Stephen's lunch bill is currently at $ 8.33. Stephen orders a fruit salad for take-out, and wants to leave $ 2.25$ as a tip for his server. He has a $\$ 10$ bill and a $5 bill. How much change should he receive after paying for his lunch, the fruit salad, and the tip?
The amount of change that Stephen receives is $______

Answer:

Area = 324ft²

Perimeter = 72ft

Step-by-step explanation:

Area of a square = length²

Area of a square = (18ft)² = 324ft²

Perimeter of a square = 4*length

Perimeter of a square = 4ft*18 = 72ft

The required 80% confidence interval is (46.15, 49.85).

In frequentist statistics, a confidence interval is a range of estimates for an unknown quantity.

The most common confidence level is 95%, but when calculating confidence intervals, other levels, such as 90% or 99%, are also occasionally employed.

So, we know that:

n = 32

χ' = 48

s = 8

Create an 80% confidence interval using the equation below:

[tex]\left(\bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}\right)[/tex]

To determine the critical value t for n-1 degrees of freedom and 1 -cl level of significance, use the formula below:

[tex]t_{0.2, d f=31}=\pm 1.309[/tex]

Create the confidence interval now:

[tex]\begin{aligned}& \left(48 \pm 1.309 \times \frac{8}{\sqrt{32}}\right) \\& (48 \pm 1.85) \\& (46.15,49.85)\end{aligned}[/tex]

Therefore, the required 80% confidence interval is (46.15, 49.85).

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Answer:

A translation is a type of transformation that moves each point in a figure the same distance in the same direction

Step-by-step explanation:

Translations are often referred to as slides. You can describe a translation using words like "moved up 3 and over 5 to the left" or with notation.

Answer:

Yes

Step-by-step explanation:

All you need to do is figure out the missing angles. We know that the three angles in a triangle add up to 180 degrees.

For angle B in ABC, 180-52-39= 89. So angle B = 89 degrees.

For angle D in DEF, 180-39-89= 52. So angle D = 52 degrees.

Then see if the order of the angles match up.

DEF = 52 degrees, 89 degrees, 39 degrees

ABC = 52 degrees, 89 degrees, 39 degrees

The order of the same angles match, so triangle DEF and triangle ABC are equal.

Answer:

Yes, triangle DEF is similar to triangle ABC because their corresponding angles are the same size.

Step-by-step explanation:

Interior angles of a triangle sum to 180°.

⇒ ∠A + ∠B + ∠C = 180°

⇒ 52° + ∠B + 39° = 180°

⇒ ∠B = 89°

⇒ ∠D + ∠E + ∠F = 180°

⇒ ∠D + 89° + 39° = 180°

⇒ ∠D = 52°

Two triangles are similar if their corresponding angles are the same size.

If ΔDEF ~ ΔABC then:

From inspection of the given diagram:

Therefore, the triangles are similar because their corresponding angles are the same size.

Answer:

16.5

Step-by-step explanation:

11/3 =3 and 1/3 so 55/3 and 1/3 = 16.5 or 16 and 1/2

To calculate the expected value of playing this game, we need to multiply the value of each possible outcome by its probability of occurring and then add these values together. In this case, there are 3 gold marbles, 7 silver marbles, and 28 black marbles in the bag, for a total of 38 marbles. So, the probability of selecting a gold marble is 3/38, the probability of selecting a silver marble is 7/38, and the probability of selecting a black marble is 28/38. The value of winning $3 if a gold marble is selected is $3 * (3/38) = $0.21. The value of winning $2 if a silver marble is selected is $2 * (7/38) = $0.37. And the value of losing $1 if a black marble is selected is -$1 * (28/38) = -$0.74. Adding these values together, we get $0.21 + $0.37 - $0.74 = -$0.16. Therefore, the expected value of playing this game is approximately -$0.16.

Answer: 1.8 rounded to the nearest tenth will remain as 1.8 because 0.8 is 8 tenths

Answer:

Step-by-step explanation:

11.3

Answer:

100.72

Step-by-step explanation:

[tex]Given,[/tex]

event requires each runner to jump 10 hurdles that are spaced 8.5 meters apart.

If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,

Solution:

runner to jump 10 hurdles that are spaced 8.5 meters apart.

Distance between 10 hurdles

=(10-1)* 8.5

=9*8.5

=76.5

If there are 13.72 meters from the starting line to the first hurdle and 10.5 meters from the last hurdle to the finish line,

Hence length of race = 13.72+76.5+10.5

=100.72

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Answer:

100.72 meters

Step-by-step explanation:

To find the total length of the race, we need to sum:

The distance from the starting line to the first hurdle is 13.72 meters.

The distance between each of the 10 hurdles is 8.5 meters.

There are 9 spaces between hurdles 1 and 10, so the distance between the hurdles is 9 × 8.5 = 76.5 meters.

The distance from the last hurdle to the finish line is 10.5 meters.

To find the total length of the race, add these distances together:

[tex]\begin{aligned}\textsf{Total length of the race} &=\sf 13.72\; meters + 76.5\; meters + 10.5 \;meters\\\\&=\sf 100.72\; meters\end{aligned}[/tex]

Therefore, the race is 100.72 meters long.

With the help of algebra mathematical model equation for demand of company's product is given by the equation d = 1800 / p.

What is algebra?

The area of mathematics known as algebra deals with the representation of problems as mathematical expressions. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

Let demand for company's product d vary inversely with its price p, which means

d ∝ ( 1/p ) or d = k * ( 1/ p) = k / p  ----- 1

As when p = 4.5, d = 400

Putting these in (1), we get 400 = k/ 4.5

Hence #k=400 x 4.5=1800 and our model equation is

d = 1800/p

Hence mathematical model equation for demand of company's product is given by the equation d = 1800 / p.

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To determine the longest wavelength photon which can remove an electron from mercury metal, we need to use the equation:

wavelength = hc/work function

Photons are just light particles. Photons are basic subatomic particles that convey the electromagnetic force (and so much more). The photon is the basic unit of electromagnetic radiation, or the "quantum."

A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is often defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm).

To determine the longest wavelength photon which can remove an electron from mercury metal, you need to use the equation:

wavelength = hc/work function

where h is the Planck constant (6.626 x 10^-34 Js), c is the speed of light (2.998 x 10^8 m/s), and work function is the minimum energy needed to remove an electron from the metal, in this case 4.475 eV.

Plugging these values into the equation gives:

wavelength = (6.626 x 10^-34 Js)(2.998 x 10^8 m/s)/(4.475 x 1.602 x 10^-19 J/eV)

This simplifies to:

wavelength = 404.4 nm

So, the longest wavelength photon which can remove an electron from mercury metal is 404.4 nm.

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Answer:

Step-by-step explanation:

x4 – 6x2 – 27 = 0

                        x=2.49,-2.49

3x4 = 2x

x=6

Answer:

14/2+4x4-4= 19

Step-by-step explanation:

calculate

7+19-4

which is 19

(BODMAS rule is used here)

14/2 + 4 × 4 - 4

7 + 4 × 4 - 4

7 + 16 - 4

7 + 12

19

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Answer:

5/8

Step-by-step explanation:

1/4=2/8

7/8-2/8=5/8

5/8 cannot be simplified

Answer:

5/8

Step-by-step explanation:

(7-2)/8

5/8

The number of different ways the coach can pick up the line of the game is 792 ways

Step-by-step explanation:

Let n- number of players, r-selection of players.

We can select them using Combination: nCr = 12C5

Combination formula nCr =[tex]\frac{n!r!}{ (n-r)!}[/tex]  = 12C5 = [tex]\frac{12!5!}{(12-5)! }[/tex]

=[tex]\frac{12!5!}{ 7!}[/tex]

= 792ways

The number of different ways the coach can pick up the line of the game is 792 ways.

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Graph the line using the slope and y-intercept, or two points.

Slope:

1

y-intercept: (0,3)

x  y

0 3

1  4

Answer:The selling price of shoes after a markup of 60% of the price will be equal to $81.60

Step-by-step explanation:

i don't think this is right

To find (f - g)(x), you can subtract g(x) from f(x):

(f - g)(x) = f(x) - g(x)

= (2x2 + 2) - (6x2 + 6)

= -4x2 + (-4)

= -4(x2 - 1)

Therefore, the result of (f - g)(x) is -4(x2 - 1).

Answer:

$ 2649.98

Step-by-step explanation:

1607 days = 1607/365 yrs

3000  =  (deposit) + deposit * i * 1607/365      where i = decimal interest 3000 =  deposit ( 1 + .03 * 1607/365)

   3000/(1 + .03 *  1607/365) = deposit = $ 2649.98  

First, we can rewrite the given equation as:

where Ï is the non real cube root of unity.

We can then multiply both sides of the equation by Ï to get:

This simplifies to:

Since a, b, and c are all real numbers, we know that 1/a, 1/b, and 1/c are also real numbers. Therefore, the sum of these three real numbers must also be a real number. The only way that 1/a + 1/b + 1/c can equal 0 is if all three of these terms are equal to 0.

Thus, we can conclude that a = b = c = 0.

Since a, b, and c are all equal to 0, we know that abc + bcd + acd + abd must also equal 0. Therefore, the answer is 0.

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In an experiment studying the effects of alcohol on social anxiety, alcohol is the dependent variable. So, correct option is option D.

Variables: The goal of all research is to describe and explain global dispersion. Variance is just the difference. That is, the fluctuations that occur naturally in the world, or the changes that occur as a result of manipulation. A variable is the name given to the variance you want to describe. A variable is the result of a force or is itself a force that changes another variable. There are two types of variables.

When researchers administer an active drug to one group of people and placebo or an inactive drug to another group of people, the independent variable is drug treatment. Each person's response to active drug or placebo is called the dependent variable.

In this case, an experiment examining the effects of alcohol on social anxiety. Alcohol is the dependent variable here.

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The equation of the line passes the origin. And the inclination of the line with the x-axis is 3/2. And the graph is given below.

An association between various factors brings about a straight model when a diagram is shown. The variable will have a level of one.

The straight condition is given as,

y = mx + c

Where m is the incline of the line and c is the y-block of the line.

The equation of the line is given below.

y = (3/2)x

The y-intercept is zero. Then the condition of the line passes the beginning. Furthermore, the tendency of the line with the x-pivot is 3/2.

The graph of the line is drawn below.

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Step-by-step explanation:

this is a college level question, and you need help with that ? elementary school students have to be able to answer this.

30 = 27 + 3

6 × 9 = 54

81 / 9 = 9

2 = 10 / 5

8 × 4 = 32

72 / 9 = 8

7 × 7 = 49

Answer:

reflection then rotation

Step-by-step explanation:

Answer:  a is a rational number

Step-by-step explanation

Rational numbers are written in p/q form.

Answer: $380

Step-by-step explanation:

    First, we will find the price per visit using addition.

$125 + $65 = $190

    Next, we notice it says "twice a month" in the question. We will multiply the value above by two to find the price per month.

$190 * 2 = $380

Answer:

twice a month of 125 + 65

2($125 + $65)

= 2($190)

= $380

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

(9-7)/10

2/10

(2:2) / (10:2)

1/5

The measure of an angle X is 11° and 3X+2°=35° , 4X-9° =35° .

In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

∠QPA = ∠UPA

3X+2 =4X- 9

4X-3X= 9 + 2

X= 11

The measure of X is 11

3X+2°=3(11)+2°

=35°

(4X-9)°=(4(11)-9)°

=35°

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The outcomes listed must be independent is false about probability distributions.

In probability theory, statistics, and the theory of stochastic processes, independence is a key concept. Informally speaking, two occurrences are independent, statistically independent, or stochastically independent if their occurrence has no bearing on either their chances or probability of occurring. Similarly to this, two random variables are independent if the probability distribution of either one is unaffected by the realization of the other.

It is important to distinguish between two definitions of independence when working with collections of more than two occurrences. Informally, mutual independence of events refers to each event being independent of any combination of other events in the collection, whereas pairwise independence of events refers to any two events in the collection being independent of each other.

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x = 5 will be the correct answer and Model is provided in attachment don't look at the beauty of my figure.

The solution of the equation 2x + 2 = 12 is x = 5. And the model and the graph are given.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Equation 2x + 2 = 12

The model for the equation is given in the attached image.

And the graph is also given in the attached image.

To solve for x:

2x + 2 = 12

Simplifying,

2x = 12 -2

2x = 10

Divide by 2,

2x / 2 = 10 / 2

x = 5.

Therefore, the solution of the equation is x = 5

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