Answer:
x = 1/10
Step-by-step explanation:
3x - 4/5 = -1/2
-1/2 + 4/5 =
-5/10 + 8/10 =
3/10
3x = 3/10
x = 1/10
Madison starts with a population of 1,000 1 , 000 amoebas that triples in size every hour for a number of hours, ℎ h . She writes the expression 1,000(3ℎ) 1,000 ( 3 h ) to find the number of amoeba after ℎ h hours. Tyler starts with a population of 1 1 amoeba that increases 30% 30 % in size every hour for a number of hours, ℎ h . He writes the expression (1+0.3)ℎ 1 + 0 . 3 h to find the number of amoeba after ℎ h hours. Use the drop-down menus to explain what each part of Madison’s and Tyler’s expressions mean.
The population is increasing at a constant rate, which can be represented by a simple exponential function.
Madison's expression: 1,000(3ℎ)
1,000 - This represents the starting population of amoebas, which is 1,000.
3 - This represents the rate of increase in size, which is a tripling of the original size every hour.
ℎ - This represents the number of hours for which the population is increasing.
So, the entire expression 1,000(3ℎ) means the number of amoebas after ℎ hours, where the population is tripling every hour.
Tyler's expression: (1+0.3)ℎ
1 - This represents the starting population of amoebas, which is 1.
0.3 - This represents the rate of increase in size, which is a 30% increase in size every hour.
ℎ - This represents the number of hours for which the population is increasing.
So, the entire expression (1+0.3)ℎ means the number of amoebas after ℎ hours, where the population is increasing by 30% every hour.
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8 a and b are integers. a+b = 800 b is 250 greater than a. Work out the values of a and b
Answer:a=275 b =525
Step-by-step explanation:
Hi there, here's your answer:
Given:
a and b are integers
a + b = 800 ....(i)
b = a + 250
Putting value of b in (i)
a + (a + 250) = 800
2a + 250 = 800
2a = 800 - 250
Or
2a = 550
Therefore, a = [tex]\frac{550}{2}[/tex] = 275
Since b is 250 greater than a,
b = 250 + 275 = 525
Hope it helps!
Find the common ratior for the geometric sequence and user to find the next three terms.
Enter your answer to six decimal places if necessary.
7, 4. 2, 2. 52, 1. 512,.
The next three terms are:
0.9072, 0.54432, 0.326592
So, the sequence is:
7, 4. 2, 2. 52, 1. 512, 0.9072, 0.54432, 0.326592
Geometric sequenceA geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is. a n= a 1 r n – 1. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.
The sequence is:
7, 4. 2, 2. 52, 1. 512,.
We have to find the next three terms.
To find r divide the 2nd term by the first:
4.2/7 = 0.6
To check if this is the same ratio for each number divide it by the ratio to get the number before it:
2.52/4.2 = 0.6
1.512/ 2.52 = 0.6
To find the next three terms multiply the last number by the ratio then repeat
(1.512)(0.6) = 0.9072
(0.9072)(0.6) = 0.54432
(0.54432)(0.6) = 0.326592
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we colored all points of r2 with integer coordinates by one of six colors. prove that there is a rectangle whose vertices are monochro- matic. can we make the statement stronger by limiting the size of the purported monochromatic rectangle?
Yes, we can make the rectangle has sides of length n and n, and all four vertices have the same color
A rectangle is a two-dimensional shape with four sides, two of which are parallel and equal in length, and the other two sides are also parallel and equal in length.
In this case, the objects are the points in the plane with integer coordinates, and the available spaces are the six colors.
Since there are an infinite number of points with integer coordinates and only six colors, it follows that there must be a color that appears at the vertices of a rectangle.
In other words, we can color the points in a manner such that there will be a rectangle in which all four vertices are the same color. This is because, if we divide the points into six different regions, there must be at least one region that contains more points than the others.
When we look for a rectangle, we look for two points in this region that are the farthest apart from each other. The rectangle that connects these two points will have all four vertices the same color.
In conclusion, we can make the statement stronger by limiting the size of the purported monochromatic rectangle.
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(4x + 2)(x -1)(3x)(2x + 3) = 194 meters squared
what is the value of X
Answer:
x ∈ {−2.18723509003, 1.68723509003}
Step-by-step explanation:
You want the value of x that satisfies the equation (4x +2)(x -1)(3x)(2x +3) = 194.
QuarticThe fact that 194 is not divisible by 3 means the real solutions will not be integer values, likely irrational. A graphical solution and some iterations tell us the solutions are ...
x = −2.18723509003
or
x = 1.68723509003
__
Additional comment
The product has units of square meters, so we presume these dimensions come in pairs of factors. It appears that both the positive and negative values of x will give factors pairs that have a positive product.
Any rational solutions would be multiples of 1/24. These solutions are not rational.
Lesson 5 Skills Practice
Draw Three-Dimensional Figures
Draw at, ad, and a front view of each solid
Three- Dimensional figures- Cube and Cylinder
Let a be the length of sides of cube and r and h be the radius and height of cylinder respectively.
Cube - All sides are of same dimensions.
Let a be the length of the dimensions
The top, bottom and side view are squares each of length a units.
The diagonal view is basically a three dimensional right angled triangle.
Cylinder- h be the length/ height of cylinder and r be the radius of the cylinder.
The top view of cylinder is basically a circle of radius.
The side view is basically curved surface of the cylinder of length h.
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A ball is dropped from 2 meters and rises up by 75%
The height of ball which is droped from 2m and rises to 75% after third bounce is equals to the 0.843 meters.
If an object is thrown from high and has a bouncing feature, each bouncing is less than the initial height until it stops. Each bounce reduces the growth rate until it reaches zero. In order to calculate the height of each bounce, so we can estimate what percentage the object will reach after each bounce. If we get the percentage of each bounce, we can easily determine the height of each bounce. We have, a ball is droped from 2 meters and bounce up to 75%. That is height of first bounce is determined by using percentage, height is 2 m × 75% = 2 m×0.75 = 1.5 m
In second bounce, height is 1.5 m × 75%
= 1.5 m×0.75 = 1.12 m
In third bounce, 1.12 m× 75%
= 1.12 m×0.75 = 0.843 m
The height the ball reaches on its third bounce is 0.843 m.
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Complete question :
A ball is dropped from a height of 2 meters and rises up by 75% of its height on each bounce. How high would the third bounce be?
A relay race team has 4 runners who run different parts of the race.
There are 16 students on your track team. How many ways can your coach
select students to compete in the race?
The number of ways coach can select students to compete in the race are 1820.
What is combination?The selections are another name for combinations. The choice of items from a predetermined group of items corresponds to combinations. We don't want to organize anything here. We are going to choose them. We use the notation nCr to indicate how many distinct r-selections or combinations there are among a set of n objects. A combination is distinct from an arrangement or a permutation. No matter how the objects are arranged, combinations are produced by choosing some or all of them.
Given;
There are 16 students on your track team with 4 runners who run different parts of the race.
Now, n=16 and r=4;
nCr = 16C4
=16*15*14*13/4*3*2*1
=4*5*7*13
=1820
Therefore, by combination there are 1820 ways.
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alicia paid 1.32 for a bag of pino beans the beans cost .55 per lb how much did the bag of pinto beans weigh
Answer:
2.4 lb
Step-by-step explanation:
We know
Alicia paid 1.32 for a bag of pinto beans
The beans cost .55 per lb
How much did the bag of pinto beans weigh?
1.32 / .55 = 2.4 lb
So, the bag of pinto beans weighs 2.4 lb.
kevin has four red marbles and eight blue marbles. he arranges these twelve marbles randomly, in a ring. determine the probability that no two red marbles are adjacent.
To determine the probability that no two red marbles are adjacent, we can calculate the number of arrangements of the 12 marbles such that no two red marbles are next to each other, and divide that by the total number of arrangements of the 12 marbles.
One way to do this is to place the red marbles first, and then the blue marbles. If we place the red marbles randomly, there are 5 gaps between the red marbles where we can insert the blue marbles. Thus, there are 5! = 120 ways to arrange the blue marbles.
Next, we need to determine the number of ways to arrange the red marbles. If we think of the red marbles as a sequence of R's and B's (where B represents a gap between red marbles), we have 4 R's and 5 B's. To avoid adjacent R's, we need to arrange the R's and B's such that no two R's are next to each other. One way to do this is to use the concept of combinations.
There are C(9,4) ways to arrange 4 R's and 5 B's in a sequence of 9 elements. This number can be calculated using the formula for combinations: C(n,k) = n! / (k! (n-k)!). In this case, C(9,4) = 126.
Finally, we divide the number of arrangements of the red marbles by the total number of arrangements of the 12 marbles to obtain the desired probability. The total number of arrangements of the 12 marbles is 12!. Thus, the desired probability is:
P = 126 / (120 * 12!) =
126 / (120 * 479001600)
= approximately 0.0000026
So, the probability that no two red marbles are adjacent is approximately 0.0000026.
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Which equation has a slope of 6 and intercepts the y-axis at -4?
Answer:
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
If the slope of the line is 6 and the y-intercept is -4, the equation of the line is y = 6x - 4. This equation describes a line with a slope of 6 that intercepts the y-axis at the point (0, -4).
Mia opened a savings account and deposited $700.00 as principal. The account earns 7%
interest, compounded annually. What is the balance after 7 years?
nt
Use the formula A = P 1 +
= P(1. + 1)", where A is the balance (final amount), P is the principal
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
After 7 years, the balance of the savings account will be $1069.39.
What is balance in savings account?An account balance is the amount of money in a financial repository at any particular time, such as a savings or checking account. The account balance is always the net amount after all debits and credits are subtracted.
The formula to calculate the balance after t years is A = P(1 + r/n)^(nt), where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
In this case, P = 700.00, r = 0.07, n = 1 (since the interest is compounded annually), and t = 7. Plugging these values into the formula, we get:
A = 700.00 * (1 + 0.07/1)^(1 * 7)
A = 700.00 * (1.07)^7
A = 700.00 * 1.527674
A = $1069.39
So, after 7 years, the balance of the savings account will be $1069.39.
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I need help plsssssss ;-;
1) Factorize. 2a² - 8
2)Among the sets, P = {3,4,5,6} , Q = {0,1,2,3} , R = {5,6,7,8,9}
i) write a pair of disjoint sets
ii)name a pair of equivalent sets
3) Out of the students in the class, 3/7 are girls. If there are 24 boys in the class, find the total number of students in the class.
Answer:
2(a[tex] 2(a^2-4)[/tex]Solve the inequality: four times a number increased by five is at least 33
Answer:
x [tex]\geq[/tex] 7
Explanation:
4x + 5 [tex]\geq[/tex] 33
4x + 5-5 [tex]\geq[/tex] 33 - 5
4x [tex]\geq[/tex] 28
[tex]\frac{4x}{4} \geq \frac{28}{4}[/tex]
x [tex]\geq[/tex] 7
HOPE IT HELPED, PLEASE MARK BRAINLIEST, THANK AND RATE!
1 - cos² 15° - cos² 75°
Answer:
1 - cos² 15° - cos² 75° can be simplified as follows:
Using the identity cos² x = 1 - sin² x, we can write the expression as:
1 - (1 - sin² 15°) - (1 - sin² 75°)
= sin² 15° + sin² 75° - 1
Using the identity sin 2x = 2sin x cos x, we can write sin 15° and sin 75° in terms of sin 30° and sin 45°:
sin 15° = sin (30° - 15°) = (1/2) * sin 30°
sin 75° = sin (45° + 30°) = sin 45° + sin 30°
Substituting these values in the above expression, we get:
sin² 15° + sin² 75° = (1/4) * sin² 30° + sin² 45° + sin 30° * sin 45°
= (1/4) * (2 * (1/2)²) + (2 * (1/2) * (1/2)) + (1/2) * (1/2)
= (1/4) + 1/2 + 1/4 = 1
So, 1 - cos² 15° - cos² 75° = sin² 15° + sin² 75° - 1 = 1 - 1 = 0.
Step-by-step explanation:
a circular patio has a diameter of 4 yards. what is the area of the patio use 3.14 tt
A. 12.56 yd2
B. 25.12 yd2
C. 50.24 yd2
D. 6.28 yd2
Answer: A
Step-by-step explanation: I just did 3.14x4
Answer:
Step-by-step explanation:
Area of a circle = πr²
r = radius and it is half of the diameter.
Diameter = 4 so radius = 2
Area = 3.14 (2)²
Area = 3.14(4)
Area = 12.56 yd²
Choice A
2. compare articles i, ii, and iii. rank them in order of length and detail. which is the longest? speculate as to why this is the case.
Comparing the articles I, II, and III of the constitution, in the descending order of length and detail, the articles are ranked as I, II, and III. Article I is the longest.
Article I of the constitution created the legislative branch, article II of the constitution created an executive branch, and article III of the constitution created a judicial constitution. Article I is the longest and more detailed part of the constitution as the powers and the duties of the legislative branch are much more varied than the executive branch. Additionally, the legislative branch is composed of more individuals than the executive branch.
Article 1 is the longest as founding fathers believed that a legislative branch is very important in a government that represents the citizens. Article 3 is the shortest part of the constitution as the founding fathers did not expect the judiciary to play a large role.
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Solve the equation and check your solution: x + 4 = -2 +
Answer:
x = -6
Step-by-step explanation:
Solving an equation:x + 4 = -2
Subtract 4 from both sides,
x + 4 - 4 = -2 - 4
x = -6
[tex]\boxed{\bf x = -6}[/tex]
Check: Substitute x = -6 in the LHS of the equation,
LHS = x +4
= -6 + 4
= -2 = RHS
I need help on this question
(-3/4) - 2/5
Answer:
Step-by-step explanation:
-1.15
Answer:
-1.15
The answer is -1.15
izzy computes each players batting average by dividing the numbers of base hits by the number of at bats. A players batting average is recorded as a decimal number
Step-by-step explanation:
HOPE IT HELPS I AM NOT SURE
Using the given equation find the missing coordinates of the points and then find the slope of the line for each equation c -3/7x+3=y; A(...; 6), B(9; ...)
To find the missing coordinates of the points A and B, you can use the equation c -3/7x + 3 = y. Plugging in the given x-coordinates for A and B, you can solve for their y-coordinates.
A: x = -2, y = -3 B: x = 9, y = 6
To find the slope of the line, you can use the formula m = (y2 - y1)/(x2 - x1). Plugging in the coordinates for A and B, you can calculate the slope as m = (6 - (-3))/(9 - (-2)) = 9/11.
To further explore the topic, you can look into how to graph equations in slope-intercept form, as well as how to find equations of parallel and perpendicular lines. You can also learn how to use the equation of a line to calculate distances between points, and how to calculate the midpoint of a line segment.
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X and Z are endpoints of a segment, and point T is on the segment. If XZ = 3x, XT = x + 3, and TZ = 13, then x = and XZ =
We can then plug this value into the given for XZ, which is 3x, to solve for the length of XZ. This comes out to be 18. Therefore, the value of x is 6, and the length of XZ is 18.
x = 6, XZ = 18
To solve for x, we can use the formula for the midpoint of a segment, which is (x + z)/2.
Plugging in the given values, we get (x + 13)/2 = 6.
Simplifying, we get x = 6.
To solve for XZ, we can simply plug in the given value for x, which is 6.
Therefore, XZ = 3(6) = 18.
Given three values related to a line segment, XZ, XT, and TZ, we can solve for both the value of x and the length of XZ. To do this, we can use the formula for the midpoint of a segment, which is (x + z)/2. Plugging in the given values for XT and TZ, we can solve for x, which comes out to be 6. We can then plug this value into the given for XZ, which is 3x, to solve for the length of XZ. This comes out to be 18. Therefore, the value of x is 6, and the length of XZ is 18.
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A fast-food worker works Monday through Friday, 8 hours per day. Daily, the worker receives a -hour break in the morning, a -hour break for lunch, and a -hour break in the afternoon. How many hours of break time does the worker receive per day? 1 1
The fast-food worker receives 3 hours of break time per day.
This breaks down to a one-hour break in the morning, one hour for lunch, and one hour in the afternoon.
Mathematically, this can be expressed as
1 hour + 1 hour + 1 hour = 3 hours.Additionally, the worker works 8 hours per day, Monday through Friday. This can be expressed as 5 days x 8 hours = 40 hours per week. The worker then receives 3 hours of break per day, which can be expressed as 40 hours - (5 days x 3 hours of break) = 25 hours of work per week.
Therefore, the fast-food worker receives three hours of break time per day and 25 hours of work time per week.
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Select all the expressions that are equivalent to -2/5(15-20d+5c).
1: -30+40d-10c
2: -6+8d-2c
3: -2c+8d-6
4: 6-8d+2c
5: -2(3-4d+c)
Please help
The equivalent expressions are;
-6+8d-2c-2c+8d-6-2(3-4d+c)The correct answer choice is option B, C and E
Which expressions are equivalent?-2/5(15 - 20d + 5c)
open parenthesis
= -30/5 + 40/5d - 10/5c
= - 6 + 8d - 2c
Check:
-6+8d-2c
True
-2c+8d-6
rearrange
= -6 + 8d - 2c
-2(3-4d+c)
open parenthesis
= -6 + 8d - 2c
Hence, the equivalent expression to -2/5(15 - 20d + 5c) are -6+8d-2c, -2c+8d-6 and -2(3-4d+c)
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assuming that the failure of a server is independent of the other servers, what is the probability that one or more of the servers is operational? (round your answer to 6 decimal places.)
The probability that one or more of the servers is operational is 0.898994.
The probability that one or more of the servers is operational is calculated as the complement of the probability that all servers fail. If the failure of each server is independent and has a probability of 0.1, the probability that all servers fail is 0.1 * 0.1 * ... (10 times) = 0.1^10 = 1e-10. The probability that one or more servers is operational is calculated as 1 - 1e-10 = 0.9999999999, which can be rounded to 0.898994. In other words, the probability of at least one server being operational is almost 90%.
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HELPPP
1) Among the sets, P = {3,4,5,6} , Q = {0,1,2,3} , R = {5,6,7,8,9}
i) write a pair of disjoint sets
ii)name a pair of equivalent sets
2) Out of the students in the class, 3/7 are girls. If there are 24 boys in the class, find the total number of students in the class.
Answer:
Question 1:
i) A pair of disjoint sets from the given sets are P and Q. Since there are no common elements between the sets P and Q, they are disjoint.
ii) A pair of equivalent sets from the given sets is Q and {0,1,2,3}. They contain the same elements and have the same number of elements.
Question 2:
The number of girls in the class is 3/7 * number of students in the class. Let's say there are n students in the class. Then, 3/7 * n = 3/7 * (24 + n) = 3 girls.
Solving for n, we get n = 84, which is the total number of students in the class.
Step-by-step explanation:
The image of a trapezoid is shown.
What is the area of the trapezoid?
17.4 m2
20.3 m2
40.6 m2
69.6 m2
Answer:
C. [tex]40.6m^{2}[/tex]
Step-by-step explanation:
= [tex]\frac{1}{2}[/tex] x ( 11 + 3 ) x 5.8
= [tex]\frac{1}{2}[/tex] x 7 x 5.8 =
[tex]40.6m^{2}[/tex]
i toss a coin and pick a card. what is the probability that i get a head in the coin toss and a letter card (a, q, k, or j)? there are 52 cards in a standard deck of cards.
The probability that I get a head in the coin toss and a letter card is 2/ 13.
Therefore the answer is 2/ 13.
There are 4 As, 4Qs, 4Ks and 4 Js, so there are 16 choices. The probability of getting a head in a coin toss is 1/2, and the probability of picking a letter card is 16/ 52 = 4/ 13. So
P(heads) = 1/ 2
P(letter card) = 4/ 13
To find the joint probability of both events happening (getting a head and picking a letter card), you multiply the individual probabilities:
P(heads and letter card) = P(heads) * P(letter card)
= (1/ 2) * (4/ 13)
= 2/ 13
So the probability of getting a head and picking a letter card is 2/13.
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a spherical balloon has volume v and radius r . by what factor is its radius reduced if you let enough air out of the balloon to reduce its volume by a factor of 27.0?
The factor of its radius reduced is 3. The result is obtained by comparing the spherical volumes.
What is the formula for a spherical volume?The volume of a spherical can be calculated by
V = 4/3 πr³
Where
V = volumeπ = 3.14 or 22/7r = radius of sphereA spherical balloon has volume v and radius r. Its volume is reduced by a factor of 27.0.
Find the factor of its radius reduced!
The factor of its volume is
V₁/V₂ = 27
We use the formula for spherical volume to find r₁/r₂.
V₁/V₂ = (4/3 πr₁³)/(4/3 πr₂³)
27 = (r₁/r₂)³
r₁/r₂ = ∛27
r₁/r₂ = 3
Hence, the radius is reduced by a factor of 3.
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What are the domain and the range of function f?
The domain and the range of function f are given as follows:
Domain: (-∞, -3) U (-3, 6) U (6, ∞).Range: (-∞, 0) U (0, 1/9) U (1/9, ∞).How to obtain the domain and the range of a function?The domain of a function is the set that contains all the input values that can be assumed by the function.
The function in this problem is a fraction, meaning that the denominator must assume values different of zero, hence the values outside the domain are:
x² - 3x - 18 = 0.
(x - 6)(x + 3) = 0
Hence:
x + 3 = 0 -> x = -3.x - 6 = 0 -> x = 6.Hence the domain is:
(-∞, -3) U (-3, 6) U (6, ∞).
The range of a function is the set that contains all the output values that can be assumed by the function.
The x - 6 term can be canceled, hence the output value that the function will never assume is of:
1/(6 + 3) = 1/9.
And also y = 0, as it would assume a value of zero at x = 6 but the denominator would also be zero.
Hence the range is of:
(-∞, 0) U (0, 1/9) U (1/9, ∞).
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