Find the equation of this line.
y =
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x + [

Answer:

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The expression that represents five less than the sum of mark's and hatch's ages is ( h + m ) - 5

Given,

Mark's age is represented by m

Hatch's age is represented by h

To find an expression that shows the required relation, that is, five less than the sum of mark's and hatch's ages, we need to establish a relation between the given variables.

Sum of mark's and hatch's ages can be represented as ( m + h )

Five less than the sum of mark's and hatch's ages can be represented as ( m + h ) - 5.

Therefore, by establishing a relation between the given variables, we get the expression that represents five less than the sum of mark's and hatch's ages as ( h + m ) - 5.

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Answer:

19c + 30

Step-by-step explanation:

Distributive property : a(b+c) = ab + ac

Explanation : simply multiply the value on the outside of the parenthesis by both the values on the inside of the parenthesis.

Here we have 1(19c + 30)

To distribute, we multiply 1 by both 19c and 30

1 x 19c = 19c

1 x 30 = 30

We're left with 19c + 30

Answer: 0.16666

Step-by-step explanation:

You need to move the decimal point over

[tex]\frac{5.9}{35.4} \\ \\ \frac{59}{354}=\frac{59.0}{354} =\frac{0.16666}{554}[/tex]

Answer: Adult tickets were sold = 325

Step-by-step explanation:

Let, A = Number of adult tickets sold

S = Number of student tickets sold

Total number of tickets=599

Therefore:

                           A + S = 599

If, there were 51 fewer student tickets sold them adult tickets.

Since,

                            S=A-51

So, substitute A-51 for the value of the first equation.    

                            A+S=599    

                        A+(A-51)=599

Expanding to get:

                            2A-51=599

Solve to get:

                          2A=599+512

                          A=650A

                          A=325

So, A=325 adult tickets were sold.

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Answer:

450 eggs

Step-by-step explanation:

if an egg box can hold 10 eggs

then 45x10=450

The parametric equations are line through (0,0,0) in the direction of the vector v=uxw=(1,2,1).

The line through (0,0,0) and perpendicular to both U=(-2,1,0) and

w=(-1,0,1)

Therefore the line through (0,0,0) and parallel to (-2,1,0)

[tex]*10919-1-2, î+1=3618 = (1) ņ - (-2)5+ (1)a • Î +21 + û[/tex]

=(1,2,1)

Therefore direction ratio of the line through (0,0,0) is (1,2,1) Therefore for equation of the line through (0,0,0) and perpendicular to both (-2,1,0) and [tex]w=(-1,0,17 is (0,, z) = (0,0,0) + x (1,2,1),[/tex] & is constant.

[tex].: X (1,4,2)= (0, 1, 0)+ [1,2,1][/tex]

Therefore parametric of the line through (0,0,0) in the direction of the vector v=uxw=(1,2,1)

Equivalent Equation of a Plane in Vector Form

The equation for a plane in the real number system R, where r is the position vector of any point on the plane and n is either a normal vector perpendicular to the plane or a parallel vector.

The normal vector must be perpendicular to both as the vectors are both parallel to the plane. Recall that a vector that is perpendicular to both vectors is created by taking the cross product of two vectors. This cross product's characteristic can be used to compute a normal vector to the plane, which results in the normal vector.

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Answer:

2 pints

Step-by-step explanation:

if you add all of it up you get 2 pints.

1/4*8 = 2 pints

The limit as a definite integral on the given interval. lim n→[infinity] n xi ln(1 xi2) δx, [2, 6] {62xlnc 1+X2} dx

As per the given question

Lim n - infinite n xi ln (1×i2) € x = (A,B) =(2,6)

We have to put the formula of Reimann sum

That is Rn = Sigma x ni = 1f (xi) ∆x

Comparing the evolved formula with the given expression we get

f (xi) = xi ln (1×2i)

Back substitute the variable x for xi

Thus the definite integral is

( 6 2 x ln (1+X2)) dx

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The area of the shaded region of the circle is 10.972 square inches.

The formula for area of a circle sector is;

A = (θ/360) * πr²

We are given;

Radius of circle = 92 inches

Central angle = 7π/15

Thus;

Area of given sector = (7π/15)/360 * π * 92²

Area of given sector = 7π/15 * 1/360 * π * 92²

Area of given sector = 10.972 square inches

Thus, we can conclude that the area of the shaded region of the circle is 10.972 square inches.

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The mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)

We use the rotation of 90 degree to find the mapping of 270 degrees.

The rotation of 270 degree clockwise is same as the anticlockwise rotation of 90 degrees about the origin.

So the mapping of 270 degree clockwise rotation is exactly the mapping of 90 degree anti clockwise rotation.

Now the mapping of 90 degree anti clockwise rotation is  (x, y) -----> (-y, x).

So the mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)

This implies that a point (x, y) on the co-ordinate plane becomes (-y, x) after a clockwise 270 degree rotation.

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(f + g) is { (2,6) ,(6,11) ,(9,14),(12,17) } and (f - g) is  { (-2,-4) ,(-2,-3) ,(-1,-2),(0,-1)}.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

Given the functions f and g

f  = {(0, 1), (2, 4), (4, 6), (6, 8)}

g = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}

Now,

f + g is nothing but the sum of x and y corresponding

For example (0,1) + (2,5) = (2 ,6)

Similarly  (0,1) - (2,5) = (-2,-4)

So,

(f + g) = { (2,6) ,(6,11) ,(9,14),(12,17) }

(f - g) = { (-2,-4) ,(-2,-3) ,(-1,-2),(0,-1)}

Hence "(f + g) is { (2,6) ,(6,11) ,(9,14),(12,17) } and (f - g) is  { (-2,-4) ,(-2,-3) ,(-1,-2),(0,-1)}".

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Answer: I think 1.2

Step-by-step explanation:

1.35

Answer:

[tex]x = 61[/tex]

Step-by-step explanation:

See the attached image for explanation

Check the picture below.

The simplified form of the given expression is x raise to the power of one-thirty.

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

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The number of hours to operate the mines to minimize cost are Mine 1 hour = 25 hours and Mine 2 hour = 10 hours

The given parameters can be represented using the following table of values

                               Mine 1 (x)              Mine 2 (y)   Available

Regular grade          5                            20             325

Low grade               18                             9              540

Operating cost      16000                     12000

Time                        37                                34

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 16000x + 12000y

Subject to:

5x + 20y >= 325

18x + 9y >= 540

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (25, 10)

This means that

Mine 1 hour = 25 hours

Mine 2 hour = 10 hours

Hence, the number of hours to operate the mines to minimize cost are Mine 1 hour = 25 hours and Mine 2 hour = 10 hours

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cluster sampling is the type of sampling is used.

In cluster sampling, a population is divided into clusters, which are smaller groups. They then choose a sample at random from these clusters. Often employed to investigate huge populations, particularly those that are extensively geographically distributed, cluster sampling is a probability sampling technique. Typically, clusters used by researchers are already-existing groups like cities or schools. Clusters are frequently more homogeneous than the population as a whole since they are typically naturally occurring groups, such as schools, cities, or houses. When conducting your study, you should be aware of this as it might compromise the validity of your findings.

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Answer:

123910-w137762 cotkw

naodiskd

Answer: V = 75.4

Step-by-step explanation: Assuming this is a cylinder we can use the formula πr^2*h. All we have to do is plug in the numbers for the equation. Since we know radius is half of the diameter we can set radius to 2. h represents height.

So since the formula is saying we need to square the radius. We multiply 2*2=4

We can then plug this in for r squared.

Making our equation=  π*4*6 = 75.4

Answer:

number of fish caught between 60 and 75 cm =40

Step-by-step explanation:

A function assigns the value of each element of one set to the other specific element of another set. The person can see upto 9.996 meters.

A function assigns the value of each element of one set to the other specific element of another set.

Given that  a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d=3.57√(h).

Now, using the same given function we can find the distance up to which the person will be able to see to the horizon. Therefore, we can write,

d=3.57√(h)

d = 3.57 √(7.84)

d = 3.57 × 2.8

d = 9.996

Hence, the person can see upto 9.996 meters.

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To change the order of operations in a formula, use parentheses around the part of the formula you want to calculate first.

Parentheses allow you to group elements in a cell.  This allows you to create more complex and more powerful formulas.

Consider the expression 6+4*2.

The above formula gives result as 14 because Excel performs multiplication before addition. The formula multiplies 4 by 2 and then adds 6 to the result.

Now consider the expression (6+4)*2.

If you use parentheses to change the syntax, Excel adds 6 and 4 together and then multiplies the result by 2 to produce 20.

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To change the order of operations in a formula, use parentheses around the part of the formula you want to calculate first.

Parentheses allow you to group elements in a cell.  This allows you to create more complex and more powerful formulas.

Consider the expression 6+4*2.

The above formula gives result as 14 because Excel performs multiplication before addition. The formula multiplies 4 by 2 and then adds 6 to the result.

Now consider the expression (6+4)*2.

If you use parentheses to change the syntax, Excel adds 6 and 4 together and then multiplies the result by 2 to produce 20.

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Answer:

3

Step-by-step explanation:

[tex]\sqrt[3]{27}[/tex]

= [tex]\sqrt[3]{3^3}[/tex]

= 3

Answer:

0.11 yards

Step-by-step explanation:

To convert centimeters to yards, find the needed unit conversions:

[tex]cm(\frac{in}{cm})(\frac{ft}{in})(\frac{yd}{ft})[/tex]

Convert centimeters to inches, inches to feet, then feet to yards!

Now replace the values with the correct quantities:

[tex]10cm(\frac{1in}{2.54cm})(\frac{1 ft}{12 in})(\frac{1 yd}{3 ft})[/tex]

Finally, simplify and cross-cancel the units:

[tex]0.10936... yd[/tex]

Round to the nearest hundredth:

[tex]0.11 yd[/tex]

Answer:

See explanation

Step-by-step explanation:

a. Skewed to the right since the tail of the graph is on the right

b. Each bar is 3 values. 7*3=21 values

c. The bars are taller for lower numbers. Hence, the question could be about age. "Who likes to watch cartoons?"

The ratio of the volume of the rigth circular cylinder a to the volume of the right circular cylinder b is 1: 18.

According to the given question.

We have two right circular cylinder, a nd b.

Also,

The radius of right circular cylinder, a is r.

The height of the right circular cylinder, a is h.

The radius of the right circular cylinder, b is 3r.

And the height of the right circular cylinder, b is 2h.

As we know that, the volume of a cylinder can be calculated using the formula V=πr^2(h). Where r is the radius and h is the height of the cylinder.

So, the volume of the right circular cylinder a  = πr^2h

And, the volume of the right circular cylinder b = π(3r)^2(2h) = 18hr^2π

Therefore,

The ratio of the volume of the rigth circular cylinder a to the volume of the right circular cylinder b

= πr^2h/18hr^2π

= 1:18

Hence, the ratio of the volume of the rigth circular cylinder a to the volume of the right circular cylinder b is 1: 18.

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Answer:

[tex]\textsf{Factored form}: \quad (a^2+4)(a-2)[/tex]

[tex]\textsf{Standard form}: \quad a^3-2a^2+4a-8[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{a^4-16}{a+2}[/tex]

Rewrite the exponent 4 as 2·2 and 16 as 4²:

[tex]\implies \dfrac{a^{2 \cdot 2}-4^2}{a+2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c[/tex]

[tex]\implies \dfrac{\left(a^2\right)^2-4^2}{a+2}[/tex]

[tex]\textsf{Apply the Difference of Two Squares Formula} \quad x^2-y^2=\left(x+y\right)\left(x-y\right):[/tex]

[tex]\implies \dfrac{(a^2+4)(a^2-4)}{a+2}[/tex]

Rewrite 4 in the second parentheses of the numerator as 2²:

[tex]\implies \dfrac{(a^2+4)(a^2-2^2)}{a+2}[/tex]

Apply the Difference of Two Squares Formula to (a² - 2²):

[tex]\implies \dfrac{(a^2+4)(a+2)(a-2)}{a+2}[/tex]

Cancel the common factor (a + 2):

[tex]\implies (a^2+4)(a-2)[/tex]

Expand:

[tex]\implies a^2(a-2)+4(a-2)[/tex]

[tex]\implies a^3-2a^2+4a-8[/tex]

The x intercept and y intercept of 7x-9y=35 is (5,0) and (0,-35/9) respectively .

X Intercept is defined as the point where the line crosses the X axis .

For Example : if the line x+y=2 crosses the x axis at 2 ,  then it's x intercept will be (2,0).

Y Intercept is defined as the point where the line crosses the Y axis.

For Example ; if the line x+y=2 crosses the y axis at 2 , then it's Y intercept will be (0,2) .

In the given question

7x-9y=35

To find the x intercept we substitute the value of y=0,

On substituting  y=0 we get

7x=35

x=5

The x intercept is (5,0).

To find the y intercept we substitute the value of x=0,

On substituting x=0 we get ,

-9y=35

y=-35/9

The y intercept is (0,-35/9) .

Therefore , the x intercept and y intercept of 7x-9y=35 is (5,0) and (0,-35/9) respectively .

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Answer:  $41.50  41 dollars and 50 cents in profit

Step-by-step explanation:

First, 1.25x48=60

Second, 60-18.50=41.50

Answer:

$41.50

Step-by-step explanation:

So we know that Gavin bought 48 water bottles before the game for $18.50. We also know that he sold the water bottles for $1.25 each.

If we want to know how much profit he made, we first have to find the amount of money he received.

To find this, we need to multiply the number of water bottles by the price for each bottle;

48 × $1.25

This gives us a total of $60.

Now to find the profit, we have to subtract the amount he paid for the water bottles by the total he made;

$60 - $18.50

This means he made a profit of $41.50.

hope this makes sense! <3