we can be sure that 6c + 3d will have a higher value than 4c + 2d if c and d are positive decimal numbers.
Explain variableA variable in mathematics is a symbol or letter that is used to indicate a quantity in a mathematical statement or equation that can have many values. It is a symbol that may be used to represent an arbitrary or undefined integer in algebraic expressions and equations.
Both expressions have the same common factor of 2, so we can simplify them as follows:
4c + 2d = 2(2c + d)
6c + 3d = 3(2c + d)
Since c and d are positive decimal numbers, we know that both 2c + d and 3(2c + d) are positive. Therefore, the expression with the higher value will be the one with the larger coefficient, which is 3 in the second expression.
So, we can be sure that 6c + 3d will have a higher value than 4c + 2d if c and d are positive decimal numbers.
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Applying Basic Probability Rules
The probability model shows the distribution of flavors of a chewable multivitamin.
Cherry
Strawberry
0.27
0.25
Flavor
Lemon
Orange
Probability
0.28
Suppose you select a multivitamin from the bottle without looking. Find each probability. Enter your answers as
decimals rounded to the hundredths place.
0.20
Answer:
0.75
Step-by-step explanation:
P (Cherry or Orange)
0.27 + 0.20 = 0.47
P (Not Strawberry)
0.27 + 0.28 + 0.20 = 0.75
Javier design a mosaic wall Mural using a 100 tiles in three different colors yellow blue and red if 64 of the tiles are yellow what percent of the tires are either red or blue
In a bubble sort, on each pass through the list that must be sorted, you can stop making pair comparisons _____. A. one comparison later B. one comparison sooner C. two comparison sooner D. two comparison later
Answer:
In a bubble sort, on each pass through the list that must be sorted, the largest value "bubbles" to the end of the list. Therefore, after each pass, the end of the list is guaranteed to be sorted. This means that we can stop making pair comparisons one comparison sooner, which is option B.
Step-by-step explanation:
Bubble sort works by repeatedly comparing and swapping adjacent elements in the list if they are in the wrong order. During each pass through the list, the largest unsorted element "bubbles up" to its correct position. As a result, after the first pass, the largest element is in its correct position, after the second pass, the two largest elements are in their correct positions, and so on.
Therefore, with each subsequent pass, you can stop making pair comparisons one comparison sooner because the elements at the end of the list are already sorted.
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Given f(x) =-3x^2 - 2r
Find f(8)
Answer: f(8) = -208
Step-by-step explanation:
To solve, we will substitute 8 into the equation for x.
Given:
f(x) = -3x² - 2x
Substitute 8 for x:
f(8) = -3(8)² - 2(8)
Square:
f(8) = -3(64) - 2(8)
Multiply:
f(8) = -192 - 16
Subtract:
f(8) = -208
An electrician is running wire from the electric box on a house to a utility pole 85 feet away. The angle of elevation to the connection on the pole is 17°. How much wire does the electrician need? (Round your answer to two decimal places.)
ft
The electrician needs approximately 296.26 feet of wire.
What is trigonometry?The links between triangle's sides and angles are studied in the mathematic discipline known as trigonometry. It entails an examination of triangle's angles, lengths, and areas as well as their angles' mathematical properties (such as sine, cosine, and tangent).
According to question:The situation described can be modeled as a right triangle, where the wire from the electric box to the pole is the hypotenuse, and the angle of elevation is one of the acute angles. Let x be the length of the wire needed in feet.
Using trigonometry, we can write:
sin(17°) = opposite / hypotenuse
where the opposite side is the height of the connection on the pole above the ground. We can solve for the hypotenuse (the length of wire needed) as follows:
hypotenuse = opposite / sin(17°)
To find the opposite side, we can use the fact that the angle of elevation is 17° and the distance from the pole to the point on the ground directly beneath the connection is 85 feet. This distance is the adjacent side of the triangle, so we can write:
tan(17°) = opposite / 85
Solving for the opposite side, we get:
opposite = 85 tan(17°)
Substituting this into the formula for the hypotenuse, we get:
hypotenuse = (85 tan(17°)) / sin(17°)
hypotenuse ≈ 296.26 feet
Therefore, the electrician needs approximately 296.26 feet of wire.
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Two similar solids have edges of 4 feet in 24 feet if the smaller saw that has a volume of 16 ft.³ find the volume of the other solid?
Answer: 3,456
Step-by-step explanation:
Please simplify the sum and show work and answer the questions in the picture below
The simplified form of the expression is written as 11x³ - 39x -2x²/(x²- 9)(x+ 3)
What are algebraic expressions?Algebraic expressions are simply described as expressions that are composed of terms, variables, constants, factors and coefficients.
These expressions are also made up of arithmetic operations such as addition, multiplication, division, subtraction, etc
From the information given, we have that;
x -2/x + 3 + 10x/x² - 9
Find the lowest common denominator and simplify
(x-2)(x² - 9) + (x-3)(10x) /(x²- 9)(x+ 3)
Now, expand the bracket, we get;
x³ - 9x - 2x² + 10x³ - 30x/(x²- 9)(x+ 3)
collect the like terms of the denominator and that of the numerator, we get;
11x³ - 39x -2x²/(x²- 9)(x+ 3)
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What is the length of the diagonal from P to Q?
Answer:
The length of the diagonal from P to Q is
[tex] \sqrt{ {9}^{2} + {12}^{2} + {8}^{2} } = \sqrt{289} = 17[/tex]
3) In a triangle ABC, [AM] is the median relative to [BC] and O is the midpoint of [AM]. (BO) cuts [AC] at D. Let E be the midpoint of [DC]. 1º) Prove that BMED is a trapezoid. 2º) Prove that D is the midpoint of [AE]; deduce that CD = 2AD. 3º) Prove that OD = 4 BD.
1) The lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.
2) CD = 2AD.
Trapezoid and mid point1) To prove that BMED is a trapezoid, we need to show that BM || ED.
Since O is the midpoint of AM, we have OB || MD (as OB and MD are both perpendicular to AM).
Also, since E is the midpoint of DC, we have DE || AC (as DE and AC are both perpendicular to BC).
Therefore, to show that BM || ED, it is enough to show that AC || OB.
We know that OB is a transversal to the parallel lines BM and AM, so we have:
∠OBD = ∠MBC (corresponding angles)
Similarly, we have:
∠OAD = ∠ABC (corresponding angles)
Since ∠MBC = ∠ABC (because [AM] is the median), we have:
∠OBD = ∠OAD
Therefore, the lines AC and BO are parallel (by alternate interior angles), so BMED is a trapezoid.
2) To prove that D is the midpoint of [AE], we need to show that AD = DE.
Since [AM] is the median, we have:
AD = MC
Also, since E is the midpoint of DC, we have:
DE = EC
So it is enough to show that MC = EC.
Since O is the midpoint of AM, we have:
OM = MA/2
But MA = MC + AC/2 (because [AM] is the median), so we have:
OM = (MC + AC/2)/2
= MC/2 + AC/4
Also, since E is the midpoint of DC, we have:
OE = EC/2
But AC = 2DC (because [AM] is the median), so we have:
OE = EC/2 = AC/4
Therefore, we have:
OM = OE
So triangle OME is isosceles, and we have:
∠OEM = ∠OME
But ∠OED = ∠OEM (because DE || AC), so we have:
∠OED = ∠OME
Therefore, triangles ODE and OME are similar, so we have:
OD/OM = OE/OE
= 1
Therefore, OD = OM.
But we also have:
OM = MA/2 = MC/2 + AC/4
= AD/2 + AC/4 (because [AM] is the median)
So we have:
OD = OM = AD/2 + AC/4
= AD/2 + DC/2 (because AC = 2DC)
= (AD + DC)/2
= AE/2 (because E is the midpoint of DC)
Therefore, we have shown that D is the midpoint of [AE].
Moreover, we have:
CD = AE/2 = AD + DC/2 = AD + AC/4 (because AC = 2DC)
= AD + MC/2 (because [AM] is the median)
= AD + AD/2 (because AD = MC)
= 3AD/2
So we have CD = 2AD.
3) To prove that OD = 4BD, we need to show that BD = (1/4)OM.
Since [AM] is the median, we have:
BM = MC
Also, since O is the midpoint of AM, we have:
OM = BM/2 + AM/2
= BM/2 + 2BM/2 (because [AM] is the median)
= 3BM/2
Therefore, we have:
BD = BM - MD
= MC - MD
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Match each equation to the value(s) of x that make the equation true. Matching!
choices= (no real solution) (x=9) (x=3) (x= -7) (x-7)
A) 3(x-5) = 2(x-11)
B) 4(3x+7) -5 = 12x +8
C) 3(x+1) -2x = x+3
Matching of the equation will be:
A) x= -7
B) x= 3
C) x= 9
How to explain the equationAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
A) 3(x-5) = 2(x-11) has x= -7 as the solution.
B) 4(3x+7) -5 = 12x +8 has x= 3 as the solution.
C) 3(x+1) -2x = x+3 has x= 9 as the solution.
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Given parallelogram ABCD, which statements would allow you to conclude that the parallelogram is a rhombus? Select all that apply.
~a.) Line Segment AD ≅ Line Segment AB
~b.) ∠DCE ≅ ∠BCE
~c.) Line Segment BC ⊥ Line Segment DC
~d.) Line Segment AC ⊥ Line Segment BD
~e.) Line Segment AB ≅ Line Segment DC
~f.) ∠ABC ≅ ∠CDA
The correct statements to conclude that a parallelogram is a rhombus are: a.) Segment AD ≅ Segment AB e.) Segment AB ≅ Segment DC
f.) ∠ABC ≅ ∠CDA
What is a parallelogram and its properties?In two dimensions, a parallelogram is a geometric figure with parallel sides. It has two parallel sides that are the same length, making it a four-sided polygon (sometimes called a quadrilateral). The sum of the adjacent angles of a parallelogram is 180 degrees. Parallelograms are a unique class of polygons.
To conclude that a parallelogram is a rhombus, we must show that all four sides are congruent (of equal length). Therefore, statements that provide information about the sides of a parallelogram can help us make this conclusion.
The correct statements to conclude that a parallelogram is a rhombus are:
a.) Segment AD ≅ Segment AB
e.) Segment AB ≅ Segment DC
f.) ∠ABC ≅ ∠CDA
These statements tell us that opposite sides are congruent and opposite angles are congruent, which are properties of a rhombus. However, the expressions b, c and d do not give information about the sides, so it cannot be concluded from them that the parallelogram is a rhombus.
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A tank on a road roller is filled with water to make the roller heavy tank is a cylinder that has a height of 6 feet and a radius of 2 feet what you were foot of water weighs 62.5 pounds fight the way of the water the tech tank
Answer: the tank filled with water weighs 4,710 pounds.
Step-by-step explanation: where:
π = 3.14 (surmised esteem of pi)
r = span = 2 feet
h = tallness = 6 feet
V = 3.14 x (2 feet)^2 x 6 feet
V = 75.36 cubic feet
Since one cubic foot of water weighs 62.5 pounds, the weight of the water within the tank can be calculated by increasing the volume of water by its weight:
Weight of water = volume of water x weight per cubic foot
Weight of water = 75.36 cubic feet x 62.5 pounds per cubic foot
Weight of water = 4,710 pounds
What is a measure of the differences of all observations from the mean, expressed as a single number
The measure of the differences of all observations from the mean, expressed as a single number is called the "standard deviation". It is a commonly used measure of the amount of variability or dispersion within a set of data.
The standard deviation is calculated by taking the square root of the variance, which is the average of the squared differences between each observation and the mean.
It is expressed in the same units as the data itself, and provides a way to understand how spread out the data is from the average or mean value.
A small standard deviation indicates that the data points tend to be close to the mean, while a large standard deviation indicates that the data points are more spread out.
The standard deviation can be used to compare the variability of different sets of data, and can also be used in statistical tests to determine if the difference between two sets of data is statistically significant.
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In the xy-plane, how many horizontal or vertical tangent lines does the curve xy2=2+xy have?
The curve xy²=2+xy has two horizontal or vertical tangent lines, namely x = 2/3 and y = -1/3, and x = -1/3 and y = 1/3.
To find the horizontal or vertical tangent lines of the curve xy²=2+xy, we need to take the derivative with respect to x and y and solve for when the derivative equals zero.
Taking the derivative with respect to x, we get:
y^2 + 2xy(dy/dx) = y(dy/dx) + 2x
Simplifying, we get
(dy/dx)(y^2 - y) = 2x - y^2
Taking the derivative with respect to y, we get
2xy + x(dy/dy)(2y) = dy/dy + x
Simplifying, we get
(dy/dy)(x-2y) = 1-x
Setting both derivatives equal to zero, we have
(dy/dx)(y^2 - y) = 2x - y^2 ...(1)
(dy/dy)(x-2y) = 1-x ...(2)
From (2), we get
dy/dy = (1-x)/(x-2y)
Substituting into (1), we get
(1-x)/(x-2y)(y^2 - y) = 2x - y^2
Simplifying, we get
y^3 - 3xy^2 + (2x^2-1)y + x = 0
This is a cubic equation in y, which can have up to three solutions. To find the horizontal or vertical tangent lines, we need to set dy/dx = 0 or dy/dy = 0.
Setting dy/dx = 0, we get
2x - y^2 = 0
Setting dy/dy = 0, we get
x - 2y = 1
Solving these equations simultaneously, we get
x = 2/3 and y = -1/3 or x = -1/3 and y = 1/3
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The given question is incomplete, the complete question is:
In the xy-plane, how many horizontal or vertical tangent lines does the curve xy²=2+xy have?
There are 3 classes of 22 students making
Ice cream sundaes. A sundae can be
made using one of 3 syrups and one of 3
candy toppings. Each student makes one
sundae. Which expression can be used to
find the total number of sundaes made by
the students?
A 3x22
B 3 x 22
C 3x3x22
D 3³x9x22
The expression that can be used to find the total number of sundaes made by the students is option B, 3 x 22.
What is expression?In mathematics, an expression is a combination of variables, numbers, and mathematical operations that can be evaluated to produce a value. It can be as simple as a single number or variable, or it can be more complex and involve multiple variables and operations. Expressions can be used to represent a wide variety of mathematical concepts and relationships, and are an essential part of algebra, calculus, and other branches of mathematics.
According to given information:The number of sundaes that can be made by one student is 3 x 3 = 9 (since each student chooses one of 3 syrups and one of 3 candy toppings).
Since there are 22 students in each class, the total number of sundaes made by one class is 22 x 9 = 198. Since there are 3 classes, the total number of sundaes made by all the students is 3 x 198 = 594.
Therefore, the expression that can be used to find the total number of sundaes made by the students is option B, 3 x 22.
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Question 6(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
After comparing the data, a measure of variability for both sets of data to be utilised to find the place with the most stable temperature: C. Range, because Sunny Town is skewed.
What exactly is skewness?Skewness is a measure of the asymmetry of a box plot (box-and-whisker plot) or histogram in mathematics, and as such, a box plot (box-and-whisker plot) or histogram has a normal distribution when it is symmetrical.
We may rationally establish that Sunny Town's box plot (box-and-whisker plot) is distorted by closely inspecting it.
Conversely, the Desert Landing box plot (box-and-whisker plot) is symmetrical (vertical line dividing the box into two equal halves), which simply means that both whiskers on either side of the box plot (box-and-whisker plot) are roughly equal and symmetric.
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How many green apples would james have if he ate 1 red apple and 2 green apples out of the 50 green apples he had got.
Answer:
48
Step-by-step explanation:
50 (total green apples) - 2 (green apples eaten) = 48 (green apples left)
A-One Talent Agency has 109 clients. 46 of the clients play piano and 58 of the clients play guitar. 17 clients play both the piano and the guitar. How many of the clients do not play either instrument?
Number of clients who do not play either the piano or the guitar is 22
To find the number of clients who do not play either instrument, we need to subtract the number of clients who play either the piano or the guitar or both from the total number of clients.
Let A be the set of clients who play the piano, and B be the set of clients who play the guitar. Then, we can use the formula A union B
|A ∪ B| = |A| + |B| - |A ∩ B|
where |A ∪ B| is the number of clients who play either the piano or the guitar or both, |A| is the number of clients who play the piano, |B| is the number of clients who play the guitar, and |A ∩ B| is the number of clients who play both instruments
Substituting the given values, we get
|A ∪ B| = 46 + 58 - 17
|A ∪ B| = 87
Therefore, the number of clients who do not play either instrument is:
109 - 87 = 22
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On the coordinate plane, rectangle JKLM has vertices J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2). What is the perimeter of rectangle JKLM? If necessary, round your answer to the nearest tenth
The perimeter of rectangle JKLM which has vertices J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2) On the coordinate plane is 30 units.
By applying the Pythagorean distance formula we calculate the length of each side of the rectangle as,
Distance, d = √{(x₁ - x₂)² + (y₁ - y₂)²} (units)
where (x₁, y₁ ) and ( x₂, y₂) are the coordinates of both the end of a side of the rectangle.
The coordinates of the rectangle JKLM are given as J( – 2,2), K(6, – 4), L(3, – 8), and M( – 5, – 2).
Thus,
| JK | = √{(-2 - 6)² + (2 +4)²} = 10 units
| JM | = √{( -2 +5)² + (2 +2)²} = 5 units
| KL | =√{(6-3 )² + (-4+8 )²} = 5 units
| LM | = √{(3+5)² + (-8+2)²} = 10 units
Therefore, JK and LM are sides opposite to each other (and let it be length) and JM and Kl are the other pair (and let it be the breadth) in the rectangle.
Thus, perimeter of a rectangle can be found with the formula,
Perimeter of JKLM = 2( length + breadth) in units
= 2(10+ 5) units
= 30 units
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I NEED HELP ON THIS ASAP!!!
1. The numeric values of the function are given as follows:
x = -4, y = 1/16.x = -3, y = 1/8.x = -2, y = 1/4.x = -1, y = 1/2.x = 0, y = 1.2. As x approaches negative infinity, y approaches zero.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The numeric values for this problem are given as follows:
x = -4, y = 1/16, as 2^(-4) = 1/2^4 = 1/16.x = -3, y = 1/8, as 2^(-3) = 1/2^3 = 1/18.x = -2, y = 1/4, as 2^(-2) = 1/2^2 = 1/4.x = -1, y = 1/2, as 2^(-1) = 1/2^1 = 1/2.x = 0, y = 1, as 2^(0) = 1/2^0 = 1.Increasing the negative exponent, the number gets closer to zero.
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. A middle school teacher conducted a survey of the 8th grade class and found that 43 students were athletes and 19 of those students drink soda. There were 33 students that were not athletes, but drank soda. Last, they found that 22 students were not athletes and did not drink soda. Given this information, how many students don't drink soda
There are 46 students don't drink soda.
Let's use a Venn diagram to represent the information given in the problem:
Athletes
/ \
/ \
Soda / \ No Soda
/ \
/ \
/ \
----------------------------------------------
| |
| |
| |
Drink No Drink
| |
| |
| |
----------------------------------------------
| |
| |
| |
19 24
| |
| |
|
----------------------------------------------
| |
| |
| |
33 10
| |
| |
| |
----------------------------------------------
| |
| |
| |
24 22
| |
| |
| |
----------------------------------------------
The diagram, we can see that there are 24 students who drink soda and are athletes, 19 who drink soda but are not athletes, 33 who are not athletes but drink soda, and 22 who are neither athletes nor soda drinkers.
The number of students do not drink soda, we need to add the number of students who are athletes but do not drink soda to the number of students who are neither athletes nor soda drinkers:
Number of students who don't drink soda
= Number of athletes who don't drink soda + Number of students who are neither athletes nor soda drinkers
Number of athletes who don't drink soda = Total number of athletes - Number of athletes who drink soda = 43 - 19 = 24
Number of students who are neither athletes nor soda drinkers = 22
The number of students who don't drink soda is:
Number of students who don't drink soda = 24 + 22 = 46.
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In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is blue or green? Write your result as a simple decimal rounded to the thousandths place.
The probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.
What is probability?The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.
The total possible outcome = 8 + 7 + 6 = 21
probability of picking a blue ball = 7/21
probability of picking a green ball = 6/21
probability of picking a blue or green ball = 7/21 + 6/21
probability of picking a blue or green ball = (7 + 6)/21
probability of picking a blue or green ball = 13/21
probability of picking a blue or green ball = 0.6190
Therefore, the probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.
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How to find the area of the shaded polygon? Will give brainliest! Thank you!
A=200in² is the area of the shaded polygon so 200in² ➗ 30in
Solving systems by eliminations; finding the coeficients
please write all the problems down on paper, 10 points for each problem, and Brainliest
On solving the provided question we can say that as a result, the system of equations' solution is: x = 12.62 and y = 4/13
What is equation?
A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions.
We wish to eliminate one of the variables, either x or y, by adding or subtracting the two equations to solve this system of equations using the elimination technique. To do this, multiply one or both equations by a constant factor such that one of the variables has the same coefficient in both equations but with opposite signs.
By multiplying the first equation by 5 and adding it to the second, we can remove x. This results in:
5x - 10y = 60
5x + 3y = -44
-13y = -4
y = 4/13
We may now plug this y value into one of the original equations to find x. Let's look at the first equation:
x - 2y = 12
x - 2(4/13) = 12
13x - 8 = 156
13x = 164
x = 12.62
As a result, the system of equations' solution is:
x = 12.62 and y = 4/13
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3. What is the vertex of each quadratic function. a) y = (x + 3)² - 6 b) y = (x-7)² + 2 c) y = (x-4)²
The vertex of the quadratic functions are (-3, -6), (7, 2) and (4, 0).
Stating the vertex of the quadratic functionsThe vertex of a quadratic function in the form y = a(x - h)² + k is given by the point (h, k).
To find the vertex, we need to rewrite the quadratic function in this form by completing the square.
a) y = (x + 3)² - 6:
We can rewrite this equation as y = (x - (-3))² - 6, which is in the form y = a(x - h)² + k.
Therefore, the vertex is (h, k) = (-3, -6).
b) y = (x-7)² + 2:
We can rewrite this equation as y = (x - 7)² + 2, which is in the form y = a(x - h)² + k.
Therefore, the vertex is (h, k) = (7, 2).
c) y = (x-4)²:
We can rewrite this equation as y = (x - 4)² + 0, which is in the form y = a(x - h)² + k.
Therefore, the vertex is (h, k) = (4, 0).
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Please answer asap
It is due today
It would be helpful
The calculated volume of the figure is 761.97 cubic inches
Calculating the volume of the figureFrom the question, we have the following parameters that can be used in our computation:
CylinderConeHollow cylinderThe volume of the figure is calculated as
Volume = Cylinder + Cone - Hollow cylinder
So, we have
Volume = 3.14 * (8/2)^2 * 18 + 1/3 * 3.14 * (8/2)^2 * 5 - 3.14 * (2)^2 * 18
Evaluate
Volume = 761.97
Hence, the volume is 761.97 cubic inches
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Make up two data sets. list all the values in each data set and write a story to describe where they come from. The data sets should meet the following conditions:
The data set should come from random samples from a population
The centers of the distribution should be similar
The variabilities of the distributions should be different
The two data sets that meet the given conditions for in centers, and variability is in the explanations.
What are the two datasets?Data Set 1 - Heights of Adults in a City:
Values in Data Set 1 (in inches): 64, 67, 65, 63, 66, 68, 62, 64, 67, 65, 63, 66, 68, 62
Story: The data set represents the heights of randomly sampled adults in a city. The city is known for having a relatively consistent height distribution, with the majority of adults falling within a similar height range. The heights in this data set range from 62 inches to 68 inches, with a center around 65 inches, which is the most common height among the sampled adults. The data set shows relatively low variability, with most heights clustering around the center, indicating that the population of adults in the city has a narrow height distribution.
Data Set 2 - Salaries of Employees in a Corporation:
Values in Data Set 2 (in thousands of dollars): 42, 45, 47, 48, 43, 50, 55, 44, 42, 45, 47, 48, 43, 50, 55
Story: The data set represents the salaries of randomly sampled employees in a large corporation. The corporation has a wide range of job positions, and as a result, the salaries of its employees show a higher variability compared to the heights of adults in the city. The salaries in this data set range from $42,000 to $55,000, with a center around $47,000, which is the most common salary among the sampled employees. The data set shows higher variability, with salaries spread out across a wider range, indicating that the population of employees in the corporation has a more diverse salary distribution. This could be due to differences in job roles, experience levels, and other factors that impact salaries within the corporation.
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ruby is using the quadratic formula to solve a quadratic equation. which of the following is the next step for simplifying x=−6±85√2 responses
x=−3±8√5
x=−3±√5
x=−3±4√5
this is fully simplified.
PLEASE HELP I NEED TO SUBMIT SOON!!
The missing measure of the square pyramid and the net would be 11.18 units.
The amount of wood that Dee needs to make the doghouse is 98 square feet of wood.
How to find the net ?The missing measure is the side of the pyramid and this can be found using the Pythagorean Theorem with 11 ft being the height of the triangle and 4/ 2 = 2 being one of the sides and the missing measure being the hypotenuse.
The side length is:
= √ (2 ² + 11²)
= √ ( 4 + 121)
= 11.18 units
To determine the amount of wood needed for Dee's doghouse, we need to calculate the surface area of the square pyramid using its net.
Calculate the area of all four triangular faces:
Total area of triangular faces = 4 x area of one triangular face = 4 x 20.5 = 82 square feet
Calculate the total surface area of the pyramid (net):
Total surface area = area of base + total area of triangular faces = 16 + 82 = 98 square feet
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given that a test statistic for testing if the true proportion exceeds 0.75 is 1.91. what is the p-value for this test? round to 3 d.p.
p-value of 0.028 is considered statistically significant at a significance level of 0.05. This suggests that we have strong evidence to reject the null hypothesis in favor of the alternative hypothesis that the true proportion exceeds 0.75.
To calculate the p-value for this test, we need to use the standard normal distribution table or a statistical software.
First, we need to find the area under the standard normal distribution curve to the right of the test statistic of 1.91.
Using a standard normal distribution table, we can find that the area to the right of 1.91 is 0.0287 (rounded to four decimal places).
Since this is a one-tailed test (the alternative hypothesis is that the true proportion is greater than 0.75), the p-value is equal to the area to the right of the test statistic, which is 0.0287.
Therefore, the p-value for this test is 0.028 (rounded to three decimal places). This means that if the null hypothesis (that the true proportion is less than or equal to 0.75) were true, we would expect to see a test statistic as extreme as 1.91 or more extreme in only 0.028 of all possible samples.
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The p-value for the test when the test statistic is 1.91 and we are testing if the true proportion exceeds 0.75 is
approximately 0.028, rounded to 3 decimal places.
Given that the test statistic for testing, if the true proportion exceeds 0.75, is 1.91, we need to find the p-value for this
test and round it to 3 decimal places.
Identify the test statistic
The test statistic provided is 1.91.
Determine the tail of the test
Since we are testing if the true proportion exceeds 0.75, it is a right-tailed test.
Find the p-value
Using a Z-table or statistical software, find the area to the right of the test statistic (1.91) under the standard normal
distribution. This area corresponds to the p-value.
The area to the right of 1.91 in the Z-table is approximately 0.028. Therefore, the p-value for this test is approximately
0.028.
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