What is the additive inverse of -7?
O A. -7
O B. 7
C. -|-7|
D. -(-(-7))

There are [tex]\frac{30!}{(3!)^{10} }[/tex] ways for the teacher to decide which student she will teach during each lesson time if she must teach each student exactly 3 times. Here, "!" represents the factorial.

A number's factorial is the result of multiplying the integer by each natural number below it. Factorial can be symbolized by the letter "!". Thus, n factorial is denoted by n! and is the result of the first n natural numbers.

A whole number's "n" factororial is the sum of that number and each whole number up to one.

When a question asks you to determine how many different ways you can arrange or order a given number of items, you use a factorial.

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The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.

According to the statement

we have given that the

Jody earns $10 per hour babysitting And jody earns $15 per hour doing yardwork.

And she worked 34 hours and earned $410

and we have to express in the linear equation terms.

So, For this purpose,

Let x represents the number hours she babysat

Let y represents the number of hours she did yardwork

And the equations become

x + y = 34.

10x + 15y = 410

And with the help of these linear equations we find the hours which are x and y.

So, The above written equations perfectly express the given conditions in the statement.

The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.

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The composition of the functions f(x) and g(x) gives the equation:

[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]

Here we want to get the composition of the two functions:

[tex]f(x) = x^2 + 3x - 3\\\\g(x) = 2x[/tex]

f(x) is a quadratic and g(x) is a linear equation.

Now we want to get the composition:

[tex]f(g(x))[/tex]

This means that we need to evaluate function f(x) in g(x), so we can replace all the "x" in the function f(x) by the notation "g(x)"

[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3[/tex]

Now we replace all the "g(x)" by the actual function g(x) = 2x, we wll get:

[tex]f(g(x)) = g(x)^2 + 3*g(x) - 3 = (2x)^2 + 3*(2x) - 3[/tex]

finally, we can simplify this to get the composition, which is a quadratic function just like f(x).

[tex]f(g(x)) = 4x^2 + 6x - 3[/tex]

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If the radius of sector is 12 centimeters and angle of 65 degrees then the arc's length is 13.6 cm.

Given a sector has a radius of 12 cm and an angle 65 degrees.

We have to calculate arc's length.

We know that arc's length is equal to Θr where Θ is in radians.

We have been given angle in degrees ,so we have to convert degrees in radians.

Angle=65*π/180=13π/36

length of arc =Θr

Putting the values in the formula above :

length =13π/36*12

=13*3.14/3

=40.82/3

=13.6

Hence if the radius of sphere is 12 cm and angle 65 degrees then the length of arc of sphere is 13.6 cm.

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Hello,

3a - 2 + 5a + 3 + 6a + 1 = 86

14a + 2 = 86

14a = 86 - 2

14a = 84

a = 84/14

a = 6

lengths :

3a - 2 = 3 × 6 - 2 = 18 - 2 = 16 cm

5a + 3 = 5 × 6 + 3 = 30 + 3 = 33 cm

6a + 1 = 6 × 6 + 1 = 36 + 1 = 37 cm

Answer:

300 gallons

Step-by-step explanation:

A saline solution is a solution of salt in water.

The percent is the percent of salt in the total amount of solution.

A 40% saline solution has 40% of salt out of the total volume.

Let the amount of pure water needed = x.

The amount of existing 40% solution is 500 gal.

Let the total amount of 25% saline solution made = y.

Equation of volumes of solutions:

500 + x = y

y = x + 500          Eq. 1

Equation of volume of salt:

500 gal of 40% saline solution has 0.4 × 500 gal = 200 gal of salt

Pure water has 0% salt.

The final product is a solution that is 25% saline. Its volume is y.

The volume of salt in the y gallons of 25% saline solution is 25% of y = 0.25y

The equation of salt content is:

200 + 0 = 0.25y

y = 800       Eq. 2

Eq. 1 and Eq. 2 form a system of equations.

y = x + 500

y = 800

Substitute 800 for y in Eq. 1.

y = x + 500

800 = x + 500

x = 300

Answer: 300 gallons of pure water

Answer:927652832

Step-by-step explanation:

using long multiplication step by step multiply.

Answer:

Step-by-step explanation:

x times 8 +12

8x+x=9x-12

Answer = 9x-12

Answer: 8.2 cm

Step-by-step explanation:

Area of a rectangle = l x w

[tex]A= 25 cm^{2}[/tex]

[tex]l= ?[/tex]

[tex]w= 2.5 cm[/tex]

[tex]25cm^{2} = l(2.5cm)[/tex]

[tex]\frac{25cm^{2} }{2.5cm}= l[/tex]

[tex]8.2 cm=l[/tex]

The  C is perpendicular to AB

When using paper, the paper perpendicular te construct to is folded so that AB is divided equally and the two sides of. line AB will lie exactly on top of each other.

When using a reflective device to construct a live perpendicular to line AB, set One end of the device to coincide with point C, and then swing the other end of the device so that the reflection of line AB coincides with the midpoint of AB

The question is incomplete hence the complete question is shown here

Select the correct answer from the drop-down menu. Compare the steps for constructing a perpendicular line to line  through point  using a reflective device and using paper. , When using paper to construct the perpendicular line, the paper is folded so that and the two sides of line  will lie exactly on top of each other. When using a reflective dewice to construct a line perpendicular to line  , set one end of the device to coincide with , and then swing the other end of the device so the reflection of line  coincides with.

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Answer:

I toke the test, I think the first one is A and  B coincide

Step-by-step explanation:

Answer: i know it

Step-by-step explanation: i know

Answer:

80

Step-by-step explanation:

To find the mean we add up all the numbers and then divide that number by the amount of numbers we added up.

So in this case we added up 65, 70, 75, 80, 85, 90 & 95. This gives us 560. Now we divide 560 by 7 as that is the amount of numbers we added up. This gives us 80 which means the answer is 80.

I hope this helped! :)

The value of the expression 6x+3y is 33

System of equations consists of two or more equation with unknown variables.

Given the equation below

8x + 4y = 44,

Factor out 4 from the equation to have:

4(2x+y) = 44

Divide both sides by 4

2x+y = 11

Determine the value of 6x+3y

6x+3y = 3(2x+y)

6x+3y = 3(11)

6x+3y =33

Hence the value of the expression 6x+3y is 33

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$662.18 needs to be saved per month.

$90,000 now at 3% inflation will become 90000*1.03^30 after 30 years.

i.e.  $218,454 is required in retirement years (for 20 years)

Calculating the PV of these payments at 7% is calculated as below.

FV = 0

1/y = 7%

n=20; PMT = 218454; calculate PV = $2,314,305

Now we want to get $2,314,305 at the start of retirement by saving per year. Enter the following in the financial calculator to get the per month amount.

FV = 2314305; PV = 0; n= 12*30; 1/y = 12%/12; calculate PMT  = $662.18

So $662.18 needs to be saved per month.

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Answer:

H. 15 ft by 15 ft

Step-by-step explanation:

area of square = side²

225 ft² = side²

side = √(225 ft²)

side = 15 ft

Answer: H. 15 ft by 15 ft

The set of numbers is included in the solution set of the compound inequality is {-7, 5, 18, 24, 32}

Inequalities are expressions not separated by an equal sign.

From the given number line, the equivalent inequality expression are

x > 22 (22 s excluded since it is an open circle) and x≤ 18 (18 is included since the circle is shaded)

Hence the set of numbers is included in the solution set of the compound inequality is {-7, 5, 18, 24, 32}

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The set of numbers that is been  included in the solution set of the compound inequality is [tex]{-7, 5, 18, 24, 32}[/tex]

The inequality can be referred to as the relationship between two values which are not equal and cannot be separated by an equal sign.

From the open circle, Checking the number set, [tex]x > 22[/tex],  22 cannot be involved, from the shaded circle, x≤ 18 , 18 can be included.

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the polar coordinates are:

(√130, 285.3°)

For rectangular coordinates (x, y), the polar coordinates are:

[tex]R = \sqrt{x^2 + y^2}[/tex]

For the angle θ we need to notice that if both coordinates are negative, like in this case, we would be on the fourth quadrant, then:

θ = arctan(y/x) + 270°

In this case, we have:

x = -11

y = -3

Then:

[tex]R = \sqrt{(-11)^2 + (-3)^2} = \sqrt{130} \\\\\theta = arctan(-3/-11) + 270\° = 285.3\°[/tex]

Then the polar coordinates are:

(√130, 285.3°)

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The mistake that Shawn made in his definition of a reflection is that D. Shawn didn't make a mistake.

It should be noted that reflection simply means ten transformation of the shape of an object.

In this case, for any point R on the line of reflection L, the image R’ is at the same point as R. Furthermore, for any point P not on the line of reflection L, the image P’ is on the other side of L such that P and P’ are the same distance from L.

Therefore, Shawn is right as no mistake was made.

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Answer:

PP' must be perpendicular to the line of reflection. Whatever the distance is between P and L, there are infinitely many points on the other side of L that are the same distance from L.

Step-by-step explanation:

Since the ratio of their similar sides are equal hence the triangles are similar

Two figures are are known to be similar if the ratio of their similar sides are equal to a constant known as the scale factor.

For the triangles given, take the ratio of the sides;

12/2 = 6

30/5 = 6

36/6 = 6

Since the ratio of their similar sides are equal hence the triangles are similar

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Answer:

Please see the picture below.

Step-by-step explanation:

Answer:

[tex]16x^2-26x+20[/tex]

Step-by-step explanation:

Since it represents the sum of interior angles, the angle is essentially: [tex]angle + angle + angle + angle + angle[/tex], and there are 5 angles since a pentagon has 5 interior angles. To find what one interior angle is, we simply divide the polynomial by 5, to do this we can just divide each coefficient by 5 (distributing the division): [tex]\frac{40x^2-65x+50}{5} = \frac{40x^2}{5} - \frac{65x}{5} + \frac{50}{5}[/tex] this simplifies to: [tex]8x^2-13x+10[/tex]. This represents what one of the interior angles is. Since we want an expression measuring two of the angles, we simply multiply this polynomial by 2, to do this we just multiply each coefficient by 2 (distributing the 2): [tex]2(8x^2-13x+10) = 16x^2-26x+20[/tex] which is the solution

Answer:

There is only one way to assign the athletes to the team by giving 5 athletes to each team

If fish are sold at [tex]10[/tex] for $[tex]864[/tex].  the cost to the nearest dollar of [tex]16[/tex]fish is $ [tex]1382[/tex]

How can we find the cost of the [tex]16[/tex] fish ?

The cost of the selling [tex]10[/tex] fish = $[tex]864[/tex]

So the cost of the [tex]1[/tex] fish is

[tex]= \frac{864}{10} \\=86.4[/tex]

So the cost of the selling [tex]16[/tex] fish

[tex]= 16* 86.4\\=1382 $[/tex]

$[tex]1382[/tex] is the selling cost of [tex]16[/tex] fish.

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Answer:

Yes

Step-by-step explanation:

As the Average speed increases, the amount of distance covered will increase. As the average speed decreases, the amount of distance traveled will decrease as well over a certain period.

Answer:

Step-by-step explanation:

The triangle would end up back where it started.  It is hard to explain without a graph.  If you have graph paper, you might want to try drawing this out.  Say that the original points are at A (1,2) B (2,0) and C(0,0).  Now, when we reflect the points over the x axis, they will be the same distance below the x that the points original were about the x axis.  Since A was 2 units above the axis, it will now be 2 units below at (1, -2).  Points B and C will stay on the x axis and will remain in place at B(2.0) and C(0,0).  Since these points are on the line, they were not above the x axis, so they will now not be below the x axis.

Now, we are going to reflect the triangle over the y axis.  Since C (0,0) is already on the y axis, it will not move.  It will remain there.  Since B(2,1) is two units to the right of the y axis, when we flip it, it will now be 2 units to the left of the y axis B (-2,0).  Point C will move one unit to the left of the y axis to become (-1,2).

The last thing left it to rotate this final triangle 180 degrees.  Since a circle is 360 degrees and 180 is half of a circle, it does not matter if we rotate clockwise or counter-clockwise.  If you could trace our new triangle and put a plus sign at the origin (0,0).  You would put your pencil on the origin  and rotate the two turns at the plus sign.  This would put your triangle right back to the beginning.  So the original value of B would be the same.  In this case C ((2,0)

The point B' would be at point B. The position of point won't change.

A reflection is a type of transformation that involves flipping a shape, known as the preimage, over a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you flipped the form over the line in order to graph a reflection.

Given:

Triangle ABC is reflected over the x‐axis, reflected over the y‐axis, and rotated 180 degrees.

Let (x, y) be the coordinates of B.

To find B':

If a figure reflected over x-axis, then

(x, y) → (x, -y)

So, let point B₁ is  (x, -y).

If a figure reflected over y-axis, then

(x, y) → (-x, y)

So, (x, -y) → (-x, -y)

So, let point B₂ is  (-x, -y).

If a figure rotated 180 degrees about the origin, then

(x, y) → (-x, -y)

(-x, -y) → (x, y)

So the B' is (x, y).

Therefore, the position of point won't change.

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The curve passes through the point (3, 3), so [tex]y=3[/tex] when [tex]x=3[/tex]. Then

[tex]y = ax^2 + bx \implies 3 = 9a + 3b \implies 3a + b = 1[/tex]

The tangent line to the curve at (3, 3) has gradient [tex]\frac{dy}{dx}[/tex] at [tex]x=3[/tex]. Compute the derivative.

[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]

Then when [tex]x=3[/tex], the gradient is 4, so

[tex]2ax + b = 4 \implies 6a+b=4[/tex]

Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we find

[tex](6a+b) - (3a+b) = 4-1 \implies 3a = 3 \implies \boxed{a=1}[/tex]

and it follows that

[tex]3 + b = 1 \implies \boxed{b = -2}[/tex]

Answer: 37.92

Step-by-step explanation: We know that 3202 / 5 = 640.4.

We subtract that by 830 to get (830 - 640.4  =) 189.6. Then we do / by five again to get 37.92. That is the answer.

Using its concept, it is found that the probability that the lawyer will flip to a page number that is not a multiple of 4 is given by:

p=19/25

Probability is a field of mathematics that deals with the numerical description of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the impossibility of the event and 1 indicating certainty.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 50 numbers, of which 50 - (48/4) = 38 are not multiples of 4, hence the probability is given by:

p=38/50 = 19/25

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Answer:

8.8

Step-by-step explanation:

If DEF///ABC

AB=4.4

Answer:

7. a) slope = 5

7. b) slope = 1/2

8. slope = 1

Step-by-step explanation:

slope = rise/run

rise is the vertical change, run is the horizontal change

7. a)

Pick any two points on your line. (0,0) and (1,5) are easy to work with.

The vertical change between the two points is 5

The horizontal change between those points is 1

so slope = 5/1 = 5

7. b)

Again, you can use (0,0) as one of your points. The point (2,4) is good as the second.

slope = 4/2 = 1/2

8. We don't have a graph, but we are given two points to work with, (1,4) and (5,8). Use the formula given...

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

= (8 - 4) / (5 - 1)

= 4/4

= 1

I hope that helped!