, n = 10000 Average loss, x ≤ $275To findthe probability that the average loss from fire in the sample is no greater than $275,
[tex]P(z\leq x)=P[z< \dfrac{(x-\mu )}{(\dfrac{\sigma}{\sqrt n})}][/tex]
[tex]P(z\leq 275)=P[z< \dfrac{(275-250 )}{(\dfrac{1000}{ \sqrt {10000}})}][/tex]
[tex]P(z\leq 275)=P[z< \dfrac{(25 )}{(10)}][/tex]
[tex]P(z\leq 275)=P[z< {(2.5)}][/tex]
[tex]P(z\leq 275)=0.9938[/tex]
P(x ≤ $275) = 99.38%
Hence, the probability that the average loss from fire in the sample is not greater than $275 is 99.38%.
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Two rockets are lauched at the same time, but from different heights. The height y in feet of one rocket after t seconds is given by y = -16t² + 150t + 5. The height of the other rocket is given by y = -16t² + 160t. After how many second are the rockets at the same height?
Answer:
0.5 seconds
Step-by-step explanation:
Two rockets are launched at the same time, but from different heights.
[tex]y = -16t^2+ 150t + 5[/tex]
[tex]y = -16t^2 + 160t[/tex]
when the heights are same then y are equal. So equation both equations and solve for t
[tex]-16t^2+ 150t + 5= -16t^2+ 160t[/tex]
Add -16t^2 on both sides
[tex]+ 150t + 5=160t[/tex]
Subtract 150 t from both sides
[tex]5=10t[/tex]
Divide 10 on both sides
t=0.5 seconds
Manuel has a boat that can move at a speed of 15 km/h in still water. He rides 140 km downstream in a river in the same time it takes to ride 35km upstream. What is the speed of the river?
Answer: the speed of the river is 9km/h
Step-by-step explanation:
Let x represent the speed of the river current.
He rides 140 km downstream in a river in the same time it takes to ride 35km upstream. This means that his speed was higher when riding downstream and it was lower when riding upstream.
Assuming he rode in the direction of the river current when coming downstream and rode against the current when going upstream.
time = distance/speed
Manuel has a boat that can move at a speed of 15 km/h
His downstream speed would be
15 + x
time spent coming downstream would be
140/(15 + x)
His downstream speed would be
15 - x
time spent going downstream would be
35/(15 - x)
Since the time is the same, then
140/(15 + x) = 35/(15 - x)
Crossmultiplying
140(15 - x) = 35(15 + x)
2100 - 140x = 525 + 35x
140x + 35x = 2100 - 525
175x = 1575
x = 1575/175
x = 9
Which function represents exponential decay? f(x) = One-half(2)x f(x) = Three-fourths(Negative one-fifth)x f(x) = 3(Seven-halves)x f(x) = 2(Two-thirds)x
Answer: [tex]f(x)=2(\dfrac{2}{3})^x[/tex]
Step-by-step explanation:
We know that the exponential decay equation is given by :-
[tex]y=Ab^x[/tex]
, where A = initial value.
b = Multiplicative growth rate ( b <1 for decay)
x= time period.
Note : b ≠1 and b>0.
Let's check all the functions:
[tex]f(x)=\dfrac{1}{2}(2)^x[/tex], here b =2 >1 , so this function does not represent exponential decay.
[tex]f(x)=\dfrac{3}{4}(-\dfrac{1}{5})[/tex]here b = [tex]-\dfrac{1}{5}[/tex] but b should be greater than 0 for exponential function, so this function does not represent exponential decay.
[tex]f(x)=3(\dfrac{7}{2})^x[/tex]
Here , [tex]b=\frac{7}{2}>1[/tex] , so this function does not represent exponential decay.
[tex]f(x)=2(\dfrac{2}{3})^x[/tex]Here , [tex]b=\dfrac{2}{3}<1[/tex] , so this function represents exponential decay.
Hence, the correct answer is [tex]f(x)=2(\dfrac{2}{3})^x[/tex] .
A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.
We will see that the correct option is:
f(x) = 2*(2/3)^x----------------------------------------
The form of the general exponential decay is:
f(x) = A*(r)^x
Where A is the initial value, x is the variable, and r is the rate at which it decreases, where r must be a number between 0 and 1.
The given options are:
f(x) = (1/2)*2^xf(x) = (3/4)*(-1/5)^xf(x) = 3*(7/2)^xf(x) = 2*(2/3)^xBecause r must be between zero and one, the only option that meets that requirement is the last one, where r = 2/3.
Then the function that represents an exponential decay is the last one:
f(x) = 2*(2/3)^xIf you want to learn more, you can read:
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Suppose a savings and loan pays a nominal rate of 1.21.2% on savings deposits. Find the effective annual yield if interest is compounded 10 comma 00010,000 times per year?
Answer:
1.21%
Step-by-step explanation:
We have been given that a savings and loan pays a nominal rate of 1.2% on savings deposits. We are asked to find the effective annual yield, when interest is compounded 10 comma 00010,000 times per year.
We will use Annual Percentage Yield formula to solve our given problem.
[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year.
[tex]1.2\%=\frac{.2}{100}=0.012[/tex]
[tex]APY=(1+\frac{0.012}{10,000})^{10,000}-1[/tex]
[tex]APY=(1+0.0000012)^{10,000}-1[/tex]
[tex]APY=(1.0000012)^{10,000}-1[/tex]
[tex]APY=1.0120722815791632-1[/tex]
[tex]APY=0.0120722815791632[/tex]
[tex]0.0120722815791632\times 100\%=1.20722815791632\%\approx 1.21\%[/tex]
Therefore, the effective annual yield would be 1.21%.
In a psychology class, 32 students have a mean score of 93.2 on a test. Then 16 more students take the test and their mean score is 63.4.What is the mean score of all of these students together? Round to one decimal place.mean of the scores of all the students =
The mean score of all the students together, after calculating the combined total score and dividing by the total number of students, is 83.1.
Explanation:The subject of this question is the computation of the mean score of all students. The first step is to find the total score of both sets of students. For the first group, the total score is the mean score multiplied by the number of students, which is 93.2 * 32 = 2974.4. For the second group, total score is 63.4 * 16 = 1014.4. The combined total score is 2974.4 + 1014.4 = 3988.8. Since there are 32 + 16 = 48 students in total, the mean score of all students is calculated by dividing the combined score by the total number of students. So, the mean score of all the students together is 3988.8 / 48 = 83.1 (rounded to one decimal place).
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Which situation below has a negative correlation?
A. The more a student studies, the higher the test grade.
B. The younger the child, the smaller the shoe size.
C. The longer you exercise, the more you sweat.
D. The younger the child, the more sleep they need.
Answer:
In terms of negative correlation, I would say it's the longer you exercise, the more you sweat.
Answer:
Its D. The younger the child, the more sleep they need.
Step-by-step explanation:
Use properties of rational exponents to simplify the expression. Assume that all variables represent positive numbers. Superscript 1 divided by 3.
Hi, your question was incomplete hence I have attached the complete version of the question below.
Answer:
5x^3 y^2
Step-by-step explanation:
Using the property of the product of the exponents on the base and removing the parentheses,
(125x^9y^6)^(1/3) = (125)^(1/3) * (x^9)^(1/3) * (y^6)^(1/3)
= (125)^(1/3) * (x)^9*(1/3) * (y)^6*(1/3)
= 5 * (x)^3 * (y)^2
= 5 x^3 y^2
hence the required result is 5 x^3 y^2
$36\%$ of the beans in Pythagoras's soup are lentils, and $33\frac13\%$ of those lentils are green. If Pythagoras removes all the green lentils from his soup, then $x\%$ of the original beans remains. What is $x$?
Question is not proper, Proper question is given below;
36% of the beans in Pythagoras's soup are lentils, and 33 1/3% of those lentils are green.
If Pythagoras removes all green lentils from his soup, then x% of the original beans remain. What is x?
Answer:
88% of the original beans remains [tex](x)[/tex] after removing green lentils.
Step-by-step explanation:
Given:
Let the Original beans be 'n'.
Now given:
36% of the beans in Pythagoras's soup are lentils.
So we can say that;
Amount of lentils = [tex]\frac{36}{100}n=0.36n[/tex]
Also Given:
33 1/3% of those lentils are green
Amount of green lentils = [tex]33\frac{1}{3}\%\ \ Or \ \ \frac{100}{3}\%[/tex]
Amount of green lentils = [tex]\frac{100}{3}\times 0.36n\times\frac{1}{100}= 0.12n[/tex]
Now we need find the percentage of original beans remain after removing green lentils.
Solution:
percentage of original beans remain ⇒ [tex]x\%[/tex]
To percentage of original beans remain after removing green lentils we will subtract Amount of green lentils from Original beans and then multiplied by 100.
framing in equation form we get;
[tex]x\%[/tex] = [tex](n-0.12n)\times 100=88n \ \ \ Or \ \ \ 88\%[/tex]
Hence 88% of the original beans remains [tex](x)[/tex] after removing green lentils.
Answer:
x = 88
Step-by-step explanation:
We know that 36% of the letters are vowels. Of these, one-third are Os
(Since 33 1/3% = 33 1/3 divided by 100 = 1/3.) One-third of 36% is 12%, so 12% of the total letters in Pythagoras' soup are Os. When these are removed from the soup, 100 - 12=88% of the original letters remain.
So, x = 88
Hope this helps!
Ana Participated in each charity walk she raise $.25 and each 1/2 That she walked the first day and I walked 11 miles a second day she walked 14 miles how much money did she raise
Question:
Ana participated in a charity walk. She raised $0.25 for each 1/2 mile that she walked.The first day Ana walked 11 miles.The second day, she walked 14 miles.How much money did Ana raised?
Answer:
Ana raised $ 12.5
Solution:
From given question,
First day walk = 11 miles
Second day walk = 14 miles
Let us first calculate the total distance she walked
Total distance = first day walk + second day walk
Total distance = 11 + 14 = 25 miles
Thus she walked for 25 miles
Given that,
She raised $0.25 for each 1/2 mile that she walked
[tex]\frac{1}{2} \text{ mile} = 0.25 \text{ dollars }[/tex]
Therefore, for 1 mile we get,
[tex]\frac{1}{2} \times 2 \text{ mile} = 0.25 \times 2 \text{ dollars }\\\\1 \text{ mile } = 0.5 \text{ dollars }[/tex]
Now calculate for 25 miles
[tex]25 \text{ mile } = 25 \times 0.5 = 12.5 \text{ dollars }[/tex]
Thus she raised $ 12.5
Which of the following is a reflection of y = |x|
The graph of y=|x| would look like graph A
The reflected graph (mirrored image) would be graph D
Plz help, Worth 40 pts, Will mark Branliest...
Answer:
$6.83
Step-by-step explanation:
To start off, we would want to graph the points.
Once we have our graph, we see our correlation is positive, meaning that every year past 1950, the price of 1 movie ticket increases.
Our next step would to figure out the linear regression, or to guess a best line of fit. Once we do so, we should see where the movie tickets should approxametly rise to.
We then use the best line of fit to estimate the price in 2015, or when x = 65 (65 years after 1950).
The answer closest to the estimate would be 6.83. Attached image is the graph on Desmos.
Determine if the numerical value describes a population parameter or a sample statistic. 75u% of all instructors at your school teach 2 or more classes. Answer1 PointKeypad Population Parameter Sample Statistic?
Answer: Population parameter.
Step-by-step explanation:
Population parameter : It is a number that summarize a term for the whole population . For example :population proportion , population mean , etc.
Sample statistics: It is a number that summarize a term for the sample . For example : sample proportion , sample mean, etc.
By considering the given statement :
Population of interest : " all instructors at school "
Since 75% of all instructors at your school teach 2 or more classes.
It means , 75% is describing population proportion of all instructors at your school teach 2 or more classes..
i.e. The numerical value describes a population parameter.
Colin is painting figurines. He spends 20 mins painting each figurine. After painting for 60 mins he still has 9 left to paint. What is the function's formula
The required function is: [tex]f(t) = -0.05t+12[/tex]
Step-by-step explanation:
We have to write a function for the remaining figurines Colin has to paint.
Here
f is the function that represents number of figurines remaining
t represents time in minutes as the unit of measurement is minutes
f will be a function of t
It is mentioned in the problem that after working for 60 minutes, he has 9 figurines left to paint.
This means that
f(60) = 9
It is also given that he takes 20 minutes to paint one figurine which means in 60 minutes he will have painted 3 figurines
So at start total figurines that needed to be painted will be:
9+3 = 12
Which means that
f(0) = 12
By using these two points we can find the slope of the function
[tex]m = \frac{Change\ in\ figurines}{Change\ in\ time}\\m = \frac{9-12}{60-0}\\m = \frac{-3}{60}\\m = -0.05[/tex]
The function will be:
[tex]f(t) = mt+b[/tex]
Putting the value of slope
[tex]f(t) = -0.05t+b[/tex]
b is the initial value of figurines so
[tex]f(t) = -0.05t+12[/tex]
Keywords: Functions, slope
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