The function based on the given parent function and transformations in the given order would be:
f(x)= -1/2√(x+2)
What is a function?Functions are often represented as equations, graphs, or tables, and they are used to model a wide range of real-world phenomena. For example, a function might describe the relationship between the time of day and the temperature outside, or the amount of money earned based on the number of hours worked.
Let's break down how each transformation affects the parent function:
Shifting units to the left: This transformation involves replacing the variable "x" with "x+2" in the parent function. This has the effect of shifting the graph 2 units to the left. The function becomes:
f(x)= √(x+2)
Stretching horizontally: This transformation involves replacing "x" with "2x" in the function obtained after the first transformation. This has the effect of stretching the graph horizontally by a factor of 1/2. The function becomes:
f(x)= √(2x+4)
Reflecting across the x-axis: This transformation involves multiplying the entire function by -1. This has the effect of reflecting the graph across the x-axis. The function becomes:
f(x)= -√(2x+4)
So the final function based on the given parent function and transformations in the given order is:
f(x)= -1/2√(x+2)
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45 points, need answers ASAP!!! Match each definition with the correct vocabulary word. The variable whose values result from counting or measuring something. The variable (often x) that does not depend on that of another. The variable (often y) whose value depends on that of another. The variable that has two or more groups, but there is no intrinsic ordering to the groups.
Answer:
Step-by-step explanation:
The matches are:
The variable whose values result from counting or measuring something: quantitative variableThe variable (often x) that does not depend on that of another: independent variableThe variable (often y) whose value depends on that of another: dependent variableThe variable that has two or more groups, but there is no intrinsic ordering to the groups: nominal variabledoes anyone know how to find the particular solution for this nonhomogeneous equation:
y"+3y'-3y=3xe^-1
Using the equations, the particular solution is y_p(x)=-3x+1+2e⁻ˣ.
What are non-homogeneous differential equations?As we already know, homogeneous equations have zero on the right side of the equation. Thus, it is said that non-homogenous differential equations are those with a function on the right side of their equation.
We are given a non-homogeneous differential equation in the form:
y′′+3y′-3y=3xe^-1
The differential equation is called non-homogeneous because it is known to have a non-zero right-hand side.
To solve this differential equation, we first need to find the complementary function, which is the solution to the corresponding homogeneous differential equation y′′+3y′-3y=0.
We then take the first and second derivatives of y_p(x) and substitute them into the differential equation, y′′+3y′-3y=3xe^-1 and simplify.
This leads to the system of equations:
a + 3c = 3
a + 3b - 3c = 0
a + b + 3c = 1
Solving this system of equations, we find that a=-3, b=1, and c=2. Therefore, the particular solution is y_p(x)=-3x+1+2e⁻ˣ.
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This set of equations can be solved, and the results show that a=-3, b=1, and c=2. As a result, the specific answer is [tex]y_{p(x)} =-3x+1+2e^{-x}[/tex].
What are non-homogeneous differential equations?Homogeneous equations, as we already know, have "0" on the right side of the equation. Therefore, it is said that differential equations with a function on the right side of the equation are non-homogenous differential equations.
A non-homogeneous differential equation of the following shape is provided to us:
[tex]y^{''} +3y^{'} -3y=3xe^{-1}[/tex]
Since the right-hand side of the differential equation is known to be non-zero, it is referred to as non-homogeneous.
Finding the complementary function, which is the answer to the related homogeneous differential equation [tex]y^{''} +3y^{'} -3y=0[/tex], is the first step in solving this differential equation.
The differential equation [tex]y^{''} +3y^{'} -3y=3xe^{-1}[/tex] is then simplified by taking the first and second derivatives of [tex]y_{p(x)}[/tex] and substituting them into
the equation.
This results in the formulae system:
a + 3c = 3
a + 3b - 3c = 0
a + b + 3c = 1
This set of equations can be solved, and the results show that a=-3, b=1, and c=2. As a result, the specific answer is [tex]y_{p(x)} =-3x+1+2e^{-x}[/tex].
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An algebraic expression is described as 14 more than the product of
3 and the difference of z and 9. What is the value of this expression
when z = 17?
The value of the expression is 38 when z = 17.
What is the value of this expression when z = 17?Given that, an algebraic expression is described as 14 more than the product of 3 and the difference of z and 9.
First, we write the expression:
The difference of z and 9 means we subtract 9 from z. We then take this result and multiply it by 3.
Finally, we add 14 to the product of 3 and the difference of z and 9.
3(z - 9) + 14
Where z represents the value that we want to substitute into the expression.
Substituting z = 17, we get:
3(z - 9) + 14
3(17 - 9) + 14
3(8) + 14
24 + 14
38
Therefore, the value of the expression is 38.
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find the sum of money that amounts to Rs- 3450 in 4 monts at the rate of 4½ %. per annam.
Answer:
To find the sum of money that amounts to Rs- 3450 in 4 months at the rate of 4.5% per annum, we can use the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
Where,
Principal = the sum of money borrowed or invested
Rate = the rate of interest per annum
Time = the time period in years
Since the time period given is 4 months, we need to convert it to years by dividing it by 12:
Time = 4/12 years = 1/3 years
Now, we can plug in the given values and solve for Principal:
Simple Interest = (Principal * Rate * Time) / 100
3450 = (Principal * 4.5 * 1/3) / 100
3450 * 100 = Principal * 4.5 * 1/3
11500 = Principal * 1.5
Principal = 11500 / 1.5
Principal = 7666.67 (rounded off to two decimal places)
Therefore, the sum of money that amounts to Rs- 3450 in 4 months at the rate of 4.5% per annum is Rs- 7666.67.
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Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below
After answering the prοvided questiοn, we can cοnclude that Tο circle cοmplete the cοpied triangle, draw a pοlygοn thrοugh pοints D, E, and F.
What is circle?A circle appears tο be a twο-dimensiοnal cοmpοnent that is defined as the cοllectiοn οf all pοints in a jet that are equidistant frοm the hub. A circle is typically depicted with a capital "O" fοr the centre and a lοwer sectiοn "r" fοr the radius, which is the distance frοm the οrigin tο any pοint οn the circle.
The fοrmula 2r gives the girth (the distance frοm the centre οf the circle), where (pi) is a prοpοrtiοnality cοnstant rοughly equal tο 3.14159. The fοrmula r² cοmputes the circumference οf a circle, which refers tο the amοunt οf space inside the circle.
Fοllοw these steps tο duplicate the οriginal triangle using οnly twο οf its sides and the included angle:
Find the pοint where the ray and the circle intersect. Place the tip οf the cοmpass at pοint E and draw an arc that intersects the circle twice. Label the pοint that is οn the same side οf side AC as pοint B as pοint F.
Tο cοmplete the cοpied triangle, draw a pοlygοn thrοugh pοints D, E, and F.
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Please help to solve b
a. The probability that a randomly selected American who moved in 2004 was an owner is 0.31. b. 0.38 c. 0.03 .
Describe probability ?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a fair coin and getting heads is 0.5, because there are two equally likely outcomes (heads or tails).
a. Probability that a randomly selected American who moved in 2004 was an owner:
Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million
Number of Americans who moved in 2004 and were owners = 11.7 million
Therefore, the probability that a randomly selected American who moved in 2004 was an owner is:
11.7 million / 38 million = 0.31 (rounded to the nearest hundredth)
b. Probability that a randomly selected American who moved in 2004 moved within the same state:
Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million
Number of Americans who moved in 2004 and moved within the same state = 11.7 million + 2.8 million
Therefore, the probability that a randomly selected American who moved in 2004 moved within the same state is:
(11.7 million + 2.8 million) / 38 million = 0.38 (rounded to the nearest hundredth)
c. Probability that a randomly selected American who moved in 2004 was a renter who moved to a different country:
Total number of Americans who moved in 2004 = (11.7 + 2.8 + 0.3 + 18.7 + 4.5 + 1.0) million = 38 million
Number of Americans who moved in 2004 and were renters who moved to a different country = 1.0 million
Therefore, the probability that a randomly selected American who moved in 2004 was a renter who moved to a different country is:
1.0 million / 38 million = 0.03 (rounded to the nearest hundredth)
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Find the exact value of b
Daisy and Oscar make £90 at a car boot sale. The split the money in the ratio 5:4. How much money did each of them make?
Answer:
Daisy made 50 and Oscar made 40.
Step-by-step explanation:
Daisy: Oscar: total
5 4 5+4 = 9
Taking the total made and dividing by 9.
90/9 = 10
Multiply each term in the ratio by 10.
Daisy: Oscar: total
5*10 4*10 9*10
50 40 90
Daisy made 50 and Oscar made 40.
In a recent year and author wrote 191 check, use the poisson distribution to find the probability that on a random select today he wrote at least one check
The probability that on a random select today he wrote at least one check is 0.407
How to solveLet X be the no.of checks the author wrote in a day
Average,
u = 191 checks per year
191/365
= 0.5233/ day
X~Poisson ( u- 0.5233)
The p.m.f of X is given by
P(X=x) =
The probability that, on a randomly selected day, he wrote at least one check = P(
= 1 - P( X < 1)
= 1 - P(X=0)
= 1 - e^-0.5233 x 0.5233^0/0!
= 1 - e^-0.5233 x 1/
= 1 - 0.59256
= 0.407
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A bond is worth $100 and grows in value by 4 percent each year. Explain why the value of the bond after t years is given by 100•1.04^t
The value of the bond is multiplied by the factor [tex](1 + 0.04)[/tex], which is the same as multiplying by 1.04. After t years, the value of the bond will be multiplied by this factor t times, giving the formula:
[tex]100(1.04)t[/tex].
So, the value of the bond after t years is given by 100 • 1.04t.
What is a factor?A factor in mathematics is an expression or number that divides another expression or number without producing a residue. In other terms, a factor is a unit of measurement that may be multiplied by another unit of measurement to yield a specific outcome.
For example, 2 and 3 are factors of 6, because 2 multiplied by 3 equals 6. Similarly, (x + 1) and (x - 3) are factors of the expression [tex]x^2 - 2x - 3[/tex], because when these factors are multiplied together, they produce the expression:
[tex](x + 1) \times (x - 3) = x^2 - 2x - 3[/tex]
The bond is worth $100 initially, and it grows in value by 4% each year. This means that after one year, the value of the bond will be:
[tex]100 + 0.04(100) = 100(1 + 0.04) = 100(1.04)[/tex]
In other words, the value of the bond after one year is the initial value (100) multiplied by a factor of 1.04.
Similarly, after two years, the value of the bond will be:
[tex]100(1.04) + 0.04(100)(1.04) = 100(1.04)^2[/tex]
After three years, the value of the bond will be:
[tex]100(1.04)^2 + 0.04(100)(1.04)^2 = 100(1.04)^3[/tex]
In general, after t years, the value of the bond will be:
[tex]100(1.04)t[/tex]
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Jayden has 8 5/6 cups of rice. He uses 3 1/4 cups to make dinner. How many cups of rice does Jayden have left
Answer: 5 [tex]\frac{7}{12}[/tex] cups
Step-by-step explanation:
Subtract whole number values:
8 - 3 = 5 cups
Subtract fractions:
* Get common denominators
5/6 ➜ 10/12
1/4 ➜ 3/12
* Subtract
10/12 - 3/12 = 7/12
Answer:
5 7/12 cups
Answer:
67/12 cups of rice
Step-by-step explanation:
We Know
Jayden has 8 5/6 cups of rice.
8 5/6 = 53/6
He uses 3 1/4 cups to make dinner.
3 1/4 = 13/4
How many cups of rice does Jayden have left?
We Take
53/6 - 13/4 = 212/24 - 78/24 = 134/24 = 67/12
So, Jayden has 67/12 cups of rice left.
help me please and if you are frogy... thanks for the anwers
Answer:
59 degrees
Step-by-step explanation:
Since all of those angles would add up to 180 degrees (since they are on a line), we need to subtract 31 degrees (from angle VYT) and 90 degrees (from the right angle on angle WYX) from 180 to get the measure of angle VYW:
180-31-90 = 59.
happy to help :)
Use the Distributive Property to write an equivalent expression for -5(4+7y)
= -5( + )
Answer:
y = -3/7
Step-by-step explanation:
Write the equation for the function described, in STANDARD FORM.
A parabola has a y-intercept of -48. The x-intercepts of the parabola are -2 and 6.
Does your graph have a max or min?
In standard form: enter numeric answer only (no letters)
A=
B=
C=
STANDARD FORM is [tex]3x^2 + 24x + 32y + 192 = 0[/tex] ,parabola has a maximum point at its vertex, which is (2, -3).
what is equation of parabola in standard form:to write the equation for the given parabola in standard form, we need to use the vertex form of the equation of a parabola, which is:
[tex]y = a(x - h)^2 + k[/tex]
where (h, k) is the vertex of the parabola and 'a' is the coefficient that determines the shape and direction of the parabola.
We know that the x-intercepts of the parabola are -2 and 6. This means that the parabola intersects the x-axis at these two points. Therefore, the roots of the quadratic equation are -2 and 6.
We also know that the y-intercept of the parabola is -48, which means that the point (0, -48) lies on the parabola.
Since the parabola is symmetric about the vertical line passing through its vertex, the x-coordinate of the vertex is the midpoint of the x-intercepts, which is (6 - 2)/2 = 2.
Therefore, the vertex of the parabola is (2, k), where k is the y-coordinate of the vertex.
Now we can use the vertex form
[tex]y = a(x - 2)^2 + k[/tex]
We need to determine the values of 'a' and 'k' to complete the equation.
Since the parabola passes through the point (0, -48), we can substitute x = 0 and y = -48 into the equation:
[tex]-48 = a(0 - 2)^2 + k[/tex]
-48 = 4a + k
Similarly, since the x-intercepts are -2 and 6, we can substitute x = -2 and x = 6 into the equation to get:
[tex]0 = a(-2 - 2)^2 + k[/tex]
0 = 16a + k
0 = a(6 - 2)^2 + k
0 = 16a + k
Solving these three equations for 'a' and 'k', we get:
a = -3/8 and k = -3
Substituting these values into the vertex form equation, we get:
[tex]y = (-3/8)(x - 2)^2 - 3[/tex]
Therefore, the equation for the parabola in standard form is:
[tex]3x^2 + 24x + 32y + 192 = 0[/tex]
This parabola has a maximum point at its vertex, which is (2, -3).
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A die is rolled. Find the probability of the given event.
Answer:
(a) [tex]\frac{1}{6}[/tex] ≈ 0.167%
(b) [tex]\frac{3}{6}[/tex] = 50%
(c) [tex]\frac{1}{6}[/tex] ≈ 0.167%
Step-by-step explanation:
We Know
A dice has 6 faces.
Numbers: 1, 2, 3, 4, 5, 6
(a) The number showing is a 2;
The probability is : [tex]\frac{1}{6}[/tex] ≈ 0.167%
(b) The number showing is an even number;
The probability is : [tex]\frac{3}{6}[/tex] = 50%
(c) The number showing is greater than 5;
The probability is : [tex]\frac{1}{6}[/tex] ≈ 0.167%
Hey team can spend no more than $300 on shirts the team has already spent $80 how many more shirts for $15 each can I still buy Rite in inequality that represents the situation
He can buy less οr equal tο 14 shirts with the mοney left and The inequality that represents this situatiοn is s (stands fοr shirts) ≤ 14.
What is inequality?In Mathematics, it is the relatiοnship between twο values that are nοt equal. Inequality means twο values that are nοt equal. When the situatiοn is tο cοmpare the values, '≤' οr '≥' sign are used.
Hey team can spend nο mοre than $300 οn shirts the team has already spent $80.
300- 80 = 220
220/ 15 = 14.6
Let us say s be the number οf shirts.
Then the inequality will be s≤14
As the numbers οf shirts cant be a fractiοnal term sο we cοnvert the fractiοnal term tο the integer οne.
Hence, the inequality that represents the situatiοn is s≤14.
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The attendance at Longwood middle school his first football game of the season is 437 people eat it at the second game is 4 to 76 people determine the approximate percent increase in attendance between the first and second game round your answer to the nearest 10th%
Approximate percent increase in attendance between the first and second game is 8.9%.
What is the approx. percentage increase in attendance between the first and second football games?
To calculate the percent increase in attendance between the first and second game, we can use the formula:
percent increase =
[(new value - old value) / old value] x 100%
where the old value is the attendance at the first game and the new value is the attendance at the second game.
Substituting the given values, we get:
percent increase = [(476 - 437) / 437] x 100%
percent increase = (39 / 437) x 100%
percent increase ≈ 8.92%
Rounding to the nearest tenth percent, we get the approximate percent increase in attendance between the first and second game as 8.9%.
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Please see the attached
A restaurant borrows $15,700 for two months from a nearby bank. For this loan, the neighbourhood bank charges simple interest at a yearly rate of 10%. Suppose a month is one-twelfth of a year.
a) $218.06 in interest will be due after two months.
b) In the event that the restaurant doesn't pay, the balance due after two months is $15,918.06.
a) To find the interest that will be owed after 2 months, we first need to calculate the monthly interest rate:
r = (10%)/12 = 0.00833333...
We can use the formula for simple interest to find the interest owed:
I = Prt
where P is the principal (the amount borrowed), r is the interest rate per period, and t is the time in periods. Since the loan is for 2 months, we have t = 2/12 = 1/6 years.
Substituting the values, we get:
I = 15700 * 0.00833333... * (1/6) = 218.0555...
Rounding to the nearest cent, the interest owed after 2 months is $218.06.
b) The total amount owed after 2 months is the sum of the principal and the interest. Using the same values as above, we have:
The total amount owed = Principal + Interest
= 15700 + 218.0555...
= 15918.0555...
Rounding to the nearest cent, the amount owed after 2 months is $15,918.06.
The complete question is:-
A restaurant borrows $15700 from a local bank for 2 months. the local bank charges simple interest at an annual rate of 10% for this loan. assume each month is 1/12 of a year. answer each below. do not round any intermediate computations, and round your final answers to the nearest cent, if necessary, refer to the lists of financial formulas.
a) find the interest that will be owed after 2 months.
b) assuming the restaurant doesn't make any payments, find the amount owed after 2 months.
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Is 2 x5/8 the same of 10 x1/8
Answer:
Step-by-step explanation:
[tex]2\times \frac{5}{8} = \frac{2}{1} \times\frac{5}{8}= \frac{10}{8}[/tex]
[tex]10\times \frac{1}{8} =\frac{10}{1} \times \frac{1}{8}= \frac{10}{8}[/tex]
So yes they are the same.
Based on the line graph shown, how did stock prices perform between March 2015 and August 2015?
A. The stock price increased.
B. The stock price decreased.
C. There is not enough information to make a determination.
D. There was no change.
Option C. Based on the given line graph, it is not possible to determine how stock prices performed between March 2015 and August 2015 as there is no information provided for that time period.
The line graph only provides information for the period from January 2015 to March 2015 and from August 2015 to November 2015. The information provided on the graph shows how the stock prices performed during those time periods. Therefore, there is not enough information on the graph to determine how the stock prices performed between March 2015 and August 2015. It is possible that the stock prices increased, decreased, or remained the same during that time period, but the graph does not provide any information to confirm any of those possibilities.
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Riley is dividing a batch of 7 1/2 cups of salsa into equal servings that are 3/4 cup each. Select all of the expressions that can be used to find the number of servings Riley will have.
Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷ 3/4.
Explain about the mixed fraction?Once kids have a firm grasp on proper fractions, they are introduced to mixed numbers and incorrect fractions. A mixed number combines an integer (whole number) and a fraction. It is also sometimes referred to as a mixed fraction (part of a whole number).
The composite number's fractional component needs to be a legal fraction (less than one whole). The numerator (top number) of a correct fraction is less than its denominator (bottom number),
Given data:
Total batch of cup of salsa = 7 1/2Serving cup size = 3/4 each cupConvert the mixed fraction 7 1/2 in the proper fraction:
= 7 1/2
= (7*2 + 1)/2
= 15/2
Number of serving cups = Total amount of salsa / Serving cup size
Number of serving cups = 15/2 ÷ 3/4
Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷ 3/4.
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Complete question:
Riley is dividing a batch of 7 1/2 cups of salsa into equal servings that are 3/4 cup each. Select all of the expressions that can be used to find the number of servings Riley will have.
2/15 ÷ 3/415/2 ÷ 3/42/15 ÷ 4/515/2 ÷ 4/315/2 ÷ 3/4Which of these would you expect to have a positive correlation? Check all that apply. HINT: There are two correct selections. Question 1 options: The number of TV shows you watch and the age of your car The shoe size of that adult and the salary they earn The value of a car and the age of the car The pages of a book you read and the time you spend reading that book A person's years of experience at a job and their salary A person's grade on a test and the number of missed homework assignments leading up to that test
Find the composition of transformations that
map ABCD to EHGF.
Reflect over the [? ]-axis, then translate
(x+[],y+[]).
Note: Enter x or y for axis.
4
7.
B C
o
Y
D
-1
3
2
0
2
3
H
4
Help
the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).
What is axis reflection ?
An axis reflection is a transformation in geometry that involves reflecting a point, a line, or an object across a given axis. In two dimensions, there are two axes of reflection: the x-axis and the y-axis.
When reflecting over the x-axis, all points stay in the same horizontal position but change their vertical position, so a point (x,y) is reflected to (x,-y).
When reflecting over the y-axis, all points stay in the same vertical position but change their horizontal position, so a point (x,y) is reflected to (-x,y).
Axis reflections can be used to transform geometric shapes such as polygons, circles, or lines. These transformations have important applications in various fields, including physics, engineering, computer graphics, and art.
To find the composition of transformations that map ABCD to EHGF, we first need to determine the individual transformations that are needed.
Reflecting over the y-axis will change the x-coordinates of the points, but leave the y-coordinates unchanged. So, to reflect over the y-axis, we negate the x-coordinates of the points.
The translation (x+4, y+7) will move each point 4 units to the right and 7 units up.
Therefore, the composition of transformations is:
Reflect over the y-axis by negating the x-coordinates:
A'(-2, 3), B'(-4, 2), C'(-4, 0), D'(-2, -1)
Translate by (4,7):
A''(2, 10), B''(0, 9), C''(0, 7), D''(2, 6)
Therefore, the composition of transformations that map ABCD to EHGF is a reflection over the y-axis followed by a translation by (4,7).
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I need help with this please
Finding the total volume of a composite figure requires breaking it down into simpler shapes and then adding up their volumes.
How to find the volume of a composite figure>To find the total volume of a composite figure, you'll need to break it down into simpler shapes and calculate their individual volumes.
Then, you can add up these volumes to get the total volume of the composite figure.
Here are the general steps you can follow:
Identify the simpler shapes: Look for the individual shapes that make up the composite figure, such as cubes, rectangular prisms, pyramids, cylinders, or spheres.
Calculate the volume of each shape: Use the appropriate formula for each shape to find its volume. For example, the volume of a cube is calculated by multiplying the length, width, and height of the cube.
Add up the volumes of all the simpler shapes: Once you have found the volume of each simpler shape, add them up to get the total volume of the composite figure.
Adjust for overlapping shapes: If there are any overlapping shapes, subtract the volume of the overlapped portion to avoid double-counting.
Check your work: Double-check your calculations and make sure your final answer makes sense based on the dimensions of the composite figure.
Overall, finding the total volume of a composite figure requires breaking it down into simpler shapes and then adding up their volumes.
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In March 2011, a California newspaper predicted that the price of gasoline in two years would be $4.10. The newspaper claimed that the prediction would be within 2% of the actual price of gasoline in March 2013. Given the data in the table, determine the percent error of the prediction. Was the newspapers claim correct or incorrect. Provide work or an explanation to justify your answer.
The newspaper's claim was incorrect, as the percent error of the prediction was 0.76%, which is greater than 2%.
What is percent error?It is the difference between the observed value and the true value, expressed as in percentage. It is used to quantify how accurately a given measurement, prediction or other value matches the true value.
The percent error of the prediction can be calculated using the following formula:
[(Predicted Price - Actual Price) / Actual Price] × 100.
For this problem, the percent error
= [(4.10 - 4.069) / 4.069] × 100
= 0.76%.
Therefore, the newspaper's claim was incorrect since the percent error did not fall within the specified 2%.
In this case, the newspaper's prediction of the price of gasoline in two years did not match the true value as closely as expected, since the percent error was 0.76%.
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1 kg of cat food costs £6.38 How much does 9 kg of cat food cost? Give your answer in pounds (£).
Answer: 9 kg of cat food costs £57.42.
Step-by-step explanation: 1 kg of cat food costs £6.38, so you must multiply the cost by 9 to see how much 9 kg is worth.
6.38 x 9 = 57.42
Therefore, 9 kg of cat food is £57.42.
Mary takes a sightseeing tour on a helicopter that can fly 378 miles against a 35 mph headwind in the same amount of time it can travel 630 miles with a 35 mph tailwind. Find the speed, in miles per hour, of the helicopter.
Answer:
The speed of the helicopter is 160mph.
Step-by-step explanation:
The speed of the helicopter is 160mph.
Speed
Speed =Distance/Time
450miles/s-35mph = 702miles/s+35
450×s+35 = 702×s-35
450s+15,750 = 702s-24,570
Collect like terms
702s-450s = 15,750 + 24,570
252s= 40,320
Divide both side by 252s
s= 40,320/252
s= 160mph
Inconclusion the speed of the helicopter is 160mph.
PLEASE HELP THIS IS DUE TODAY
In conclusion the value that correctly fills in the blank in the table is 0.69.
Why it is?
To find the relative frequency of boys, we need to use the information given in the frequency table. We know that the total number of boys is 120 - 37 = 83, since the total number of students is 120 and the number of girls is 37.
We can then calculate the relative frequency for boys by dividing the number of boys who prefer math or social studies (40 + 43 = 83) by the total number of students (120):
Relative frequency for boys = (40 + 43) / 120 ≈ 0.69
Rounding to the nearest hundredth, we get:
Relative frequency for boys ≈ 0.69
Therefore, the value that correctly fills in the blank in the table is 0.69.
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help pls show ur work
The polygons are similar, therefore the missing lengths are: 12) 4; 13) 24
13. The triangles are similar by the SAS similarity theorem; 14. They are not.
How to Find the Sides of Similar Triangles?Recall that every pair of corresponding sides of similar triangles are always proportional to each other.
11. Let the missing side be x.
x/24 = 6/36
x/24 = 1/6
Cross multiply
6x = 24
x = 24/6
x = 4
12. x/20 = 36/30
x/20 = 6/5
Cross multiply:
5x = 120
x = 120/5
x = 24
13. m<VWU ≅ m<SWR based on vertical angles theorem [one pair of congruent included angles]
WV/WS = 40/5 = 8
WU/WR = 40/5 = 8 [two pair of proportional sides]
Therefore, both triangles are similar by the SAS similarity theorem.
14. The triangles are not similar because:
56/24 ≠ 28/13
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Find the arithmetic mean of 4 and 18
Answer:
The arithmetic mean of two numbers is found by adding them together and dividing the sum by 2.
So, the arithmetic mean of 4 and 18 is:
(4 + 18) / 2 = 22 / 2 = 11
Therefore, the arithmetic mean of 4 and 18 is 11.
Step-by-step explanation:
Answer:
STEP 1:let the arithmetic mean be p, q, r hence 4,p, q, r, 18
STEP 2:U5=18=a+4d
a+4d=18
we're a=4 therefore
4+4d=18
STEP 3:4d/4=(18-4)÷4=14/4
d=14/4=3.5
p=U2=a+d=4+3.5=7.5
q=U3=a+2d=4+(2×7.5)
=