Answer: [-3, 13)
A square bracket [] means it includes the number, and a round bracket () means that value is not included.
A sweater is on sale for a 20% discount. The amount of the discount is $12. What is the original cost of the sweater?
The original cost of the sweater is $60.
What is Percentage?Percentage is simply defined as the parts of a number per fraction of 100.
Percentage is usually denoted by the symbol '%'.
Percentage of a number in a whole can be calculated by dividing the number by the whole and then multiply with 100.
Given that,
A sweater is on sale for a 20% discount. The amount of the discount is $12.
Percentage of discount = 20%
Amount of the discount = $12
Let x be the original cost of the sweater.
20% of x = 12
0.2x = 12
x = 60
Hence the original price of the sweater was $60.
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HEEELP MEE!!
The population of a colony started with 1,120 grows at an annual rate of 4.98%. How much more would you have, at the same time if you used continuous growth, compared to a growth rate when the continuous reaches 3,480?
The time that is taken by the colony is 23 years.
What is the time taken for the growth?The exponential growth function can be used to account for the exponential increase in the number of the organisms that are to be found in the colony.
Given that we have that;
P=Poe^rt
P = Number at time t
Po = Number initially present
r = rate of growth
t = time taken
Thus;
3480 = 1120e^0.0498t
3480/1120 = e^0.0498t
3.1 = e^0.0498t
ln(3.1) = 0.0498t
t = ln3.1/0.0498
t = 23 years
There are 23 years
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what is (-5,-3) reflected over the Y axis
The point (-5,-3) reflected over the y-axis is (5, -3).
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
(-5, -3)
Along y-axis:
(x, y) → (-x, y)
So,
(-5, -3) → (-(-5), -3) = (5, -3)
Thus,
(5, -3) is the reflected point.
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Let G be an abelian group and let H be the subset of G consisting of all elements of G of finite order. That is,
H={α∈G∣the order of a is finite}.
Prove that H is a subgroup of G.
H is a subgroup of G since it is closed under the group operation, contains the identity element and inverses of its elements.
A subset H of a group G is a subgroup of G if it satisfies the following three properties:
1. Closure: H is closed under the group operation, that is, if α, β∈H then αβ∈H.
2. Identity element: H contains the identity element e of G.
3. Inverses: For each element α∈H, its inverse (or reciprocal) α−1 is also an element of H.
In this case, the subset of G consisting of elements of finite order (H) satisfies all of these three properties. Since H is closed under the group operation, if α, β∈H then αβ∈H. The identity element of G, e, is also an element of H since the order of the identity element is always 1, which is finite. Finally, for each element α∈H, its inverse α−1 is also an element of H since the inverse of a finite order element is also of finite order. Therefore, by satisfying all of the three properties of a subgroup, H is indeed a subgroup of G.
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=
Use the Percentiles flow chart interactive to answer the following question.
When finding the 35th percentile from a sample of 200 IQ scores, the locator L is found to be 80. What is the value of the 35th percentile?
Choose the correct answer below.
OA. The 80th IQ score in the sorted list
OB. The IQ score that is midway between the 35th and 36th scores in the sorted list.
OC. The IQ score that is midway between the 80th and 81st scores in the sorted list.
OD. The 35th IQ score in the sorted list
Next
C. An IQ score of 80 is more unusual than an IQ score of 120
is the false answer
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
Firstly we need to find the probability of the test score to be less than 90(P<90) then we will continue finding the probability of the IQ score to be between 90 and 110(90<P<110) then we find the probability of the IQ score being more than 110 (P>110).
For P<90
Firstly we compute this using a scientific calculator where we choose the stat option and enter the mean of 100 and a standard deviation of 10, so we check if we make the normal random variable(X) to be 90 the outcome or answer for that is 0.16 so now we know the probability of the IQ score to be less than 90 is 16% chances.
For 90<P<110
then we check with the same method what will be the probability for an IQ score to be between 90 and 110 for a mean of 100 and a standard deviation of 10 we again check a normal random variable(X) of 110 to see what will be the probability of P<110 which we find an answer of 0.84 which is 84% chances so now therefore the probability of an IQ score to be more than 110 is 0.
therefore this tells us an IQ score of 120 is more unusual than an IQ score of 120.
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If the mass of a typical star is 2.5x 1034 grams and there are approximately 600,000,000,000 stars in a galaxy, what
is the total mass of these stars?
Answer:
1.55 x [tex]10^{15}[/tex]
or 1,550,000,000,000,000
Step-by-step explanation:
2.5 x 1.034 x [tex]10^{3}[/tex] x 6 x [tex]10^{11}[/tex]
15.51 x [tex]10^{14}[/tex]
1.551 x [tex]10^{15}[/tex]
A rectangle is 1/2 feet long and 3/4 feet wide. What is the area of the rectangle? pls hurry i give brainliest for whos answer first
Answer:
3/8 feet²
---------------------------
Area of the rectangle is the product of its two dimensions:
A = lwSubstitute the dimensions and find the area:
A = 1/2 × 3/4 = 3/8 feet²A laboratory technician needs to make a 28-liter batch of a 40% acid solution. How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 20% to get the desired concentration?
The total amount of acid in the final equation solution is 700% + 420% = 1120%, which is 40% of the total volume:
What is equation?In arithmetic equations, the identical sign (=) is used to denote the equivalence of two assertions. It is demonstrated that using mathematical methods, which have acted as manifestations of reality, it is feasible to compare different numerical factors. For fact, the equal sign splits the number 12 into two separate parts, even if the answer is y + 6 = 12. It is possible to determine how many letters are also present on either end of this character.
Here,
Let x be the number of liters of pure acid solution needed, and y be the number of liters of 20% acid solution needed to make 28 liters of a 40% acid solution.
x + y = 28 (total volume of the solution)
100x + 20y = 40(28) (total amount of acid in the solution)
Simplifying the second equation, we get:
100x + 20y = 1120
Dividing both sides by 20, we get:
5x + y = 56
Now we can solve the system of equations by substitution or elimination. Here we will use the substitution method.
Solving the first equation for y, we get:
y = 28 - x
Substituting this expression for y into the second equation, we get:
5x + (28 - x) = 56
Simplifying and solving for x, we get:
4x = 28
x = 7
So the technician needs 7 liters of pure acid solution and 21 liters of 20% acid solution to make 28 liters of a 40% acid solution.
To check this answer, we can calculate the amount of acid in each solution and verify that the total amount of acid in the final solution is indeed 40%.
7 liters of pure acid solution contain 7 × 100% = 700% acid.
21 liters of 20% acid solution contain 21 × 20% = 420% acid.
The total amount of acid in the final solution is 700% + 420% = 1120%, which is 40% of the total volume:
1120% ÷ 28 liters = 40%
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A Ferris wheel at a carnival has a diameter of 52 feet. Suppose it turns at a rate of 3 revolutions per minute.
The angular speed of the wheel is 0.314 rad/sec and the linear speed of the car is 8.164 feet/second .
What is angular speed ?Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ/ t
one revolution = 360°
180° = π
360° = 2π
3 revolution = 3× 2π = 6π
1 minute = 60 ×1 = 60s
angular speed = 6× 3.14/60
= 0.314 rad/s
The linear velocity =
V = wr
r = d/2
r = 52/2 = 26 feet
V = wr
V = 0.314× 26
V = 8.164 feet/second
Question: A Ferris wheel at a carnival has a diameter of 52 feet. Suppose it turns at a rate of 3 revolutions per minute. i. What is the angular speed of the wheel.
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9.03 divided by 0.15
9.03 divided by 0.15 is equal to 60.2.
What do you know about division?The opposite of multiplication in arithmetic is called division. It's used to determine how many times one quantity is contained inside another. Division is done by dividing the dividend by the divisor, which can be done visually by using the division sign () or a fraction bar (/). The quotient, which shows how many times the dividend can be divided by the divisor, is the operation's output. For instance, if you split up eight apples into four equally sized pieces, each piece would contain two apples. This division is denoted by the equation 8/4 = 2, where 8 is the dividend, 4 is the divisor, and 2 is the quotient.
The division of 9.03 by 0.15 can be calculated as follows:
9.03 ÷ 0.15 = 9.03 / 0.15
= 60.2
So, 9.03 divided by 0.15 is equal to 60.2.
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The resultant of four forces is 1000 N in the direction 30° west of north. Three of the forces are 400 N, 60° north of east; 200 N, south; and 400 N, 530 west of south. Find the rectangular components of the fourth force. 2.7 Ans: F = 380N. F₁ = 960,3N. F₁ = 1003N. 21.6°W of N.
List all numbers from the given set that are: a. natural numbers, b. whole numbers, c. integers, d. rational numbers,
e. irrational numbers, f. real numbers.
{-7.2/-3.0.0.1. √5.3.5. √64}
Natural numbers: 0.1 Whole numbers: 0, Integers: -7, -3, 0, 1, Rational numbers: -7.2, -3.0, 0.1, 3.5,Irrational numbers: √5, √64, Real numbers: -7.2, -3.0, 0.1, √5, 3.5, √64.
What is the Natural numbers ?Natural numbers are the positive integers, 1, 2, 3, 4, 5, and so on. They are also known as the counting numbers or the positive integers. They are the numbers used for counting and measuring. Natural numbers are the building blocks of mathematics, and are used in the formation of other number systems, such as integers, rational numbers, real numbers, and complex numbers.
Natural numbers are also used in the formation of equations and formulas, as well as in the counting of objects, in the measurement of distances, and in many other areas of mathematics. Natural numbers are an important part of everyday life, and are used in everything from telling time to counting money.
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Look at square ABCD below.
What is its perimeter?
A. 12√2 units
B. 3√2 units
C. 18 units
D. 12 units
The perimeter of the square is 12√2 units
What is perimeter of a square?A square is a quadrilateral that has all it's sides equal and all it's angles equal. The sum of interior angles of a square is 360°. This means that each angle of a square is 90°.
The perimeter of a square is obtained by adding all the sides.
Therefore the perimeter of a square = 4l
A (-1,4) and B ( 2,7)
line AB = √2-(-1))² + (7-4)²
AB = √ 3²+3²
AB = √9+9
AB = √18 units
therefore since the sides of a square are equal, the perimeter = 4× √18
= 4×3√2
= 12√2 units
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Answer:
Option A. 12√2 units
Step-by-step explanation:
x^2-6x-3=(x-a)^2-b, where a and b are constants
Answer:
Below
Step-by-step explanation:
This is an exercise in 'completing the square'
x^2 - 6x -3
take 1/2 of the x coefficient (6) square it and add it and subtract it
x^2 - 6x + 9 - 9 - 3 Now you can reduce the underlined portion
(x-3)^2 - 12 a = 3 b= -12 Done
8. Write a new function, N(t), that represents the amount of money in Jennifer’s new account after t years. Be sure to use correct notation
The new function of Jennifers's investment is f(t) = 50000 * (1.15)^t
How to determine the new functionFrom the question, we have the following parameters that can be used in our computation:
Initial investment, a = 50000
Rate of growth, r = 15%
Using the above as a guide, we have the following:
f(t) = a * (1 + r)^t
Substitute the known values in the above equation, so, we have the following representation
f(t) = 50000 * (1 + 15%)^t
So, we have
f(t) = 50000 * (1.15)^t
Hence, the function is f(t) = 50000 * (1.15)^t
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Complete question
ennifer starts a new investment account that grows exponentially. Her financial advisor tells her the initial investment of $50,000 grows at a rate of about 15% annually.
Write a new function, N(t), that represents the amount of money in Jennifer’s new account after t years. Be sure to use correct notation
Explain two ways that knowing the probability of an event occurring can
be useful.
If knowing the probability of an event occurring is known then it can be turned into one's favour as well as it can be obstructed if not in favour.
What is probability?A way to determine the likelihood of something occurring is through probability. Many things are hard to predict with 100 percent certainty. We can only predict the likelihood of an event occurring or how likely it is using it. A probability can be between 0 and 1, with 0 signifying an impossibility and 1 signifying a certainty.
If the likelihood of an event occurring is known, one can attempt to influence the outcome in accordance with the likelihood.
The possibility of altering the likelihood that the event will go in one's favour is another useful tool.
Therefore, being aware of the probability can be beneficial.
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my equation is on the photo I need help
Answer: A = 6
Step-by-step explanation: Here to help! So, if "a" wants to know the numerator of the fraction, all you have to do is to multiply 0.6 by 10, and that would get you 6/10. 6/10 is equivalent to 60% or 0.6. :))))
Find the perimeter of a parallelogram with sides measuring 3 3/10 meters 8 5/10 meters 3 3/10 meters and 8 5/10
The perimeter of this parallelogram is equal to 236/10 or 23 6/10 meters.
What is a parallelogram?In Mathematics, a parallelogram simply refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
Mathematically, the perimeter of a parallelogram can be calculated by using this mathematical expression;
Perimeter = A + B + C + D
Where:
A, B, C, and D represents the length of sides of a parallelogram.
Substituting the given parameters into the perimeter of a parallelogram formula, we have the following;
Perimeter = 3 3/10 + 8 5/10 + 3 3/10 + 8 5/10
Perimeter = 33/10 + 85/10 + 33/10 + 85/10
Perimeter = 66/10 + 170/10
Perimeter = 236/10 or 23 6/10 meters.
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The table below displays the adult literacy rate in Bolivia for several different years. The adult literacy rate is the percentage of people ages 15 and above who can both read and write with understanding a short simple statement about their everyday life.
Data downloaded on 2/19/2020 from https://ourworldindata.org/grapher/literacy-rate-adults?tab=chart&time=1973..2016.
Year 1976 2001 2012
Literacy Rate 63.2% 86.7% 94.5%
When answering the questions below, round to four decimal places in your intermediate computations.
Use interpolation or extrapolation (whichever is appropriate) to predict the literacy rate in Bolivia in 1992. Round your answer to one decimal place. You only get one submission for the unit.
Use interpolation or extrapolation (whichever is appropriate) to predict the literacy rate in Bolivia in 2050. Round your answer to one decimal place. You only get one submission for the unit.
Is your 2050 prediction realistic? You must select all correct responses at the same time to receive credit for this problem. You get two submissions.
Yes, the 2050 prediction is realistic because it is possible for a literacy rate to exceed 100%.
No, the 2050 prediction is not realistic because the literacy rate will not grow at the exact same rate for more than 40 years.
Yes, the 2050 prediction is realistic because it was made using a mathematical formula.
No, the 2050 prediction is not realistic because the literacy rate cannot exceed 100%.
Is your 2050 prediction realistic?
No, the 2050 prediction is not realistic because the literacy rate cannot exceed 100%
How to solveGiven data is
x0=1976, y0=63.2
x1=2001, y1=86.7
x2=2012, y2=94.5
Then the Lagrange interpolation formula is
[tex]y - y_1 = \frac{y_2 - y_1}{x_2 -x_1} (x - x_1)[/tex]
Here we have to interpolate to predict the literacy rate in 1992.
i.e. x=1992.
It lies between 1976 and 2001.
Then
x1=1976, y1=63.2
x2=2001, y2=86.7
Then interpolation function become
[tex]63.2 + \frac{23.5}{25}(16)[/tex]
= 63.2 + 15.04 = 78.24
i.e. The predicted literacy rate in 1992 is 78.24%.
Now, to find the literacy rate in 2050, we have to use extrapolation.
Since, 2050 is not in between any of the given data, we will have to take last two datas.
i.e.
x1=2001, y1=86.7
x2=2012, y2=94.5
And x=2050.
Then our extrapolation formula become
[tex]86.7 + \frac{7.8}{11} (49)[/tex]
= 86.7 + 34.75
=121.45
i.e. The literacy rate in 2050 is 121.45%.
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I need help on This question I’ll give you brainliest
2. The mean incubation time of fertilized chicken eggs kept in an incubator is 21.3 days. Suppose that the incubation times are normally distributed and the standard deviation is 1.1 days. (4 pts)
Mean = 21.3
Sd= 1.1
a. What is the 22nd percentile for incubation times of chicken eggs? (2 pts)
b. Determine the two incubation times that mark off the middle (center) 95% of fertilized chicken eggs. (2 pts)
a) The 22nd percentile for incubation times of chicken eggs is of: 20.5 days.
b) The middle 95% of incubation times is in this following interval: (19.1, 23.5) days.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters for this problem are given as follows:
[tex]\mu = 21.3, \sigma = 1.1[/tex]
The 22nd percentile is the value of X when Z has a p-value of 0.22, hence X when Z = -0.77, thus:
-0.77 = (X - 21.3)/1.1
X - 21.3 = -0.77 x 1.1
X = 20.5 days.
The middle 95% of incubation times is obtained from X when Z = -1.96(2.5th percentile) to X when Z = 1.96(97.5th percentile), hence:
-1.96 = (X - 21.3)/1.1
X - 21.3 = -1.96 x 1.1
X = 19.1 days.
1.96 = (X - 21.3)/1.1
X - 21.3 = 1.96 x 1.1
X = 23.5 days.
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A) Identify the odd one.
A) 5y + 6 - 2xy
B) 5k - k(1 + 3)
C ) 7j - (j +4) = 25
D) 8k
B) Which is not an option?
A) x2+3
B) x6
C) (x)(x)(x)(x)(x)(x)
D) (x3)2
Answer:8k
Step-by-step explanation:i did the test and got it write
Find the missing dimension of the cylinder. Round your answer to the nearest whole number.
Volume = 10,000π in.3
h ≈
in.
r ≈
cm
The Height is 10 inch and radius is 10 inch.
What is Volume?Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. While capacity can be measured in virtually any other unit, such as litres, gallons, pounds, etc., volume is measured in cubic units.
Given:
Volume = 10,000π in³
Volume of b= π r² h
So, 10,000π= π r² h
10,000 = r² h
r² h = 10 x 10 x 10
r² h = 10² x 10
Now, comparing the values
r= 10 inch and h= 10 inch
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Step by step please, need help. Good luck and thank you for your help
Angle of triangle AFC is 37°
What is an angle?An angle is the formed when two lines meet at the same vertex. It is measured is degrees. There are three types of angles based on their measurements.
From the given figure consider ABCF as trapezium,
Given that angle of triangle BCF is 37°
Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non-parallel side, add up to 180°
Therefore, ∠BCF + ∠CBF = 180°
⇒∠B = 180° - 37°⇒143°
Similarly ∠A = ∠B = 143°
⇒∠A+∠F=180°
⇒∠F=180°-143° ⇒ 37°
Hence, m∠AFC = 37°.
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what is the equation of 2x=50
Answer:
A vertical line that passes through the coordinate (25, 0).
Equation of the vertical line is x = 25
Step-by-step explanation:
2x = 50
x = 25
Required information Consider the following diagrams: Diagram 1 Diagram 2 7 7 6- 6 5 5 4 4 3 3 2 2 1 1 - 0 0 0 0 1 2 3 4 5 6 7 1 2 3 4 -10 8 7 Diagram 3 Diagram 4 7 7 9 6 5 40 st 4- 3 3 FZ 2 - 1 - 1 - 2 3 4 6 0 0 O O 1 3 2 4 5 6 2 4 7 3 6 5 7 c. Research shows that organic produce sales are higher among more educated consumers. Correct diagram: (Click to select) Slope: (Click to select)
To better understand the relationship between education level and organic produce sales, we need to have data on these variables.
The data would typically be in the form of a table or a graph, with education level on one axis and organic produce sales on the other. Once we have the data, we can look at the pattern of the points to determine the relationship between education level and organic produce sales. If there is a positive relationship between the two variables, then as the education level increases, we would expect to see an increase in organic produce sales. This positive relationship could be represented by a line that slopes upward from left to right on a graph.
The slope of the line represents the rate of change of organic produce sales with respect to education level. A steep slope would indicate that even small changes in education level lead to significant changes in organic produce sales, while a shallow slope would suggest that changes in education level have little effect on organic produce sales.
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Andrea is making a sandbox for her children. She has made a wooden frame for her backyard that is 8 feet long, 5 feet wide, and 4 feet deep. She can purchase sand for the sandbox for $20 per cubic meter. How much will it cost Andrea to purchase sand? (Hint: 1 foot = 0.3048 meters.)
(Round your answer to the nearest dollar.)
Answer:
Step-by-step explanation:
The wooden frame is a cuboid
and the volume of a cuboid = Length x Width x Depth
Therefore,
The volume of this wooden frame = (8 feet) x (5 feet) x (4 feet)
= 160 cubic feet
The purchasing rate for the sand is $20 per cubic meter (which is NOT the same as cubic feet)
Unit conversion has to be applied then:
1 foot = 0.3048 meters
1 cubic feet = (0.3048 meters) x (0.3048 meters) x (0.3048 meters)
1 cubic feet = [tex]0.3048^{3}[/tex] cubic meters
Therefore: 160 cubic feet = (160)([tex]0.3048^{3}[/tex]) cubic meters
Cost of sand:
1 cubic meter = $20
Therefore: (160)([tex]0.3048^{3}[/tex]) cubic meters = $(20)(160)([tex]0.3048^{3}[/tex])
= $90.61
= $91 (Rounded to the nearest dollar)
It will cost Andrea $91 to purchase sand for the sandbox
What is the surface area of a sphere with radius 8? Use 3.14 for pi and round your answer to the nearest hundredth if necessary.
Answer:
The formula for the surface area of a sphere with radius r is 4πr^2. Plugging in the given radius of 8, we get:
Surface area = 4π * 8^2 = 4π * 64 = 256π
Using an approximate value of π = 3.14, the surface area of the sphere is approximately:
256 * 3.14 = 803.84
Rounding to the nearest hundredth, the surface area of the sphere is approximately 803.84 square units.
Answer:
803.84cm²
SolutionArea of a sphere = 4πr²
When we put the given values we get
Area of a sphere = 4x3.14x8²
Area of a sphere = 4x3.14X16
= 804.25cm²
Rounding to the nearest hundredth we get,
803.84cm²
Evaluate −2x+17 when x=−8.
A quadratic equation whose roots are -2 and 5, and whose leading coefficient is 2.
[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -5 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{since the leading coefficient is 2, let's a = 2}}{2(x+2)(x-5)=y} \\\\\\ 2\stackrel{\textit{F O I L}}{(x^2-3x-10)=y}\implies \boxed{2x^2-6x-20=y}[/tex]