Answer:
6km
Step-by-step explanation:
Area of circle = πr²
Where r = radius, π= 3.14, A = 28.26km²
A = 3.14 x r²
3.14 r2 = 28.26
Divide both sides by 3.14
r²= 28.26/3.14
r² = 9
Square root both sides
r= √9
r= 3
Radius = 3km
Note : Diameter = 2 x radius
Diameter = 3 x 2
Diameter = 6km
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What is a initial population for an exponential function represented in an equation that represents the function?
The initial population is represented by [tex]P_{0}[/tex] which is the population at [tex]t=0[/tex], in other words [tex]P_{0}=20,000[/tex]
Explanation:Suppose you have the following problem:
The population of Naguanagua in 2019 is estimated to be 20,000 people with an annual rate of increase of 4%. Which equation models the population of Naguanagua in t years?
Let:
[tex]P:Population \ of \ Naguanagua \\ \\ t:Number \ of \ years \ since \ 2019 \\ \\ r:Rate \ of \ increase[/tex]
So the population of Naguanagua can be modeled by the following equation:
[tex]P=P_{0}(1+r)^t \\ \\ P_{0}=20,000 \\ \\ r=4\%=0.04 \\ \\ \\ P=20,000(1+0.04)^t \\ \\ P=20,000(1.04)^t[/tex]
So the initial population is represented by [tex]P_{0}[/tex] which is the population at [tex]t=0[/tex], in other words [tex]P_{0}=20,000[/tex]
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LOTS OF POINTS PLS
1) 216
2) 1
3) 450 ml
4)15 packs
5)12 sq m
Step-by-step explanation:
Step 1:
1) The series given is the cube of the first n natural numbers. Hence the nth term of the series can be obtained by n³.
Here we need the 6th term, so the cube of 6 is 216
Step 2 :
2 ) Area of the cube is given as 8000 cubic cm.
Hence side of the cube is 20 cm cube
The radius of the sphere is 20 cm as the diameter is given as 10 cm.
Hence number of spheres that can be placed in a cube of side 20 cm is 20/20 = 1
Step 3 :
3)
Total quantity of the mixture purchased from the chemist is 750 ml
Syrup and alcohol are in the ration 3:2
Hence the quantity of syrup in the mixture = 3/5 * 750 = 450 ml
Step 4 :
4)
Length and breadth of the given room is 17 m and 15 m
Hence its area is 17 * 5 = 85 sq m.
Size of the tiles is 1 sq m
So for covering 85 sq m we need 85/1 = 85 tiles
Since the tiles are bought in packs of 6 we need 85/6 packs which is approximately 15 packs of tiles.
Step 5 :
5)
Surface area of the given box with length as l, breadth as b and width as w is
2lw+2 lh+2 wh
here we have l,b,w as 3,2,2
so surface area is 3*2*2 = 12 sq m
Answer:
1) 216
2) 1
3) 450 ml
4)15 packs
5)12 sq m
Step-by-step explanation:
Step 1:
1) The series given is the cube of the first n natural numbers. Hence the nth term of the series can be obtained by n³.
Here we need the 6th term, so the cube of 6 is 216
Step 2 :
2 ) Area of the cube is given as 8000 cubic cm.
Hence side of the cube is 20 cm cube
The radius of the sphere is 20 cm as the diameter is given as 10 cm.
Hence number of spheres that can be placed in a cube of side 20 cm is 20/20 = 1
Step 3 :
3)
Total quantity of the mixture purchased from the chemist is 750 ml
Syrup and alcohol are in the ration 3:2
Hence the quantity of syrup in the mixture = 3/5 * 750 = 450 ml
Step 4 :
4)
Length and breadth of the given room is 17 m and 15 m
Hence its area is 17 * 5 = 85 sq m.
Size of the tiles is 1 sq m
So for covering 85 sq m we need 85/1 = 85 tiles
Since the tiles are bought in packs of 6 we need 85/6 packs which is approximately 15 packs of tiles.
Step 5 :
5)
Surface area of the given box with length as l, breadth as b and width as w is
2lw+2 lh+2 wh
here we have l,b,w as 3,2,2
so surface area is 3*2*2 = 12 sq m
Step-by-step explanation:
Which is a common effect of inflation?
Answer: Fills up something like how inflating a ballon fills it with air
Step-by-step explanation:
Hope it helped
In a year the number of people dying from cancer was 5 times the number who died from accidents. If the number of deaths from these two causes totaled 360,000, how many people died from each cause?
Based on the number of people dying from both causes and their relationship with each other, we can calculate that the number of people dead from cancer was 300,000 and those from accidents was 60,000.
Assuming x number of people died from accidents, the number that died from cancer would be 5 times that:
= 5x
The number of people dead from accidents is:
360,000 = 5x + x
6x = 360,000
x = 60,000 people
The number dead from cancer is:
= 5x
= 5 × 60,000
= 300,000 people
In conclusion, 60,000 died from accidents and 300,000 people died from cancer.
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Final answer:
To solve the problem, we created two equations: c = 5a and c + a = 360,000. After substituting and solving these equations, we found that 300,000 people died from cancer and 60,000 from accidents.
Explanation:
The question refers to a situation where the number of people dying from cancer is five times the number who died from accidents, and the total deaths from these two causes amounted to 360,000. To solve this, we can set up a system of equations. Let ‘c’ be the number of cancer deaths and ‘a’ the number of accident deaths. We are given:
c = 5a (the number of cancer deaths is five times accident deaths)c + a = 360,000 (the total number of deaths is 360,000)Substituting the first equation into the second, we get:
5a + a = 360,0006a = 360,000a = 60,000Then we substitute the value of ‘a’ back into the first equation to find ‘c’:
c = 5 * 60,000c = 300,000Therefore, 60,000 people died from accidents and 300,000 from cancer.
Cristiano is rolling a number cube. What is the probability of rolling a , or
a 6 followed by a 3 or a 4?
The probability of rolling a 6 followed by either a 3 or a 4 on a six-sided die is calculated by multiplying the probability of rolling a 6 (1/6) by the probability of then rolling either a 3 or a 4 (1/3), resulting in a combined probability of 1/18.
The question posed is about the probability of rolling a 6 followed by either a 3 or a 4 on a standard six-sided die. To find this, we first consider that the probability of rolling a specific number, such as a 6, on a six-sided die is 1/6. This is because there are 6 outcomes and only one of those outcomes is the desired number.
When rolling for the second number, which could either be a 3 or a 4, we have two desired outcomes out of the six possible outcomes on the die. Therefore, the probability of rolling either a 3 or a 4 is 2/6, which simplifies to 1/3.
To find the overall probability of rolling a 6 followed by either a 3 or a 4, we multiply the two probabilities together: (1/6) * (1/3) = 1/18. Therefore, the probability of this event occurring is 1/18.
The following two triangles have the same angles, and are similar. What is the ratio of hypotenuse to base for the triangles?
Answer:
A) The ratio of hypotenuse to base for the triangles is 0.75
Step-by-step explanation:
Here, the given question is INCOMPLETE.
The following two triangles have the same angles, and are similar. What is the ratio of height to base for the triangles?
A) .75
B) 1.00
C) 1.25
D) 2.50
Here, given that the two triangles are similar.
In triangle one:
Height = 6 units , Base = 8 units
In triangle one:
Height = 3 units , Base = 4 units
Now,as the two given triangles are similar.
⇒Their corresponding sides are PROPORTIONAL.
[tex]\implies \frac{H}{h} = \frac{B}{b} = \frac{6}{8} = \frac{3}{4} = 0.75[/tex]
So, in both the triangles, the corresponding side ratio is 0.75.
Hence, the ratio of hypotenuse to base for the triangles is 0.75
12x+60y≥540 what is x 4 times more than y
Answer: if y is equal to 18 and x is equal to 72
Step-by-step explanation: 18*4=72
what is the slope of a line that passes through the points (3,-6) and (0,-1)
Answer:
Step-by-step explanation:
[tex]\frac{-1+6}{0-3}\\\\\frac{5}{-3}\\ m = -1.6667[/tex]
Together, teammates Pedro and Ricky got 2681 base hits last season. Pedro had 283 more hits than Ricky. How many hits did each player have
Answer:
Ricky had 1199 hits.
Pedro had 1482 hits.
Step-by-step explanation:
State your variables
let "p" be the number of Pedro's base hits
let "r" be the number of Ricky's base hits
Create equations using information from the problem
p + r = 2681 [1]
p = r + 283 [2]
Substitute equation [2] in equation [1] replacing 'p'
p + r = 2681
r + 283 + r = 2681
Combine like terms to simplify
2r + 283 = 2681
Isolate '"r" to solve for Ricky's base hits.
2r + 283 - 283 = 2681 - 283 Subtract 283 on both sides
2r = 2398
2r/2 = 2398/2 Divide both sides by 2
r = 1199 Number of Ricky's hits
Substitute r = 1199 into any equation to find "p". I will use [2].
p = r + 283
p = 1199 + 283 Add
p = 1482 Number of Pedro's hits
Therefore Ricky had 1199 hits and Pedro had 1482 hits.
Ricky had 1199 hits and Pedro had 1482 hits.
Explanation:To solve this problem, we can set up a system of equations. Let x represent the number of hits Ricky had. Pedro had 283 more hits, so Pedro's number of hits would be x + 283.
Together, their hits add up to 2681, so we can write the equation:
x + (x + 283) = 2681
Combining like terms:
2x + 283 = 2681
Subtracting 283 from both sides:
2x = 2398
Dividing both sides by 2:
x = 1199
Ricky had 1199 hits and Pedro had x + 283 = 1199 + 283 = 1482 hits.
The bottom of Ignacio's desktop is
74.5 cm from the floor. Ignacio sits in his adjustable chair, and the tops of his legs are 49.3 cm from the floor. Each clockwise rotation of the knob on the chair raises Ignacio's legs by 4.8 cm Write an inequality to determine the number of clockwise rotations, r, Ignacio could make with the knob without his legs touching the desk.
Answer:
The inequality to determine the number of rotations is given by
r ≤ 5.25
Therefore the maximum number of rotations possible is 5.
Step-by-step explanation:
i.) The bottom of Ignacio's desktop is 74.5 cm from the floor.
ii.) The tops of his legs are 49.3 cm from the floor.
iii.) the difference between the bottom of Ignacio's desktop and the top of his legs = 74.5 - 49.3 = 25.2 cm.
iv.) Each clockwise rotation of the knob on the chair raises Ignacio's legs by 4.8 cm.
v.) let the number of clockwise rotations be r.
vi.) therefore the inequality to determine the number of rotations is given by
4.8r ≤ 25.2 therefore r ≤ 25.2/4.8 therefore r ≤ 5.25
simplify 3(2m^3n^-2)^4
Answer:
(48 m^12)/n^8
Step-by-step explanation:
Simplify the following:
3 ((2 m^3)/(n^2))^4
Multiply each exponent in (2 m^3)/(n^2) by 4:
3×2^4 m^(4×3) n^(-2×4)
4 (-2) = -8:
3×2^4 m^(4×3) n^(-8)
4×3 = 12:
(3×2^4 m^12)/(n^8)
2^4 = (2^2)^2:
(3 (2^2)^2 m^12)/(n^8)
2^2 = 4:
(3×4^2 m^12)/(n^8)
4^2 = 16:
(3×16 m^12)/(n^8)
3×16 = 48:
Answer: (48 m^12)/n^8
Answer:
On the screen shot
Step-by-step explanation:
pretty basic. you can't evaluate it to a single digit if there are 2 variables. lmk which variable you are solving for.
14 divided by 0.5 equals
Answer:
[tex]28[/tex]
Step-by-step explanation:
[tex] = \frac{14}{0.5} \ \\ \\ = \frac{14 \times 10}{5} \\ \\ = 14 \times 2 \\ = 28[/tex]
Answer:
[tex]28[/tex]........
of 900 centimeters. The table shows the height of each bounce.
Bounce Height (cm)
1 800
2 560
3 392
The heights form a geometric sequence.
How high does the ball bounce on the 5th bounce? Round your answer to the nearest tenth of a centimeter, if necessary.
Answer:
Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.Explanation:
The ball is dropped from a height of 900 centimeters.
Since the heights form a geometric sequence, you can find a common ratio between consecutive terms. This is:
Height bounce 2 / height bounce 1 = 560 / 800 = 0.7Height bound 3 / height bounce 2 = 392 / 560 = 0.7Hence, the ratio of the geometric sequence is 0.7, and taking bounce 1 as the start of the sequence, the general term of the sequence is:
[tex]a_n=800(0.7)^{n-1}[/tex]
With that formula you can find any term:
[tex]n=1,a_1=800(0.7)^{(1-1)}=800(0.7)^0=800\\ \\ n=2,a_{2}=800(0.7)^{(2-1)}=800(0.7)=560\\ \\n=5,a_{5}=800(0.7)^{(5-1)}=800(0.4)^4=192.08[/tex]
Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.
11 less than 7 times a number
is 5 more than 6 times the
number. Find the number
Answer:
5 i think. im not good at math. sorry if wrong
Need help completing the table!!
Answer:
time | distance
2 | 50
1.5 | 37.5
t | 25*t
2 | 50
12 | 300
d/25 | d
Step-by-step explanation:
solve the proportional equation 3/m-2 = 7/m+2
Answer:
The answer is m = 5
Step-by-step explanation:
Let's solve the proportional equation, this way:
3/m-2 = 7/m+2
3 * (m + 2) = 7 * (m - 2) [Lowest common denominator (m + 2) * (m - 2)]
3m + 6 = 7m - 14
-4m = -14 - 6 (Like terms)
-4m = -20
m = -20/-4
m = 5
The answer is m = 5
what is 62% of eighty
Answer:
49.6 or 49 3/5
Step-by-step explanation:
62/100*80
Simplify the 62/100 (meaning to make it to its simplest terms as possible).
62/100= 31/50
Now we can solve:
31/50*80= 49.6 or 49 3/5
Answer:
Step-by-step explanation divide 62 by 100 and multiply by 80
= 49.6
if m=a/b, m=18, and a=7, find b
Answer:
11
Step-by-step explanation:
You will move the 7 to 18 but bc there is a equal sign you will change the positive sign to negative and just solve -7 plus 18 you will get 11 and that’s b
Answer:
Step-by-step explanation:
18 = 7/b
18b=7
b=7/18
The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board? ( A=3.14r2)
Step-by-step explanation:
Given , The length of side of the square is 8 feet.
Since a circle is inscribed in the square. Then the diameter of the circle is equal to the length of side of the square .
Therefore the diameter of the circle is = 8 feet.
Radius of the circle is(r) = [tex]\frac{8}{2}[/tex] feet = 4 feet
The area of the circle is= 3.14 r²
= 3.14 × 4² square feet
= 50.24 square feet
The area of the square is = side × side
= 8×6 square feet
=64 square feet
Therefore the area of remaining board = (64- 50.24)square feet
=13.76 square feet
A bag contains 90 marbles some red and some blue. If there are 60 blue marbles what is the ratio of blue to red marbles
Answer:
2:1
Step-by-step explanation:
Answer:60:30
Step-by-step explanation:
90-60=30 so 60 blue to 30 red is 60:30
10x+4y+ 12z=120
11x +77y =220
8x +2y +32z =160
Answer:
x=8.94 ; y = 1.58; z=2.02
Step-by-step explanation:
solve 10x+4y+12z = 120 → 5x+2y+6z = 60
8x + 2y +32Z = 160 → 4x+y+16z = 80
To eliminate z multiply first equation by 16 and second equation by 6.
80x+32y+96z = 960
24x+6y+96z = 480
on subtractionwe get 56x+26y = 480
dividing by 2 we get, 28x + 13y = 240
Now we have a given equation 11x + 77y = 220 → x + 7y = 20
solving 28x + 13y = 240 and x + 7y = 20
28x + 13y =240
28x + 216y = 560
subtracting we get, 203y = 320
y = 1.58
x = 8.94
z = 2.02
(9x – 8) /
x + 10)
(x+2)
Answer:
15
Step-by-step explanation:
you work it out
solve the system using eliminationx+7y=-37 2x-5y=21
Answer:
y = -5
x = -2
Step-by-step explanation:
x+7y=-37
2x-5y=21
Multiply first equation by -2
-2 × (x + 7y) = -37 ➡ -2x -14y = 74
now add the equation up
2x-5y -2x -14y = 21 + 74 (-2x will eliminate 2x)
-19y = 95 divide both sides by 19
y = -5 we can find the value for x by using this information
x + 7y = -37 replace y by -5
x + 7×(-5) = -37
x = -2
Can you prove that DEF is congruent to HGF.!? Justify your answer.
Answer C seams like a likely answer ssa
Step-by-step explanation:
So I work at a welding shop,I cut alot of metal,if I cut a 17ft piece of metal and I need to punch 8 holes in it,how can I figure out how far apart each hole needs to be from each other so they can be even
Answer: 2.125 ft
Step-by-step explanation:
17/8=2.125
In order words each hole needs to be 2 ft and 1 and 1/2 inches apart.
9.5 , 9 3/4 , 9.125 , 9 3/4 from greatest to least
Answer:
9 3/4, 9 3/4, 9.5, 9.125
Step-by-step explanation:
*I converted to decimal form*
9 3/4= 9.75
9.75 is greater than both 9.5 and 9.125, so therefore it is first on the list.
Next, since 9.5 is greater than 9.125, it is arranged next on the list.
9.125 is the only number left, and is clearly the smallest out of all of the numbers shown.
We want to order the given set of numbers from greatest to lest.
The correct order is:
{9 3/4, 9 3/4, 9.5, 9.125}
Let's see how to get that.
The given set is:
{9.5, 9 3/4, 9.125, 9 3/4}
Here we can see that we have two times the mixed number (9 3/4).
This can also be written as:
9 + 3/4
And we know that 3/4 = 0.75
Then:
9 + 3/4 = 9.75
Then the mixed number is the largest number.
Then comes the 9.5, and finally the 9.125
Then the correct order is:
{9 3/4, 9 3/4, 9.5, 9.125}
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Simplify.
Rewrite the expression in the form 4^n
(4^6)(4^-8) =
Answer:
4^-2
Step-by-step explanation:
The rules of exponents tell you ...
(a^b)(a^c) = a^(b+c)
This means ...
(4^6)(4^-8) = 4^(6-8) = 4^-2
To simplify the expression (4^6)(4^-8), add the exponents and rewrite the expression as 4^(-2). Then, use the rule that states any number raised to the power of -1 is the reciprocal of that number to rewrite 4^-2 as 1/(4^2) which equals 1/16.
Explanation:To simplify the expression (4^6)(4^-8), we can use the rule that states when you multiply two powers with the same base, you add their exponents. In this case, 4^6 multiplied by 4^-8 will be equal to 4^(6 + (-8)). Simplifying the exponent, we have 4^(-2). Since any number raised to the power of -1 is the reciprocal of that number, we can rewrite 4^-2 as 1/(4^2) which is equal to 1/16.
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A line passes through (5,3) with a slope of 3/5. Plot 3 points on this line
Answer:
y=3/5*x, A(0,0), B(1,3/5), C(2,6/5)
Step-by-step explanation:
A(5,3)=(x1,y1)....x1=5, y1=3
m=3/5
y-y1=m(x-x1)
y-3=3/5(x-5)
y-3=3/5*x-3/5*5
y-3=3/5*x - 3
y=3/5*x-3+3
y=3/5*x
x=0, y=3/5*x, y=3/5*0=0 A(0,0)
x=1, y=3/5*1=3/5 B(1,3/5)
x=2, y=3/5*2=6/5 C(2,6/5)
What is it (6+9)-7-7
Answer:
1
Step-by-step explanation:
Solve using elimination
-3x + 4Y = 16
3x - y +14
Answer:
x = 8
y = 10
Step-by-step explanation:
We are given the equations;
-3x + 4Y = 16
3x - y =14
We are required to solve the two equations simultaneously using elimination
In this case, we will eliminate one unknown;
We eliminate x by adding the two equations;
That is;
-3x + 4Y = 16
3x - y =14
.............................
3y = 30
y = 10
Solving for x
3x - (10) = 14
3x = 14 +10
3x = 24
x = 8
Therefore, the solution of the equation is x=8 and y=10