Answer:
Mean: =0.76
SD= (squarerootof) 0.76(0.24)/150
Step-by-step explanation:
The mean of the sampling distribution is 0.76 and the standard deviation is approximately 0.00344.
What is the standard deviation?The standard deviation mathematical and statistical analysis tool used to explain the diversity of treatments or values around the Mean is the standard deviation, which is also known as the square root of variance.
The mean of the sampling distribution of the proportion of US adults who believe that public libraries help them learn new things is equal to the proportion of all adults in the US who believe that public libraries help them learn new things, which is 76% = 0.76.
The standard deviation of the sampling distribution is equal to the standard error of the proportion, which can be calculated as follows:
standard error = √((76% × 24%) / 150)
= √((0.76 × 0.24) / 150)
= √(0.01824 / 150)
= √(0.0000121)
= 0.00344
Therefore, the standard deviation is approximately 0.00344.
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URGENT!!
Samuel wants to deposit $4,000 and keep that money in the bank without deposits or withdrawals for three years. He compares two different options. Option 1 will pay 1.8%, compounded quarterly. Option 2 will pay 1.5% interest, compounded continuously.
a) How much does option 1 pay?
b) How much does option 2 pay?
Answer:
First option pays $480.60 in interest and the second option pays $442.84 in interest
Step-by-step explanation:
Several friends go to a casino and do some gambling. The following are the profits each of these friends make: $120, -$230, $670, -$1020, $250, -$430, and -$60. What is the average profit of this group? A. $100 B. -$100 C. -$1020 D. $397
The average profit of this group is B. -$100.
The average represents the total profits and losses generated by the group of friends, divided by the number in the group.
The average is the data set's mean after performing the mathematical operations of addition and division on the data values.
Friends Profits
A $120
B -$230
C $670
D -$1020
E $250
F -$430
G -$60
Total -$700
Average profit = -$100 (-$700/7)
Thus, we can conclude that the friends generated an average profit of B. -$100 from gambling or a total loss of $700.
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Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A) 1 cm and 15 cm
B) 2 cm and 7 cm
C) 3 cm and 5 cm
D) 4 cm and 4 cm
The possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm
How to determine the possible rectangle's length and width?The given parameters are
Area = 15 square cm
The area is given as
Area = 15 square cm
The formula of area is
Area = Length x Width
Using the above formula, we have:
A) 1 cm and 15 cm ⇒ 15 square cm
B) 2 cm and 7 cm ⇒ 14 square cm
C) 3 cm and 5 cm ⇒ 15 square cm
D) 4 cm and 4 cm ⇒ 16 square cm
Hence, the possible rectangle's length and width are A) 1 cm and 15 cm and C) 3 cm and 5 cm
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Possible question
The area of a rectangle is 15 square cm
Which of the following could be the rectangle's length and width?
(Area = length x width)
Choose all answers that apply:
A) 1 cm and 15 cm
B) 2 cm and 7 cm
C) 3 cm and 5 cm
D) 4 cm and 4 cm
Real numbers a and b satisfy
a + ab = 250
a - ab = -240
Enter all possible values of a, separated by commas.
The only possible value of "a" that satisfies the given equations is a = 5.
The possible values of "a" that satisfy the given equations, let's solve the system of equations:
a + ab = 250 ---(1)
a - ab = -240 ---(2)
We can solve this system by using the method of substitution. Rearranging equation (2), we get:
a = ab - 240 ---(3)
Substituting equation (3) into equation (1), we have:
(ab - 240) + ab = 250
2ab - 240 = 250
2ab = 250 + 240
2ab = 490
ab = 490/2
ab = 245
Now we have the value of "ab."
We can substitute this back into equation (3) to solve for "a":
a = (245) - 240
a = 5
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find the measure of the missing angle
Answer:
50
Step-by-step explanation:
40 plus 90 equals 130 and triangle must be 180 so we need 50 degree
50°
Let x be the missing angle.
90°(right angle) + 40°(given) + x = 180° ( the sum of degrees of interior angles of triangle)
x = 180°-130°
x = 50°
How many GRAMS of aluminum are present in 1.40 grams of aluminum sulfate,
Al2(SO4)3?
54 grams of aluminium is present in aluminium sulphate Al₂(SO₄)₃.
What is meant by the term molecular mass/weight?A substance's molecular mass is the sum of the atomic masses of all of the atoms in the molecule of a substance.
It is applied to substances with molecules as constituent particles.The molecular mass expresses the mass of a molecule in relation to the mass of the 12C atom, that is assumed to be 12. Although molecular mass is indeed a dimensionless quantity, it is provided the unit Dalton or atomic mass unit to indicate that the mass is relative to 1/12th this same mass of a single carbon-12 atom.For the given question, the expression is;
aluminium sulphate Al₂(SO₄)₃
As three of aluminium is present in the aluminium sulphate.
And, molecular mass of one aluminium atom is 27 grams;
Thus, for 2 aluminium atoms = 2×27 = 54 grams.
Therefore, the compound aluminium sulphate contains 54 gram of aluminium in it.
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Horacio is solving the equation-3/4 + 2/5x = 7/20x -1/2. Which equation represents possible ways to begin solving for x?
The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2
Which equation represents possible ways to begin solving for x?From the question, we have the following parameters that can be used in our computation:
-3/4 + 2/5x = 7/20x -1/2
The first step is to collect the like terms
So, we have
2/5x - 7/20x = 3/4 - 1/2
This represents an equation of the possible way to begin solving for x
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A test consists of 18 multiple choice questions, each with 3 options. A student who didn’t study randomly guesses on all the questions. What is the probability that she will get a passing score (i.e. 13 out the 20 correct).
Using the binomial distribution, it is found that there is a 0.0008 = 0.08% probability that she will get a passing score.
For each question, there are only two possible outcomes, either she answers it correctly, or she does not. The probability of answering a question correctly is independent of any other question, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
18 questions, thus \(n = 18\)Guess one of three correct options, thus \(p = \frac{1}{3} = 0.3333\).A passing score is at least 13 correct, thus, the probability is:
\(P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)\)
Then
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 13) = C_{18,13}.(0.3333)^{13}.(0.6667)^{5} = 0.0007\)
\(P(X = 14) = C_{18,14}.(0.3333)^{14}.(0.6667)^{4} = 0.0001\)
The others, until P(X = 18), will be approximately 0, thus:
\(P(X \geq 13) = P(X = 13) + P(X = 14) = 0.0007 + 0.0001 = 0.0008\)
0.0008 = 0.08% probability that she will get a passing score.
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Solve the system of equation.
+3=17
x
+
3
y
=
17
−+2=8
−
x
+
2
y
=
8
Step 1: Find the LCM to eliminate the x.
Step 2: Write the new equation.
Step 3: Divide to solve for y.
Answer:
Equation 1: x + 3y = 17
Equation 2: -x + 2y = 8
Add Equation 2 to Equation 1:
x + 3y = 17
+ -x + 2y = 8
5y = 25
Divide both sides by 5:
\(\sf \implies \dfrac{5y}{5}=\dfrac{25}{5}\)
\(\sf \implies y=5\)
Find the maximum of Q = xy if x + y = 52.
Answer:Q = 26(52-26) = 26*26 = 676
Step-by-step explanation:
2. Abigail and Curtis Siebert: $270,000 mortgage at 7% for 20 years.
M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1). Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.
Abigail and Curtis Siebert have a $270,000 mortgage at an interest rate of 7% for a term of 20 years.
To calculate the monthly mortgage payment, we can use the formula for an amortizing mortgage:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1),
where M is the monthly mortgage payment, P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of monthly payments.
First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is 7% divided by 12, which is approximately 0.5833%.
The total number of monthly payments is the term of the mortgage multiplied by 12. In this case, it's 20 years * 12 months, which equals 240 months.
Now, we can substitute the values into the formula:
M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).
Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.
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Help pleasee! I need to find the domain and range
Answer:
Domain: (-∞, -4) U (-4,∞)
range: (0,∞)
which one of them has no solution
Write a multiplication equation to show an equivalent fraction of 15 using fifteenths.
Explain how the two fractions are equivalent.
A multiplication equation to show an equivalent fraction of 15 using fifteenths would gives 10/75
What is a fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
We have to write an equivalent fraction of 15 using fifteenths.
2/15
So let multiply by 5 .
2 / 15 x 5/ 5 = 10/75
Thus, 10/75 is equivalent expression.
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I need help quickly
Using L'hopital we can see that the limit is equal to 1/22
How to solve the limit?Here we want to take the limit of x tending to zero for x/sin(22x)
Notice that when x = 0, both numerator and denominator are zero, so we need to take the limit of the first derivatives, for:
y = x
y' = 1
And for:
y = sin(22x)
y' = 22*cos(22x)
Now taking the limit we will get:
\(\lim_{x \to 0} \frac{1}{22cos(22x)} = \frac{1}{22cos(0)} = 1/22\)
That is the value of the limit.
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15. Kate has 63 pens. She gives all the pens to her 9 friends. Each friend gets
the same number of pens.
Kate said that when she divided the number of pens that each friend got by 9,
the answer was equal to 63. Her friend Margo said that when the number of
pens each friend got was multiplied by 9, the answer was equal to 63.
Which girl is correct? Explain your answer. I will mark as brainlist and vote if you answer
The girl which is correct between kate and her friend Margo is Margo.
The correct answer option is option B
How to multiply?Number of pens Kate has = 63Number of Kate's friends = 9If each friend gets the same number of pens;
Number of pens each friend get = Number of pens Kate has / Number of Kate's friends
= 63 / 9
= 7
Check:
Number of pens each friend get × Number of Kate's friends = Number of pens Kate has
7 × 9 = 63
Therefore, Kate's friend, Margo is correct.
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6. How much heat is lost cooling 25 grams of water from 90°C to 45°C?
Answer:
4,7025 (kJ).
Step-by-step explanation:
1) according to the condition: m=25 gr.; t₂=90; t₁=45; c=4.18 J/(g°C);
2) the formula of required heat is
Q=c*m*(t₂- t₁);
3) according to the formula of heat:
Q=4.18*25*45=4702.5 (J).
Extrema interpreting functions
Answer:
In mathematics, the extrema of a function refer to the maximum and minimum values that the function can take on. These values can be local extrema, which occur within a certain range of the function, or global extrema, which are the maximum and minimum values over the entire domain of the function.
To find the extrema of a function, one can use a variety of techniques, such as taking the derivative of the function and setting it equal to zero to find the points of stationary values, or using the second derivative test to determine whether a stationary point is a local maximum or minimum.
Interpreting the extrema of a function can provide valuable information about the behavior of the function. For example, the global maximum of a function might represent the highest possible value that the function can attain, while the global minimum might represent the lowest possible value. Local extrema can also be important, as they can indicate changes in the slope or concavity of the function, which can have important implications for applications such as optimization or modeling real-world phenomena.
Which statement correctly compares the centers of the distributions? A. The median of Southview HS is greater than the median of East Hills HS B. The mean of Southview HS is greater than the mean of East Hills HS C.The range of East Hills HS is greater than the range of Southview HS D. The Mean of East Hills HS is greater than the Mean of South view HS
The statement that correctly compares the centers of the distributions is this:
D. The mean of East Hills HS is greater than the mean of Southview HS.
Since, The statement that correctly describes the centers of the distributions is option D. To find out, we will calculate the mean of the two distributions as follows:
For East Hills HS
25 * 1 + 29 * 1 + 31 * 2 + 33 * 4 + 35 * 5 + 37 * 8 + 39 * 4
= 875
And, Frequency = 1 + 1 + 2 + 4 + 5 + 8 + 4 = 25
Hence,
Mean = 875/25
Mean = 35
For Southview
25 * 2 + 27 * 6 + 29 * 9 + 31 * 6 + 33 * 2
= 725
Frequency = 2 + 6 + 9 + 6 + 2 =25
Hence, Mean = 29
So, from our calculation, the mean of East Hills HS is greater than the mean of Southview HS.
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I need help solving this. I need to find the domain and range of the problem given.
Answer: Domain x<7 Range y<0 In this case I think it would be D
Step-by-step explanation: The domain is x<7 and the range is y<0
Factor the polynomial 6x^2-3x+2
Shopping at Kohl's, Lisa buys her children four shirts and three pairs of pants for $85.50. She returns the next week and buys three shirts and five pairs of pants for $115.00.
Answer:
Step-by-step explanation:
x=shirt
y=pants
a) First week 4x+3y=85.50
b)3x+5y=115.00
C)
D) This point represent when the price is the same but the number of shirt are different for the first and second week.
Please help this is really hard
A football coach needs to divide 48 players into two groups he wants the ratio of players in group one to players and group 2 to be 1 to 3 how many players will be in group 2
Answer: 36
Step-by-step explanation: If the coach wants to divide the team by the ratio of 1 to 3, then we will take 48 and divide by 4.
This leaves us with 12 x 4 = 48. Then we calculate 48 - 12 = 36
Now you have your 1 to 3 ratio with the teams being split into team 1 with 12 and team 2 with 36.
I need help with this
Answer:
The length of AB is 18
Step-by-step explanation:
Do the pygotham theorem
24^2 + 7^2 = 625
Square root the answer
\(\sqrt{625}\) = 25
Line BO equals 7 because CO is 7 and they are both radiuses
Subtract the answer to the length BO
25 - 7 = 18
18 is the length of AB bro
I’m confused can someone help
Answer:
The answer is 20
Step-by-step explanation:
Given;Mariana is the youngest of four siblings.The sum of their ages is 86To Find;Mariana's age.Now, we know that their ages are consecutive integers.
Let their ages be (x), (x + 1), (x + 2) and (x + 3). Where, Mariana's age is x.
Here, The sum of their ages is 86.
(x) + (x + 1) + (x + 2) + (x + 3) = 86
x + x + 1 + x + 2 + x + 3 = 86
4x + 6 = 86
4x + 6 – 6 = 86 – 6
4x = 80
4x/4 = 80/4
x = 20
We assumed that Mariana's age is x and the value of x is 20.
Thus, The age of Mariana is 20.
Find the volume of the cone. Use 3.14 for π. Remember that there is a formula for calculating the volume of a cone.
The volume of the cone is 314cm³
What is volume of a cone?A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex, to all the points of a circular base(which does not contain the apex). The distance from the vertex of the cone to the base is the height of the cone.
The volume of the cone is 1/3πr²h
h²= 13²-5²
h = √169 - 25
h = √144
h = 12 cm
V = 1/3πr²h
V = 1/3 ×3.14 × 5² × 12
V = 942/3
V = 314 cm³
therefore the volume of the cone is 314cm³
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Washington, DC is 389 miles from Statesville, NC. If you wanted to drive there,
how long would it take you driving on interstates with an average of 65 mph?
O 5.98 hours
07.07 hours
O 5.56 hours
07.78 hours
O 6.48 hours
Suppose your car gets 29 miles per gallon on the interstate and gas costs
$3.89/gallon. How much will it cost you to drive to Washington, DC?
O $0.29
O $43,883.09
$52.18
O $3.45
O $2,900.00
It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.
To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.
Time = Distance / Speed
Time = 389 miles / 65 mph
Time ≈ 5.98 hours
Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.
To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.
Number of gallons = Distance / Mileage
Number of gallons = 389 miles / 29 miles per gallon
Number of gallons ≈ 13.41 gallons
The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.
Cost = Number of gallons * Cost per gallon
Cost ≈ 13.41 gallons * $3.89/gallon
Cost ≈ $52.18
Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.
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David wants to sell laptops and smartphones, he can sell up to 18 devices and wants to earn at least $4500, given that laptops are $425 and smartphones are $125 each.
Part #1: Write 2 inequalities that represents the number of laptops L and smartphones S, David has a goal of selling no more than 18 devices, and another to represent the number of laptops and smartphones he can sell to earn at least $4500.
Part #2: If David sells 8 laptops, what is the minimum number of smartphones he needs to sell to reach his goal of making at least $4500
Part#3: David prefers to sell smartphones, what is the maximum number of phones he can sell in order to reach his goal of $4500 and not sell more than 18 devices?
Part#1: 425L + 125S ≥ 4500 (David wants to earn at least $4500)
Part#2: David can reach his goal of making at least $4500 by selling 8 laptops and 10 smartphones.
Part#3: The maximum number of smartphones he can sell is 18 - 1 = 17, and the minimum number of smartphones he needs to sell is 18 - 8 = 10
What is linear inequalities?
Linear inequalities are used to model the constraints on the number of devices that can be sold (L + S ≤ 18, L ≥ 0, and S ≥ 0) and the minimum amount of money that must be earned (425L + 125S ≥ 4500).
Part #1:
Let L be the number of laptops sold and S be the number of smartphones sold.
To represent the number of laptops L and smartphones S that David can sell, we have the following inequalities:
L + S ≤ 18 (David can sell up to 18 devices)
L ≥ 0 (The number of laptops sold cannot be negative)
S ≥ 0 (The number of smartphones sold cannot be negative)
To represent the amount of money David can earn, we have the following inequality:
425L + 125S ≥ 4500 (David wants to earn at least $4500)
Part #2:
If David sells 8 laptops, he has 10 devices left to sell (18 - 8 = 10). Let's assume he sells all of these devices as smartphones. Then, the total amount he earns from the smartphones would be:
125 x 10 = 1250
The total amount he earns from the laptops and smartphones would be:
425 x 8 + 125 x 10 = 3400 + 1250 = 4650
Hence, he can reach his goal of making at least $4500 by selling 8 laptops and 10 smartphones.
Part #3:
If David sells only smartphones, the maximum number he can sell is given by the inequality:
125S ≥ 4500
S ≥ 36
So, David needs to sell at least 36 smartphones to reach his goal of making at least $4500. However, he cannot sell more than 18 devices, so he needs to sell a combination of laptops and smartphones that adds up to 18 devices.
Let's assume he sells x laptops and (18 - x) smartphones. Then, the total amount he earns from the laptops and smartphones would be:
425x + 125(18 - x) = 2125x + 2250
To earn at least $4500, we need:
2125x + 2250 ≥ 4500
2125x ≥ 2250
x ≥ 1.06
Since x represents the number of laptops sold, David can sell at most 1 laptop (since he can only sell whole numbers of laptops), and the remaining devices must be smartphones.
Hence, the maximum number of smartphones he can sell is 18 - 1 = 17, and the minimum number of smartphones he needs to sell is 18 - 8 = 10 (as found in part #2).
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A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
Answer:
f(x) = x³ - 4x + 6
f'(x) = 3x² - 4
a) f'(2) = 3(2²) - 4 = 12 - 4 = 8
6 = 8(2) + b
6 = 16 + b
b = -10
y = 8x - 10
b) 3x² - 4 = 0
3x² = 4, so x = ±2/√3 = ±(2/3)√3
= ±1.1547
f(-(2/3)√3) = 9.0792
f((2/3)√3) = 2.9208
c) 3x² - 4 = 8
3x² = 12
x² = 4, so x = ±2
f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6
6 = -2(8) + b
6 = -16 + b
b = 22
y = 8x + 22
f(2) = 6
y = 8x - 10
The equation perpendicular to the tangent is y = -1/8x + 25/4
-The smallest slope on the curve is 2.92
The curve has the smallest slope at the point (1.15, 2.92)
The equations at tangent points are y = 8x + 16 and y = 8x - 16
Finding the equation perpendicular to the tangentFrom the question, we have the following parameters that can be used in our computation:
y = x³ - 4x + 6
Differentiate
So, we have
f'(x) = 3x² - 4
The point is (2, 6)
So, we have
f'(2) = 3(2)² - 4
f'(2) = 8
The slope of the perpendicular line is
Slope = -1/8
So, we have
y = -1/8(x - 2) + 6
y = -1/8x + 25/4
The smallest slope on the curveWe have
f'(x) = 3x² - 4
Set to 0
3x² - 4 = 0
Solve for x
x = √[4/3]
x = 1.15
So, we have
Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6
Smallest slope = 2.92
So, the smallest slope is 2.92 at (1.15, 2.92)
The equation of the tangent lineHere, we set f'(x) to 8
3x² - 4 = 8
Solve for x
x = ±2
Calculate y at x = ±2
y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)
y = (2)³ - 4(2) + 6 = 6: (2, 0)
The equations at these points are
y = 8x + 16
y = 8x - 16
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