Solution
No, the sampling distribution of the proportion is the distribution of the proportions from all samples, not just one.
If a bank represents deposits with positive numbers and withdrawals as negative numbers, what could 6+ (-60) represent ?
Given:
A positive number shows a deposit
A negative number shows withdrawals.
Find-: What could $6+
-60 represent
Sol:
+6 represent is:
[tex]6\rightarrow\text{ Deposits}[/tex]-60 represent is:
[tex]60\rightarrow\text{ Withdrawals}[/tex]So the answer is:
$6 deposit followed by a $60 withdrawal
Richard Gaziano is a manager for Health Care, Inc. Health Care deducts Social Security, Medicare, and FIT (by percentage method) from his earnings. Assume a rate of 6.2% on $118,500 for Social Security and 1.45% for Medicare. Before this payroll, Richard is $1,000 below the maximum level for Social Security earnings. Richard is married, is paid weekly, and claims 2 exemptions.
What is Richard’s net pay for the week if he earns $2,200?
Richard’s net pay for the week if he earns $2,200 is equal to $1,797.65.
How to calculate net pay?Mathematically, net pay can be calculated by using this formula:
Net pay = Gross pay - Deductions.
First of all, we would determine Richard's Medicare tax and Social Security tax on $1,000 as follows:
Medicare tax = $2,200 × 1.45/100
Medicare tax = $31.9
Social Security tax = $1,000 × 6.2/100
Social Security tax = $62
Since Richard claims 2 exemptions and paid weekly, we would calculate the withholdings from his weekly pay by using the information provided in Table 1 (see attachment):
Two (2) exemptions = $76.9 × 2 = $153.8
Withholdings = $2,200 - $153.8
Withholdings = $2046.2
Since Richard claims to be married, we would calculate his federal tax withholdings by using the information provided in Table 1 (see attachment):
Over $1,606 = $198.40 plus 25%
= $2046.2 - $1,606 = $440.2
Federal tax withholdings = $198.40 + (25/100 × $440.2)
Federal tax withholdings = $198.40 + $110.05
Federal tax withholdings = $308.45
Now, we can calculate Richard's net pay as follows:
Richard's net pay = Gross pay - Medicare tax - Social Security tax - Federal tax withholdings
Richard's net pay = $2,200 - $31.9 - $62 - $308.45
Richard's net pay = $1,797.65
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Ximena needs to order some new supplies for the restaurant where she works. The restaurant needs at least 333 spoons. There are currently 255 spoons. If each set on sale contains 6 spoons, which inequality can be used to determine
s
s, the minimum number of sets of spoons Ximena should buy?
In linear equation, Joshua should buy is 255 + 6s ≥ 333.
What is linear equation in math?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.Let the sets of spoons be represented by s
The restaurant needs at least 333 spoons.
Each set on sale contains 8 spoons
There are currently 333 spoons.
At least as an inequality is ≥
Hence:
255 + 6 × s ≥ 333
255 + 6s ≥ 333
Therefore, inequality tha can be used to determine s the minimum number of sets of spoons Joshua should buy is
255 + 6s ≥ 333
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what is 6^9 divided by 6^3
Answer:
Step-by-step explanation:
46656
The website for Company A receives 8 * 10 ^ 6 visitors per year. The website for Company B receives 4 * 10 ^ 3 visitors per year. Determine how many times more visitors per year the website for Company A receives than the website for Company B.
1) Let's find out how many times there are more visitors by dividing the number of visitors from A by B's visitors:
Dividing firstly 8 by 4, and then using the exponents pro
[tex]undefined[/tex]my teacher was teaching us this earlier but she didn't actually explain because she focuses on the class but I'm on virtual
________________________________
x= red titles
two times = 2x
50
2x= 0.5x + 75
2x - 0.5x = 75
(2- 0.5) x = 75
1.5 x = 75
x= 75/ 1.5
x= 50
_______________________
Can you see the updates?
_________________________
Answer
Option D = 50
____________________
Do you have any questions regarding the solution?
Multiply the sum of 4 and 5 by the difference of 14 and 8
We need to know the simple mathematical operations to solve this problem. The final answer on multiplying the sum of 4 and 5 by the difference of 14 and 8 is 54.
We have to use addition, subtraction and multiplication to solve the question. First we need to find the sum which means add 4 and 5. Next we need to find the difference between 14 and 8 which means we need to subtract 8 from 14. Finally we have to multiply both the values to get the final answer.
4+5=9
14-8=6
(4+5) x (14-8)=9 x 6=54
Therefore the final value that we get on multiplying the sum of 4 and 5 by the difference of 14 and 8 is 54.
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Solve the equation for y.y/a - 16 = h
we have
y/a - 16 = h
solve for y
that means -----> isolate the variable y
so
Adds 16 both sides
y/a=(h+16)
Multiply by a both sides
y=a(h+16)I am trying to simplify a composition of functions.(f o g) (7.5)f(x) = -x + 7f(g) = -4x -2
There can be two methods that we can use to solve this problem. As per composition of the function, we substitute the function g(x) on the x's of f(x) o get fog. We have
[tex]\begin{gathered} (f\circ g)(x)=-(-4x-2)+7 \\ (f\circ g)(x)=4x+2+7 \\ (f\circ g)(x)=4x+9 \end{gathered}[/tex]We then substitute 7.5 on the resulting function above to evaluate (f o g) (7.5). We get
[tex]\begin{gathered} (f\circ g)(7.5)=4(7.5)+9 \\ (f\circ g)(7.5)=39 \end{gathered}[/tex]The other way around is to start evaluating g(x) for x = 7.5 and then the value that we got in g(x) will be substituted on f(x). We got
[tex]\begin{gathered} g(7.5)=-4(7.5)-2 \\ g(7.5)=-32 \\ \Rightarrow\Rightarrow f(-32)=-(-32)+7=39 \end{gathered}[/tex]3 cookies and 5 brownies cost $19; 2 cookies and 10 brownies cost $26. How much do 13 cookies and 6 brownies cost?
ANSWER
$51
EXPLANATION
Let the cost of one cookie be c.
Let the cost of one brownie be b.
3 cookies and 5 brownies cost $19. This means that:
3 * c + 5 * b = 19
3c + 5b = 19 ___(1)
2 cookies and 10 brownies cost $26. This means that
2 * c + 10 * b = 26
2c + 10b = 26 ____(2)
We have two simultaneous equations:
3c + 5b = 19 ___(1)
2c + 10b = 26 ____(2)
From (2):
2c = 26 - 10b
Divide through by 2:
c = 13 - 5b
Put this in (1):
3(13 - 5b) + 5b = 19
=> 39 - 15b + 5b = 19
Collect like terms:
-15b + 5b = 19 - 39
-10b = -20
Divide through by -10:
b = -20 / -10
b = $2
Remember that:
c = 13 - 5b
=> c = 13 - 5(2)
c = 13 - 10
c = $3
Therefore, one cookie costs $3 and one brownie costs $2.
Therefore, the cost of 13 cookies and 6 brownies is:
13 * 3 + 6 * 2
=> 39 + 12
=> $51
13 cookies and 6 brownies cost $51
Find all the missing elements.Round to the nearest tenth.aba = 5b = 2A C = 6BСA = [?]° B =[ 1°C = [ 1°Inter
Explanation:
Taking into account the law of cosines, we can write the following equation:
[tex]a^2=b^2+c^2-2bc\cos A[/tex]Then, replacing the values for a, b, and c, we get:
[tex]\begin{gathered} 5^2=2^2+6^2-2(2)(6)\cos A \\ 25=4+36-24\cos A \\ 25=40-24\cos A \end{gathered}[/tex]Solving for cos A, we get:
[tex]\begin{gathered} 25-40=40-24\cos A-40 \\ -15=-24\cos A \\ \frac{-15}{-24}=\frac{-24\cos A}{-24} \\ 0.625=\cos A \end{gathered}[/tex]Therefore, the value of angle A is:
[tex]\begin{gathered} \cos ^{-1}(0.625)=A \\ 51.3=A \end{gathered}[/tex]Now, we can use the law of sines, we can write the following equation:
[tex]\frac{\sin B}{b}=\frac{\sin A}{a}[/tex]So, replacing the values and solving for B, we get:
[tex]\begin{gathered} \frac{\sin B}{2}=\frac{\sin 51.3}{5} \\ \sin B=\frac{\sin 51.3}{5}\times2 \\ \sin B=0.3121 \\ B=\sin ^{-1}(0.3121) \\ B=18.2 \end{gathered}[/tex]In the same way, Angle C is equal to:
[tex]\begin{gathered} \frac{\sin C}{c}=\frac{\sin A}{a} \\ \frac{\sin C}{6}=\frac{\sin 51.3}{5} \\ \sin C=\frac{\sin51.3}{5}\times6 \\ \sin C=0.9365 \\ C=\sin ^{-1}(0.9365) \\ C=69.5 \end{gathered}[/tex]So, the answers are:
A = 51.3°
B = 18.2°
C = 69.5°
You take a quiz with 6 multiple choice questions. After you studied, you estimated that you would have about an 80% chance of getting any individual question right. What are your chances of getting them all right? The random numbers below represent a simulation with 20 trials. Let 0-7 represent a correct answer and let 8-9 represent an incorrect answer.
0.262144 = 26.2% of getting all the 6 questions correctly.
What is Binomial probability ?
The binomial probability is the probability of exactly x successes on n repeated trials, and each trial can only have two outcomes.
This is a binomial distribution problem
Binomial distribution function is represented by :
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 6 multiple choice questions
x = Number of successes required = 6 (we want to get it all right.
p = probability of success = 0.8 (80% chance of getting any individual question right; 0.8 probability of getting each question correctly)
q = probability of failure = 1 - 0.8 = 0.2
P(X = 6) = ⁶C₆ (0.8)⁶ (0.2)⁶⁻⁶
= 1(0.262144)(1)
= 0.262
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171 is 0.9% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 171, slightly less than 171, slightly greater than 171, or a lot greater than 171? Explain. 171 is 0.9% of?
171 is 0.9% of 19000
Explanation:let the unknown number be = y
0.9% * y = 171
0.9% = 0.009
0.009 × y = 171
0.009y = 171
DIvide both sides by 0.009:
0.009y/0.009 = 171/0.009
y = 19,000
Hence, 171 is 0.9% of 19000
We would expect the answer to be a lot greater than 171 because the percentage is quite small (less than 1%). Divindg a number by a very small decimal makes the result large.
Hence, the number would be large.
greatest to least -4.081, -4.018, -5.3, -5.043
This question is stunning me. It wasn’t taught to me in math class.
The next three terms of the following sequences are:
7. The next three terms are 2, 2, and 3.
8. The next three terms of the sequence are 4, 8, and 16.
9. The next three terms of the sequence are 3, 6, and 9.
10. The next three terms of the sequence are 1, 2, and 3.
7.
Consider the recursive formula,
f( 0 ) = 3, f( n ) = f( n - 1 ) + ( n - 2 )
The next three terms of the sequence will be n = 1, 2, and 3.
Then,
f( 1 ) = f( 1 - 1 ) + ( 1 - 2 )
f( 1 ) = f(0) - 1 = 3 - 1 = 2
The second term of the sequence,
f( 2 ) = f( 2 - 1 ) + ( 2 - 2 )
f( 2 ) = f( 1 ) + 0
f( 2 ) = 2
The third term,
f( 3 ) = f( 3 - 1 ) + ( 3 - 2 )
f( 3 ) = f( 2 ) + 1
f( 3 ) = 2 + 1 = 3
8.
Consider the recursive formula,
f( 1 ) = 2, f(n ) = 2f( n - 1 )
The next three terms of the sequence will be n = 2, 3, 4.
Therefore,
f( 2 ) = 2f( 2 - 1 )
f( 2 ) = 2( f (1) )
f( 2 ) = 4
f( 3 ) = 2f( 3 - 1 )
f( 3 ) = 2f( 2 )
f( 3 ) = 8
f( 4 ) = 2f( 4 - 1 )
f( 4 ) = 2f( 3 )
f( 4 ) = 16
Hence, the next three-term are 4, 8, and 16.
9.
Consider the recursive formula,
f( 0 ) = 0, f( n ) = f( n - 1 ) + 3
The next three terms of the sequence will be n = 1, 2, 3.
Then,
f( 1 ) = f( 1 - 1 ) + 3
f( 1 ) = 0 + 3 = 3
f( 2 ) = f( 2 - 1 ) + 3
f( 2 ) = 3 + 3 = 6
f( 3 ) = f( 3 - 1 ) + 3
f( 3 ) = f( 2 ) + 3
f( 3 ) = 6 + 3 = 9
10.
Consider the recursive formula,
f( 0 ) = 1, f( 1 ) = 1, f( n ) = f( n - 1) + f( n - 2 ), for n > 1
Then, the next three terms will be n = 2, 3, 4
f( 2 ) = f( 2 - 1 ) + f( 2 - 2 )
f( 2 ) = f( 1 ) + f( 0 )
f( 2 ) = 1 + 0 = 1
f( 3 ) = f( 3 - 1 ) + f( 3 - 2 )
f( 3 ) = f( 2 ) + f( 1 )
f( 3 ) = 1 + 1 = 2
f( 4 ) = f( 4 - 1 ) + f( 4 - 2)
f( 4 ) = f( 3 ) + f( 2 )
f( 4 ) = 2 + 1
f( 4 ) = 3
The next three terms of the sequence are 1, 2, and 3.
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help meee
solve for system of equations with steps shown please
1.
x+4y=0
3x+2y= 20
2.
6x+3y=54
2x+y=18
3.
x-3y=-2
10x+8y=-20
4.
3x-y=-8
5x+2y=5
The solutions to the equations are :
1. x= 8 ; y = -2
2.infinitely many solutions.
3. x= - 2 ; y = 0
4. x= -1 ; y = 5
How are the equations solved?
1. x+4y=0 --(1)
3x+2y= 20 ---(2)
(1)*3
3x+ 12y =0 ---(3)
(3) - (2)
(3x+ 12y) -(3x+2y -20)
10y +20= 0
10 y = -20
y = - 2
Substituting y in equation(1)
x+ 4 (-2) = 0
x = 8
The solutions to the equations are x= 8 and y = -2
2. 6x+3y=54 --(1)
2x+y=18 ----(2)
(2)*3
6x+3y=54 --(3)
(3) = (1)
0 = 0
The equations have infinitely many solutions.
3. x -3y= -2 --(1)
10x+8y=-20 ---(2)
(1)*10
10x - 30y +20 = 0--(3)
(3) - (2)
(10x - 30y +20 )- (10x+8y +20)
-38y = 0
y = 0
Substituting y in equation(1)
x - 0 = -2
x = -2
The solutions to the equations are x= - 2 and y = 0
4.
3x-y=-8 ---(1)
5x+2y=5 ---(2)
(1)*2
6x -2y+16 =0---(3)
(3) +(2)
(6x -2y+16) +(5x+2y-5)
11x +11 = 0
11x = -11
x = -1
Substituting x in equation(1)
3(-1) -y = -8
-3- y = - 8
- y = -8+3
-y = -5
y = 5
The solutions to the equations are x= -1 and y = 5
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Solve the given linear system of equations:6serбу9y– 120 +18One solution:O No solutionO Infinite number of solutions
no solution (2nd option)
Explanation:
8x - 6y = 6 .....equation 1
-12x + 9y = 18 .....equation 2
Using elimination method:
we will eliminate y by making both coefficient of y to be the same.
This is done by multiplying equation 1 by 3 and equation 2 by 2
24x - 18y = 18 .....equation 1
-24x + 18y = 36 ....equation 2
Adding both equation:
24x - 24x -18y + 18y = 18 + 36
0 + 0 = 54
[tex]\begin{gathered} 0\ne\text{ 54} \\ \end{gathered}[/tex]Since 0 is not equal to 54, there is no solution (2nd option)
4. CONSTRUCTION A 30-foot ladder
leaning against the side of a house makes
a 70.1 angle with the ground.
70.1
30 ft
a. How far up the side of the house does
the ladder reach?
b. What is the horizontal distance
between the bottom of the ladder
and the house?
The answers to both subparts are with the help of trigonometric functions:
(A) The side of the house to the ladder reach: x = 28.208 ft(B) Horizontal distance: x = 10.211 ftWhat are trigonometric functions?The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others. Sine, Cosine, and Tangent are the three fundamental trigonometrical operations.So, (A) The side of the house to the ladder reach:
Sin70.1 = x/30x = 28.208 ft(B) The horizontal distance between the bottom of the ladder and the house:
Cos70.1 = x/30x = 10.211 ftTherefore, the answers to both subparts are with the help of trigonometric functions:
(A) The side of the house to the ladder reach: x = 28.208 ft(B) Horizontal distance: x = 10.211 ftKnow more about trigonometric functions here:
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2ax-b=cx+d solve for x
We have to solve the following equation for the variable x:
[tex]2ax-b=cx+d[/tex]For doing so, we assume that the variables a, b, c and d behave as normal numbers, and we will move the terms with x to the left side, and those who doesn't have it, to the right.
[tex]\begin{gathered} 2ax-b-cx=cx+d-cx \\ 2ax-cx-b=d \\ 2ax-cx-b+b=d+b \\ 2ax-cx=d+b \end{gathered}[/tex]Now, we will factor the variable x, as we want to have just one expression with x, thus:
[tex](2a-c)x=d+b[/tex]And lastly, we will divide both sides by 2a-c, and we obtain:
[tex]x=\frac{d+b}{2a-c}[/tex]Which is the asked expression for x.
In 2000, the profit of Company A was $9,875,000. Each year after 2000, the profits fell by $29,532 on average. Construct a linear model for this scenario and use it to solve for profits in the year 2030.
Given:
In 2000, the profit of Company A was $9,875,000.
Each year after 2000, the profits fell by $29,532 on average.
So, the losses of the profit per year = $29,532
We will construct a linear model for this scenario
Let the number of years after 2000 = x
And the profit after the year 2000 = y
the linear model will be: y = mx + b
Where m is the slope which represents the losses per year and the b is the initial profit of the year 2000
So, the linear model will be:
[tex]y=-29,532x+9,875,000[/tex]now, we will use the equation to find the profit in the year 2030
so, x = 2030 - 2000 = 30
substitute x = 30 into the equation:
[tex]y=-29,532(30)+9,875,000=8,989,040[/tex]So, the answer will be:
The equation of the model: y = -29532x + 9875000
The profit in the year 2030 = 8989040
Jake drew a rectangle ABCD. He will transform the rectangle by using the translation (x,y) -> (x+5, y-1).What would be the coordinate of A after the translation?
c) (1,0)
1) In order to perform this translation firstly, locate point A in the graph. A is at (-4, 1).
2) Secondly, apply the given rule for this translation for this point.
Pre-image rule Image
(-4,1) (x+5, y-1) (-4+5, 1-1)= (1, 0)
Since the question just asks us A' then We can stop it here and say A' will be at (1,0)
3) So A', is going to be located at point ( 1,0)
The graph of a function is shown below.Find one value of x for which f(x) = -3 and And /(o).
The graph of a function is given.
When the function of x is -3, that is
[tex]f(x)=-3[/tex]That means the input value which is x, gives us negative 3.
Looking at negative 3 from the graph, the value of x where the graph equals negative 3 (on the vertical axis, or y-axis) is either negative 2 or 1. That is
Also, when the input of the function is zero, then you'll have the output as
[tex]f(0)=1[/tex]This means when the value of x is zero, then the output as shown on the graph is 1 (that is the graph touches the y-axis at 1)
Therefore;
(a) One value of x for which f(x) = -3 is -2 (OR 1)
(b) f(0) = 1
What is the value of y^2-x^4y
2
−x
4
y, squared, minus, x, start superscript, 4, end superscript when y=8y=8y, equals, 8 and x=2x=2x, equals, 2?
The value of the given expression is -64.
what is value?
Any specific mathematical thing can, in general, have one mathematical meaning. The numeral or other mathematical object assigned to a vector, constant, or other mathematical object is its value. When the expression's variables and constants are given b, the formula stated in this expression yields the result of the mathematical equation.The number that a function assumes for each given value assigned toward its argument(s) is known as the function's value. Real-value variables, expressions, and functions simply assume real values. A complex-valued variables, expression, or function simply assumes complex values in the same way.Given expression:
y^2-x^4y
=y^2-x^4y
=y(y-x^4)
Putting value x=2, y=8
8(8-2^4)
=-64
The value of the given expression is -64.
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If y varies directly as x, find the constant of variation and the direct variation equation for the situation.
y = 32 when x = 20
The constant of variation is 1.6, and then the direct variation equation is:
y = 1.6*x
How to find the constant of variation?A direct variation between two variables can be written as:
y = k*x
Where k is called the constant of variation.
Here we know that when x = 20, the value of y is 32, replacing that in the above equation we get:
32 = k*20
Solving this for k we get:
32/20 = k = 1.6
Then the equation is:
y = 1.6*x
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Which numbers are irrational numbers?
Select each correct answer.
Responses
110−−√
square root of fraction 1 over 10 end fraction
116−−√
square root of fraction 1 over 16 end fraction
14√
square root of fraction 1 over 4 end fraction
12√
square root of fraction 1 over 2 end fraction
18√
square root of fraction 1 over 8 end fraction
Answer:Here I hope this helps
1/10=irrational
1/16=rational
1/4=rational
1/2=irrational
1/8=irrational
Step-by-step explanation: you can go into desmos graphing calculator and plug in each number into the square root and it will tell you if its irrational or not.
A real estate agent received $5,880 commission on a sale of an &84,000 home.what is the rate of commission
As given by the question
There are given that the agent received $5880 commission on a sale of $84000.
Now,
The rate of commission is:
[tex]\begin{gathered} \frac{5880}{84000}\times100=0.07\times100 \\ =7\% \end{gathered}[/tex]Hence, the rate of commission is 7%.
How do u solve 8t-2 I can’t figure out how to solve it
Answer:
2(4t - 1)
Step-by-step explanation:
8t - 2
The common multiple is 2 because 2 will go into both 8 and 2. Move the multiple of 2 outside, and add ():
2(4t - 1)
Maureen measured a house and its lot and made a scale drawing. The scale she used was
1 inch 8 feet. If the actual length of the house's driveway is 24 feet, how long is the
driveway in the drawing?
The most appropriate choice for unitary method will be given by-
Length of driveway in the drawing is 3 inch
What is unitary method?
Unitary method is the method in which value of a single unit can be calculated from the value of a multiple unit and value of a multiple unit can be calculated from the value of a single unit.
Sometimes value of single unit is less than value of multiple unit
For example - cost of food and quantity of food
Sometimes value of single unit is more than value of multiple unit
For example- Number of men and time taken by those men to do a work
Here,
Scale used by Maureen is 1 inch = 8ft
Actual length of house's driveway = 24 feet
8 ft of room is equal to 1 inch on scale
1 ft of room is equal to [tex]\frac{1}{8}[/tex] inch on scale
24 feet of room is equal to [tex]\frac{1}{8} \times 24[/tex] inch on scale
24 feet of room is equal to 3 inch on scale
Length of driveway in the drawing is 3 inch
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How many times can 2/7 be subtracted from 6/7
Answer:
Exactly three times.
Step-by-step explanation:
(6/7) / (2/7) = (6/7) * (7/2) = 3/1 * 1/1 = 3
the trapezoids shown below are similar. find Y
Since it is given that trapezoids are similar so,
[tex]\begin{gathered} \frac{y}{25}=\frac{12}{15} \\ y=\frac{4}{5}\times25 \\ y=20 \end{gathered}[/tex]So value of y is 20.
