keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]x-y=8\implies -y=-x+8\implies y=\stackrel{\stackrel{m}{\downarrow }}{1}x-8\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}{ 1 \implies \cfrac{1}{\underline{1}}} ~\hfill \stackrel{reciprocal}{\cfrac{\underline{1}}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1} \implies \text{\LARGE -1}}}[/tex]
Change the following equation of a line into slope-intercept form. X =(y-2)÷2
Equation in the standard slope-intercept form: y = 2X + 2
What is slope-intercept form?The slope intercept form of an equation is represented as follows:
y = mx + c
where, m = slope, c = y-intercept
We want to rewrite the equation X = (y - 2) ÷ 2 in slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's isolate y on one side of the equation by multiplying both sides by 2:
2X = y - 2
Next, let's add 2 to both sides:
2X + 2 = y
Finally, let's switch the sides to get the equation in the standard slope-intercept form:
y = 2X + 2
So the slope of the line is 2 and the y-intercept is 2.
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A business organization needs to make up a 8 member fund-raising committee. The organization has 6 accounting majors and 7 finance majors. What is the probability that at least 4 accounting majors are on the committee?
a) 0.4079
b) 0.0171
c) 0.1795
d) 0.0163
e) 0.5874
The probability that at least 4 accounting majors are on the committee is E. 0.5874.
How to find the probabilityProbability operates on the principle of dividing the number of expected outcomes by the number of total outcomes. To find the probability that at least 4 accounting majors are on the committee, we can begin by determining the probability of having exactly 4, 5, 6, and 7 accounting majors on the committee. After finding these probabilities, we can then sum up the figures.
First, the total number of ways to choose 8 members from a group of 6+7=13 is:
13! / (8! * 5!) = 1287
Next, we will find the number of ways to choose exactly 4 accounting majors and 4 finance majors is:
6 choose 4 * 7 choose 4 = 15 * 35 = 525
Also, the number of ways to choose exactly 6 accounting majors and 2 finance majors is:
6 choose 6 * 7 choose 2 = 1 * 21 = 21
Finally, the number of ways to choose exactly 7 accounting majors and 1 finance major is:
6 choose 7 * 7 choose 1 = 0 * 7 = 0
Now, we will sum the total number of ways to choose a committee with at least 4 accounting majors as follows:
525 + 210 + 21 + 0 = 756
756 / 1287 = 0.587
Therefore, the probability of selecting a minimum of 4 accounting majors is thus 0.5874.
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A tank in the shape of a hemisphere has a diameter of 12 feet. If the liquid that fills the tank has a density of 92.5 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
In linear equation, 1161.8 lb is the total weight of the liquid in the tank, to the nearest full pound.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
d = 12 ft
r = 12 ft/2 = 6 ft
volume of sphere = (4/3)πr³
volume of hemisphere = (1/2)(4/3)πr³
volume = (2/3)π(6 ft³) = 12.56 ft³
weight = volume × density
weight = 12.56 ft³ × 92.5 lb/ft³
weight = 1161.8 lb
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Please help with this
Compare the square root of 32 and twenty one fourths using >, <, or =. twenty one fourths is less than the square root of 32 the square root of 32 is less than twenty one fourths twenty one fourths is equal to the square root of 32 the square root of 32 is less than twenty one fourths
Answer: >
Step-by-step explanation:
In a large population of nurses, suppose 20% of the nurses would prefer the night shift. If a random sample of 10 nurses is taken, what is the probability less than 3 are nurses that prefer the night shift?
Please Hurry!!
Which polar coordinates represent the point plotted on the graph? Select all that apply and explain your answer.
Answer:
D
[tex]3. \frac{11\pi}{6} [/tex]
Step-by-step explanation:
When we determine the point's coordinates, first we have to write the polar ones (they are on the horizontal line) and then the south ones (they are around the circle)
I think this is the right answer
A circular path 2feet wide has an inner diameter of 550 feet . How much farther is it around the outer edge of the path than around the inner edge?
Answer:
[tex]L_c=12.56 \ \text{feet}[/tex]
Step-by-step explanation:
From the question we are told that
Width of circular path [tex]w_c=2 \ \text{feet}[/tex]
Inner Diameter [tex]d_{in}=550 \ \text{feet}[/tex]
Outer diameter [tex]d_{out}=550+2\times2[/tex] (inner diameter + 2 circular path width)
[tex]d_{out}=550+4[/tex]
[tex]d_{out}=554 \ \text{feet}[/tex]
Generally the equation for inner circumference of the circle is mathematically given by
[tex]C_1=\pi d_{in}[/tex]
[tex]C_1=3.14\times550[/tex]
[tex]C_1=1727 \ \text{feet}[/tex]
Generally the equation for outer circumference of the circle is mathematically given by
[tex]C_2=\pi d_{out}[/tex]
[tex]C_2=3.14\times554[/tex]
[tex]C_2=1739.56 \ \text{feet}[/tex]
Generally the difference in length of the two circumference is mathematically given by
[tex]L_c=C_2-C_1[/tex]
[tex]L_c=1739.56-1727[/tex]
[tex]L_c=12.56 \ \text{feet}[/tex]
PLEASE ANSWER THIS ASAP What is the exact surface area of a cylindrical propane tank with a radius of 1 m and a height of 10 m?
2π m²
20π m²
22π m²
24π m²
22π m² is the exact surface area of a cylindrical propane tank.
What are volume and surface area?
The entire area of all the faces makes up the surface area of a three-dimensional form. We measure the areas of each face and put them together to determine the surface area of a shape.
The surface-area-to-volume ratio, also known as the surface-to-volume ratio or abbreviated as SA:V, refers to how much surface area there is in each unit volume of an object or collection of objects.
A=2πrh+2πr²
=2π * 1* 10 +2π* 1²
= 2π( 10 + 1)
= 2π * 11
= 22π m²
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100 points!!
f (x) = −√x + 2 + 3
Fully explain the three transformations required to produce this function from the
parent function.
Answer: the first thing is your answer :)
thx for the points
Step-by-step explanation:
g
(
x
)
=
x
2
−
3
The parent function is the simplest form of the type of function given.
f
(
x
)
=
x
2
The transformation being described is from
f
(
x
)
=
x
2
to
g
(
x
)
=
x
2
−
3
.
f
(
x
)
=
x
2
→
g
(
x
)
=
x
2
−
3
The horizontal shift depends on the value of
h
. The horizontal shift is described as:
g
(
x
)
=
f
(
x
+
h
)
- The graph is shifted to the left
h
units.
g
(
x
)
=
f
(
x
−
h
)
- The graph is shifted to the right
h
units.
In this case,
h
=
0
which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of
k
. The vertical shift is described as:
g
(
x
)
=
f
(
x
)
+
k
- The graph is shifted up
k
units.
g
(
x
)
=
f
(
x
)
−
k
- The graph is shifted down
k
units.
Vertical Shift: Down
3
Units
The graph is reflected about the x-axis when
g
(
x
)
=
−
f
(
x
)
.
Reflection about the x-axis: None
The graph is reflected about the y-axis when
g
(
x
)
=
f
(
−
x
)
.
Reflection about the y-axis: None
Compressing and stretching depends on the value of
a
.
When
a
is greater than
1
: Vertically stretched
When
a
is between
0
and
1
: Vertically compressed
Vertical Compression or Stretch: None
Compare and list the transformations.
Parent Function:
f
(
x
)
=
x
2
Horizontal Shift: None
Vertical Shift: Down
3
Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: None
image of graph
the area of a table top is a whole number of square feet. Could the length and width be decimal numbers each one with decimal place?
Yes, the length and width can be decimal numbers each one with decimal place, but not in every case.
Define areaThe size of a two-dimensional surface or region is expressed in terms of area. Square units like square inches, square feet, or square metres are frequently used to measure it. The area of a shape or region is determined by counting the number of unit squares that can fit inside it without overlap.
for example, lets take length =2.5 feet
and width=3.2 feet
area of table top=8 feet²
Taking another case:
length =1.2 feet
and width=3.5 feet
area of table top=4.2 feet²
if the length and width are decimal numbers, then the area would also be a decimal number or whole number, But, this is not possible in every cases.
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The complete question is:
The area of Kamar’s tabletop is a whole number of square feet. Could the length and width be decimal numbers each with one decimal place? Explain your answer.
Find the interest rate for the given deposit and compound amount.
$4000 accumulating to $5994.75, compounded monthly for 7 years.
Answer:
The interest rate is 5.79% (to the nearest hundredth).
Step-by-step explanation:
To find the interest rate for the given deposit of $4000 accumulating to $5994.75, compounded monthly for 7 years, use the compound interest formula.
Compound Interest Formula[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = Final amount.P = Principal amount.r = Interest rate (in decimal form).n = Number of times interest is applied per year.t = Time (in years).Given values:
P = $4,000A = $5,994.75n = 12 (monthly)t = 7 yearsSubstitute the given values into the formula and solve for r.
[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{12 \times 7}[/tex]
[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{84}[/tex]
[tex]\implies \sf \dfrac{5994.75}{4000}=\left(1+\dfrac{r}{12}\right)^{84}[/tex]
[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}=1+\dfrac{r}{12}[/tex]
[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1=\dfrac{r}{12}[/tex]
[tex]\implies \sf r=12\left(\sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1\right)[/tex]
[tex]\implies \sf r=0.057937950...[/tex]
[tex]\implies \sf r=5.7937950...\%[/tex]
Therefore, the interest rate is 5.79% (to the nearest hundredth).
Kayne runs a specialty running store. Last year, he earned $50,000 in revenue and had explicit costs of $20,000. Kayne could have made $42,000 selling video games on the Internet and received an additional $5,000 if he rented out the store and equipment. Calculate Kayne’s implicit costs.
A pool can be filled by one pipe in 4 hours and by a second pipe in 5 hours. How long will it take using both pipes to fill the pool?
Step-by-step explanation:
Rate A = 1 pool / 4 hrs = 1/4 pool/hr
Rate B = 1 pool / 5 hrs = 1/5 pool / hr
Now combine the rates to fill 1 pool
1 pool / ( 1/4 pool/hr + 1/5 pool / hr) = 1 / ( 1/4 + 1/5) hr = 2.22 hrs
( or 2 hrs 13.3 min)
HELP PLEASE I DO NOT UNDERSTAND THIS
The simplified expression for x+2x-8+3x+1-2x is 4x - 4.
What is expression?Expression is a term used to describe a wide variety of communication methods such as verbal, nonverbal, written, and artistic. It is the way we communicate our thoughts, feelings, and ideas to others. It is an important part of our lives, from the simplest forms of communication like body language to more complex forms like written literature. Expression is a powerful tool for self-expression, communication, and connection.
The expression x+2x-8+3x+1-2x can be simplified by combining like terms.
First, the x-terms can be combined, resulting in 4x:
x + 2x + 3x - 2x = 4x
Next, the remaining constants can be combined, resulting in -4:
4x - 8 + 1 = -4
Finally, the resulting expression can be written as 4x - 4.
Therefore, the simplified expression for x+2x-8+3x+1-2x is 4x - 4.
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please help me on this question
Answer:To calculate how much money Evie will owe after 12 years, we need to use the formula:A = P(1 + r)^nWhere:
A = the amount owed after n years
P = the initial amount borrowed
r = the annual interest rate as a decimal
n = the number of yearsIn this case, P = £600, r = 24% = 0.24, and n = 12. Plugging these values into the formula, we get:A = 600(1 + 0.24)^12
A = 600(1.24)^12
A = 600(7.8905)
A = £4,734.30 (rounded to the nearest penny)Therefore, after 12 years, Evie will owe approximately £4,734.30
Step-by-step explanation: I Helped you Can You help me
Part 1
Use the Pythagorean theorem to find the unknown side of the right triangle.
Answer:
Hypotenuse length = 37Step-by-step explanation:
According to the question we are given with a right traingle Where base is 35 and the perpendicular is 12.
We need to find the unknown side that is the longest side (Hypotenuse) .
By using pythagoras theorem :
[tex]\longrightarrow \rm \: \: (H)^2 = (B)^2 + (P)^2 \\ [/tex]
here,
H represents hypotenuseB represents base P represents Perpendicular.Putting the required values in the Pythagoras theorem we will get,,
[tex]\longrightarrow \rm \: \: (H)^2 = (35)^2 + (12)^2 \\ \\ \longrightarrow \rm \: \:(H)^2 =1225 + 144 \\ \\ \longrightarrow \rm \: \:(H)^2 = 1369 \\ \\ \longrightarrow \rm \: \:H = \sqrt{1369} \\ \\ \longrightarrow \rm \: \:H = 37 \\ [/tex]
Therefore, Unknown side of the right triangle i.e hypotenuse is 37 .
Of 10 test scores, seven are less than or equal to 85. What is the percentile rank of a test score of 85?
Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test scores.
Explain about the Percentile?A percentile in statistics refers to a score's position in relation to other scores in a given set. Although percentile has no one fixed meaning, it is frequently described as the proportion of numbers within a collection of data scores that are lower than a particular value.
Percentile shows the proportion of persons who fall below a given value. When we declare that a score of 365 out of 400 represents the 90% percentile on an exam, it means that 90% of test-takers received scores that were lower than or equal to 365.
Give: Seven of the ten test results are inside the 85th percentile.
The percentage of those who received less than or equal to 85 is just as follows: 7/10 = 0.7.
percentile rank:
0.7*100 = 70
Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test scores.
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what is μ (∠FNL)? this is crazy stuff
The angle ∠FNL in the given trapezium shows that ∠FNL is 122°
What are the opposite angles of a trapezium?The opposite angles of a trapezium are not necessarily equal, unlike in a parallelogram.
However, the opposite angles of a trapezium are supplementary, which means that the sum of one pair of opposite angles equals 180 degrees.
In other words, if we label the angles of a trapezium as F, D, N, and L (with F and L being opposite angles, and D and N being opposite angles), then we have:
∠F + ∠L = 180 degrees
∠D + ∠L = 180 degrees
Thus, ∠FDL + ∠FNL = 180
4x - 14 + 9x - 40 = 180
13x - 54 = 180
13x = 234
x = 18
∠FNL = 9x - 40
∠FNL = 9(18) - 40
∠FNL = 122°
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How do you convert 72 kilograms to pounds? show the mathmatical steps
Incorrect Which statement is NOT one of the axioms of Euclidean geometry? XO A. C. D ****? All these pictures i got answers off of Bainly and here are the wrong ones!!
The statement that is NOT one of the axioms of Euclidean geometry is D. If two planes intersect, their intersection is a point.
What are the axioms of Euclidean geometry?Euclidean geometry is a branch of mathematics that deals with the study of two-dimensional and three-dimensional figures using a set of axioms or postulates.
The axioms of Euclidean geometry are a set of five statements that are used as the foundation for all of the theorems and proofs in Euclidean geometry.
The first two axioms are relatively straightforward and intuitive, while the third axiom involves the use of circles to construct geometric figures. The fourth axiom establishes the concept of a right angle, which is a 90-degree angle, while the fifth axiom deals with the concept of parallel lines and their relationship to intersecting lines.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTSp
Answer:
f(x) = 3x-5
Step-by-step explanation:
Plug in the domain 0, in the other answer options
f(x) = -3x + 4 turns into f(x) = -3(0) + 4 and thats equal to 4, there is no value set to 4 in the range so that option is cancelled out
f(x) = x+2 turns into f(x) = 0+2 =2, there is no value set to 2 in the range so that option is cancelled out
f(x) = -5x + 3 turns into f(x) = -5(0) + 3, and thats equal to 3, there is no value set to 3 in the range so that option is cancelled out
f(x) = 3x-5 turns into f(x) = 3(0) - 5, and thats equal to -5, there is a value in the range that equals -5, you could also try any domain value into this equation and it would result into either -11, -5, 1, 7, or 13.
keep in mind f(x) is the range
Friends ordered a large circular pizza of a certain diameter, however the diameter of the baked pizza was 10% smaller than the one ordered. By the way percentage of the area of the cooked pizza is smaller than the one ordered?
Answer:
19% smaller
Step-by-step explanation:
A=πr^2
r=d/2
A=pi(d/2)^2
A=pi(.9d/2)^2=
81% of original
100%-81%=19%=Give this answer a like!
Solve the equation 101 = k +33 for k
K=
Answer:
101 = k + 33
101 - 33 = k + 33 - 33
68 = k
this is your required answer
6. Find the first three terms of the expansion of the following in acceding powers of
x
2
1
2
x
x
The first three terms in decreasing powers of X are as follows.
x5−10x4X−1+40x3X−2+…
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from
A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
Hence, The first three terms in decreasing powers of X are as follows.
x5−10x4X−1+40x3X−2+…
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please answer it asap.
Answer:
8^2
Step-by-step explanation:
Which statement is true?
The correct statement about diagram is m∠1 > m∠4. So correct option is D.
Describe Angles?In mathematics, an angle is a measure of the amount of rotation between two rays or line segments that share a common endpoint, known as the vertex. The rays or line segments are typically referred to as the sides of the angle.
Angles are usually measured in degrees or radians, with a full rotation or circle being 360 degrees or 2π radians. Angles can be classified into different types based on their degree of rotation, such as acute angles, which are less than 90 degrees, right angles, which are exactly 90 degrees, obtuse angles, which are greater than 90 degrees but less than 180 degrees, and straight angles, which are exactly 180 degrees.
Angles can be added, subtracted, multiplied, and divided, and they can be used to solve a wide range of problems in geometry and trigonometry. For example, angles are used to calculate the measurements of geometric shapes, such as triangles, circles, and polygons, and they are also used to calculate distances and heights using trigonometric functions such as sine, cosine, and tangent.
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(1000y) -1/2 * (3/x+1) when x = 1/3 and y = 1/10
The value of simplification is 95.
What is simplification?
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easily with calculations and solving.
Here, we have
Given: (1000y) -1/2 * (3/x+1) when x = 1/3 and y = 1/10
we have to simplify the given expression.
= (1000y) -1/2 * (3/x+1)
When x = 1/3 and y = 1/10
Now we put the value of x and y in the given equation and we get
= (1000/10) -1/2 × (3×3+1)
= 100 - 10/2
= 100 - 5
= 95
Hence, the value of simplification is 95.
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The following equation involves multiple angles. Solve the equation on the interval [0, 2π). cos 4x= 1/2
[tex]\cos(4x)=\cfrac{1}{2}\implies 4x=\cos^{-1}\left( \cfrac{1}{2} \right)\implies 4x= \begin{cases} \frac{\pi }{3}\\\\ \frac{5\pi }{3} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 4x=\cfrac{\pi }{3}\implies \boxed{x=\cfrac{\pi }{12}}~\hfill 4x=\cfrac{5\pi }{3}\implies \boxed{x=\cfrac{5\pi }{12}}[/tex]
Name two pairs of adjacent angles.
Answer:
the definition of adjacent mathematically means two angles if they have a common side and a common vertex.
Step-by-step explanation:
a would b adjacent to d. c would be adjacent to d.