Josh works for a construction company that uses 150 pounds of gravel for each driveway they pour. He can buy a dump truck load with 30,000 pounds of gravel or a pick-up truck load with 2,500 pounds. Which amount should he buy so that no gravel is left after all of the driveways are poured and why?

Answer:

41 inches

Step-by-step explanation:

The formula for Area of a rectangle is ;

A = L × W

L = Length

W = Width

A rectangle has a length of 31 inches less than 3 times its width.

L = 3W - 31

If the area of the rectangle is 984 square inches, find the length of the rectangle

Hence,

984 = (3W - 31) × W

984 = 3W² - 31W

Hence

3W² - 31W - 984

3W(W - 24) + 4(W - 24) = 0

(3W + 41)(W - 24) = 0

W - 24 = 0

W = 24 inches

We have to find the Length

L = 3W - 31

L = 3(24) - 31

L = 72 - 31

L = 41 inches

The Length = 41 inches

The Length of the rectangle is 41 inches

Answer:

The probability is [tex]P(X>30)=0.75[/tex]

Step-by-step explanation:

We know that the probability of testing the fire alarm during this period is uniformly distributed that is [tex]X[/tex] ~ [tex]U(0,120)[/tex].

We need to find [tex]P(X>30)[/tex]

Given a continuous random variable [tex]X[/tex] with distribution :

[tex]X[/tex] ~ [tex]U(a,b)[/tex] , where ''[tex]a[/tex]'' and ''[tex]b[/tex]'' are real numbers

The probability density function is :

[tex]f_{X}(x)=\frac{1}{b-a}[/tex]    if x ∈ (a,b)

[tex]f_{X}(x)=0[/tex]  if x ∉ (a,b)

In the exercise we have [tex]X[/tex] ~ [tex]U(0,120)[/tex] , therefore the probability density function is :

[tex]f_{X}(x)=\frac{1}{120}[/tex] if x ∈ (0,120)

[tex]f_{X}(x)=0[/tex] if x ∉ (0,120)

If we want to find [tex]P(X>30)[/tex] we need to perform the integral

[tex]\int\limits^i_d {f_{X}(x)} \, dx[/tex]

Where [tex]d=30[/tex] and ''[tex]i[/tex]'' represents + ∞

Now, given that [tex]f_{X}(x)[/tex] is 0 when x ∉ (0,120), we will need to integrate between 30 and 120 to find the probability.

If we perform this integral ⇒

[tex]\int\limits^e_d {\frac{1}{120}} \, dx[/tex]

Where [tex]d=30[/tex] and [tex]e=120[/tex] ⇒

[tex]\int\limits^e_d {\frac{1}{120}} \, dx=\frac{3}{4}=0.75[/tex]

Answer:

2 teams are full and the last team has 8 members

Step-by-step explanation:

Simple subtraction 26-9=17 so theres one team, then 17 minus 9 is 8 so there is another team so the awnser is 2 and 8/9

Answer:

120

Step-by-step explanation:

solve for x then substitute

Answer:

m<WTS = 9 degrees

Step-by-step explanation:

<WTS = <TRS + <TSR  By exterior <'s

14x-6=7x-9+66             Substitute

7x=63                           Algebra

x=9

Answer:

distance from Houston to Galveston in  kilometers will be: 80km

Step-by-step explanation:

Given

The distance from Houston to  Galveston is about 50 miles.

i.e.

Kilometers in 1 Mile = 1.6 km

As the distance from Houston to  Galveston is about 50 miles, so

The distance from Houston to Galveston in  kilometers will be:

50(1.6) = 80   ∵ Kilometers in 1 Mile = 1.6 km

Therefore,

The distance from Houston to Galveston in  kilometers will be: 80km

Answer:

false, false, true

Step-by-step explanation:

0 times anything is always 0. 7 with an exponent of 3 is never 7*3, it's 7*7*7. for the last one, 2*2*2*2 is 16 and so is 4*4. lol im pretty dumb too tbh

Answer:

Universal set

Step-by-step explanation:

A universal set is a set which contains all the elements or objects of other sets, including its own elements. It is usually denoted by the symbol 'U'. Therefore, Set U has all the elements of Set A and Set B. ...

Answer:

y = 5x² + 3x

(5x) x (5x) = 25x

y = 25x + 3x

25x + 3x = 28x

y =/= 28x

( =/= )  <---- is supposed to be the non equal sign

144+ 18x=360

..............................

Answer:

They left the beach at 2:30

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'd suggest you find the two intercepts and draw a line through them.

y-intercept:  value of y when x = 0.  Here, f(0) = -15(0) + 4, so the y intercept is the point (0, 4).

x-intercept:  value of x when y = 0.  Letting f(x) = y = 0, we get

0 = -15x + 4, so that 15x = 4, and x = 4/15.  The x-intercept is (4/15, 0).

Plot the points (0, 4) and (4/15, 0) and draw a line thru them.

Answer: x=-1; x=-5

Step-by-step explanation:

1) [tex]-|x+3|=-2[/tex]

2)[tex]|x+3|=2[/tex]

3) [tex]x+3=2[/tex] or [tex]x+3=-2[/tex]

4) [tex]x=-1; x=-5[/tex]

Answer:

x = 60°

Step-by-step explanation:

Step 1:

Triangles = Equilateral Triangles           Given

Step 2:

3x = 180          Equation

Step 3:

x = 180 ÷ 3          Divide

Answer:

x = 60°

Hope This Helps :)

Answer:

-3=9/5c +32

-3*5c=9/5c*5c+32*5c

-15c=9+160c

-15c -160c =9

c(-15-160)=9

c(-15-160)/(-15-160)=9/(-15-160)

c=9/(-15-160)

Answer:  3 =92

               4 = 88

Step-by-step explanation: because angle 4 = 180-42+46 = 92 and angle 3 is 180-92 = 88

Answer:

∠3=88 , ∠4=92

Step-by-step explanation:

∠4 + 42° + 46° = 180° (angle sum property of a triangle)

∠4 + 88° = 180°

∠4 = 180° - 88°

∠4 = 92

∠3 + ∠4 = 180° (linear pair)

∠3 + 92° = 180°

∠3 = 180° - 92°

∠3 = 88°

Answer:

Step-by-step explanation:

Step one:

given data

length of rectangle= 24.5m

let the width be x

width of square= 14m

let the length be x

Step two:

we know that the area of a rectangle is

Ar= Length * width

Ar=24.5*x-----------1

Also, the area of the square is

As= Length * width

for square L=W

As= 14*14-----------------2

As=196m^2

equating 1 and 2 we have

14*14=24.5x

196=24.5x

divide both sides by 24.5

x=196/24.5

x=8m

The Breadth/width of the rectangular park is 8m

Answer:

The coordinate of [tex]Z[/tex] is 13.36.

Step-by-step explanation:

According to the statement, we have the following information:

[tex]\frac{XY}{XZ} = \frac{5}{12}[/tex] (1)

[tex]\frac{YZ}{XZ} = \frac{7}{12}[/tex] (2)

[tex]X = 0.4[/tex] (3)

[tex]Y = 5.8[/tex] (4)

From (2), we have the following expression:

[tex]YZ = \frac{7}{12}\cdot XZ[/tex]

[tex]Y-Z =\frac{7}{12}\cdot (X-Z)[/tex]

[tex]Y - Z = \frac{7}{12}\cdot X -\frac{7}{12}\cdot Z[/tex]

[tex]Y-\frac{7}{12}\cdot X = Z-\frac{7}{12}\cdot Z[/tex]

[tex]\frac{5}{12}\cdot Z = Y-\frac{7}{12}\cdot X[/tex]

[tex]5\cdot Z = 12\cdot Y-7\cdot X[/tex]

[tex]Z = \frac{12}{5}\cdot Y-\frac{7}{5}\cdot X[/tex] (5)

If we know that [tex]Y = 5.8[/tex] and [tex]X = 0.4[/tex], then the coordinate of [tex]Z[/tex] is:

[tex]Z = \frac{12}{5}\cdot (5.8)-\frac{7}{5}\cdot (0.4)[/tex]

[tex]Z = 13.36[/tex]

The coordinate of [tex]Z[/tex] is 13.36.

Answer:

32

Step-by-step explanation:

9514 1404 393

Answer:

  x = 1

Step-by-step explanation:

Subtracting 2 puts the equation in standard form:

  2x^2 +x -3 = 0

The product of the solutions is the ratio of the constant term to the leading coefficient: -3/2.

For solutions -3/2 and 'p', we have ...

  -3/2p = -3/2

  p = 1

The other solution is x = 1.

Answer:

since she subtracted 15 5 time a total of 5 rafts are needed

Step-by-step explanation:

Answer:

19.2

Step-by-step explanation:

12x1.6=19.2

Answer:

7.5 miles

Step-by-step explanation:

if one mile = about 1.6 km then you would take the 12 and divide it by 1.6 which will give u 7.5 miles

(also it says high school because of the grade you probably put in)

Answer: 8.75 is your answer

Answer:

8 3/4

Step-by-step explanation:

Answer:14 is H

Step-by-step explanation:

Answer:

3x+21 (H)

Step-by-step explanation:

9-3(3x-4)+12x

9-(9x-12)+12x

9-9x+12+12x

(9+12)+(-9x+12x)

21+3x or 3x+21