There were 30 families that had a parakeet.
By using the concept of Sets :
- Total number of families surveyed (denoted as N) = 240.
- Number of families with dogs (denoted as D) = 91.
- Number of families with cats (denoted as C) = 70.
- Number of families with both dogs and cats (denoted as D ∩ C) = 31.
- Number of families with neither cats nor dogs nor parakeets (denoted as neither) = 91.
- Number of families with cats, dogs, and parakeets
(denoted as D ∩ C ∩ P) = 7.
We want to find the number of families that had parakeets
(denoted as P).
To find the number of families with parakeets, we can use the principle of inclusion-exclusion. It states that:
N(D ∪ C ∪ P) :
= N(D) + N(C) + N(P) - N(D ∩ C) - N(C ∩ P) - N(D ∩ P) + N(D ∩ C ∩ P).
Substitute the given values:
240 = 91 + 70 + P - 31 - N(C ∩ P) - N(D ∩ P) + 7.
Now, we can calculate the number of families with both cats and parakeets (C ∩ P) and the number of families with both dogs and parakeets (D ∩ P):
C ∩ P + D ∩ P = (C + D + P) - (N(D) + N(C) + N(P)) = 240 - 91 - 70 - P = 79 - P.
From the given information, we also know that the number of families with neither cats nor dogs nor parakeets is 91. Therefore, we can write:
neither + N(D ∩ P) + N(C ∩ P) + N(D ∩ C ∩ P) = 91.
Substitute the values:
91 + N(D ∩ P) + C ∩ P + 7 = 91.
Now, we can solve for C ∩ P:
C ∩ P = 91 - N(D ∩ P) - 7.
Substitute the value of C ∩ P we found earlier:
79 - P = 91 - N(D ∩ P) - 7.
Now, we can find N(D ∩ P):
N(D ∩ P) = 79 - P - 91 + 7 = -P - 5.
However, we know that the number of families cannot be negative. So, we ignore this solution. Instead, we use the previously calculated value of C ∩ P:
C ∩ P = 91 - N(D ∩ P) - 7.
91 - (79 - P) - 7 = 91 - 79 + P - 7 = P - 7.
P - 7 = 30.
Finally, we get the value of P:
P = 30.
Therefore, there were 30 families that had a parakeet.
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Find the complete factorization of the expression.
10xyz + 24xy + 6xz
A) xyz(5 + 12 + 3)
B) 2x(5zy + 12y + 3z)
C) x(10zy + 24y + 6z)
D) 2(5xzy + 12xy + 3xz)
Answer:
B) 2x(5zy + 12y + 3z)
Step-by-step explanation:
First, all coefficient for each term are a pair number, therefor 2 is common factor for all these
[tex]10xyz + 24xy + 6xz=>2(5zxy + 12xy + 3xz )[/tex]
then, the variable X is present for each term of the funtion [tex](5zxy + 12xy + 3xz)[/tex], so, the variable X is a common factor to.
[tex]2(5zxy + 12xy + 3xz )=> 2x(5zy + 12y + 3z )[/tex]
A towns population went from 25.800 to 42,600 in 15 years. What was the percent increase?
Which expression is equivalent to −4.6+(−0.4)+(−7.2) ?
−(4.6−0.4)+(−7.2)
(4.6+0.4+7.2)
−4.6−(0.4+7.2)
(4.6+0.4)+(−7.2)
I took the test it's −4.6−(0.4+7.2)
The expression equivalent to −4.6+(−0.4)+(−7.2) is -4.6 - ( 0.4 + 7.2 )
Here,
The given expression is −4.6+(−0.4)+(−7.2)
We have to find expression equivalent to −4.6+(−0.4)+(−7.2)
What is Number system?
A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
Now,
The given expression is,
−4.6+(−0.4)+(−7.2) = -4.6 - 0.4 - 7.2
= -4.6 - (0.4 + 7.2) ( we take common negative sign )
Hence,
The expression equivalent to −4.6+(−0.4)+(−7.2) is -4.6 - ( 0.4 + 7.2 ).
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What is 0.003 of 1/10 as much as
There is a sales tax of $6 on an item that costs $88 before tax and. The sales tax on a second item is $21. How much does the second item cost before tax
For the past 7 years, George and Sue have deposited $10,000 in a retirement account with a simple interest rate of 4%. They plan to continue to make annual deposits for the next 15 years. Explain how their money will grow over time. Note: You do not need to extend their entire savings for 22 years in your explanation. Focus on the earning for the first several years and explain how their money will grow.
Answer:
George and Sue's money will grow due to both to their contributions and the simple interest that they accrue. Simple interest means that the interest they receive will be applied to the principle, but not the interest that has been accrued. This means that for every $10,000 they put in, they will receive $400 dollars in interest every year, and this number will not change with time.
Right now, they've deposited 10,000 every 7 years for a total of 70,000 dollars. Their annual interest therefore is 400 * 7 = 2800. With every 10,000 dollars they deposit, the yearly interest will grow by $400. This is different from compounding interest, in which annual interest will grow by more than $400 dollars every year since the rate will be applied to principle and all accrued interest.
Step-by-step explanation:
Solve the equation. 6^2x-4=14701 to 4 decimal places. (Doing Logs)
how many shelves will display 2 cars if 8 of the shelves each display 1 car
To determine the number of shelves that will display 2 cars each when 8 shelves display 1 car each, simply divide 8 by 2. The answer is 4 shelves.
To solve this problem, we'll use basic arithmetic. If each of the 8 shelves displays 1 car, then to display 2 cars on a shelf, we would need to combine pairs of shelves. This means we would take the 8 shelves, and divide by 2 cars per shelf to find the number of shelves needed for 2 cars each. So, 8 shelves divided by 2 cars per shelf equals 4 shelves.
Therefore, the answer is that 4 shelves will display 2 cars each if there were originally 8 shelves with 1 car each.
The formula f 5280m can be used to convert a measurement of f feet to an equivalent measurement of m miles. If an airplane flies at 21,120 feet above the ground, how much is that in miles?
4 miles?
5.3 miles?
111,513,600 miles?
132,620,600 miles?
An implicit equation for the plane passing through the point (-1,-4,5) that is perpendicular to the line l(t) = <1+2t,1+t,5+3t> is
Final answer:
The implicit equation of the plane is 2x + y + 3z - 14 = 0, found using the direction vector of the line as the normal vector for the plane and the given point to determine the specific plane equation.
Explanation:
To find an implicit equation for the plane passing through the given point (-1,-4,5) and perpendicular to the given line, we need to determine the direction vector of the line which will also serve as the normal vector to the plane. The equation of the line is given as l(t) = <1+2t, 1+t, 5+3t>, which suggests that the directional vector of the line (and thus the normal vector of the plane) is <2, 1, 3>.
Now, the general equation of a plane in 3D space can be given by Ax + By + Cz + D = 0, where <A, B, C> is the normal vector to the plane. Thus, substituting the normal vector and the given point into this equation will allow us to find the value of D and hence the implicit equation of the plane. In this case, the equation is given by:
2(x + 1) + 1(y + 4) + 3(z - 5) = 0, simplifying this gives:
2x + y + 3z - 14 = 0,
which is the implicit equation of the desired plane.
Final answer:
The implicit equation of the plane passing through the point (-1, -4, 5) and perpendicular to the line ℒ(t) is 2x + y + 3z - 9 = 0.
Explanation:
To find an implicit equation for a plane that is perpendicular to a given line, we first need the direction vector of the line. The line ℒ(t) = <1+2t, 1+t, 5+3t> has a direction vector of <2, 1, 3>, which also serves as the normal vector of the plane. The normal vector (A, B, C) and a point (x0, y0, z0) on the plane can provide an equation via the dot product: A(x - x0) + B(y - y0) + C(z - z0) = 0.
For the given point (-1, -4, 5), the equation becomes 2(x + 1) + 1(y + 4) + 3(z - 5) = 0. Simplifying, we get:
2x + 2 + y + 4 + 3z - 15 = 0
2x + y + 3z - 9 = 0
This is the implicit equation of the plane that passes through the point (-1, -4, 5) and is perpendicular to the given line.
A high rise building has a sink on the fourth floor located 2-feet above the floor. Each floor is 10-feet above the other. Calculate the psi at the sink where when the street pressure is 80 psi. The building does not have a pressure reducing device due to fire codes.
Kira is saving money to buy a bike that costs $133 . She has $42 and will save an additional $7 each week. In how many weeks will she have enough money to buy the bike?
how do I set up 37 and 43
2w-5w=27 can you tell me how to solve this to where I can understand
Recall that you can use the built-in functions rem(m,n) or mod(m,n)to find the remainder of the division m/n.
The 'rem(m, n)' and 'mod(m, n)' methods in mathematics provide the remainder of the division operation m / n. When dealing with numbers in exponential form, you divide the base numbers and subtract the exponents to simplify the terms. An understanding of these operations is essential for solving more complex equations.
Explanation:In mathematics, there are two ways to find the remainder of a division operation: rem(m,n) or mod(m,n). These functions take two numbers m and n, and return the remainder when m is divided by n.
For example, in the case of 106 divided by 103, you would first divide the 'base' numbers (10/10) which equals 1, and then subtract the exponents (6-3) which equals 3. So, the result is 103 or 1000. Another example is 4.5 x 109 divided by 103. Here, first you divide 4.5 by 1 (since 10/10 = 1) and then subtract 9-3 equals 6. Therefore, the answer is (4.5) x 106.
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what is 75% of 400? Write an evaluate an expression to find the answer. Then explain how to use the model to justify the answer
Answer:
Step-by-step explanation: love your self
64 is 55% of what number
The distance to the first delivery is 12 1/3miles. The distance between the next three delivery is is 8 3/4 miles, 17 2/8 miles, and 23 2/3 miles respectiviely. The distance from the final delivery to the shop is 10 5/10 miles. What is average distance for all segments of this trip?
What is 0.650 , 0.065 , 0.605 , 0.560 in least to greatest
Jim is helping his dad cook hamburgers for his family and friends. There are 15 people. Each person wants two hamburgers. Three people want hamburgers with cheese. Two people want hamburgers with mustard. Two people want hamburgers with catsup. The rest want them plain. How many plain hamburgers will Jim and his dad make?
A: 8
B:16
C:21
D:23
The number of people who do not want plain hamburgers is 3+2+2 = 7, so 15-7 = 8 people want plain hamburgers. Each person wants 2 hamburgers, for a total of ...
... B: 16
plain hamburgers.
Jim and his dad will make 23 plain hamburgers.
Explanation:To find the number of plain hamburgers Jim and his dad will make, we need to subtract the number of hamburgers with special toppings from the total number of hamburgers. There are 15 people in total, and each person wants 2 hamburgers, so Jim and his dad need to make 15 x 2 = 30 hamburgers in total.
Out of the 30 hamburgers, 3 people want hamburgers with cheese, 2 people want hamburgers with mustard, and 2 people want hamburgers with catsup. Therefore, the total number of hamburgers with special toppings is 3 + 2 + 2 = 7 hamburgers.
Subtracting the number of hamburgers with special toppings from the total number of hamburgers, we get 30 - 7 = 23 plain hamburgers. Therefore, Jim and his dad will make 23 plain hamburgers.
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Students in a class were asked to name their favorite flavor of ice cream. The results are shown in the circle graph. How many times more students prefer cookies and cream than prefer strawberry?
Cookies and Cream: 18%
Strawberry: 2%
Cookie Dough: 35%
Vanilla: 25%
Chocolate Chip: 20%
Answer: 9 times
Step-by-step explanation:
Let the total number students be x.
Then the number of students liked cookies and cream = 18% of x= 0.18 x
The number of strawberry = 2% of x = 0.02 x
Clearly, 0.18 x> 0.02 x
The number of times more students prefer cookies and cream than prefer strawberry =[tex]=\frac{0.18x}{0.02x}=9[/tex]
Hence, The students prefer 9 times cookies and cream than prefer strawberry.
I am having difficulty solving this problem
Square EFGH has vertices: E = (-1,1), F = (-1,2), G = (-2,1), H = (-2, 2). In which quadrant will the image of vertex E' be if the square is rotated 270° clockwise about the origin O?
Answer:
Quadrant III
Step-by-step explanation:
Did this lesson, just checked the answer key.
the shop has 1260 ounces of cranberry juice and 650 ounces of passion fruit juice.ifvthe juices are used to make crazy cranberry smoothies, which juice will run out first?how much of the other juice will be left over?
figure ABCD is a rectangle with point A (-2, 5). What rule would rotate the figure 90 degree clockwise?
the difference of 9 and the square of a number
0.06 is 10 times as much as 0.600
What is 225 percent as a decimal or fraction in simpilist form
i have forgotten how to share a number into ratio!! help please!
The price of stamps just increased by $0.03. Beth wants to send out 30 party invitations. Write a formula that will help her determine how much it will cost. Let’s let p=old price per stamp
t=total cost for stamps