If each of the n production workers in a factory assembles one instrument every t minutes, how many instruments does the factory assemble in 7.5 hours of production

Answer:

9.8 units

Explanation:

According to Pythagoras theorem, the square of length of the hypotenuse is equal to the sum of squares of lengths of other two sides.

Let the third side be x units.

Then,

x² + 10² = 14²

=> x² + 100 = 196

=> x² = 196 - 100

=> x² = 96

=> x = √96

=> x = 4√6

=> x = 9.79....

=> x = 9.8 (Rounding to the nearest tenths)

So, the length of the third side is 9.8 units.

Answer:

Extraneous Solutions An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation. Example 1: Solve for x, 1 x − 2 + 1 x + 2 = 4 (x − 2) (x + 2).

Answer: 75%

Step-by-step explanation:

Only 9 students have taken fewer than 21 courses

9/12 = 0.75 or 75%

4x -8 > -40

Add 8 to both sides:

4x > -32

Divide both sides by 4:

X > -8

Answer: x > -8

Answer:

It is the diagram A

Answer:

The value of this number is 31.

Step-by-step explanation:

To solve this you could set up an equation and solve for x.

Sum means add, so you are going to add 2n and 13 to get 75.

2n + 13 = 75

Subtract 13 from both sides.

2n = 62

To get n alone, divide by 2 on both sides.

n = 31

The value of this number is 31.

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Answer:

x=24,y=33

hopefully this answer can help you to answer the next question

Answer:

A= 5 8 11

     7 10 13

     11 14 17

x=3 y=2 z=-1 w=1/2

Step-by-step explanation:

Let matrix A= a11 12 13

                      a21 a22 a23

                      a31 a32 a33

aij=2^i+3j

When i=1 and j=1,

aij=2^1+3*1=2+3=5

Solve for all the elements and you'll get,

A= 5 8 11

     7 10 13

     11 14 17

For no 7,

x+y  0           =       5    2w-1

1       x-y               z+2      1

Equating,

x+y =5       z+2=1     2w-1=0    x-y=1

x=5-y         z=-1        w=1/2      From 1st 5-y-y=1   -2y=-4 y=2

x=5-2(from last)

x=3

We know

[tex]\boxed{\sf cos\Theta=\dfrac{b}{h}}[/tex]

[tex]\\ \sf\longmapsto cos22=\dfrac{x}{47}[/tex]

[tex]\\ \sf\longmapsto 0.9=\dfrac{x}{47}[/tex]

[tex]\\ \sf\longmapsto x=47(0.9)[/tex]

[tex]\\ \sf\longmapsto x=42.3[/tex]

Answer:

2.07648468018

Step-by-step explanation:

Answer:

x = 16.6

Step-by-step explanation:

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

tan theta = opp / adj

tan 71 = x /5.7

5.7 tan 71 = x

x=16.55400

Rounding to the nearest tenth

x = 16.6

Answer:

3.398

Step-by-step explanation:

log(10) 2500 = log(10) (5^2*10^2) = log(10) 5^2 + log(10) 10^2 = 2*log(10) 5 + 2=3.398

Answer: x = 52

Step-by-step explanation:

You'd first deal with the 4 outside the parentheses, multiplying 10x-20 by 4. This would result in 40x - 80 = 200.

You'd then further isolate x, adding 80 on both sides, resulting in 40x = 2080. Divide by 40 on both sides and You'd get your answer of x = 52.

9 in 8956 = 900

9 in 95675 = 90000

9 = 9 in 124569

9 in 68795 = 90

90000 = 9 in 2549652.........

hope it helps...

Answer: 3 and 47/100

Step-by-step explanation:

Answer: He bought 20 ice cream bars and 14 popsicle

Step-by-step explanation:

To solve this I used the elimination method, you could use substitution as well

Here are our two equations

x+y=34 Because the total number of ice creams bought must be given to 34 children and no more

2x+5y=128 because that is the cost for each ice cream and the amount he spent

For the elimination method we have to cancel out one of the variables, I decided to cancel out the x, so I multiplied the top equation by -2. So i got -2x-2y=-68

2x+5y=128 Then we get

3y=60 so

y=20

Now we can go back to the first equation and plug in y.

x+20=34

  -20  -20

x=14

So he bought 14 popsicles and 20 ice cream bars.

Answer:

9.7959 sec

Step-by-step explanation:

For the arrow to reach the same height as the bow again, - 4.9x^2+48x=0, 48=4.9x, x=48/4.9=9.7959

The time arrow take to come back to a height even with his bow height is 9.79 seconds.

We have an equation of the height of the arrow with respect to time -[tex]y = -4.9x^{2} +48x[/tex] where y is the height of the arrow in meters above Andrew's bow and x is the time in seconds since Andrew shot the arrow.

We have to find out - how long it takes the arrow to come back to a height even with his bow height.

It is an example of two - dimensional Projectile motion.

We have the function that depicts the variation of height of the arrow with respect to time given by -

[tex]y=-4.9x^{2} +48x[/tex]

To find the time taken by the arrow to come to a height even with his bow height, we should equate y = 0.

[tex]y=-4.9x^{2} +48x=0\\-4.9x(x-9.79)=0\\-4.9x=0\;\;\;and\;\;\;x-9.79=0\\x =0\;\;\;and\;\;\;x=9.79[/tex]

Time cannot be 0, hence the time arrow take to come back to a height even with his bow height is 9.79 seconds.

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Answer:

6

Step-by-step explanations:

The remainder is what is left over after dividing whatever from d. So if you add one to d, then the remainder would increase from 5 to 6.

Hope this helps.

Answer:

864 ft³ is the volume

Step-by-step explanation:

Volume = width · height · length

= 12 · 9 · 8

= 864

Answer:

Step-by-step explanation:

Volume of rectangular solid = length * width * height

                                              = 9 * 12 * 8

                                              = 864 ft³

Answer:

Step-by-step explanation:

30

Answer:

Step-by-step explanation:

8) [tex]\sqrt{x^{3}} = x\sqrt{x}[/tex]

9) [tex]\sqrt[3]{3^{6} } = 3^{2} = 9[/tex]

10) [tex](x^{\frac{1}{2} } )^{9} = x^{2} \sqrt{x}[/tex]

11) [tex]7^{2} = 49[/tex]

12) [tex]27^{\frac{2}{3} } = \sqrt[3]{27} ^{2} = 9[/tex]

13) 9x[tex]\sqrt[3]{3xy^{2} }[/tex]

Answer:

hope this help

Step-by-step explanation:

Answer:

90

51

10

Step-by-step explanation:

Answer:

x=5.9

Step-by-step explanation:

tan(26)=x/12. x=12*tan(26)=5.9

Answer:

q = 3+1/2 r

Step-by-step explanation:

10q -5r = 30

Add 5r to each side

10q -5r+5r = 30+5r

10q = 30 +5r

Divide by 10

10q/10 = 30/10 +5r/10

q = 3+1/2 r

Answer:

Step-by-step explanation:

Answer:

7x the answer i think

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf -2 \ is \ not \ a \ solution}}[/tex]

Step-by-step explanation:

We are asked to check is -2 is the solution of the following equation.

[tex]2-x= 4x+3[/tex]

We must substitute -2 in for x and solve both sides of the equation. If the two sides are equal, then -2 is the solution.

[tex]2- (-2) = 4(-2)+3[/tex]

Solve both sides of the equation according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Let's start with the left side.

[tex]2+2= 4(-2)+3 \\[/tex]

[tex]4= 4(-2)+3[/tex]

Now solve the right side. Remember to multiply first.

[tex]4= -8+3[/tex]

[tex]4= -5[/tex]

[tex]4\neq -5[/tex]

4 is not equal to -5, so -2 is not the solution for this equation.

Step-by-step explanation:

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The image of this question is missing and so i have attached it.

Answer:

dd/dt = 4.47 ft/s

Step-by-step explanation:

From the image attached, let's denote the following;

d = horizontal distance beneath pulley

h = height of pulley

l = diagonal from the pulley to the head of the person

v = velocity of rope rising

Using pythagoras theorem;

l² = d² + h²

Differentiating with respect to time and considering h = c^(te) gives;

2l(dl/dt) = 2d(dd/dt)

We are given;

d = 20 ft

h = 10 ft

v = 4 ft/s

We know that velocity in this case is change in diagonal distance with time. Thus;

v = dl/dt = 4 ft/s

From earlier, we saw that;

2l(dl/dt) = 2d(dd/dt)

Thus, reducing it gives

(dl/dt)(l/d) = dd/dt

Now, l² = d² + h²

l = √(d² + h²)

Also, v = dl/dt = 4

Thus;

4(√(d² + h²))/d = dd/dt

4(√(20² + 10²))/20 = dd/dt

dd/dt = 4.47 ft/s