Answer:
The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.
Step-by-step explanation:
The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Here, given that,
Robert's salary after working for n years can be determined using the equation
S = 5000n + 60000.
Hence, The slope is 5000,
this means that for each additional year Robert works at the company, he earns 5000 more dollars.
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Review the proof of de Moivre’s theorem (not in order).
Proof of de Moivre's Theorem
[cos(θ) + isin(θ)]k + 1
A = [cos(θ) + isin(θ)]k ∙ [cos(θ) + isin(θ)]1
B = cos(kθ + θ) + isin(kθ + θ)
C = cos(kθ)cos(θ) − sin(kθ)sin(θ) + i[sin(kθ)cos(θ) + cos(kθ)sin(θ)]
D = [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)]
E = cos[(k + 1)θ] + isin[(k + 1)θ]
Which steps must be switched to put the proof in order?
steps B and C
steps B and D
steps C and D
steps C and E
Answer:
steps B and D
Step-by-step explanation:
the correct chart is below :)
The steps which must be switched to put the proof in order are steps B and D
Since [cos(θ) + isin(θ)]k + 1
= [cos(θ) + isin(θ)]k ∙ [cos(θ) + isin(θ)]1
= [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)]
= cos(kθ)cos(θ) − sin(kθ)sin(θ) + i[sin(kθ)cos(θ) + cos(kθ)sin(θ)]
= cos(kθ + θ) + isin(kθ + θ)
= cos[(k + 1)θ] + isin[(k + 1)θ]
Since the step after A is [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)] = D, and the step after C is cos(kθ + θ) + isin(kθ + θ) = B.
So, steps B and D must be switched.
The steps which must be switched to put the proof in order are steps B and D.
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What is the slopeWhat is the slope of this
linear equation:
2x+3y= -4x+9 of this linear equation: 2x+3y= -4x+9
Answer:
Slope = -2
Step-by-step explanation:
Equation in slope intercept form:
y = -2x + 3
Meaning slope equals -2
Mark reeds 42 pages of a book every 3/4 of an hour write an equation that models the relationship between Z, the number of hours mark reads, NY, the number of pages of the book He reads
Answer:
The equation that models the relationship between Z and N is N = 56 Z
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
m is the rate ⇒ slopeb is the initial amount ⇒ y-intercept∵ Mark reads 42 pages of a book every [tex]\frac{3}{4}[/tex] of an hour
→ Find his rate per hour by dividing the number of pages by its time
∴ His rate of reading = 42 ÷ [tex]\frac{3}{4}[/tex] = 42 × [tex]\frac{4}{3}[/tex] = 56 pages per hour
∵ His rate = 56 pages/hour
∴ m = 56
∵ Z represents the number of hours Mark reads
→ That means replace x in the form of the equation above with Z
∵ N represents the number of pages of the book he reads
→ That means replace y in the form of the equation above with N
∴ N = 56 Z + b
∵ There is no initial amount of reading
∴ b = 0
∴ N = 56 Z
The equation that models the relationship between Z and N is N = 56 Z
Hey now please just anser if itnus a try i will still give 5 stars. THE Question is what is the most easy way to SOLVE THE NINES TABLE IK THIS BUT I WANT to see who else knows sorry fir the big ketters i did not means to put that
Answer:
Tbh, I think the easiest way is to count on your fingers. I still do it, however I can now do my chart tables to 17x17 by using fingers. People may tease, however, it is a good way to make sure you do not mess up as much as memorizing. You should memorize, and count on your fingers at the same time to solve extremely fast.
Step-by-step explanation:
9x4
You can pretend that your thumb equals nine, and count 9 plus 9 plus 9 plus 9, with each other finger, such as your ring finger, pointer, middle, and pinky , which equals 36. 5x9, you have five fingers on each hand, so each finger can equal nine (I don't care if people say that your thumb isn't a finger, just take it and move on lol).
Kayla measures a distance of 50 inches. She needs to find the equivalent number of meters. Which conversion factors should she use? Check all that apply.
(A) StartFraction 2.54 centimeters Over 1 inch EndFraction
(B) StartFraction 1 inch Over 2.54 centimeters EndFraction
(C) StartFraction 1 meter Over 100 centimeters EndFraction
(D) StartFraction 100 centimeters Over 1 meter EndFraction
Answer: A and C
Step-by-step explanation: :)
Answer:
A and C [: (edg 2021)
Step-by-step explanation:
I got it correct on my assignment!
Q13. A stone is dropped from a height of 5 km. The distance it falls through varies directly with the
square of the time taken to fall through that distance. If it falls 64 min 4 seconds. find the distance the
stone covers in the 5th second?
A. 36 m
B. 58 m
C. 72 m
D. 100 m
Answer:
The stone covers 36 m in the 5th second. Correct choice: A.
Step-by-step explanation:
Proportions
Two variables are said to be proportional if one of them can be calculated by multiplying the other by a constant of proportionality. If y and x are those variables, then:
y=k.x
There are other similar proportions where the relation is not linear. For example, if y is proportional to the square of x, then:
[tex]y=k.x^2[/tex]
According to the conditions of the question, the distance traveled by a stone dropped from a height of 5 Km varies directly with the square of the time taken to fall through that distance. If d is the distance and t is the time, then;
[tex]d=k.t^2[/tex]
To find the value of k, we use the given condition: The stone falls d=66 meters in t=4 seconds. Substituting:
[tex]64=k.4^2=16k[/tex]
Solving:
[tex]k=64/16=4[/tex]
Substitute the value of k into the equation to get the complete model.
[tex]d=4.t^2[/tex]
Now we calculate the distance when t=5 seconds:
[tex]d=4\cdot 5^2=4\cdot 25=100[/tex]
The stone has covered 100 m in 5 seconds. But we need to find the distance covered in the 5th second, that specific interval between 4 sec and 5 sec.
Since we already know the distance for t=4 sec (64 m), and the distance for t=5 sec (100 m), then:
distance in the 5th second = 100 m - 64 m = 36 m
The stone covers 36 m in the 5th second. Option A.
Linearize the data. Then find the least squares regression equation
Answer:
C
Step-by-step explanation:
Suppose that you roll a die 8 times. What is the probability that you roll a six three or fewer times
Answer:
0.96
Step-by-step explanation:
Given that the a die is rolled 8 number of times.
[tex]n[/tex] = 8
Probability of getting a 6 on roll of a die, [tex]p=\frac{1}{6}[/tex]
Probability of not getting a 6 on roll of a die, [tex]q=1-p=1-\frac{1}{6}=\frac{5}{6}[/tex]
Probability of getting 6 three or fewer times:
[tex]P(r \le 3)=P(r=0)+P(r=1)+P(r=2)+P(r=3)[/tex]
Formula:
[tex]P(r=k)=_nC_k.p^k.q^{n-k}[/tex]
Putting the values using this formula:
[tex]P(r \le 3)=_8C_0.\frac{1}{6}^0.\frac{5}{6}^{8-0}+_8C_1.\frac{1}{6}^1.\frac{5}{6}^{8-1}+_8C_2.\frac{1}{6}^2.\frac{5}{6}^{8-2}+_8C_3.\frac{1}{6}^3.\frac{5}{6}^{8-3}\\\Rightarrow P(r \le 3)=1.\frac{5}{6}^{8}+8.\frac{1}{6}.\frac{5}{6}^{7}+28.\frac{1}{36}^2.\frac{5}{6}^{6}+56.\frac{1}{216}.\frac{5}{6}^{5}\\\Rightarrow P(r \le 3)=0.23+0.37+0.26+0.1=\bold{0.96}[/tex]
A criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating the undesirable behavior. The test is normed so that it has a mean of 140 and a standard deviation of 40. Suppose an individual is in the 67th percentile in this exam.What is his or her corresponding recidivism score
Answer:
157.6
Step-by-step explanation:
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score,
μ is the population mean, and
σ is the population standard deviation.
From the question:
Mean = 140
Standard deviation = 40
Recidivism score = x score = ??
z = z score of 67th percentile = 0.44
Hence,
0.44 = x - 140/40
Cross Multiply
0.44 × 40 = x - 140
17.6 = x - 140
x = 140 + 17.6
x = 157.6
Therefore, his corresponding recidivism score is 157.6
Anya purchased $124.35 worth of home improvement items at the hardware store. If the sales tax rate in her city is 6.75%, what is the total cost of her purchase!
Answer:
124.35 X 6.75
Step-by-step explanation:
The total cost of Anya's purchase of home improvement hardware is 132.74 dollars.
What is percentage?
The percentage is the value per hundredth.
It is given that, the sales tax is 6.75% which is not there in the home improvement hardware which cost 124.35 dollars to Anya.
The total cost of purchase including the sales tax is ( 100 + 6.75)% = 106.75% of 124.35 dollars which is,
= (106.75/100)×124.35 dollars.
= 1.0675×124.35 dollars.
= 132.74 dollars.
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when writing fraction from a graph does the x axis number go on top or bottom
Answer:
x ax-s can be horizontal and top
y axis is bottom
Step-by-step explanation:
There are (26)3⋅ 20 bacteria in a sample. What is the total number of bacteria in the sample? (1 point)
Answer: If we multiply then I guess it’s 26*3=78 and 78*20=1,560
Step-by-step explanation:
I will give brainliest :D
Which equation matches this scenario?
A family buys 8 tickets to a show. They also pay a $5
parking fee. They spend $61 to see the show.
• 5x+8=61
• 61+8x=5
• 8+5x=61
• 8x+5=61
Answer: 8x + 5= 61
Step-by-step explanation: x represents the cost of one ticket for the show, 8 is the amount of tickets, 5 is the extra fee, 61 is the total.
Which is a correct way to subtract from a number? (A). Add 100 then subtract 1 (B). Add 100 then add 2. (C). Subtract 100 then add 2 (D). Subtract 100 then add 1.
Answer:
A is the answer
Step-by-step explanation:
According to BODMAS (or DMAS), first we add and then subtract
if both operations are of add, we add it at the same time
please help meeeeeeeeeeeeee
What is the slope of the points (2,5) and (0,-4)?
To find the slope of two points, we have to first assign our points as x1, y1 and x2, y2.
In our problem,
x1 = 2 and y1 = 5
x2 = 0 and y2 = -4
We know that that slope = y2 - y1 / x2 - x1. Let's plug our numbers into this formula.
Slope = -4 - 5 / 0 - 2 = -9 / -2 = 9 / 2
A florist must make 5 identical
bridesmaid bouquets for a wedding. The budget is
$160, and each bouquet must have 12 flowers. Roses
cost $2.50 each, lilies cost $4 each, and irises cost
$2 each. The florist wants twice as many roses as the
other two types of flowers combined.
Answer:
A. 40x + 10y + 10z = $160
B. 8 Roses, 2 lilies and 2 irises
C.
1. 20x + 5y + 5z = $80
2. 4x + y + z = $16
3. 8x + 2y + 2z = $32
Step-by-step explanation:
Cost for each flower = $160/5 = $32
So we have $32 for each bouquet consisting of 12 flowers each.
Roses = x = $2.50 each
lilies = y = $4 each
irises = z = $2 each
8x + 2y + 2z = $32
8($2.50) + 2($4) + 2($2) = $32
$20 + $8 + $4 = $32
$32 = $32
a. Maximum budget is $160
40x + 10y + 10z = $160
40($2.50) + 10($4) + 10($2) = $160
$100 + $40 + $20 = $160
$160 = $160
b. From above
8x + 2y + 2z = $32
8 Roses, 2 lilies and 2 irises
c. No. There are other solutions If total cost is not limited
1. 20x + 5y + 5z
20($2.50) + 5($4) + 5($2)
$50 + $20 + $10
= $80
2. 4x + y + z
4($2.50) + $4 + $2
$10 + $4 + $2
= $16
3. 8x + 2y + 2z
8($2.50) + 2($4) + 2($2)
$20 + $8 + $4
= $32
Mary used 1/2 of a can of paint to cover 1/8 of the outside of her house. How many cans of paint will Mary need to cover the entire outside of her house?
Answer:
4 cans of paint
Step-by-step explanation:
Half of a can = 1/8 of the outside of the house.
2 halves = whole can of paint
8/2=4
4 cans of paint
I WILL BRAINLIST ITS ONLY ONE PROBLEM !!!!!!!!!!!!!!!
Answer:
11/200
Step-by-step explanation:
This is the correct answer boo
Walt multiples 25 times 16 using partial products what did walt do wrong
Answer:
first what the full question and if 25*16/2=200
Step-by-step explanation:
5x-(x+3)=1/3(9x+18)-5
Answer: x=4
Step-by-step explanation:
FIRST RIGHT GETS BRAINLIEST
Answer:
-4+-6=-10
Step-by-step explanation:
An airplane pilot over the Pacific sights a ship wreck at an angle of depression of 5°. At this time, the horizontal distance from the airplane to the wreck is 4629 meters. What is the height of the plane to the nearest meter?
405 m
Answer:
The height of the plane is 405 meters
Step-by-step explanation:
Trigonometric Ratios
The situation can be represented as shown in the image below. The ground, the height H, and the direct distance to the plane to the shipwreck form a right triangle, where the trigonometric ratios stand.
Since the known distance is adjacent to the angle, and the required height is opposite to the given angle, we use the tangent ratio, defined as:
[tex]\displaystyle \tan\ x=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 5^\circ=\frac{H}{4629}[/tex]
We need to find H, so we solve for H:
[tex]H=4629\cdot\tan5^\circ[/tex]
H=405 m
The height of the plane is 405 meters
What is 86.929 rounded to the nearest tenth ?
Answer:
86.9
Step-by-step explanation:
This is because after the decimal point, it goes to the tenths place and then the thousands place, therefore, if you round it, it would be 86.9.
Write 310,763,029 expanded form
Answer:
300,000,000
10,000,000
700,000
60,000
3,000
20
9
Step-by-step explanation:
Your god mother is baking a cake for your Halloween
party. She has a giant cake pan makes a cake four times
the size of any regular cake. The giant cake needs five
cups of flour. How many cups does a regular size cake
need?
Answer:
2
Step-by-step explanation:
Divide 4 into an even number, so its 2.
Answer:
1.25 or 1 and 1/4th
Step-by-step explanation:
you have to divide the cups of flower by the size of the pan
fplzz ans my question
factorize p^4+4
Answer:
Step-by-step explanation:
(p²)²+2²
(p²+2)²-2p²2
(p²+2)²-4p²
(p²+2)²-(2p)²
(p²+2-2p)(p²+2+2p)
Enter the equivalent distance in km in the box.
1 km = 1000 m
1 m = 100 cm
35,000 cm =
km
Answer:
0.350 km
Step-by-step explanation:
Hi there !
35000 cm = 35000/100 m = 350 m
350 m = 350/1000 km = 0.350 km
Good luck !
If f(x)=x^2 and g(x) =3x-1 find [g • f](x)
Answer:
3x²-1
Step-by-step explanation:
f(x) = x²
g(x) = 3x-1
[g·f](x)
g(f(x))
3(x²)-1
in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)
Answer:
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].
Step-by-step explanation:
Let [tex]\vec u[/tex] and [tex]\vec a[/tex], from Linear Algebra we get that component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] by using this formula:
[tex]\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a[/tex] (Eq. 1)
Where [tex]\|\vec a\|[/tex] is the norm of [tex]\vec a[/tex], which is equal to [tex]\|\vec a\| = \sqrt{\vec a\bullet \vec a}[/tex]. (Eq. 2)
If we know that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec a=(4,-4,2,-2)[/tex], then we get that vector component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] is:
[tex]\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
Lastly, we find the vector component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] by applying this vector sum identity:
[tex]\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}[/tex] (Eq. 3)
If we get that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex], the vector component of [tex]\vec u[/tex] is:
[tex]\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
[tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex]
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].