Mathematics High School
Answers
Answer 1
The probability that a randomly chosen return shows an adjusted gross income of $50,000 or more is 33.2%.
For mutually exclusive events, use the following addition rule:
P(A or B) = P(A) +P(B)
The corresponding probabilities is :
P( income > $50000) = P( >50)
= P(50 - 90) +P( 100 - 499) +P( ≥ 500)
= 0.215 + 0.100 +0.006
= 0.321
Therefore, the probability of a random selection returning is
P( income > 50000) = 0.321
Now ,
P( income ≥ 50000 and ≥ 100000 ) = P( > 100000)
= 0.100 + 0.006
= 0.106
The Probability Condition is:
P(A/B) = P(A and B) / P(B)
Therefore,
P( ≥ $100000 / $ $50000)
= P( ≥ $100000 and $ $50000)/ P( ≥ $50000)
= 0.106/ 0.321
≈ 0.3302
= 33.2%
Therefore, the conditional probability of earning at least $50000 and more is 33.2%
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Related Questions
Classify abc by its sides
A(2, 3), B(6, 3). C(2.7)y
Answers
Answer: this triangle is isosceles
Step-by-step explanation:
A(2,3) B(6,3) C(2,7)
[tex]AB=\sqrt{(6-2)^2+(3-3)^2} \\\\AB=\sqrt{4^2+0^2}\\\\ AB=\sqrt{4^2} \\\\AB=4\ units[/tex]
[tex]BC=\sqrt{(2-6)^2+(7-3)^2} \\\\BC=\sqrt{(-4 )^2+(7-3)^2}\\\\BC=\sqrt{16+4^2}\\\\BC=\sqrt{16+16} \\\\BC=\sqrt{32} \\\\BC=4\sqrt{2} \ units\\\\[/tex]
[tex]AC=\sqrt{(2-2)^2+(7-3)^2} \\\\AC=\sqrt{0^2+4^2} \\\\AC=\sqrt{4^2} \\\\AC=4\ units[/tex]
Hence, AB=AC
Thus, this triangle is isosceles
one year it snowed a total of 20 in. in January and February, it snowed three times as many inches in January then in February. how much did it snow each month?
Answers
Make an equation where x is the amount it snowed in February.
3x+x=20
4x=20
X=5
It snowed 5 in. in February.
5(3)=15
It snowed 15 in. in January.
kylie noticed that her golden retriever puppy has gained 30% more weight than her labrador puppy. when she first got the dogs, they both weighed 20 lbs., but the retriever now weighs 46 lbs. how much does the labrador weigh?
Answers
kylie noticed that her golden retriever puppy has gained 30% more weight than her Labrador puppy. when she first got the dogs, they both weighed 20 lbs , but the retriever now weighs 46 lbs. Now, the Labrador weigh is between 35 - 45 lbs.
We know that at 8 months the weight of golden retriever is 45 - 55 lbs and the weight of Labrador is 35 - 45 lbs.
Despite being cousins of Retrievers, Labs and Goldens come from different parts of the world. Labrador Retrievers originate from the island of Newfoundland in the easternmost province of Labrador in Canada. Interestingly, he actually exists three different types of Golden He Retriever, each from England, America and Canada.
Seeing these dogs, especially yellow or golden labs and golden retrievers cuddled up, there is a slight sporting resemblance to the canine family, but there are also important points that help distinguish them. I have.
One of the differences between Golden Retrievers and Labrador Retrievers is the shape of the muzzle. The nose is still bookable on both!
Both retrievers are double coated breeds, so blow dry them at least twice a year. But if there were any discarded medals, Myers says there is a clear winner. 's smoother coat helps them glide through the water more easily.
But if you've read this far, you already know. However, there is a mixed breed known as the Gladder that has both Golden and Labrador Retriever parents, so the pretty yellow color can come from either.
That's why Myers says the good guys in the lab keep the coffee table bare. Its paddle-like tail is strong because it provides the driving force for swimming! Golden retrievers usually have fan-shaped tails.
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What is the solution of the equation, 7a = 28
Answers
The value of the equation 7a = 28 is a = 4
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
7a = 28
On simplifying the equation , we get
Divide by 7 on both sides of the equation , we get
a = 28 / 7
a = 4
Therefore , the value of a is 4
Hence , The value of the equation 7a = 28 is a = 4
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1. SHADOWS George
in the middle of the day
George's shadow is 15 feet long, and
pole's shadow is 45 feet long
If George is 6 feet tall, how tall is the light pole ?
Answers
Answer:
Step-by-step explanation:
15 (poles hight) divided by 6 (mans hight) is 2.5, so you would devide 45 by 2.5, and you get 18
If Carissa can eat 2 pints of ice cream in 6 days, how long will it take here to eat 10 pints of ice cream?
SOLVE USING PROPORTIONS
Answers
Answer:
30 days
Step-by-step explanation:
2 pints : 6 days = 10 pints : x days
2/6 = 10/x
1/3 = 10/x
1 × x = 3 × 10
x = 30
Answer: 30 days
A spinner is divided into five equal sections labeled 1, 2, 3, 4, and 5. Another spinner is divided into two equal sections labeled A and B. Nigel will spin each spinner one time.
How many of the possible outcomes have a number less than 3 or an A?
A.) 9
B.) 5
C.) 7
D.) 2
Answers
Answer:
D) 0.2
-------------------------
Spinner 1
1 and 2 are less than 3 and it is out of possible 5.
The probability of less than 3 is:
2/5 = 0.4
Spinner 2
It has two equal sides and the probability of any is:
1/2 = 0.5
Total outcome of both events is:
0.4*0.5 = 0.2
The matching choice is D.
Iready math work book 289-290
Answers
Answer:
subtract and then subtract again until you get to one answer
Consider the trapezoids.
Which sequence of transformations maps Trapezoid WXYZ onto Trapezoid W′X′Y′Z′ ?
Dilation by a factor of 2 about the origin and a translation 1 unit down
Dilation by a factor of 12 about the origin and a translation 1 unit up
Dilation by a factor of 2 about the origin and a translation 1 unit up
Dilation by a factor of 12 about the origin and a translation 1 unit down
Answers
Answer:
Step-by-step explanation:i think the answer is B
The Sugar Sweet Company is going to transport its sugar to market. It will cost $5000 to rent trucks, and it will cost an additional $200 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S, and then graph your equation using the axes below.
Answers
Please find attached the graph of the linear equation for the total cost of transportation of sugar created with MS Excel is attached.
What is a graph of an equation?
A graph is a pictorial representation of the relationship between the variables in an equation.
The amount it costs to rent the truck = $5000
The amount it cost to transport a ton of sugar = $200
The amount of sugar transported in tons = S
The equation for the total cost C is; C = 5000 + 200·s
The graph of the equation for the cost of transportation can be created with a spreadsheet application such as MS Excel, by entering the formula, = 5000 + 200*RefCell, in a cell and the value of S in an adjacent cell, the values for S are then populated and the values of C are generated using the formula in the cell
The two columns are then selected
Then the insert, Chart menu is then used to create the graph.
Please find attached the required graph created with MS Excel
The graph for the total cost for the transportation is therefore a straight line graph with a slope of 200 and a y-intercept of 5,000,
The
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Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse axis and values of a = 8 and b = 9?
Answers
The standard equation of a hyperbola centered at the origin and a vertical tranaverse axis is y²/64 - x²/81 = 1
What is a hyperbola?
A hyperbola is a locus of points in such a way that the distance to each focus is a constant greater than one.
What is the standard equation of a hyperbola centered at the origin and a vertical tranaverse axis ?
The standard equation of a hyperbola centered at the origin and a vertical tranaverse axis is given by
y²/a² - x²/b² = 1
Now, for the given hyperbola, we have that
a = 8 and b = 9.
So, substituting the values of the variables into the equation, we have that
y²/a² - x²/b² = 1
y²/8² - x²/9² = 1
y²/64 - x²/81 = 1
So, the standard equation is y²/64 - x²/81 = 1
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Solve four and three-fourths times two and one-third equals blank.
Answers
Answer:
Below
Step-by-step explanation:
This is your posted line:
4 3/4 = 19 / 4
2 1/3 = 7/3
19/4 * 7/3 = (19*7) /(4*3) = 133/12 = 11 1/12
BUT the question in the picture shows
2 4/7 * 2/3 =
18/7 * 2/3 = (18*2) / ( 7*3) = 36/21 = 1 15/21 = 1 5/7
(3x + 4y)³ what is the expand?
Answers
Answer: three x plus 4 y raised to the power of three
Step-by-step explanation:
the product of three consecutive positive integers is $8$ times their sum. what is the sum of their squares?
Answers
the sum of squares of number of 6,7 and 8 is 149.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
the product of three consecutive positive integers is 8 times thier sum.
So if 1st number is x
So the sum will be x+x+1+x+2 = 3x+3
and multiply will be x(x+1)(x+2)
according to question x(x+1)(x+2) = 24(x+1)
x³+3x²+2x = 24x+24
x = 6
So all the numbers will be 6,7 and 8
Hence the sum of their square is 36+49+64= 149
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Two-fifths of your yard is covered with grass. This is equal to what decimal?
Answers
Answer: 0.4
Step-by-step explanation:
Two-fifths is 2/5
If you were to put this into a calculator, you would get 0.4.
If this were to come up in a non-calculator test, I would mentally multiply both the numerator and denominator by 2 to get 4/10, which you can then divide quickly to get 0.4. :)
Margarite wants to take a trip to japan in 8 years. She knows she will need about $4,200. How much should she deposit into an account now that pays 3. 5% interest, compounded daily, to meet her goal? round to the nearest dollar.
Answers
Margarite must deposit $3174 as the principal in her account.
What is meant by compound interest?
The addition of interest to the principal of a loan or deposit is known as compound interest, sometimes known as interest on principal and interest. It occurs when interest is reinvested, added to the lent capital instead of being paid out, or the borrower is required to pay it, resulting in the next period's interest being generated on the principal amount plus any accumulated interest. Finance and economics both use compound interest frequently.
In contrast to simple interest, which does not compound since past interest is not added to the current period's principal, compound interest allows for the accumulation of interest from prior periods.
As given:
42000 dollars are required for the journey to Japan.
Let P be the account's principal deposit.
Interest rates are 3.5% each day, compounded.
The duration is 8 years.
4200=P(1+(3.5/365×100))³⁶⁵⁽⁸⁾
4200=P(1.00009589)²⁹²⁰
4200=P×1.323110
P=4200/1.323110
P=3174.33
≈P=$3174
Therefore, Margarite must deposit $3174 as the principal in her account.
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What is the length of AB?
Answers
By using the fact that all the triangles are equilateral, we will see that AB = 32 units.
What is the length of AB?
Here we have a figure made of equilateral triangles. Remember that all the sides of an equilateral triangle have the same measure.
Now we can see that FE = 16, then with that we can conclude that each segment of two consecutive vertices also measures 16 unints.
Now, we can write AB as:
AB = AD + DB
And we know that:
AD = 16 units
DB = 16 units.
Then:
AB = 16 + 16 = 32 units
That is the length of segment AB.
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Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.What conclusion can they reach based on the above output when they set the significance level to be 0.10?a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.d.Two of the above are correct.e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
Answers
The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above.
So, option e is correct.
What is meant by null hypothesis?
The null hypothesis, often known as H₀, is the assertion that there is no difference between two sets of data or variables under analysis, or that there is no relationship between them. Because there is no underlying causative relationship, the null hypothesis holds that any experimentally detected difference is merely the result of chance; therefore, the name "null."
We can create a z-test hypothesis by assuming that the amount of rain produced by thunderheads follows a distribution that is nearly normal:
300 acre feet is the null hypothesis for the average quantity of rain that thunderheads produce on their own without fertilizing the clouds.
Alternative Hypothesis: The amount of rain that thunderheads often produce by seeding the clouds is greater than 300 acre feet.
This test has a right tail.
So, The conditions are not met by the extreme outliers, hence we are unable to draw inferences based on the statistical output presented above.
So, option e is correct.
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What is a square answer?
Answers
Square may be defined a closed figure having four equal sides.
Within mathematics there are many figures. One of the closed figures is Square. Square is formed when four sides of equal length are enclosed to from a closed figure. It is a two dimensional figure. A square has four vertices as well as four internal angles. All the internal angles of the square are equal and have a value equal to 90°. The opposite sides of a square are equal as well as parallel to each other. The diagonals of the square are equal in length and all the diagonals of square intersect each other at an angle equal to 90°. if a square has length of its side equal to 'a', then the area of the square will be equal to a². The perimeter of the square will be equal to 4a.
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BANKING Vera opened a savings account with $3500 that earns 1.1% simple interest annually. After how many years will the balance of the account be $3827.25? Round to the nearest tenth, if necessary.
Answers
Answer: It will take about 8.5 years for the balance of the savings account to reach $3827.25.
Step-by-step explanation:
To find the number of years it will take for the balance of the savings account to reach $3827.25, we can set up the following equation:
$3500 * (1 + 0.011 * t) = 3827.25$
We can then solve for t, the number of years, by dividing both sides of the equation by 3500 and then rearranging the terms to get t by itself:
$t = \frac{3827.25 - 3500}{3500 * 0.011}$
Next, we can plug in the given values and solve for t to find the number of years it will take for the balance of the account to reach $3827.25:
$t = \frac{3827.25 - 3500}{3500 * 0.011} = \frac{327.25}{38.5} = 8.5$
Therefore, it will take about 8.5 years for the balance of the savings account to reach $3827.25.
If you can buy 2 bags of chips for $125. How many bags of chips can you get with $9,455 dollars? $7,600?
$1,000,000? Use a Ratio, ratio table, or equation to solve.
Answers
Answer:
Step-by-step explanation:
it is 75 and a half
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).
c(x) = 5.50 + 20.50x
c(x) = 5.50x + 20.50
c(x) = 5.50 + 21.60x
c(x) = 5.50x + 21.60
Answers
The linear function (A) c(x) = 5.50 + 20.50x represents the total cost when x tickets are applied.
What is a linear function?
The term "linear function" in mathematics applies to two different but related ideas:
A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
So, c ⇒ the overall expense.
The quantity (x) of tickets
The price of one ticket without a service charge.
The fact that:
108 = 5.50 + 5z
5z = 108 - 5.50
5z = 102.5
z = 102.5/5
z = $20.5
Equating the linear function is:
c(x) = 5.50 + 20.50x
Therefore, the linear function (A) c(x) = 5.50 + 20.50x represents the total cost when x tickets are applied.
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Correct question:
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).
a c(x) = 5.50 + 20.50x
b c(x) = 5.50x + 20.50
c c(x) = 5.50 + 21.60x
d c(x) = 5.50x + 21.60
Select the row of Pascal’s triangle that is used to expand the binomial expression (2x^3+3y^2)^7
Answers
The row of Pascal's triangle required for the binomial expansion is: 1 7 21 35 35 21 7 1
Pascal's triangle is a principle that can be used to expand a given bracket to any given power by the process termed binomial expansion. It can be used to expand brackets to a power starting from zero; but majorly applied when the power is greater than 3.
Now considering the given question, for the binomial expansion of (2x^3+3y^2)^7, the required terms of expansion using Pascal's triangle is:
1 7 21 35 35 21 7 1.
So that the binomial expansion would give;
128x^21 + 1344x^18y^2 + 6048 x^15y^4 + 15120x^12y^6 + 22680x^9y^8 + 20412x^6y^10 + 10206x^3y^12 + 2187y^14
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Is natural numbers closed under addition example?
Answers
Yes, natural numbers are an example of closed under addition.
Natural numbers are closed under addition and also multiplication. The addition of two or more natural numbers results in always a natural number. while for the case of subtraction and division, natural numbers don't obey the closure property, which means dividing or subtracting two natural numbers might not give a natural number. for example, considering two numbers 5 and 7, when we add both of them the result we come up with is 12, which is also a natural number.
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Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint. Let y represent the area (in square meters) left to paint after x hours.
Answers
Slope and a point that is not an intercept is the information about the graph of the relationship is given.
The Painting rate = 8 m²/h
Room area left to paint after 3 hours = 28 square meters . Let y be the area left to paint after x hours in square meters. To describe a point on a graph, we need a corresponding (x,y) pair. In our case , we need information about the rate of change of the relationship between the area left to paint and after the hours. Painting speed of Hiro is 8 square meters per hour. So, the corresponding slope is 8 or equation , Y = 8x --(1)
Y = 28 square meters, substituting this value into the above formula 28 = 8X
=> X = 7/2
which is the point (7/2, 28 ) and not an intercept.
In other words, the point that is not the intersection with the slope.
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Complete question:
Hiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 square meters left to paint. Let y represent the area (in square meters) left to paint after x hours.
Which of the following information about the graph of the relationship is given?
a)Slope and x-intercept
b) Slope and y-intercept
c)X-intercept and y-intercept
d) Y-intercept and a point that is not an intercept
e)Two points that are not intercepts
f)Slope and a point that is not an intercept
Houa and her children went into a grocery store and she bought $9
worth of bananas and peaches. Each banana costs $0.50 and each
peach costs $1.50. She bought a total of 10 bananas and peaches
altogether. Graphically solve a system of equations in order to
determine the number of bananas, x, and the number of peaches, y,
that Houa bought.
Answers
The number of bananas are 6 and the number of peaches are 4.
What is system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
Given:
Hua and her children went into a grocery store and she bought $9
worth of bananas and peaches.
Each banana costs $0.50 and each
peach costs $1.50. She bought a total of 10 bananas and peaches altogether.
Let
B = number of bananas
P = number of peaches
0.5 * B = cost of number of bananas purchased
1.5 * P = cost of number of peaches purchased
So,
B + P = 10 ..(1)
0.5B + 1.5P = 9 ..(2)
From equation (1),
B = 10 - P ..(3)
Plug value of B in equation (2),
0.5(10 - P) + 1.5P = 9
5 - 0.5P + 1.5P = 9
5 + P = 9
P = 4
Plug P = 4 in equation (3)
B = 10 - 4
B = 6
Hence, the number of bananas are 6 and the number of peaches are 4.
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74. At the gym suppose that 10% of adults belong to health clubs, and 40% of these health club members go to the club at least twice a week. What percent of all adults go to a health club at least twice a week?
Write the information given in terms of probabilities,
and use the general multiplication rule.
Answers
The proportion of all adults go to a health club at least twice a week is 4%.
What is percent?
A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.
Given:
At the gym suppose that 10% of adults belong to health clubs, and 40% of these health club members go to the club at least twice a week.
The proportion of adults who belong to health clubs is 10% that is 0.10.
The proportion of these adults (health club members) go to the club at least twice a week is 40%, that is 0.40.
Hence, the proportion of all adults go to a health club at least twice a week is
0.10 × 0.40 = 0.04, that is 4%
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Help me please! I’m struggling
Answers
Answer:
x3+y3+z3=k, with k being all the numbers from one to 100
Step-by-step explanation:
your welcome, hmm i think your brain cells might have been disrupted because of all that tikt.
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Question 14(Multiple Choice Worth 2 points) (Angle Relationships MC) One angle measures 24°, and another angle measures (7d-4)°. If the angles are complementary, what is the value of d? Od=80 Od=17 Od = 10 Od=3
Answers
10 is the value of d.
What is Angle?
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Given that One angle measure is 24°,
Another angle measure is (7d-4)°.
The angles are complementary, We need to find the value of d.
The sum of angles is 90 degrees is called as complementary angles.
24+7d-4=90
20+7d=90
Subtract 20 from both sides
7d=70
Divide both sides by 7
d=10
Hence, the value of d is 10.
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the product of "-1.8" and 3 more than a number as the same as 1 / 10 what is the number
Answers
The product of -1.8 and = -1.8 x ?
3 more than a number = 3 + n
The product of -1.8 and 3 more than a number = -1.8(3 + n)
Is the same as 1/10 = equals (equal sign) 1/10
Full Equation: -1.8(3 + n) = 1/10
Steps to solve:
1. Divide both sides by -1.8 (or - 9/5)
(3 + n) = 1/10 x -5/9
3 + n = -5/90
2. Subtract 3 from both sides
n = -5/90 - 270/90
n = -30 5/9
Hope this helps!