Answer:
6068 rabbits
Step-by-step explanation:
Given
[tex]Rabbits = 200[/tex]
[tex]Reduction = 3\ daily[/tex]
[tex]Squirrels = 18[/tex]
[tex]Increment = 2\ daily[/tex]
Required
Determine number of rabbits caught up till the day when they caught more squirrel.
Let the number of days be n
On any n day,
The number of rabbits they catch is:
[tex]Rabbit = 200 - 3n[/tex]
The minus symbol is used because there's a reduction in the numbers of Rabbit caught, each day.
The number of squirrel they catch is:
[tex]Squirrel = 18 + 2n[/tex]
The addition symbol is used because there's an increment in the numbers of Squirrel caught, each day
First, we need to solve for n
The expression when they catch more rabbits than squirrel is:
[tex]Squirrel > Rabbit[/tex]
Substitute values for Squirrel and Rabbit
[tex]18 + 2n > 200 - 3n[/tex]
To solve the above expression, we start by collecting like terms
[tex]2n + 3n > 200 - 18[/tex]
[tex]5n > 182[/tex]
Solve for n
[tex]n > \frac{182}{5}[/tex]
[tex]n > 36.4[/tex]
Days must be an integer. So, we have to round the above value.
[tex]n > 36[/tex]
The above expression shows that they caught more squirrel on a day greater than 36.
This day is 37.
i.e.
[tex]n = 37[/tex]
The reduction in the number of rabbits daily is an indication of Arithmetic progression.
So, to calculate the number of rabbits caught up till the day when they caught more squirrel, we make use of Sum of n terms of an AP using:
[tex]S_n = \frac{n}{2}(2a + (n-1)d)[/tex]
In this case:
[tex]n = 37[/tex]
a = Initial Number of rabbits;
[tex]a = 200[/tex]
d = the reduction (common difference)
[tex]d = -2[/tex]
Substitute these values in the given formula:
[tex]S_n = \frac{n}{2}(2a + (n-1)d)[/tex]
[tex]S_{37} = \frac{37}{2}(2 * 200 + (37 - 1) * -2)}[/tex]
[tex]S_{37} = \frac{37}{2}(2 * 200 + 36 * -2)}[/tex]
[tex]S_{37} = \frac{37}{2}(400 -72)}[/tex]
[tex]S_{37} = \frac{37}{2} * 328[/tex]
[tex]S_{37} = 37 * 164[/tex]
[tex]S_{37} = 6068[/tex]
Up till that day, the number of rabbits is 6068
Jasim has invested 600 dinars in a business at the rate of 4 % for 3 years. Find his
i- simple interst ?
ii- total amount after 3 years
Answer:
1) Simple interest is 72 dinars
2) Total amount after 3 years is 672 dinars.
Step-by-step explanation:
Principal Amount P = 600 dinars
Interest Rate= 4% = 0.04
Time = 3 years
i) Simple Interest
The formula used to calculate interest is [tex]I=P\times r \times t[/tex]
Putting values and finding interest
[tex]I=P\times r \times t\\I=600\times 0.04 \times 3\\I=72[/tex]
So, simple interest is 72 dinars
ii) Total amount after 3 years
The formula to calculate total amount is: [tex]A=P(1+rt)[/tex]
Putting values and finding future amount A
[tex]A=P(1+rt)\\A=600(1+(0.04*3))\\A=600(1+0.12)\\A=600(1.12)\\A=672[/tex]
So, Total amount after 3 years is 672 dinars.
The function g(x)=2x^2+16x+31 is at a minimum when x=-4. True or False?
Answer:
The answer is true.
Step-by-step explanation:
The sum of two numbers is 22 and the sum of their squares is 250. Find the following information numbers
Answer:
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE100016784994
Step-by-step explanation:
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Helen is typing a report and is using two different sizes of fonts, as shown below. What is the ratio of the height of a letter typed using font I to the height of a letter typed using font II?
2/9
1/3
3
9
WILL RECIEVE BRAINLIST
Answer: 2/9
Step-by-step explanation:
Given that a=10, b=40, and A=30 degrees, how many triangles can possibly be formed?
Answer:
None
Step-by-step explanation:
The minimum requirement is 180.
Charlotte wants to know which website has more user engagement per a single dollar expense.
Answer:
Part 1:
Total number of comments divided by the expenses
Total number of likes divided by the expenses.
Part 2:
Yes. According to both definitions, website A has more user engagement per a single dollar expense.
Step-by-step explanation:
User Engagment: Likes and comments
Website A:
500 comments/$20,000= .025
3500 likes/$20,000= .175
Website B:
450 comments/$47,000= .0095
3500 likes/$47,000= .07
Website A has more user engagement per a single dollar expense.
Answer:
Top Answer Worked for me
Step-by-step explanation:
The value of y is directly proportional to the value of x.If y when x = 40, what is the value of y when x = 140?
Answer:y=14
Step-by-step explanation:
simplify expression -(9x-1)
Answer:
9
Step-by-step explanation:
It's really not that hard
If h(x)=2(x^2+5)+10, what is the value of p(13)
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]h(x) = 2( {x}^{2} + 5) + 10 [/tex]
[tex]h(x) = 2 {x}^{2} + 10 + 10[/tex]
[tex]h(x) = 2 {x}^{2} + 20[/tex]
_________________________________
[tex]h(13) = 2 \times ({13})^{2} + 20[/tex]
[tex]h(13) =( 2 \times 169 )+ 20[/tex]
[tex]h(13 )= 338 + 20[/tex]
[tex]h(13) = 358[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Pedro answered 10 math problems in 4 minutes. Which ratio accurately compares math problems to minutes?
Answer:
can't see the answers but I think it's 2.5
whats the value of y in the eaquation log(1,000,000)=y
a.y=6
b.y=4
c.y=5
The answer is a. y=6 :)
solving slope with work tho please
Answer:
First is 5/2
second is 1
Answer:
1. A. slope = 5/2
2. A. slope = 1
Step-by-step explanation:
To find the slope you can input the x and y values of two points into this expression: [tex]\frac{y2 -y1}{x2 - x1}[/tex]
1. To find the slope, I'm going to use points (2, 3) and (4, 8). Let's input them into the expression:
[tex]\frac{8-3}{4-2}[/tex]
Simplify:
8 - 3 = 5
4 - 2 = 2
The slope is 5/2.
2. To find the slope, I'm going to use points (0, 0) and (1, 1). Let's input them into the expression:
[tex]\frac{1-0}{1-0}[/tex]
Simplify:
1 - 0 = 1
1 - 0 = 1
The slope is 1/1, or just 1.
Solve for the missing angle. Round to the nearest hundredth.
18
?
13
? =
degrees
Answer:
[tex]\theta \:=43.76^{\circ \:\:}[/tex]
Step-by-step explanation:
The right triangle has the hypotenuse = 18
Let 'Ф' be the missing angle
we know that
cos Ф = adjacent/hypotenuse
Here,
The adjacent to Ф = 13The hypotenuse = 18so
cos Ф = adjacent/hypotenuse
[tex]cos\:\theta \:=\frac{13}{18}[/tex]
[tex]\theta \:=\cos ^{-1}\left(\frac{13}{18}\right)[/tex]
[tex]=43.76^{\circ \:}[/tex]
Therefore, the missing angle is:
[tex]\theta \:=43.76^{\circ \:\:}[/tex]
what's the greatest common factor of 90 and 135
Answer:45
Step-by-step explanation:
the factors for 90= 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
the factors for 135=1,3,5,9,15,45
the highest numbers that is divide both numbers is 45
Find the distance between the two points M(-4,-1) and Z (3, 3).
Answer:
d = 8.062258
Step-by-step explanation:
d=√ (3−(−4))2+(3−(−1))^2
d=√ (7)^2+(4)^2
d=√ 49+16
d=√ 65
d=8.062258
A turtle dives towards deeper water at a rate of 8 inches per second. It continues for a total of 16 seconds. Which expression represents this situation?
a distributor wants to make 1000 pounds of trail mix that is 8% raisins. He will use a mix that is 5% raisins and a mix that is 20% raisins. How many pounds of each should he use?
Answer:
200 pounds 20% raisins
800 pounds 5% raisins
Step-by-step explanation:
Let number of 5% be x
and number of 20% be y
x + y = 1000
Also;
5% of x + 20-% of y = 8% of 1000 pounds
= 0.05x + 0.2y = 80
From i , x = 1000-y
0.05(1000-y) + 0.2y = 80
50-0.05y + 0.2y = 80
0.15y = 30
y = 200
x = 1000 - y
= 1000-200 = 800
He will use 800 pounds for a mix that is 5% raisins and 200 pounds for a mix that is 20% raisins.
Given that,
A distributor wants to make 1000 pounds of trail mix that is 8% raisins.
He will use a mix that is 5% raisins and a mix that is 20% raisins.
We have to determine,
How many pounds of each should he use.
According to the question,
Let number of 5% raisins be x,
And number of 20% raisins be y.
Then,
He will use a mix that is 5% raisins + A mix that is 20% raisins = Distributor trail mix.
[tex]x + y = 1000[/tex]
And,
He will use a mix that is 5% raisins of x + and a mix that is 20% raisins of y = 1000 pounds of trail mix that is 8% raisins.
5% of x + 20% of y = 1000 of 8% raisins
[tex]0.05 x+ 0.20y = 80[/tex]
On solving both the equation,
[tex]x + y =1000\\\\x = 1000-y[/tex]
Substitute the value of x in the equation 2,
[tex]0.05 (1000-y) + 0.20y = 80\\\\0.05 \times 1000 - 0.05y + 0.20y = 80\\\\50 + 0.15y = 80\\\\0.15y = 80-50 \\\\0.15y = 30\\\\y = \dfrac{30}{0.15}\\\\y = 200[/tex]
Substitute the value of y in the equation 1,
[tex]x + y = 1000\\\\x + 200 = 1000\\\\x = 1000-200\\\\x = 800[/tex]
He will use x = 800 pounds a mix that is 5% raisins and y = 200 pounds for a mix that is 20% raisins.
Hence, He will use 800 pounds for a mix that is 5% raisins and 200 pounds for a mix that is 20% raisins.
To know more about Equations click the link given below.
https://brainly.com/question/18916524
The highest point in California is Mount Whitney at 14,494 feet above sea level. The lowest point in California is in Death Valley at 282 feet below sea level. What is the difference in elevations?
distribute 4(3-5x²).
Answer:
[tex]12-20x^{2}[/tex]
Step-by-step explanation:
[tex]4(3-5x^{2}) = (4*3)-(4*5x^{2} )[/tex]
[tex]4*3 = 12[/tex]
[tex]4*5x^{2} =20x^{2}[/tex] since you only multiply the numbers
[tex]12-20x^{2}[/tex]
The difference between two same side interior angles of two parallel lines is 35 degrees. Find the measures of these two angles.
Answer:
107.5° and 72.5°
Step-by-step explanation:
x + y = 180 same side interior angles of two parallel lines add up to 180
x - y = 35
___________
2x = 215 add above two equations
x = 107.5° divide by 2 to isolate x
Substitution to find y:
x + y = 180
107.5 + y = 180
y = 72.5°
The measure of these two angles is 107.5° and 72.5°.
Given that,
The difference between two same-side interior angles of two parallel lines is 35 degrees.We need to find the measure of the two angles. Here we assume the two angles be x and y.Based on the above information, the calculation is as follows:
x + y = 180
And,
x - y = 35
So, after solving it, it comes
2x = 215
x = 107.5°
So, y = 180 - 107.50 = 72.5
Therefore we can conclude that the measure of these two angles is 107.5° and 72.5°.
Learn more: brainly.com/question/13549064
Therefore we can conclude that
A cereal box says that now it contains 20% more. Originally, it came with 18.5 ounces of cereal. How much more cereal is in the box now?
Answer:
3.7 oz more of cereal
Step-by-step explanation:
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Mr. Stack and Coach Pugh are racing down the highway. Coach Pugh is going five miles more an hour than twice Mr. Stack's speed. If Coach Pugh is going one hundred and five miles and hour, how fast is Mr. Stack going?
Answer:
50
Step-by-step explanation:
2(Mr stack's speed) = Coach Pugh's speed - 5mph
Mr stack's speed = (105mph - 5mph)/2
Mr stack's speed = 100mph/2
Mr stack's speed = 50mph
I NEED HELP PLEAZE i hate math i hate math i hate math.
Answer:
B. 9
Step-by-step explanation:
3^4/3^2
lets expand it
3 * 3 * 3 * 3/ 3 * 3
just get rid the 3's needed to get rid of the denominator which is 2, so get rid of 2 threes from the top
3 * 3 = 9
And it's okay, I dislike math too. Hope you feel better.
Answer:
b
Step-by-step explanation:
Someone help me please!!
Answer:
( h − 4 ) ( h + 12 )
Step-by-step explanation:
I'm not even sure if this helps but it factored
plz help and give explaination of how to do it
Answer:
25% decreased by 60% is 10
Step-by-step explanation:
New value =
25 - Percentage decrease =
25 - (60% × 25) =
25 - 60% × 25 =
(1 - 60%) × 25 =
(100% - 60%) × 25 =
40% × 25 =
40 ÷ 100 × 25 =
40 × 25 ÷ 100 =
1,000 ÷ 100 = 10
hope this helps :)
**
Which of the following could be the equation
of the graph shown to the left?
a. y+5=-12x-3
b. y+5=-12x+3
c. y-5=-12x-3
d. y-5=-12(x+3)
Answer:
b
Step-by-step explanation:
b should be the answer
A triangle is translated by using the rule (X.Y) =(x-4.y+1). Which describes how the figure is moved?
2
four units left and one unit down
O four units left and one unit up
one unit right and four units down
O one unit right and four units up
WILL GIVE BRAINLIEST TO CORRECT ANSWER(S)!
Part A: What is the value of the correlation coefficient?
A: 0.42
B: -0.65
C: 0.65
D: ± 1.00
E: -0.42
Part B: How strong is the relationship between the two data sets?
A: Very strong
B: Moderately strong
C: No strength
D: perfect
E: weak
Part C: Choose the function that best represents the data.
A: f(x)=-0.65x+260.08
B: f(x)=260.08x-3.66
C: f(x)=0.41x+260.08
D: f(x)=-3.66x+260.08
E: f(x)=3.66x+260.08
Part D: If the trend stays the same, how much should Gracie expect to pay for her energy bill when the mean temperature for the next month is forecasted to be 10°F?
A: $296.08
B: $2,597.18
C: $223.48
D: $253.58
E: $264.18
Answer:
A and E are the answers
A company that teaches self-improvement seminars is holding one of its seminars in Belmont. The company pays a flat fee of $250 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $4 to purchase books and supplies. Each attendee will pay $14 for the seminar. Once a certain number of attendee register, the company will be breaking even. How many attendees will that take?
Answer:
Step-by-step explanation:
250 for place 4 for books each.
If they charge 14 per person, 4 of that goes for the books and 10 will be applied to the rental fee.
250/10= 25 people to break even. Any people beyond that is a profit of 10.00 since the other 4 will still go to the books.
Find the distance between the two points in simplest radical form.
(9,4) and (3,-4)
Answer:
10
Step-by-step explanation: