There is a theoretical probability of approximately 26.2% that at least one of the 27 students in the group has the H1N1 influenza virus.
To calculate the theoretical probability that at least one of the 27 students has the H1N1 influenza virus, we can use the complement rule. The complement of the event "none of the 27 students have the H1N1 influenza virus" is the event "at least one of the 27 students has the H1N1 influenza virus."
The probability that a student does not have the H1N1 influenza virus is 1 - 0.01 = 0.99. Since the students are selected independently, the probability that none of the 27 students have the virus is (0.99)^27.
Using the complement rule, the probability that at least one of the 27 students has the H1N1 influenza virus is:
1 - (0.99)^27 ≈ 0.262
Expressed as a percentage with 3 decimal places, the theoretical probability is approximately 26.2%.
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each user on a computer system has a password, which is 6 to 8 characters long, where each character is anuppercase letter or a digit. each password must contain at least one digit. how many possible passwords arethere?
The total number of possible passwords can be calculated by finding the number of possible combinations for each character position in the password and multiplying them together.
Since each character can be an uppercase letter or a digit, there are a total of 36 possible characters (26 letters + 10 digits). The number of passwords that do not contain any digits can be found by calculating the number of possible passwords with only uppercase letters (26 possible characters) and then multiplying it by the number of possible positions in the password (6 to 8 characters). Therefore, the total number of possible passwords is: 36⁶ + 36⁷ + 36⁸ - 26⁶ - 26⁷ - 26⁸
= 2,176,782,336 + 78,364,164,096 + 2,821,109,907,456 - 308,915,776 - 8,031,810,176 - 208,827,064,576
= 2,584,618,967,360
So there are a total of 2,584,618,967,360 possible passwords that meet the given criteria.
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A: Scribe
B: Sage
4) Ava is at a Maroon 5 concert and is sitting 60 meters above the
ground floor. If the distance between Ava and Maroon 5 is 135
meters, what is the measure of the angle of depression? Round to
the nearest whole degree.
The measure f the angle of depression is 66 degrees
How to determine the valueTo determine the value of the angle, we need to know that there are six different trigonometric identities.
These identities are enumerated as;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
The adjacent side = 60 meters
The opposite side = 135 meters
Using the tangent identity, we have that;
tan θ = 135/60
Divide the values, we have;
tan θ = 2. 25
Find the tangent inverse of the value
θ = 66. 0 degrees
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Note: The information given does not require diagrams and thus is self - explanatory.
Draw the triangle and label all parts.
Triangle ABC is a right triangle.
Angle A = 18 degrees
Angle B = 90 degrees
AC = 25 cm
Find AB. Do not label. Round your final answer to the nearest tenth.
The Length of side AB is approximately 72.4 cm.
To draw triangle ABC, we can start by drawing a straight line AB and then drawing a perpendicular line segment BC that meets AB at a 90-degree angle. This gives us a right triangle where angle B is 90 degrees. Finally, we can draw a line segment AC to connect points A and C, making sure that the length of AC is 25 cm since that is given in the problem.
To label the parts of the triangle, we can use the following conventions:
- Side AB is the hypotenuse of the right triangle and is opposite the right angle B.
- Angle A is opposite side AC, and angle C is opposite side BC.
Using this labeling convention, we can write:
- AB is the hypotenuse.
- AC is the side opposite angle A.
- BC is the side opposite angle C.
To find the length of AB, we can use the trigonometric ratio for the sine of angle A:
sin A = opposite / hypotenuse
sin 18 = AC / AB
Multiplying both sides by AB, we get:
AB * sin 18 = AC
Substituting the value of AC as 25 cm, we get:
AB * sin 18 = 25
Dividing both sides by sin 18, we get:
AB = 25 / sin 18
Using a calculator, we can evaluate this to get:
AB ≈ 72.4 cm (rounded to the nearest tenth)
Therefore, the length of side AB is approximately 72.4 cm.
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Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree 4; zeros: -2-5i; 4 multiplicity 2
The polynomial with degree 4 and the given zeros is f(x) = ((x+2)² + 25)(x-4)²
If a polynomial has complex zeros with non-zero imaginary parts, then the complex conjugate of each complex zero must also be a zero of the polynomial with the same multiplicity.
Therefore, the zeros of the polynomial with degree 4 are:
-2-5i, -2+5i, 4, and 4 (with multiplicity 2).
To find the polynomial, we can start by writing out the factors corresponding to each zero:
(x - (-2-5i))(x - (-2+5i))(x - 4)²
Simplifying the factors, we get:
((x+2)+5i)((x+2)-5i)(x-4)²
Expanding the factors, we get:
((x+2)² - (5i)²)(x-4)²
((x+2)² + 25)(x-4)²
Thus, the polynomial with degree 4 and the given zeros is:
f(x) = ((x+2)² + 25)(x-4)²
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If 1/64 = 4^2s-1. 16^2s+2, what is the value of s? a. -1
b. 0
c. 1
d.no solution
Answer:
a ) -1
Step-by-step explanation:
[tex]\frac{1}{64} = 4^{2s-1} . 16^{2s+2}\\ 4^{-3} = 4^{2s-1+4s+4}\\ 4^{-3} = 4^{6s+3}\\ 6s + 3 = -3\\6s = -6\\s = -1[/tex]
Three tenis balls are stored in a cylindrical container with a height of 8. 6 inches and a radius of 1. 39 inches. The circumference of a tennis ball is 8 inches. Find the amount of space within the cylinder not taken up
The space within the cylinder not taken up by the three tennis balls can be found by first determining the volume of the cylinder and the total volume of the three tennis balls.
The volume of the cylinder is given by the formula:
V_cylinder = πr^2h
where r is the radius and h is the height. Substituting the given values, we get:
V_cylinder = π(1.39)^2(8.6) = 50.168 cubic inches
The total volume of the three tennis balls can be found by multiplying the volume of one tennis ball by three. The volume of a tennis ball can be approximated by the formula for the volume of a sphere:
V_ball = (4/3)πr^3
where r is the radius. Since the circumference of a tennis ball is 8 inches, we can solve for the radius using the formula:
C = 2πr
8 = 2πr
r ≈ 1.27 inches
Substituting this value, we get:
V_ball = (4/3)π(1.27)^3 ≈ 8.48 cubic inches
Therefore, the total volume of the three tennis balls is:
V_total = 3V_ball = 25.44 cubic inches
Finally, we can find the amount of space within the cylinder not taken up by the tennis balls by subtracting the total volume of the tennis balls from the volume of the cylinder:
V_not_taken_up = V_cylinder - V_total = 50.168 - 25.44 = 24.728 cubic inches
Therefore, the amount of space within the cylinder not taken up by the tennis balls is approximately 24.728 cubic inches.
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Given the unit conversion 3 teaspoons = 15 milliliters
(mL), convert 61.4 mL to teaspoons.
Answer:
307.5 milliliters
Step-by-step explanation:
Ratio 3:15, 1:5
61.4 is 1 un 1:5
61.5 x 5= 307.5
307.5 milliliters
Help me pls need this done
Answer:
B
Step-by-step explanation:
The positive 9 shows that it's moving up 9 units, the negative in front of the square root reflects the equation over the x-axis, and the positive 3 shows that it has been moved to the left 3 units.
Outside of equation: positive numbers translate up, negative translate down. (ex: [tex]x^{2}+3, x^{2}-3[/tex]. The three would move the equation up or down.)
Inside of equation: positive numbers translate left, negative translate right. (ex: [tex](x-3)^{2},(x+3)^{2}[/tex]. The 3 would move left or right.)
a math 110 student decides to make quarterly payments of $2,500 into a retirement account paying 2% interest per year compounded continuously. if the student continues to make these payments for 40 years, compute each of the following values.
Answer:
Sure. Here are the values that you requested:
Future Value: The future value of the investment is $1,388,903.23.
Interest Earned: The total interest earned is $1,263,903.23.
Number of Payments: The total number of payments is 160 (40 years * 4 quarters/year).
Average Balance: The average balance of the account is $432,203.28.
Here is the formula that I used to calculate the future value of the investment:
FV = PV * (1 + r)^n
Where:
FV is the future value
PV is the present value (the initial deposit)
r is the interest rate
n is the number of years
In this case, the present value is $2,500, the interest rate is 2%, and the number of years is 40.
FV = 2500 * (1 + 0.02)^40 = 1388903.23
Here is the formula that I used to calculate the interest earned:
Interest = FV - PV
In this case, the future value is $1,388,903.23 and the present value is $2,500.
Interest = 1388903.23 - 2500 = 1263903.23
Here is the formula that I used to calculate the number of payments:
Number of Payments = Years * Periods/Year
In this case, the number of years is 40 and the number of periods per year is 4.
Number of Payments = 40 * 4 = 160
Here is the formula that I used to calculate the average balance of the account:
Average Balance = (PV + FV)/2
In this case, the present value is $2,500 and the future value is $1,388,903.23.
Average Balance = (2500 + 1388903.23)/2 = 432203.28
Step-by-step explanation:
Bookwork code: M47 allowed
This distance-time graph shows part of the journey of a bee travelling away from
its hive.
Calculate the average speed of the bee for this part of the journey,
If your answer is a decimal, give it to 1 d.p.
The average speed for this part of the journey is 6 m/s.
Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
The parameters for this problem are given as follows:
Change in distance of 90 - 30 = 60 m.
Change in time of 10 - 0 = 10 s.
Hence the average speed for this part of the journey is given as follows:
60/10 = 6 m/s.
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what are the terminal points determined by π/2, π, −π/2, and 2π?
angles that differ by a multiple of 2π have the same terminal point, because they complete the same number of full circles around the unit circle.
The terminal point determined by an angle in standard position (i.e., with the initial side along the positive x-axis) is the point where the terminal side of the angle intersects the unit circle. Here are the terminal points determined by π/2, π, −π/2, and 2π:
The angle π/2 (90 degrees) has a terminal point at (0, 1), which is the point on the unit circle that is directly above the origin.
The angle π (180 degrees) has a terminal point at (-1, 0), which is the point on the unit circle that is to the left of the origin.
The angle −π/2 (-90 degrees) has a terminal point at (0, -1), which is the point on the unit circle that is directly below the origin.
The angle 2π (360 degrees) has a terminal point at (1, 0), which is the point on the unit circle that is to the right of the origin.
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3. Find the measure of Arc BED. *
O 180 degrees
O142 degrees
O218 degrees
O 72 degrees
The measure of arc BED is:
180 degrees
How to find the measure of Arc BED?The arc of a circle is the segment or part of the circumference of a circle. The measure of an arc is the angle at which the arc is subtended.
You will notice that AD is the diameter of the circle.
Since the measure of arc CD is 90°.
Thus, the measure of arc AB is:
90 - 52 = 38°
Arc ED = arc AB (vertically opposite angles are equal)
Therefore, the measure of Arc BED will be:
Arc BED = Arc BC + arc CD + arc ED
Arc BED = 52° + 90° + 38°
Arc BED = 180°
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Find area of pqrs, leave answer in simplest radical form
The required area of the trapezoid PQRS is 144+72√3 square units. Option A is correct.
Area of trapezoid PQRS = [PQ+RS]/2 * QB
We are given PQ=18, QR = 24
The vertical line from Q to line SR is given as,
sin30 = V/24
V = 12
And horizontal measure over SR is given as,
cos30 = H/QR
H = 12√3
The length of QR is given as,
QR = 6 + 12√3
Area of trapezoid PQRS = [PQ+RS]/2 * QB
= [18+6+12√3]/2*12
= 144+72√3
Thus, the required area of the trapezoid PQRS is 144+72√3 square units.
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Sandals are on sale for 75% off. The original price of one pair of sandals is $30. What is the new cost of the sandals after discount?
Answer:$7.50
Step-by-step explanation:The original cost of the sandals is $30 and the discount if is 75%.That means only 25% of the original cost of the sandals remain so we do 30x.25=$7.50
need help with #3, 4, 5
1. It will cost Dave $646.62 to refill his truck's fuel tank.
2. The cost of concrete for Greg's driveway will be $9,720.
3. Total cost of the topsoil needed from suppliers is $726.90 from Holland Growers and $919.55 from Night Growers.
How much will it cost Dave to refill his truck?A refill refers to filling something again with more of same thing such as fuel, water etc.
We need to convert the fuel capacity of Dave's truck from gallons to liters.
1 US gallon = 3.78541 liters
So, 180 US gallons will give us:
= 180 * 3.78541 liters
= 681.37 liters
We will calculate total cost of refilling Dave's truck which is:
= 681.37 liters * 0.949 dollars/liter
= $646.62013
= $646.62.
2. To get volume of concrete needed, we will convert thickness of the driveway from inches to meters. 4 inches is equal to 0.1 meters.
The volume of the driveway is:
V = l x w x h
V = 20m x 36m x 0.1m
V = 72 cubic meters
The cost of the concrete for the driveway is:
= Volume x Price per cubic meter
= 72 cubic meters x $135/cubic meter
= $9,720.
3. To get total cost of the topsoil, we have to calculate volume of soil required for each planter box:
Volume = Length x Width x Depth
Volume = 44" x 24" x 18"
Volume = (44/36) yards x (24/36) yards x (18/36) yards
Volume = 1.22 yards³
Since she needs to build 35 planter boxes, the total volume of soil required is:
= 1.22 yards³ x 35
= 42.7 yards³
The cost from Holland Growers will be:
= Total Volume x $17/yd
= 42.7 yards³ x $17/yd
= $726.90
The cost from Night Growers will be:
= Total Volume x $21.50/yd²
= 42.7 yards³ x $21.50/yd²
= $919.55.
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use the area and circumstance formulas to find the radius or diameter
The radius and diameter of each measure to their approximation is as follows;
7) 14 km 8) 5 yards 9) 23 inches 10) 20 feet 11) 17.5 mm 12. 22.5 cm
13) 95feet² 14) 92.2 mm 15) 119.6 m 16)227 inches²
How do we find the radius and diameter of a circle using area?For each problem, we use the formulas;
Area of a circle: A = πr²
Circumference of a circle: C = 2πr or C = πd
a) Find the radius of a circle with an area of 615.75 square kilometers.
A = πr²
∴ r = √(A/π)
√(615.75/π)
= 14 km
b) Find the diameter of a circle with a circumference of 15.71 yards.
C = πd
∴ d = C/π
15.71/π = 5 yards
c) Find the diameter of a circle with an area of 415.48 square inches.
A = πr²
∴ r = √(A/π)
√(415.48/π) = 11.5 inches,
∴ d = 2r = 23 inches
d) Find the radius of a circle with a circumference of 125.66 feet.
C = 2πr
∴ r = C/(2π)
125.66/(2π) = 20 feet
e) Find the diameter of a circle with an area of 240.25 square millimeters.
sqrt(240.25/π) = 8.75 mm,
∴ d = 2r = 17.5 mm
f) Find the radius of a circle with a circumference of 45π centimeters.
45π/(2π) = 22.5 cm
g) Find the area of a circle with a circumference of 11π feet.
11π/(2π) = 5.5 feet,
A = πr² = π×(5.5)² = 95 feet²
h) Find the circumference of a circle with an area of 676 square millimeters.
A = πr²
∴ r = √A/π) =√(676/π) = 14.67 mm,
∴ C = 2πr = 2π×14.67 = 92.2 mm
i. Find the circumference of a circle with an area of 1,134.11 square meters.
√(1,134.11/π) = 19.03 m,
C = 2πr = 2π×19.03 = 119.6 m
j. Find the area of a circle with a circumference of 53.41 inches.
C = 2πr
∴ r = C/(2π) = 53.41/(2π) = 8.5 inches,
∴ A = πr² = π×(8.5)² = 227inches²
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Grant is going to drain his hot tub. The volume, in gallons, after the pool has been drained can be modeled by 45t^2 − 108t + 63, where t is the time in seconds.
Choose the correct expression to solve for the amount of time it takes to drain the hot tub.
A) (9t - 9)(5t - 7)
B) (9t + 9)(5t + 7)
C) 450(0)^2 - 108(0) + 63
D) 9(5t^2 -12t + 7)
I know that the correct answer is A, but I don't understand what the correct process is.
The correct expression to solve for the amount of time it takes to drain the hot tub is: A) (9t - 9)(5t - 7)
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.By using the sum-product pattern, we have the following:
45t² − 108t + 63
45t² − 63t - 45t + 63
By writing the common factor from the two pairs, we have the following:
(45t² − 63t) - (45t + 63)
9t(5t - 7) - 9(5t - 7)
By rewriting in factored form, we have the following:
(9t - 9)(5t - 7)
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HELP PLEASE!!!!!!!!!!!!
Answer:
Anything you want
Step-by-step explanation:
This is a problem where you have your own choice about whether you agree or disagree with the choice.
if you flip a coin 40 times and get heads every time. what is the likelihood of flipping a tails the 41st time
The probability of getting tails on the 41st flip remains the same as any other individual flip: 0.5 or 50%.
When you flip a fair coin, there are two possible outcomes: heads (H) or tails (T). Since it's a fair coin, each outcome has an equal probability of occurring, which is 0.5 or 50%.
Now, let's consider the scenario you mentioned. You have already flipped the coin 40 times, and each time it landed on heads (H). In this case, the probability of getting heads on each of those 40 flips is (0.5)⁴⁰, which is an incredibly small probability because it's unlikely to get heads on 40 consecutive flips of a fair coin.
However, the key point is that each coin flip is an independent event. The outcome of one flip does not affect the outcome of the next flip. So, regardless of the previous 40 flips landing on heads, the probability of getting tails on the 41st flip is still 0.5 or 50%. The coin has no memory of the previous flips and doesn't "know" that it needs to "balance out" the previous heads with a tails.
Therefore, the probability of getting tails on the 41st flip remains the same as any other individual flip: 0.5 or 50%.
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in the diagram, points B and C are points of tendency. Solve for x
The value of the variable x is 7
What is point of tangency?Point of tangency is described as the point where tangent meets the circle.
It is perpendicular to the radius of the circle, with which it intersects
From the information given, we have that;
BD = 46
CD = x² - 3
Since tangent lines are equal
We have that;
46 = x² - 3
collect the like terms, we get;;
x² = 46 + 3
Add the values
x² = 49
Find the square root of both sides, we have;
x = √49
Find the value
x = 7
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Calcular el ángulo de elevación del Sol en el momento en que un árbol de 32.5m de altura proyecta una sombra de 75 m.
The angle of elevation of the Sun is approximately 23.85 degrees.
This problem can be solved using the tangent trigonometric ratio.
If we call "x" the angle of elevation of the Sun, then we can write:
tan(x) = height of the tree / length of the shadow
tan(x) = 32.5 / 75
To find the value of x, we can take the inverse tangent (tan⁻¹) of both sides of the equation:
x = tan⁻¹ (32.5 / 75)
x ≈ 23.85 degrees
Therefore, the angle of elevation of the Sun is approximately 23.85 degrees.
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Jamie had a bag filled with sour candies. There were 3 lemon-lime, 6 watermelon, and 5 grape sour candies. What is the correct sample space for the sour candies in the bag?
Sample space = lemon-lime, watermelon, grape
Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, watermelon, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
Sample space = 3, 5, 6
Sample space = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
The Sample space includes all possible combinations of the three types of sour candies, taking into account that there can be multiple candies of the same type in the bag.
The correct sample space for the sour candies in the bag is:
Sample space = {lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape}
Each element in the sample space represents a different possible outcome of selecting a sour candy from the bag. The sample space includes all possible combinations of the three types of sour candies, taking into account that there can be multiple candies of the same type in the bag.
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The correct sample space for the sour candies in the bag is (c) Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, watermelon, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
What is the correct sample space for the sour candies in the bag?from the question, we have the following parameters that can be used in our computation:
3 lemon-lime, 6 watermelon, and 5 grape sour candies
The correct sample space for the sour candies in the bag is the list of items in the bag
So, we have
Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, watermelon, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape
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Find the measure of the missing angles.
PLEASEE ANSWER FAST!!!
I've already tried x = 52 and y = 90 but it won't work
Answer:
x= 52° and y= 142°
Step-by-step explanation:
x combined with angle next to it make a right angle, so you can find x by subtracting 38 from 90. y would be 90 plus 52 because the other angle is the same as x.
Answer:
x = 52° and y = 142°
Step-by-step explanation:
38 + x + the right angle are on straight line.
angles on straight line add up to 180.
so x = 180 - 90 - 38 = 52.
y is the big angle, not the 90.
again, angles on straight line:
y = 180 - 38 = 142
alison made a three-layer gelatin dessert that was 15 cm long by 10 cm wide. the heights of the layers were 3 cm,2 cm, and 1 cm.a 3-layer prism. the bottom layer has a length of 15, height of 3, and width of 10. the middle layer has a length of 15, height of 2, and width of 10. the top layer has a length of 15, height of 1, and width of 10.what is the total volume?the volume of the bottom layer is 150 cm3.the volume of the middle layer is cm3.the volume of the top layer is cm3.the total volume is 900 cm3.
Answer:
3rd layer: 450
2nd layer: 300
1st layer: 150
Total: 900
Step-by-step explanation:
got it correct!
The total volume of the three-layer gelatin dessert is 900 cm³.
What is Volume?The space occupied within the boundaries of an object in three-dimensional space is known as volume.
To calculate the volume of each layer, we multiply the length, width, and height of each layer.
The volume of the bottom layer:
Volume = length × width × height
Volume = 15 cm × 10 cm×3 cm
Volume = 450 cm³
The volume of the middle layer:
Volume = length×width × height
Volume = 15 cm× 10 cm ×2 cm
Volume = 300 cm³
The volume of the top layer:
Volume = length×width × height
Volume = 15 cm × 10 cm× 1 cm
Volume = 150 cm³
To find the total volume, we add up the volumes of each layer:
Total Volume = 450 cm³ + 300 cm³ + 150 cm³
Total Volume = 900 cm³
Hence, 900 cm³ is the total volume of the three-layer gelatin dessert.
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In 2010, the population of a city was 246,000. From 2010 to 2015, the population grew by 7%. From 2015 to 2020, it fell by 3%. To the nearest 100 people, what was the population in 2020?
The population of the city in 2020 is approximately 255 100
How to determine the population in 2020To find the population in 2020 we first need to find the population in 2015 after the 7% growth from 2010.
Population in 2015 = 246 000 + 0.07 x 246 000 = 263,220
we need to find the population in 2020 after the 3% decrease from 2015
Population in 2020 = 263 220 - 0.03 x 263,220 = 255 027.6
Rounding to the nearest 100 people the population in 2020 is approximately 255 100
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Calculate the perimeter and area of each of the following figures. All curves are semicircles or quadrants.
The perimeters and areas of each figures are
Area = 4.48 m²; Perimeter = 11.312 metersArea = 3400 cm²; Perimeter = 393 centimetersArea = 98.125 m²; Perimeter = 39.25 metersArea = 12.46 cm²; Perimeter = 9.03 centimetersArea = 392.5 cm²; Perimeter = 54.95 centimetersCalculating the perimeters and areas of each figuresGiven that all curves are semicircles or quadrants., we have
Figure 1
The area is calculated as
Area = 1.6 * 2.8
Area = 4.48 m²
The perimeter is calculated as
Perimeter = 2 * (1.6 + 2.8) + 3.14 * 1.6/2
Perimeter = 11.312 meters
Figure 2
The area is calculated as
Area = 50 * 68
Area = 3400 cm²
The perimeter is calculated as
Perimeter = 2 * (50 + 68) + 3.14 * 50
Perimeter = 393 centimeters
Figure 3
The area is calculated as
Area = 3.14 * 5² + 2 * 3.14 * (5/2)² * 1/2
Area = 98.125 m²
The perimeter is calculated as
Perimeter = 2 * 3.14 * 5 + 2 * 1/2 * 3.14 * 5/2
Perimeter = 39.25 meters
Figure 4
The area is calculated as
Area = 3.14 * (4.6/2)²/2 + 3.14 * (2.3)²/4
Area = 12.46 cm²
The perimeter is calculated as
Perimeter = 3.14 * (4.6/2) + 3.14 * (2.3)/4
Perimeter = 9.03 centimeters
Figure 5
The area is calculated as
Area = 3.14 * (15)²/2 + 2 * 3.14 * (5)²/2 - 3.14 * (5)²/2
Area = 392.5 cm²
The perimeter is calculated as
Perimeter = 3.14 * (15) + 2 * 3.14 * (5)/2 - 3.14 * (5)/2
Perimeter = 54.95 centimeters
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diego bought a 3-kilogram bag of carrots from the grocery store. he added 0.8 kilograms of carrots to a pot of vegetable soup. then, he grated 400 grams of carrots for his carrot cake. how many kilograms of carrots does he have left?
Therefore, Diego has 1.8 kilograms of carrots left.
Diego initially had 3 kilograms of carrots. He used 0.8 kilograms for the soup and 0.4 kilograms (400 grams) for the carrot cake.
So the total amount of carrots he used is:
0.8 + 0.4 = 1.2 kilograms
To find out how many kilograms of carrots he has left, we can subtract the amount he used from the initial amount:
3 - 1.2 = 1.8 kilograms
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Why is f(x) = cos^2x + sin^2x a straight line
Answer:
The function f(x) = cos^2x + sin^2x is not a straight line, but rather a constant function that always evaluates to 1 for any value of x.To see why this is the case, recall the trigonometric identity that states that the square of the cosine of an angle added to the square of the sine of the same angle equals 1:cos^2x + sin^2x = 1Since this identity holds for all values of x, it follows that f(x) = 1 for all x. Therefore, the graph of this function is a horizontal line at y = 1, not a straight line.
Step-by-step explanation:
18. If the expansion, in ascending powers of x, as far as the term in x², of (2-x)(1+ ax)^6 is (1 + bx²+....) find the value of a and of b.
The value of a = 1/3 and b = 2.
We can expand the given expression using the binomial theorem:
Binomial theorem statement that for any positive integer n the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form in the sequence of terms, the index r takes on the successive values 0, 1, 2,…, n.
Equation.
(2-x)(1+ax)⁶ = (2-x) × [1 + 6a x + 15a² x² + ...]
Multiplying this out gives:
(2-x)(1+ax)⁶ = 2 + (6a-2x) x + (15a² - 12ax + x²) x² + ...
Comparing the coefficient of x and x² with the given expansion we get:
6a - 2 = 0 (coefficient of x)
15a² - 12a + 1 = b (coefficient of x²)
From the first equation, we get:
6a = 2
a = 1/3
Substituting this value of a into the second equation, we get:
15(1/3)² - 12(1/3) + 1 = b
5 - 4 + 1 = b
b = 2
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What is the equation, in slope-intercept form, of the line that is perpendicular to the line
y-4=(x-6) and passes through the point (-2,-2)?
0 y=-x-10
Oy=-3x+10
Oy=2x-1
O y = 2x+1
Answer:
y = (3/2)x + 1
Step-by-step explanation:
straight line equation format is y -y1 = m(x - x1)
where y1 is y-coordinate of a point, x1 is x-coordinate of the same point, m is the slope (gradient).
slope of y - 4 = -2/3 (x - 6) is -2/3, since that's the number before x.
this means that slope of perpendicular line = -(1/ (-2/3)) = 3/2.
it passes through (-2, -2)
equation is y - -2 = 3/2 (x - - 2)
y + 2 = 3/2 (x +2) = (3/2) x + 3
subtract 2 from both sides
y = (3/2)x + 1
