(a) You and a randomly selected student from your class both earn A's in this course.
Answer: Here selection of one student is independent of the other.
Therefore it is independent.
(b) You and your class partner both earn A's in this course.
Answer: Here enough data is not available to comment whether the given event is mutually exclusive or independent.
Therefore it is neither.
(c) If two events can occur at the same time, they must be independent.
Answer: If both the events occur at the same time then it is not necessary they are independent.
Therefore it is False.
The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?
Replace the values of h and k in the equation.
g(x) = 2x+h + k
When the function f is transformed to g, the equation is g(x) = 2x + 14 - 1
How to determine the equation of function g?The equation of function f is given as
f(x) = 2x - 1
The transformation is given as
Horizontal shift of 7 units left.
The above transformation rule can be represented as
Horizontal shift of 7 units left.: (x, y) = (x + 7, y)
When the above rule is applied, we have the following equation
g(x) = f(x + 7)
So, we have
g(x) = 2(x + 7) - 1
Open the brackets
g(x) = 2x + 14 - 1
Hence, the equation of function g is g(x) = 2x + 14 - 1
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2) Jennifer makes a hexagon by arranging 6 equilateral triangles, each of which has a vertex at
the center of the hexagon. If the length of one side of a triangle is 4, what is the area in
square units of the hexagon? Leave in simplest radical form if necessary. Show work and
circle final answer
The area in square units of the hexagon will be 12√3.
What is Hexagon?
A polygon with six sides are called a hexagon.
Given that;
Jennifer makes a hexagon by arranging 6 equilateral triangles.
The length of one side of a triangle is 4.
Now, To find the area of hexagon, we find the height of the equilateral triangle and then multiply by the 6.
So, In ΔABC;
AB = BC = CA = 4
Then, Measure of DC = BD = 2
Now, using Pythagoras theorem to find height of triangle (AD) as;
AD² = AC² - DC²
AD² = 4² - 2²
AD² = 16 - 4
AD² = 12
Take square root both side;
AD = √12
AD = 2√3
So, The area of hexagon = 6 × Height of triangle
= 6 × 2√3
= 12√3
Thus, The area in square units of the hexagon will be 12√3.
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Solve for Lowercase w
There are 6 triangles and 15 squares. What is the simplest ratio of triangles to squares?
Answer:
2:5
Step-by-step explanation:
6:15= 2:5
Ms.Vega read 20% of the Star Wars book. She read 8 pages of the book
The total number of the pages in the star war book which Ms. Vega is reading is 40.
percentage- a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part.
Let the number of pages = X
percentage of read pages = 20%
Number of read pages by her = 8
to find the total number in star war book
20% of X = 8
20/100 x X = 8
X = (8 x 100)/ 20
X = 4 X 10
X = 40
Total number of pages in star war book is 40.
The question is incomplete the complete question is
Ms. Vega read 20% 8of the Star Wars book. She read 8 pages of the book. Write pages in the Star Wars book.
The total number of the pages in the star war book which Ms. Vega is reading is 40.
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Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.a. What is her ending balance after the year, to the nearest cent?b. How much interest does she earn, to the nearest cent?c. What is her annual percentage yield to the nearest hundredth of a
Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.
a. What is her ending balance after the year, to the nearest cent?
b. How much interest does she earn, to the nearest cent?
c. What is her annual percentage yield to the nearest hundredth
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$4,300
t=1 year
r=2.3%=2.3/100=0.023
n=365
Part a
Find out the value of A
substitute the given values in the formula
[tex]A=4,300(1+\frac{0.023}{365})^{365\cdot1}[/tex]A=$4,400.04
Part b
I=A-P
I=4,400.04-4,300
I=$100.04
Part c
we have
4,300 -----> represent 100%
so
Applying proportion
Find out how much percentage is 4,400.04
100/4,300=x/4,400.04
x=(100/4,300)*4,400.04
x=102.33%
therefore
102.33-100=2.33%
Determine the solution of the given system of equations.
-x+y=-5
-4x - 5y=7
Answer:
x =2 y = -3
Step-by-step explanation:
hope it helps!!!!!
Use the number line to answer the question.
A number line is shown with end points 0 and 2. Hash marks are at every 0.2. Heavy marks are at 0, 1, and 2.
Zach bought 8 pieces of bubble gum that were $0.20 each. He used a number line to find the total cost. Choose the numbers to complete the sentences.
Zach started on the number line at 0.2 for the cost of one piece of gum. He moved
Choose...
hash marks. The total cost is
Choose...
.
Zach began at 0.2 for the price of one piece of gum on the number line. Has moved eight times. The whole price is $1.60.
Since each hash mark is worth.2, moving eight times will result in 1.6, or eight times $0.20.
This is further explained below.
What is a Number line?Generally, A number line is a depiction of a graded straight line that is used to represent real numbers visually.
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments is referred to as a number line.
How the number on the line may be answered depends on the numbers present. How a number is utilized depends on the issue it is associated with, such as when graphing a point
In conclusion, On the number line, Zach started at 0.2, which was equal to the cost of one piece of gum. Has relocated a total of eight times. The whole cost is a dollar and sixty cents.
Moving eight times will result in 1.6, which is equal to eight times $0.20, given that each hash mark is worth.2.
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PLS HELP MEEEEEEEEEEEEEEEEEEEEE PLS I BEG U
how could you use a graph of a proportional relationship to find any ratio in the the proportional relationship why does this work?
The fact that a connection is proportional if its graph is a line that runs through its origin should be stressed. This can be used to find the ratio in the proportional relationship.
How to explain the information?When the graph of a connection is a line passing through the origin, the connection is proportionate. If it is not a line or ray that fails to do this, the ratio is not proportional. The equation for the proportionality constant is K = y/x. This is the same equation used to get the slope of a straight line with respect to the origin.
If the graph of a relationship is a line or ray that goes through the origin, the relationship is proportional. If the line or ray does not pass through the origin, it is not proportional.
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find the slope of the line that goes through the given points (-2,-4) (1/4,5)
Solution
find the slope of the line that goes through the given points (-2,-4) (1/4,5)
[tex]\begin{gathered} slope\text{ =m} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} x_1=-2 \\ x_2=\frac{1}{4} \\ y_1=-4 \\ y_2=5 \end{gathered}[/tex][tex]m=\frac{5--4}{\frac{1}{4}--2}=\frac{9}{2.25}=4[/tex]Therefore the slope of the line = 4
Based on this data what is the probability that the next car will not be white why
The probability of the next car not being a white car is 0.92
What is probability?The probability of an event is the chance or the likelihood that the event would occur.
Note that the chance or the likelihood is represented as a numerical value
How to determine the probability?The complete question is added as an attachment
From the attached question, we have the following parameters
P(White Vehicle) = 0.25
P(Car) = 0.36
P(White Car) = 0.08
Using the complement rule of probability, we have the following equation
P(White Car) + P(Not White Car) = 1
Substitute the known values in the above equation
So, we have the following equation
0.08 + P(Not White Car) = 1
Subtract 0.08 from both sides of the equation
So, we have
P(Not White Car) = 1 - 0.08
Evaluate the difference
P(Not White Car) = 0.92
Hence, the probability that the next car will not be a white car is 0.92
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What happens to the x and y-values when you translate an object up?
When we translate an object up, the values of x remain the same, but the values of y change by a positive value.
what is the image point (6,-9) after the rotation of 270 degrees counterclockwise about the origin
Image of the point (6,-9) after rotation in the cartesian plane of 270 degrees counterclockwise about the origin will be (-9, -6)
As per the question statement, we are supposed to find the image of the point (6,-9) after rotation in the cartesian plane of 270 degrees counterclockwise about the origin.
We should know that a 270° anticlockwise rotation is exactly the same thing as a 90° clockwise rotation.
So the point (x, y) becomes (y, -x)
So the image of the point (6,-9) after rotation in the cartesian plane of 270 degrees counterclockwise about the origin will be (-9, -6)
Cartesian Plane: A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.To learn more about Cartesian Plane, click on the link given below:
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15 POINT AND BRANLIEST
A 15-gallon gas tank. If you can drive 330 miles on a full tank of gas, what is the unit rate of miles per gallon he gets?
The unit rate he can drive in mile per gallon is 22 miles per gallon.
How to find unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1.
In other words, a unit rate describes the ratio of two different units for the quantity of one.
Therefore, the unit rate in miles per gallon can be calculated as follows:
Hence,
unit rate = number of miles / number of gallons
number of miles = 330 miles
number of gallons = 15 gallons
unit rate = 330 / 15
Therefore,
unit rate = 22 miles per gallon
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Use the table of values for
y = f(x)
to complete a table for
y = f −1(x).
(Order your answers from smallest to largest x-value.)
The table containing the values of the inverse function is given at the end of the answer.
How to find the set of points (x,y) of a inverse function?A function will have a set of points (x,y). In the inverse function, the values of x and y are exchanged with each other, hence the rule is:
(x,y) -> (y,x).
Hence, the points are found as follows:
On the original function, when x = -4, f(x) = 10. Then, on the inverse function, when x = 10, f^-1(x) = -4.On the original function, when x = -3, f(x) = 0. Then, on the inverse function, when x = 0, f^-1(x) = -3.On the original function, when x = -2, f(x) = -10. Then, on the inverse function, when x = -10, f^-1(x) = -2.On the original function, when x = -1, f(x) = -20. Then, on the inverse function, when x = -20, f^-1(x) = -1.On the original function, when x = 0, f(x) = -30. Then, on the inverse function, when x = -30, f^-1(x) = 0.On the original function, when x = 1, f(x) = -40. Then, on the inverse function, when x = -40, f^-1(x) = 1.The table containing these values is given at the end of the answer.
What is the missing information?The tables are missing, and are given at the end of the answer.
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The line y=kx+4 goes through the point (2,-2)
K=-3
Sketch the graph of the line (need ASAP!)
The graph of the linear equation:
y = -3x + 4
Can be seen in the image at the end.
How to sketch a graph of the line?
Here we know that the equation for the line is:
y = k*x + 4
We know that this line goes through the point (2, -2), then we can replace these values in the above line so we get the value of k.
-2 = k*2 + 4
With this, we can find the value of k.
-2 - 4 = k*2
-6 = k*2
-6/2 = k = -3
Then the line is:
y = -3*x + 4
If we evaluate in x = 0, we get:
y = -3*0 + 4 = 4
So, at this point we know that the line passes through points (0, 4) and (2, -2), so to graph the line, we just need to graph these two points and draw a line that connects them, like in the example below.
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Solve the quadratic equation using the method indicated. See attached photo. Thanks in advance!
The quadratic formula is given by th following formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a, b and c are the coefficients of the quadratic equation. In this case, you have:
a = 6
b = 9
c = -22
replace the previous values into the quadratic formula and simplify:
[tex]\begin{gathered} x=\frac{-9\pm\sqrt[]{(9)^2-4(6)(-22)}}{2(6)} \\ x=\frac{-9\pm\sqrt[]{609}}{12} \\ x_1\approx1.31 \\ x_2\approx-2.81 \end{gathered}[/tex]Hence, the solutions for the given equation are 1.31 and -2.81
Perform the indicated operation. Don't forget to simplify if possible.
Subtract 6x + 2 from 4x-6.
Answer: 2x + 8
Step-by-step explanation:
( 6x + 2 ) - ( 4x - 6 ) =
6x - 4x = 2x
2 - -6 = 8
How many units are (-2,-3) & (5,7) from each other on the coordinate plane
Let's begin by listing out the information given to us:
(x, y) = (-2, -3), (5, 7)
The distance between the two points is given by:
[tex]\begin{gathered} d=\sqrt[]{\mleft(\mleft(x_2-x_1\mright)^2+\mleft(y_2-y_1\mright)^2\mright)} \\ d=\sqrt[]{(5--2)^2+(7--3)^2} \\ d=\sqrt[]{7^2+10^2} \\ d=\sqrt[]{49+100} \\ d=12.207\approx12.21 \\ d=12.21 \end{gathered}[/tex]Two accounts each begin with a deposit of $9000. Both accounts have rates of 3.1%, but one account compounds interest once a year while
the other account compounds interest continuously. Make a table that shows the amount in each account and the interest earned after one
year, five years, ten years, and 20 years.
Given : Initial deposit or the principal amount = $ 9000
Rate of interest = 3.1 %
Compound interest annually
= principal (1 + r/ 100)^t
here put value principal rate and time period 1, 5 10 and 20 years
and we get the amount for each time period
than for interest = amount - principal we get interest
as that we calculate all value:
given in the attachment
When do we use compound interest ?When interest on a balance in a savings or investment account is reinvested, you receive compound interest, which results in higher interest payments. Money makes money, a wise man once said. And money makes money by making more money. Compound interest speeds up the long-term growth of your savings and investments.
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Which has a terminal point of (square root 2/2 and square root 2/2). What is the terminal point of 5pi/4?
To find 5π/4 as terminal point, we will take the angle as 5π/4
The first coordinate is the x coordinate = cos θ
The second coordinate is the y coordinate = sin θ
[tex]\begin{gathered} We\text{ n}eed\text{ to convert the angle to degre}e\colon \\ 1\pi\text{ rad = 180}\degree \\ \frac{5\pi}{4}\text{ rad = 225}\degree \\ \\ sin\text{ is negative in third quadrant} \\ 225\text{ - 180 = 45} \\ \sin \text{ 45 = }\frac{\sqrt[]{2}}{2} \\ \\ \sin \text{ 225}\degree\text{ =- }\frac{\sqrt[]{2}}{2} \end{gathered}[/tex][tex]\begin{gathered} \theta\text{ = 225}\degree\text{ }is\text{ in third quadrant} \\ \\ 180\text{ -225 = 45}\degree \\ \cos \text{ 45}\degree\text{ = }\frac{\sqrt[]{2}}{2} \\ \text{ 225 is negative in third quadrant} \\ \\ \cos \text{ 225}\degree\text{ =- }\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]Hence, the terminal of 5π/4:
[tex]\text{(-}\frac{\sqrt[]{2}}{2},\text{ -}\frac{\sqrt[]{2}}{2})\text{ (option C)}[/tex]The Nutty Professor sells cashews for $7.20 per pound and Brazil nuts for $4.10 per pound. How much of each type should be used to make a 32 pound mixture that sells for $5.75 per pound?
They have to use 17.03 pounds of cashews and 17.03 pounds of nuts to make a 32 pounds mixture that sells for $5.75 per pounds
The cost of cashews per pounds = $7.20
The cost of nuts per pounds = $4.10
Consider the number of pounds of cashews as x and number of pounds of nuts as y
Total pounds of mixture = 32 pounds
The equation will be
x+y = 32
x = 32-y
Cost of the mixture for one pound = $5.75
Cost of the mixture for 32 pounds = 32×5.75
= $184
Then the equation will be
7.20x+4.10y = 184
Here we have to use the substitution method
Substitute the value of x in the equation
7.20(32-y)+4.10y = 184
230.4-7.20y+4.10y = 184
230.4-3.1y = 184
-3.1y = 184-230.4
-3.1y = -46.4
y = 14.97 pounds
x+y = 32
x+14.97 = 32
x = 17.03 pounds
Hence, they have to use 17.03 pounds of cashews and 17.03 pounds of nuts to make a 32 pounds mixture that sells for $5.75 per pounds
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1)
Solve the equation for y. Then, complete the
5x + 4y = 20
y=
Preview
20
Answer:
-5/4
Step-by-step explanation:
debemos de usar la ecuacion dy/dx
In 2008, 1.7m iPhones were sold. In 2012, 35.2m iPhones were sold. Assuming the sales of iPhones increases exponentially, how many iPhones should be expected to be sold in 2017?
The number of iPhones that should be sold in 2017 (since growth is exponential) is $ 6,476,635 x 10⁶. See the explanation below.
What is exponential Growth?Exponential growth is a data pattern that exhibits greater increases with time. Compounding produces exponential profits in finance. Compounding interest savings accounts may provide exponential growth.
The calculation for the above solution is as follows:
Recall that the formula for exponential growth is:
f(x) = a (1+r)ˣ
Where:
f(x) = exponential growth function
a = initial amount
r = growth rate
{x} = number of time intervals
Hence f(x) = 1.7 (1+ r)⁵
Note that x = 2017-2012 =5
r = (present value - past value)/ past value
Present value = 35.2
Past Value = 1.7
Hence r = (35.2-1.7)/1.7
r = 19.7058823529
Approximately 19.71
Hence,
f(x) = 1.7 (1+ 19.71)⁵
= 1.7 (20.71)⁵
= 1.7 x 3809785.2361
= 6476634.90137
Which is approximately = 6,476,635
Recall that our computation was done in millions hence the answer if left in standard notation is:
Increase in 2017 = $ 6,476,635 x 10⁶
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Find the surface area and volume of the hemisphere FormulaSA = 3 * 3.14 * r^2V = 2/3 * 3.14 * r^3
ANSWER
[tex]\begin{gathered} SA=98\pi ft^2 \\ V=228.7\pi ft^3 \end{gathered}[/tex]EXPLANATION
To find the surface area of the hemisphere, we apply the formula for the surface area of a hemisphere (without a base):
[tex]SA=2\cdot\pi\cdot r^2[/tex]where r = radius = 7 ft
Therefore, the surface area of the hemisphere is:
[tex]\begin{gathered} SA=2\cdot\pi\cdot7^2 \\ SA=98\pi ft^2 \end{gathered}[/tex]To find the volume of the hemisphere, we apply the formula for the volume of a hemisphere:
[tex]V=\frac{2}{3}\cdot\pi\cdot r^3[/tex]Therefore, the volume of the hemisphere is:
[tex]\begin{gathered} V=\frac{2}{3}\cdot\pi\cdot7^3 \\ V=228.7\pi ft^3 \end{gathered}[/tex]Which statements about the line that passes through (-2, 0) and (2, -4) are true? Select all that apply.
OA. The slope of the line is 1.
B. The line intersects the y-axis at (0, -2).
Considering the expression of a line, the statements:
"The line intersects the y-axis at (0, −2).""The equation of the line is y = −x − 2.""The line intersects the x-axis at (−2, 0)."about the line that passes through (-2, 0) and (2, -4) are true.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷(x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
This caseBeing (x₁, y₁)= (-2, 0) and (x₂, y₂)= (2, -4), the slope m can be calculated as:
m= (-4 - 0)÷(2 - (-2))
m= (-4)÷ 4
m= -1
Considering point 1 and the slope m, you obtain:
0= -1×(-2) + b
0= 2 +b
-2= b
Finally, the equation of the line that passes through the pair of points (-2,0) and (2,-4) is y= -x -2, wich has a slope of -1. The line intersects the x-axis at (−2, 0).
If x=0, you get:
0= -x -2
2= -x
2÷ (-1)=x
-2= x
Finally, the line line intersects the y-axis at (0, −2).
Your question was incomplete. Please check below the full content.
Which statements about the line that passes through (−2, 0) and (2, −4) are true? Select all that apply.
A. The slope of the line is 1.
B. The line intersects the y-axis at (0, −2).
C. The equation of the line is y = −x − 2.
D. The line intersects the x-axis at (−2, 0).
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Help.
A. RS
B. ST
C. Ut
Answer: THE ANSWER TO THAT IS B
Step-by-step explanation:
Given P(A) = 0.2, P(B) = 0.31 and P(AB) = 0.152, find the value of
P(AUB), rounding to the nearest thousandth, if necessary.
Probability - The value of P(AUB) = 0.557
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
P(A) = 0.2,
P(B) = 0.31 and
P(A/B) = 0.152,
Since, we know that
P(A⋃B) = P(A)+P(B)-P(A⋂B)
So, we have to find P(A⋂B)
We know that,
P(A/B) = P(A⋂B)/P(B)
Putting the values we get,
0.152 = P(A⋂B) / 0.31
P(A⋂B) = 0.152 x 0.31
P(A⋂B) = 0.047
Now, lets find the value of P(A⋃B)
P(A⋃B) = P(A)+P(B)-P(A⋂B)
Putting the values we get,
P(A⋃B) = 0.2 + 0.31 + 0.047
P(A⋃B) = 0.557
Hence the value of P(A⋃B) = 0.557
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solve for x if the equation is[tex]3 \sqrt{x + a - z = b} [/tex]
EXPLANATION
Given the expression:
[tex]b=\sqrt[3]{x+a-z}[/tex]Applying the cubic power to both sides:
[tex]b^3=(\sqrt[3]{x+a-z})^3[/tex]Simplifying the cubic root with the cubic power:
[tex]b^3=x+a-z[/tex]Subtracting -a to both sides:
[tex]b^3-a=x+a-a-z_{}[/tex]Adding z to both sides:
[tex]b^3-a\text{ +z = x + a - a -z + z}[/tex]Simplifying terms:
[tex]b^3-a+z=x[/tex]Switching sides:
[tex]x=b^3-a+z[/tex]A company borrows $68,000 for 8 years at a simple interest rate of 15.5%. Find the interest paid on the loan and the total amount paid.
The interest paid on the loan and the total amount paid are $84,320 and $152,320 respectively.
It is given in the question that:-
Money borrowed by the company (Principal) = $68,000
Time period for which the money is borrowed = 8 years
Simple Interest rate = 15.5 %
We have to find the interest paid on the loan and the total amount paid.
We know that,
Simple interest = (Principal * Interest * Rate)/100
Hence, we can write,
Simple interest = (68000 * 15.5 * 8)/100 = $84,320
Also, we know that,
Amount = Principal + Interest
Hence, we can write
Amount = 68,000 + 84,320 = $152,320
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