ASAP!!!
Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number, if necessary.
5 units
12 units
16 units
25 units
Answers
The perimeter of the triangle ABC is 12 units. Hence, option (B) is correct.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given right angle triangle,
The vertices are A(-3, 2), B(-3, -1) and C(1, -1)
The distance between AB = 3,
And the distance between BC = 4
To find the distance of AC, use Pythagoreans theorem,
AC² = AB² + BC²
= 3² + 4²
= 9 + 16
AC² = 25
AC = 5
The perimeter of triangle ABC = AB + BC + AC
= 3 + 4 + 5
= 12
The perimeter of the triangle ABC is 12 unit.
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Related Questions
The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute - rpm) and the cube of the diameter. if the shaft of a certain material 3 inches in diameter can transmit 45hp at 100 rpm, what must the diameter be in order to transmit 60hp at 150rpm?
Answers
The the diameter of the shaft is to be in order to transmit 60 hp at 150 rpm 1.88 inch.
Explain the term horsepower?Power is measured in hp, which is the standard abbreviation for horsepower. The rate of job completion can be used to describe power in this context. Most frequently, the term "horsepower" is used to describe an engine or motor's output.We must first obtain the formula for calculating horsepower.
The phrase to use is as follows:
hp = k × v × d³ ......eq(1)
Where:
hp is horsepowerv is speed (in rpm)d is diameterk is constant of horsepower.Since k is a constant, it will always have the same value when the shaft is transferring 60 horsepower at 150 rpm.
Therefore, using the first set of information, we can determine the value of k and subsequently the diameter.
When we solve for k in (1), we get:
k = hp / (v × d³)
Put the values;
k = 45 / (100 × 3³)
k = 0.02
Put the value of k and solve for diameter.
d = ∛hp / (k × v)
d = ∛60 / (150 × 0.06)
d = 1.88 inch
Thus, the the diameter of the shaft is to be in order to transmit 60 hp at 150 rpm 1.88 inch.
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In Exercise 5.18, Y1 and Y2 denoted the lengths of life, in hundreds of hours, for components of types I and II, respectively, in an electronic system. The joint density of Y1 and Y2 isReferenceAn electronic system has one each of two different types of components in joint operation. Let Y1 and Y2 denote the random lengths of life of the components of type I and type II, respectively. The joint density function is given by(Measurements are in hundreds of hours.) Find P(Y1 > 1, Y2 > 1).
Answers
In an electrical system, components of categories I and II have a life expectancy measured in hundreds of hours, respectively. The probability of finding the combined density of Y1 and Y2 is equal to e^(−2).
The components of type I and type II, respectively, have random life spans denoted by the letters Y1 and Y2, respectively. Given by is the joint density function (Measurements are in hundreds of hours.)
Probability P(Y1 > 1, Y2 > 1) = ∫2¹∫1¹ (1/2)e^(−x−y) dx dy = e^(−2).
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what is the probability that someone who tests positive has the genetic disease? (enter the value of the probability in decimal format and round the final answer to three decimal places.)
Answers
The probability that someone who tests positive has the genetic disease is 0.142
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Let E be the people test positive
Let F be the people who has disease
P(F)= 1/10000 = 0.0001
P(E/F)= 99.5% = 0.995
P(E/F bar ) = 0.06 % = 0.0006
Baye's theorem:
P(F/E) = [ P(E/F) * P(F) ] / [ P(E/F) * P(F) + P(E/F bar ) * P( F bar ) ]
conditional probability :
P(B/A) = P ( A [tex]\cap[/tex] B ) / P(A)
Complement rule is given by:
P (F bar ) = 1 - P(F) = 1 - 0.0001 = 0.9999
The probability that someone who tests positive has the genetic disease :
P(F/E) = [ P(E/F) * P(F) ] / [ P(E/F) * P(F) + P(E/F bar ) * P( F bar ) ]
= ( 0.995 * 0.0001 ) / ( 0.995 * 0.0001 + 0.0006 *0.9999)
= 0.142
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hannah claims that -3 is not a rational number because it is not written as a ratio of integers. is she correct? explain why or why not
Answers
Answer: -3 is a rational number
Step-by-step explanation:
-3 is a rational number because it can be written as a fraction -3/1 and have the same value of -3. Therefore -3 is a rational number and Hannah is correct.
If the area of the pentagon is 36, what is the area of the larger pentagon?
Answers
If the area of the pentagon is 36, then the area of the pentagon FGHIJ is 64.
What are Similar figures?Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
Given that the length of the side of the smaller pentagon is 12, while the length of the side of the larger pentagon is 16.
Since the two of the given figures are similar figures, therefore, we can write,
(Area of smaller pentagon)/(Area of larger pentagon) = (Ratio of the sides)²
(Area of pentagon ABCDE)/(Area of pentagon FGHIJ) = (AE / FJ)²
(36)/(Area of pentagon FGHIJ) = (12/16)²
Area of pentagon FGHIJ = 36 × (16/12)²
Area of pentagon FGHIJ = 36 × (256/144)
Area of pentagon FGHIJ = 64
Hence, the area of the pentagon FGHIJ is 64.
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an architect is making a floor plan for a rectangular gymnasium. if the gymnasium is 80 feet long and 60 feet wide, what will the distance be between opposite corners?
Answers
Answer:
the length of the gym will be 80 feet
Step-by-step explanation:
Are x=0 and y=3 perpendicular?
Answers
Answer:
Yes
Step-by-step explanation:
x = 0 is a vertical line. It's the y-axis.
y = 3 is a horizontal line.
x = 0 and y = 3 are perpendicular lines because they intersect
Answer:
Step-by-step explanation:
Yes, you can figure it out by drawing it out. Unfortunately, you can't compare slopes in this case as vertical lines are undefined.
the distribution of heights of adult american men is approximately normal with mean 69 inches and standard deviation 2.5 inches. what percent of men are between 64 and 66.5 inches tall?
Answers
By using normal distribution of probability, it can be calculated that
13.59 %of men are between 64 and 66.5 inches tall
What is normal distribution of probability?
Normal distribution of probability is a continuous type probability distribution whose probability density function is given by
f(x) = [tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}}[/tex] where z = [tex]\frac{x - \mu}{\sigma}[/tex]
[tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.
Here, normal distribution of probability is used
Mean = 69 inches
Standard deviation = 2.5 inches
P(64 < X < 66.5) = P(X <66.5) - P(X < 64)
For X < 64
z = [tex]\frac{64 - 69}{2.5}[/tex] = -2
P(X < 64) = P(z < -2) = 0.0228
For X < 66.5
z = [tex]\frac{66.5 - 69}{2.5}[/tex] = -1
P(X < 66.5) = P(z < -1) = 0.1587
P(64 < X < 66.5) = 0.1587 - 0.0228 = 0.1359
13.59 % men are between 64 and 66.5 inches tall
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Please help me with this
-2 2/3 - (-1 3/5)
Answers
Answer:
The answer is -17/15
(Decimal: -4.733333)
the process of reasoning from a premise or premises to a conclusion based on those premises is known as
Answers
The process of reasoning from a premise or premises to a conclusion based on those premises is known as deductive reasoning.
According to the question,
We have to find the name of the process of reasoning from a premise or premises to a conclusion based on those premises.
We know that there are two types of reasoning. One is inductive reasoning and the second one is deductive reasoning.
In deductive reasoning, we make a final statement which is often called conclusion from various statements which are given. For example, if we say 25th November is my birth date and today is my birth date then the conclusion is today is 25th November.
Hence, the process of reasoning from a premise or premises to a conclusion based on those premises is known as deductive reasoning.
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y-2/3x =-6 what does y equal.
Answers
Answer:
Solve for Y
by simplifying both sides of the equation, then isolating the variable.
Hope this helped
Step-by-step explanation:
The answer would be: y=-18x+2
At higher altitudes, water boils at lower temperatures. This relationship between altitude and boiling point is linear. At an altitude of 1000 feet, water boils at 210 °F. At an altitude of 3000 feet, water boils at 206 °F. Use an equation in point-slope form to find the boiling point of water at an altitude of 6000 feet.
Answers
Answer: Water at sea level boils at a temperature of 212 degrees Fahrenheit. For every increase in altitude of 1000 feet, the boiling point drops by 1.8 degrees. Write a linear function that gives the boiling point of water as a function of the altitude. What is the boiling point of water at 15,000 feet?
Draw a chart with the column heading as follows
Step-by-step explanation:
the probability distribution function for the discrete random variable where x is equal to the number of red lights drivers typically run in a year is as follows. x 0 1 2 3 p(x) 0.72 0.11 0.02 (a) fill in the missing probability. x 0 1 2 3 p(x) 0.72 0.11 0.02 0.15 correct: your answer is correct. (b) what is the mean of this discrete random variable?
Answers
(a) The value of p(x) is 0.15 when x = 3.
(b) The mean of the discrete random variable is 0.1
What is meaning of discrete random variable?
A discrete random variable has a countable number of different possible values, such as 0,1,2,3,4, etc. Usually, but not always, discrete random variables are counts. A random variable is discrete if it can only take a finite number of different values.
Given table is
X 0 1 2 3
P(x) 0.72 0.11 0.02
The sum of the probability of an event is 1.
Therefore
P(0) + P(1) + P(2) + P(3) = 1
Putting the value of P(0), P(1), P(2)
0.72 + 0.11 + 0.02 + P(3) = 1
0.85 + P(3) = 1
P(3) = 1- 0.85
P(3) = 0 .15
The mean of the discreate random variable is Σ xp(x) / Σ x
=[(0 × P(0)) + (1 × P(1)) + (2 × P(2)) + (3 × P(3))]/(0 + 1 + 2 + 3)
= (0 + 0.11 + 0.04 + 0.45) / 6
= 0 .1
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Which pairs of triangles are similar? check all that apply. △abc ~ △def △def ~ △ghi △ghi ~ △abc △ghi ~ △jkl △jkl ~ △abc
Answers
The pairs of triangles that are similar are △jkl ~ △abc and their corresponding angles are congruent.
The fact that, When two triangles are comparable, their corresponding sides have a proportional ratio and their corresponding angles have a congruent relationship.
In this issue
△jkl ~ △abc
Because the proportion between its corresponding sides
Verify
CA/LJ=BC/KL
replace the specified values
14/7=20/10
2=2 >>>>> is correct
so
The proportion between the corresponding sides is linear.
therefore △jkl ~ △abc are similar.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
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Answer: b & e
Step-by-step explanation: cuz
14.95x4.1
HELPPPPPP
me please i need helppp
Answers
Answer:
down below
Step-by-step explanation:
Assuming you meant multiplying:
61.295
Hope this helps! :)
explain why two lines through the origin that meet at a right angle can be considered orthogonal subspaces of r2 but two planes through the origin that meet at a right angle can not be considered orthogonal subspaces of r3.
Answers
There is a difference between orthogonal and orthogonal subspaces. According to this, two planes cannot be orthogonal in R3.
Considering, in the case of the orthogonal planes, each plane should have a basis of orthogonal vectors, and also, one of the pairs in each of the vector, is shared between the two planes and the other vector that is present, should form a orthogonal pair to each other.
Taking the case of orthogonal subspaces, the main requirement is that each vector of each of the pairs should be orthogonal to each vector of each of the other pair. Also, the dimension of the ambient pair should be not less than 4 (2+2).
When we talk about two planes in R3, planes are orthogonal if and only if, their normal vectors are orthogonal. If this condition is not present, then planes are not orthogonal in R3.
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When two pipes fill a pool together, they can finish in 4 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 9 hours. How long will it take each pipe to fill the pool if it were working alone?
How many hours for one pipe to fill the pool? How many hours for the other pipe to fill the pool?
Answers
One pipe takes 6 hours to fill the pool and the other takes 12 hours.
Pipe A fills 1/x of the pool per hour, and Pipe B fills 1/y of the pool per hour. In other words, A takes x hours to fill the pool and B takes y hours to fill the pool.
Together, they fill 1/x + 1/y of the pool per hour. So, 4 hours times that rate should equal 1 full pool, since together they take 4 hours to fill the pool. That gives you your first equation:
4(1/x + 1/y) = 1
You're also told that if one pipe fills half the pool and the other takes over to fill the rest, it will take 9 hours. We don't know how long Pipe A works, so call that number of hours t. Pipe B must work for 9 - t hours.
So, Pipe A, working for t hours, fills half the pool:
t(1/x) = 1/2
And Pipe B, working for 9 - t hours, fills half the pool:
(9-t)(1/y) = 1/2
You now have a system of three equations (because this is an exceptionally complicated pipe-filling-pool problem):
4(1/x + 1/y) = 1
t(1/x) = 1/2
(9-t)(1/y) = 1/2
Solve for t in that second equation, then plug it into the third equation:
t(1/x) = 1/2
t = x(1/2)
t = x/2
(9 - x/2)(1/y) = 1/2
Now you've got a system of two equations:
4(1/x + 1/y) = 1
(9 - x/2)(1/y) = 1/2
Solve for y in the second equation, then plug that into the first equation:
(9 - x/2)(1/y) = 1/2
(9 - x/2) = y(1/2)
2(9 - x/2) = y
18 - x = y (this is a really nice-looking form of that equation; we'll use it again later)
4(1/x + 1/y) = 1
4(1/x + 1/(18-x)) = 1
4/x + 4/(18-x) = 1
(4(18-x))/(x(18-x)) + (4x)/(x(18-x)) = 1
(4(18-x) + 4x)/(x(18-x)) = 1
4(18-x) + 4x = x(18-x)
72 - 4x + 4x = 18x - x2
72 = 18x - x2
x2 - 18x + 72 = 0
(x - 6)(x - 12) = 0
x - 6 = 0 OR x - 12 = 0
x = 6 OR x = 12
So, Pipe A takes either x = 6 or x = 12 hours to fill the pool alone.
When Pipe A takes 6 hours to fill the pool, Pipe B takes 12. When Pipe A takes 12 hours to fill the pool, Pipe B takes 6.
These cases are equivalent, since the original problem makes no distinction between the pipes.
Hence, one pipe takes 6 hours to fill the pool and the other takes 12 hours.
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Wyatt buys eggs and onions at the store. • He pays a total of $20. • He pays $2.52 for the eggs. • He buys 4 bags of onions that each cost the same amount. Wrote an equation that could be used to represent the context of X represents how much each bag of onions costs?
Answers
Answer:
X=437 over 100
Step-by-step explanation:
PLEASE HELP ME I NEED TO ACE THIS ILL GIVE BRAINLY PLSSSSS
SS MEANS SCREENSHOT
What is the constant of proportionality in the table below?
fist ss*
Do the values in the table form a proportion? If so, what is the constant of proportionality?
second ss*
Which table shows a proportional relationship between x and y?
third ss*
Answers
The constant of proportionality of the given table is k = 2.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
We know the constant of proportionality between the variable x and y can be written as y = kx, where k is the constant of proportionality.
From the table when x = 2, y = 4.
∴ 4 = 2k.
k = 2.
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treatment treatment treatment a b c 32 44 33 30 43 36 30 44 35 26 46 36 32 48 40 sample mean 30 45 36 sample variance 6.00 4.00 6.50 a. at the level of significance, can we reject the null hypothesis that the means of the three treatments are equal? compute the values below (to decimal, if necessary). sum of squares, treatment 570 sum of squares, error 66 mean squares, treatment 285 mean squares, error 5.4 calculate the value of the test statistic (to decimals). 51.81818182 the -value is less than 0.01 what is your conclusion? conclude that not all treatment means are equal b. calculate the value of fisher's lsd (to decimals). 2.17881283 use fisher's lsd procedure to test whether there is a significant difference between the means for treatments a and b, treatments a and c, and treatments b and c. use . difference absolute value conclusion significant difference significant difference no significant difference c. use fisher's lsd procedure to develop a confidence interval estimate of the difference between the means of treatments a and b (to decimals). enter negative values as negative numbers.
Answers
The value is less than 0.01
What is Null hypothesis?
The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.
Explanation:
[tex]Grand \ mean = \frac{30+45+36}{3} \\\\Grand \ mean = \frac{111}{3} \\\\Grand \ mean = 37[/tex]
TrSS = 5(30-37)²+5(45-37)²+5(36-37)²
TrSS = 570
SSE = (5-1)6²+(5-1)4²+(5-1)(6-5)²
SSE = 66
[tex]HST_{r} = SST_{s}[/tex]
according to given question p value is less than 0.00001 point. Therefore, The value is less than 0.01.
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if a researcher is using a one sample t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the one sample t statistic?
Answers
If a researcher is using a one sample t statistic to test a null hypothesis about a population, he needs average, standard deviation and sample size to calculate the one sample t statistics.
What is t- Statistic test ?
Comparing the means of two groups is done statistically using a t test. It is frequently used in hypothesis testing to ascertain whether a method or treatment truly has an impact on the population of interest or whether two groups are distinct from one another.
Since the researcher wants to use one sample t statistic to test a null hypothesis about a population, the formula for t statistic will be followed which can be computed by using some figures which are the average, standard deviation and sample size to calculate the one sample t statistic.
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Multiples of 3 and factors of 45??
Answers
Answer:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30
Factors of 45: 1, 3, 5, 9, 15, and 45
Step-by-step explanation:
need help as quickly as possible
Answers
The measure of the unknown angles in the kite are as follows;
x = 66 degreesy = 158 degreesHow to find the measure of a kite?A kite has two pairs of adjacent equal sides.
In other words, a kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.
One pair of opposite angles is equal. Diagonals are perpendicular to each other.
A kite has four interior angles and the sum of these interior angles is 360°
Therefore, the measures of the
x = 66 degrees.
Let's find y.
y = 360 - 70 - 66 - 66
y = 158 degrees.
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a page is to contain 24 square inches of print. the margins at top and bottom are 1.5 inches and 1 inch at the sides. find the most economical length (in inches) of the page.
Answers
The most economical length of the paper is 9 inches and width is 6 inches.
What is a derivative of a function?
The derivative of a function of a single variable at a chosen input value. It is the rate of change of a function with respect to a variable.
Let us consider,
Width of the printed part, in inches be 'x'
height of the printed part, in inches be 'y'
According to question,
Area of the printed part, in square inches = xy = 24
So,
y=24/x
width of the page, in inches = x + 2×1 = x+2
height of the page, in inches = y + 2×1.5 = y + 3
The area of the page (in square inches) is , A
= (x+2) (y+3)
= xy + 3x + 2y + 6
= 24 + 3x + 2y + 6
= 3x + 2y + 30
= 3x + 2×24/x + 30
= 3x + 48/x + 30
The minimum length can be found by calculating the derivative dA/dx, where A is the area of the paper
Solving the equation for dA/dx=0,
[tex] \frac{dA}{dx} = \frac{d(3x + \frac{48}{x} + 30)}{dx} [/tex]
[tex] \frac{dA}{dx} = 3 + \frac{48}{ {x}^{2} } [/tex]
[tex]\frac{dA}{dx} = 3 + \frac{48}{ {x}^{2} } = 0[/tex]
[tex]3 + \frac{48}{ {x}^{2} } = 0[/tex]
x = 4
then,
y = 24/4 = 6
The width and height of the paper are
x+2=4+2=6 and
y+3=6+3 =9
The dimensions of the page, so that the least amount of paper is used must be 6 inches wide by 9 inches tall.
Hence, the most economical length of the paper is 9 inches and the width is 6 inches.
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in 1970, about 10 percent of the u.s. population was age 65 and older. what is the projected percentage for 2060
Answers
The projected percentage for 2060 is nearly double from 52 million in 2018 to 95 million by 2060.
Given in 1970, about 10 percent of the u.s. population was age 65 and older.
Demographic Shifts
The number of Americans ages 65 and older is projected to nearly double from 52 million in 2018 to 95 million by 2060, and the 65-and-older age group's share of the total population will rise from 16 percent to 23 percent. The older population is becoming more racially and ethnically diverse.
Hence the answer is the projected percentage for 2060 is nearly double from 52 million in 2018 to 95 million by 2060.
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1. Write a rule for g(x)=3f(x) + 1 when f(x) = x³ - 2x + 3.
2. Describe the graph if g as a transformation of the graph of f.
Answers
The equation of transformation in g(x ) is 3x³ - 6x + 8
what is transformation?
A point, line, or geometric object can be changed in four different ways that are all collectively referred to as transformations. The pre-image is the shape of the object as it was originally, and the transformed shape of the object is termed the image.
solution:
1. f(x) = x³ - 2x + 3.
Then g(x) = 3f(x) + 1
substitute f(x) in g(x)
g( x ) = 3 (x³ - 2x + 3) + 1
= 3x³ - 6x + 9 + 1
g( x ) = 3x³ - 6x + 8
2. The graph of the function f(x) = x³ - 2x + 3 is obtained by just moving the graph of g( x ) = 3x³ - 6x + 8 by 2 units up.
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Weight
Weight
9. John mixed cashews and almonds.
Weight
John bought 4 pounds of almonds for a total cost of $22
The cost per pound for cashews is 60% more than the cost per
pound for almonds.
John bought enough cashews that, when he mixed them with the
almonds, the mixture had a value of $6.50 per pound
Approximately what percent of the mixture by weight was cashews?
Answers
Answer:
30%
Step-by-step explanation:
4 pounds of almonds is $22 --> 1 pound of almonds is $5.50
Cashew price per pound = 160/100 * $5.50. = $8.80
22 + 8.80x = 6.50(4+x)
22 + 8.80x = 26 + 6.50x
2.30x = 4
x = 1.739130435 approx 1.74 lbs of cashews
percent of the mixture, by weight, for cashews =
1.739130435 / (4 + 1.739130435) = 0.303030303 approx 30%
what is the sampling process used on dollar street? in other words, the sample of families on the dollar street page were collected using a sample that is .
Answers
The sampling process used on dollar street is stratified sampling.
Given,
Use of dollar street;
Dollar street offers a fresh perspective on families all throughout the world. Every family is arranged down a street, with the wealthiest household on the right and the lowest on the left. Each family's earnings are expressed in US dollars.
Here,
Stratified sampling;
To complete the sampling process, stratified sampling is a form of sampling technique in which the entire population is divided into smaller groups or strata.
Therefore,
Stratified sampling is used in dollar street for sampling process.
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what is the solution to the following equation
x2 + 3x + 7 = 0
Answers
Answer:
its C.
Step-by-step explanation:
How much is 76 divided by 6?
Answers
Answer:
If you divide 76 by 6, you would get 12.6666667.
76 divided by 6 is equal to 12 and 2/3, or simply 12.67 when expressed as a decimal.
To divide 76 by 6, we perform the division operation to find the quotient.
When dividing, we start with the largest multiple of 6 that is less than or equal to 76, which is 72. We divide 72 by 6, which equals 12.
Next, we subtract the product of 6 and 12 from 76 to find the remainder:
76 - (6 x 12) = 76 - 72 = 4
Since there is still a remainder of 4, we can express the result as a mixed number: 12 and 4/6.
To simplify the mixed number, we can reduce the fraction. The greatest common divisor of 4 and 6 is 2, so we can divide both the numerator and denominator by 2:
4/2 ÷ 6/2 = 2/3
Therefore, 76 divided by 6 is equal to 12 and 2/3, or simply 12.67 when expressed as a decimal.
To learn more about the division;
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