A bus averages 2 miles per hour faster than a motorcycle. If the bus travels 165 miles in the same time it takes the motorcycle to travel 155 miles, then what is the speed of each?

Answer:

69.76

Step-by-step explanation:

The mean is the average of the numbers. It can be gotten by adding all the numbers, then divide by how many numbers available.

Variance (σ2) measure the spread between numbers in a data set. That is, it measures how far each number in the set is from the mean .

mean value can be computed using below expression

= ∑x(i)P(x(i))

= 3(0.10)+11(0.30)+19(0.20)+27(0.40)

= 18.2

Therefore, the mean value is 18.2

The variance can be calculated using below expression

variance

= ∑(x(i)-mean)^2 P(x(i))

= (3-18.2)^2 (.10) + (11-18.2)^2 (.30) + (19-18.2)^2 (.20)+(27-18.2)^2(0.40)

= 69.76

Therefore, the variance Vale is 69.76

Answer:

10,9.75,9.5,9.25,9, 8.75 , 8.5, 8.25, 8...

Step-by-step explanation:

Subtract 0.25 from each to find the next number

Answer:

8.25

Step-by-step explanation:

If you substract .25 from each number until you get to a8 you will get 8.25

Answer: [tex]-44\dfrac{4}{9}[/tex]

Step-by-step explanation:

The given expression: [tex]-36\dfrac{4}{9}-(-10\dfrac{2}{9})-(18\dfrac{2}{9})[/tex]

Here, [tex]36\dfrac{4}{9}=\dfrac{36\times9+4}{9}=\dfrac{328}{9}[/tex]

[tex](10\dfrac{2}{9})=\dfrac{92}{9}\\\\(18\dfrac{2}{9})=\dfrac{9\times18+2}{9}=\dfrac{164}{9}[/tex]

That is

[tex]-36(\dfrac{4}{9})-(-10\dfrac{2}{9})-(18\dfrac{2}{9}) = -\dfrac{328}{9}-(-\dfrac{92}{9})-\dfrac{164}{9}\\\\=-\dfrac{328}{9}+\dfrac{92}{9}-\dfrac{164}{9}\\\\=\dfrac{-328+92-164}{9}\\\\=\dfrac{-400}{9}\\\\=-44\dfrac{4}{9}[/tex]

[tex]\\ \sf\longmapsto 3x^2+5x-8-(2x^2-4x+3)[/tex]

[tex]\\ \sf\longmapsto 3x^2+5x-8-2x^2+4x-3[/tex]

[tex]\\ \sf\longmapsto 3x^2-2x^2+5x+4x-8-3[/tex]

[tex]\\ \sf\longmapsto x^2+9x-11[/tex]

Answer:

(3×2+5x-8)-(2×2-4x-3) = (6+5x-8)-(4-4x-3)

= 6+5x-8-4+4x+3

= -3+9x

Answer:

what do you mean ?? i don't understand it con you tell us the question

Answer:

[tex]\theta[/tex] =2mπ + π/3 for m ∈ Z.

Step-by-step explanation:

Given the equation [tex]2sin\theta - \sqrt{3} = 0[/tex], we are to find all the values of [tex]\theta[/tex] that satisfies the equation.

[tex]2sin\theta - \sqrt{3} = 0\\\\2sin\theta = \sqrt{3} \\\\sin\theta = \sqrt{3}/2 \\\\\theta = sin{-1} \sqrt{3}/2 \\\\\theta = 60^0[/tex]

General solution for sin[tex]\theta[/tex] is [tex]\theta[/tex] = nπ + (-1)ⁿ ∝, where n ∈ Z.

If n is an even number say 2m, then [tex]\theta[/tex] = (2m)π + ∝ where ∝ = 60° = π/3

Hence, the general solution to the equation will be [tex]\theta[/tex] = 2mπ + π/3 for m ∈ Z.

Answer:

-7/5≤d≤4∕5

Step-by-step explanation:

-1≤d+2/5≤6∕5

Subtract 2/5 from all parts

-1-2/5≤d+2/5-2/5≤6∕5-2/5

-5/5-2/5≤d+≤4∕5

-7/5≤d≤4∕5

Answer:

The critical value is 6.26.

Step-by-step explanation:

It is provided that there are 5 independent variables involved in a multiple regression model and the sample consist of 10 data points.

The critical value of F to test the significance of the model is:

[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]

Here,

k = number of independent variables

n = number of observations.

Then the critical value is:

[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]

                      [tex]=F_{\alpha, (5, 10-5-1)}\\=F_{0.05,(5, 4)}\\=6.2561\\\approx 6.26[/tex]

*Use a F-table.

Thus, the critical value is 6.26.

Answer: y=(4/3)x+2/3

Step-by-step explanation:

Slope-intercept form is expressed as y=mx+b

First, find the slope (m):

m= rise/run or vertical/horizontal or y/x (found between the highlighted points)

m = 4/3

Second, find b:

Use one of the highlighted points for (x, y)

2=4/3(1)+b

6/3=4/3+b

2/3=b

b=2/3

Plug it into the equation:

You get y=(4/3)x+2/3 :)

Answer:

4x-3 is the expression to your question

Answer:

3[tex]\leq[/tex]4x

Step-by-step explanation:

Hi

35/100= 140/ X

X = 100*140 /35

X= 14000/35

X= 400

There are 400 computer in the compagny.

9514 1404 393

Answer:

  1260

Step-by-step explanation:

The required number is the Least Common Multiple of the box sizes:

  LCM(20, 28, 36) = 4·5·7·9 = 1260

1260 pieces of fruit will be delivered so that none is left over.

Answer:

L = 29,550 mm (as per BS8110 the length is to the nearest 25)

Step-by-step explanation:

Lets make it so simple and easy.

Let A = 600mm

Let B = 300mm

Let C = 16 as number turns

Let d = 20mm

L = [tex]\sqrt{(3.14 * (600 - 20))^{2} + 300^{2}[/tex]  x 16

L = 29,550 mm (as per BS8110 the length is to the nearest 25)

Answer:

Step-by-step explanation:

Whenever you add two number x and -x and it becomes 0 . IT is the identity property.

Ex:

-1/3 + 1/3 = 0

-1 + 1 = 0

-58 + 58 = 0

Answer:

First Attachment : Option A,

Second Attachment : Option C

Step-by-step explanation:

We are given that,

z₁ = [tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))[/tex] and z₂ = [tex]4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]

Therefore if we want to determine z₁( z₂ ), we would have to find the trigonometric form of the following expression,

[tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))*4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]

( Combine expressions )

= [tex]12(\cos ( \pi /6+\pi / 3 ) + i\sin (\pi /6 +\pi / 3 )[/tex]

( Let's now add [tex]\pi / 6 + \pi / 3[/tex], further simplifying this expression )

[tex]\frac{\pi }{6}+\frac{\pi }{3} = \frac{\pi }{6}+\frac{\pi 2}{6} = \frac{\pi +\pi 2}{6} = \frac{3\pi }{6} = \pi / 2[/tex]

( Substitute )

[tex]12(\cos ( \pi /2 ) + i\sin ( \pi /2 ) )[/tex]

And therefore the correct solution would be option a, for the first attachment.

______________________________________________

For this second attachment, we would have to solve for the following expression,

[tex]\frac{3\left(\cos \left(\frac{\pi \:}{6}\right)+i\sin \left(\frac{\pi \:}{6}\right)\right)}{4\left(\cos \left(\frac{\pi \:}{3}\right)+i\sin \left(\frac{\pi \:}{3}\right)\right)}[/tex]

From which we know that cos(π/6) = √3 / 2, sin(π/6) = 1 / 2, cos(π/3) = 1 / 2, and sin(π/3) = √3 / 2. Therefore,

[tex]\:\frac{3\left(\cos \left(\frac{\pi }{6}\right)+i\sin \left(\frac{\pi }{6}\right)\right)}{4\left(\cos \left(\frac{\pi }{3}\right)+i\sin \left(\frac{\pi }{3}\right)\right)}:\quad \frac{3\sqrt{3}}{8}-i\frac{3}{8}[/tex]

[tex]\frac{3\sqrt{3}}{8}-i\frac{3}{8} = \frac{3\sqrt{3}}{8}-\frac{3}{8}i[/tex]

Our solution for the second attachment will be option c.

Answer:

Step-by-step explanation:

This is a bit ambiguous. I will answer it as (-4) - 3 = - 4 - 3 = - 7

However it could be (-4)(-3) = 12

Moral, with this editor use brackets.

Answer:

Step-by-step explanation:

speed is calculated using formula v=d/t

m= 7.5m

t= 3 min

v=?

v= 7.5m/3min

v= 2.5m/min

Answer:

(-3,-3)

B=(6-9,6+3)

Answer:

x=−5+√29 or x=−5−√29

Step

Let's solve your equation step-by-step.

x2+10x+10=14

Step 1: Subtract 14 from both sides.

x2+10x+10−14=14−14

x2+10x−4=0

For this equation: a=1, b=10, c=-4

1x2+10x+−4=0

Step 2: Use quadratic formula with a=1, b=10, c=-4.

x=

−b±√b2−4ac

2a

x=

−(10)±√(10)2−4(1)(−4)

2(1)

x=

−10±√116

2

x=−5+√29 or x=−5−√29

Answer:

March through August

Step-by-step explanation:

Ok, in order to solve this problem, we must start by building an equation to solve. The original equation was:

[tex]S=56.9-40.7cos (\frac{\pi}{6}t)[/tex]

and we need to figure out the months when the sales exceed 7700 units. Since the equation is given in hundreds of units, we need to divide those 7700 units into one hundred to get 77 hundred units. So we can go ahead and substitute that value in the equation:

[tex]77=56.9-40.7cos (\frac{\pi}{6}t)[/tex]

if you wish you can rewrite the equation so the variable is on the left side of it but it's up to you. So you get:

[tex]56.9-40.7cos (\frac{\pi}{6}t)=77[/tex]

and now we solve for t

[tex]-40.7cos (\frac{\pi}{6}t)=77-56.9[/tex]

[tex]-40.7cos (\frac{\pi}{6}t)=20.1[/tex]

[tex]cos (\frac{\pi}{6}t)=\frac{20.1}{-40.7}[/tex]

[tex]cos (\frac{\pi}{6}t)=-0.4938[/tex]

[tex]\frac{\pi}{6}t=cos^{-1}(-0.4938)[/tex]

[tex]\frac{\pi}{6}t=2.087[/tex]

[tex]t=\frac{2.087(6)}{\pi}[/tex]

[tex]t=3.98 months[/tex]

but there is a second answer to this problem. Notice that the function cos can be 2.87 at [tex]2\pi-2.087=4.1962 rad[/tex] as well, so we repeat the process:

[tex]\frac{\pi}{6}t=4.1962[/tex]

[tex]t=\frac{4.1962(6)}{\pi}[/tex]

[tex]t=8.014 months[/tex]

So now we need to determine on which period of times the number of items sold exceed 77 hundred units so we build different intervals for us to test:

(1,3.98)  (3.98,8.014) and (8,014, 13)

and find a test value for each of the intervals and test it.

(1,3.98) t=2

[tex]S=56.9-40.7cos (\frac{\pi}{6}(2))[/tex]

S=36.55

this is less than 77 so this is not our answer.

(3.98,8.014) t=5

[tex]S=56.9-40.7cos (\frac{\pi}{6}(5))[/tex]

S=92.15

this is more than 77 so this is our answer.

(8.014,13) t=10

[tex]S=56.9-40.7cos (\frac{\pi}{6}(10))[/tex]

S=36.55

this is less than 77 so this is not our answer.

so, since our answer is the interval (3.98,8.014)

this means that between the months of march and august we will be sellin more than 7700 units.

Answer:

M= 521.1 g

Step-by-step explanation:

1st.  Find the volume of the cube:   V=3³=27 cm³

As the weight of V= 1 cm³ cube  is 19.3 g the weight of the cube=27 cm³ is

M=27*19.3= 521.1 g

Answer:

12/155

Step-by-step explanation:

Total number of cookies:

Probability of getting a peanut butter cookie at first attempt is 9 out of 31:

Probability of getting a peanut butter cookie at second attempt is 8 out of 30 as one already taken and the total number has changed as well:

Probability of getting 2 peanut butter cookies is the product of each probability we got above:

Answer:

x = 38.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan x = 8/10

taking the inverse tan of each side

x = tan ^-1 (8/10)

x=38.65980825

To the nearest tenth

x = 38.7

Answer:

A. x < -3 or x > -3

Step-by-step explanation:

Let's start with the equation -4x + 60 < 72.

-4x + 60 < 72

First using the order of operations, subtract 60 from both sides.

-4x + 60 - 60 < 72 - 60

- 4x < 12

Next we want to divide -4 from both sides to isolate the variable.

-4x/-4 < 12/-4

x > -3

When you divide a negative number, always make sure the change the sign.

Solve the next equation, 14x + 11 < -31, the same way we solved the last.

14x + 11 < -31

Subtract 11 from both sides.

14x + 11 - 11 < -31 -11

14x < -42

Divide 14 from both sides.

14x/14 < -42/14

x < -3

The equations have different signs.

A. x < -3 or x > -3

Answer:

E(x)  [tex]= \frac{n+1}{2}[/tex]

Var(x) [tex]= \frac{1}{4} [ n - 1 ][/tex]

Step-by-step explanation:

Hint x = 1 + x1 + ......... Xn-1

[tex]X_{i} = \left \{ {{1} if the ith adjacent pair of magnets repel each other \atop {0} if ith adjacent pair of magnets join} \right.[/tex]

attached below is the detailed solutioN

usually like poles of magnets repel each other and unlike poles of magnets attract each other forming a block

Answer:

  71°

Step-by-step explanation:

Consider triangle BDH. x is the external angle that is remote to internal angles B and D, so is equal to their sum:

  x° = 41° +30°

  x° = 71°

Answer: 5 and 6

Step-by-step explanation:

X^2 - 11 = (X-1)^2

X^2 - 11 = X^2-2X+1

X^2 - X^2 + 2X = 11+1

2X = 12

X = 6

The preceding number is 5

(6)(6)=36 and (5)(5)=25

36-25=11

The number required is 6

If the number is multiplied by itself, it becomes x²

If the result is 11 greater than the preceding number when it is multiplied by itself is expressed as:

x² - 11  = (x - 1)²

x² - 11 = x² - 2x + 1

2x = 11 + 1

2x = 12

x = 6

Hence the number required is 6

Learn more on equation here: https://brainly.com/question/2972832

9514 1404 393

Answer:

  (√65)/7

Step-by-step explanation:

We can use the relation between the secant and the tangent:

  sec(θ)² = tan(θ)² +1

  sec(θ) = √(1 + (-4/7)²) = √(65/49)

  sec(θ) = (√65)/7 . . . . . . secant is positive in the 4th quadrant

Step-by-step explanation:

36 pages in 3 days, 36/3=12 pages per day.

45 pages in 5 days, 45/5=9 pages per day.

Difference is 3 pages per day

Answer:

Deon read 3 more  pages per day than Emily.