Robert accepted a new job at a company with a contract guaranteeing annual raises.
Robert's salary after working for n years can be determined using the equation
S = 5000n + 60000. What is the slope of the equation and what is its
interpretation in the context of the problem?

Answer:

300,000,000

10,000,000

700,000

60,000

3,000

20

9

Step-by-step explanation:

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

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)

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

Answer:

3x²-1

Step-by-step explanation:

f(x) = x²

g(x) = 3x-1

[g·f](x)

g(f(x))

3(x²)-1

Answer:

first what the full question and if 25*16/2=200

Step-by-step explanation:

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

Answer:

11/200

Step-by-step explanation:

This is the correct answer boo

Answer:

Slope = -2

Step-by-step explanation:

Equation in slope intercept form:

y = -2x + 3

Meaning slope equals -2

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

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.

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

∵ 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

Answer: x=4

Step-by-step explanation:

Answer:

x ax-s can be horizontal and top

y axis is bottom

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

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!

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).

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.

learn more about percentage here :

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#SPJ5

Answer:

-4+-6=-10

Step-by-step explanation:

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.

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

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].

Answer: If we multiply then I guess it’s 26*3=78 and 78*20=1,560

Step-by-step explanation:

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

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]

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.

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 !

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

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.

Learn more about De Moivre's theorem here:

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