the average mass of 9 boys is 50 kg. what is their total mass​

For the given vectors u and v:

u = (-1, 6)

v = (6, 9)

u · v = 48

d(u, v) = √58

Given:

u = (-1, 6)

v = (6, 9)

1. Magnitude of u:

The magnitude (length) of vector u is calculated as follows:

|u| = √(u₁² + u₂²)

|u| = √((-1)² + 6²)

|u| = √(1 + 36)

|u| = √37

So, the magnitude of u is √37.

2. Magnitude of v:

The magnitude of vector v can be calculated similarly:

|v| = √(v₁² + v₂²)

|v| = √(6² + 9²)

|v| = √(36 + 81)

|v| = √117

So, the magnitude of v is √117.

3. Dot product of u and v:

The dot product of two vectors is given by the formula:

u · v = u₁ * v₁ + u₂ * v₂

u · v = (-1 * 6) + (6 * 9)

u · v = -6 + 54

u · v = 48

Therefore, the dot product of u and v is 48.

4. Distance between u and v:

The distance between two points u and v can be calculated using the formula:

d(u, v) = √((v₁ - u₁)² + (v₂ - u₂)²)

d(u, v) = √((6 - (-1))² + (9 - 6)²)

d(u, v) = √(7² + 3²)

d(u, v) = √(49 + 9)

d(u, v) = √58

So, the distance between u and v is √58.

To know more about vectors, refer here:

https://brainly.com/question/24256726

#SPJ4

Answer:

12

Step-by-step explanation:

let the number=x

7(x-10)=x+2

7x-70=x+2

7x-x=2+70

6x=72

x=72/6=12

1800 lawns were mowed. 800 driveways were shoveled.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Given Data

Let mowed grass be x

Let shoveled snow be y

Last year you mowed grass and shoveled snow for 12 houses

x + y = 12

y = 12 -x

You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.

225x + 200y = 2600

Equating value of y

225x + 200(12-x) = 2600

225x + 2400 - 200x = 2600

225x - 200x = 2600 - 2400

25x = 200

x = 8

For value of y,

y= 12 -x

y = 12 - 8

y = 4

Lawn mowed = 225(8)

Lawn mowed = 1800

Shoveled snow = 200(4)

Shoveled snow = 800

1800 lawns were mowed. 800 driveways were shoveled.

To learn more about equation, visit:

https://brainly.com/question/10413253

#SPJ13

The number of pillows requiring \(\frac{2}{3}\) yards that can be made from \(3\frac{1}{3}\) yards is 5. Thus the right answer to the given question is C.

Material required for making one pillow = \(\frac{2}{3}\) yards

Total material = \(3\frac{1}{3}\) yards

To find the number of pillows made we have to divide the material required for one pillow by the total material available to Kevin for making pillows

Number of pillows = \(3\frac{1}{3}\) ÷ \(\frac{2}{3}\)

=  \(\frac{10}{3}\) ÷ \(\frac{2}{3}\)

To divide two fractions, we take the reciprocal of the second number and multiply it by the first number.

=  \(\frac{10}{3}\) * \(\frac{3}{2}\)

= 5

Thus, the number of pillows made is 5.

Learn more about Division:

https://brainly.com/question/28722090

#SPJ4

Answer:

y=-x+4

Step-by-step explanation:

Answer: y= x+4

Step-by-step explanation:

Answer:

   give brainliest --- \(\sqrt{247}\)

Step-by-step explanation:

the height, radius, and circumference of the cone form a right triangle. So we use pythagorean theorem:

3^2+h^2=16^2

simplify

9+h^2=256

h^2=247

h = \(\sqrt{247}\)

PLS GIB BRAINLIEST

Answer:

15.7cm

Step-by-step explanation:

use Pythagoras theorem

16^2-3^2=a

a=15.7cm(1d.p.)

and thats the height

please mark as brainliest

Exhibit Corp. would recognize a $6,000 gain on disposal if it sells the equipment for $12,000 cash.

To determine the gain or loss on disposal of equipment, we need to compare the selling price with the net book value of the equipment. The net book value is the cost of the equipment minus its accumulated depreciation.

In this case, the cost of the equipment is $22,000, and the accumulated depreciation is $18,000. Therefore, the net book value is $22,000 - $18,000 = $4,000.

If the equipment is sold for $12,000, which is higher than its net book value of $4,000, there is a gain on disposal. The gain is calculated by subtracting the net book value from the selling price: $12,000 - $4,000 = $8,000.

Since the question asks for the gain or loss, we consider the sign of the amount. A gain is positive, so the correct answer is c. a $6,000 gain on disposal.

To know more about gain or loss on disposal of equipment, click here: brainly.com/question/31859665

#SPJ11

Answer:

1) sixty-eight million, six hundred and thirty-four thousand

2) acute triangle

3) 6

4) either 4 inches if it is one inch long or 8 inches if 2 long

5) 162

I really need brainliest please

Answer:

313003.6

Step-by-step explanation:

The number increases by 3 percent every year so 313003.6 is it.

Answer:

Step-by-step explanation:

You want the zeros of f(x) = x³ -5x² -22x -16, given that a factor is x+2.

Using synthetic division (see attachment), we find the quadratic factor to be (x² -7x -8), so we have ...

  f(x) = (x +2)(x² -7x -8)

The quadratic can be factored using our knowledge of the divisors of -8 to give ...

  f(x) = (x +2)(x +1)(x -8)

The zeros of f(x) are the values of x that make these factors zero:

  x = -2, -1, 8 . . . . . zeros of f(x)

__

Additional comment

We know the product of binomial factors is ...

  (x -a)(x +b) = x² -(a-b)x -ab

This means we can factor the quadratic by looking for factors of 8 that have a difference of 7. We know that 8 = 8·1 and that 8-1=7, so the values of 'a' and 'b' we're looking for are a=8, b=1.

The "zero product rule" tells you a product is zero only if one of the factors is zero. That is how we know to look for the zeros of the binomial factors of f(x). For example, x+2=0 ⇒ x=-2 is a zero of f(x). (The remainder of 0 in the synthetic division also tells us f(-2)=0.)

<95141404393>

The expected value of the mean, variance and standard deviation are-

For the given data in the question-

The formula for the mean;

μ = n×n /N

Put the values,

μ = 5×5/7

μ = 3.57

μ ≈ 4 (mean)

The formula for the variance is;

σ = nμ/N × (N - μ)(N - n)/N(N - 1)   ....eq 1

σ = 5×4/7 × (7 - 4)(7 - 5)/7(7 - 1)  

σ = 0.61 (variance)

For the calculation of the standard deviation-

δ = √σ   ...eq 2

δ = √0.61

δ = 0.78 (standard deviation).

Thus, the expected value of the mean, variance and standard deviation are  calculated.

To know more about the mean of the data, here

https://brainly.com/question/1136789

#SPJ4

Answer:

26

Step-by-step explanation:

If you need step by step, reply to this comment.

Answer:

3,-2

Step-by-step explanation:

set y =0 and solve

(-x-2)(x-3)=0

the values 3, -2 solve the equation and are your x-intercepts

Answer:

Answer is 41.4 ft

Step-by-step explanation:

formula for triangle is 1/2 base x height

1/2x4.6x18

=4.6x9

=41.4

so the area = 41.4 ft

Answer:

2x-32=24

Step-by-step explanation:

2x-32=24

2x=56

x=28

Hope this helps!

Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

put 12.4* 20 and you get D

The probability that the arborist will break a saw chain on a day in which he spends 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking is 0.007

We are given the probabilities of an arborist breaking a saw chain in a day's work are 0.004 for a small climbing saw, 0.008 for a medium limbing saw, and 0.04 for a large felling and bucking saw.

The time that he spends on each saw are 1/2 of his time climbing, 3/8 limbing, and 1/8 felling and bucking.

Let us find the probability that he will break a chain when he uses the small climbing saw.

P(small climbing saw) = 1/2P(Break a chain using small climbing saw) = 0.004

Using the medium limbing saw: P(medium limbing saw) = 3/8P(Break a chain using medium limbing saw) = 0.008

Using the large felling and bucking saw: P(large felling and bucking saw) = 1/8P(Break a chain using large felling and bucking saw) = 0.04

Now, to find the probability that he will break a chain on a day, we use the weighted average. Probability is a weighted average because the probability of breaking the saw chain is different for each saw that he uses.

Hence, the probability that he breaks a saw chain when he uses each saw is weighted according to how much time he spends on that saw.

P = P(small climbing saw)* P(Break a chain using small climbing saw) + P(medium limbing saw) * P(Break a chain using medium limbing saw) + P(large felling and bucking saw) * P(Break a chain using large felling and bucking saw)P = (1/2 * 0.004) + (3/8 * 0.008) + (1/8 * 0.04)P = 0.007

To know more about probability refer here:

https://brainly.com/question/30034780#

#SPJ11

Answer:

XY = 13 cm

Step-by-step explanation:

Area of a triangle formula:

area = base × height / 2

a = bh / 2

Plug numbers into equation:

32.5 = b × 5 / 2

Multiply both sides by 2 to isolate the variable

65 = b × 5

Divide both sides by 5 to isolate the variable

13 = b

Check your work:

32.5 = 13 × 5 / 2

32.5 = 65 / 2

32.5 = 32.5

Correct

Answer:

13

Step-by-step explanation:

Area=½×b×h

32.5=½×b×5

32.5=5/2b

To get be multiply each side by reciprocal of 5/2 which is 2/5

b =13

Answer: The equation is y=2x

Answer:

i'm sorry if i get it wrong but i think it's c

Step-by-step explanation:

Based on the given mean delivery time of 10:28am and the standard deviation of 0:55 mins, the estimated times within which 95% of the deliveries are made is (a) between 8:38 am and 12:18 pm.

To calculate this interval, we need to use the z-score formula, where we find the z-score corresponding to the 95th percentile, which is 1.96. Then, we multiply this z-score by the standard deviation and add/subtract it from the mean to get the upper and lower bounds of the interval.

The upper bound is calculated as 10:28 + (1.96 x 0:55) = 12:18 pm, and the lower bound is calculated as 10:28 - (1.96 x 0:55) = 8:38 am.

Therefore, we can conclude that the interval between 8:38 am and 12:18 pm represents the estimated times within which 95% of the deliveries are made based on the given mean delivery time and standard deviation.

Know more about mean delivery time here:

https://brainly.com/question/14268332

#SPJ11

Answer:

3

Step-by-step explanation:

Pick two points on the line

(0,0) and (10,30)

Using the slope formula

m = (y2-y1)/(x2-x1)

    = (30-0)/(10-0)

    = 30/10

    = 3

Answer:

A= 12

B = -4

Step-by-step explanation:

( -3,0) & (0,9) should satisfy the equation Ax + By = -36

when ( -3,0)

-3A+ 0 = -36

A = 12

when (0,9)

0 + 9B = -36

B = -4

The value of A and B is 12 and -4.

Given that,

Based on the above information, the calculation is as follows:

Ax + By = -36

When (-3,0)

So,

-3A+ 0 = -36

A = 12

Now  

when (0,9)

So,  

0 + 9B = -36

B = -4

Therefore we can conclude that the value of A and B is 12 and -4.

Learn more: brainly.com/question/3334417

The evaluation of one side of the equation for the divergence theorem for the cylindrical shell enclosed by r = 2 to r = 4 and z = 0 to z = 4 yields

To evaluate one side of the equation for the divergence theorem, we need to calculate the surface integral of the vector field D over the cylindrical shell's surface. The given vector field is D = f10e-2r + 252², where f is a scalar function, r represents the radial distance, and z represents the vertical distance.

First, we determine the outward unit normal vector n for the cylindrical shell's surface. The outward normal vector points away from the enclosed region and is given by n = (nᵣ, nᵣ, n_z) = (cosθ, sinθ, 0), where θ is the angle between the radial direction and the x-axis.

Next, we calculate the dot product of the vector field D and the outward unit normal vector n, i.e., D · n. Since the z-component of n is zero, we only need to consider the radial components of D and n. The dot product D · n simplifies to f10e-2r · cosθ + 252² · sinθ.

Now, we integrate D · n over the surface of the cylindrical shell. We consider the limits of integration: r = 2 to r = 4 and z = 0 to z = 4. However, since the given vector field does not have a z-component, the integration over the z-coordinate becomes trivial. We are left with integrating D · n over the curved surface of the cylindrical shell.

Learn more about the: divergence theorem

brainly.com/question/31272239

#SPJ11

Answer:

Step-by-step explanation:

You're correct that this problem involves finding the least common multiple (LCM) of 8 and 10, which will give us the number of seconds after which both fireflies will flash at the same time again.

To find the LCM of 8 and 10, we can use their prime factorizations:

8 = 2^3

10 = 2 × 5

The LCM of 8 and 10 is the product of the highest powers of all the prime factors involved, which in this case are 2^3 and 5. Therefore:

LCM(8, 10) = 2^3 × 5 = 40

So after 40 seconds, both fireflies will flash at the same time again. We can check this by dividing 40 by each of the individual flash intervals to see if we get a whole number:

40 ÷ 8 = 5

40 ÷ 10 = 4

Both of these divisions result in whole numbers, which confirms that 40 is the least common multiple of 8 and 10. Therefore, both fireflies will flash at the same time again after 40 seconds.

Answer:

40 sec

Step-by-step explanation:

So here we want to find the LCM of 8 and 10

➝ 8 = 2×2×2 = 2³

➝ 10 = 2×5

LCM(8,10) = 2³×5 = 40

So they will flash again after 40 sec.

Answer:

#3; Domain stays the same, but the range changes.

Step-by-step explanation:

All of the x values, stay the same, but because of the reflection the y-values change due to everything becoming greater than 2 rather than less than 2.

Answer:

C) The domain stays the same, but the range changes.

✿---✿--❀---❀---✿---✿

hope it helps...

have a great day!!

Note: we are assuming that Kunicki filled the 80-ounce bowl with 4 large cups and 12 medium cups of liquid.

To answer this question, we have to translate the situation into algebraic language as follows:

"He first filled an 80-ounce bowl with 8 large cups and 4 medium cups of liquid."

We have that the unknowns are l (the number of ounces for the large cup), and m (the number of ounces for the medium cup).

And we also have that:

He also filled the 80-ounce mixing bowl with "4 large cups and 12 medium cups of liquid", and we translate this as:

In this case, we end up with a linear system of equation, and we can solve this as follows:

We multiply the second equation by -2, then, we add this equation to the first equation, and then we found the value for the number of ounces of the medium cup.

To find the value of the number of ounces for the large cup, we can substitute the value of m in the first equation as follows:

Then, the number of ounces for the large cup is 8 ounces.

In summary, we found that the large cup holds 8 ounces, and the medium cup holds 4 ounces.

The first five terms of the sequence are 27, 22, 17, 12, and 7.

To find the first five terms of the sequence given by a₁=27 and d=-5,

we can use the formula for the nth term of an arithmetic sequence:

\(a_n=a_1+(n-1)d\)

Substituting the given values, we have:

\(a_n=27+(n-1)(-5)\)

Now, we can calculate the first five terms of the sequence by substituting the values of n from 1 to 5:

\(a_1=27+(1-1)(-5)=27\)

\(a_1=27+(2-1)(-5)=22\)

\(a_1=27+(3-1)(-5)=17\)

\(a_1=27+(4-1)(-5)=12\)

\(a_1=27+(5-1)(-5)=7\)

Therefore, the first five terms of the sequence are 27, 22, 17, 12, and 7.

To learn more about sequence visit:

brainly.com/question/23857849

#SPJ11