find the slope of a line parallel to y=(2/5)x + (4/5)

Answer: -8

Step-by-step explanation:

Answer:

It will take them approximately 51.43 minutes to complete the project together

Step-by-step explanation:

This is what is called a "shared job" problem.

The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.

So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project

Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.

We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).

Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.

In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:

[tex]\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min[/tex]

So it will take them approximately 51.43 minutes to complete the project together.

Answer:

sorry i meant c

Step-by-step explanation:

Answer:

a = 35º

b = 140º

c = 40º

d = 140º

e = 58º

Step-by-step explanation:

Angle A is supplementary to the angle that is 145º, and supplementary angles always add up to 180º. Therefore, 180 - 145 = 35, the measure of angle a. Angle B is supplementary to the 40º angle, so its measure is 140. Angle C is opposite the 40º angle, and opposite angles are congruent, so its measure would also be 40º. Angle D is also 140º because it is opposite of angle B. Angle E is supplementary to the angle that measures 122º, so 180 - 122 = 58. Hope this helped!

Answer:

17.3 Inches

Step-by-step explanation:

Given that the diagonal of a cube = 30 inches

For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]

Therefore:

[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]

Side Length of the cube is 17.3 Inches.

Answer:

17.3

Step-by-step explanation:

Edge 2020

Answer:

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Step-by-step explanation:

Answer:

The quarter circle's area is 38.47 yard²

Step-by-step explanation:

The area of a full circle is pi * r ²

The area of a quarter circle is 1/4 * pi * r ²

Given:

Use 3.14 for pi

Round to the nearest hundredths.

Perimeter of quarter circle is 24.99 yards

For r you must leave it as 'r' because we do not know it for now...

1. Circumference of a full circle = 2* pi * r

2. 1/4 * ( 2 * pi * r )

1/4 * ( 2 * 3.14 * r )

1/2 * 3.14 * r

1.57 * r

3 Since r = 'r'

We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.

4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch

1.57 * r + 2 * r = 24.99

( 1.57 + 2 ) * r = 24.99

3.57 * r = 24.99

Divide left and right of the = sign by 3.57

3.57 / 3.57 * r = 24.99 / 3.57

1 * r = 24.99 / 3.57

r = 7

The area of a quarter circle is 1/4 * pi * r ²

1/4 * pi * 7²

1/4 * 49 * pi

49/4 * pi

49/4 * 3.14

38.465

Round to the nearest hundredths gives 38.47 yard²

The quarter circle's area is 38.47 yard²

Answer:

2 x [tex]\pi[/tex] x 10.7 = 67.2

Step-by-step explanation:

Step-by-step explanation:

c=2πr

c=2×π×10.7m

c=67.2m

so about 67

Step-by-step explanation:

area of parallelogram= height * length of base

Answer:

a) The function is [tex]f(x,y,z) = xyz+2z^2[/tex]

b) The value of the integral is 18

Step-by-step explanation:

a) We are given that [tex] F(x,y,z) (yz,xz,xy+4z)[/tex]. We want to find a function f such that the gradient of f is F. That is [tex]\nablda f = F[/tex] . Suppose that such f does exist, if that is the case, then by definition of the gradient, we have that

[tex] F(x,y,z) = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/tex]

From here, we have that

[tex] yz = \frac{\partial f}{\partial x}[/tex]

if we integrate both sides with respect to x, we get that

[tex] f(x,y,z) = xyz+ g(y,z)[/tex]

where g is a function that depens on y and z only. Now, we differentiate this equation with respect to y and make it equal to the 2nd component of F. That is

[tex] xz + \frac{\partial g}\partial{y} = xz[/tex]

This implies that [tex]\frac{\partial g}{\partial y} =0[/tex]. This means that g actually depends only on z. Until now, f is of the form

[tex] f(x,y,z) = xyz+g(z)[/tex]

If we repeat the previous step, by differentiating with respect to z and making it equall to the third component of F we get

[tex] xy + \frac{\partial g}{\partial z} = xy + 4z[/tex]

This implies that [tex] \frac{\partial g}{\partial z} = 4z[/tex] . If we integrate both sides with respect to z, we get that [tex] g(z) = 2z^2[/tex]

So f is of the form [tex] f(x,y,z) = xyz+2z^2[/tex]

b) To calculate the integral over the given segment, we can use the function f. Since the path is from (1,0,-2) to (6,4,1), then the value of the integral is given by evaluatin f at the end point and the substracting the value of f at the start point, that is

[tex] \int_C F \cdot dr = f(6,4,1) -f(1,0,-2) = 24+2(1)^2- (0+2(-2)^2)) = 18[/tex]

Answer:

[tex]<38,52>[/tex]

Step-by-step explanation:

[tex]u=<4,-3>\\v=<-2,5>\\w=<0,-6>[/tex]

We are required to express 7u-5v+w in the form <a,b>.

[tex]7u-5v+w =7<4,-3>-5<-2,5>+<0,-6>\\=<28,-21>-<-10,25>+<0,-6>\\=<28-(-10)+0, -21-25-6>\\=<38,52>\\$Therefore:$\\7u-5v+w=<38,52>[/tex]

Answer:

P(greater than 1.25 minutes) = 0.8611 (Approx)

Step-by-step explanation:

Given:

Waiting time = 0 - 9 minutes

Find:

Probability that selected passenger has a waiting time greater than 1.25 minutes.

Computation:

⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =

⇒  P(greater than 1.25 minutes) = [9-1.25] / 9

⇒ P(greater than 1.25 minutes) = [7.75] / 9

⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)

Answer:

x = -1 and y = 1/2

Step-by-step explanation:

Let u = 1/x, and v = 1/y

Then the pair of equations

-3/x + 4/y = 11

1/x - 2/y = -5

Can be written as

-3u + 4v = 11 .................................(1)

u - 2v = -5......................................(2)

From (2)

u = 2v - 5 .......................................(3)

Substituting (3) into (1)

-3(2v - 5) + 4v = 11

-6v + 15 + 4v = 11

-6v + 4v = 11 - 15

-2v = -4

v = 4/2 = 2

Substituting this value of v in (3)

u = 2v - 5

u = 2(2) - 5

= 4 - 5

= -1

That is

u = -1, v = 2

Since u = 1/x, and v = 1/y, we have

1/x = -1

=> x = -1

And

1/y = 2

=> y = 1/2

Therefore

x = -1 and y = 1/2

Answer:

#1

Step-by-step explanation:

The four yellow boxes represent x so together they are 4 * x or 4x. The blue boxes seem to represent -1 and since there are three of them together they are -1 * 3 = -3. 4x + (-3) = 4x - 3.

Answer:

The number of the possible outcomes are:

12,13,14,15,16,17

21,23,24,25,26,27

31,32,34,35,36,37

41,42,43,45,46,47

51,52,53,54,56,57

61,62,63,64,65,67

71,72,73,74,75,76

The total number of possible outcomes = 42

Step-by-step explanation:

Given that :

the numbers 1 through 7 are written on different pieces of paper; &

Two of these numbered pieces of paper are selected without replacement;

Also,

a 2-digit number is formed using the first number drawn in the tens place and the second number drawn used in the ones place.

Then:

if the first number drawn is 1 , then the possible outcomes will be :

12,13,14,15,16,17

If the  first number drawn is 2; then the possible outcomes will be:

21,23,24,25,26,27

If the  first number drawn is 3; then the possible outcomes will be:

31,32,34,35,36,37

If the  first number drawn is 4; then the possible outcomes will be:

41,42,43,45,46,47

If the  first number drawn is 5; then the possible outcomes will be:

51,52,53,54,56,57

If the  first number drawn is 6; then the possible outcomes will be:

61,62,63,64,65,67

If the  first number drawn is 7; then the possible outcomes will be:

71,72,73,74,75,76

The number of the possible outcomes are:

12,13,14,15,16,17

21,23,24,25,26,27

31,32,34,35,36,37

41,42,43,45,46,47

51,52,53,54,56,57

61,62,63,64,65,67

71,72,73,74,75,76

The total number of possible outcomes = 7 × 6 = 42

Answer:

(B) Centers: The crocodiles have a greater median length than the alligators

(C) Spreads: The lengths of the alligators are more spread out

Step-by-step explanation:

The question is incomplete without the diagram. Find attached the diagram used in solving the question

Centers: this is the median of the distribution

Spread: this is the variation of the data distribution. The range can be used to find the spread. If the range is large, the spread is larger and If the range is small, the spread is smaller.

Range = highest value - lowest value

From the diagram:

Median of crocodile = 17

Median of the alligator = 9

Therefore, for Centers: The crocodiles have a greater median length than the alligators (option B)

Spread for crocodile data = from 15 to 19

Range = 19-15 = 4

Spread for alligator data = from 7 to 15

Range = 15-7 = 8

For Spreads: The lengths of the alligators are more spread out.

Answer: b and c

Step-by-step explanation:

Answer:

The equation are

    [tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]

    [tex]y = \frac{12-z }{12} 8sin (2z)[/tex]

    z = z

Step-by-step explanation:

From the question we are told that

   The radius of the conical helix is  [tex]r= 8[/tex]

    The height of the conical helix is  [tex]h = 12[/tex]

    The angular frequency  is  [tex]w = 2[/tex]

The plot of the conical helix is  shown on the first uploaded image

 Generally  the parametric equation of a conical helix is mathematically represented as

for x -axis

     [tex]x =\frac{ h-z }{h} r cos (wz)[/tex]

substituting values

      [tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]

for  y-axis

     [tex]y = \frac{h-z }{h} rsin (wz)[/tex]

substituting values

      [tex]y = \frac{12-z }{12} 8sin (2z)[/tex]

for  z-axis

   z = z

Answer:

  M(h) = 73.18025h

Step-by-step explanation:

The composite function is ...

  M(B(L(h))) = M(B(28.75h)) = M(1.78(28.75h)) = M(51.175h)

  = 1.43(51.175h) = 73.18025h

The composite function is ...

  M(h) = M(B(L(h))) = 73.18025h

Answer:

a

Step-by-step explanation:

Answer:

Per hour: 2.40740740741

Step-by-step explanation:

you have to divided 65 and 27 so

65/27

which is 2.40740740741

Answer:

Sqrt(13)

Step-by-step explanation:

d = sqrt(3^2 + 2^2) = sqrt (13)

Answer:

96

Step-by-step explanation:

Rectangle area:

(8)(10)=80

Triangle area:

(1/2)(4)(8)=16

Total area:

16+80=96

Answer:

[tex]96 {ft}^{2} [/tex]

Step-by-step explanation:

[tex]area = \frac{1}{2} (a + b)h \\ = \frac{1}{2} \times (10 + 14) \times 8 \\ = \frac{1}{2} \times 24 \times 8 \\ = 96 {ft}^{2} [/tex]

Answer:

The amount of heat lost by the aluminum is 31,500 J

Step-by-step explanation:

Given;

mass of aluminum, m =  500 g

initial temperature of the aluminum, θ₁ = 100° C

final temperature of the aluminum, θ₂ = 30°C

specific heat capacity of water, C = 4.18 J/g °C

specific heat capacity of aluminum , C = 0.90 J/g

Heat lost by the aluminum is equal to heat gained by the water.

The amount of heat lost by the aluminum, is calculated as;

Q = MCΔθ

Q = 500 x 0.9 (100 - 30)

Q = 500 x 0.9 x 70

Q = 31,500 J

Therefore, the amount of heat lost by the aluminum is 31,500 J

Answer:

30 mph

Step-by-step explanation:

Distance travelled=300 miles

Time travelled=10hours

At a constant rate,k

Let distance travelled=d

Time travelled=t

Then,

d=kt

300=k*10

300=10k

k=300/10

=30

k=30mph

30 miles per hour

30 MPH                                                                                       ............................................................................................................

Answer:

The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they are willing to pay more for the service, or they are not. Customers are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

40% of the customers are willing to pay more for the service.

This means that [tex]p = 0.4[/tex]

Now we have selected 10 customers randomly.

This means that [tex]n = 10[/tex]

What are the expected value and standard deviation

[tex]E(X) = np = 10*0.4 = 4[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.4*0.6} = 1.55[/tex]

The expected number of customers that pay more for the service is 4 and the standard deviation is 1.55.

Answer:

54 square units

Step-by-step explanation:

The formula for the area of a triangle is:

[tex]\frac{1}{2}[/tex] x base x height

The base is 12

The height is 9

So 1/2 x 12 x 9 = 54 square units

Answer:

8 and 64

Step-by-step explanation:

[tex]2^3[/tex] and [tex]4^3[/tex]

[tex]2^3=8[/tex]

[tex]4^3=64[/tex]

For (2,6) the 2 is the x value which is the left/right position and 6 is the y value which is the up/down position.

Moving 2 units to the right, you would add 2 to the x value. Moving 3 units down you would subtract 3 from the y value.

The answer would be (4,3)

Answer:

c) 81.5

Step-by-step explanation:

Listing the 25 ages in crescent order:

60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92

The upper or third quartile's position is given by:

[tex]Q_3=N_{\frac{3}{4}(n+1)}\\Q_3}=N_{\frac{3}{4}(25+1)}=N_{19.5}[/tex]

This means that the third quartile is the average between the 19th and 20th numbers:

[tex]Q_3=\frac{81+82}{2} \\Q_3 = 81.5[/tex]

The upper quartile is 81.5.

Answer:

4

Step-by-step explanation:

T(n) = n² + 3

T(1) = 1² + 3 = 1 + 3 = 4

Answer:

Step-by-step explanation:

To find the average rate of change, find the change in function value, and divide that by the length of the interval.

1. ((g(1) -g(-1))/(1 -(-1)) = ((-4·1³ +4) -(-4(-1)³ +4)/(2) = (-8)/2 = -4

The average rate of change of g(x) on [-1, 1] is -4.

__

2. ((g(3) -g(-2))/(3 -(-2)) = ((6·3³ +3/3²) -(6·(-2)³ +3/(-2)²))/5

  = (6·27 +1/3 -6·(-8) -3/4)/5 = (2515/12)/5

  = 503/12 = 41 11/12

The average rate of change of g(x) on [-2, 3] is 41 11/12.

Answer:

4: 4[tex]\pi^2[/tex]

Step-by-step explanation:

2[tex]\pi[/tex] x 5 x [tex]x[/tex] = 10[tex]\pi x[/tex]

10[tex]\pi x[/tex] = 40[tex]\pi ^3}[/tex]

x = 4[tex]\pi^2[/tex]

Answer:

4π units

Step-by-step explanation:

v=lwh

40π^3=2π×5×h

40π^3=10π^2×h

h=40π^3/10π^2

h=4π units

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