In a group of 31 students, 7 study both Art and Biology.
14 study Biology but not Art.
7 study neither subject.
Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
Answers
Answer:
7/10 or 0.7 or 70%
Step-by-step explanation:
I would use a venn diagram, and fill it in! Then there are 7 do A &B and 3 who just do A. That as a probaility, your answer!
Related Questions
If sin = 2/5, what is csc ? (Answer must be in fraction form)
Answers
Answer:
csc x = \(\frac{5}{2}\)
Step-by-step explanation:
using the identity
csc x = \(\frac{1}{sinx}\)
then
csc x = \(\frac{1}{\frac{2}{5} }\) = \(\frac{5}{2}\)
write a rule for the nth term of geometric sequence a1= 3 and r= 1/2
Answers
The formula for the n-th term is:
aₙ = 3*(1/2)⁽ⁿ⁻¹⁾
How to find the rule for the n-th term?For a geometric sequence where the first term is a₁ and the common ratio is r, the formula for the n-th term is:
aₙ = a₁*(r)⁽ⁿ⁻¹⁾
Here we know that the first term is a₁ = 3 and the common ratio is r = 1/2.
Then the formula for the n-th term of the sequence is:
aₙ = 3*(1/2)⁽ⁿ⁻¹⁾
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Given: BC bisects EBA. m EBC = 62°.
Sketch a picture of this situation, then use your picture to find each angle measure.
Draw and label a picture (required)
Find each angle measure.
(No work needs to be shown.)
m2 EBC = 62°
mZEBA =
m2 CBA =
Answers
Answer:
m∠EBC = 62°
m∠EBA = 124°
m∠CBA = 62°
Step-by-step explanation:
It's given in the question that a line BC bisects angle EBA.
And m∠EBC = 62°
Since, BC is an angle bisector of ∠EBC,
Therefore, m∠EBC = m∠CBA = 62°
Since, m∠EBA = 2(m∠EBC)
Therefore, m∠EBA = 2 × 62° = 124°
Help plz really important
Answers
Answer:
No because they although have the same shape but they have different sizes
Step-by-step explanation:
Two water balloons were launched into the air at different moments and collided. The water balloons were modeled by the quadratic functions: y = −7x2
Answers
The quadratic function y = -7x² represents the trajectory of one of the water balloons. Since it is a quadratic function, it forms a parabola. The coefficient of x², -7, determines the shape of the parabola.
Since the coefficient is negative, the parabola opens downwards.
The x-axis represents time, and the y-axis represents the height of the water balloon. The vertex of the parabola is the highest point the water balloon reaches before falling back down. To find the vertex, we can use the formula
x = -b/2a.
In this case,
b = 0 and a = -7.
Thus, x = 0.
So, the water balloon reaches its highest point at x = 0.
Plugging this value into the equation, we find that y = 0.
Therefore, the water balloon starts at the ground, reaches its highest point at x = 0, and then falls back down.
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Since the quadratic functions for the two water balloons are identical, the collision happens at all moments. The water balloons collide at every height and time, forming a continuous collision.
The quadratic function \(y = -7x^2\) represents the height (y) of a water balloon at different moments (x). When two water balloons collide, it means their heights are equal at that particular moment. To find when the collision occurs, we can set the two quadratic functions equal to each other:
\(-7x^2 = -7x^2\)
By simplifying and rearranging, we get:
0 = 0
This equation is always true, which means the water balloons collide at every moment. In other words, they collide continuously throughout their trajectory.
In conclusion, since the quadratic functions for the two water balloons are identical, the collision happens at all moments. The water balloons collide at every height and time, forming a continuous collision.
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A restaurant has 9 3/5 pounds of onions. The restaurant's manager ordered 4 4/5 more pounds of onions. The onions then were mixed and kept in 2 baskets with each basket having equal pounds on onions. How many pounds of onions does each basket contain?
Answers
Answer:
7 1/5 pounds in each basket
Step-by-step explanation:
Original pounds of onion = 9 3/5
New pounds of onion = 4 4/5
The onions then were mixed and kept in 2 baskets with each basket having equal pounds on onions
Total onions = Original pounds of onion + New pounds of onion
= 9 3/5 + 4 4/5
= 48/5 + 24/5
= 48+24/5
= 72 / 5 pounds
How many pounds of onions does each basket contain?
Pounds in each basket = Total pounds /2 basket
= 72/5 ÷ 2
= 72/5 × 1/2
= 72 / 10
= 7 2/10
= 7 1/5 pounds in each basket
Mrs. Walters drove 360 miles on 25 gallons of gas. Mr. Walters drove 480 miles on 32 gallons of gas.
b. Find the mileage per gallon for Mr. Walters's car.
Please explain how you got this answer
Answers
Answer:
Mr.Walters car can go 15 miles on one gallon of gas.
Step-by-step explanation:
To find this, you first want to put it into a ratio.
480:32
Next, you want to divide.
480/32
After you divide, you get 15. That tells you that you get 15 miles off of one gallon of gas.
Answer:
15 miles
Step-by-step explanation:
Answer the following problem using the SOLVE Method Math Club members are selling Math club members are selling Pi Day T-shirts for $7.50 each. The goal is to raise $500 by Friday. The figure below shows how much they have raised by Wednesday. What is the minimum number of T-shirts they must still sell in order to reach their goal? Explain your reasoning.
Answers
The minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts
Let x represent the number of Pi Day T-shirts sold.
They are selling Pi Day T-shirts for $7.50 each, So to raise $500:
7.5x > 500
Dividing through by 7.5:
7.5x / 7.5 > 500 / 7.5
x > 66.7
Hence, the minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts
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Is it possible for polygon ABCDE to be dilated to figure VWXYZ? Explain yourreasoning.
Answers
In the given figures, ratio of all corresponding sides are
\(\frac{1}{2}\)Except the ratio of AE and VZ
\(\begin{gathered} \frac{AE}{VZ}=\frac{10}{12} \\ =\frac{5}{6} \\ \ne\frac{1}{2} \end{gathered}\)Hence, the polygon ABCDE can't be dilated to VWXYZ because ratio of corresponding sides are not equal.
So, the correct answer is (C)
During the past five years, you owned two stocks that had the following annual rates of return: Year Stock T Stock B 1 0.18 0.10 2 0.12 0.03 3 -0.05 -0.10 4 -0.02 0.02 5 0.12 0.06 Compute the arithmetic mean annual rate of return for each stock. Round your answers to one decimal place. Stock T: % Stock B: % Which stock is most desirable by this measure? -Select- is more desirable because the arithmetic mean annual rate of return is -Select- . Compute the standard deviation of the annual rate of return for each stock. (Use Chapter 1 Appendix if necessary.) Do not round intermediate calculations. Round your answers to three decimal places. Stock T: % Stock B: % By this measure, which is the preferable stock? -Select- is the preferable stock. Compute the coefficient of variation for each stock. (Use the Chapter 1 Appendix if necessary.) Do not round intermediate calculations. Round your answers to four decimal places. Stock T: Stock B: By this relative measure of risk, which stock is preferable? -Select- is the preferable stock. Compute the geometric mean rate of return for each stock. Round your answers to three decimal places. Stock T: % Stock B: %
Answers
The arithmetic mean annual rate of return for each stock is as follows:
- Stock T: 6.6%
- Stock B: 4.2%
Based on the arithmetic mean annual rate of return, Stock T is more desirable because it has a higher average return compared to Stock B.
To calculate the standard deviation of the annual rate of return for each stock, we can use the following steps:
1. Calculate the difference between each annual return and the mean return for that stock.
2. Square each difference obtained in step 1.
3. Calculate the average of the squared differences.
4. Take the square root of the average obtained in step 3.
After performing these calculations, we find the standard deviations for each stock:
- Stock T: 7.583%
- Stock B: 5.067%
By this measure, Stock B is the preferable stock since it has a lower standard deviation, indicating lower volatility compared to Stock T.
The coefficient of variation for each stock is calculated by dividing the standard deviation by the mean and multiplying by 100. The formula is:
Coefficient of Variation = (Standard Deviation / Mean) * 100
Calculating the coefficient of variation for each stock, we get:
- Stock T: 114.924%
- Stock B: 120.641%
By this relative measure of risk, Stock T is the preferable stock since it has a lower coefficient of variation, indicating relatively less risk compared to Stock B.
Finally, to calculate the geometric mean rate of return for each stock, we multiply all the annual rates of return together and take the nth root, where n is the number of years. The formula is:
Geometric Mean = (1 + r1) * (1 + r2) * ... * (1 + rn)^(1/n) - 1
Calculating the geometric mean rate of return for each stock, we find:
- Stock T: 2.84%
- Stock B: 1.91%
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Help thanks Thanks Thanks 2 systems of equation for each one of them
Answers
We need to give an example of 2 systems of linear equation where we have 0 solution, 1 solution and infinitely many solution. Then we will provide an explanation to determine each of them without graphing.
Example for 1 solution:
\(\begin{gathered} 2x\text{ + y = 4 . . .\lparen1\rparen} \\ 3x\text{ + y = 6 . . .\lparen2\rparen} \end{gathered}\)To ascertain the two linear equations give one solution, we will have a value for x
Subtract equation (1) from (2):
\(\begin{gathered} 3x\text{ - 2x + y - y = 6 - 4} \\ x\text{ + 0 = 2} \\ x\text{ = 2} \\ Since\text{ there is a value for x, it is one solution} \end{gathered}\)Example for 0 solution:
\(\begin{gathered} 3x\text{ - y + 5 = 0 . . . \lparen1\rparen} \\ \text{3x - y + 7 = 0 . . .\lparen2\rparen} \end{gathered}\)To determine 0 solution system of linear equations, when we solve for the variable the left hand side will not be equal to the right hand
solving the above linear equation:
\(\begin{gathered} 3x\text{ - y + 5 = 0 . . . \lparen1\rparen, 3x - y + 7 = 0 . . .\lparen2\rparen} \\ Rewriting:\text{ }3x\text{ + 5 = y \lparen1\rparen, 3x + 7 = y} \\ Equate\text{ bot equations: y = y} \\ 3x\text{ + 5 = 3x + 7} \\ collect\text{ like terms:} \\ 3x\text{ - 3x + 5 = 7} \\ 0\text{ + 5 = 0 + 7} \\ 5\text{ = 7} \\ left\text{ hand side is not equal to right hand side \lparen the values contradict each other\rparen} \end{gathered}\)Example of infintely many solutions:
\(\begin{gathered} 2y\text{ + x = 1 . . . \lparen1\rparen} \\ 6y\text{ +3 x = 3 . . .\lparen2\rparen} \end{gathered}\)To determine that the solution is infinitely many solutions, the left hand side will be equal to right hand side.
\(\begin{gathered} 2y\text{ + x = 1 . . . \lparen1\rparen} \\ 6y\text{ +3 x = 3 . . .\lparen2\rparen} \\ from\text{ equation \lparen1\rparen, x = 1 - 2y} \\ substitute\text{ for x in equation \lparen2\rparen:} \\ 6y\text{ + 3\lparen1 - 2y\rparen = 3} \\ 6y\text{ + 3 - 6y = 3} \\ 3\text{ = 3} \\ left\text{ hand side = right hand side} \end{gathered}\)Behaviour of the solution of the system of equations when graphed:
For a system of 2 linear equations with 1 solution:
The lines will intersect at a point. The point of intersection is 1 and it will be the solution of the system of equations
For a system of 2 linear equations with 0 solution:
The lines from both equations will be parallel to each other. Indicating the lines do not intersect. Hence, there is no solution
For a system of 2 linear equations with infinitely many solutions:
Both equation will give same line when graphed. So, the solution will be infinitely many
Solve for x: 8(3x-6)=6(4x+8)
Answers
Answer: there are no values of x that make the equation true .
So the answer is there is: No solution
Step-by-step explanation:
Factor by grouping plz show steps!
Answers
Answer:
Step-by-step explanation:
4y(y^2+6)+7(y^2+6)
answer:(4y+7)(y^2+6)
Explain the mathematical expression of the first law of thermodynamics for any state.Discuss the physical meaning of each term in an explicit form of it.Then,deduce the explicit form of energy balance equation for the following scenarios by drawing appropriate schematics.
Answers
The first law of thermodynamics, mathematically expressed as:
ΔU = Q - W
Where:
ΔU represents the change in internal energy of the system,
Q represents the heat added to the system, and
W represents the work done by the system.
The first law of thermodynamics, also known as the law of energy conservation, states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.
The term "internal energy" (ΔU) refers to the total energy possessed by the system, including the kinetic and potential energy of its molecules. It is a measure of the system's thermal energy.
The term "heat" (Q) represents the transfer of energy between the system and its surroundings due to temperature difference. It is a form of energy transfer that occurs spontaneously from higher temperature regions to lower temperature regions.
The term "work" (W) represents the energy transfer resulting from forces applied to the system, causing displacement. It can take different forms, such as mechanical work, electrical work, or expansion work.
For different scenarios, the explicit form of the energy balance equation can be derived by considering the specific types of work and heat involved in the system. By drawing appropriate schematics, one can identify the relevant forms of work and heat transfer. Examples include:
Adiabatic Process: In this scenario, no heat transfer occurs (Q = 0). The energy balance equation simplifies to ΔU = -W, where the work done by the system contributes to the change in internal energy.
Isothermal Process: In this case, the temperature remains constant (ΔU = 0). The energy balance equation becomes Q = W, indicating that the heat added to the system is fully converted into work.
Isobaric Process: Here, the pressure remains constant. The energy balance equation can be written as ΔU = Q - PΔV, where P is the constant pressure and ΔV is the change in volume. This equation accounts for both heat transfer and work done against the constant pressure.
Therefore, by applying appropriate schematics and considering the specific conditions of a given scenario, one can deduce the explicit form of the energy balance equation and understand the interplay between heat, work, and the change in internal energy.
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62+41+(2)+(4) what is the answer to this
Answers
Answer:
109.
Step-by-step explanation:
62+41+(2)+(4) we can remove the brackets:
= 62 + 41 + 2 + 4
= 109.
a rotating sprinkler can reach up to 14 feet through a 300 degree angle. find the total area covered by the sprinkler in one sweep. round to the nearest tenth. What is the area of the lawn, to the nearest square foot, that receives water from this sprinkler?
Answers
In one sweep, the area covered by the sprinkler is 77.19 sq ft (approx). The area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).
We know that a rotating sprinkler can reach up to 14 feet through a 300-degree angle. Area covered by the sprinkler in one sweep = area of the sector whose radius = 14 feet and angle = 300°Area of sector = (θ / 360) × πr²Where θ = 300°, r = 14 ftArea of sector = (300/360)× π(14)²= 77.19 sq ft (approx) Therefore, the area covered by the sprinkler in one sweep is 77.19 sq ft (approx).
We need to find the total area of the lawn that receives water from this sprinkler. The sprinkler rotates 360 degrees, so it will cover a full circle whose radius is 14 feet. Area of a circle = πr²= π(14)²= 615.752 sq ft (approx) Therefore, the area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).
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A meteorologist says that there is a 50% greater chance of rain than no rain on Wednesday. What is the probability that it will rain on Wednesday?
Answers
Answer:
2/3
Step-by-step explanation:
The probability that it will rain on wednesday will be 0.75.
What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -
P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes.
We have a meteorologist who says that there is a 50% greater chance of rain than no rain on Wednesday.
Assume that the probability that it will rain on wednesday be [x]. Now, we can write -
P[R] = P[N.R.] + 1/2
P[R] + P[R] = P[N.R.] + P[R] + 1/2
2 P[R] = 1 + 1/2
2 P[R] = 1.5
P[R] = 1.5/2
P[R] = 0.75
Therefore, the probability that it will rain on wednesday will be 0.75.
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Isla has 225 trading cards and Lily has 180 trading cards. a) Calculate the number of Isla's trading cards as a percentage of the number of Lily's trading cards. b) Calculate the number of Lily's trading cards as a percentage of the number of Isla's trading cards. Give your answers to the nearest 1%.
Answers
(a) Isla's trading cards are 125% of Lily's trading cards.
(b) Lily's trading cards are 80% of Isla's trading cards.
Given that,
There are 225 trading cards and Lily has 180 trading cards.
To calculate the percentage of Isla's trading cards compared to Lily's,
We can use this formula:
⇒ Isla's trading cards / Lily's trading cards x 100%
Plugging in the values we get:
⇒ (225 / 180) x 100% = 125%
Therefore,
Isla's trading cards are 125% of Lily's trading cards.
b) To calculate the percentage of Lily's trading cards compared to Isla's, we can use the formula:
⇒ Lily's trading cards / Isla's trading cards x 100%
Plugging in the values we get:
(180 / 225) x 100% = 80%
Therefore,
Lily's trading cards are 80% of Isla's trading cards.
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help asappppppppppppp
Answers
Answer:
113 degrees
Step-by-step explanation:
2 and 7 are equal, so 0 and 2 will equal the same as 3 and 7, and both equal 180... Do 180-67=113
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EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
What is the coefficient of the third term in this expression?
–k2n+5mn3–9n3–m3n
Answers
Answer:
27
Step-by-step explanation:
9x3 is 27. Coefficient is the number in the term.
In art class students are mixing blue and red paint to make purple paint. Hawa mixes 1 cup of blue paint and 5 cups of red paint. Jacob mixes 4 cups of blue paint and 13 cups of red paint. Use Hawa and Jacob’s percent of red paint to determine whose purple paint will be redder.
Hawa percent of red paint (to nearest whole number) =
%
Jacob percent of red paint (to nearest whole number) =
%
Hawa ’s purple paint will be redder.
Jacob’s purple paint will be redder.
The two purple paints will be equally red.
attempt 1 out of 2
Miracle Jackson
Which is more? (Percent Comparison)
Apr 10, 6:51:14 PM
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In art class students are mixing blue and red paint to make purple paint. Hawa mixes 1 cup of blue paint and 5 cups of red paint. Jacob mixes 4 cups of blue paint and 13 cups of red paint. Use Hawa and Jacob’s percent of red paint to determine whose purple paint will be redder.
Answers
Answer:
Step-by-step explanation:
Please help me! Thank you in advance!
Answers
Answer: 16
Step-by-step explanation:
The diameter of the circle is the length of the square as well meaning the area of the square is 4 x 4 = 16
A number line going from negative 5 to positive 5. Which of the following statements is true when comparing numbers using a number line? The number closest to zero is always the least. The number farthest from zero is always the greatest. The number farthest right is always the least. The number left is always the least.
Answers
1: The number closest to zero is not always the least.
2: The number farthest from zero is not always the greatest.
3: The number farthest right is not always the least.
4: The number left is always the least.
The first statement, "The number closest to zero is always the least," is not necessarily true.
It depends on whether the numbers being compared are positive or negative.
For example, -2 is closer to zero than -4, but it is actually greater than -4.
The second statement, "The number farthest from zero is always the greatest," is also not necessarily true.
Just like the first statement, it depends on whether the numbers being compared are positive or negative.
For example, -5 is farther from zero than -3, but -3 is actually greater than -5.
The third statement, "The number farthest right is always the least," is definitely not true.
The direction of the number line (left or right) has nothing to do with whether a number is greater or lesser than another number.
That leaves us with the fourth statement, "The number left is always the least."
This statement is true! On a number line going from negative to positive numbers, the numbers to the left of zero (the negative numbers) are always less than the numbers to the right of zero (the positive numbers).
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Pablo decide ahorrar su dinero en una alcancía y cada día ahorra $100 más que el día anterior ¿cuánto ahorraría el día "20" si el primer día tenía $100? Expresa la función y resuelve
Answers
Answer:
Pablo decides to save his money in a piggy bank and each day he saves $ 100 more than the day before. How much would he save on day "20" if he had $ 100 on the first day? Express the function and solve
Step-by-step explanation:
(8x²+4) + (-x² -3x)
solve this
Answers
i think this is the answer
Divide 2.875 x 106 by 2.3 x 103.
Answers
Answer:
1.25 x 10^3
Step-by-step explanation:
i took the test
Answer these in true or false
Answers
Answer: True, False, False
Step-by-step explanation:
Answer:
8. true
9. false
10. false
Three scoops of whey powder contain 45 grams of protein. How many scoops of whey powder contain 135 grams of protein?
Answers
Answer:
9 scoops
Step-by-step explanation:
3 scoops = 45g
3/45 scoops = 1g
3/45*135 scoops = 135g = 9 scoops
the shapes of the curves in the as/ad model are based upon the:
Answers
The shapes of the curves in the AS/AD (Aggregate Supply/Aggregate Demand) model are based upon the relationship between the price level and the output level in an economy.
The AD curve shows the relationship between the overall price level and the quantity of goods and services demanded by all buyers in an economy. It has a negative slope, indicating that as the price level increases, the quantity of goods and services demanded decreases.
The AS curve shows the relationship between the overall price level and the quantity of goods and services that firms are willing and able to supply. In the short run, the AS curve is upward sloping, indicating that as the price level increases, firms are willing to supply more output due to higher profits. In the long run, the AS curve becomes vertical, indicating that the level of output is determined by the factors of production and technology, not the price level.
Thus, the shapes of the curves in the AS/AD model are based on the behavior of buyers and sellers in an economy and their response to changes in the overall price level.
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9. (X + 8)^2 - 5 = 0
Answers
Answer:
x + 59 = 0
X= -59
Step-by-step explanation: