Answer:
Each child will have 3/16 pound of Halloween candy.
Step-by-step explanation:
To find out how much candy each sibling gets, we need to divide 3/4 by 4
3/4 divided by 1/4 = 3/16
Therefore, our answer is 3/16.
Which graph represents the equation y equals one half times x minus 1?
graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
The correct graph which represents the equation y = 1/2x - 1 is,
⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ y = 1/2x - 1
Now, After draw the equation we get;
Graph of a line passing through the points (-2, - 2) and (0, - 1).
Thus, The correct statement is,
⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.
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How do you find the length of the third leg of a triangle?
The third side of the triangle can be found out by using the Pythagoras theorem or the Heron's formula.
When there is a right angle triangle (A triangle whose on angle is of 90 degrees) then we use the Pythagoras theorem to find the third side.
The relation says that the sum of the square of the base and perpendicular is equal to the square of the hypotenuse.
In case of the scalene triangle the heron's formula is used to find out the value of the third side of the triangle.
There are several methods also present to find the value of the third side of the triangle.
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For each object, choose an appropriate scale for a drawing that fits on a regular sheet of paper.
Objects (A-E)
Scales (1 - 7)
А
Scales
AA person
1. 1:17
B A footballfeld (220 yards by 53 yards)
2. 1 cm: 1m
c The state of Washington (about 240 miles by 380 miles) 3 1:1000
The floor plan of a house
4. Itimile
E A rectangular farm (5 miles by 2 mile)
5 1:100,000
& 1 mm 1 km
7. 1:10,000,000
B
С
E
The appropriate scale for a drawing are-
2) 1 cm: 1 m 3) 1:10005) 1:100,0001) 1 in: i ft4) 1 ft : 1 mileExplain the term scale of drawing?When ever a drawing is said to be "to scale," it signifies that each piece is proportionate to the genuine or hypothetical entity; it may be smaller or larger by a specific amount.The scale describes the actual length that each length just on scale graphic corresponds to.The appropriate scale for a drawing that fits on a regular sheet of paper
A. A person : 2) 1 cm: 1m B. A football field (120 yards by 5 1/3 yards) : 3) 1:1000C. The state of Washington (about 240 miles by 360 miles) : 5) 1:100,000D. The floor plan of a house : 1 in: i ftE. A rectangular farm (6 miles by 2 mile) : 4) 1 ft : 1 mileTo know more about the scale of drawing, here
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The correct question is attached-
a group of classmates surveyed how other students travel to school the results of the survey are shown in the table at right make a circle graph showing the results of the survey using percents, bus- 90, ride bike- 30, ride in car- 75, walk- 45.
So, on solving the provided question, we can say that equation of diagonal WY is 13.03 units
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
by d=√((x2 – x1)² + (y2 – y1)²).
Coordinates of W = (-4,5) and Y = (3,-6)
= √((3 – (-4))² + (-6 – 5)²)
= √170
= 13.03 units
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The question is in the picture I would appreciate if you could explain how to get the answer thank you.
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
The slope of an equation:
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in determining if the lines are parallel, perpendicular, or none at all.
The slope intercept form of a line is y = mx + c
Where, c - y-intercept and m - the slope of the line
Given that
The cost of using the internet at an internet cafe is equal to a fee plus a certain rate per minute.
4 minutes of internet costs $ 3
8 minutes of internet costs $ 4
[ We can represent the given situation as given below ]
And the coordinates formed are (4, 3) and (8, 4)
The slope of the line formed = (4 - 3)/(8 - 4) = 1/4
Let y = mx + c be the equation to the model situation
=> y = (1/2)x + c
=> 2y = x + c ---- (1)
As we know (1) will pass through (4, 3)
=> 2(3) = 4 + c
=> 6 = 4 + c
=> c = 6 - 4
=> c = 2
=> 2y = x + 2
=> x - 2y + 2 = 0
Therefore,
The equation that is modeled to the situation is x - 2y + 2 = 0 and the slope of the line is 1/2.
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Analyzing
K
Which statements correctly describe the properties of heat? Select all that apply.
A. Heat is an essential component of life on Earth.
B. Heat is energy that flows from one object to another.
%
4
&
Prt Scna
Thus , Heat moves from a hotter object to a colder one, which accurately sums up the properties of the heat equation. Energy moves from one item to another in the form of heat.
What is equation?An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate
Here,
Heat's characteristics
The direction of this transmission is always determined by the temperature differential between the bodies.
To achieve an equilibrium temperature, heat is transferred from the hotter to the cooler body.
As a result of the fact that a body and its surrounds are at different temperatures, we can infer that heat is the energy that is transferred between them.
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what is the legend of variables of combined gas law
The combined gas law for a gas is discussed below.
What is a gas?Gas is one of the four fundamental states of matter – the others being solid, liquid, and plasma. A pure gas may be made up of individual atoms, elemental molecules made from one type of atom, or compound molecules made from a variety of atoms.Given is the combined gas law.
The ideal combined gas law is given by →
PV = nRT
Where -
{P} = pressure {T} = temperature {V} = volume
{n} = number of moles {R} = gas constant
Non ideal gases are often modelled by the Van der Waals equation as →
(p + n²a/V²)(V - nb) = nRT
Where -
{a} and {b} = constants for a particular gas
{p} = pressure {v} = volume
{n} = number of moles {t} = temperature
{R} = gas constant
Therefore, the combined gas law for a gas is discussed above.
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by means of the definition, find the derivative of the function 'F' f(x)=6
We know that the derivative means the rate of change of the function. Graphically, this means that the derivative is the slope of the graph of that function.
How do you find the derivatives by using the Definition?The derivative of a function is the slope of the curve for the specified function. Physically speaking, the derivative of a function is the instantaneous rate of change of a function with respect to the variable at a location.
A securities with a price that is based on or derived from one or more underlying assets is referred to as a derivative. A contract between two or more parties based on the asset or assets constitutes the derivative itself. Changes in the underlying asset's value affect its value.
The instantaneous pace at which a function changes with regard to one of its variables is known as the derivative. Finding the slope of the tangent line to the function at a certain location is equal to doing this.
lim/h→0f(x+h)−f(x)h=f'(x).
lim/h→06−6/h=0.
f'(x)=limΔx→0
f'(x)=limΔx→0
f(x+Δx)−f(x)Δx=
f'(x)=limΔx→06−6Δx=0
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A small radio transmitter broadcasts in a 31 mile radius. If you drive along a straight line from a city 41 miles north of the transmitter to a second city 42 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter
On solving the provided question, we can say that the slope's the intersection points are: (20.698, 42.197) and (43.998,16.527), the transmitter is within range between those to points along the line.
what is slope?A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
city - north at (0,65)
city-east at (59,0)
Slope is m=(-65/59)
[tex]B= y - mx = 65 - (-65/59)(0) = 65[/tex]
The equation of the line between the cities is y = (-65/59)x + 65
[tex]x^2 + ( (-65/50)x + 65) )^2 = 47^2[/tex]
the intersection points are:
(20.698, 42.197) and (43.998,16.527)
The transmitter is within range between those to points along the line.
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If a piece of luggage has a height of 20.5 inches and a length of 14.75 inches, what is the maximum width
allowed for that piece of luggage?
A)9.75in
B)10.2in
C)10.25in
D)11.8in
The maximum possible width of the box will be equivalent to
w = (V/302.4).
What is the volume of the cuboid?The volume of cuboid is given by -
V{C} = Length x Breadth x Height
Given is a piece of luggage has a height of 20.5 inches and a length of 14.75 inches.
We can write the volume of the box as -
V{b} = L x B x H
Assume the volume of the box is {V} cubic inches and its width be {w} inches. So, we can write the inequality as -
(20.5 x 14.75 x w) = V
w = (V/302.4)
Therefore, the maximum possible width of the box will be equivalent to
w = (V/302.4).
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Enrique earns 101010 points for each question that he answers correctly on a geography test. Write an equation for the number of points, yyy, Enrique scores on the test when he answers xxx questions correctly.
On his first geography test, Enrique answered 333 questions correctly. On his second test, Enrique answered 777 questions correctly.
Place points on the graph to show Enrique's first and second geography test.
An equation for the number of points y, and the correct answers x is y = 10x.
Define the term equation?One mathematical expression makes up a term. It could be a single variable (a letter), a single number (negatively or positively), or a number of variables multiplied but just never added as well as subtracted.
For the stated question-
Since Enrique receives 10 points for every question on the a geography test that is answered properly,Again for number of points, "y," Enrique receives on the test if he successfully answers "x" questions, we must formulate an equation.Consequently, the total points earned equal the total points earned for each question. number of questions with accurate responses.
Consequently, points earned = 10x
y = 10x.
First geography test: x = 3
y = 10*3 = 30
Second geography test: x = 7
y = 10*7 = 70
Thus, the graph for the enrique's first and second geography test is plotted.
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The correct question is-
Enrique earns 10 points for each question that he answers correctly on a geography test. Write an equation for the number of points, y Enrique scores on the test when he answers x questions correctly.
On his first geography test, Enrique answered 3 questions correctly. On his second test, Enrique answered 7 questions correctly.
Place points on the graph to show Enrique's first and second geography test.
Are undecidable problems unsolvable?
Therefore , the solution to the given problem of algorithm comes out to be it fall under the category of undecidable questions, which is a subtype of unsolvable problems.
Define algorithm.An algorithm is a process for carrying out a computation or resolving a challenge. Algorithms work as a detailed set of guidelines that lead hardware- or software-based routines through a series of predetermined actions step by step. Algorithms are frequently used in all areas of IT.
Here,
A problem is considered undecidable if there is no algorithm that can be created that will consistently return a true or false answer for each input value.
Only issues that should have a yes-or-no response (such as: does my code contain a bug?) fall under the category of undecidable questions, which is a subtype of unsolvable problems.
Therefore , the solution to the given problem of algorithm comes out to be it fall under the category of undecidable questions, which is a subtype of unsolvable problems.
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expert that helps you learn core concepts.
See Answer
Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 2x2 + 16
g(x) = √5x^3
The required function that gives [tex]f(g(x))[/tex] that represents the total amount of money Raul earned is
[tex]f(g(x)) = 10x^{3}+16[/tex]
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Mostly functions are written as f(x) where x is the input of the function.
Given,
[tex]f(x) = 2x^{2}+16[/tex]
[tex]g(x)[/tex] = [tex]\sqrt{5x^{3} }[/tex]
If [tex]f(x)[/tex] represents amount of money Raul earns per ticket and [tex]g(x)[/tex] represents number of tickets Raul sells per hour, where x is the number of hours he works, then,
[tex]f(g(x))[/tex] represents the total amount of money Raul earned in a day.
To find [tex]f(g(x))[/tex], substitute value of [tex]g(x)[/tex] in the place of x in function [tex]f(x)[/tex] .
[tex]f(g(x))[/tex] = [tex]f[/tex]([tex]\sqrt{5x^{3} }[/tex])
= 2( [tex]\sqrt{5x^{3} }[/tex])² +16
= 10x³ + 16
Therefore the required function is [tex]f(g(x)) = 10x^{3}+16[/tex].
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How do you prove a number is irrational?
To prove a number is irrational we divide the integer by another integer is the decimal is non terminating and non repeating then it will be a irrational number .
What are Irrational Numbers ?
The Irrational numbers can be defined a number that cannot be expressed as a fraction [tex]\frac{p}{q}[/tex] for any integers p and q.
The Irrational numbers have decimal expansions that do not terminate nor repeat (periodic) . Every transcendental number is an irrational number .
(i) To prove a number irrational when we divide an integer by another integer, and if decimal expansion does not terminate and do not repeat then it is an irrational .
(ii) if the number cannot be expressed in the form of [tex]\frac{p}{q}[/tex] , then also the number will be called as irrational numbers .
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On a negatively skewed curve, which is true?
The statistical model is not good, and this is true for a negatively skewed curve.
What means negatively skewed curve?It is a statistical term implies that a curve is skewed at the left side.
In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.
Which is true for negatively skewed curve?In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.
In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.
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Latifa writes down a number
She says
If i find the cube root of that number and then quadruple the answer,I get 16
What number did Latifa write down?
Answer:
64?
Step-by-step explanation:
Basically the idea is we suppose the number she thinks of is "x"
She says that if she cube roots the number and then quadruples it (means multiply by 4 I think) she gets 16. We set this up as equation below:
[tex]4\sqrt[3]{x} = 16\\\sqrt[3]{x} = 4\\x = 4^{3}\\ x= 64[/tex]
This is my best guess, not totally sure sorry
A train moving at a constant speed travels 325 mi in 8 hr. At this rate, how many miles does the train travel in 12 hr?
ANSWER ASAP!!!
Answer:
Step-by-step explanation:
In 12 hours, the train will travel 487.5 miles
8/325=40.625
40.625 x 12 = 487.5
convert 20% profit into profit amount
Answer: To convert 20% profit into a profit amount, you would multiply 20% by the revenue or cost of the item or service.
Let's say,
You have revenue of $1000
So,
20/100 * 1000 = $200
So the 20% profit on the revenue of $1000 is $200.
It's important to note that profit is the amount of money you make after you subtract your costs from your revenue. It's the amount you have left after all the expenses, taxes and other deductions are made.
Step-by-step explanation:
Mrs. Read can knit one pair of children's mittens with a ball of yarn six inches in diameter. How many pairs of identical mittens can she knit with a ball of yarn twelve inches in diameter
She can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter
In the given question, Mrs. Read can knit one pair of children's mittens with a ball of yarn six inches in diameter.
We have to find how many pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter.
The radius of a ball of yarn six inches in diameter is
r = 6/2 = 3 inches
The radius of a ball of yarn twelve inches in diameter is
r = 12/2 = 6 inches
Now, the volume of the six inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]
The volume of the six inches yarn = [tex]\frac{4}{3} \pi (3)^3[/tex]
The volume of the six inches yarn = 36π
Now, the volume of the twelve inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]
The volume of the twelve inches yarn = [tex]\frac{4}{3} \pi (6)^3[/tex]
The volume of the twelve inches yarn = 288π
Now we finding the numbers of pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter
= 288π/36π
= 8
Hence, she can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter.
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what is x if 2/9+x=11/18?
Answer:
x = 7/18
Step-by-step explanation:
what is x if 2/9+x=11/18?
2/9 + x = 11/18
x = 11/18 - 2/9
x = 63/162
x = 7/18
check
2/9 + 7/18 = 11/18
11/18 = 11/18
the answer is goodAt which points are the equations y = x2 3x 2 and y = 2x 3 approximately equal?
The quadratic equations are approximately equals at the points (0.618,4.236) and (-1.618 , -0.236)
What in mathematics is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem.
we have
y = x² + 3x + 2 .............(a)
y = 2x + 3 ...................(b)
To solve the system of equations equate equation A to equation B
x² + 3x + 2 = 2x + 3
Group terms that contain the same variable
x² + 3x + 2 - 2x - 3 = 0
x² + x - 1 = 0
The formula to solve a quadratic equation of the form ax² + bx+ c is equal to
in this problem we have
x² + x - 1 =0
so, a= 1
b = 1
c = -1
substitute in the formula
x = -1 ± √1² - 4(1)(-1)/2(1)
x = -1 ±√5/2
x = -1+√5/2 = 0.618
x = -1 - √5/2 = - 1.618
Find the values of y
for x = 0.618
y = 2(0.618) + 3 = 4.236
for x = - 1.618
y = 2(-1.618) + 3 = -0.236
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The complete question is -
At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal?
Find the equation for the line running
to y = -5x + 5 and passes through the
perpendicular
point (10,7).
let's reword this a bit differently, since it looks jumbled
let's find the equation of a line that is perpendicular to y = -5x + 5, and it also passes through (10 , 7), well, keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-5}x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ -5 \implies \cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5} \implies \cfrac{1}{ 5 }}}[/tex]
so we're really looking for the equation of a line with a slope of 1/5 and that it passes through (10 , 7)
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \\\\\\ y-7=\cfrac{1}{5}x-2\implies {\Large \begin{array}{llll} y=\cfrac{1}{5}x+5 \end{array}}[/tex]
Draw a quadrilateral aBCD whose vertices are A (0,0) B(5,0), C(3,2) and D (0,2)
A graph of quadrilateral ABCD whose vertices are A (0, 0) B(5, 0), C(3, 2) and D (0, 2) is shown in the image attached below.
What are the types of quadrilateral?In Geometry, there are different types of quadrilateral and these include the following:
ParallelogramSquaresRectangleRhombusTrapeziumNext, we would use an online graphing calculator to construct (plot) quadrilateral ABCD on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral ABCD on the x-coordinate and y-coordinate respectively as shown in the table.
By critically observing the graph of quadrilateral ABCD, we can reasonably infer and logically deduce that it represents a trapezium.
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3.5 x 4 + 11 x 2.2 = 38.2 i used a calculator already but i need to show i how got the answer i dont know if i can give the brain thing
Step-by-step explanation: To solve this equation, you'll need to use the order of operations to determine the correct sequence of steps to follow. The order of operations is a set of rules that specifies the order in which calculations should be performed in a math problem. It helps to prevent ambiguity and ensures that all calculations are performed consistently.Here is the order of operations:Perform any calculations inside parentheses or brackets first.Perform all multiplications and divisions, working from left to right.Perform all additions and subtractions, working from left to right.Using this order, we can solve the equation as follows:3.5 x 4 + 11 x 2.2 = 14 + 11 x 2.2
3.5 x 4 + 11 x 2.2 = 14 + 24.2
3.5 x 4 + 11 x 2.2 = 38.2Therefore, the solution to the equation is 38.2.
Using BODMAS,
B-Bracket
O-Of
D-Division
M-Multiplication
A-Addition
S-Subtraction
Multiplication comes first before addition, so
3.5×4=17
+
11×2.2=24.2
17+24.2=41.2
The average price for houses in the area is $280,000, and the standard deviation is $12,000. What is
the price of a house whose z score is 2.5?
When working with a normal distribution, you can use the z-score to determine how many standard deviations away from the mean a certain data point is.
Given that the average price for houses in the area is $280,000 and the standard deviation is $12,000, we can use the z-score formula to find the price of a house whose z-score is 2.5:
z = (x - mu) / sigma
where x is the price of the house, mu is the mean price of houses in the area, and sigma is the standard deviation of the price of houses in the area.
In this case, we are looking for the value of x, which is the price of a house whose z-score is 2.5, so we can rearrange the formula to solve for x:
x = (z * sigma) + mu
x = (2.5 * $12,000) + $280,000
x = $350,000
So the price of a house whose z-score is 2.5 is $350,000
It's worth noting that the value of Z-Score 2.5 is considered an outlier, it is usually very rare to find houses that far from the average and standard deviation.
Directions: The Johnson family is redesigning their backyard this spring. They want to include a sandbox area,
a swing set area, a patio area, a pool area and a grill area. Their plans for the yard layout in feet is shown in the
figure below. Use the figure and your knowledge of polynomials, perimeter, and area to solve the following:
1) The formula for area is,
⇒ Area of rectangle = Length × Width
And, The formula for perimeter is,
⇒ Perimeter = 2 (Length + width)
2) An expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
3) The simply expression for the length of the south side of the yard is,
⇒ Length = 2x² - 2x + 5
4) An expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
5) 5) The simply expression for the perimeter of the pool area is,
⇒ Perimeter = 2x² + 16x + 36
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The Johnson family is redesigning their backyard this spring. They want to include a sandbox area, a swing set area, a patio area, a pool area and a grill area.
Now,
1) The formula for area is,
⇒ Area of rectangle = Length × Width
And, The formula for perimeter is,
⇒ Perimeter = 2 (Length + width)
2) An expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
3) The simply expression for the length of the south side of the yard is,
⇒ Length = (5x + 2) + (x² - 9) + (x² - 7x + 12)
= 5x + 2 + x² - 9 + x² - 7x + 12
= 2x² - 2x + 5
4) An expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
5) The simply expression for the perimeter of the pool area is,
⇒ Perimeter = 2 ( (x² + 10) + (8x + 8) )
= 2 (x² + 10 + 8x + 8)
= 2 (x² + 8x + 18)
= 2x² + 16x + 36
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Sandra has taken 3 Test this Quarter. She has scored an 78%, 76%, and a 93%. Sandra wants
to earn at least and 85% for the Quarter. What score will she need to earn on her Final Test in
order for her to Average at least an 85% for the Quarter? Then Explain what your answer
means.
*****This Question is similar to Question #8 in Thursdays Homework Quiz.
1. Write an Equation or Inequality you use to help you solve this Question. 5 pts.
2. Solve the Equation or inequality. 5 pts.
3. Explain what your answer means based on your solution you get. 10 pts.
Sandra needs to score at least 87.67% to get an average score of 85%.
What is average?Let's look at the average formula in more detail in this part and use some examples to illustrate how it may be used. The following is an example of the average formula for a specific set of data or observations: Average = (Sum of Observations) ÷ (Total Numbers of Observations).
Given, Sandra has taken 3 Test this Quarter. She has scored an 78%, 76%, and a 93%.
Now as per the question she needs 85%.
The average of the 1st three tests is 78+76+93/3 = 247/3 = 82.33
Now to get 85%, we have to average out as 82.33+x/2 = 85
x+82.33 = 85*2 = 170
x = 170-82.33 = 87.67
Hence, Sandra needs to score at least 87.67% to get an average score of 85%.
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Lesson 1. 12
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth.
Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point.
Assume at x= O the buoy is at normal ocean depth.
Find the following:
Period =
Equation of the mideline:
Amplitude =
Maximum =
Minimum =
For the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
What is the sine function?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.
They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Asin(Bx)+C is the usual sine function formula.
A buoy bobs 6 meters up and down.
That is, the amplitude of the buoy shifts by 6 meters both vertically and horizontally.
A=6 Amplitude
The x-axis distance that constitutes one complete oscillation is known as the period.
We are aware that it takes a buoy 10 seconds to go from its greatest position to its lowest point (half oscillation).
20 seconds make up the complete oscillation period.
⇒ 20 (B) = 2π
B=2π /20
= π/ 10
Given that the buoy is 10 meters under the ocean's surface, C equals –10.
Using the formula's whole range of values:
⇒y = 6sin ( (π/ 10) x ) - 10
The midline is the initial point.
x=0 is the first point.
⇒y=6sin(0)-10
y= -10
The line is drawn from the origin at y = -10.
Either the highest or smallest value is at the second point.
Therefore, (5,-4) and (15, -16.)
Therefore, for the described situation, y = 6sin ( (π / 10) x ) - 10 is the sine function.
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Complete question:
At an ocean depth of 10 meters, a buoy bobs up and then down 6 meters from the ocean's depth. Ten seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Assume at x = 0 the buoy is at normal ocean depth. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
∆ABC is divided into three smaller triangles and one quadrilateral. Area of ∆AFE is 4, Area of ∆AFC is 9, area of ∆DFC is 7. Find the area of quadrilateral BEFD.
The area of quadrilateral BEFD is 15.32units²
How to find the area of quadrilateral BEFD?Let the area of ∆ABC be A
Let the area of ∆AFE be X
Let the area of ∆AFC be Y
Let the area of ∆DFC be Z
Using Ladder theorem:
1/A + 1/Y = 1/(X+Y) + 1/(Y+Z)
Since X = 4, Y = 9 and Z = 7, we have:
1/A + 1/9 = 1/(4+9) + 1/(9+7)
1/A + 1/9 = 1/13 + 1/16
1/A = 1/13 + 1/16 - 1/9
1/A = 53/1872
A = 1872/53
A = 35.32
area of ∆ABC = area of ∆AFE + area of ∆AFC + area of ∆DFC + area of quadrilateral BEFD
35.32 = 4 + 9 + 7 + area of quadrilateral BEFD
35.32 = 20 + area of quadrilateral BEFD
area of quadrilateral BEFD = 35.32 - 20
area of quadrilateral BEFD = 15.32unit²
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Write a polynomial function in standard form
-6,0,0,2