By definition of slope , we have seen that Slope = 4/3 and 4/3 = 16/12
How to find the slope of a Line?The slope of a line is basically a measure of its steepness. Mathematically, the slope is calculated as rise over run.
To find the slope, we divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. This is change in y divided by change in x.
From definition of slope, we know that;
Slope between line D and E is; Slope = 4/3
Similarly, by definition of slope, we know that;
Slope between line D and E is; Slope = 16/12
Now, 16/12 can be reduced to 4/3 and as such;
4/3 = 16/12
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the number of complex numbers z such that |z – 1| = |z + 1| = |z – i| equals
By using the concept of complex number, it can be calculated that
There is only one complex number which satisfies |z – 1| = |z + 1| = |z – i|
What is a complex number?
Any number of the form a+ib where, a and b are real numbers and i = [tex]\sqrt{-1}[/tex] are called complex number.
Let z = x + iy
[tex]|z - 1|^2 = |z + 1|^2 = |z - i|^2[/tex]
[tex]|x + iy - 1|^2 = |x+iy + 1|^2 = |x+iy - i|^2\\(x-1)^2+y^2 = (x+1)^2+y^2 = x^2+(y -1)^2[/tex]
So the point (x, y) is equidistant from (1, 0), (-1, 0) and (0, 1)
(0, 0) is the only point which is equidistant from (1, 0), (-1, 0) and (0, 1)
z = 0 is the only complex number which satisfies |z – 1| = |z + 1| = |z – i|
There is only one complex number which satisfies |z – 1| = |z + 1| = |z – i|
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Anita started making sugar cookies for her friends at 9:55 A.M. It took her 1 hour and 15 minutes to make the dough and 40 minutes to bake all of the cookies. Then, Anita spent 15 minutes decorating the cookies with icing and sprinkles. What time was it when Anita finished making the cookies?
The time when Anita finished making the cookies is 12.05 pm.
How to calculate the time?From the information illustrated, Anita started making sugar cookies for her friends at 9:55 A.M, it took her 1 hour and 15 minutes to make the dough and 40 minutes to bake all of the cookies and then, Anita spent 15 minutes decorating the cookies with icing and sprinkle.
It should be noted that the time that she finishes will be the addition of the time given. This will be:
9.55 + 1.15 + 40 + 15
= 9.55 + 1.15 + 55
= 9.55 + 2.10
= 12.05
The time is 12.05 pm
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1.2.what are the complex eigenvalues of the matrix a that represents a rotation of jr3 through the angle () about a pole u?
A rotation matrix has two complex eigenvalues e−iθ and eiθ.
These are matched by complicated eigenvectors.
We are aware that the rotational axis is represented by the eigenvector with the eigenvalue 1 in it. how to demonstrate that the angle of rotation is represented by the complex eigenvalue.
It is simple to compare it with a rotation matrix for rotation about the x, y, or z axes, but how can one draw this conclusion for a general R that belongs to SO (3).
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix rotates points in the xy plane counterclockwise through an angle θ with respect to the positive x axis about the origin of a two-dimensional Cartesian Plane.
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a runner is participating in half marathon he has run 12 of the 15 miles course what percent of the course has he run so far?
a radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t)=15e^(-0,02t) where m(t) is measured in kilograms.
a. Find the mass at time t=3
b. How much of the mass remains after 20 days?
For the given data, a) The mass at the time t = 3 is 14.13 kg. and b) The mass remaining after 20 days is 10.05 kg.
What is radioactive decay?
The spontaneous breakdown of an atomic nucleus of a radioactive substance resulting in the emission of radiation from the nucleus is known as Radioactive decay.
The Radioactive Formula is given by
[tex]N = N_{0} e^{-\lambda T}[/tex]
Given, [tex]m(t) = 15e^{-0.02t}[/tex]
where m(t) is measured in kilograms
a) To find the mass at time t=3, then
m(3) = [tex]15e^{-0.02*3}[/tex] = [tex]15e^{-0.06}[/tex] = 14.13 kg
Therefore, the mass at the time t=3 is 14.13 kg.
b) To find how much of the mass remains after 20 days,
m(20) = [tex]15e^{-0.02*20}[/tex] = [tex]15e^{-0.4}[/tex] = 10.05 kg
Therefore, the mass remaining after 20 days is 10.05 kg.
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the country of transylvania contains 2.3 million people (vampires not included) and covers 800,000 square miles. in the year after the last census, the crude birth rate was 48 out of 1000 and the crude death rate was 47 out of 1000. 1. what is the population growth rate (r)? 2. in how many years will the population of transylvania double?
In 700 years the population of Transylvania will double
What is growth rate ?
the typical annual rate of population change during a particular period for a certain nation, region, or geographic area. In most cases, a factor of 100 is used to describe the ratio between the annual growth in population size and the total population for the year.
Growth rate equals Absolute Change divided by Previous Value. Calculate the percentage of change: Percent of change = Growth rate x 100 is the formula that may be used to calculate the percent of change.
To calculate in how many years the population of Transylvania double
= 70 / 0.1
= 700 years
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find an equation of variation in which y varies directly as x and the following is true. yequals 21.25 when xequals 4.25
Answer:
y = 5x
Step-by-step explanation:
the equation of variation in which y varies directly as x is
y = kx ← k is the constant of variation
to find k use the given y = 21.25 when x = 4.25
21.25 = 4.25k ( divide both sides by 4.25 )
5 = k
y = 5x ← equation of variation
if angles of a triangle are congruent then are the sides also congruent
Answer:
yes
Step-by-step explanation:
You want to know if the sides are congruent in a triangle with congruent angles.
Law of sinesThe Law of Sines tells us the sides of a triangle are proportional in length to the sines of the opposite angles.
If the angles are congruent, their sines are equal, and the sides are congruent.
Congruent anglesA triangle with congruent angles has all angles 60°. Such a triangle is called an equilateral triangle. The name "equilateral" refers to the fact that the sides are the same length.
in a family with 3 children, excluding multiple births, what is the probability of having 2 boys and 1 girl ? assume that a girl is as likely as a boy at each birth
The probability of having 2 boys and 1 girl would be [tex]\frac{3}{8}[/tex]
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given that:
family with 3 children.
Condition: Girl is as likely as a boy at each birth.
s will be the sample space.
The sample space has 8 elements:
s = {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}
n(s) = [tex]\frac{1}{8}[/tex]
We need 2 boys and 1 girl, regardless of order,
sample space for 2 boys and 1 girl, regardless of order would be 3.
s = 3
Then, probability will be
[tex]Probability \ of\ having\ 2 \ boys\ and \ 1\ girl =\frac{3}{8}[/tex]
Hence, The probability of having 2 boys and 1 girl would be [tex]\frac{3}{8}[/tex]
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Work out 2.151 x 10²
Answer:
215.1x
Step-by-step explanation:
2.151x(102)
=2.151*x*100
=215.1*x
=215.1x
Answer:
The answer would be 215.1x
Step-by-step explanation:
2.151 x 10^2 = 215.1x
10^2 = 100
Then multiply 100 and 2.151x
100 x 2.151x = 215.1x
simplify the expression 8s−11s+6
hana is 4 year older than her brother. 2 years ago, her brother’s age was ¾ of her age. how old will her brother be in 5 years?
hana is 4 year older than her brother. 2 years ago, her brother’s age was ¾ of her age then brother age will be 19 years
The concept of age describes how old a person is at a particular point in time. It is defined as the measure of the time elapsed from date of live birth to a specific point in time, usually the date of collection of the data
Hana is 4 years older then her brother
let x be brother present age
and x+4 be the hana present age
2 year ago
hana was x+2
and brother was x-2
according to the question
x-2= 3/4 * ( x+2)
x= 14
after 5 years he will be 19 years
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Trey believes there is a correlation between the number of texts sent in class and gpa. he collected data and found that the line of best fit for the data can be modeled by the equation y = 4.0 − 0.5x. identify the slope and the type of association. the slope is −4.0, which indicates a negative correlation. the slope is −0.5, which indicates a negative correlation. the slope is 4.0, which indicates a positive correlation. the slope is 0.5, which indicates a positive correlation.
Answer:
The slope is -0.5, which indicates a negative correlation.
Step-by-step explanation:
y = mx + b
Is a slope-intercept form of the equation.
The y represents the distance of the line from the y-axis. (if u were to graph the problem)
M represents the slope of the line.
An the value of b is equal to y when x = 0
The equation that was given is y = 4.0 - 0.5x, which wasn't written the normal way, like y = mx + b, they just switched the spots from y = mx + b, to y = b + mx.
So the slope is the 0.5. (which is also -0.5)
Trust me, I took a test and it had this answer, and I got it right.
Answer:
B- -0.5
Step-by-step explanation:
-.05 is a negative correlation
Negative Correlation definition- Is a situation or an event where two variables move in the opposite direction
(Plus I also Took the test and got it right)
Could someone help me understand what v is
The value of v in the triangle is 15 degrees.
How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
The exterior angle theorem is used to find the value of v.
Therefore,
31 + 4v + 44 = 9v
31 + 44 = 9v - 4v
75 = 5v
divide both sides by 5
v = 75 / 5
v = 15
Therefore,
v = 15
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In the league, the Leos play 8 games. Their win to loss ratio is 5:3. The Tigers play 11 games. Their win to loss ratio is 7:4. a) Which team has the better record? Explain.
Answer:
The Tiger has the better record, because the Leo won 5 games out of 8 and the Tiger won 7 games out of 11. When we change both denominator to the same number, the Leo's is 55/88 and the Tiger is 56/88, so the Tiger has the better record
The length of a rectangle is 5 more than twice the width. The perimeter is 130 in. What is the area?
Answer:
900
Step-by-step explanation:
l = 2w + 5
2(2w + 5) + 2w = 130
4w + 10 + 2w = 130
6w + 10 = 130
6w = 120
w = 20
l = 2(20) + 5
l = 40 + 5
l = 45
130 = 2(45) + 2(20)
130 = 90 + 40
130 = 130
A = l × w
A = 45 × 20
A = 900
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17/-2n=-8.5 (with steps please)
Linda was selling tickets for the school play. She sold 10 more adult tickets than children tickets and she sold twice as many senior tickets as children tickets. Find an expression for the total number of tickets sold by Linda.
Answer:X+(X+10)+(2X)
Step-by-step explanation:
Lets say X is the amount of children tickets sold.
So she sold some kid tickets and we get an X
So X
and then she sold ten more than X tickets to adults
So now we have
X+(X+10)
And then she sold twice as many senior tickets than kids tickets
so now we have
X+(X+10)+(2X)
hope that helped at all!
recipe for sparkling grape juice calls for 1 1/2 quarts of sparkling water and 3/4 quart of grape juice, how much grape juice would you need for 15/4 quarts of sparkling water
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
15/8 quart of grape juice is needed for 15/4 quart of sparkling water.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The recipe for sparkling grape juice calls for 1(1/2) quart of sparkling water and 3/4 quart of grape juice,
This means,
1(1/2) quart of sparkling water = 3/4 quart of grape juice
3/2 quart of sparkling water = 3/4 quart of grape juice
Multiply 15/6 on both sides.
15/6 x 3/2 quart of sparkling water = 15/6 x 3/4 quart of grape juice
15/4 quart of sparkling water = 15/8 quart of grape juice
Thus,
15/8 quart of grape juice is needed for 15/4 quart of sparkling water.
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Solve for x. Show your steps
The value of x is -7.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
We are given the equation as
[tex]8^{x + 3} = 2 ^{x - 5}[/tex]
Solving the equation as;
[tex]8^{x + 3} = 2 ^{x - 5}\\\\2^{3(x + 3)} = 2 ^{x - 5}[/tex]
Then we have;
3x + 9 = x - 5
2x = -14
x = -7
The value of x is -7.
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find the f-test statistic to test the claim that the population variances are equal. both distributions are normal. the standard deviation of the first sample is 2.1971 7.32 is the standard deviation of the second sample.
the f-test statistic to test the claim that the population variances are equal is F test = 2.54
We are given two samples
Standard deviation of the first sample = 2.1971
Standard deviation of the second sample = 7.32
F test statistic = Variance of the Larger sample/ Variance of the smaller sample
Variance = (Standard deviation)²
Variance for the first sample = 2.1971²
= 4.8272
Variance for the second sample = 7.32² = 53.5824
F test = 53.5824/4.8272
= 11.100
Therefore, the F test approximately = 11.100
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A hot-air balloon travels 2,016 miles in
96 hours. It travels the same number
of miles each hour. How many miles
does the balloon travel in 1 hour?
Answer: 21 miles
Step-by-step explanation:
We know that it travels 2016 miles in 96 hours.
So we just need to get 2016 divided by 96 = 21 miles/ per hour
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Hence, the miles does the balloon travel in one hour is [tex]21[/tex] miles/ per hour.
What is the miles?
Mile is a customary unit used for measuring length or distance. More About Mile Mile is denoted by the symbol 'mi'.
Here given that,
A hot-air balloon travels [tex]2,016[/tex] miles in [tex]96[/tex] hours. It travels the same number of miles each hour.
As we know that it travels [tex]2016[/tex] miles just only in [tex]96[/tex] hours.
[tex]\frac{2016}{96}=21[/tex] miles/ per hour
Hence, the miles does the balloon travel in one hour is [tex]21[/tex] miles/ per hour.
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what is the maximum number of electrons in an atom that can have the given sets of quantum numbers n=4?
The maximum number of electrons in an atom that can have the given sets of quantum numbers n=4 is 32.
In the given question we have to find the maximum number of electrons in an atom that can have the given sets of quantum numbers n=4.
As we know that;
A negatively charged subatomic particle known as an electron can either be free or attached to an atom (not bound). One of the three main types of particles within an atom is an electron that is bonded to it; the other two are protons and neutrons. The nucleus of an atom is made up of electrons, protons, and neutrons altogether.
So the maximum number of electrons in an atom is;
Number of Electron = 2*n^2
Number of Electron = 2*(4)^2
Number of Electron = 2*16
Number of Electron = 32
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X is 19 units to the left of 0. Use the drop-down menus to complete the statement about −X.
Options:
-19
-9
0
9
19
The value of ''- X'' will be;
⇒ - X = 19
What is Number line?
Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.
Given that;
X is 19 units to the left of 0.
Now,
Since, X is 19 units to the left of 0.
Hence, The value of X = - 19
So, We get;
The value of - X = - (- 19)
= 19
Thus, The value of ''- X'' will be;
⇒ - X = 19
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If the function f (x) is the absolute value of 3 more than the value of x. Select all the true statements.
The x-intercept of the function is 3.
The range of the function is (f (x) f(x) E R).
The function is positive in the interval -3 < x < 00.
The function is increasing in the interval -3 < x < [infinity]0.
The function is negative in the interval -[infinity]o < x < -3.
The function is decreasing in the interval -[infinity]o < x < -3
Answer:
The function is positive in the interval -3 < x < ∞.The function is increasing in the interval -3 < x < ∞.The function is decreasing in the interval -∞ < x < -3.Step-by-step explanation:
You want to identify the true statements about the function f(x) = |x+3|.
GraphA graph of the function is attached. It shows the function is decreasing to the left of x = -3, increasing to the right of that point, and has an x-intercept at x = -3. The function is positive everywhere.
The true descriptions are ...
The function is positive in the interval -3 < x < ∞.The function is increasing in the interval -3 < x < ∞.The function is decreasing in the interval -∞ < x < -3.find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm. what is the maximum volume?
The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.
The maximum volume of right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.
How to find volume of Right Circular Cylinder?
Right cylinders are cylinders with axes that are perpendicular to the bases.
Volume of a Right Circular Cylinder= πr²h
where,
r = radius of the base
h = height of right circular cylinder
Maximum volume of right circular cylinder that can be inscribed in a sphere will be,
[tex]\pi r^{2} h-\frac{\pi }{4} h^{3}\\\\= \frac{4\pi r^{3} }{3\sqrt{3} }[/tex]
given that, radius=70cm=0.0.7 m
so,
[tex]Maximum\ volume=\frac{4\pi r^{3} }{3\sqrt{3} } \\\\= \frac{4\pi (70)^{3} }{3\sqrt{3} }\\\\=2640.4\pi \ m^{3}[/tex]
Using volume of right circular cylinder,
[tex]h=\frac{2r}{\sqrt{3} }\\\\ h = \frac{2(0.07)}{\sqrt{3} }\\\\h= 0.08\ m[/tex]
Hence, The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be r=0.0.7 m and h=0.08 m.
The maximum volume of right circular cylinder of maximum volume that can be inscribed in a sphere of radius 70 cm will be 2640.4 m³.
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If you invest $1,500 at 3% annual compound interest for 30 years, how much
interest would you earn? Round your answer to two decimal places.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
sus
Linda received a $25.00 gift card for a photo center. She used it to buy prints that cost 25 cents each. The remaining balance, B (in dollars), on the card after
buying x prints is given by the following.
B=25.00-0.25x
What is the remaining balance on the card if Linda bought 30 prints?
Answer:$17.50 remaining
Step-by-step explanation: 0.25 x 30 = 7.50
7.50 - 25.00 = $17.50 remaining
Answer:
$17.5
Step-by-step explanation:
B = 25 -0.25(30)
B = 25 - 7.5
B = 25.0 - 7.5
B = $17.5
number of days absentprobability 00.60 10.20 20.12 30.04 40.04 50.00 what is the standard deviation of the number of days absent?
The standard deviation of the number of days absent is found as 1.1616.
Define the term standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.For the stated question-
Number of Days Absent/Probability
0 - 0.601 - 0.202 - 0.123 - 0.044 - 0.045- 0.00Thus, the mean is found as;
Mean = (0x0.60) + (1x0.20) + (2x0.12) + (3x0.04) + (4x0.04)
Mean = 0.72
Standard deviation σ = (0-0.72)² x 0.60 + (1-0.72)² × 0.20 + (2-0.72)² × 0.12 + (3-0.72)² × 0.04 + (4-0.72)² × 0.04
Standard deviation = 1.1616
Thus, the standard deviation of the number of days absent is found as 1.1616.
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The complete question is-
A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month.
Number of Days Absent/Probability
0 0.60
1 0.20
2 0.12
3 0.04
4 0.04
5 0.00
What is the standard deviation of the number of days absent?
ten points labeled a, b, c, d, e, f, g, h, i, j are arranged in a plane in such a way that no three lie on the same straight line. (a) how many straight lines are determined by the ten points?
Total number of straight lines are 45 and it can be found out using combination.
What is combination?
A combination could be a choice of things from a collection that has distinct members, such the order of choice doesn't matter.
Main body:
Total points = 10
we need to find no three lie on the same straight line.
so , to find we can select 2 lines out of 10 and assume packing them together so no 3 points lie on a line .
selection of 2 points out of 10.
C(10,2) = ¹⁰C₂
= 10!/2!8!
= 10*9/2
= 45 lines.
Hence ,Total number of straight lines are 45 .
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