Sample space={ A,B,C,D,E,F}
Event of choosing A or C = {A,C}
What is sample space?
A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.
i.e. the sample space while flipping a coin is: {H,T}
The sample space while tossing a six-sided die is: {1,2,3,4,5,6}
Here it is given that:
A bag has six balls labeled: A,B,C,D,E,F
One ball will be randomly picked, and its letter will be recorded as the outcome.
This means that the sample space is given by:
Sample space={ A,B,C,D,E,F}
Now, when the event is choosing a letter from A or C.
Then the sample space is:
Sample space= {A,C}
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Is the sequence an arithmetic sequence? 2. -12,4,0, 2....... Yes or No 3. -6,0, 6, 12 ..... Yes or No
For a sequence to be an arithmetic sequence the terms have to have a constant difference between them
2) We have the sequence: -12, 4, 0, 2...
The difference between the terms is not constant, so this is not a arithmetic sequence.
For example, from 4 to 0, there is -4 and from 0 to 2, is 2.
3) The sequence -6,0, 6, 12,... is an arithmetic sequence, because it has a constant difference between the terms (it always add 6 in each step).
Answer:
2. -12,4,0, 2....... No
3. -6,0, 6, 12 ..... Yes
Write two equivalent fractions.
2/3
Answer:
5/10
15/30
Step-by-step explanation:
The triangles are similar, so the lengths of corresponding sides are in the same ratio.
One pair of corresponding sides is 5 and 10.
10 is twice 5.
5/10
The other pair of corresponding sides is 15 and ?.
? must be twice 15, so ? is 30.
15/30
The weight (W kg) of a decaying radio active substance after n years is given by W= Wo(1/2)^n/100, where Wo kg is the initial weight of the substance. 1. Find the number of years for the radioactive substance to decay to half of its initial weight.
We have the equation:
[tex]W=W_0(\frac{1}{2})^{\frac{n}{100}}[/tex]And we want to find the value n, correspondign to the number of years necessary in order to the substance to decay in half.
Let's say that we have 1 Kg of the substance, this is Wo, the initial weight. Since we want to find the the decay of half the substance we use W = 1/2
And write:
[tex]\frac{1}{2}=1\cdot(\frac{1}{2})^{\frac{n}{100}}[/tex]Now we can use a property of logarithms:
[tex]\ln (a^b)=b\ln (a)[/tex]Thus applying natural log on both sides:
[tex]\ln (\frac{1}{2})=\ln (\frac{1}{2}^{\frac{n}{100}})[/tex]By the property:
[tex]\ln (\frac{1}{2})=\frac{n}{100}\ln (\frac{1}{2}^{})[/tex]We can divide on both sides by ln(1/2):
[tex]\begin{gathered} 1=\frac{n}{100} \\ n=100 \end{gathered}[/tex]The number of years for the radioactive substance to decay to half its initial weigh are 100 years.
The step to get rid of the ln(1/2) is:
[tex]\begin{gathered} \ln (\frac{1}{2})=\frac{n}{100}\ln (\frac{1}{2}^{}) \\ \frac{\ln (\frac{1}{2})}{\ln (\frac{1}{2})}=\frac{n}{100}\frac{\ln (\frac{1}{2}^{})}{\ln (\frac{1}{2})} \\ 1=\frac{n}{100}\cdot1 \\ 1=\frac{n}{100} \end{gathered}[/tex]
Help in solving question 5 please. System needs to be solved using the elimination method. Thanks!
Given: A system of linear equations in three variables x, y, and z as follows-
[tex]\begin{gathered} 2x+y-z=9 \\ -x+6y+2z=-17 \\ 5x+7y+z=4 \end{gathered}[/tex]Required: To solve the system using elimination.
Explanation: Let the given system as-
[tex]\begin{gathered} 2x+y-z=9\text{ ...}(1) \\ -x+6y+2z=-17\text{ ...}(2) \\ 5x+7y+z=4\text{ ...\lparen3\rparen} \end{gathered}[/tex]We can solve the system by reducing the system to a system of 2 variables. Suppose we would like to remove the variable z.
Multiplying equation (1) by 2, adding to equation (2) as follows-
[tex]\begin{gathered} (4x+2y-2z)+(-x+6y+2z)=18+(-17) \\ 3x+8y=1\text{ ...}(4) \end{gathered}[/tex]Now, add equations (1) and (3) as follows-
[tex]\begin{gathered} (2x+y-z)+(5x+7y+z)=9+4 \\ 7x+8y=13\text{ ...}(5) \end{gathered}[/tex]Now, equations (4) and (5) represent a system of linear equations in two variables. Subtracting the equations as follows-
[tex]\begin{gathered} (3x+8y)-(7x+8y)=1-13 \\ -4x=-12 \\ x=3 \end{gathered}[/tex]Substituting x=3 in equation (4)-
[tex]\begin{gathered} 9+8y=1 \\ 8y=-8 \\ y=-1 \end{gathered}[/tex]Substituting x=3 and y=-1 in equation (1) as follows-
[tex]\begin{gathered} 6-1-z=9 \\ z=-4 \end{gathered}[/tex]Final Answer: The solution to the system is-
[tex]\begin{gathered} x=3 \\ y=-1 \\ z=-4 \end{gathered}[/tex]Hi, I was absent today in class and I really need help with question 15, I will be much appreciated if you show work and the step so I can be more understanding thank you!
We have the following equation
[tex]\log _2(4x+10)-\log _2(x+1)=3[/tex]Now we solve for "x", we must use the logarithmic properties
[tex]undefined[/tex]What are the intercepts of 5x+y=5? Graph the equation.
The y-intercept is found replacing x = 0 into the equation as follows:
5*0 + y = 5
y = 5
Then, the line intercepts the y-axis at (0, 5)
The x-intercept is found replacing y = 0 into the equation as follows:
5x + 0 = 5
5x = 5
x = 5/5
x = 1
Then, the line intercepts the x-axis at (1, 0)
The line is graphed connecting these two points
Peter hired two combine operators to harvest his 260 acres of wheat. He expected a yield of 50 bushels per acre. The first operator had a 3% grain loss, and the second operator had 5% grain loss. Each operator harvested the same number of acres in the same time. How much was saved by the first operator if wheat sold for $11.97 perbushel?
Answer:
The amount in dollars of wheat saved by the first operator is;
[tex]\text{ \$1,556.10}[/tex]Explanation:
Given that Peter hired two combine operators to harvest his 260 acres of wheat.
And it yeilds 50 bushels per acre.
The total amount of bushels of wheat on the field is;
[tex]\begin{gathered} T=260\times50 \\ T=13,000\text{ bushels} \end{gathered}[/tex]Since each operator harvest the same amount;
[tex]\text{opertor 1= Operator 2 = }\frac{13000}{2}=6500\text{ bushels each}[/tex]If operator 1 loss 3%, the remaining amount is;
[tex]\begin{gathered} A_1=6500-3\text{ \% of 6500} \\ A_1=6500-(0.03)6500 \\ A_1=6305\text{ bushels} \end{gathered}[/tex]Operator 2 loss 5%, the remaining amount is;
[tex]\begin{gathered} A_2=6500-0.05(6500) \\ A_2=6175\text{ bushels} \end{gathered}[/tex]The amount of bushels save by the first operator compared to the second operator is;
[tex]\Delta A=A_1-A_2=6305-6175=130\text{ bushels}[/tex]if wheat is sold for $11.97 per bushel, the amount in dollars of wheat saved by the first operator is;
[tex]\begin{gathered} C=130\text{ bushels }\times\text{ \$11.97 per bushel} \\ C=\text{ \$1,556.10} \end{gathered}[/tex]The amount in dollars of wheat saved by the first operator is;
[tex]\text{ \$1,556.10}[/tex]what is the solution to the equation 5x-1+7x=11
the expression is
5x - 1 + 7x = 11
5x + 7x = 11 + 1
12x = 12
x = 12/12
x = 1
so the answer is x = 1
Tracey paid $180 for an item that was originally priced at $560. What percent of the original price did Tracey pay?
To find the percentage that Tracey paid, we can use the rule of three:
Now, the original price $560 represent the 100%.
If $560 ----------- 100%
then $180----------- x
where x =($180*100)/$560
x = 32.14
Therefore, the percent that Tracey paid was 32.14%
The answer is rounded to the nearest hundredth.
Use the angle relationships present to find angle P
Answer:
65 degress
Step-by-step explanation:
I did a problem like this before
Can you help and explain Apply the zero peoduct theorem to solve for value of x[tex]x { = 9}^{2} [/tex][tex]27x {}^{2} = 9x[/tex]
Solution
We want to solve
[tex]27x^2=9x\text{ using zero product thorem}[/tex]The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.
For the question,
[tex]\begin{gathered} 27x^2=9x \\ \text{Divide both sides by }9 \\ 3x^2=x \\ \text{Subtract x from both sides} \\ 3x^2-x=0 \\ \text{Factorize} \\ x(3x-1)=0 \\ \text{Applying the zero theroem, we have} \\ x=0\text{ or 3x-1=0} \\ x=0\text{ or 3x = 1} \\ x=0\text{ or x = }\frac{1}{3} \end{gathered}[/tex]The answer is x = 0 and x = 1/3
Jasmine is helping her father plant trees to create a border around the back yard. Jasmine plants a tree every 25 minutes, and her father plants a tree every 15 minutes. If they started together, how long before they would finish planting a tree at the same time?
can you help me with this place
The diameter of Keisha's favorite marble is 2.5cm
The radius of the sphere is the half of the diameter : Radius = Diameter/2
Given diameter of marble = 2.5 cm
So, radius = diameter/2
Radius of the marble = 2.5/2
Radius of the marble = 1.25 cm
The general expression for the volume of sphere with radius 'r' is :
[tex]\text{ Volume of Sphere =}\frac{4}{3}\Pi\times radius^3[/tex]So, the volume of one sphere is :
Substitute the value of r = 1.25 cm
[tex]\begin{gathered} \text{ Volume of Sphere =}\frac{4}{3}\Pi\times radius^3 \\ \text{ Volume of Sphere =}\frac{4}{3}\times3.14\times1.25^3 \\ \text{ Volume of Sphere = 8.18 cm}^3 \end{gathered}[/tex]As, Keisha take 6 marbles
So, the volume of 6 marbles = 8.18 x 6
Volume of 6 marbles = 49.08 cm³
It is given that : 1 cubic centimeter has the massof 2.6 grams
1 cm³ = 2.6 gm
As the volume of 6 marbles is 49.08cm³
So, The mass of 49.08cm³ = 49.08 x 2.6
The mass of 6 marbles = 127.608 gm
127.608 to the nearest whole number is 128
Mass of the 6 marbles is 128 gm
Answer : 128 gm
I need help. The answers has to be exact so I can’t use decimals
Answer
The exact value of the lateral surface area = 395 cm²
The exact value of the total surface area = 572 cm²
Explanation
The solid shape is a cone with a height of 15 cm and the diameter of the base of the solid shape is 15 cm.
The Lateral Surface Area of the Solid Shape:
The formula to calculate the lateral surface area (LSA) of a cone is given by:
[tex]LSA=π(radius\times length)[/tex]The radius will be = diameter/2 = 15cm/2 = 7.5 cm
To find legth, we use Pythagoras rule:
[tex]\begin{gathered} l^2=h^2+r^2 \\ \\ l^2=15^2+7.5^2 \\ \\ l^2=225+56.25=281.25 \\ \\ l=\sqrt{281.25} \\ \\ l=16.77cm \end{gathered}[/tex]Put π = 3.14, r = 7.5 cm, and l = 16.77 cm into the lateral surface area formula:
[tex]\begin{gathered} LSA=3.14\times7.5cm\times16.77cm \\ \\ LSA=394.93\text{ }cm^2 \\ \\ LSA\approx395\text{ }cm^2 \end{gathered}[/tex]Therefore, The exact value of the lateral surface area = 395 cm²
Total Surface Area of the Solid Shape:
To find the exact value for the total surface area of the solid shape, we use the total surface area (TSA) formula of a cone which is:
[tex]TSA=\pi r^2+\pi rl[/tex]put π = 3.14, r = 7.5 cm, and l = 16.77 cm
[tex]\begin{gathered} TSA=(3.14\times(7.5cm)^2)+(3.14\times7.5cm\times16.77cm) \\ \\ TSA=176.63cm^2+394.93cm^2 \\ \\ TSA=571.56cm^2 \\ \\ TSA\approx572\text{ }cm^2 \end{gathered}[/tex]The exact value of the total surface area = 572 cm²
A 12-quart cooling system is tested and found filled with a 60% antifreeze solution. The ideal mixture should be a 50% antifreeze solution. How many quarts of solution need to be drained and replaced with pure water to reach the ideal mixture?
Answer:
2 quarts
Explanation:
Let the number of quarts to be drained and replaced = x
From the given problem:
60% of (12-x)=50% of 12
[tex]\begin{gathered} 0.6(12-x)=0.5\times12 \\ 0.6(12-x)=6 \\ 12-x=\frac{6}{0.6} \\ 12-x=10 \\ x=12-10 \\ x=2 \end{gathered}[/tex]2 quarts of the solution needs to be drained and replaced with pure water to reach the ideal mixture.
The following table represents the highest educational attainment of all adult residents in a certain town. If a resident who is aged 0 - 39 is chosen at random, what is the probability that they bave completed a bachelor's degree and no more? Round your answer to the nearest thousandth .
ANSWER:
The probability is 0.107 or 10.7%
STEP-BY-STEP EXPLANATION:
The probability is calculated with the number of people who are in that age range and meet the study conditions and the total number of people.
We can determine both data in the table, therefore
[tex]p=\frac{1707}{15921}=0.107\cong10.72\text{\%}[/tex]The parent function f(x)=x2 has been transformed to make the function g(x) by reflection f(x) over the x-axis , vertically shrinking by a factor of 1/2 and translating 2 units up. The equation for g(x) is expressed in which of the functions below
Given:
There are given that the parent function:
[tex]f(x)=x^2[/tex]Explanation:
According to the concept:
The function reflected over the x-axis means, we need to multiply with a negative sign.
That means:
[tex]g(x)=-x^2[/tex]And,
Vertically shrinking by a factor of 1/2 means, multiply by 1/2 in the entire function:
So,
[tex]g(x)=-\frac{1}{2}x^2[/tex]Then,
Translating 2 units up means, adding 2 in the entire function:
So,
[tex]g(x)=-\frac{1}{2}x^2+2[/tex]Final answer:
Hence, the correct option is C.
Erin spent $6.75 on art supplies and made cards to sell. On Monday she sold $3.50 worth of cards and on Tuesday she sold $5.25 worth of cards. What was Enn's overall profit or loss? o $1.75 loss o $2.00 profit 0 $8.75 loss O $15.50 profit
He spent $6.75 on art supplies and made the cards .
she sold the made cards on monday and tuesday.
Monday sales = $3.50
Tuesday sales = $5.25
Total sales = 3.50 + 5.25 = $8.75
profit = sales - cost
profit = 8.75 - 6.75 = $2.00
Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Because angle 5 and 6 are supplementary, the only true statement is:
m∠5 + m∠6 =180°
Which statement is always true?By using the diagram we can see that:
Angles ∠1 and ∠2 are supplementary.Angles ∠3 and ∠4 are supplementary.Angles ∠5 and ∠6 are supplementary.Where two angles are supplementary if their measures add up to 180°, then:
∠1 + ∠2 = 180°∠3 + ∠4 = 180°∠5 + ∠6 = 180°Then the statements that are true are:
m∠5 + m∠6 =180°
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Solve for x:
X=
100⁰
70°
x +41
Answer: x=107=0.7
Step-by-step explanation:
1001=70xMultiply both sides by 70.1001×70=xMultiply 1001 and 70 to get 10070.10070=xReduce the fraction 10070 to lowest terms by extracting and canceling out 10.107=xSwap sides so that all variable terms are on the left hand side.x=107
A recipe for trail mix requires 5/6 cup of raisins for 1 batch. Alaina 1 2/3 cups of rasisins to make trial mic Enter tje number of batches of trial mix Alaina makes.
SOLUTION :
Step 1 :
In this question, we have that the recipe for trail mix requires
5/6 cup of raisins for 1 batch.
Then, Alaina uses
[tex]1\text{ }\frac{2}{3}\text{ cups of raisins to make trial mix.}[/tex]Step 2 :
To get the number of batches of trial mix Alaina makes, we have that :
[tex]\begin{gathered} 1\text{ }\frac{2}{3\text{ }}\text{ divided by }\frac{\text{ 5}}{6} \\ \frac{5}{3}\text{ x }\frac{6}{5}\text{ = }\frac{30}{15}\text{ = 2 batches} \end{gathered}[/tex]CONCLUSION :
There would be 2 batches .
An automobile windshield wiper 11 inches long rotates through an angle of 60∘. If the rubber part of the blade covers only the last 10 inches of the wiper, find the area of the windshield cleaned by the windshield wiper. Answer exactly or round to the nearest tenth of a square inch
the area of the windshield, cleaned by the windshield wiper is mathematically given as 0.096inche^2
This is further explained below.
What is a windshield?The term "acute area of the windshield glazing" refers to the section of the windshield that measures eight and one-half inches by eleven inches and is located immediately in front of the driver's line of sight, as seen in the image.
Then, let's call the part of the windshield labeled "ABC" A.
[tex]A=\frac{1}{2} r^2 \theta[/tex]
Now, substituting the given values we get,
[tex]\begin{aligned}&A=\frac{1}{2} r^2 \theta \\&A=\frac{1}{2} \times(7)^2 \times \frac{\pi}{180} \\\end{aligned}$$[/tex]
A=0.4276
Then let the area of the windshield, ADE, be denoted by the letter A',
[tex]A^{\prime}=\frac{1}{2} r^2 \theta[/tex]
Now, after replacing those values with the ones we were provided,
[tex]\begin{aligned}&A^{\prime}=\frac{1}{2} r^2 \theta \\&A^{\prime}=\frac{1}{2} \times(1)^2 \times 60 \times \frac{\pi}{180} \\&A^{\prime}=0.5236\end{aligned}[/tex]
In conclusion, In order to calculate the area of the windshield, you need to take the difference between A and A'.
0.5236-0.4276=0.096
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Solve for n if 7056n - 4577n = 2257n
Answer:
n=0
Step-by-step explanation:
Question 2a)Tell is this relationship is a direct variation.The equations -15x + 4y = 0 relates the length of a videotape in inches x to its approximate playing time in seconds y.Please enter yes, or nob)Question 3Using the previous function from question 2 , could you please find the playing time of a videotape 1 foot long? seconds
If two variables x and y are proportional (direct variation), one can be written in terms of the another using a constant of proportionality, which is often represented using a letter k:
[tex]y=kx[/tex]Isolate y from the given relationship:
[tex]\begin{gathered} -15x+4y=0 \\ \Rightarrow4y=15x \\ \Rightarrow y=\frac{15}{4}x \end{gathered}[/tex]As we can see, the variable y can be written in terms of x through a constant of proportionality equal to 15/4. Then, the relationship is a direct variation. The answer to Question 2 is: yes.
To find the playing time, replace the value of x. Since 1 foot is equal to 12 inches and the equation y=15/4 x works when x is in inches and y is in seconds, replace x=12 to find the playing time in seconds:
[tex]\begin{gathered} y=\frac{15}{4}\times12 \\ =45 \end{gathered}[/tex]Then, the playing time for a tape 1 foot long is 45 seconds. The answer to Question 3 is: 45.
Emma and her aunt shared 9 oranges each, how many oranges did they each get?
Answer:
4 and 1/2.
Step-by-step explanation:
There are 9 oranges, so there are not enough for both to get a whole amount.
They will split the last one into half, so they has 4 and 1/2 oranges each.
Answer: 4 and 1/2
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Can a table with the same Input and output be a function ?
In this relation table value of x = ( 2,5,7,-4) are following same pattern .
but x = 5 is not input and output of a function.
What is input and output of a function in math?
A function can be represented as an input-output table, such as the one below. According to the same function rule, every pair of integers in the table is connected.The input and output of a function are, respectively, what goes into it and what it produces. Also known as the domain and range, respectively, are the input variable and output variable. The collection of all values that the function will accept as inputs, or its domain, is what makes up the function.x = 2 * 1 = 2 , y = 2
x = 5 * 1 = 5 , y = 5
x = 7 * 1 = 7 , y = 7
x = -4 * 1 = -4 , y = -4
x = 5 * 2 + 1 = 11 , y = 11
In this relation table value of x = ( 2,5,7,-4) are following same pattern .
but x = 5 is not .
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The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.v(t) = 19, 900 * (0.84) ^ tRound your answers to the nearest dollar as necessary.Find the initial value of the car and the value after 11 years.
Given
[tex]v(t)=19900(0.84)^t[/tex]a) The car has its original (initial) value when no time has passed since it was bought; in other words t=0. Then,
[tex]\text{ initial value: }v(0)=19900(0.84)^0=19900*1=19900[/tex]The initial value is 19900.
b) After 11 years, t=11; then,
[tex]\begin{gathered} v(11)=19900(0.84)^{11}=2923.64894... \\ \Rightarrow v(11)\approx2924 \end{gathered}[/tex]Rounded to the nearest tenth, the second answer is 2924
Select the names of the sides of the triangle. The 2 answer options are leg and hypotenuse.
Given:
[tex]\text{side(c)}=\text{Hypotenus}[/tex][tex]\text{side(a)}=\text{lag}[/tex][tex]\text{side(b)}=\text{lag}[/tex]I NEED HELP PLEASE!!!!!!!!!!
a) The inverse of a statement : If If two angles are not supplementary then the angles are not a linear pair. FALSE
b) The converse of a statement : If the angles are a linear pair, then the two angles are supplementary. TRUE
c) The contrapositive of a statement : If the angles aren't supplementary, then they aren't linear pair . FALSE
The given statement is : If two angles are supplementary then the angles are a linear pair .
(a) The inverse of a statement : If If two angles are not supplementary then the angles are not a linear pair.
This statement is FALSE because supplementary angles do not have to be adjacent, whereas a linear pair must be adjacent and create a straight line. So, no, supplementary angles are not always linear pairs. However, linear pairs are always supplementary.
(b) The converse of a statement : If the angles are a linear pair, then the two angles are supplementary.
This statement is TRUE because in a linear pair, if the two angles have a common vertex and a common arm, then the non-common side makes a straight line and the sum of the measure of angles is 180°. Linear pairs are always supplementary.
(c) The contrapositive of a statement : If the angles aren't supplementary, then they aren't linear pair .
This statement is FALSE because if they are adjacent and share a vertex and one side. See the first picture below. They might not form a linear pair, like in a parallelogram.
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please help me solve now
Answer:
(3000/(5-3))(3+5)
= (3000/2) 8
= 12000
Step-by-step explanation: