Live wants to have his birthday party at the bowling alley with a few of his friends but he must be a less than $80 the bowling alley charge a flat fee of $45 for a private party +5.50 per person

Explanation:

When solving a function, you plug in the given [tex]x[/tex]-value (what's inside the parentheses next to the [tex]g[/tex] or [tex]f[/tex]) into the corresponding equation (what [tex]f(x)[/tex] and [tex]g(x)[/tex] are set equal to).

Before starting the worksheet, take a simpler example:

Given the function [tex]h(x) = x + 2[/tex],

the following work solves for [tex]h(3)[/tex].

[tex]h(3) = 3 + 2[/tex]

[tex]h(3) = 5[/tex]

Essentially, to solve for the value of a function for a given [tex]x[/tex]-value, simply plug in that value in for [tex]x[/tex] and simplify the resulting expression.

Onto problem 14 from the given worksheet:

We are given [tex]f(x) = 3x + 2[/tex] and are asked to solve for [tex]f(4)[/tex].

Hence, all we have to do is plug [tex]4[/tex] in for [tex]x[/tex]:

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

[tex]f(4) = 12 + 2[/tex]

[tex]f(4) = 14[/tex]

You can apply this concept to the rest of the problems.

To solve complex fractions there are two methods -

1 - Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator and then simplify further if necessary.

2 - Multiply the numerator and denominator of the overall complex fractions and then simplify further if necessary.

What is a complex fraction?

A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction.

There are two ways to solve a complex fraction -

Method 1 : Take an example - (1/3-1/4)/(1/8+1/2)

Step 1 - If necessary, combine the denominator and numerator into a single fraction.

Add the numerator -

=1/3-1/4

=(4-3)/12

=1/12

Add the denominator -

=1/8+1/2

=(1+4)/8

=5/8

Combine back to form a complex fraction -

=(1/12)/(5/8)

Step 2: Multiply the numerator by the denominator's reciprocal, then divide the result by the denominator.

Step 3: Simplify the rational expression if necessary.

=(1/12)×(8/5)

=8/60

=2/15

Method 2: Take an example - [(2x+1)/(x^2-25)]/[(4x^2-1)/(x-5)]

Step 1 - Divide the LCD of the smaller fractions by the numerator and denominator of the total complex fractions.

(x^2-25)=(x+5)(x-5)

The denominator of the denominator’s fraction  has the following factor -

(x-5)

Using the highest exponent and combining all the other factors, we arrive at the LCD shown below for all the little fractions -

(x+5)(x-5)

By multiplying the LCD by the numerator and denominator -

=[{(2x+1)/(x+5)(x-5)}×(x+5)(x-5)]/[{(2x+1)(2x-1)/(x-5)}×(x+5)(x-5)]

=(2x+1)/(2x+1)(2x-1)(x+5)

Step 2 - Simplify the rational expression if necessary.

=(2x+1)/(2x+1)(2x-1)(x+5)

=1/(2x-1)(x+5)

Therefore, there are two methods to solve complex fractions.

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Answer:

68%

Step-by-step explanation:

Answer:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

5/6 roughly equals to 0.8

The answer is C

Which of the following best estmates the sum: 1/2 + 1/3

Answer: C) 0.8

Answer:

1/4

Step-by-step explanation:

Answer: 4 1/4

Step-by-step explanation: Decimal= 4.25

Answer:

Exact form: 17/4

Decimal Form: 4.25

Mixed number form: 4 1/4

This is an undefined problem

Answer:

x = -3

Step-by-step explanation:

Hi there!

Typically, linear equations would be organized in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis).

However, notice how the two x-coordinates of the given points are the same. They're both -3. This means that this is a vertical line, and vertical lines are organized in this equation: x=d where d is the x-intercept (the value of x when the line crosses the x-axis).

We know that the x-intercept is -3, since all the x-coordinates of the points that a vertical line passes through are the same. Therefore, the equation of this line is x=-3.

I hope this helps!

Answer:

One number is 5 and the other is 1.

Step-by-step explanation:

Let the numbers be x and y.  Then x + y = 6 and x - y = 4.  We must solve this system of equations:

x + y = 6

x - y = 4

Combining these equations temporarily eliminates y:

x + y = 6

x - y = 4

--------------

2x     = 10

Then x = 5.  Since x - y = 4,

5 - y = 4

and so y must be 1.

The solution is (5, 1).  One number is 5 and the other is 1.

The coordinate pair of the given system is (-1,9)

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Multiply the first equation by 2 and add the equation 2(6x - y) = 2(-15)

Add the new equation 12x - 2y = -30 to the second equation

12x - 2y = -30, x+2y = 17, add the two equations to eliminate y

13x = -13

x = -1

Substitute -1 back into the equation x+2y = 17.

-1 + 2y = 17

2y = 18

y = 9

So the solution of the system is x = -1, y = 9

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They have 0.875 pounds of gummy each

Just divide by 2

Logical Error: In computer programming language, a logic error is a bug or in a program or code that causes it to operate incorrectly, but not to terminate abnormally (or crash).

A logic error developed unintended or undesired output or other behavior, although it may not immediately be recognized as such.

For example, assigning a value to the wrong variable may cause a many of unexpected program errors.

These errors can be programmer mistakes or sometimes machine less memory to load the code.

if(x>=5) {

// program

}

else if(x==5) {

//program

}

else(x<=5) {

//program

}

they all do not give any error.

x=5 gave an error because it is value assigning to 5.

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Answer:

92°

Step-by-step explanation:

We can say that the angle that is of x degrees is an inscribed angle because its vertex is on the circle and its sides are made up of rays. When you have an inscribes angle, it measures exactly half the angle it intercepts. In this case that angle is 184°. So, because of this we can say:

x = 184° / 2

x = 92°

Answer:

5 x 10^7

Step-by-step explanation:

(5 x 10^4)·(1 x 10³) = 5 x 10^7 = 50 million

The area of the frame is 196.73 x²

What is area ?

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth.

(15x)^2 = 225x^2

Area of the frame

= π (3x)²

= 28.27 x²

Metal area surrounding the frame

225 x² - 28.27 x²

= 196.73 x²

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A. ∠F corresponds to ∠F' is True.

B. Segment EE' is parallel to segment FF' is False.

C. The distance from point D' to the origin is One-third the distance of point D to the origin is True.

D. The measure of ∠E' is One-third the measure of ∠E is False.

E. △DEF ~ △D'E'F' is True.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.

Given:

As triangle DEF was dilated according to the rule DO, One-third(x, y)(one-third x, one-third y) to create similar triangle D'E'F'.

and, The center of dilation = (0, 0)

Also, Triangle FDE has points: (- 9, 3), (- 9, 9), (- 6, 6).

Triangle F'D'E' has points : (- 3, 1), (- 3, 3), (- 2, 2)

A) ∠F corresponds to ∠F'. ( True)

B) Segment EE' is parallel to segment FF'. (False)

As they intersect each other at the origin.

C) The distance from point D' to the origin is One-third the distance of point D to the origin.    ( True)

Now, the length of DE

D = √(-9-0)² + (-9-0)²

D = 9√2

and, length of D'E'

D = √(-3-0)² + (-3-0)²

D = 3√2

Thus, DE / D'E' =  3√2/  9√2 = 1/3

D) The measure of ∠E' is One-third the measure of ∠E. ( False)

E)  △DEF ~ △D'E'F'.  ( True)

As they are similar triangles.

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Answer:

A. ∠F corresponds to ∠F'.

C. The distance from point D' to the origin is 1/3 the distance of point D to the origin.

E. △DEF ~△D'E'F'

Step-by-step explanation:

got it right on edge 23

Answer:

I'm pretty sure the answer is B.

Step-by-step explanation:

so you multiply 3x4 and get 12. Then you multiply 5x11 and get 55. last but not least multiply 12 and 55 and get 660 so yeah hope it helps

The residual of the given situation is 0.8

The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.

Given that, The grade can be modelled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. We are asked to find residual if student who was in attendance for 75 days and has a grade of 82%,

Finding the actual value,

y = 0.66 × 75 + 33.3

y = 82.8

The predicted value = 82

Residual = actual y value − predicted y value

Therefore,

Residual = 82.8-82 = 0.8

Therefore, y = 0.8

Hence, the residual of the given situation is 0.8

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Answer:

V=87.92

Step-by-step explanation:

v=bh,V=3.14*2*2*7

The value of x would be 32.

What are a congruent quadrilaterals?

In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.

In the given figure PQRS ~ WXYZ

x = YZ

x = 32.

Hence, the value of x would be 32.

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By analyzing the figure, The value of x would be 32.

In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.

In the given figure PQRS ~ WXYZ

x = YZ

x = 32.

Hence, the value of x would be 32.

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9514 1404 393

Answer:

  WV = 6

Step-by-step explanation:

The hash marks indicate the corresponding lines are the same length. That is, W is the midpoint of YZ, because YW ≅ WZ. Similarly, V is the midpoint of XY, because XV ≅ VY.

Using this information, it can be shown that ∆YWV ~ ∆YZX. This means corresponding sides have the same ratio.

Because YW is half of YZ, WV is half of ZX.

  YW/YZ = 1/2 = WV/ZX = WV/12

Multiplying by 12 gives the value of WV:

  WV = 12(1/2)

  WV = 6

_____

This is a long way to say that the midsegment (WV) is half the length of the base (ZX) of a triangle.

Answer:

Yes. 70% is a good percentile, most people understand the workings of a free throw (where you stand on the line, how to place your feet, how to shoot) and standing still gives you an advantage. For the people who don’t understand the workings, they are apart of that 30%.

Answer:

x = 5

Because, if you substitute 5 for x you will get 35.

5^2 + 2*5= 25+10, or 35

Step-by-step explanation:

Answer:

-4/3

Step-by-step explanation:

-2 - 1 is -3

6-2 is 4

Answer:

$3

Step-by-step explanation:

28-10=18

18/6=3

Answer:

56 Cola-flavored gumballs remaining.

Step-by-step explanation:

There are 180 gumballs. Bob purchased 40 gumballs, which leaves 140 gumballs remaining.

There are four flavors. This is the chance (shown as a percentage) of each flavor Bob recieved:

║GR: 4 ⇒ 10%

║CH: 12 ⇒ 30%

║CO: 16 ⇒ 40%

║OR: 8 ⇒ 20%

So, how can we predict the number of Cola flavored gumballs remaining?

[There is a 40% chance of getting a Cola-flavored gumball from the machine. If we find 40% of 140, we can predict that is close to the number of Cola gumballs left in the machine]

║0.40 ⋅ 140 = 56

40% of 140 is 56, so we can predict there are 56 Cola-flavored gumballs remaining.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=13.33 \end{cases}\implies V=\pi (3)^2(13.33)\implies V\approx 376.90[/tex]

The 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

n a triangle, the longest side (the hypotenuse) is opposite the largest angle, and the other two sides are opposite the smaller angles. According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the length of the third side. So, if the longest side of Karen's triangle measures 8 inches, it means that the sum of a and b (the two shorter sides) must be greater than 8 inches. Therefore [tex]a+b > 8 inches[/tex].

For the second part of your question, only one triangle can be drawn with side lengths 3, 5, and 9. The three numbers 3, 5, and 9 form a Pythagorean triple, meaning they can be used as the lengths of the sides of a right triangle. Since the longest side (the hypotenuse) must be greater than the other two sides, the 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

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here's the solution,

we know :

[tex] \sin( \theta) = \dfrac{perpendicular}{hypotenuse} [/tex]

So,

[tex] \dfrac{p}{h} = \dfrac{12}{13} [/tex]

so.. let the perpendicular be 12x and hypotenuse be 13x

now,

by applying pythagoras theorem,

where,

So,

so,

hope it helps !!

The expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.

Therefore, the game is not a good bet, as you are expected to lose money in the long run.

What is the probability distribution?

A probability distribution is a mathematical function that describes the probability of different possible values of a variable.

The probability of winning on a $5 bet on a specific number in chuck-a-luck is determined by the number of ways that the number can appear on the three dice and the total number of possible outcomes.

If the number appears on exactly one die, there are 3 ways that this can happen out of a total of 6^3 = 216 possible outcomes, giving a probability of 3/216 or 1/72.

If the number appears on exactly two dice, there are 3 ways to choose the two dice on which it appears, and 3 ways to choose the third die, giving a total of 33 = 9 ways out of 216 possible outcomes, giving a probability of 9/216 or 1/24.

If the number appears on all three dice, there is only 1 way this can happen out of 216 possible outcomes, giving a probability of 1/216.

If it appears on none of the dice, there are (543) ways this can happen, giving a probability of (54*3)/216 = 20/216.

We can use this information to construct the probability distribution for chuck-a-luck:

x P(x)

-5 (losing the bet) 20/216

5 (winning the bet for one appearance) 1/72

10 (winning the bet for two appearances) 1/24

15 (winning the bet for three appearances) 1/216

To find the expected winnings on a $5 bet, we can multiply the value of each outcome by its corresponding probability, and sum the results:

E(X) = (-5)(20/216) + (5)(1/72) + (10)(1/24) + (15)(1/216)

E(X) = -5/43.2 + 5/72 + 5/12 + 15/216

E(X) = -0.1157

Hence, the expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.

Therefore, the game is not a good bet, as you are expected to lose money in the long run.

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