Answer:
Trends:
In the graph or a table you easily can see trends in the data, for example, parts where if x increases also does y, or things like that.
Of course you, with some mathematical knowledge, also can notice those things when you have the equation, so this is a thing that the 3 have in common.
Range:
You usually can see the whole range (all the possible y values) of your equation by looking at the graph or the data set. And obviously, if you have the equation you can easily find the range of it.
After the closing of the mill, the town of Sawyerville experienced a decline in its population.
The relationship between the elapsed time, t, in years, since the closing of the mill, and the town's
population, P(t), is modeled by the following function.
P(t) = 12,000 - 2^-t/15
In how many years will Sawyerville's population be 9000?
Round your answer, if necessary, to the nearest hundredth.
Step-by-step explanation:
P(t) = 12,000 (2)^(-t/15)
9,000 = 12,000 (2)^(-t/15)
0.75 = 2^(-t/15)
ln(0.75) = ln(2^(-t/15))
ln(0.75) = (-t/15) ln(2)
-15 ln(0.75) / ln(2) = t
t = 6.23
The time it would take for Sawyerville's population to decrease to 9000 can be calculated by setting the population function equal to 9000 and solving for 't'. After a series of algebraic transformations, you can isolate 't' and calculate its value with a scientific calculator.
Explanation:To find the amount of time it will take for Sawyerville's population to fall to 9000 people, we can set up the equation: P(t) = 9000. Therefore, we have 9000 = 12,000 - 2-t/15.
To solve this equation, we first need to isolate the exponential term by subtracting 9000 from both sides, getting 3000 = 2-t/15. Then, we take the natural logarithm (ln) of both sides to remove the exponential term, resulting in ln(3000) = -t/15*ln(2). Divide both sides by -ln(2) and multiply them by 15 to find 't'. The final equation is: t = -15*ln(3000)/ln(2).
In this particular problem, you may need the help of a scientific calculator to compute the value of 't'.
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Find the area of the shaded polygons:
Answer:
For the green one the answer is 8 square units
For the red one the answer is 9 square units
Hope this helps
The area of the shaded green polygon is equal to 8 square units.
The area of the shaded red polygon is equal to 9 square units.
In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):
Area of triangle = 1/2 × b × h
Where:
b represent the base area.h represent the height.Note: When the green polygon is dissected, three triangles would be formed.
By substituting the given side lengths into the formula for the area of a triangle, we have the following;
Area of triangle = (1/2 × 1 × 1) + (1/2 × 3 × 1) + (1/2 × 3 × 4)
Area of triangle = 0.5 + 1.5 + 6
Area of triangle = 8 square units.
In order to determine the area of the shaded red polygon, we would have to apply Pick's theorem;
Area of polygon = (b/2 + i) - 1
where:
i is the number of lattice points inside a polygon.b is the number of lattice points on the perimeter of a polygon.By substituting the number of lattice points, we have the following;
Area of polygon = (b/2 + i) - 1
Area of red polygon = (4/2 + 8) - 1
Area of red polygon = 10 - 1
Area of red polygon = 9 square units.
If 18 is more than 2 times a number is -10, what is the number
Answer:
-14
Step-by-step explanation:
-10-18=-28 -28/2=-14
Find the sum and write it in standard form
(6x^3+3x^2+3)+(2x^3−5x+1)
Answer:
[tex] 8 {x}^{3} + 3 {x}^{2} - 5x + 4[/tex]
Step-by-step explanation:
[tex](6 {x}^{3} + 3 {x}^{2} + 3) + (2 {x}^{3} - 5x + 1) \\ = 6 {x}^{3} + 2 {x}^{3} + 3 {x}^{2} - 5x + 3 + 1 \\ = 8 {x}^{3} + 3 {x}^{2} - 5x + 4[/tex]
What is the sum of all the exterior angles for a 99-gon?*
Answer:
360
Step-by-step explanation:
The sum exterior angles of any number of side polygon is always 360
What is the factored form of x2 – x – 2?
Answer:
(x-2)(x+1)
Step-by-step explanation:
x²-x-2 can be factored into:
(x-2)(x+1)
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A monkey is swinging from a tree. On the first swing, she passes through an arc whose length is 24 m 24 m24, start text, space, m, end text. With each swing, she travels along an arc that is half as long as the arc of the previous swing.
Answer:
24*(1-0.5^n)/0.5
Step-by-step explanation:
Suppose that after I wrote this problem, Richard Rusczyk thought he could be more clever than I could, so he wrote his own problem. Suppose that both of our problems are in the set of 12 problems you are currently working on. If you sat down at your computer this morning and randomly loaded 4 of the 12 problems, what is the probability that both this problem and Richard Rusczyk's problem were among the four you loaded?
Answer:
P = 0.0909
Step-by-step explanation:
To know the number of ways or combinations in which we can select x elements from a group of n elements, we can use the following equation:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, if you sat down at your computer and randomly loaded 4 of the 12 problems, there are 495 different possibilities and it is calculated as:
[tex]12C4=\frac{12!}{4!(12-4)!}=495[/tex]
Then, from 495 different possibilities, there are 45 possibilities that both this problem and Richard Rusczyk's problem were among the four you loaded. This 45 possibilities are calculated as:
[tex](1C1)*(1C1)*(10C2)=(\frac{1!}{1!(1-1)!})*(\frac{1!}{1!(1-1)!})*(\frac{10!}{2!(10-2)!})=45[/tex]
Because you need to select: this problem and there is only one, the problem that Richard Rusczyk wrote and there is only one, and 2 problems from the other 10.
Finally, the probability that both this problem and Richard Rusczyk's problem were among the four you loaded is equal to:
[tex]P=\frac{45}{495}=0.0909[/tex]
Find the sum of
(3a+7)+(a−1)
The sum is ___
Answer:
4a+6
Step-by-step explanation:
To find the answer to this problem, you need to combine the like terms. (3a+7)+(a-1)=(3a+a)+(7-1)=4a+6. Hope this helps!
The of the given expression is 4a+6.
What is an expression?An algebraic expression is formed by using integers, constants, variables, and arithmetic operations. Variables and constants can be combined in an algebraic expression through mathematical operations.
Given that, an expression (3a+7)+(a−1), we need to find sum,
So,
(3a+7)+(a−1)
Opening the brackets,
3a+7+a-1
Combining the like terms,
3a+a+7-1
= 4a+6
Hence, the of the given expression is 4a+6.
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What is the area of the triangle?
A right triangle with side lengths 3.6 feet, 6 feet, and 4.8 feet. The base is 4.8 feet and the height is 3.6 feet.
8.64 feet squared
10.8 feet squared
14.4 feet squared
17.28 feet squared
Answer:
8.64 feet squared
Step-by-step explanation:
The formula for calculating the area of a triangle is 1/2(bh) or base * height divided by 2,
So first multiply 4.8 and 3.6
(4.8) (3.6) = 17.28
Then divide that by 2
17.28/2 = 8.64
Answer:
A. 8.64 feet squared
Step-by-step explanation:
A = 1/2bh
A = 1/2(4.8 x 3.6)
A = 1/2(17.28)
A = 8.64 feet²
Solve:5m=0.95 solve this please
Answer:
m=0.19
Step-by-step explanation:
To work this out you would divide 0.95 by 5. this is because 0.95 is equal to 5*m and so so work out m you would divide 0.95 by 5.
[tex]0.95/5=0.19\\m=0.19[/tex]
Find the area of the circle. Leave your answer in terms of pi.
Answer:
[tex]\pi \: {r}^{2} \\ \pi \: {6}^{2} \\ = 36\pi[/tex]
In the function f(x)=(x-2)^2+4, the minimum value occurs when x is
A.)-2
B.)2
C.)-4
D.)4.
Answer:
B
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
f(x) = (x - 2)² + k ← is in vertex form
with (h, k) = (2, 4)
Thus the minimum value is 4 when x = 2 → B
Determine the distance between -3 and 6.
A)
-9 units
B)
-3 units
X
0
3 units
D)
9 units
Answer:
D)
9 units
Step-by-step explanation:
[tex]distance = 6 - ( - 3) = 6 + 3 = 9 \: units[/tex]
Answer:
A) -9 units is the distance between -3 and 6
Please answer quickly! (30 pts)
Answer:
Option A
Step-by-step explanation:
If you take a look at the translation described in option A, the x value is increased by 1 (from -2 to -1), and the y value is decreased by 5 (from -5 to -10), meaning that you have made this jump with just one translation. Hope this helps!
Which expression is equivalent to (x + y)(x – y)?
We can't see any choices but it doesn't matter. That's the factorization of the difference of two squares. It's important to recognize either side when you see it; the usual next move is to replace it with the other side.
(x + y)(x – y) = x² - y²
Answer: x² - y²
What is 4x + 2y = 20 in slope-intercept form?
Y = -4x + 20
Y =-2x + 10
Y = 2x + 20
Y = 2x + 10
I need this quickly if at all possible. I´ll giver brainliest to the first answer!
A certain medication comes in the form of a capsule, as shown below. The fluid inside the capsule contains several ingredients, including the active medication.
What is the volume of the capsule? Round to the nearest tenth.
V = ____ mm3
If the density of the active medication in the liquid is
0.7 mg/mm3, how many milligrams of the active medication are in one capsule?
Round to the nearest tenth.
_____ mg
Answer:
mme 3 is 20
Step-by-step explanation:
i dont like to do work
Answer:
V= 103.9 mm^3 and 72.7 mg
Step-by-step explanation:
Edge
A drawer contains 10 blue pens, 10 black pens, and 10 red pens. Without looking. Mr. Lopez is going to take one pen from the drawer, use it, and then put it back into the drawer. Then he is going to take another pen from the drawer to use. What is the probability of Mr. Lopez taking a red pen first and then taking a blue pen?
Answer:
1/9
Step-by-step explanation:
There are 30 pens in total, 1/3 of the pens are each the following colours: blue; black; red.
This will result in a one in three chance of picking up a red pen. As Mr.Lopez puts the pen back, the fractions stay the same as it's the same possibility both times.
As it's again a one in three chance, we just have to multiply it for the possibility of him picking a blue pen, which is 1/3.
1/3 * 1/3 = 1/9
What’s the answer???
Answer:
81
Step-by-step explanation:
9*7 = 63
6*3 = 18
63 + 18 = 81
Maria is painting a mural on a brick wall. She is painting 4 circles with radii of 2 inches, 4 inches, 9 inches, and 14 inches. How much paint will she need to fill in all four circles?
She will need ____? square inches of paint for all the circles.
Answer:
932.58 in ^ 2 is needed
Step-by-step explanation:
What we need to do is calculate the area of all the circles and add it up, so we know how many square inches of paint are going to be needed.
We know that the area of a circle has the following formula:
A = pi * r ^ 2
there are 4 circles:
radio of 2 inches:
A = 3.14 * 2 ^ 2 = 12.56 in ^ 2
radio of 4 inches:
A = 3.14 * 4 ^ 2 = 50.24 in ^ 2
radio of 9 inches:
A = 3.14 * 9 ^ 2 = 254.34 in ^ 2
radio of 14 inches:
A = 3.14 * 14 ^ 2 = 615.44 in ^ 2
12.56 + 50.24 + 254.34 + 615.44 = 932.58
a total of 932.58 in ^ 2 is needed
Please answer this correctly
Answer:
3:30 pm
Step-by-step explanation:
Games : 1 hour
Cleaning : 1 hour
Homework: 30 minutes
Total time
1+1+ 30 minutes
She started at 1 pm
1 + 2 hour 30 minutes
1 +2 hours = 3 pm
3+30 minutes = 3:30
Answer:
1:00 pm + 1 hr = 2:00pm
2:00pm + 1 hr= 3:00pm
3:00pm +30 mins = 3:30 pm
Here you go good luck guys!
Answer:
25.9666 m
Step-by-step explanation:
The 4 arches combine to for a circle, so then you can find the area of the shaded region by subtracting the area of the square from the area of the circle.
The formula for area of a circle is A=[tex]\pi[/tex]r^2
Since the radius of the circle would be 11/2 or 5.5, the area if the circle would be [tex]\pi[/tex] x 5.5^2. This equals 95.0334.
The area of the square would be 11 x 11 = 121.
The 121-95.0334= 25.9666 m
The area of a trapezoid is 20ft2. The sum of its two bases is 10 ft. What is the height of the trapezoid?
A. 0.5 ft
O B. 14
C. 26
D.
4 ft
Answer:
d. 4 ft
Step-by-step explanation:
1/2h(b1+b2)
1/2h(10)=20
multiply both sides by 2
h(10)=40
divide both sides by 10
h=4
10. Marvin is painting three squares shaped like
The ones below. If it takes him exactly four cans
of paint to paint square 3 and five cans of paint
To paint square 2, how many cans of paint should
he need to paint square 1?
Marvin would need 6.25 cans of paint for square 1.
Using ratio of paint used
We are given that it takes 4 cans of paint to paint square 3 and 5 cans of paint to paint square 2.
This suggests a possible ratio between the amount of paint needed for different squares. Let's assume this ratio remains constant.
If the ratio between squares 2 and 3 is r, then:
Paint needed for square 2 = 5 cans = r * Paint needed for square 3
Paint needed for square 3 = 4 cans
Solving for r: r = 5 cans / 4 cans = 1.25
Assuming the same ratio applies to square 1 and 2:
Paint needed for square 1 = r * Paint needed for square 2
Paint needed for square 1 = 1.25 * 5 cans = 6.25 cans
Therefore, Marvin would need 6.25 cans of paint for square 1.
Complete question:
Marvin is painting three squares shaped like the one below. If it takes him exactly four cans of paint to paint square 3 and five cans of paint to paint square 2, how many cans of paint should he need to paint square 1?
A number cube for a game has a volume of 64 mm
What is the length of one side of the cube?
3.27 mm
4 mm
6.46 mm
8 mm
Answer:
6.46 mm
Step-by-step explanation:
A word processing program requires a user to enter a 7-digit registration code made up of the digits 1,2,4,5,6,7 and 9. Each number has to be used, and no number can be used more than once. How many codes are possible?
Final answer:
To find the number of possible codes, we can use the concept of permutations. There are 7 digits to choose from and we need to select all of them. Therefore, there are 5,040 possible registration codes.
Explanation:
To find the number of possible codes, we can use the concept of permutations.
Since the code must be made up of 7 digits and each digit can only be used once, we can calculate the number of permutations of the 7 digits. The formula to use is nPr = n! / (n - r)!, where n is the total number of elements and r is the number of elements to be selected.
In this case, there are 7 digits to choose from and we need to select all of them.
So we plug in n = 7 and r = 7 into the formula:
nPr = 7! / (7 - 7)! = 7! / 0! = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040
Therefore, there are 5,040 possible registration codes.
Two points on a lone are (3,8) and (-3,2). What is the slope of the line?
Find the volume of a right circular cone that has a height of 5.3 fr and a base with a circumference of 19.1 ft. Round your answer to the nearest tenth of a cubic foot.
For this case we have that by definition, the volume of a cone is given by:
[tex]V = \frac {1} {3} * \pi * r ^ 2 * h[/tex]
Where:
r: It is the radius of the cone
h: Is the height of the cone
We must find the radius knowing that the circumference of the base of the cone is[tex]19.1 \ ft[/tex]
[tex]2 \pi * r = 19.1\\r = \frac {19.1} {2 \pi}\\r = 3.04 \ ft[/tex]
Thus, we substitute in the formula:
[tex]V = \frac {1} {3} * \pi * (3.04) ^ 2 * 5.3\\V = \frac {1} {3} * \pi * 9.25 * 5.3\\V = \frac {1} {3} * 154.0165\\V = 51.34[/tex]
Thus, the volume of the cone is: [tex]51.34 \ ft ^ 3[/tex]
Answer:
[tex]51.3 \ ft ^ 3[/tex]
Answer:
51.3 ft^3
Step-by-step explanation:
(01.01 LC)
Which of the following is a rational number? (1 point)
square root of 36, square root of 37, square root of 38, square root of 39
Group of answer choices
square root of 36
square root of 37
square root of 38
square root of 39
Answer:
Square root of 36.
Step-by-step explanation:
The square root of 36 = 6 so this is rational.
Recall that a rational number is one that can be written as a/b where a and b are not 0. 6 can be written as 6/1.
Answer:
6
Step-by-step explanation:
The square root of 36 is 6