The number of students who participate in competition for each grade are 223 and 208 and their sum is 431.
What is a fraction?A fraction is a number written in the form a / b, where a and b are integers and b ≠ 0.
The number a is called as the numerator and b is the denominator.
(a) The total number of students are 595.
Then, the number of students in seventh grade is 3/5 × 595 = 357
Now, the number of students participated in competition is given as,
5/8 × 357
⇒ 223.125
Since, the number of students cannot be a decimal, it is taken as 223.
(b) The number of students in eighth grade is 2/5 × 595 = 238
Now, the number of students participated in competition is given as,
7/8 × 238
⇒ 208.25
Since, the number of students cannot be a decimal, it is taken as 208.
(c) The total number of students participating in competition is given as,
⇒ 223 + 208 = 431
Hence, the required number of students for 7th and 8th grade and their sum are given as 223, 208 and 431 respectively.
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The sketch shows a curve with equation y = ab* where a and b are constants and b>0 The curve passes through the points (0,5) and (2,45) Calculate the value of a and b.
NEED WORKING OUT AND CORRECT ANSWERS
Step-by-step explanation:
32 / 2 using long division
what is the slope of the line
Answer:
[tex] \frac{5}{2} [/tex]
Step-by-step explanation:
5 up, 2 right
Use a proof by contraposition to prove that if m and n are integers and mn is even, then m is even or n is even
m and n are integers such that mn is even, but m and n are both odd. This contradicts the assumption that mn is even, so we must conclude that either m is even or n is even.
Proof:
Assume m and n are integers such that mn is even and m is not even and n is not even.
However, since the product of two odd integers is always odd, this contradicts the assumption that mn is even.
Therefore, it must be true that m is even or n is even.
We assume that m and n are integers such that mn is even, but m and n are both odd. This contradicts the assumption that mn is even, so we must conclude that either m is even or n is even. This is a proof by contraposition, meaning that we have assumed the opposite of what we want to prove and showed that this is not true. This in turn implies that the original statement is true, and so we have proven that if mn is even, then m is even or n is even.
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graph theequation f(x)=-x^2-4x+5
Answer:
Graph attached below
Step-by-step explanation:
A comic-strip writer churns out different numbers of comic strips each day. The writer logged the number of comic strips he wrote each day for 16 days and sorted the data in ascending order to create this data set.
1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8
The data in the distribution is
. If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference of the mean and the median for the new data set is
.
The difference of the mean and the median for the new data set is 0.28 and 0.50 respectively.
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
We are given that 1st Data set: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8
mean: 3.5
median: 3
Now 2nd Data set: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 7, 8
mean: 3.78
median: 3.5
Therefore, we need to calculate the differences If the writer writes for two more days and creates 5 and 7 comic strips,
The difference in mean:
3.78 - 3.5 = 0.28
The difference in median:
3.5 - 3 = 0.50
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The data in the distribution is positively skewed (skewed to the right). If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference between the mean and the median for the new data set is 0.28.
(✿◕‿◕✿)
Consider a Markov chain defined by the below transition matrix. What is its steady state? [ 1/3 2/3 1/5 4/5]
a. [1/3 2/3] b. [1/5 4/5] C. (10/13 3/13] d. [3/13 10/13]
a Markov chain is the probability defined by the below transition matrix. [ 1/3 2/3 1/5 4/5] has the steady state C. (10/13 3/13]
The steady state of a Markov chain is the probability distribution of possible states of the system. In this case, the steady state from the transition matrix ( Matrix can also be used to represent relationships between different variables.It is commonly used in mathematics, science and engineering to represent a variety of data. ) can be found by solving the system of equations:
P(X0) = P(X0) * 1/3 + P(X1) * 2/3
P(X1) = P(X0) * 1/5 + P(X1) * 4/5
Solving this system of equations yields the steady state of (10/13, 3/13).
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Round the answer to the nearest tenth please
Answer:
28.42
Step-by-step explanation:
pretty sure its correct
For the system
x - 7y = 4
5x - 4y = -11
what is the solution?
Answer:
point form (-3, -1)
equation form x=-3, y=-1
Step-by-step explanation:
y=mx + b what does this equal??
Answer:
Its slope-intercept form
Step-by-step explanation:
The "Y" is the output the "M" is the slope, the "X" is the unknown input and the "B" equals the Y-intercept
URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
The value of x that will make the two given solids similar is: d. x = 31.
What are the Dimensions of Similar Solids?If two solids are said to be similar to each other, it means that one is a scale copy of the other, and one is enlarged by a scale factor to get the dimension of the other.
Thus, the corresponding linear dimensions of two similar solids are proportional or they have equal ratio.
Based on this definition, the equation below would be created to find the value of x that would make both solids similar to each other.
29/14.5 = x/15.5
Cross multiply:
14.5x = (15.5)(29)
14.5x = 449.5
14.5x/14.5 = 449.5/14.5
x = 31.
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help find slope or equation
Using composition of functions, determine if the two functions are inverses
of each other.
F(x)=√x-6
G(x) = (x+6)²
OA. Yes, but only within the domain x ≥ 0.
OB. No, because the composition does not result in an answer of x.
OC. Yes, because F(x) is equal to - G(x).
OD. No, because the functions contain different operations.
Answer:
A. Yes, but only within the domain x ≥ 0
Step-by-s+tep explanation:
What you need to know to solve the question:
1. To find an inverse function (f⁻¹(x)) of f(x), rearrange the equation in terms of f(x), in other words, it should be in the form of x = ...
2. Rules of rearranging equations
3. The domain of √x is: x ≥ 0, since you cannot find the square root of a negative number (i.e. < 0)
Find the inverse function of F(x):
According to principles 1 and 2:
F(x) = √x - 6
F(x) + 6 = √x
(F(x) + 6)² = x
x = (F(x) + 6)²
So, the inverse function is:
F⁻¹(x) = (x + 6)²
And since:
G(x) = (x + 6)²
G(x) = F⁻¹(x)
Therefore, the answer is, also in light of principle 3:
A. Yes, but only within the domain x ≥ 0
Scientific notation of 93000000
Answer:
9.3 × 10^7
Step-by-step explanation:
93000000 / 10000000 = 9.3
10000000 = 10^7
So scientific notation of 93000000 = 9.3 × 10^7
Let W represent the number of attempted experiments to get one experiment that is not successful.
The random variable W has a geometric distribution with mean 4 and standard deviation 3.5. Which of the following is the best interpretation of the standard deviation?Values of W typically vary from 4 by about 3.5 attempted experiments, on average.
Answer:
The standard deviation is a measure of how much the values of a random variable tend to vary from the mean of the variable. In this case, the standard deviation of the random variable W is 3.5, which means that the values of W typically vary from the mean of 4 by about 3.5 attempted experiments. Therefore, the best interpretation of the standard deviation, in this case, is that values of W typically vary from 4 by about 3.5 attempted experiments, on average.
classify the following as discrete or continuous metric: i. the number of automobile accidents per year in virginia. ii. the length of time to play 18 holes of golf. iii. the amount of milk produced yearly by a particular cow. iv. the number of eggs laid each month by a hen. v. the number of building permits issued each month in a certain city. vi. the weight of grain produced per acre.
From the given i) and v) are discrete metric and ii), iii), iv) and vi) are continuous metric.
What distinguishes discrete from continuous data?
Two categories of quantitative variables are discrete and continuous: Discrete variables are count-based (e.g. the number of objects in a collection). Measurable amounts are represented by continuous variables (e.g. water volume or weight).i) 'X' : is discrete because Number of automobile accidents per year is countable (45, 78, 90) and cannot be fraction (4.5)
ii) 'Y' : is continuous because it could take any time to play 18 holes of golf. (15.10 min)
iii) 'M' : is continuous because volume measured can be in fraction. Like 15.6 liters of milk produced by a cow
iv) 'N' : is discrete because eggs are countable . no half eggs or broken eggs are counted. example: 30 eggs per month by a hen.
v) 'P' : is discrete because permits issued are in countable amount and cannot go beyond or like half permit.
vi) 'Q': is continuous because weight can be less or more and can be in fraction. 20 AND HALF OR 56,6 Kg.
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Which statements are true the ordered pair (1, 2) and the system of equations?
y = -2x + 4
y = 7/2x - 3/2
Answer:
Statements:
- When (1, 2) is substituted into the second equation, the equation is true
- The ordered pain (1, 2) is a solution to the system of linear equations
- When (1, 2) is substituted into the first equation, the equation is true.
Step-by-step explanation:
Statement 1:
y= 7/2x - 3/2
2= 7/2 * 1 - 3/2
2= 7/2 -3/2
2=4/2
2=2
Statement 2:
y= -2x + 4
2= -2 ( 1 ) + 4
2= -2 + 4
2 = 2
Statement 6:
y= 7/2x - 3/2
2= 7/2 * 1 - 3/2
2= 7/2 -3/2
2=4/2
2=2
y= -2x + 4
2= -2 ( 1 ) + 4
2= -2 + 4
2 = 2
2/5 3
How do I make this to a whole fraction?
Answer: 17/5
Step-by-step explanation:
Assuming your question asked to convert 3 + 2/5 to a whole fraction:
1. change the whole number to a fraction with the denominator of the remainder (2/5)
3*5/5 = 15/5
2. Add the numberators
15/5 + 2/5 = 17/5
3. circle your answer and celebrate
Evaluate{3(x+4)(x+1)}/{(x+2)(x-2)} for x=4
A. 10
B.-{10}/{3}
C.{10}/{3}
D. -10
Answer:
a) 10
Step-by-step explanation:
Given information,
→ [3(x + 4)(x + 1)]/[(x + 2)(x - 2)]
→ x = 4
Let's evaluate the expression,
→ [3(x + 4)(x + 1)]/[(x + 2)(x - 2)]
→ [3(4 + 4)(4 + 1)]/[(4 + 2)(4 - 2)]
→ [(3 × 8)(5)]/(6 × 2)
→ (24 × 5)/12
→ 120/12 = 10
Therefore, the answer is 10.
The diameter of the low power field of a certain microscope is 1.6 millimeters. The diameter of a cell that is half the diameter of the field is…
Show work please
Answer:
0.8 mm
Step-by-step explanation:
You want a diameter that is half one that is 1.6 mm.
HalfHalf of 1.6 mm is ...
0.5 × 1.6 = 0.8 . . . . mm
The cell diameter is 0.8 mm.
In a chemistry class a hot liquid is placed into a refrigerator and it’s temperature in degrees Fahrenheit is modeled as a function of the number of minutes since it was place in the refrigerator. The model formed was linear function T(n)=-8n+175 give a interpretation of the parameters -8 and 175 within the context of this problem.
Answer:
In this problem, the temperature of the hot liquid (T) is being modeled as a function of the number of minutes (n) that it has been in the refrigerator. The model is a linear function, which means that the temperature will change at a constant rate as the number of minutes increases.
The parameter -8 represents the rate at which the temperature is changing. Specifically, it represents the amount by which the temperature decreases in degrees Fahrenheit for every one minute that passes. For example, if the hot liquid has been in the refrigerator for 10 minutes, its temperature will have decreased by (-8 * 10) = -80 degrees Fahrenheit.
The parameter 175 represents the initial temperature of the hot liquid when it was first placed in the refrigerator. This is the temperature at n = 0, or when no time has passed.
So in the context of this problem, the parameters -8 and 175 represent the rate at which the temperature changes and the initial temperature of the hot liquid, respectively.
The U.S Department of Transportation maintains statistics for mishandled bags per 1,000 airline passengers. In February 2013, Delta mishandled 2,05 bags per 1,000 passengers. What is the probability that in the next 1,000 passengers, Delta will have
a. no mishandled bags?
b. at least one mishandled bag?
c. at least two mishandled bags?
A: The probability of no mishandled handbags is 0.2328
B: The probabilty of at least one mishandled bags is 0.7672.
C: The probability of at least two mishandled bags is 0.197.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Calculation:Probability of mishandling is 205/1000 = 0.205
Probability of not mishandling is 795/1000 = 0.795
A: Probability of no mishandled bags is [tex](0.795)^{1000}[/tex] = 0.2328
B: Probability of at least one mishandled bags is = 1 - p(no mishandled)
= 1- 0.2328 = 0.7672
C: Probability of at least 2 mishandled bags is = 1 - p(none mishandled)-p(1 mishandled)
p(1 mishandled) = 100c1 ×[tex]p^{1}[/tex]×[tex]p^{999}[/tex] = 0.5986
∴p(atleast two mishandled) = 0.795 - 0.5986 = 0.197.
A: The probability of no mishandled handbags is 0.2328
B: The probabilty of at least one mishandled bags is 0.7672.
C: The probability of at least two mishandled bags is 0.197.
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TRUE OR FALSE There were three rounds of QE: $600 billion in QE1 in early 2009, QE2 in November 2010 that was $600 billion worth of securities purchases, and QE3 that started in September 2012 and rose up to $85 billion per month worth of securities purchases that continued until October 2014
TRUE, There were three rounds of QE: $600 billion in QE1 in early 2009, QE2 in November 2010 that was $600 billion worth of securities purchases, and QE3 that started in September 2012
Exports = $300 billion
Imports = $500 billion
Trade surplus/(deficit) = $300 billion - $500 billion
= ($200 billion)
Considering all the options,
Purchases = $800 billion
Sales = $600 billion
Trade surplus/(deficit) = $600 billion - $800 billion
= ($200 billion)
Hence the right answer is c. The U.S has a trade deficit. The U.S. purchases $800 billion worth of foreign assets and foreign countries purchase $600 billion worth of U.S. assets.
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make a sketch of a linear relationship with slope of 3 that is not a proportional relationship,show how you know that the slope is 3
y = 3x + 5 is a linear relationship with a slope of 3.
Describe linear graph.A straight line is formed on the graph by the equation y=2x+1, which is a linear equation. The value of y eventually rises by twice the value of x + 1. This happens when the value of x grows.
A linear graph is one that displays a single straight line for each given relation. A straight line is what the word "linear" denotes. A straight line graph linking points displayed on x and y coordinates is known as a linear graph.
A linear non - proportional relationship could be written with as a slope - intercept with a non - zero intercept value. One such relationship with a slope of 3 can be expressed thus :
y = 3x + 5
Here, the linear relationship, has a slope value of 3 and an intercept value of 5. The function cannot be proportional due to the presence of a non-zero constant
Hence, Using a graphing calculator, the sketch of the linear relationship is attached.
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TRUE OR FALSE : artificial selection takes a relatively long time to occur while natural selection takes a relatively short time to occur.
Artificial selection takes a comparatively longer time to occur while natural selection takes a comparatively shorter time to occur.
Thus, the given statement is False.
Artificial selection takes a very short time related to natural selection. The time taken to choose the individual having the required character and then making them produce the offspring is the only time needed for the entire process.
Artificial selection can be demonstrated as the series of steps for selecting the required character and making the individuals having those character to produce the offspring having the desired character.
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Find the volume of a cone with a height of 8 in and a base diameter of 6 inch
Answer:
75.4cm³
Step-by-step explanation:
height(h) = 8
2radius(diameter) = 6
radius = 6/2 = 3
volume of a cone = ⅓ πr²h
= ⅓ × 3.142 × 3² × 8
= ⅓ × 3.142 × 9 × 8
= 226.224/3
= 75.408
= 75.4cm³
pls rate as brainliest i need to move to the next rank
Answer: around 75.4
Step-by-step explanation:
Cone volume formula
V=[tex]\pi r^{2}[/tex][tex]\frac{h}{3}[/tex]
v= volume, r = radius, h=Height
find the radius of the base
r=6/2
r=3
V=[tex]\pi 3^{2} \frac{8}{3}[/tex]
v=75.4
1. A student is helping a family member build a storage bin for their garage. They would like for the bin to have a volume of 240 ft3. If they already have the length measured at 8 feet and the width at 6 feet, what is the height needed to reach the desired volume?
2. The volume of a rectangular prism is 6,142.5 cm3. If the height is 16.25 cm and the length is 28 cm, what is the value of the width?
3.If the volume of a rectangular prism is 26,214 m3 and it has a height of 17 m, what is the value of B, the area of the base?
The height needed to reach the desired volume is 5 feet
The width is 13.5 cmThe base area is 1542 square mWhat is the height needed to reach the desired volume?From the question, we have the following parameters that can be used in our computation:
Length = 8 feet
Volume = 240 cubic feet
Width = 6 feet
The height is calculated as
Height = Volume/(Length x Width)
Substitute the known values in the above equation, so, we have the following representation
Height = 240/(8 x 6)
Evaluate
Height = 5
What is the value of the width?Here, we have
Length = 28 cm
Volume = 6142.5 cubic cm
Height = 16.25 cm
The width is calculated as
Width = Volume/(Length x Height)
Substitute the known values in the above equation, so, we have the following representation
Width = 6142.5/(28 x 16.25)
Evaluate
Width = 13.5
What is the area of the base?Here, we have
Volume = 26214 cubic m
Height = 17 cm
The base area is calculated as
Base area = Volume/Height
Substitute the known values in the above equation, so, we have the following representation
Base area = 26214/17
Evaluate
Base area = 1542
Hence, the base area is 1542 square m
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The National Health Statistics Reports dated Oct. 22, 2008, stated that for a sample size of 277 18-year-old American males, the sample mean waist circumference was 86.3 cm. A somewhat complicated method was used to estimate various population percentiles, resulting in the following values.
5th 10th 25th 50th 75th 90th 95th
69.6 70.9 75.2 81.3 95.4 107.1 116.4
(b)Suppose that the population mean waist size is 85 cm and that the population standard deviation is 14 cm. How likely is it that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm? (Round your answers to four decimal places.)
(c) Referring back to (b), suppose now that the population mean waist size in 80 cm. Now what is the (approximate) probability that the sample mean will be at least 86.3 cm? (Round your answers to four decimal places.)
the probability that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm is 0.9982.(c)The probability that a random sample of 277 individuals will result in a sample mean waist size of at least 86.3 cm is 0.9817.
To answer (b), we first need to calculate the z-score for 86.3 cm using the population mean of 85 cm and standard deviation of 14 cm. This gives us a z-score of 0.7. We can then use the normal distribution table to calculate the probability of a sample mean of at least 86.3 cm with a z-score of 0.7, which is 0.9982. To answer (c), we need to calculate the z-score for 86.3 cm using the population mean of 80 cm and standard deviation of 14 cm. This gives us a z-score of 1.5. We can then use the normal distribution table to calculate the probability of a sample mean of at least 86.3 cm with a z-score of 1.5, which is 0.9817.
Part (b):
Z-score = (86.3 - 85) / 14
= 0.7
Probability = 0.9982
Part (c):
Z-score = (86.3 - 80) / 14
= 1.5
Probability = 0.9817
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suppose baby kittens' weights are normally distributed with a mean of 12.3 and a standard deviation of 2.2. the z-score tells you how many units above the average (if z-score is positive) or below the average (if z-score is negative) any particular baby kitten's weight is. find the baby kitten weight that corresponds to the following z-scores given below. hint: use the formula x
X-μ Use the formula Z where is the mean, o is the standard deviation, and X is the baby kitten σ weight. a. Z= 1.98, X = b. Z-2.87, X =
Using the formula X=μ+Zσ, the baby kitten's weight corresponds to the z-scores Z=1.98 and Z=2.87 are 16.656 and 18.614.
In a normal distribution, data points are referred to as x, whereas in a z distribution, they are referred to as z or z scores. A z score is a standard score that indicates how many standard deviations an individual statistic is from the mean (x). The formula used to calculate this z-score is Z= (X-μ)/σ where x is the raw score, σ is the population standard deviation, and μ is the population means. From this formula, X can be calculated as X=μ+Zσ.
For the first z-score, Z = 1.98, σ = 2.2 and μ = 12.3, then
X = 12.3+1.98(2.2) = 16.656
For the second z-score, Z = 2.87, σ = 2.2 and μ = 12.3, then
X = 12.3+2.87(2.2) = 18.614
The answers are 16.656 and 18.614.
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ASAP HELP!! Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number if necessary.
A: 7 units
B: 14 units
C: 25 units
D: 26 units
Answer:
B: 14 Units
Step-by-step explanation:
We have the same homework and that's what I got.
Which ordered pairs lie on the graph of the exponential function f(x)=2(x+4)−8? Select each correct answer.
(24, 1)
(−2,−4),
(2, 56)
(8, 0)
The ordered pair that lie on the graph as per the equation will be equal to (-2, -4). Hence, option B is correct.
What is a graph?In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.
Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.
As per the given information in the question,
The given equation is,
f(x) = 2(x + 4) - 8
Let's check as per the points given in the question,
A. (24, 1)
f(x) = 2(24 + 4) - 8
f(x) = 48
So, the supplied exponential function's graph does not contain the point (24, 1) mentioned.
B. (-2, -4)
f(x) = 2(-2 + 4) - 8
f(x) = 4 - 8
f(x) = -4
As a result, the points (-2, -4) are located on the graph of the supplied exponential function.
C. (2, 256)
f(x) = 2(2 + 4) - 8
f(x) = 4
So, the supplied exponential function's graph does not contain the point (2, 56) mentioned.
D. (8, 0)
f(x) = 2(8 + 4) - 8
f(x) = 16
So, the supplied exponential function's graph does not contain the point (8, 0) mentioned.
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