Answer:
that answer should be wrong?
Answer:
-84
Step-by-step explanation:
To simplify the expression 20^2 - 22^2, we'll first square both 20 and 22:
20^2 = 20 * 20 = 400
22^2 = 22 * 22 = 484
Now, we can substitute these values back into the original expression:
400 - 484 = -84
So 20^2 - 22^2 = -84.
Two types of memberships are available for a water park
an unlimited use membership for $70 per month, or
a monthly $10 fee plus $5. 00 per visit
enter an equation that can be used to find the number of visits (v) per month needed for the two membership types to cost the same amount
Answer:
10+5v=70
Step-by-step explanation:
this is because you need to consider the outright monthly cost of $10 first. then you don't know how many visits you'll need so you have to fill in v and multiply it by the cost per visit. and it must equal 70 so that it is equal to the other membership.
The equation 70 = 10 + 5v is used to determine the number of visits per month needed for two membership types to cost the same. Solving the equation would provide that 12 visits a month will make both memberships cost the same.
Explanation:The subject of this question is Mathematics, and it is related to the topic of linear equations. Given the problem, we know that there are two types of membership options:
An unlimited use membership for $70 per month. This can be represented as: Y = 70, A membership that costs a monthly $10 fee plus $5 per visit. This can be represented as: Y = 10 + 5v.Here, Y represents the total cost of the membership each month and v represents the number of visits to the water park per month. You can set these two equations equal to each other in order to find the number of visits (v) needed for the two membership types to cost the same amount:
70 = 10 + 5v
You solve the equation for v to get: v = (70 - 10) / 5 = 12
Therefore, it would take 12 visits per month for both memberships to cost the same.
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Consider APQR in the figure below.
The perpendicular bisectors of its sides are SV, TV, and UV. They meet at a single point V.
(In other words, V is the circumcenter of APQR.)
Suppose UV=30, PS= 64, and RV=78.
Find PU, PR, and QV.
Note that the figure is not drawn to scale.
The given values are below:
PU = 72PR = 128QV = 78How to get the valuesNote that point V is the intersection of the three perpendicular bisectors of a triangle which is also the center of the subtriangle circumference
So QV = RV = PV = 78
Point S is the midpoint of PR
So PR = 2,
PS = 2 x 64 = 128.
Because triangle QUV is a right triangle,
QV = 78.
UV= 30
QV^2 + UV^2 = QV^2
Therefore, PU = 72
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geometry, please help.
Answer:
MN ≈ 92.1
Step-by-step explanation:
given the figures are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{MN}{IJ}[/tex] = [tex]\frac{KL}{GH}[/tex] ( substitute values )
[tex]\frac{MN}{21}[/tex] = [tex]\frac{57}{13}[/tex] ( cross- multiply )
13 MN = 21 × 57 = 1197 ( divide both sides by 13 )
MN ≈ 92.1 ( to the nearest tenth )
What percent is 14 out of 26
Answer:
53.85 %
Step-by-step explanation:
use ratio to solve.
14/26 = x/100
1400/26 = x
x = ~53.85%
The perimeter of rectangle ABCD is 105 inches. Use this information to solve for x.
D
c
7x + 1
Round your answer to the nearest tenths place if needed.
For rectangle ABCD, the value of x is 6.44 inches
Consider the following diagram.
From this figure we can observe that the dimansions of the rectangle: length is given by expression (7x + 1) and width is given by expression 'x'
We know that tha formula for the perimeter of the rectangle,
P = 2 × (length + width)
Here, the perimeter of rectangle ABCD is 105 inches.
Using above formula of perimeter we get an expression,
P = 2 × ((7x + 1)+ x)
105 = 2 × (8x + 1)
We solve above equation for x.
105/2 = 8x + 1
52.5 - 1 = 8x
8x = 51.5
x = (51.5)/8
x = 6.44 inches
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A Six Sigma program has how many defects per million? 27006 times the standard deviation3410003.4
By standard deviation, 3.4 defects per million that a six sigma program has. Whereas the remaining ones are not appropriate in this context.
What does standard deviation mean ?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean.
Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Describe standard deviation using an example?
The dispersion of the data around the mean value is measured by the standard deviation. It might be helpful when comparing data sets that may have the same mean but a different range.
The means of the two numbers 15, 15, 15, 14, 16, and 2, 7, 14, 22, 30 are the same, for instance. The second is, however, obviously more dispersed.
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if 3x-9=6 whats the value of x
Answer:
the value of x is 5
Step-by-step explanation:
3x=6+9
3x=15
x=5
Find the area of a rhombus whose altitude is 4 cm and perimeter is 36 cm.
Answer:
36 cm²
-------------------------
Rhombus has four equal sides. Since perimeter is 36 cm, each side is:
36/4 = 9 cmArea of rhombus is the product of base and altitude:
A = bh = 9*4 = 36 cm²Answer: 36cm
Step-by-step explanation:
The function f(x) = 500(1 − 0.19 )x2 models the price of a share of stock over time. Part A The price of the stock models exponential Choose... . What is the rate of exponential growth or exponential decay? % Part B Which expression is equivalent to the function f(x) = 500(1 − 0.19 )x2 ? A. f(x) = 202.5x B. f(x) = 20.1246x C. f(x) = 500(0.9)x D. f(x) = 500(1.0909)x
The function f(x) = 500(1 - 0.19)^x² is an exponentially decaying function.
The rate of decay is 0.19 or 19% and an equivalent expression to it is
f(x) = 500(0.9)^x.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f(x) = 500(1 - 0.19)^x² for the price of a share of stock.
This would be an exponentially decaying function because (1 - 0.19) is less than 1.
The rate of exponential decay is 0.19 or 19%.
An equivalent expression to the function f(x) = 500(1 - 0.19)^x² is,
f(x) = 500(0.9)^x.
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exponents and powers
find n
(2²n)4x(2^n)2=2^16-1
The value of "n" is approximately 2.6666667.
What is exponent ?Exponent is a mathematical operation that represents repeated multiplication of the same number.
We can start by simplifying the left side of the equation:
(2^(2n))^4 * (2^n)^2 = 2^16 - 1
Using the exponent rules:
a^m * a^n = a^(m + n)
We can simplify the left side of the equation further:
2^(4n + 2n) = 2^16 - 1
Combining the exponents:
2^(6n) = 2^16 - 1
Now we can use the fact that if a^m = a^n, then m = n to solve for "n":
6n = 16
Dividing both sides by 6:
n = 16/6 = 8/3
Therefore, The value of "n" is approximately 2.6666667.
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Lin ran 2 3/4 miles in 2/5 of an hour.
2
Noah ran 8 2/3 miles in 4/3
of an hour.
c) How far would Noah run in 1 hour?
Answer:The distance cover by Noah in 1 hour to cover distance is 6.5 miles
Step-by-step explanation:
how many lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed? choose all that apply.
The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.
What is combination?In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
here, we have,
Given data:
{1 ,2, 3 ,4, 5}
Formula for combinations is used since the order does not matter and repetition is allowed.
nCr = (n + r -1) /(r! * (n-1)!)
where n is the total number of items and r is the items to be picked
now, we get,
5C3 = (5 + 3 - 1)! /(3! * (5 -1)!
5C3 = 7!/(3! *4!) Simplifying the factorials)
5C3 = 5040/(6*24)
5C3 =5040/144
5C3 = 35
Hence, The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.
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Caleb is comparing the growth of plants using two different fertilizers Use the measurement of the center from the box plots to make an inference about the data
Part A:
Based on the medians, the plants in Group A grew less on average, as compared to the plants in Group B.
Part B:
The range and IQR are greater in Group B as compared to Group A, so there is less variability in the growth of plants in Group B.
What is the box-and-whisker plot?A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.
Given:
Caleb is comparing the growth of plants using two different fertilizers.
The box-and-whisker plot is given.
From the diagram, we can clearly see that the median of A is less than the median of B.
Part A:
Based on the medians, the plants in Group A grew less on average, as compared to the plants in Group B.
Part B:
The range and IQR are greater in Group B as compared to Group A, so there is less variability in the growth of plants in Group B.
Therefore, the blanked words are given above.
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Which of the following is equal to the rational expression when x ≠ -2 or 3?
The simplification of the given rational expression when x is not equal to 2 or negative 3 is determined as (x + 1)/(x + 3).
What is Simplification of expression?Expressions can be made simpler by expanding any brackets, multiplying or dividing any terms, using the laws of indices if necessary, grouping like terms together by adding or subtracting, and finally rewriting the expression. The BODMAS rule states that when an expression has brackets ((),, []), we must first solve or simplify the bracket before moving on to "order" (which refers to powers and roots, etc.), followed by division, multiplication, addition, and subtraction from left to right.
The simplification of the given expression when x is not equal to 2 or negative 3 is determined as follows;
[tex]$=\frac{(x+1)(x-2)}{(x-2)(x+3)}$[/tex]
cancel "[tex]$\mathrm{x}$-2[/tex]" since it is common to numerator and denominator
[tex]$$=\frac{(x+1)}{(x+3)}$$[/tex]
Thus, the simplification of the given rational expression when [tex]$\mathrm{x}$[/tex]is not equal to 2 or negative 3 is determined as [tex]$(x+1) /(x+3)$[/tex].
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Sales of the smart phone continued to grow exponentially beyond 2011.
In 2010, approximately 39.99 million smartphones of this brand were sold worldwide.
In 2011, approximately 72.9 million smartphones of this brand were sold worldwide.
In which year did the number of smartphones the brand sold exceed 200 million?
Answer: This question can be solved using exponential growth formula:
N = N0 * e^(rt)
Where N is the number of smartphones, N0 is the initial number, r is the growth rate, t is the number of years and e is the base of the natural logarithm (approximately equal to 2.718).
First, we need to find the growth rate:
r = (ln(N/N0)) / t
Using the data from 2010 and 2011:
r = (ln(72.9/39.99)) / 1
Next, we can find the year when the number of smartphones sold exceed 200 million:
N = 200 million
N0 = 39.99 million
t = (ln(N/N0)) / r
t = (ln(200/39.99)) / r
To find the year, we need to add t to the initial year 2010.
The number of smartphones the brand sold exceeded 200 million in the year 2023.
Step-by-step explanation:
Use the equation below to find A, if b=4 and h = 6.
A=bh
Answer: A = 24
Step-by-step explanation:
Hi, I think you may be looking for the Area of a square, or rectangle.
Step 1. A = bh
Step 2. A = (4 * 6)
Step 3. A = 24
Answer:
24
Step-by-step explanation:
plug in the values of b and h into the equation
Since b=4 we would put:
A=4*h
Now plug in h, which is equal to 6
A = 4*6
So, 4 multiplied by 6 equals 24. This means A is equal to 24
An ancient Chinese problem: "A pool of water is 10 feet across, and in the middle of it stood a reed which
projected one foot above the water. When the wind blows the reed over, the top just reached to the edge of
the pool. How deep is the water?" Illustrate and solve. Show all work!
According to the question, the depth of the water is 11 feet.
What is the depth ?The depth of something refers to how deep or far down it goes. It can refer to physical measurements such as the depth of a lake or ocean or the depth of a hole, or to metaphorical measurements such as the depth of knowledge or the depth of emotions. In terms of physical measurements, depth is usually referred to in terms of length or distance.
Let x be the depth of the water
The reed is 11 feet tall (10 feet in the water + 1 foot above the water)
The circumference of the pool is 10π feet
The volume of water in the pool = (circumference x depth) = 10πx
The volume of the reed = (area of base x height) = π(5²) x 11 = 275π
The total volume of the pool and reed = 10πx + 275π
10πx + 275π = 10π(11)
10πx = 110π
x = 11
Therefore, the depth of the water is 11 feet.
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a woman making $2500 per month has her salary reduced by 10% because of sluggish sales. one year later, after a dramatic improvement in sales, she is given a 20% raise over her reduced salary. find her salary after the raise. g
After the raise, the salary of woman becomes $2700.
Salary Reduction and RaiseThe answer was determined through simple arithmetic calculations.
First, the initial salary of $2500 was reduced by 10%, which is calculated as $2500 * 0.1 = $250.So the new salary after the reduction was $2500 - $250 = $2250.Next, a 20% raise was given over the reduced salary of $2250, which is calculated as $2250 * 0.2 = $450.Finally, the raise was added to the reduced salary, resulting in $2250 + $450 = $2700.So, the woman's salary after the raise is $2700.This method of calculation can be applied to any similar scenario where an initial salary is reduced by a certain percentage and then increased by another percentage. The formula used can be generalized as:
Final Salary = (Initial Salary - Initial Salary * Reduction Percentage) * (1 + Raise Percentage)
It's a simple and straightforward method that can be easily applied to find the final salary in similar cases.
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4. Are the triangles similar?
If yes, which angles are congruent?
By AA similarity Triangle PQR and TQS are similar.
What is Similarity?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given:
As, PR || TS then
<RPQ = <TSQ (Alternate Interior Angle)
< <QTS = <QRP (Alternate Interior Angle)
So, Triangle PQR and TQS are similar by AA similarity criteria.
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Please helpppp
graph 0.2 and its opposite
graph 9 and its opposite
Answer:
I need the answer tooo
In quadrilateral PQRS, the exterior angle at Q when ⎯⎯⎯⎯⎯⎯
is extended measures 155 and PS = QR. What measure of ∠PSR would confirm that PQRS is a parallelogram?
The measure of the angle ∠PSR will be equal to 25 degrees.
One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
Given that In quadrilateral PQRS, the exterior angle at Q when PQ is extended measures 155 and PS = QR.
The measure of the angle PSR will be calculated as:-
∠Q exterior = 155
∠PQR = 180 - 155
∠PQR = 25
∠PQR = ∠PSR = 25°
Therefore, the value of the angle ∠PSR is 25°.
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solve the inequality 5x<-28 show your work
Answer:
x < -28
Step-by-step explanation:
5x < -28
x < -28/5
Need help please thank you
The numeric values of the graphed function at x = 1 and x = 3 are given as follows:
f(1) = 0.7.f(3) = 0.4.How to obtain the numeric values?Tracing a vertical line through the coordinate x = 1, we have that the line would cross the graph at approximately y = 0.7, hence the numeric value is estimated as follows:
f(1) = 0.7.
Following the same procedure through x = 3, the line would cross the graph at approximately y = 0.4, hence the numeric value is estimated as follows:
f(3) = 0.4.
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Trevor pet goat weighed 6 3/8 pounds when it was born. By age 3, the goat weighed 8 times as much. Fill each box with a number or symbol from the list to show how to find the weight of Trevor goat at age 3. 8 3/8 8 3 6 3/8 + x are the symbols
The weight of Trevor's goat will be 51 pounds at age 3.
We can use the following equation to calculate the weight of Trevor's goat at age 3,
Weight at age 3 = 6 3/8 × 8
First, we require to convert 6 3/8 to an improper fraction, so we multiply 6 by 8 to get 48 and then add the numerator 3 to get 51. So, 6 3/8 can be composed as 51/8.
Next, we multiply 51/8 by 8 to calculate the weight at age 3,
51/8 × 8 = 408/8 = 51
Therefore, the weight of Trevor's goat will be 51 pounds at age 3.
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--The given question is incomplete; the complete question is
"Trevor's pet goat weighed 6 3/8 pounds when it was born. By age 3, the goat weighed 8 times as much. Fill each box with a number or symbol from the list to show how to find the weight of Trevor's goat at age 3."--
A composite figure is shown.
Which of the following represents the total area of the figure?
Answer:
16.425 in²
Step-by-step explanation:
Surface area of composite figure:Area of upper triangle:
b = 2.5 in ; h = 2.3 in
[tex]\sf \boxed{\bf Area \ of \ triangle = \dfrac{1}{2}bh}[/tex]
[tex]\sf =\dfrac{1}{2}*2.5 * 2.3\\\\ =\dfrac{5.75}{2}\\\\=2.875 \ in^2[/tex]
Area of bottom triangle:
h = 5.2 - 2.3
= 2.9 in
[tex]\sf Area \ of \ bottom \ triangle = \dfrac{1}{2}*3*2.9[/tex]
= 4.35 in²
Area of rectangle:
Area of rectangle = l * w
= 4 * 2.3
= 9.2 in²
Area of composite figure = area of upper triangle + area of bottom triangle + area of rectangle
= 2.875 + 4.35 + 9.2
= 16.425 in²
the high level of airline ticket sales that travel agencies experience during summer is an example of what component of a time series? a. long-term trend b. cyclical variation in. seasonal variation d. random variation
The high level of airline ticket sales that travel agencies experience during summer is an example of (option C.)Seasonal component of a time series.
A time series is a set of observations collected over a period of time, and it can be decomposed into various components, including trend, cyclical, seasonal, and random variation.
The trend component represents the overall pattern of the time series, such as an upward or downward trend. The cyclical component represents the repeating patterns that are not related to the regular seasons or calendar years. The seasonal component represents the regular variations that occur at specific times of the year, such as the summer months in this example. The random variation represents the unpredictable fluctuations in the time series.
Since the high level of airline ticket sales during summer is a regular variation that occurs every year at the same time, it is an example of the Seasonal component of a time series.
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Complete question:
The high level of airline ticket sales that travel agencies experience during summer is an example ofwhich component of a time series?
A.Trend.
B.Cyclical.
C.Seasonal.
D.Random variation
Can someone help me with this and find the amount budgeted
Answer:
Step-by-step explanation:
ok so it is 100 amount budgeted i calculated all of them dont be mad if i did it wrong i am really bad at math and here is a calmng photo to calm you and elp you think
[tex]\sqrt{x}[/tex]Lesley's fruit salad contains 40% grapes. Which figure represents 40%?
A. A hundred grid with five columns of ten squares shaded
B. A hundred grid with four columns of seven squares shaded
C. A hundred grid with three columns of ten squares shaded
D. A hundred grid with four columns of ten squares shaded
Answer:
The answer is D
Step-by-step explanation:
Percentages can be represented in Hundred Grid. It is a 10*10 grid that helps solves problems like yours.
In your case, it says 'Which figure represents 40% ?'
This means that you must shade 4 whole columns.
Because number 1, Each row or column contains 10 squares which can also represent 10%. And if you were to shade 2 rows or columns that would mean it is 20%.
So to sum it up:4 whole columns = 40% out of 100
So a hundred grid with 4 columns of ten square shaded should be your answer.
I'm always happy to help!
Find the HCF :
2x^3+x^2-3x and x^3-x
Answer: To find the highest common factor (HCF) of two polynomials, we can use the Euclidean algorithm for polynomials. The Euclidean algorithm involves dividing the larger polynomial by the smaller polynomial and continuing the division process until the remainder is zero. The last non-zero remainder is the HCF of the two polynomials.
In this case, we have:
2x^3 + x^2 - 3x = (2x^3 - x^3) + x^2 - 3x
= x^3 + x^2 - 3x
Now, we divide x^3 + x^2 - 3x by x^3 - x
x^3 + x^2 - 3x = x^3 - x * (1 + x - 3)
= x^3 - x * (x^2 - 2x + 3)
We cannot simplify this expression further, so the HCF of 2x^3 + x^2 - 3x and x^3 - x is x^3 - x.
Step-by-step explanation:
Please help thank you
Answer:
∠ A = 138° , ∠ C = 75°
Step-by-step explanation:
ABCD has parallel bases and is a trapezium
each lower base angle is supplementary to the upper base angle on the same side.
∠ A + 42° = 180° ( subtract 42° from both sides )
∠ A = 138°
∠ B + ∠ C = 180 , that is
12x - 3 + 9x - 6 = 180
21x - 9 = 180 ( add 9 to both sides )
21x = 189 ( divide both sides by 21 )
x = 9
Then
∠ C = 9x - 6 = 9(9) - 6 = 81 - 6 = 75°