The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop machines and the other four have chosen desktop machines. Suppose that only two of the setups can be done on a particular day, and the two computers to be set up are randomly selected from the six (implying 15 equally likely outcomes; if the computers are numbered 1, 2,…, 6, then one outcome consists of computers 1 and 2, another consists of computers 1 and 3, and so on). a. What is the probability that both selected setups are for laptop computers

Answer:use a VPN and also write down your passwords, never keep them saved on your computer in case of a leak/breach of privacy and information

Step-by-step explanation:

Other than that all you got a do is download a VPN and also write your passwords and then proceed to be careful by not sharing any private/key info to identify who you are

Answer:

  0.148623∠321.93°

Step-by-step explanation:

You can work these without too much brain work by converting the coordinates to rectangular coordinates, adding those, then converting back to a vector length and angle as may be required.

  0.111∠90° + 0.234∠300° = 0.111(cos(90°), sin(90°)) +0.234(cos(300°), sin(300°))

  = (0, 0.111) + (0.117, -0.2026499) = (0.117, -0.0916499)

The magnitude of this is found using the Pythagorean theorem:

  |E+F| = √(0.117² +(-0.0916499)²)  ≈ 0.148623

The angle can be found using the arctangent function, paying attention to the quadrant. This sum vector has a positive x-coordinate and a negative y-coordinate, so is in the 4th quadrant.

  ∠(E+F) = arctan(y/x) = arctan(-0.0916499/0.117) ≈ -38.07° = 321.93°

The vector sum is E+F = 0.148623∠321.93°.

__

You can also draw the triangle that has these vectors nose-to-tail and find the magnitude of the sum using the Law of Cosines. The two sides of the triangle are the lengths of the given vectors and the angle between those can be seen to be 30°. Then the length of the 3rd side of the triangle is ...

  |E+F|² = |E|² +|F|² -2·|E|·|F|·cos(30°) = .012321 +.054756 -.044988 = 0.0220887

  |E+F| = √0.0220887 ≈ 0.148623

The direction of the vector sum can be figured from the direction of vector E and the internal angle of the triangle between vector E and the sum vector. That angle can be found from the law of sines to be ...

  (angle of interest) = arcsin(sin(30°)·|F|/|E+F|) = 128.07°

Then the angle of the vector sum is 450° -128.07° = 321.93°.

A diagram is very helpful for keeping all of the angles straight.

  |E+F| = 0.148623∠321.93°

Answer:

6

Step-by-step explanation:

Let's setup a proportion to find AB.

AB corresponds to A'B'.

BC corresponds to B'C'.

So setting up proportion this would look like:

[\tex]\frac{AB}{A'B'}=\frac{BC}{B'C'}[/tex]

[\tex]\frac{AB}{15}=\frac{3.8}{9.5}[/tex]

Cross multiply:

[tex]AB(9.5)=15(3.8)[/tex]

Divide both sides by 9.5:

[tex]AB=\frac{15(3.8)}{9.5)}[/tex]

Put into calculator:

[tex]AB=6[/tex]

Answer: AB=6 so A is correct, hope this help! Branliest would be awesome :)

Step-by-step explanation:

Since the larger rectangle and the smaller rectangle are essentially the same just bigger, they will be proportionate.

Therefore..

9.5/3.8=15/AB

You can cross multiply to find AB...

9.5AB=57

Divide 57 by 9.5 to separate AB, which you can think of like x...

AB=57/9.5

AB=6

Answer:

B. 259

Step-by-step explanation:

This is an exercise in PEMDAS, the order of mathematical operations:

Parentheses, Exponents, Multiplication and Division, Addition and Subtraction

Parentheses:          [(18 − 6)⋅3 + 1]⋅7

       Subtraction: = [(12)·3 +1]·7

    Multiplication: = [36 + 1]·7

            Addition: = [37]·7

Parentheses:       = 37·7

    Multiplication: = 259

Answer:

259

Step-by-step explanation:

Answer:

y = 107x + 20

Step-by-step explanation:

The points that represent the number of credits and the cost of those credits in coordinate form are (9, 983) and (13, 1411).

We can use the slope formula to first find the slope of the line containing those 2 points:

[tex]m=\frac{1411-983}{13-9}=\frac{428}{4}=107[/tex]

The slope is 107.  Now we can pick one of the 2 points and use it in the point-slope form of a line to get the equation we are looking for:

[tex]y-983=107(x-9)[/tex] simplifies to

[tex]y-983=107x-963[/tex] so in slope-intercept form:

y = 107x + 20

Answer:

  (4, -3)

Step-by-step explanation:

-2u +v = -2(-1, 5) +(2, 7) = (-2(-1)+2, -2(5)+7)

  = (4, -3)

Answer:

The y-intercept is (0,-407/5).

Step-by-step explanation:

The y-intercept can be found by setting x to 0 and solving for y.

10x-5y=407

10(0)-5y=407

   0-5y=407

     -5y=407

Divide both sides by -5:

       y=(407/-5)

       y=-407/5

The y-intercept is (0,-407/5).

Answer:

The probability of hitting the bullseye at least once in 6 attempts is 0.469.

Step-by-step explanation:

It is given that a mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt.

The probability of hitting bullseye in each attempt, p = 0.10

The probability of not hitting bullseye in each attempt, q = 1-p = 1-0.10 = 0.90

Let x be the event of  hitting the bullseye.

We need to find the probability of hitting the bullseye at least once in 6 attempts.

[tex]P(x\geq 1)=1-P(x=0)[/tex]       .... (1)

According to binomial expression

[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]

where, n is total attempts, r is number of outcomes, p is probability of success and q is probability of failure.

The probability that the dart thrower not hits the bullseye in 6 attempts is

[tex]P(x=0)=^6C_0(0.10)^0(0.90)^{6-0}[/tex]

[tex]P(x=0)=0.531441[/tex]

Substitute the value of P(x=0) in (1).

[tex]P(x\geq 1)=1-0.531441[/tex]

[tex]P(x\geq 1)=0.468559[/tex]

[tex]P(x\geq 1)\approx 0.469[/tex]

Therefore the probability of hitting the bullseye at least once in 6 attempts is 0.469.

Answer:

[tex]\large\boxed{x>-2+\sqrt{14}\ \vee\ x<-2-\sqrt{14}}\\\boxed{x\in(-\infty,\ -2-\sqrt{14})\ \cup\ (-2+\sqrt{14},\ \infty)}[/tex]

Step-by-step explanation:

[tex]x^2+4x>10\\\\x^2+2(x)(2)>10\qquad\text{add}\ 2^2=4\ \text{to both sides}\\\\x^2+2(x)(2)+2^2>10+4\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2>14\Rightarrow x+2>\sqrt{14}\ \vee\ x+2<-\sqrt{14}\qquad\text{subtract 2 from both sides}\\\\x>-2+\sqrt{14}\ \vee\ x<-2-\sqrt{14}[/tex]

Answer:

$1.45

Step-by-step explanation:

The cost of a dozen doughnuts in 1970 is $1.44.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

To calculate the cost of a dozen doughnuts in 1970 we have to know the percentage increase in the price index from 1960 to 1970 and this will be:

Rate = [(48.2 – 29.6) / 29.6] × 100%

Rate = (18.6 / 29.6) × 100%

Rate = 62.83 %

Let's represent the price of a dozen doughnuts in 1970 by X and solve. This will be:

62.83  = (X - 0.89) × 100 / 0.89

(62.83  × 0.89 ) = 100X - 89

55.9 = 100X - 89

100X = 144.9

X = 144.9 / 100

X = $1.44

X = $1.44

Therefore, the cost of a dozen doughnuts in 1970 is $1.44.

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Answer: Option B.

Step-by-step explanation:

Given the polynomial:

[tex]16x^2-36x+9[/tex]

 Observe that [tex]16x^2[/tex] and [tex]9[/tex] are perfect squares. Then, you can rewrite the polynomial in this form:

[tex](4x)^2-36x+(3)^2[/tex]

You can identify that:

[tex]A=4\\B=3[/tex]

Then, we can check if [tex]2AB=36[/tex]

 [tex]2(4x)(3)=36x\\\\24x\neq 36x\\\\2AB\neq36x[/tex]

Since [tex]2AB\neq36x[/tex], the polynomial [tex]16x^2-36x+9[/tex] IS NOT a perfect square trinomial of the form [tex]A^2 - 2AB + B^2[/tex]

Answer: B

Step-by-step explanation:

For this case we have by definition that the area of a parallelogram is given by:

[tex]A = b * h[/tex]

Where:

b: It's the base

h: It's the height

According to the data we have:

[tex]b = 38\ m\\h = 12 \ m[/tex]

Substituting in the formula:

[tex]A = 38 * 12\\A = 456[/tex]

The area of the parallelogram is [tex]A = 456 \ m ^ 2[/tex]

Answer:

[tex]A = 456 \ m ^ 2[/tex]

Answer:

A=456m²

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

Add the ratios together to get the sum of them is 19.  Since the perimeter is 380, divide 380 by 19 to get 20.  

The shortest side is 3(20) = 60,

the next side is 5(20) = 100, and

the longest side is 8(20) = 160

Answer:

5

Step-by-step explanation:

Since this is a rectangle, opposite sides are congruent.

That is, the perimeter in terms of w is:

(2w-1)+(2w-1)+(w)+(w)

or

2(2w-1)+2(w)

We can simplify this.

Distribute:

4w-2+2w

Combine like terms:

6w-2

We are given that the perimeter, 6w-2, is 28.

So we can write an equation for this:

6w-2=28

Add 2 on both sides:

6w   =30

Divide both sides by 6:

w   =30/6

Simplify:

w   =5

w is 5

Check if w=5, then 2w-1=2(5)-1=10-1=9.

Does 5+5+9+9 equal 28? Yep it does 10+18=28.

Answer:

w=5

Step-by-step explanation:

To find the perimeter of the rectangle

P = 2(l+w)

where w is the width and l is the length

Our dimensions are w and 2w-1 and the perimeter is 28

Substituting into the equation

28 = 2(2w-1 +w)

Combining like terms

28 = 2(3w-1)

Divide each side by 2

28/2 = 2(3w-1)/2

14 = 3w-1

Add 1 to each side

14+1 = 3w-1+1

15 = 3w

Divide each side by 3

15/3 =3w/3

5 =w

Answer:

  neither

Step-by-step explanation:

The number of laps John has run is 3 + the number of laps David has run. That is, both numbers are not zero at the same time, so the relationship cannot be proportional.

The numbers have a constant difference, not a constant product, so they are not inversely proportional, either.

David's laps and John's laps are neither proportional nor inversely proportional.

The relationship between the number of laps David runs and the number of laps John has run is proportional because they increase at the same rate, with John always maintaining a 3-lap lead.

The question asks whether the relationship between the number of laps that David runs and the number of laps that John has run is proportional, inversely proportional, or neither. Since John and David are running at the same speed, but John started with a 3-lap lead, the relationship is linear. The more laps David runs, the more John runs as well, maintaining a constant gap of 3 laps. Thus, this scenario illustrates a proportional relationship where the number of laps run by each, ignoring the start difference, increases at the same rate. This relationship can be represented by a linear equation like y = x + 3, where x is the number of laps David runs, and y is the number of laps John runs.

Answer:

[tex]w=\frac{A}{l}[/tex]

Step-by-step explanation:

The formula to find the area of a rectangle is: [tex]A=w \times l[/tex], where [tex]w[/tex] is width and [tex]l[/tex] is length.

So, if we knoe the area [tex]A[/tex] and the length [tex]l[/tex], we can find the width with the formula

[tex]w=\frac{A}{l}[/tex]

You can get this answer by using the defintion of area, which is the first equation, and isolating [tex]w[/tex].

Remember, when we want to move a factor to the other side of the equalty, we must pass it with the opposite operation. So, in this case, width was multiplying, and it passed to the other side dividing.

Therefore, the answer here is [tex]w=\frac{A}{l}[/tex]

The answer is 40 shirts.

Explanation

Equation: y= ((616-(14*12))/16)+12

First, multiply the 12*14 because we know that 12 shirts were $14. You'll get $168. Next, subtract that from 616, the total number of dollars, to get the 12 shirts out of the way. Your answer will be $448. Then, divide by 16 because that's the remaining money that was spent on the $16 shirts. You'll get 28 shirts. However, we can't forget about the dozen $14 shirts, so add 12 to your answer and you get 40 shirts.

Answer: [tex]278\°14'24''[/tex]

Step-by-step explanation:

 You know that:

[tex]1\ hour=60\ minutes\\\\1\ minute=60\ seconds[/tex]

Then, in order to convert the given decimal degree to Degrees Minutes Seconds (DMS), you need to follow these steps:

1) The whole number  278 gives you the degrees.

2)  Multiply 0.24 by 60:

[tex]0.24*60=14.4[/tex]

The whole number 14 gives you the minutes.

3)  Multiply 0.4 by 60:

[tex]0.4*60=24[/tex]

This gives you the seconds.

Therefore, 278.24 written in DMS form is:

[tex]278\°14'24''[/tex]

Answer:

The answer is 278°14'24''

Step-by-step explanation:

Given :  278.24

To find : written in DMS form.

Solution : We have given that 278.24

Multiply 24 by 60 to convert it into minute

We can write it as  278 + .24(60).

278°14.4'

Rewrite 278°14+.4'

4' = 4 ( 60) to convert minute in to second.

278°14+.4(60)

278°14'24''

The answer is 278°14'24'' ....

Answer:

50 degrees

Step-by-step explanation:

The measure of an inscribed angle of a circle is half the degree measure of the intercepted arc.

m<Q = (1/2)m(arc)RS

m<Q = (1/2)(100 degrees)

m<Q = 50 degrees

Answer:

∠Q = 50°

Step-by-step explanation:

An inscribed angle whose vertex lies on a circle and whose sides are two chords of the circle is one half the measure of its intercepted arc.

arc RS is the intercepted arc, hence

∠Q = 0.5 × 100° = 50°

Answer:

There are 15 partitions of 7.

Step-by-step explanation:

We are given that a partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the numbers in the sum .

We have to find the partition of 7

We are given an example

Partition of 4

4=4

4=3+1

4=2+2

4=1+2+1

4=1+1+1+1

There are five partition of 4

In similar way  we are finding  partition of 7

7=7

7=6+1

7=5+2

7=5+1+1

7=3+3+1

7=3+4

7=4+2+1

7=3+2+2

7=4+1+1+1

7=3+1+1+1+1

7=2+2+2+1

7=3+2+1+1

7=2+2+1+1+1

7=2+1+1+1+1+1

7=1+1+1+1+1+1+1

Hence, there are 15 partitions of 7.

Answer:

Bonnie needs [tex]67.8\ in[/tex] of ribbon

Step-by-step explanation:

we know that

A Kite is a quadrilateral that has two pairs of equal sides

so

To find out how much ribbon Bonnie needs calculate the perimeter of the kite

[tex]P=2(L1+L2)[/tex]

where

L1 is the length of one side

L2 is the length of the other side

[tex]P=2(13.2+20.7)=67.8\ in[/tex]

Answer:

546 nuts

Step-by-step explanation:

727272 / 666 = 1092 nuts in each location

crow stole half nuts in 1 location

1092 / 2 = 546 nuts stolen

Answer:

6 nuts.

Step-by-step explanation:

The number of nuts in each location  is 72 / 6 = 12 nuts.

So the crow stole 1/2 * 12 = 6 nuts.

Answer:

The tip of the man shadow moves at the rate of [tex]\frac{20}{3} ft.sec[/tex]

Step-by-step explanation:

Let's draw a figure that describes the given situation.

Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.

Here it forms two similar triangles.

Let's find the distance "y" using proportion.

From the figure, we can form a proportion.

[tex]\frac{y - x}{y} = \frac{6}{15}[/tex]

Cross multiplying, we get

15(y -x) = 6y

15y - 15x = 6y

15y - 6y = 15x

9y = 15x

y = [tex]\frac{15x}{9\\} y = \frac{5x}{3}[/tex]

We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).

[tex]\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt}[/tex] ----(1)

We are given [tex]\frac{dx}{dt} = 4 ft/sec[/tex]. Plug in the equation (1), we get

[tex]\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec[/tex]

Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.

To find the speed at which the tip of the man's shadow is moving, we need to solve a proportional relationship between the length of the shadow and the distance of the man from the pole. Using similar triangles and setting up a ratio, we can find the length of the shadow and then find its rate of change with respect to time. The tip of the shadow is not moving when the man is 45 ft from the pole.

To solve this problem, we need to use similar triangles. Let's call the length of the shadow x. The height of the pole is 15 ft and the height of the man is 6 ft. So, we can set up the following ratio:

15 / x = 6 / (x + 45)

To find x, we can cross-multiply:

(15)(x + 45) = 6x

Now, we can simplify and solve for x:

15x + 675 = 6x

9x = 675

x = 75 ft

To find the rate of change of the shadow's tip, we can take the derivative of x with respect to time:

dx/dt = 0

So, the tip of the shadow is not moving when the man is 45 ft from the pole.

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Answer:

  sin(2x) = 120/169

Step-by-step explanation:

A suitable calculator can figure this for you. (See below)

__

You can make use of some trig identities:

Then your function value can be written as ...

  sin(2x) = 2sin(x)cos(x) = 2(sin(x)/cos(x))cos(x)² = 2tan(x)/sec(x)²

  = 2tan(x)/(tan(x)² +1)

Filling in the given value for tan(x), this is ...

  sin(2x) = 2(12/5)/((12/5)² +1) = (24/5)/(144/25 +1) = (120/25)/((144+25)/25)

  sin(2x) = 120/169

Answer:

C [tex]P(v)=2(v+7)[/tex]

Step-by-step explanation:

Lets say that [tex]P(v)=y[/tex] for simplicity.

In order to find the inverse of a function, we must switch the location of the variable, v, and y. Then we have to solve for y.

As we are already given the inverse, doing the same process again will give us the original function.

First we can set up the equation

[tex]y=\frac{1}{2} v-7[/tex]

Next we can switch the location of the variables

[tex]v=\frac{1}{2} y-7[/tex]

Now we can solve for y

[tex]v=\frac{1}{2} y-7\\\\v+7=\frac{1}{2} y\\\\y=2(v+7)\\\\P(v)=2(v+7)[/tex]

This gives us the function

[tex]P(v)=2(v+7)[/tex]

Answer:

C P(v) = 2(v+7)

Step-by-step explanation:

To find P(v), we need to take the inverse of P^-1 (v)

y = 1/2 v-7

Exchange y and v

v = 1/2 y-7

Solve for y

Add 7 to each side

v+7 = 1/2 y -7+7

v+7 = 1/2y

Multiply each side by 2

2(v+7) = 1/2 y*2

2(v+7) = y

P(v) = 2(v+7)

Answer:

one large box is 40 pounds

one small box is 30 pounds

Step-by-step explanation:

let large be l and small be s ,

l + s = 70 ------- equation1

70l + 55s. = 4450 ------- equation 2

equation 1 multiply by 55,

55l + 55s = 3850 ------ equation 3

equation 3 - equation 2 ,

(70l + 55s) - (55l +55s) = 4450 - 3850

70l + 55s - 55l - 55s = 4450 - 3850

15l = 600

l = 40

sub l = 40 into equation 1

40 + s = 70

s = 70 - 40

s = 30

Answer:

  $46,141.71

Step-by-step explanation:

This looks about right, based on weekly deposits for the duration. However, I cannot vouch for it entirely, as the number of weekly deposits in 15 years will actually be 782.

_____

Computing this by hand doing the initial balance separately from the weekly deposits, I get a total of $46,252.10 using 782 weekly deposits. For that purpose, I tried to figure an equivalent weekly interest rate given monthly compounding and the fact there are 52 5/28 weeks in a year on average.

I suspect the only way to get this to the cent would be to build a spreadsheet with payment dates and interest computation/payment dates. Some months, there would be 5 deposits between interest computations; some years there would be 53 deposits.

The value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1

According to the law of base change

[tex]\rm \log _b a = \dfrac{ log _d b}{log_d a}[/tex]

The given expression is

[tex]\rm { log _3 5}\times{log_{25} 9}[/tex]

This can be written as

[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 9 }{log_{10} 3*log _{10}25}[/tex]

[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 3^2 }{log_{10} 3*log _{10}5^2}[/tex]

[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *2log _{10} 3 }{log_{10} 3* 2 log _{10}5}[/tex]

On solving this the value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

This equation is a positive parabola, opening upwards.  Parabolas of this type have a vertex that is a minimum value.  In order to find the year where the population was the lowest, we have to complete the square to find the vertex.  The rule for completing the square is to first set the parabola equal to 0, then next move the constant over to the other side of the equals sign.  The leading coefficient on the x-squared term HAS to be a positive 1.  Ours is a .5, so will factor it out.  Doing those few steps looks like this:

[tex].5(t^2-19.3t)=-100[/tex]

Next we take half the linear term, square it, and add it to both sides.  Don't forget the .5 sitting out front there as a multiplier.  Our linear term is 19.3.  Taking half of that gives us 9.65, and 9.65 squared is 93.1225

[tex].5(t^2-19.3t+93.1225)=-100+46.56125[/tex]

In this process, we have created a perfect square binomial on the left.  Stating that binomial and doing the addition on the right looks like this:

[tex].5(t-9.65)^2=-106.8775[/tex]

Now finally we will divide both sides by .5 then move over the constant again to get the final vertex form of this quadratic:

[tex](t-9.65)^2+106.8775=y[/tex]

From this we can see that the vertex is (9.65, 106.8775) which translates to the year 2009 and 107,000 approximately.

In our situation, that means that the population was at its lowest, 107,000 in the year 2009.

For part b. we will replace the y in the original quadratic with a 200,000 and then factor to find the t values.  Setting the quadratic equal to 0 allows us to factor to find t:

[tex]0=.5t^2-9.65t-199900[/tex]

If you plug this into the quadratic formula you will get t values of

642.02 and -622.72

The two things in math that will never EVER be negative are distances/measurements and time, so we can safely disregard the negative value of t.  Since the year 2000 is our t = 0 value, then we will add 642 years to the year 2000 to get that

In the year 2642, the population in this town will reach 200,000 (as long as it grows according to the model).

Answer:

Step-by-step explanation:

A graph shows the only real zero to be at x = 3.

Factoring that out gives the quadratic whose vertex form is ...

  y = (x -10)² +1

The roots of this quadratic are the complex numbers x = 10 ± i.

_____

For y = (x -10)² +1, the zeros are ...

  (x -10)² +1 = 0

  (x -10)² = -1 . . . . . . . . . . subtract 1

  x -10 = ±√(-1) = ±i . . . . .take the square root

  x = 10 ± i . . . . . . . . . . . . add 10

Answer:

3, 10±i

Step-by-step explanation:

Given is a function [tex]f(x) = x^3 - 23x^2 + 161x -303.[/tex]

By rational roots theorem, this can have zeroes as ±1, ±3,±101

By trial and error checking we find f(3) =0

Hence x-3 is a factor

f(x) = [tex](x-3)(x^2-20x+101)[/tex]

II being a quadratic equation we find zeroes using formula

[tex]x=\frac{20±\sqrt{400-404} }{2} =10+i, 10-i[/tex]

zeroes are 3, 10±i