A raffle Prize of 14x2/15 dollars is to be divided among 7x people. Write an expression for the amount of money that each person will recieve.

The vector v (-6, 6, -5) points in the direction of itself, so we start there.

We can capture all points on the line through the origin and the point (-6, 6, -5) by scaling v by an arbitrary real number t.

The line through point P and pointing in the same direction as v is parallel to the other line that passes through the origin. Then the line we want can be obtained by translating the line through the origin by a vector p that points to (-4, 5, 2), so the vector equation for this line is

r (t ) = p + t v

r (t ) = (-4, 5, 2) + t (-6, 6, -5)

r (t ) = (-4 - 6t, 5 + 6t, 2 - 5t )

To get the parametric equations, simply take out the components:

x (t ) = -4 - 6t

y (t ) = 5 + 6t

z (t ) = 2 - 5t

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The median is the middle number in a set of numbers.

First what we need to do is put the numbers from least to greatest (ascending order).

1, 2, 10,6, 4, 4, 6, 3, 1, 4

1, 1, 2, 3, 4, 4, 4, 6, 6, 10

Now that we have ordered them, which one(s) is/are in the middle?

We have two numbers that share the middle. They are 4 and 4.

In cases where two numbers share the middle, we average them out. We do this by adding our two numbers together and then dividing by 2.

4 + 4 = 8

8 ÷ 2 = 4

Therefore our median is 4!

Answer:

Step-by-step explanation:

Answer -

a) 50% or 1/2

Explanation -

12+12=24

therefore, 12/24 = 1/2 which is 50%

b) 46.43% or 13/28

Explanation -

15+13=28

therefore, 13/28 which is 46.6%

Answer:

20 %

Step-by-step explanation:

$10/100%    $2/?

10/ what to get 2 so you do 10/5=2 so 100/5= 20.

Answer:

11 cm

Step-by-step explanation:

The strip of paper is 66 cm and it is folded into 6 different parts. It is used to form a model of a honeycomb cell.

To find the length of one side of the model, all we have to do is divide 66 cm by 6. That is:

66 / 6 = 11 cm

The length of one side of the model is 11 cm.

Answer:

1. 6 6/10

2. 7 6/10

Step-by-step explanation:

Answer:

1. 8 6/10

2. 9 6/10

Step-by-step explanation:

Answer:

324

Step-by-step explanation:

A number is a perfect square when there are two factors that are identical to one another. 324 is a perfect square since its two identical factors are 18 and 18.

Answer:

324

Step-by-step explanation:

18*18. Hope that helped, vote, thanks, brainliest ;)

Have a great day!

Answer:

y' = y

Step-by-step explanation:

The slopes are independent of x.  So the only possible answer is y' = y.

Multiplying a negative number by a negative number will give you a positive product.

When multiplying two negative integers, it comes out as positive.

For example, we are given the equation -4 * -4.

Using the rule [ -(-a) = a ], the answer for the equation is 16.

Best of Luck!

Answer:c

Step-by-step explanation:

Took test

Answer:use a calculator

Step-by-step explanation:

The unit rate for a proportional relationship is y = 6x.

The proportional relationship, can be find by the formula,

y = kx.........................1

Where,

X- position at X- cordinate= 1

Y - position at Y- coordinate = 6

k - constant of proportionality

put the values in the equation,

6 = k1

k = 6

Put the value of k into equation 1,

y = 6x

Therefore, the unit rate for a proportional relationship is y = 6x.

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Answer:

trevon ran 49 miles

Step-by-step explanation:

9+40=49

Answer:

49 miles

Step-by-step explanation:

Norachi ran 40 miles less than Trevon.

So, Trevon ran 40 miles more than Norachi

Distance covered by Trevon = 40 +9 = 49 miles

Answer:

x = -2.67

Step-by-step explanation:

6.8x + 9.3 = -9.4 + 3.4(-3x)

6.8x + 10.2x = -9.4 - 9.3

17x = -18.7

x = -2.67

Answer:

17 is added to both numerator and denominator.

Step-by-step explanation:

Given:

Fraction = 1/10

New fraction = 2/3

Find:

Number added to both numerator and denominator.

Computation:

Assume,

a is added to both numerator and denominator.

[tex]\frac{1+a}{10+a}=\frac{2}{3}\\\\3 + 3a=20+2a\\\\3a-2a=20-3\\\\a=17[/tex]

Therefore, 17 is added to both numerator and denominator.

I hope this helps you

Answer:

B represents area of the right triangle

Step-by-step explanation:

Given;

Area of a triangle is A = 0.5bh

where;

b is the base of the triangle

h is the height of the triangle

Given, formula for the volume of a prism is V = Bh

For a right triangle prism, the formula for the volume is, V = Bh

Where;

B is the area of the right triangle

h is the height of the prism

Therefore, B represents area of the right triangle

Answer:

D

Step-by-step explanation:

-4 x 3/2 = -12/2; which equals -6

so -6x.

-4 x -1/2 = 4/2; which equals 2

This means that:

-6x + 2 = 15; so 'D' is the answer

Answer:

D

Step-by-step explanation:

The distributive property states that a(b+c)=ab+ac. In this problem -4 is a, 3/2x is b, and -1/2 is c. -4(3/2) is 6, and -4(-1/2) is 2. So we have -6x+2=-15.

Answer:x+3

Step-by-step explanation:

5×3=15

5+3=8x

Answer:

A

Step-by-step explanation:

Answer: So, an Engineer will use a topography while working to locate the elevation for a given region. They provide the numerical value of an elevation. So from the list of options the closest to it is to determine the best location for a new road.

I hope this is helpful.

Answer:

B

Step-by-step explanation:

Answer:

Angle BEA

Step-by-step explanation:

They share the same straight line and their degrees add to 180

The quadratic has one root with multiplicity 2 if the discriminant is 0, which is

[tex](2m+4)^2-4(4-m)(8m+1)[/tex]

(That is, for a quadratic [tex]ax^2+bx+c[/tex], the discriminant is [tex]b^2-4ac[/tex].)

Set the discriminant equal to 0 and solve for [tex]m[/tex]:

[tex](2m+4)^2-4(4-m)(8m+1)=0[/tex]

[tex]4m^2+16m+16+32m^2-124m-16=0[/tex]

[tex]36m^2-108=0[/tex]

[tex]36m(m-3)=0[/tex]

[tex]\implies m=0\text{ or }m=3[/tex]

Answer:

The answer is 66 ways .

Step-by-step explanation:

You have to use Combination because it says choosing 10 out of 12 as the position is not important :

12C10 = 66 ways of arrangements

The number of different 10-person teams are 66.

A combination is a mathematical technique for determining the number of potential arrangements in a set of objects where the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

We have out of the 12 girls who tried out for the softball team, 10 will be chosen for the team.

Using Combination

C(n, r) = n!/ r! (n- r)!

Here n = 12, r= 10

So, C(12, 10)= 12! / 10! (12- 10)!

                   = 12 x 11 x 10! / 10! x 2

                   = 6 x 11

                   = 66

There are 66 10-person teams.

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Answer:

314.97

Step-by-step explanation:

Answer:

5.(345)=1,780/333

Step-by-step explanation:

5.(345)=(5,345-5)/999=5,340/999=1,780/333

The fraction corresponds to given decimal is 1780/333.

What is fraction form?

A fraction is used to show how much of something is left over. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Let x=5.345

The repeating number is 345

Multiply both sides by 1000

1000x=5345.345

Subtract x=5.345 from the obtained equation,

999x=5340

Solve for x,

x=5340/999

x=1780/333

Therefore, the fraction corresponds to given decimal is 1780/333.

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Answer:

2083.33 trouts

Step-by-step explanation:

Total population of fish in the pond is unknown, therefore, let's us represent this using letter Z

The ratio of banded , caught and released trout to the total trout population is represented as 250 : Z

We can solve this type of problem with a proportion:

Total number of fishes that was tagged and caught/ Total number of fishes that was caught = Total number of tagged fishes in the pond/ Total number of fishes in the pond.

In the question, we were given this values:

Total number of banded trout's that was caught and released into the pond = 250

Total number of trouts that was caught and had bands in the lake= 30

Total number of trouts that was caught in the lake = 250

Total number of fishes in the pond = Z

Hence we have:

30/250 = 250/ Z

We cross mulitply

30× Z = 250 × 250

30Z = 62500

We divide both sides by 30

30Z/ 30 = 62500/30

Z = 2083.33

Therefore, the expected population of trout is 2083.33 trouts

Answer:

1. B

2. A

3. B

4. ???

5. A

6 ???

7. I can't see it

Step-by-step explanation:

Answer:

θ = π/3 and 5π/3

Step-by-step explanation:

x = r cos θ and y = r sin θ.  Therefore:

dy/dx = (dy/dθ) / (dx/dθ)

dy/dx = (r cos θ + r' sin θ) / (-r sin θ + r' cos θ)

In this case, r = 1 + cos θ and r' = -sin θ.

dy/dx = ((1 + cos θ) cos θ + (-sin θ) sin θ) / (-(1 + cos θ) sin θ + (-sin θ) cos θ)

dy/dx = (cos θ + cos²θ − sin²θ) / (-sin θ − sin θ cos θ − sin θ cos θ)

dy/dx = (cos θ + cos²θ − (1 − cos²θ)) / (-sin θ (1 + 2 cos θ))

dy/dx = (cos θ + 2 cos²θ − 1) / (-sin θ (1 + 2 cos θ))

The tangent line is horizontal when the numerator of dy/dx is 0 and the denominator of dy/dx is not 0.

0 = 2 cos²θ + cos θ − 1

0 = (cos θ + 1) (2 cos θ − 1)

cos θ = -1 or 1/2

θ = π/3, π, 5π/3

0 = -sin θ (1 + 2 cos θ)

sin θ = 0 or cos θ = -1/2

θ = 0, 2π/3, π, 4π/3

Therefore, the answer is θ = π/3 and 5π/3.

Answer:

The initial amount of money Tyra has is $90

Step-by-step explanation:

Let the initial money Tyra has be equal to y

She spent ⁴/₅ of her initial money on gas for her car = ⁴/₅ of y

She spent ¹/₂ of the remainder on sandwiches;

the remainder = 1 -  ⁴/₅  = ¹/₅

¹/₂ of the remainder = ¹/₂ x ¹/₅ = ¹/₁₀

Thus, she spent ¹/₁₀ of her money on sandwiches = ¹/₁₀ of y

Amount she spent on sandwiches = $9 = ¹/₁₀ of y

[tex]\frac{y}{10} = \$ 9\\\\y = \$ 90[/tex]

Therefore, the initial amount of moneyTyra has is $90

Answer:

x = 26.45

Step-by-step explanation:

Cos theta = adjacent side / hypotenuse

cos 50 = 17 /x

Switch the x and the cos 50

x = 17 / cos 50

x =26.44730506

Rounding to 2 decimal places

x = 26.45