The 2 events are independent because the outcome of the first draw doesn't affect the outcome of the second.
ANSWER
independent
15,20,25,30 and then there is 3,4,5,6. Find the constant proportionality
Cans of paint (k) = Birdhouses painted
x= cans of paint
y= Birdhouses painted
y= kx
Where k is the constant of proportionality.
Replace with a set of points and solve for k
(x,y) = (3,15)
15= k 3
15/3 = k
k=5
A customer claims to have 40 gallons of a cleaning solution that contains 20% soap.
Your company sells a cleaning solution that contains 50% soap. How many gallons of
the 50% solution must the customer purchase if they wish to create a 40% solution?
The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.
How much 50% solution must he purchase?A customer has 40 gallons of a cleaning solution that contains 20% soap.
The company sells a cleaning solution that contains 50% soap.
The customer wishes to create a 40% solution.
Solution:
By mixture and allegation method,
1 gallon 1 gallon
50% 20%
40%
20 10
To create a 40%Soap solution, one must mix 20 gallons of 50% soap solution and 10 gallons of 20% Soap solution.
Therefore, the ratio is 20 : 10 = 2:1
The customer has 40gallons of a cleaning solution that contains 20% soap, therefore in a 2:1 ratio, 1 part is 40 gallons.
Then for 2 parts = 2*40 = 80 gallons.
The customer must purchase 80 gallons of 50% solution if they wish to create a 40% soap solution.
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Use the graph to evaluate the expressions below.
f(2) = 3
f⁻¹(2) = 1
f⁻¹(0) = -1
(f⁻¹o f)(1) = 1
The graph of f(x) is given. Here, f(x) = y and f⁻¹(y) = x.
That is, f(x) are y values corresponding to the given x-values and f⁻¹(y) is the x-value corresponding to the given y-value.
From the graph, f(2) is the y value when x = 2.
So, f(2) = 3
Now f⁻¹(2) is the x-value when y = 2.
So, f⁻¹(2) = 1
Also f⁻¹(0) =-1
Since f(1) = 2,
(f⁻¹o f)(1) = f⁻¹(f(1)) = f⁻¹(2) = 1
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9h - 27 What is the greatest common?factor Expand the expression
Given
9h-27
Answer
[tex]\begin{gathered} 9h-27 \\ 9(h-3) \\ \end{gathered}[/tex]Greatest common factor = 9
Question 2(Multiple Choice Worth 2 points)
(02.05 MC)
Solve x2 + 12x+6=0 using the completing-the-square method.
Answer:
Hhhhhhhhhhhhhhhhhh : x=-2
Suppose that the functions h and g are defined as follows.
h(x) = (x+5)(x+5)
g(x) = 4x+5
h
¹(²)(-1).
(a) Find
h
(b) Find all values that are NOT in the domain of
g
If there is more than one value, separate them with commas.
For the given functions, we have that:
a) The numeric value of the division function at x = 4 is of (h/g)(4) = 81/21 = 3.86.
b) The value that is not in the domain of the division function is of x = -1.25.
Division functionIn this problem, the functions that we are given are defined as follows:
h(x) = (x + 5)(x + 5).g(x) = 4x + 5.To find the quotient function of h(x) and g(x), we just divide the function h(x) by the function g(x), that is:
h(x)/g(x) = [(x + 5)(x + 5)]/(4x + 5).
At x = 4, the numeric value is found replacing each instante of x by 4, hence:
(h/g)(4) = [(4 + 5)(4 + 5)]/(4(4) + 5)) = 81/21 = 3.86.
The denominator of a fraction cannot be zero, as division by zero does not exist, hence the value of x that is not on the domain of the division function is found as follows:
4x + 5 = 0.
4x = -5.
x = -5/4
x = -1.25.
What is the missing information?The complete problem is given by the image at the end of the answer. There are lots of instances of this problem, just with different functions, so we use the functions given in this problem and not on the image.
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Jeremy and Justine work for a company that receives $45 for each unit of output sold. The company has a variable cost of $25 per item and a fixed cost of $1600.
Based on this information, Jeremy and Justine make some projections about potential profit.
Jeremy states that for every 100 units of output sold, the company will make $3,600 in profit.
Justine states that for every 300 units of output sold, the company will make $4,400 in profit.
Part A
Determine a function that models the profit for the company based upon the conditions for revenue and expense.
Part B
Are the claims about profit that Jeremy and Justine made true? Explain why Jeremy and Justine are each correct or incorrect and justify your reasoning.
The function for profit given the conditions for revenue and expense is P = $20a - $1,600.
The first claim is incorrect because profit is $400
The first claim is incorrect because profit is $4,400.
What is the profit?Profit is revenue less total cost. Total cost consists of fixed cost and variable cost. Fixed cost is the cost that does not change with the level of output. Variable cost is the cost that changes with output. It increases as the level of output increases. Revenue is output multiplied by price per unit.
Profit = revenue - total cost cost
Profit = (price x output) - fixed cost - variable cost
P = ($45 x a) - $1,600 - ($25 x a)
P = $45a - $1,600 - $25a
P = $20a - $1,600
Where:
P = profit
a = output
Profit when 100 units is sold:
P = (20 x 100) - $1,600
$2,000 - $1,600 = $400
Profit when 300 units are sold
P = (300 x 20) - $1600
$6,000 - $1,600 = $4,400
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Find the average of
8,11,14,13,14, 9,15
Answer:
12
Step-by-step explanation:
(8+11+14+13+14+9+15)/7 = 12
Answer:
MedianTotal obs. = 7
if odd —Average = (n + 1 )/2
n = no. of obs.Average = 7 + 1 /2
= 8/2 = 4th obs.
=> 13Mean= Sum of obs./ Total obs.
= 8,11,14,13,14,9,15/7
= 84/7
=> 12Given the diagram below as shown, find the value of x, y, and m
The unknown variables and angles are as follows:
x = 10y = -5m∠YTE = 36°How to find angles?The sum of angles on a straight line is 180 degrees.
Therefore, the sum of angles on line STA is 180 degrees.
CT bisect STE
Angle STE Is a right angle.
Therefore,
5x + y + 3 + 3x + 12 = 90
5x + 3x + y + 12 + 3 = 90
8x + y + 15 = 90
8x + y = 90 - 15
8x + y = 75
Ty bisect ETA
Angle ETA Is a right angle.
Therefore,
y + 41 + 5x + 4 = 90
5x + y + 45 = 90
5x + y = 90 - 45
5x + y = 45
Combine the equation
8x + y = 75
5x + y = 45
subtract equation(ii) from equation(i)
3x = 30
x = 30 / 3
x = 10
y = 75 - 80
y = -5
Therefore,
m∠YTE = y + 41 = -5 + 41 = 36°
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Solve the application problem.
While shopping, Betty spent three times as much as Nan. If they spent a total of $120, how much did each person spend?
Betty spent $90 and Nan spent $ 30
What is basic algebra ?Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.
Given that :While shopping, Betty spent three times as much as Nan. And they spent a total of $120,
Let the Betty spent total $x and Nan spent total $Y
then,
x = 3y ....(i)
x +y =120 .....(ii)
put value of c from i equation to equation ii
4y = 120
y = 30
x = 90
Hence Betty spent $90 and Nan spent $ 30
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Point A is 3 units to the right of, and 20 units lower than, point B. Find the
slope of the line connecting points A and B.
O 20
3
O 20
3
O
-17
3
20
Answer:
02987329619
Step-by-step explanation:
02987329619
Answer:
kk
Step-by-step explanation:
-4-(1+i)-(5+9i). Just subtract them... also please show steps
The resulting complex number is -10 - 10i.
How to subtract complex numbers?When subtracting complex numbers, the real and imaginary components of each complex number are taken into account independently. The real and imaginary components of one complex number are then subtracted from the real and imaginary components of the other complex number, respectively. The equation for subtracting complex numbers is as follows:z₁ - z₂ = (a + ib) - (c + id)
= (a - c) + i(b - d)
Given complex number: -4-(1+i)-(5+9i)
-4-(1+i)-(5+9i)
Remove the parentheses and combine the real and the imaginary parts respectively.
(- 4 -1 -5) - i(1 + 9)
-10 - 10i
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HELPPPP PLEASEEE!!!
(MATH AND CHEMISTRY RELATED)
I really need help with this
The equation of the lines are:
5. y - 5 = -3(x - 1)
6. y - 3 = 2(x + 4)
7. y - 6 = -4/3(x - 1)
8. y - 8 = -12/9(x + 2)
9. y = -5x + 1
10. y + 1 = -2(x - 2)
11. y - 1 = 2/3(x - 3)
How to Write the Equation of a Line?For any given line, the equation that represents the line can be written as:
y = mx + b, in slope-intercept form, where m is the slope and b is the y-intercept of the line.y - b = m(x - a), in point-slope form, where m is the slope and (a, b) is a point on the line.5. Substitute m = -3, and (a, b) = (1, 5) into y - b = m(x - a):
y - 5 = -3(x - 1) [equation in point-slope form]
6. Substitute m = 2, and (a, b) = (-4, 3) into y - b = m(x - a):
y - 3 = 2(x - (-4))
y - 3 = 2(x + 4) [equation in point-slope form]
7. Given the points, (4, 2) and (1, 6)
Find the slope (m):
Slope (m) = change in y/change in x = (6 - 2)/(1 - 4)
Slope (m) = -4/3
Substitute m = -4/3, and (a, b) = (1, 6) into y - b = m(x - a):
y - 6 = -4/3(x - 1) [equation in point-slope form]
8. Given the points, (-2, 8) and (7, -4)
Find the slope (m):
Slope (m) = change in y/change in x = (-4 - 8)/(7 -(-2))
Slope (m) = -12/9
Substitute m = -12/9, and (a, b) = (-2, 8) into y - b = m(x - a):
y - 8 = -12/9(x - (-2))
y - 8 = -12/9(x + 2) [equation in point-slope form]
9. y - 6 = -5(x + 1)
y - 6 = -5x - 5
y - 6 + 6 = -5x - 5 + 6 [addition property of equality]
y = -5x + 1 [equation in slope-intercept form]
10. Find the slope (m):
Slope of the line (m) = rise/run = -2/1
Slope (m) = -2
Substitute m = -2, and (a, b) = (2, -1) into y - b = m(x - a):
y - (-1) = -2(x - 2)
y + 1 = -2(x - 2) [equation in point-slope form]
11. Find the slope (m):
Slope of the line (m) = rise/run = 2/3
Slope (m) = 2/3
Substitute m = 2/3, and (a, b) = (3, 1) into y - b = m(x - a):
y - 1 = 2/3(x - 3) [equation in point-slope form]
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What type of linear equation is X +1 equals X +1?
It depicts horizontal linear equation, as the slope is 0.
The slope of horizontal lines is zero. Consequently, m = 0 in the slope-intercept equation y = mx + b. Y = b, where b is the y-coordinate of the y-intercept, results in the equation.
The y-coordinate of every point on a horizontal line is the same. The line's equation is y=b if two points share the same y coordinate, b. The point (0,b) is the y-intercept of the horizontal line y=b. Horizontal lines don't have an x -intercept other than the line y=0.
A horizontal line is a line that is perpendicular to the x-axis. Because the value of x never changes, the graph of a relation of the form x = 5 is a line parallel to the y-axis.
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HELPPPP PLEASEEE
Pleaseee help it’s due today!!!
A point that lies in the middle of a line and is equally spaced from its ends is the line's midway. The formula for the line's midpoint is [(x)1 + (x)2]/2, [(y)1 + (y)2]/2 if the line's endpoints are (x)1, (y)1, and (x), (y), respectively.
Explain about the midpoint?Using the equations [(x)1 + (x)2]/2, [(y)1 + (y)2]/2, one may get the midway. Here, the coordinates of two points are (x), (y), (x)2, (y)2, and the midway is a location that is equally spaced from both of these positions.
The exact middle number between two numbers is referred to as the midway. The midpoint calculation is the same as the two-number average calculation. Therefore, by adding any two numbers together and dividing by two, you may find the halfway between any two integers.
The distance formula, which is derived from the Pythagorean Theorem, is employed to determine the separation between two points in the plane. The Pythagorean Theorem is based on a right triangle where the angles are a and b.
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he formula in cell C2 is =A$2. Autofill is used by dragging C2's autofill box across to D2, E2, and F2. What formulas will appear in D2, E2, and F2, respectively?
B$2, C$2, D$2
B$2, B$3, B$4
A$2, A$3, A$4
C$3, C$4, C$5
The formulas that will appear in D2, E2, and F2, respectively are
B$2, C$2, D$2. Option A
This is further explained below.
What is a formula?Generally, A mathematical formula or a chemical formula, for example, are both examples of formulas, which are condensed ways of expressing information via the use of symbols.
When used informally within the realm of science, the word "formula" refers to the overall construction of a connection between a set of determinable variables.
Because of the formula =A$2, row 2 is considered to be anchored.
At this point, D2 is located to the right of C2, but still in the same row.
And the cell that is direct to the right of A2 is labeled B2.
As a result, the formula for D2 will equal B times 2.
In the same manner, the formula in E2 will be C$2, and the formula in F2 will be D$2.
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Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a variance of 1,960,000 and a mean life span of 13,000 hours. If a monitor is selected at random, find the probability that the life span of the monitor will be more than 15,240 hours. Round your answer to four decimal places.
The probability that the life span of the monitor will be more than 15,240 hours = 0.055
Given,
Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a variance σ^2 = 1,960,000 of and a mean life span of μ = 13,000 hours.
Here, σ = [tex]\sqrt{1,960,000}[/tex] = 1,400
Let x represents the life span of a monitor.
Then , the probability that the life span of the monitor will be more than 15,240 hours will be :-
= P(x > 15,240) = P[(x - μ)/σ > (15,240 - 13,000)/ 1,400 ]
= P (z > 1.6) = 1 - P(z ≤ 1.6) [∵ P(Z > z ) = 1 - P(Z ≤ z) ]
= 1 - 0.9452 = 0.0548 ~ 0.055
Hence, the probability that the life span of the monitor will be more than 15,240 hours = 0.055
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PLEASE HELP ME!!!!!!!!
Answer:
In point-slope form: y + 4 = -2(x + 1)
In slope-intercept form: y = -2x - 6
In standard form: 2x + y = -6
Step-by-step explanation:
y + 4 = -2(x + 1)
y + 4 = -2x - 2
y = -2x -6
2x + y = -6
Given f(x) = 3(4-x), what is the value of f( − 2)? Enter your answer in the answer box.
Answer:
f(-2) = 18
Step-by-step explanation:
In order to calculate a function of x, we replace x
For example
f(x) = x
f(-2) = -2
In this specific scenario
f(x) = 3 * (4 - x)
f(-2) = 3 * (4 - -2)
- -2 turns positive
f(-2) = 3 * (4 + 2)
Now we use PAMDAS (parentheses, exponents, multiplication, division, addition) as an operation order, so we first solve the parantheses
f(-2) = 3 * 6
f(-2) = 18
Jenny ended a hike at an elevation of 3, 000 feet above sea level.
She had started at an elevation of 2, 000 feet above sea level.
Which integer represents Jenny's change in elevation?
-1000 represents Jenny's change in elevation.
What is an integer?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The boldface Z is a common mathematical symbol for the set of integers. A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043.
Given Data
Jenny ended a hike at an elevation of 3, 000 feet above sea level.
She had started at an elevation of 2, 000 feet above sea level.
Hike remaining = 3000 - 2000
Hike remaining = 1000
-1000 represents Jenny's change in elevation.
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The following table shows the profit rates for Nike and Adidas
Nike -2 (x - 2)
Adidas -17 + x
If x represents the number of shoes purchased, how many shoes have to be purchased until both companies earn the same amount? Create and solve the equation.
The number of shoes that have to be purchased until both companies earn the same amount is 21.
How to calculate the number of shoes?Based on the information, the profit rates for Nike and Adidas are illustrated as:
Nike -2 (x - 2)
Adidas -17 + x
In this case, x represents the number of shoes purchased,
The number of shoes that have to be purchased until both companies earn the same amount will. be:
2(x - 2) = 17 + x.
2x - 4 = 17 + x
2x - x = 17 + 4
x = 21
The number of shoes will be 21.
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Order these numbers from least to greatest
6.3071, 6.7 6.408, 6.47
Answer:
6.3071, 6.408, 6.47, 6.7
Step-by-step explanation:
6.3071, 6.408, 6.47, 6.7, hope this helped!
Answer:
In bold below.
Step-by-step explanation:
6.3071, 6.7 6.408, 6.47
= 6.3071, 6.408, 6.47, 6.7
A traditional individual retirement account (IRA) is a special type of retirement account in which the money you invest is exempt from income taxes until you withdraw it. If you deposit $100
each month into an IRA earning 6% interest, how much will you have in the account after 20 years?
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the end of the period}}{\textit{Future Value of an ordinary annuity}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pmt=\textit{periodic payments}\dotfill &100\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each months, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]
[tex]A=100 \left[ \cfrac{\left( 1+\frac{0.06}{12} \right)^{12 \cdot 20}-1}{\frac{0.06}{12}} \right] \\\\\\ A=100 \left[ \cfrac{\left( 1.005 \right)^{240}-1}{0.005} \right]\implies A \approx 46204.09[/tex]
A sector of a circle has a central angle of 150∘. Find the area of the sector if the radius of the circle is 17 cm.
Answer:
378.3 [tex]cm^{2}[/tex]
Step-by-step explanation:
a =[tex]\pi[/tex][tex]r^{2}[/tex] for a whole circle, but we only want the area for part of a circle
a = [tex]\frac{150}{360}[/tex] [tex]\pi[/tex][tex]17^{2}[/tex]
a = 378.3 [tex]cm^{2}[/tex] rounded to the nearest tenths place
Kendra spent $22 on 11 song downloads. How much did each song cost?
Answer:
$2
Step-by-step explanation:
To find the unit cost, divide the entire price of all the songs (22), by how many songs you bought (11)
22 Dollars / 11 Songs = 2 Dollars / Song (2 Dollars per Song)
Solve for g.
0.2 =
g + 17.5
-1
Answer: g=-16.3
Step-by-step explanation:
ya welcome
We can dilate more than one point at a time! P and R will be dilated using C as the center of dilation with a scale factor of 3. Drag P' and R' so that P and R would dilate to each point. HELP PLEASE!
The attached figure shows the location of P' and R' in the figure, after the dilation
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor, where the scale factor does not equal one.
How to determine the location of P' and R' in the figure?The figure that completes the question is added as an attachment
From the figure, we have the following parameters
Center of dilation = Point CLength CR = 2.6 unitsLength PR = 5 unitsScale factor of dilation = 3The image of dilation using the above parameters is the scaled factor of the given figure
As a general rule, the following are the properties of a scaled copy of another figure
If the scale factor is greater than 1, the side lengths would be greater than the original figureIf the scale factor is less than 1, the side lengths would be less than the original figureThe angles of both figures are the sameThe side lengths may or may not be whole numbersThe above means that
New lengths = Old lengths * Scale factor
So, we have
P'R' = PR * Scale factor
C'R' = CR * Scale factor
This gives
P'R' = 5 * 3
P'R' = 15
C'R' = 2.6 * 3
C'R' = 7.8
Using the above as a guide, the location of P' and R' are identifies in the figure
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i need help please plaeswwosadcwefcuwn
The true statement is that both √15 and √0.001 are irrational , the correct option is (c).
Rational Numbers can be defined as the numbers that can be expressed in the form of p/q , where p and q are integers and q not equal to 0 .
For Example : 2/3 , 2, 8/3 are all Rational Numbers.
Irrational Numbers can be defined as the numbers that cannot be expressed in the form of p/q where , p and q are integers and q not equal to 0 .
For Example : √2 , √37 are irrational as they cannot be expressed in the form of p/q.
In the question ,
two numbers √15 and √0.001 are given .
the first number √15 is not a perfect square , hence not an integer ,
So, √15 is an irrational number .
the second number
√0.001 = √(1/1000) = 1/√1000 = [tex]\frac{1}{10\sqrt{10} }[/tex]
we see that √10 is not an integer , hence √0.001 is an irrational number .
Therefore , the true statement is that both √15 and √0.001 are irrational , the correct option is (c).
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Reynado ordered 12 large pepperoni pizzas. The total cost was $101.40. Write a direct variation function for the cost of one large pepperoni pizza. How much would 5 large pepperoni pizzas cost?
Answer:
(1) y = 8.45x
(2) Total cost: $42.25
Step-by-step explanation:
Let's see by constructing a first-hand example of the information we have.
$101.40 = 12x
Divide 12 on both sides.
When we divide 12 from both sides, we get the simplified answer of:
x = 8.45
This means that each pizza will be $8.45 each, therefore this will be out=r equation
y = 8.45x
(where x is the number of pizzas and y is the total amount cost.
To find the cost of 5large pepperoni pizzas, we use our equation above (y = 8.45x) and input a 5 in x;
y = 8.45(5)
y = 42.25
The total cost for the 5 pizzas will be $42.25.