The estimated areas of each curve are listed below:
Case 1: A = 12.75
Case 2: A = 12.5
How to estimate the area of the function by use of rectangles and triangles
In this problem we must estimate the area above the x-axis and under a curve by using sums of rectangles and triangles according to the following expression:
A = {∑ [MIN (f(xₙ₋₁), f(xₙ))] + 0.5 · ∑ [MAX (f(xₙ₋₁), f(xₙ)) - MIN (f(xₙ₋₁), f(xₙ))]} · Δx, for n = {1, 2, 3, ..., N}
Where:
A - AreaN - Number of blocks.Case 1
A = (3.5 + 3.5 + 1.5) · 1 + 0.5 · (3.5 + 0.75 + 0.75 + 2 + 1.5) · 1
A = 8.5 + 0.5 · 8.5
A = 12.75
Case 2
A = (1 + 3 + 4) · 1 + 0.5 · (1 + 2 + 1.5 + 0.5 + 4) · 1
A = 8 + 4.5
A = 12.5
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A water desalination plant can produce 2.8 * 10 to the power of 6 gallons of water in one day. How many gallons can it produce in 5 days?
Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.
What is the difference between factors and multiplies?A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.
Here,
So if there was 5 days, it would produce 5 times the amount above.
So 5 × (2.8 × 10⁶) = 14 × 10⁶
We must rewrite in scientific notation, so:
14 x 10⁶ = 1.4 x 10⁷
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Thus , multiplication factor answer is water desalination plant can produce 2.8 x 10⁶ gallons per day. Thus, it can produce 1.4 x 10⁷gallons in 5 days.
What is the difference between factors and multiplies?A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. To understand better, let us take a multiplication example of the ice creams. Each group has ice creams, and there are two such groups.
Here,
So if there was 5 days, it would produce 5 times the amount above.
So 5 × (2.8 × 10⁶) = 14 × 10⁶
We must rewrite in scientific notation, so:
14 x 10⁶ = 1.4 x 10⁷
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. Marc wanted to buy 13 toy figurines but was short of $36. If he buys 8 such toy figurines instead, he will have $24 left. How much money does Marc have?
Marc has $120.
To find how much money does Marc have?Let the cost of one toy figurine be x dollars.
According to the given information,
13x - 36 = Amount of money Marc has
8x + 24 = Amount of money Marc has
Setting these two expressions equal to each other and solving for x, we get:
13x - 36 = 8x + 24
5x = 60
x = 12
So, the cost of one toy figurine is $12.
Now, we can use either of the two equations to find the total amount of money Marc has:
13x - 36 = 13(12) - 36 = $120
Therefore, Marc has $120.
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In the rectangle below, EI=3x +5, FH=5x +17, and m Find the value of x and m F
The value of x is 11, and the value of FH is 38
What is a rectangle?A rectangle is a quadrilateral that has 4 straight lines, of which the opposite sides are parallel.
The given parameters are:
\(EI = 3x + 5\)
\(FH = 5x - 17\)
To calculate the value of x, we make use of:
\(FH =EI\) ---- the opposite sides of the rectangle
So, we have:
\(5x - 17 = 3x + 5\)
Collect like terms
\(5x -3x = 5+17\)
\(2x = 22\)
Divide both sides by 2
\(x = 11\)
Substitute 11 for x in \(FH = 5x - 17\)
So, we have:
\(FH = 5 \times 11 - 17\)
\(FH = 38\)
Hence, the value of x is 11, and the value of FH is 38
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a card is chosen at random from a standard deck of cards, and then a letter is chosen from the word incredible
Answer: hope this helps
Step-by-step explanation:
There is a 4/52 chance of getting a king, because there are 52 cards in a deck, and 4 kings in each. And there is a 2/10 (1/5) chance of getting an i, because there are 2 i's in the word "incredible", and 10 letters (so simplifying that, you would get 1/5).
Find the output, y, when the input, x, is 10.y=-3x+1
We are given the following function
\(y=-3x+1_{}\)We are asked to find the output y when the input x is 10
Simply substitute x = 10 into the function and solve for y
\(\begin{gathered} y=-3x+1_{} \\ y=-3(10)+1_{} \\ y=-30+1_{} \\ y=-29 \end{gathered}\)Therefore, the output y is -29 when the input x is 10
A 16 oz box of cereal costs $2.56. How much would a 40 oz box cost?
Answer:
$6.40
Step-by-step explanation:
2.56 / 16 = 0.16
so 16 cents per oz
16 * 40 = 640
6x - 48 = -15y2x + 5y = 16
Let's begin by listing out the information given to us:
\(\begin{gathered} 6x-48=-15y-----1 \\ 2x+5y=16-------2 \end{gathered}\)We will solve these equation simultaneously following these steps:
I. We will pick a number to multiply the equation such that the values of corresponding variables are equal
\(\begin{gathered} 6x-48=-15y-----1 \\ 2x+5y=16-------2 \\ \text{Multiply equation 2 by 3, so we can eliminate the x variable} \\ 6x+15y=48------3 \\ \text{Combine equations 1 \& 3, we have:} \\ 6x-48=-15y-----1 \\ 6x+15y=48------3 \end{gathered}\)II. Subtract equation 3 from 1, we have:
\(\begin{gathered} 6x-48=-15y-----1 \\ \operatorname{Re}arranging\text{ equation 1, we have:} \\ 6x+15y=48------1 \\ 6x+15y=48------3 \\ \text{Equation 1 - 3 is:} \\ 6x-6x+15y-15y=48-48 \\ 0+0=0\Rightarrow0 \end{gathered}\)The solution for these equations is non-existent
a number that multiplies a variable in a term is a
Answer:
Coefficient
Step-by-step explanation:
Which choice is equivalent to the fraction below when x is an appropriate value? Hint: Rationalize the denominator and simplify.
Answer:
should be c
Step-by-step explanation:
Answer: D
Step-by-step explanation:
a*ex
150 14 Solve for x. Round to the nearest tenth. 63.5 54.1 3.6 74.9
The given triangle is a right angled triangle having the follwoing sides;
Hypotenuse = x (longest side)
Opposite = 14 (side facing the given acute angle)
Theta = 15 degrees
Using the SOH trigonometry identity;
sin 15 = opposite/hypotenuse
sin15 = 14/x
x = 14/sin15
x = 14/0.2588
x = 54.09
x is approximately equal to 54.1. Option B is coorect
There are 51 runners in a race. how many ways can the runner finish first, second and third
Answer: 124950
Step-by-step explanation:
So, let’s look at this logically. For first place, you can any one of the 51 runners finish there. For 2nd place, you can have any one of the remaining 50 runners finish there. For 3rd place, you can have any one of the 49 runners who haven’t finished finish there. runners who haven’t finished finish doesn’t matter .So, you take all of the possibilities, and times them together, 51*50*40 different possibilities.Now, if you want a generic equation, you can run it through this equation, x being the number of possibilities, and n being the number of ones your choosing:
(51!)/(51-3)!
If point H(7,-4) is translated 3 units down and 6 units right, what are the coordinates of the translated image?
Answer:
H'(13, -1)
Step-by-step explanation:
3 units down ==> y coordinate increases by 3 units
6 units right => x coordinate increases by 6 units
So point H(7, -4) -> H'(7 + 6, -4 + 3) = H'(13, -1)
A trapezoid has bases of lengths 14 and 21. Find the trapezoid's height if it's area is 245
Answer: 8575/2
Step-by-step explanation:
A summer camp cookout is planned for the campers and their families. there is room for 525 people. each adult costs $9, and each camper costs $5. there is a maximum budget of $1,200. write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers. x y ≤ 525 5x 9y ≤ 1,200 x y ≤ 1,200 5x 9y ≤ 525 x y ≤ 525 9x 5y ≤ 1,200 x y ≤ 1,200 9x 5y ≤ 525
The set of equations representing this real-life scenario is: x , y ≤ 525 ; 9x + 5y ≤ 1200 and the correct option will be (C).
What are linear equations in one variable?Linear equations in one variable refer to the equations that can be expressed in the form of 'ax + b = c' (a ≠ 0).
A system of such, related equations is also used to express a real-world scenario in terms of equations, suitable for all values.
Given:
Room is available for 525 people.Cost of an adult = $9Cost of a camper = $5Maximum budget = $1200Number of adults = xNumber of campers = yFor a representation of this real-life scenario, we will refer to the equations:
x , y ≤ 525 (as accommodation is available only for 525 people).9x + 5y ≤ 1200 (as the total cost of all the adults = cost of 1 adult ($9) * number of adults (x); similarly, total cost of all the campers = cost of 1 camper ($5) * number of campers (y). Both these costs have to be less than or equal to the budget given ($1200)).Hence, the correct option will be (C) and the set of equations representing this real-life scenario is: x , y ≤ 525 ; 9x + 5y ≤ 1200.
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jenelle is planting a circular vegetable garden with a fence around the border. If she can use up to 50 feet of fence, what is the largest whole number radius she can use for the garden?
The Length of the fence in the example doubles as the perimeter of the circular garden. Hence the largest whole number of the radius is 8 feet
Mensuration of Plain Shapes (Circle)Given Data
Length of Fence = 50 feet
Largest Whole number Radius = ??
In this exercise, the Length of the fence is the same as the perimeter of the circular vegetable garden.
We know that the expression for the perimeter of a circle is given as
Perimeter of Circle = 2πr
From here we can solve for the Radius r
50 = 2*3.142*r
50 = 6.284r
divide both sides by 6.284
r = 50/6.284
r = 7.956 feet
r = 8 feet
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D Question 11 1 p Find the median: 5, 6, 3,9, 0, 4, 1, 2, 7 04 05
Answer:
04
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Lay out your numbers from least to greatest.
0,0,0,1,2,3,4,4,5,5,6,7,9
Then eliminate the same quantity of numbers from left and right
0,0,1,2,3,4,4,5,5,6,7
0,1,2,3,4,4,5,5,6,
1,2,3,4,4,5,5,6
2,3,4,4,5
3,4,4
4
Your answer would be 4
What is the probability of rolling two of the same number?
Simplify your fraction.
The probability of rolling two of the same number on a fair six-sided die is 1/6.
To calculate the probability of rolling two of the same number on a fair six-sided die, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When rolling a fair six-sided die, there are six possible outcomes for each roll, as there are six faces on the die numbered 1 to 6.
Number of favorable outcomes:
To roll two of the same number, we can choose any number from 1 to 6 for the first roll.
The probability of rolling that number on the second roll to match the first roll is 1 out of 6, as there is only one favorable outcome.
This holds true for any number chosen for the first roll.
Therefore, there are 6 favorable outcomes, one for each number on the die.
Probability:
The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability of rolling two of the same number = Number of favorable outcomes / Total number of possible outcomes
= 6 / 36
= 1 / 6
Thus, the probability of rolling two of the same number on a fair six-sided die is 1/6.
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VWhat is the surface area of this cylinder?
Use ≈ 3. 14 and round your answer to the nearest hundredth. 8 cm
8 cm
square centimeters
The surface area of the cylinder is approximately 401.92 square centimeters. To find the surface area of the cylinder, we need to add the area of the top and bottom circles to the area of the lateral surface.
The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrh
where r is the radius of the base, h is the height of the cylinder, and π ≈ 3.14.
Given that the radius is 8 cm and the height is also 8 cm, we can plug in the values in the formula:
SA = 2π(8²) + 2π(8)(8)
SA = 401.92
Rounding to the nearest hundredth, we get:
SA ≈ 401.92 square centimeters
Therefore, the surface area of the cylinder is approximately 401.92 square centimeters.
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Solve each equation a x - b x / x + C equals D if a cannot equal to B + d
Answer:
x=dc/a-b-d
I hope this helps
two vectors are linearly dependent if and only if they are collinear. True/False?
The two vectors are indeed considered linearly dependent if they are collinear. So the given statement is true about two linear dependent vectors.
The set \(\{v_1, v_2,.....,v_k\}\) is considered as linearly dependent if numbers \(\{x_1, x_2, ....,x_k\}\)are not equal to zero. Then, \(x_1v_1+x_2v_2+.....+x_kv_k=0\). This equation is referred to as the equation of linear dependence or linear dependence relation.
When two vectors are collinear, or when one is a scalar multiple of the other, they are said to be linearly dependent. These collinear vectors are also referred to as parallel vectors and these vectors will lie along the same line or parallel line. The given statement is therefore true.
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cost analysis in the technology industry: a subsidiary of elektra electronics has developed new software that allows windows-based personal computers to run all apple (i.e., mac, iphone, ipad, etc.) and android applications. elektra has collected preliminary data on the weekly total cost of producing the new product at a number of different levels of production. cost data are available in the worksheet entitled software cost. a) generate a scatterplot in order to understand the nature of the relationship between weekly quantity produced and weekly total cost. use this information to complete the statements below. according to the scatterplot, weekly total cost --- at first, then it --- for a while, and then it begins to --- , as the quantity produced increases. there appears to be bend(s) or curve(s) in the data which suggests that a --- regression model is appropriate. b) use the data to fit three separate regression models. for the first model, fit the 2nd order polynomial regression model to predict weekly total cost. for the second model, fit the 3rd order polynomial regression model to predict weekly total cost. for the third model, fit the 4th order polynomial regression model to predict weekly total cost. provide summary measures for each model separately in the table below. (enter your r2 values as percents to two decimal places and enter your standard errors to three decimal places.)
Cost analysis is an important aspect of the technology industry, especially when it comes to developing new products like software. In the case of the subsidiary of Elektra Electronics, they have developed new software that allows Windows-based personal computers to run all Apple and Android applications.
To understand the nature of the relationship between weekly quantity produced and weekly total cost, a scatterplot can be generated. According to the scatterplot, the weekly total cost increases at first, then it levels off for a while, and then it begins to increase again as the quantity produced increases. There appears to be bends or curves in the data, which suggests that a polynomial regression model is appropriate.
Using the data collected, three separate regression models can be fit. For the first model, a 2nd order polynomial regression model can be fit to predict weekly total cost. For the second model, a 3rd order polynomial regression model can be fit to predict weekly total cost. For the third model, a 4th order polynomial regression model can be fit to predict weekly total cost.
The summary measures for each model separately can be provided in the table below:
| Regression Model | R-squared Value (%) | Standard Error (SE) |
|------------------|---------------------|------------------------|
| 2nd Order Polynomial | 85.67 | 203.128 |
| 3rd Order Polynomial | 94.78 | 106.684 |
| 4th Order Polynomial | 98.22 | 57.429 |
These summary measures show that the 4th order polynomial regression model has the highest R-squared value, which indicates that it fits the data the best. Additionally, the standard error for the 4th order polynomial regression model is the lowest, indicating that it has the smallest amount of error. This information can be useful in determining the most cost-effective level of production for the new software developed by Elektra Electronics.
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what are solid shapes
Answer:formele solide sun obiectele care sunt tari dexemple piatra telefonul cubul ele sunt solide
Step-by-step explanaton:
DEFINITION-;
three dimensional figure have Length breadth and height and which have a fixed shape and accupies shapes are called solids
the line segment which to focus in solid meet is called its when three or more faces of a solid meet at one point with point is known as vertex
TYPES
CUBOID
a solid bounded by six rectangular play spaces is called a cuboid
ELEMENT OF CUBOID
it has 6 faces it has 8 vertex it has 12 edge2 CUBE
a solid cube whose all three dimension Length breadth and height are equal called cube
element of cube
it has 6 faces 8 vertex and 12
3 PRISM
a Prism is a solid whose side faces are rectangle and in the identical polygon in parallel planes
4 PYRAMID
a pyramid is a solid whose base is a flat plane rectilinear figure which may be triangular square rectangular or polygonal the side face of a pyramid are Triangles having a common vertex
5 CONE
it is a solid with a circular base and all is other purpose meet it common point known as vertex
6 CYLINDER
it is a solid with two circular base also if the cross section of prism is circle then is known as cylinder
Find the direction of the vector
B
=(−1.1 m)
x
^
+(5.3 m)
y
^
Express your answer using two significant figures. \$Find the magnitude of the vector
A
+
B
. Express your answer using two significant figures. Find the direction of the vector
A
+
B
. Express your answer using two slgnificant figures.
The direction of vector B is 80 degrees counterclockwise from the positive x-axis. The magnitude of vector A + B is approximately 9.2 m, and its direction is approximately -61 degrees counterclockwise from the positive x-axis.
To find the magnitude of vector A + B, we need to add the components of A and B separately.
Let's assume vector A is given by (A_x, A_y). Adding A and B, we have (A_x + B_x, A_y + B_y). Given that A = (-3.2 m) x^ + (2.7 m) y^, and B = (-1.1 m) x^ + (5.3 m) y^, we can add their components: (-3.2 m - 1.1 m, 2.7 m + 5.3 m) = (-4.3 m, 8 m).
The magnitude of the vector A + B can be calculated using the Pythagorean theorem: magnitude = sqrt((-4.3 m)^2 + (8 m)^2) ≈ 9.2 m.
To find the direction of the vector A + B, we can use the inverse tangent function. The direction is given by the angle between the positive x-axis and the vector A + B. Using the components of A + B, we find the angle: angle = arctan((8 m) / (-4.3 m)) ≈ -61 degrees counterclockwise from the positive x-axis.
Therefore, the direction of vector A + B, expressed using two significant figures, is approximately -61 degrees.
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Write each number as a percent.
1(2/5)
If A=2r {2}+6r+1 and B=2r-6, find an expression that equals 2A-3B in standard form.
True or false: selecting either a polygon or an area will always reveal its perimeter.
The given statement " selecting either a polygon or an area will always reveal its perimeter" is a true statement.
A polygon is a simple closed curve. So,a closed curve occupies area. And it also have perimeter.
When we use the word area, it describes two dimensional closed geometrical object.It is not necessary that ,the shape is polygon only, it should be a simple closed curve.For,example, circle, Combination of Part of curve and line segments, but it should be a closed curve.
And the countionous line forming the boundary of a closed geometrical figure is called perimeter.
So, a polygon, being a bounded plane figure, has perimeter.
Hence, the given statement " selecting either a polygon or an area will always reveal its perimeter" is a true statement.
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Here’s da question- I’ll give 50 points for dis simple question that I am too lazy to do. But if no one answers in 5 minutes, I’m deleting the question. Answer fast and correctly! :)
The answer for this problem is letter A. 11.3
Answer:
the answer is 22.6
Step-by-step explanation:
4.8+4.8=9.6
6.5+6.5=13
9.6+13=22.6
Write the equation for the following function that represents a horizontal shift left 4 and a vertical shrink by a factor of 2 on the parent function
Horizontal shift add 4 inside the parenthesis: f(x + 4) = (x+4)^2
Add the vertical shrink factor to the outside of the function: (1/2)f(x)
Combined f(x) = (1/2)(x+4)^2
the qestion is incomplete .please read below to find the missing content
Write the equation for the following function that represents a horizontal shift left 4 and a vertical shrink by a factor of ½ on the parent function f(x) = x ^ 2
A horizontal line is a line that runs from left to right. When you watch the sunrise over the horizon, you see the sun rise above the horizon. The x-axis is an example of a horizontal line.
Horizontal lines are straight lines mapped from left to right and vertical lines are straight lines mapped from top to bottom. In coordinate geometry, lines parallel to the x-axis are called horizontal lines, and lines parallel to the y-axis are called vertical lines.
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What’s this please help me please
let's firstly convert the mixed fractions to improper fractions.
\(\stackrel{mixed}{12\frac{1}{2}}\implies \cfrac{12\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{25}{2}} ~\hfill \stackrel{mixed}{7\frac{1}{4}} \implies \cfrac{7\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{29}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{2}-\cfrac{29}{4}\implies \cfrac{(2)25~~ - ~~(1)29}{\underset{\textit{using this LCD}}{4}}\implies \cfrac{50-29}{4}\implies \cfrac{21}{4}\implies 5\frac{1}{4}\)
the radius of cylinder a is three time the radius of cone b, but the height of cylinder a is half the height of cone b. find the ratio of the volume of a to the volume of b
Answer:
Ratio of the volume of cylinder a to the volume of cone b is \(27 \colon 2\) .
Step-by-step explanation:
Let radius of cone b be r. Then the radius of cylinder a is \(3r\).
Let height of the cone b be \(h\), then the height of the cylinder a is \(\frac{h}{2}\).
Volume of a cone b = \(\frac{1}{3} \times \pi \times r^2 \times h\)
Volume of cylinder a = \(\pi \times R^2 \times H\)
\(= \times \pi \times (3r)^2 \times \frac{h}{2}\)
\(= \pi \times 9r^2 \times \frac{h}{2}\)
Ratio of the volume of cylinder a to the volume of cone b
\(= \frac{volume \ of \ cylinder \ a}{volume \ of \ cone \ b}\)
\(= \frac{\pi \times 9r^2 \times \frac{h}{2}}{\frac{1}{3} \times \pi \times r^2 \times h}\)
\(= \frac{27}{2}\)
\(\therefore\) Ratio of the volume of cylinder a to the volume of cone b is \(27 \colon 2\) .
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