There are 80 birds in the flock of cardinals.
Solution:Given:- A flock of 20 seagulls or we can say
Number of seagulls in a flock = 20
The new flock is no larger than 100 birds
So, let Total number of birds of new flock = 100
To find out the number of birds in cardinals we have to subtract number of seagull in flock from total number of birds of new flock.
Number of birds in cardinal = Total number of birds of new flock - Number of seagulls in a flock
Number of birds in cardinal = 100 – 20 =80
Hence there are 80 birds in the flock of cardinals.
The answer explains how to determine the number of birds in the flock of cardinals based on the given conditions.
The number of birds in the flock of cardinals can be calculated as follows:
Let x be the number of birds in the flock of cardinals.
Since the new flock is no larger than 100 birds, the total number of birds after merging is 20 (seagulls) + x (cardinals).
Therefore, the equation to represent this situation is x + 20 ≤ 100, and solving for x, we get x ≤ 80. Thus, there were at most 80 birds in the flock of cardinals.
-2(x+2)=-12 .............
Answer:
x=4
Step-by-step explanation:
-2(x+2)=-12
x+2=-12/-2
x+2=6
x=6-2
x=4
What’s the answer for
8x+20=11x-31
Answer:
x=17
Step-by-step explanation:
8*17=136+20=156
11*17=187-31=156
156=156
There are 12 chairs in the meeting hall and odd number of tables each table has the same number of chairs how many tables are there use prime factorization to solve two different ways
Answer:
There may be 3 tables or 1 table.
Step-by-step explanation:
If we factorize 12 into its prime factors then we get 12 = 2 × 2 × 3
If there are an odd number of tables and each table has an equal number of chairs and there are a total of 12 chairs, then the possibilities of the number of tables are 1 and 3.
{Since 1 and 3 both are odd numbers}
Now, for 3 tables there will be 4 chairs each to make the total chairs (3 × 4) = 12 and for 1 table there will be 12 chairs in the table to make the total number of chairs (1 × 12) = 12. (Answer)
To solve using prime factorization, the factors of 12 are 2, 2, and 3. We need an odd number of tables, so only the factor 3 is used. There are 3 tables with 4 chairs each.
Explanation:The question involves a scenario where there are 12 chairs in a meeting hall and an odd number of tables. Each table has the same number of chairs. The question prompts us to use prime factorization to determine how many tables there could be. Since there is a fixed total of 12 chairs, we need to find the factors of 12 that are odd numbers because the number of tables has to be odd.
Using prime factorization, 12 can be broken down into its prime factors: 2 x 2 x 3. To have an odd number of tables, we cannot include the factor of 2 because it would result in an even number of tables. Hence, we only consider the factor of 3. In this scenario, this would mean there are 3 tables with 4 chairs each because 3 (an odd number) times 4 equals 12 (total number of chairs).
Another way to use prime factorization to solve this is to look for combinations of the factors that multiply to 12 but in groups that have an odd factor. The only possible combination is again 3 tables with 4 chairs each, as any other multiplication involving the factor 2 would result in an even number of tables.
5x + y = 10
5y = 3x - 6
Solution: (0,0)
Solve for system of equations
Answer:
x=2, y=0. (2, 0).
Step-by-step explanation:
5x+y=10
5y=3x-6
-------------
y=10-5x
5(10-5x)=3x-6
50-25x=3x-6
50-25x-3x=-6
50-28x=-6
28x=50-(-6)
28x=50+6
28x=56
x=56/28
x=2
5(2)+y=10
10+y=10
y=10-10
y=0
Jack is 4 times as old as Lacy. 5 years from now the sun of their age will 70. How old are they now?
Answer:
Lacy is 14 and Jack is 56
Step-by-step explanation:
simplify these expressions
9(w+6)+4 f+4(f-2)
2m+7+9m 3.1(p-2.7)
5(3+m)-7
Answer:
9w+8f+46, 11m+7, 3.1p-8.37, 8+5m.
Step-by-step explanation:
9(w+6)+4f+4(f-2)
9w+54+4f+4f-8
9w+54-8+8f
9w+46+8f
---------------------
2m+7+9m=2m+9m+7=11m+7
-------------------------------------------
3.1(p-2.7)=3.1p-8.37
---------------------------
5(3+m)-7=15+5m-7=8+5m
solve the problems
A) X/840 = 1/21
B) 14/X = 16/20
Answer:
Step-by-step explanation:
A) x/840=1/21
x=(1/21)*840=840/21=40
x=40
------------------
B) 14/x=16/20
simplify 16/20 into 4/5
14/x=4/5
x=14/(4/5)=(14/1)(5/4)=70/4
simplify
x=35/2
2. Ryan gets a raise. He now earns $9 an hour. Ryan decides to
start saving for a car. He works 9 hours a week.
Part A
How many hours does Ryan need to work to earn
enough money to buy the car, as well as pay for the
taxes, title, and plates as shown? Draw bar diagrams
to help write and solve equations.
Used car: 52,753
Taxes, title, and
plates: $235
Part B
About how many weeks will Ryan need to work to buy the car and pay
for the taxes, title, and plates? Explain.
Part
How many actual weeks does Ryan need to work to buy the car and pay
for the taxes, title, and plates? Show your computations. Explain why your
solution is reasonable.
Answer:
A. He has to work 5,887hrs and 55 min
B. 3,504 weeks
Step-by-step explanation:
A. He earns $9 an hr. He works 9hrs a week, or 1hr 17 min a day. $11.52 per day.
The car costs $52,753, + $235(taxes, titles, and plates)= $52,988.
52,988/9=5,887:55
B. One week= 168 hrs. 5,887:55/168=3,504 weeks
Ryan needs to work approximately 5888 hours, which translates to about 654 weeks or 12.5 years, to save enough to buy a used car and pay for taxes, title, and plates at his current wage of $9 an hour.
To determine how many hours Ryan needs to work to afford a used car plus additional costs, we first add the price of the car to the taxes, titles, and plates. The cost of the used car is $52,753, and the taxes, titles and plates amount to $235, giving us a total cost of $52,988.
Ryan earns $9 per hour. To find out how many hours he needs to work to earn $52,988, we divide the total cost by his hourly wage.
$52,988 / $9 per hour = 5887.555... hours
Ryan would need to work approximately 5888 hours to afford the car and the extra costs.
For part B, we calculate how many weeks Ryan needs to work. Since Ryan works 9 hours a week, we divide the total hours needed by his weekly hours.
5888 hours / 9 hours per week = 654.222... weeks
Ryan would need to work approximately 654 weeks, which is roughly 12.5 years, assuming he works every week without any breaks or holidays.
0.5x+7/3 = 21/4 cross multiply
Answer:
Step-by-step explanation:
I'm not sure I would cross multiply as my first step.
How about subtracting 7/3 first.
0.5x = 21/4 - 7/3
0.5x = 21*3/(4*3) - 7*4/(3*4)
0.5x = 63 / 12 - 28/12
0.5x = 35/ 12 Now multiply by 2
2*0.5x = 35*2 / 12
x = 70/12
x = 5 10/12 or
x = 5 5/6 or
x = 5.8333333
There might be a slightly easier way of doing this.
Suppose you multiply by 2 to begin with
x + 14/3 = 42/4
x + 14/3 = 21/2
x = 21/2 - 14/3
x = 63/6 - 28/6
x = 35/6
x = 5 5/6
I don't think there is much difference in how you do it. The numbers are just plain ugly.
3x - 4y = -16
2x - 4y = -8
what is x and y
Answer:
x = -8 , y = -2
Step-by-step explanation:
Solve the following system:
{3 x - 4 y = -16 | (equation 1)
2 x - 4 y = -8 | (equation 2)
Subtract 2/3 × (equation 1) from equation 2:
{3 x - 4 y = -16 | (equation 1)
0 x - (4 y)/3 = 8/3 | (equation 2)
Multiply equation 2 by 3/4:
{3 x - 4 y = -16 | (equation 1)
0 x - y = 2 | (equation 2)
Multiply equation 2 by -1:
{3 x - 4 y = -16 | (equation 1)
0 x+y = -2 | (equation 2)
Add 4 × (equation 2) to equation 1:
{3 x+0 y = -24 | (equation 1)
0 x+y = -2 | (equation 2)
Divide equation 1 by 3:
{x+0 y = -8 | (equation 1)
0 x+y = -2 | (equation 2)
Collect results:
Answer: {x = -8 , y = -2
the solution to the system of equations is [tex]\( x = -8 \) and \( y = -2 \).[/tex]
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method here.
Given equations:
1.[tex]\(3x - 4y = -16\)[/tex]
2.[tex]\(2x - 4y = -8\)[/tex]
We can see that both equations have the same term ( -4y), so we can eliminate ( y) by subtracting equation 2 from equation 1:
[tex]\[(3x - 4y) - (2x - 4y) = (-16) - (-8)\][/tex]
[tex]\[3x - 4y - 2x + 4y = -16 + 8\][/tex]
[tex]\[(3x - 2x) - 4y + 4y = -16 + 8\][/tex]
[tex]\[x = -8\][/tex]
Now that we have found ( x = -8 ), we can substitute this value into either of the original equations to find ( y ).
Let's substitute ( x = -8 ) into equation 1:
[tex]\[3(-8) - 4y = -16\][/tex]
[tex]\[-24 - 4y = -16\][/tex]
[tex]\[-4y = -16 + 24\][/tex]
[tex]\[-4y = 8\][/tex]
[tex]\[y = \frac{8}{-4}\][/tex]
[tex]\[y = -2\][/tex]
So, the solution to the system of equations is [tex]\( x = -8 \) and \( y = -2 \).[/tex]
Write in vertex form y=x^2+16-71
The vertex form of y = x² + 16x - 71 is (x + 8)² - 135
Step-by-step explanation:
The vertex form of the quadratic function y = ax² + bx + c, is
y = a(x - h)² + k, where
a is the coefficient of x²b is the coefficient of xc is the y-intercept (numerical term)(h , k) are the coordinates of the vertex point of the parabola which represents the quadratic function graphicallyh = [tex]\frac{-b}{2a}[/tex] and k = y when x = h∵ The quadratic function is y = x² + 16x - 17
- Compare it with the general form of the quadratic function above
∴ a = 1 , b = 16 and c = -71
∵ [tex]h=\frac{-b}{a}[/tex]
- Substitute the value of a and b is h
∴ [tex]h=\frac{-16}{2(1)}[/tex]
∴ [tex]h=\frac{-16}{2}=-8[/tex]
∵ k = y when x = h
- Substitute x by -8 in the function above
∴ k = (-8)² + 16(-8) - 71
∴ k = 64 - 128 - 71
∴ k = -135
∴ The vertex point is (-8 , -135)
∵ The vertex form is y = a(x - h)² + k
∵ a = 1 , h = -8 , k = -135
- Substitute these values in the vertex form above
∴ y = 1(x - (-8))² + (-135)
∴ y = (x + 8)² - 135
The vertex form of y = x² + 16x - 71 is (x + 8)² - 135
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After spending 1/4 of his allowance on a book and 1/3 of the remainder on stationery, John has $18 left. Find the cost of the book.
This problem is tricky. Let's break it down.
1/4 - book
------------------------------------------------------
1/3 of the remainder(3/4) - stationery
"OF" MEANS MULTIPLY
1/3 x 3/4 = 1/4
So, 1/4 of total allowance on stationery.
Meaning, he spent 1/2 of his allowance in all, and 1/2 of his allowance is $18.
Since the book cost 1/4 of his allowance, and (1/4)2 = 1/2, the book cost 18/2 = $9.
Sixty-four tickets are issued for a school
dance, and 96 brownies are ordered for
the refreshment table. Each student gets
the same number of tickets as every
other student. Each student also gets the
same number of brownies as every other
student.
Each student will get — tickets and _
brownies.
Answer:
Each students will get 3 tickets and 2 brownies .
Step-by-step explanation:
Given as :
The total number of tickets issued for the school dance = 64
The number of brownies ordered for refreshment table = 96
Let the number of tickets given to each student = x
And The number of brownie given to each student = y
Now,
According to question
The tickets and brownies is distributed equally among students
So , Now, consider the tickets and brownies = n
Or, [tex]\dfrac{n}{64}[/tex] - [tex]\dfrac{n}{96}[/tex] = 1
Or, Taking LCM we get
[tex]\dfrac{3 n - 2 n}{192}[/tex] = 1
Or, [tex]\dfrac{n}{192}[/tex] = 1
∴ n = 192
Now,
The number of tickets given to each student = x = [tex]\dfrac{192}{64}[/tex]
I.e x = 3
And The number of brownie given to each student = y = [tex]\dfrac{192}{96}[/tex]
I.e y = 2
Hence Each students will get 3 tickets and 2 brownies . Answer
To ensure each student gets an equal number of tickets and brownies, we distribute 64 tickets and 96 brownies among the students. Each student gets 2 tickets and 3 brownies.
To determine how many tickets and brownies each student gets, follow these steps:
Identify the variables: Let the number of students be denoted by x.Equate the tickets: Each student gets an equal number of tickets. Thus, 64 tickets are distributed equally among x students, so each student gets 64/x tickets.Equate the brownies: Similarly, 96 brownies are distributed equally among x students, so each student gets 96/x brownies.Find common divisors: To ensure each student gets an equal and whole number of tickets and brownies, x must be a common divisor of both 64 and 96.Calculate the greatest common divisor (GCD): The GCD of 64 and 96 is 32. Therefore, there are 32 students.Determine distribution: Each student gets 64/32 = 2 tickets and 96/32 = 3 brownies.Hence, Each student will get 2 tickets and 3 brownies.
2y=5x+8 in standard form
Answer:
5x-2y + 8 =0
Step-by-step explanation:
2y=5x+8
5x-2y + 8 =0
Which set of numbers is the most reasonable to describe a person’s hat size?
Answer:
Rational Numbers
Step-by-step explanation:
A hat size cannot be integers as that would include negative numbers. For example a person who's hat size is 7 & 5/8 which would make the answer 7.625 which is a rational number.
Answer:
"Rational numbers" is the set of numbers among the choices that are given in question that is the most reasonable to describe a person's hat size.
Step-by-step explanation:
rational numbers are by far the most reasonable description. The circumference of the human head certainly is not always an integer or whole number.
For this item, i go with letter D. Rational. The hat size cannot be integers as it includes negative numbers. For instance the person's hat size is 7 + 5/8 which leads to an answer of 7.625. That is a rational number.
hope this helps you
if this is correct can you give me the brainliest
Please answer this correctly
Answer:
6:32 is my answer to this question
so if it is three minutes to one that means it is
12:57
in 6 hours and 34 minutes will be
12:57 + 6= 6:57
if you add 34 (i didnt do it above to make it easier) to 57 you get 91.
because minutes dont go past 60 you have to subtract..
91 - 60 = 31 and because you only subtracted 60 once you only add one hour..
so your answer is 7:31
i hope this helps you !!!
The population of a county is growing at a rate of 9% per year, compounded continuously. How many years will it take for the population to quadruple according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.
There are 16 years will it take for the population to quadruple i.e. four times the initial population.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
Given that a population of a country grows exponentially and continuously at a rate of 9% per year.
The number of years it takes for the population to quadruple i.e. four times the initial population.
As per the given condition, the required solution would be as:
⇒ 4p = p[tex]e^{0.09t}[/tex]
Divided by p into both sides of the above equation,
⇒ 4p/p = p[tex]e^{0.09t}[/tex]/p
⇒ 4 = [tex]e^{0.09t}[/tex]
Take the natural logarithm of both sides of the equation,
⇒ ln 4 = ln [tex]e^{0.09t}[/tex]
⇒ ln 4 = 0.09t ln e
∵ ln e = 1
⇒ ln 4 = 0.09t
Divided by 0.09 into both sides of the above equation,
⇒ ln 4 / 0.09 = 0.09t / 0.09
⇒ t = 16
Thus, there are 16 years will it take for the population to quadruple.
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Which of the following matches the graph?
Y=3/4x
Y=1/4x
Y=1/3x
Y=4x
Y=4/3
Answer:
B) y=1/4x
Step-by-step explanation:
Because the slope of this graph is 1/4. You can find this because slope=rise/run. On the graph, it's always 1 upward and 4 rightwards, therefore, the slope is 1/4. Also, the y-intercept is 0 in this case.
Jenna and Heidi together have $60. Jenna has $9 more than twice Heidi’s amount. How much money does each have?
Jenna has $43 and Heidi has $17.
Step-by-step explanation:
Total amount = $60
Let,
Amount of Jenna = x
Amount of Heidi = y
According to given statement;
x+y=60 Eqn 1
x=2y+9 Eqn 2
Putting value of Eqn 2 in Eqn 1;
[tex](2y+9)+y=60\\2y+9+y=60\\3y=60-9\\3y=51[/tex]
Dividing both sides by 3,
[tex]\frac{3y}{3}=\frac{51}{3}\\y=17\\[/tex]
Putting y=17 in Eqn 2
[tex]x=2(17)+9\\x=34+9\\x=43[/tex]
Jenna has $43 and Heidi has $17.
Keywords: linear equations, substitution method
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The numbers 3 and 10 are on a number line.
Use a model to explain how to find the
distance between the numbers.
Explain in words how to find the distance
between 3 and 10 on the number line.
Answer:
7
Step-by-step explanation:
Using subtraction method, the distance between 3 and 10 is 7. On the number line, the starting point is 3; therefore, from 3 movement will take seven times to get to 10.
2 docters is ---- % of 25 docters
Answer:
8 percent
Step-by-step explanation:
When you're trying to find the percentage, first, you divide what you're trying to find over the total amount.
2/25.
What you get from this is 0.08. However, this is a decimal, not a percent. When converting from decimal to percent, you multiply the decimal by 100 to get 8 percent.
Answer:
8%
Step-by-step explanation:
2/25=8/100=0.08=8%
(
4.
What is the volume of the composite
figure?
he composite vi
10x7
6 in.
2 in
7 in
360
10 in.
6x2.212
3
Answer: I think something is missing ?? sorry comment down below
Step-by-step explanation:
i need 7-12 please!!!
Answer:
number 7 is y= [tex]\frac{-ax+c}{b}[/tex]
Step-by-step explanation:
What is the mean of the following data? 53, 71, 89, 10, 62
62. If you add up all of the numbers, you get 310, then take this number and divide it by 5. you divide it by five because there are five numbers given.
Answer:
57 is the mean.
When you add up all of the numbers, you get 285.
Divide 285 by 5 and you get 57.
what is the percentage of 35
Answer:
0.35
Step-by-step explanation:
Answer:
it is 0.35
Step-by-step explanation:
this is because 35/100= 0.35
Please simplify.
13[tex]\frac{1}{3}[/tex] - 7[tex]\frac{7}{9}[/tex]
A. 6[tex]\frac{8}{27}[/tex]
B. 5[tex]\frac{5}{9}[/tex]
C. 7
D. 6[tex]\frac{2}{3}[/tex]
Answer:
B) 5 5/9
Step-by-step explanation:
13 1/3=40/3
7 7/9=70/9
-----------------
40/3-70/9=120/9-70/9=50/9=5 5/9
ABCE is a trapet AD is parallel to BC DE=4cm area of ABCE=60cm?area of ABCD=48cm work out the values of f and g show all your working please be quick thank youuuu
Answer:
The value are
f = 6 cm
g = 8 cm
Step-by-step explanation:
Given:
ABCE is Trapezium
AD || BC
AD = BC = f
CD = g
Area of ABCE = 60 cm²
Area of ABCD = 48 cm²
To Find :
f = ?
g = ?
Solution:
In the figure ∠ C = 90° and AD || BC
∴ ∠ D = 90° .....Corresponding angles are equal
∴ ABCD is RECTANGLE With Length = f and Breadth = g
∴ [tex]\textrm{Area of Rectangle}=Length\times Breadth\\\textrm{Area of Rectangle}=f\times g\\[/tex]
[tex]\textrm{Area of Triangle AED}= \textrm{Area of Trapezium ABCE}-\textrm{Area of Rectangle ABCD}\\=60-48\\=12\ cm^{2} \\\therefore \textrm{Area of Triangle AED} = \frac{1}{2}\times AD\times DE\\12 =\frac{1}{2}\times f\times 4\\ f=\frac{24}{4}\\\therefore f= 6\ cm[/tex]
Now,
∴ [tex]\textrm{Area of Rectangle}=Length\times Breadth\\\textrm{Area of Rectangle}=f\times g\\[/tex]
[tex]\therefore 48 = f\times g\\48= 6\times g\\\therefore g =\frac{48}{6}\\ g=8\ cm[/tex]
The value are
f = 6 cm
g = 8 cm
does this sum converge: show steps
Answer:
Yes
Step-by-step explanation:
[tex]\sum_{n=1}^{\infty} e^{-\sqrt{n} } \\\sum_{n=1}^{\infty} (\frac{1}{e})^{\sqrt{n} }[/tex]
If we say u = √n, then:
[tex]\sum_{u=1}^{\infty} (\frac{1}{e})^{u}[/tex]
This is a geometric series. Since |1/e| < 1, the series converges.
An isosceles triangle has an angle that measures 40 degrees. Which other angles could be in that isosceles triangle? Choose all that apply
• 70
• 40
• 100
• 20
An isosceles triangle has an angle that measures 40 degrees. 70 and 100 are other angles could be in that isosceles triangle
Solution:
Given that isosceles triangle has an angle that measures 40 degrees.
If a triangle is isosceles then it has 2 identical angles and the third different one.
Let the two identical angles be "a"
We know that sum of angles in a triangle is 180 degree
a + a+ 40 = 180
2a + 40 = 180
2a = 180-40
a = 70
Thus the two identical angles are 70 degree and 70 degree
Now let the identical two angles be "40" and the third angle be "a"
Now sum of angles = 180 degree
40 + 40 + a = 180
80 + a = 180
a = 100
Thus the third angle in this case is 100
70 and 100 are other angles could be in that isosceles triangle
Answer:
70, 40, and 100
Step-by-step explanation:
I am taking the IXL and wanted to know what t was and i got it wrong because someone answered it was only 70 and 100 when it is actually 40 100, and 70. Trust me i just got it wrong and IXL gave me the right answers.
What is the total number of funny numbers between 30 and 60
Answer:
Not exactly sure what "funny numbers" are but I'm assuming you mean prime numbers? In that case there are a total of 7 prime numbers between 30 and 60.
Step-by-step explanation:
Answer:
42 but with no 0