At the city park there were 15 blue jays, 6 cardinals, and 9 mockingbirds. For each of the following questions set up a proportion equation and solve for the unknown. 1. If there were 6 mockingbirds, how many cardinals would there be at the park? 2. If there were 5 blue jays, how many cardinals would there be at the park? 3. If there were 20 cardinals, how many mockingbirds would there be at the park?
Which of the following functions are homomorphisms?
what is the 3sqaure root of 0.027y^9 = ?
What is the factorization of 49b2 − 81? (7b – 9)(7b – 9) (7b – 9)(7b + 9) (7b2 – 9)(7b2 – 9) (7b2 – 9)(7b2 + 9)
The factorization of 49b² - 81 using the difference of squares formula is (7b - 9)(7b + 9).
Explanation:The question is asking to factorize the expression 49b² - 81, which is a difference of two squares. The difference of squares formula is a² - b² = (a - b)(a + b). In your question, a² is 49b² and b² is 81. Therefore, a would be 7b (since square root of 49b² is 7b) and b would be 9 (since square root of 81 is 9).
Thus, using the formula, the factorization of 49b² - 81 will be (7b - 9)(7b + 9). This provides an explanation of the concepts involved and the steps followed in the solution.
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For a certain bathtub, the hot water faucet can fill the tub in 13 minutes. The cold water faucet can fill the tub in 12 minutes. If both faucets are used together, how long will it take to fill the tub?
It will take approximately 6.24 minutes for both faucets to fill the bathtub when used simultaneously.
To solve this problem, we need to find the combined rate at which both faucets can fill the bathtub. The hot water faucet can fill the tub in 13 minutes, and the cold water faucet can fill it in 12 minutes. We can express their rates as fractions of the tub they can fill per minute as 1/13 and 1/12, respectively.
When we add these rates together, we get the combined rate:
Rate of hot water faucet + Rate of cold water faucet = combined rate
1/13 + 1/12 = (12 + 13) / (13 imes 12) = 25 / 156
The combined rate is 25/156 tubs per minute. To find out how long it will take for both faucets to fill the tub together, we take the reciprocal of the combined rate:
Time to fill the tub = 1 / (combined rate) = 156 / 25 = 6.24 minutes
Therefore, it will take approximately 6.24 minutes for both faucets to fill the bathtub when used simultaneously.
A model for the population in a small community after t years is given by P(t)=P0e^kt.
a)If the initial population doubled in 5 years, how long will it take to have tripled its initial population?
b)In addition, if the population of the community is 10,000 in 3 years, what was its initial population?
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A middle-school band holds a car wash to raise money. The sixth-grade band members wash 16 cars. The seventh-grade band members wash 75% as many cars as the sixth-graders. The eighth-grade band members wash half as many cars as the sixth- and seventh-grade band members combined.
If the band charges $5 per car, how much money did the members raise altogether?
write words to match the expression
3+(4×12)
Find the mean of the given set of numbers. 3, 3, 8, 6, 7, 3
Algebraically determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, the origin or has no symmetry.
Final answer:
Algebraically, the relation y = x^3 - 4x is not symmetric to the x-axis or y-axis but is symmetric with respect to the origin when both x and y are replaced with their negatives.
Explanation:
To determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, or the origin, we perform a series of tests substituting -x for x (to test y-axis symmetry), -y for y (to test x-axis symmetry), and both -x for x and -y for y (to test origin symmetry).
Y-axis symmetry test:
Replace x with -x:
y = (-x)3 - 4(-x)
y = -x3 + 4x ≠ x3 − 4x (not symmetric to y-axis)
X-axis symmetry test:
Replace y with -y:
-y = x3 - 4x ⇒ y = -x3 + 4x ≠ x3 − 4x (not symmetric to x-axis)
Origin symmetry test:
Replace both x with -x and y with -y:
-y = (-x)3 - 4(-x)
-y = -x3 + 4x
y = x3 − 4x (symmetric to origin)
Will the standard form 3.2 × 10^–4 be more or less than 1? Explain what effect the negative exponent has.
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Costumers can pick their own berries at the gooseberry farm....
Simplify 7x+3y-2+6x-1-y^2
Write an equation of a line that does not have a y intercept
What is 4 - ( -h ) = 68?
100.6 - 30.06 show me it in vertically form (show work)so I can understand how to regroup it.
To vertically subtract 30.06 from 100.6, start by borrowing 1 from the tens place and adding it to the ones place. Then, borrow 10 from the hundreds place and add it to the tens place. Finally, combine the result to get 70.54.
Explanation:To vertically subtract 30.06 from 100.6, you'll need to line up the decimal points vertically. Start by subtracting the hundredths place (0.06) from the hundredths place (0.00). Since 6 is bigger than 0, you'll need to regroup. Borrow 1 from the tens place by making it 9, and add it to the ones place, making it 10. Then, you can subtract 6 from 10, which gives you 4. Next, subtract the whole number part (30) from the whole number part (100). Since 0 is smaller than 3, regroup again by borrowing 10 from the hundreds place and adding it to the tens place, making it 20. Then, subtract 3 from 10, which gives you 7. Finally, combine the result by placing the decimal point in the correct position, which gives you the answer: 70.54.
Javier By 48 cards at a yard sale. Of the cards 3/8 were basketball cards how many cards were baseball card
A television game has 6 shows doors, of which the contests must pick 2. behind two of the doors are expensive cars, and behind the other 4 doors are consolation prizes. Find the probability that the contestant wins exactly 1 car? no car? or atleast one car?
what if they had to pick 3 doors? and all of the other information wast the same
The sum of three numbers is 45 the second of the three numbers is three more than twice the first number, ×. The thurd number is two more than the first number, ×. Which equation can be used to solve the first number
Answer:
Step-by-step explanation:
We know that the 1st equation + 2nd equation + 3rd equation = 45. Now we just need to identify from the infor given what these equations are, then set them to equal 45.
It has already been determined that the 1st equation is x.
The second equation is "3 more than twice the first". Twice the first is 2x, and 3 more is +3; therefore, the second equation is: 2x + 3.
The third equation is "2 more than the first". 2 more than is +2, so the third equation is x + 2.
Now we have all 3:
1st: x
2nd: 2x + 3
3rd: x + 2
Add them all up and set them equal to 45:
x + 2x + 3 + x + 2 = 45.
You don't have choices listed, so it's either that one above, or simplified down to:
4x + 5 = 45
After that, any simplification done will be solving the equation.
Higher order thinking if 1/2 is multiplied by 1/2 will the product be greater than half explain
Estimate how many times larger 7 x 10^10 is than 13 x 10^8. A.50 B.100 c.200 d.400
the formula of the area of a triangle is A=1/2bh what is the length of the base if the area is 22cm and the height is 8cm
Number of solutions to equations -2+10+7z=16z+7
The given equation resulting in one solution, which is z = 1/9.
To find the number of solutions to the equation -2 + 10 + 7z = 16z + 7, we first simplify and solve for z. Start by combining like terms on the left side:
-2 + 10 = 8, so the equation becomes 8 + 7z = 16z + 7.
Next, we get all the terms with z on one side and the constants on the other:
Subtract 7z from both sides:
8 = 16z - 7z + 7
Combine z terms:
8 = 9z + 7
Subtract 7 from both sides:
1 = 9z
Divide both sides by 9:
z = 1/9
Describe two situations in which opposite quantities combine to make zero
In the situation, x + (-x) is combined making zero and other y + (-y) is making zero.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.
Summation = addition of two or more numbers or variable
Subtraction = Minus of any two or more numbers with each other called subtraction.
Division = divide any two numbers or variable called division.
Multiplication = to multiply any two or more numbers or variables called multiplication.
If we combine any two opposite quantities then their summation must be zero.
For example,
if you combine 5 and -5 then it will be 0.
If you combine 10 and -10 then it will be 0.
So,
The first situation ⇒
Combining x and -x
x + (-x) = 0
The second situation ⇒
Combining y and -y
y + (-y) = 0
Hence, In the situation, x + (-x) is combined making zero and other y + (-y) makes zero.
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Kristin jogs around a park that has a perimeter of 12 mile. Kristin jogged around the park 4 times in 50 minutes.
What is the unit rate of Kristin's speed?
12 *4 = 48 total miles in 50 minutes
48 / 50/60 = 57.6 miles per hour
Kyra typed 140 words in 5 minuets. Then, she typed 196 words in 7 minutes. Was her rate of words per minute constant? If so, what is the constant of proportionality?
Simplify (4.5)(5)(−2).
A running cheetah begins to slow down. For each meter the cheetah travels, its speed changes by −3.4 kilometers per hour. The cheetah travels a total of 21.5 meters.
What is the total change in the cheetah's speed during this time?
Drag and drop the correct answer into the box.
73.1.
71.9.
-71.9.
-73.1.
Where is the hole for the following function located? mc005-1.jpg
The holes of the graph are located at (5, 3) and (-1, 11)
How to determine the hole of the graph
From the question, we have the following parameters that can be used in our computation:
The graph
The holes of the graph are at (5, 3) and (-1, 11)
This is so because the function is not defined at this value
Also, we can see that
The function has it vertical asymptotes are x = 2 and x = -2
how would i write y= -7x+25 In Standard form?
please help:)