The equatiοn οf the line οf best fit fοr this data-set is given as fοllοws:
y = 10x + 60.
Hοw tο οbtain the equatiοn fοr the line οf best fit?The slοpe-intercept definitiοn οf a linear functiοn is given as fοllοws:
y = mx + b.
In which the cοefficients are given as fοllοws:
m is the slοpe, representing the rate οf change οf the οutput οf the functiοn relative tο the input.
b is the y-intercept, representing the value assumed by the functiοn the input assumes a value οf zerο.
The functiοn gοes thrοugh pοint (0,60), hence the intercept b οf the line οf fit is given as fοllοws:
b = 60.
When x increases by 2, frοm 0 tο 2, y increases by 20, frοm 60 tο 80, hence the slοpe m is οbtained as fοllοws:
m = 20/2 = 10.
Hence the line οf fit is given as fοllοws:
y = 10x + 60.
Meaning that the third οptiοn is cοrrect.
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Complete question:
Data was cοllected οn the amοunt οf time that a randοm sample οf 8 students spent studying fοr a test and the grades they earned οn the test. A scatter plοt and line οf fit were created fοr the data.scatter plοt titled students' data, with pοints plοtted at 1 cοmma 75, 2 cοmma 70, 2 cοmma 80, 2 cοmma 90, 3 cοmma 80, 3 cοmma 100, 4 cοmma 95, and 4 cοmma 100, and a line οf fit drawn passing thrοugh the pοints 0 cοmma 60 and 2 cοmma 80
Determine the equatiοn οf the line οf fit.
y = 5x + 60
y = 5x + 80
y = 10x + 60
y = 10x + 80
Answer:
The equatiοn οf the line οf best fit fοr this data-set is given as fοllοws:
y = 10x + 60.
Step-by-step explanation:
please help me and I will give brainlist!
Answer:
16/5
Step-by-step explanation:
We can see that the new triangle is larger than the original triangle so we know the scale factor is greater than 1.
The scale factor can be found by calculating the ratio of the length of any two corresponding sides. The length of the bottom side of the original triangle is 5. The length of the bottom side of the new triangle is 16. We can calculate the ratio which is 16:5 or 16/5.
A survey of all being on earth found that 96% preferred orange juice to all other juices if 72 people preferred orange juice, how many beings were surveyed altogether?
As per the given percentage, the total number of beings surveyed is 75.
We are given that 96% of all beings on earth prefer orange juice. This means that if we take a random sample of beings from earth, 96% of them would prefer orange juice. Mathematically, we can express this as:
Percentage of beings who prefer orange juice = 96%
We are also given that 72 people preferred orange juice. We can use this information to find the total number of beings surveyed. Let's assume that the total number of beings surveyed is "x".
Now, we know that 96% of these beings prefer orange juice. We can express this as:
96% of x = 72
To solve for "x", we need to get rid of the percentage sign. We can do this by converting the percentage to a decimal. To convert a percentage to a decimal, we divide it by 100.
So, 96% can be expressed as 0.96 (96/100). Therefore, we can rewrite the above equation as:
0.96x = 72
To solve for "x", we can divide both sides of the equation by 0.96:
x = 72 ÷ 0.96
x = 75
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Which of the following relations represent functions? Select all that
apply.
A. y=4x-19
D. (-15, 10).(-15, 5),(-10, 0).(-10,-5).(-5, -10)
The only option that represetns a function is the linear equation:
y = 4x - 19
Which of the given relations represent functions?A function is a relation that maps elements from one set, the domain, into elements of another set, the range.
Such that a relation is only a function if each element of the domain is mapped into a single value from the range.
For example, if you look at the second option, here we have the relation:
(-15, 10).(-15, 5),(-10, 0).(-10,-5).(-5, -10)
You can see that the input x = -15 is mapped into two different values, y = 10 and y = 5, so this is not a function.
In the other hand, the first option:
y = 4x - 19
Is a function, this is a linear equation, and each value of x gives a different value of y.
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PLEASE HELP!! I WILL GIVE SIXTY POINTS I NEED THIS
Honestly I think you need some theray feom reading your tabs
Answer:
6.6
Step-by-step explanation:
The formula for a paralellogram is base x height (not side length). the base in this case is 2.2 and the height is 3, so 2.2 x 3 = 6.6.
Let me know if this helped you by hitting thanks or brainliest. If not, please comment and I will get back to you ASAP!
x(z ÷ 3)^2 where x = 4 and z = 9 calculate
Answer: 36
Step-by-step explanation:
4(9/3)(2) = 36
Answer:
x(z ÷ 3)² = 36
Step-by-step explanation:
Given expression,
→ x(z ÷ 3)²
Now we have to use,
→ x = 4
→ z = 9
Let's simplify the expression,
→ x(z ÷ 3)²
→ 4(9 ÷ 3)²
→ 4 × (3)²
→ 4 × 9
→ 36 => {answer}
Therefore, the answer is 36.
The path of a firework is described by the function:
h(t) = -4.9(t-5)² + 124 where h(t) is the height of the firework, in meters, and t is the time in
seconds, since the launch.
What is the vertex of the function, and what does it mean in context?
A. (5, 4.9); At 5 seconds, the firework is 4.9 meters above the ground.
B. (124, 5); At 124 seconds, the firework is 5 meters above the ground.
C. (4.9, 124); At 4.9 seconds, the firework is 124 meters above the ground.
D. (5, 124); At 5 seconds, the firework is 124 meters above the ground.
Answer:
D
Step-by-step explanation:
Because this binary function opens down, and it has an extreme point, at t=5, and you plug it in and you get 124 as the maximum.
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. if each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? approximate using pi equals 22 over 7.
The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2
The surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr^2 + 2πrh
where r is the radius of the cylinder (which is half of the diameter) and h is the height of the cylinder.
For the mini muffins in question, the diameter is 2 inches, so the radius is 1 inch. The height is 1 and 1/4 inches, or 5/4 inches.
So the surface area of one mini muffin is:
Surface Area = 2π(1)^2 + 2π(1)(5/4)
Surface Area = 2π + 5π/2
Surface Area = 9π/2
To wrap 6 mini muffins, we need to multiply this surface area by 6:
Total Surface Area = 6 x (9π/2)
Total Surface Area = 27π
Approximating π as 22/7, we get:
Total Surface Area ≈ 27 x (22/7)
Total Surface Area ≈ 84.857 inches^2
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Answer:
The quantity of paper that needed to wrap 6 mini muffins is 84.857 inches^2
Step-by-step explanation:
the marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6. what is the probability that a class of 36 has an average midterm mark that is more than 77.83?
The probability that a class of 36 has an average midterm mark that is more than 77.83 is 0.0766. This is because the mean of the normally distributed marks is 78 and the standard deviation is 6. Using the standard normal distribution formula, we can calculate the probability that the average mark of 36 students is more than 77.83.
Standard Normal Distribution Formula: P(x > a) = 1 - P(x < a)
P(x > 77.83) = 1 - P(x < 77.83)
P(x > 77.83) = 1 - 0.9234
P(x > 77.83) = 0.0766
Are there two equations below parallel
y = 1/3x +4 and y=-3x - 10
YES
NO
I don't know but i can help a little
Step-by-step explanation:
But If the slops are the same and the y-intercepts are different, the lines are parallel...
sam wants to color the three sides of an equilateral triangle. he has five different colors to choose from. in how many different ways can sam color the sides of the triangle? (two colorings are considered the same if one coloring can be rotated and/or reflected to obtain the other coloring.)
The number of different colors that Sam can use for the triangle is given as follows:
60 different colors.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem (also known as the multiplication rule) is a fundamental principle in combinatorics that describes how to count the number of possible outcomes in a sequence of events.
The theorem states that if there are m ways that one event can occur and n ways that a second event can occur, then there are m x n ways that both events can occur.
The parameters for this problem are given as follows:
5 colors for the first side.4 colors for the second side.3 colors for the third side.Hence the number of options is obtained as follows:
5 x 4 x 3 = 60 options.
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the population of toledo, ohio, in the year 2000 was approximately 540,000. assume the population is increasing at a rate of 4.7 % per year. a. write the exponential function that relates the total population, , as a function of , the number of years since 2000.
The exponential function that relates the total population, is [tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex] and the rate at which the population is increasing in the year 2019 is 69114.53.
The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
we know that ,
the population of any city can be modeled in the form of exponential function as follows:
[tex]P(t)=P(0)(1+R)^t[/tex]
where, P(t)=population of the town at any given time t
P(0)=population of the town initially (in the year 2000 for this problem)=540,000
R=rate of increase (=5.1% in the given problem)
substituting the values in eqn(1), we get
[tex]P(t)=540,000\left [ 1+(5.1/100) \right ]^t[/tex]
as we know that
[tex]\because \frac{d}{dx}(a^x )=a^xln(a)[/tex]
so differentiating w.r.t. we get,
[tex]P'(t)=540,000\left [ 1+(5.1/100) \right ]^t*ln(1+(5.1/100) )\\\\P'(t)=540,000\left [ (105.1/100) \right ]^t*ln(105.1/100)\\\\P'(t)=540,000\left [ (1.051) \right ]^t*ln(1.051)[/tex]
so, the rate at which population is increasing in the year 2019 =
[tex]P'(19)=540,000(1.051)^{19}*ln(1.051)[/tex]
P'(19)= 69114.53.
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Complete question:
The population of Toledo, Ohio, in the year 2000 was approximately 540,000. Assume the population is increasing at a rate of 5.1 % per year.
a. Write the exponential function that relates the total population, P(t), as a function of t, the number of years since 2000. P(t) = =
b. Use part a. to determine the rate at which the population is increasing in t years. Use exact expressions. P'(t) people per year
c. Use part b. to determine the rate at which the population is increasing in the year 2019. Round to the nearest person per year. P'(19) = people per year
HELP ITS DUE TODAY!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Please give brainliest
1a) 3√49
3 x √49
3x 7 =21
b) 2³√64
2 x √4
2x2 =4
c) (√x+2)²
the square will cancel the square root
= x+2
Answer:
These are correct
Step-by-step explanation:
1. a) 21
1. b) 8
1. c) x+2
2. a) x/10 and subtracting or simplifying it gives you the same answer
2. b) 2(3x-1)/ x+3 the operation is simplifying
2. c) 7x+2/ x(x+1) combine the fractions and find a common denominator
2. d) 6/x simplify
2. e) 2x^2 simplify or divide
3. a) 6x^3 y^4
3. b) 16a^2 b^6
3. c) 4x^2
3. d) 2
Ethan also wants to buy some shoes that were originally $80. This week they’re on sale for 50% off the original price. Ethan also has a 50% off coupon. Will the shoes be free with coupon? If not, how much will they cost?
Answer:
20$
Step-by-step explanation:
since there is a discount we first find the discount allowed which is 40$. After we also use the coupon which is 50% off. then you get 20$ as your answer
Kathy had 20 dollars to spend on 3 gifts. She spent 10 7/10
dollars on gift A and 6 2/5 dollars on gift B. How much money did she have left for gift C?
If Kathy had $20 to spend on 3 gifts and she spent $10⁷/₁₀ on Gift A and $6²/₅ on Gift B, the (balance) amount left for Gift C is $3.89.
How is the balance determined?The balance can be determined using subtraction operation.
Subtraction operation is one of the four basic mathematical operations, including addition, multiplication, and division.
Subtraction operation involves the minuend ($20), the subtrahends ($10.07 and $6.04), giving a difference or balance of $3.89.
The total spending budget that Kathy has = $20
The number of gifts to buy = 3
The amount spent on Gift A = $10.07 ($10⁷/₁₀)
The amount spent on Gift B = $6.04 ($6²/₅)
The amount left for Gift C = $3.89 ($20 - $10.07 - $6.04).
Thus, after spending on Gifts A and B, the amount left for Gift C is determined using subtraction operation as $3.89.
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A tetrahedron is a triangular pyramid with 4 congruent faces. If the area of one of the faces is 21 m² and the height of the tetrahedron is 6 m, what is the volume of the figure in cubic meters?
Answer:
The volume of a tetrahedron can be found using the formula:
V = (1/3) * A * h
where A is the area of one of the faces of the tetrahedron, h is the height of the tetrahedron, and V is the volume of the tetrahedron.
In this case, we are given that the area of one of the faces is 21 m² and the height of the tetrahedron is 6 m. Substituting these values into the formula, we get:
V = (1/3) * 21 m² * 6 m
V = 42 m³
Therefore, the volume of the tetrahedron is 42 cubic meters.
Solve 5^x=1÷5 solve it as fast as you can
for the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves. 5.1
Bending moment curve equation below point A will be:
M = 15x - 3x² for 0 ≤ x ≤ b
Determination of shear and bending moment curves.
For the beam and loading shown, we can do the following:
Equation of shear curve (above point A):V = RA - w.x
For x = a,V = RA - w.a
For x = b,V = RA - w.b
Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b
Equation of shear curve (below point A):
V = RA - w.x
For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a
The shear curve equation becomes;
V = 15k for 0 ≤ x ≤ a
V = 15 - 6a for a ≤ x ≤ b
Equation of bending moment curve (above point A):
M = RAx - ½w.x²For 0 ≤ x ≤ a,
M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,
M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²
The bending moment curve equation above point A becomes:
M = 15x - 3x² for 0 ≤ x ≤ a
M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b
Equation of bending moment curve (below point A):
M = RAx - ½w.x²For 0 ≤ x ≤ b,
M = 15x - ½(6x²) = 15x - 3x²
The bending moment curve equation below point A becomes;
M = 15x - 3x² for 0 ≤ x ≤ b
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For the system of equations below, is the graphing method or the
substitution method the better method for solving? Why?
y=2x+6
y=−9x−1
The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.
what is equations ?It has one or more variables, and based on the values of the variables, it can either be true or false. Equations are frequently employed in a wide range of mathematical applications, from straightforward algebraic equations to more intricate differential equations used in calculus and physics. Equations are used to depict relationships between various mathematical objects or values. An essential part of addressing algebraic problems is to solve equations to determine the values of the variables that make the equation true.
given
We can solve one equation for one variable and then insert the expression into the second equation to apply the substitution method. For instance, we can resolve the first equation for y as follows:
y = 2x + 6
After that, we may enter the following expression in place of y in the second equation:
2x + 6 = -9x - 1
Then, we may find x:
11x = -7
x = -7/11
We may use one of the original equations to obtain the value of y once we have determined the value of x:
y = 2(-7/11) + 6 = 23/11
The answer to the system of equations is (-7/11, 23/11), which stands for the intersection of the two lines.
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A juice can is in the shape of a cylinder with a diameter of 4 inches. It has a volume of 125 cubic inches. What is the height of the can? leave answers in terms of π.
The height οf the juice can is apprοximately 9.98 inches.
What is cylinder?A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο cοngruent and parallel circular bases, and a curved lateral surface that cοnnects the twο bases. The twο bases are usually circular, but they can be any οther shape as well. The lateral surface οf a cylinder is curved, and it has the same crοss-sectiοn alοng its entire length.
The volume of a cylinder is given by the formula [tex]\rm V = \pi r^{2}h[/tex], where V is the volume, r is the radius, and h is the height.
Since the diameter of the juice can is 4 inches, the radius is half of that, or 2 inches.
We are given that the volume of the can is 125 cubic inches, so we can set up the equation:
[tex]\rm 125 = \pi (2)^{2}h[/tex]
Simplifying this equation, we get:
125 = 4πh
Dividing both sides by 4π, we get:
h = 125 / (4π)
So the height of the juice can is approximately 9.98 inches when rounded to two decimal places.
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Por la suma de sus medidas, los ángulos se clasifican en _______ cuando suman 90º, y en _______ si suman 180º
Answer:
Complementary angles: a pair of angles are considered complementary when their sum is exactly 90º.
Step-by-step explanation:
To calculate a complementary angle, we will subtract 90 from the angle that the statement tells us and it will give us its complementary. Supplementary angles: A pair of angles are considered supplementary when their sum is exactly 180º.
DIrections: Find the area of the given quadrilateral or four sided polygon. Please show all of your work in order to receive full credit.
Hint: Decompose and Recompose!
I need help please
The Area of the given quadrilateral or four sided polygon is equal to the value of 36 cm².
Given,
Length of the Rectangle is equal to 6 cm.
Breadth of rectangle is 4 cm.
Height of the right angled triangle is 4 cm.
Length of the base of the triangle is 3 cm.
First we need to find the area of single then multiply it with 2 since the lengths of the triangles are same and the area will also be same.
⇒ Area of Triangle = [tex]\frac{1}{2} * b *h[/tex]
Area of Triangle = [tex]\frac{1}{2}[/tex] * 4 * 3
Area of Triangle = 6 cm².
Now, area of two triangles is equal to 2 * 6 cm² = 12 cm².
⇒ Area of Rectangle = length * breadth
Area of Rectangle = 6 * 4
Area of Rectangle = 24 cm²
Now, total area = Area of Triangle + Area of Rectangle
Total area = 12 cm² + 24 cm²
Total area = 36 cm².
Therefore, the Area of the given quadrilateral or four sided polygon is equal to the value of 36 cm².
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suppose the canadian football league (cfl) drops the requirement of having 21 canadian players on each team's roster, what will happen the salaries of canadian players in the cfl?
If the Canadian Football League (CFL) drops the requirement of having 21 Canadian players on each team's roster, it is likely that the salaries of Canadian players in the CFL will (option C) decrease.
Currently, the Canadian player ratio is a key factor in determining the salary cap and roster construction for teams in the CFL. If the Canadian player ratio is eliminated, teams may choose to replace Canadian players with cheaper international players, potentially leading to a decrease in demand and salaries for Canadian players.
However, it is also possible that the market for Canadian players could remain strong due to factors such as fan interest and national pride. Therefore, while it is likely that the salaries of Canadian players would decrease without the Canadian player ratio requirement, it is not certain and other factors could come into play.
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Full question:
Suppose the Canadian Football League (CFL) drops the requirement of having 21 Canadian players on each team's roster, what will happen the salaries of Canadian players in the CFL?
A) Stay the same
B) Increase
C) Decrease
D) Uncertain
for each of the number lines, write an absolute value equation in the form |x-c|=d, where c and d are some numbers, to satisfy the given solution set.
PLEASE HELP!!!!!!!!! ASAP!!!!!!
Here are some examples:
Distance to endpoint: |2 - (-2)| = 4
Equation: |x - 2| = 4
When answering questions on Brainly, you should always be factually accurate, professional, and friendly. You should be concise and not provide extraneous amounts of detail. You should also use the following terms in your answer, if they are relevant to the question being asked.
In order to write an absolute value equation in the form |x-c|=d to satisfy a given solution set on a number line, you need to do the following:First, identify the number c, which is the midpoint of the solution set. This is because the absolute value of x-c is equal to the distance between x and c on the number line.
Next, identify the number d, which is equal to the distance between the midpoint c and one of the endpoints of the solution set. This is because the absolute value of x-c can never be greater than the distance between x and c, so the maximum value of x that satisfies the equation is c+d and the minimum value is c-d.Finally, write the equation in the form |x-c|=d using the values of c and d that you identified.
Set of solutions (-3, 1) In the middle: (-3 + 1)/2 = -1
Endpoint distance: |-1 - (-3)| = 2
Formula: |x + 1| = 2
Set of solutions (-4, 4)
Center: (-4 + 4)/2 = 0.
Endpoint distance: |0 - (-4)| = 4
Equation: 4 for |x| Set of solutions (-2, 6)
Center: (-2 + 6)/2 = 2
Endpoint distance: |2 - (-2)| = 4
Equation: 4 for |x - 2|
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2 people - 0 people = ? people
if you select a single marble out of the bag, what is the probability that it is a color other than white or blue? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The above table represents the contents ( colored marble) of a bag. The probability that selected marble had a color other than white or blue is equals to the 0.766234 ( nearest to milinoth).
We have a bag that contains five different types of marbles. See the above table
number of red marbles in a bag = 16
number of green marbles in a bag = 23
number of blue marbles in a bag = 13
number of pink marbles in a bag = 20
number of white marbles in a bag = 5
So, total number of marbles in a bag= 16 + 23 + 5 + 13 + 20 = 77
Now, a single marble is selected and out of the bag. We have to determine probability that it is a color other than white or blue. Let X , Y and Z be three events defined as the following
X = selected marble is white
Y = selected marble is blue
Z = selected marble is other than blue or white
Probability of seclecting white marble, P(X) = 5/77
Probability of seclecting blue marble, P(Y)
= 13/77
Probability of seclecting blue or white marble, P(Y UX) = P(X) + P(Y) = 5/77 + 13/77 = 18/77
So, probability that selected marble has a color other than white or blue, P(Z) = 1 - P( X UY) = 1 - 18/77
= 59/77 = 0.76623376623
Hence, required probability is 0.766234.
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Complete question :
The above table discribes the contents of a bag that contains red,green, blue,pink and white marbles if you select a single marble out of the bag, what is the probability that it is a color other than white or blue? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Jaxon invested $710 in an account paying an interest rate of 8\tfrac{7}{8}8 8 7 % compounded quarterly. Jason invested $710 in an account paying an interest rate of 8\tfrac{5}{8}8 8 5 % compounded continuously. After 8 years, how much more money would Jaxon have in his account than Jason, to the nearest dollar?
Answer:
I attached your answer along with an explanation
Step-by-step explanation:
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Kendrick bought a calculator priced at $71. Shipping and handling cost an additional 25% of the price. What was the total cost of the calculator, including shipping and handling?
Answer:
The answer to our problem is, $17.75
Step-by-step explanation:
First we need to find out what is 25% of 71
25% of 71 is 17.75. Or [tex]17\frac{3}{4}[/tex] We would need to stick to the term in decimals because of we are using money. Have you ever heard of a fraction in money my guess is no. So let’s stay with decimals. 17.75
How I got it:
25 percent * 71
= (25:100)* 71
= (25* 71):100
= 1775:100
= 17.75
Percentage solution with steps:
Step 1: Our output value is 71.Step 2: We represent the unknown value with x.Step 3: From step 1 above, 71 = 100%.Step 4: Similarly, x = 25%.Step 5: This results in a pair of simple equations:71 = 100% (1)
X = 25% (2)
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of bothequations have the same unit (%); we have
[tex]\frac{71}{x} = \frac{25}{100}[/tex]
X = 17.75
Thus the answer to your problem is, $17.75
A'B'C' is the image of ABC under a dilation whose center is P and scale factor is 1/3
A graph of the image of ABC under a dilation whose center is P and scale factor is 1/3 is shown in the image below.
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.
In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 1/3 centered at P.
Based on the image (see attachment), we can logically deduce that each vertex is 1/3 times as far from center P as the original vertex and each segment is 1/3 times as long as the original:
Side length AC = 6.7/3 = 2.2
Side length AB = 12.4/3 = 4.1
Side length CB = 12.7/3 = 4.2
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Complete Question:
Draw the image of triangle △ABC under a dilation whose center is P and scale factor is 1/3.
mr. henderson, the principal of blue creek academy, is getting soaked by the splash tank on the last day of school! each time a student hits the target, a 5-quart bucket of water dumps on his head. if 20 students hit the target, how many gallons of water will be dumped on mr. henderson's head?
25 gallons of water will be dumped on Mr. Henderson's head.
To solve the problem, we first need to find the total amount of water dumped on Mr. Henderson's head by all the students. Since each student dumps a 5-quart bucket of water, we can find the total amount by multiplying the number of students by the amount of water per student:
Total amount of water = 20 students x 5 quarts/student = 100 quarts
Next, we convert the total amount of water from quarts to gallons since the problem asks for the answer in gallons. Since 1 gallon equals 4 quarts, we can divide the total amount of water by 4 to get the answer in gallons:
Total amount of water = 100 quarts ÷ 4 quarts/gallon = 25 gallons.
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a 90% confidence interval for the average number of children per household based on a simple random sample is found to be (.7, 2.1). can we conclude that 90% of households have between .7 and 2.1 children?
No, we cannot conclude that 90% of households have between .7 and 2.1 children based on the confidence interval alone.
Based on the confidence interval alone, we cannot come to the conclusion that 90% of households have a number of children between .7 and 2.1. A confidence interval only provides a range of values that likely contains the true population parameter (in this case, the average number of children per household) with a certain level of confidence (in this case, 90%). It does not provide information about the distribution of the variable within the population. Therefore, we cannot make any conclusions about what percentage of households have a certain number of children based on the confidence interval alone.
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