3. For the graph above, what is the approximate y-value of the point of intersection?
0-1
04
03
02

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$9200\\ r=rate\to 4.9\%\to \frac{4.9}{100}\dotfill &0.049\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &5 \end{cases} \\\\\\ A=9200\left(1+\frac{0.049}{4}\right)^{4\cdot 5}\implies A=9200(1.01225)^{20} \implies A \approx 11736.63[/tex]

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

12% of peanut M&M’s = brown

15% = yellow

12% = red

23% = blue

23% = orange

15% = green

Here, Probability of an event is represented as P

a) P(not green) = 100% - 15%

                        = 85%

                        = 0.85

b) P(yellow or red) = 15% + 12%

                               = 27%

                               = 0.27

c) P(three blue) = 0.23*0.23 *0.23

                         = 0.012 (rounded to 3 decimal places)

d) P(not green if you choose 6 )= [tex](0.85)^{6}[/tex]

                                                    = 0. 377

e) P(at least 1 green if you choose 6 ) = 1 - 0.377

                                                              = 0.623

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The spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.

An average is a single number taken as representative of a list of numbers, generally the sum of the numbers divided by how many numbers are in the list (the arithmetic mean).

The formula to calculate the average of given numbers is equal to the sum of all the values divided by the total number of values. Average = Sum of Values / Number of Values.

So, in this case:

Values: 25, 50, 75

Number of Values: 3

Thus, the average:

Sum of Values / Number of Values = (25 + 50 + 75) / 3 = 50

Hence, the spreadsheet formula that would correctly calculate the average (mean) of the given values is: (25 + 50 + 75) / 3 = 50.

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Answer:

1309.10

Step-by-step explanation:

1200 = 110%

(1200/110)*120 = 1309.10

Answer:

159

Step-by-step explanation:

To find half of an amount, multiply the amount by 1/2 which is the same as dividing the amount by 2.

318 × 1/2 =

= 318 ÷ 2

                        159

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

              2  |  318

                   - 2

               ------------

                      11

                    - 10

                   -------

                        18

                      - 18

                      ------

                          0

318 × 1/2 = 318 ÷ 2 = 159

The given expression evaluates to -19.

We have the following expression -

- 6 - 13

The given expression evaluates to -

x = - 6 - 13

x = - 19

Therefore, the given expression evaluates to -19.

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Answer: 24

Step-by-step explanation:

A=5 so F(x)=5^2-1

F(x)=24

Answer:

Bachelor's Degree: $55,000
Master's Degree: $61,000

Step-by-step explanation:

First start defining variables for each of the salaries

Let M be the salary of the master's individual

Let B be the salary of the bachelor's individual

Given:
Average yearly salary of an individual whose final degree is a master's is $49 thousand less than twice that of an individual whose final degree is a bachelor's

can be translated into the equation

M = 2B - 49,000

Subtract M from both sides and add 49,000 to both sides:

49,000 = 2B - M

Switch sides:

2B - M = 49,000   [1]

Together they earned 116,000 becomes

B + M = 116,000   [2]

Add equations [1] and [2] to eliminate M
2B - M + B + M = 49,000 +116000
3B = 165000

B = 165000/3 = 55,000

Using equation 2, B + M = 116000 we get

55000 + M = 116000

M = 116000 - 55000 = 61,000

Solution
Bachelor's Degree: $55,000
Master's Degree: $61,000

Answer:

[tex]\huge\boxed{\sf v = 0.4\ mph}[/tex]

Step-by-step explanation:

Distance = S = 4/5 miles = 0.2 miles

Time = t = 1/2 hour = 0.5 hours

Speed = v = ?

v = S/t

v = 0.2/0.5

[tex]\rule[225]{225}{2}[/tex]

Answer: 8/5 mph

Step-by-step explanation:

According to definition, an object's speed is determined by:

s=d/t where,

d is the object's travel distance, and t is the amount of time it takes.

We can replace these values with:

Since, s= (4/5) / (1/2) mph

=> s= 8/5 mph

The object's speed to cover 4/5 miles in 30 minutes is: 8/5 mph

Answer:

C

Step-by-step explanation:

it is still C, as the angle-angle-angle information of D is not enough. the sides could all grow or shrink (in the same relation, but still) and the angles would still be the same.

so, D is not enough (although we have 3 pieces of information, but this is the special case, where even that is not enough - we need at least one side in the mix).

Answer:gat big

Step-by-step explanation:

La franja amarilla del rectángulo tiene un área de 30 centímetros cuadrados.

En este problema tenemos un rectángulo formado por dos cuadrados que se traslapan uno al otro. La franja amarilla es el área en la que los cuadrados se traslapan. La anchura del rectángulo es descrita por la siguiente ecuación:

(10 - x) + 2 · x = 17

Donde x se mide en centímetros.

A continuación, despejamos x en la ecuación descrita:

10 + x = 17

x = 7

Ahora, el área de la franja amarilla se determina mediante la fórmula de area de un rectángulo:

A = b · h

Donde:

A = (10 - 7) · 10

A = 3 · 10

A = 30

El área de la franja amarilla del rectángulo es igual a 30 centímetros cuadrados.

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Total percentage of students in each department, to the whole of Lee Business School is 85.5298308   11.48709 0 2.983081     100.

What is percentage ?

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The sign "%" is frequently put after the number to indicate percentages.

Department Undergrad Master Doctoral Total

 Total % Total % Total % Numbers %

Accounting 390 17.364203 83 3.695459 0 0 473 21.05966

Economics 467 20.79252 20 0.890472 0 0 487 21.68299

Finance 215 9.5725735 7 0.311665 0 0 222 9.884239

Management, E&T 590 26.268923 75 3.33927 1 0.044524 666 29.65272

Marketing and I.B. 259 11.531612 10 0.445236 1 0.044524 270 12.02137

MBA 0 0 63 2.804987 65 2.894034 128 5.69902

Total 1921   258   67   2246  

Percentage of total students 85.5298308   11.48709 0 2.983081     100

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The inequality is y > 2x-3

option C is correct

What is inequality in math?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

The line intersects the y- axis at point (0,-3)

i.e., The y-intercept =-3

We know that,

Equation of lime, y= mx + b

                                                        b: y-intercept

                                                         m: Slope of the line

Slope of the line,

m = 0-(-3)/3/2 = 2

m ⇒ 2

∴ Equation of line,  y = 2x - 3

The shaded are is above the line, and line is represented with dotted lines,

hence the inequality is,

y > 2x - 3

Hence, option C is correct

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By AAS congruence theorem, ΔABD is congruent ΔCDB.

Quadrilateral ABCD is given in the figure.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given, AB║DC

Consider ΔABD and ΔCDB

m∠A=m∠C=90° (Given)

m∠ABD=m∠BDC (Alternate interior angles)

BD = BD (Common)

Using AAS congruence theorem, ΔABD ≅ ΔCDB

Hence, by AAS congruence theorem, ΔABD is congruent ΔCDB.

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The slope represents the average number of weeks it is Shawn to run laps is true about Shawn's line.

The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.

Given,

Graph to show number of taps he is scheduled to run a week.

True statement is,

The slope represents the average number of weeks it is Shawn to run laps.

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Answer:

50%

Step-by-step explanation:

numerator divided by denominator

1 divided by 2  =  .5

.5  x 100  =  50%

By using fraction, it can be calculated that

30 boards are required to cover a floor of width 205 inches wide

What is fraction?

Suppose there is a collection and a part of collection has to be taken.

The part which is taken is called fraction. In other words part of a whole is called fraction.

The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

This is a word problem on fraction

Width of each board = [tex]6\frac{5}{6}[/tex] inches = [tex]\frac{41}{6}[/tex] inches

Total width of floor = 205 inches

Number of boards required = [tex]205 \div \frac{41}{6}[/tex] = [tex]205 \times \frac{6}{41}[/tex] = 30

30 boards are required

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Answer:

$27.69

Step-by-step explanation:

To find the two points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13, you can use the distance formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the coordinates of the first point, and (x2, y2) is the coordinates of the second point.

In this case, you can use the distance formula to find the y-coordinates of the two points having an x-coordinate of 3:

Distance = √((3 - (-2))^2 + (y - (-1))^2)

= √(5^2 + (y + 1)^2)

= √(25 + y^2 + 2y + 1)

= √(26 + y^2 + 2y)

= 13

If you set the distance equal to 13 and simplify the equation, you get:

y^2 + 2y + 12 = 0

This is a quadratic equation, which means it can be solved using the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation.

Substituting the values into the quadratic formula, you get:

y = (-2 ± √(-2^2 - 4 * 1 * 12)) / (2 * 1)

= (-2 ± √(-4 - 48)) / 2

= (-2 ± √(-52)) / 2

Since the square root of a negative number is not a real number.

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Answer:

When factoring, you want to get all of the terms on one side first and set all of it equal to 0. Many of the problems here are already in this format =0, but there are some where you'll have to move the terms around.

In these examples, it also looks like the highest power you have is x^2. This makes things easier to work with.

Let's just start with the first one, x^2 - 9x + 18 = 0.

We need to find two numbers that multiply to give us 18, and add together to give us -9. That would be -6 and -3.

-6 + -3 = -9

- 6 * -3 = 18

We can rewrite it now. This is the factored form.

(x - 6) * (x - 3) = 0

If you want to, you can go back to expanded form using the acronym 'FOIL'. First, Outside, Inside, Last. This refers to the order of multiplying the terms.

(x - 6) * (x - 3)

x * x = x^2

x * -3 = -3x

-6 * x = -6x

-6 * -3 = 18

Simplify

x^2 - 3x - 6x + 18 = 0

And we're back to where we started.

x^2 - 9x + 18 = 0

Hope this helps.

Simplify the [tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex] we will get  20 · √30.

What do you mean by exponent and radicals?

Exponents are a convenient way of describing repeated multiplication of the same number. Radicals include the use of radical characters √

These are sometimes called surdos. The exponent is the power p of an expression of the form [tex]a^{p}[/tex]

The process of raising a base number to a given power is called exponentiation. (where a ≠ 0)

Given:

[tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex]

= (2 × 5)· [tex](\sqrt{10}\times \sqrt{12)}[/tex]

= 10 · [tex]\sqrt{120}[/tex]

= 10 · 2 · [tex]\sqrt{30}[/tex]

= 20 · √30

Therefore, [tex]2\sqrt{10}[/tex] · [tex]5\sqrt{12}[/tex] = 20 · √30

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The correct option C: -4 ≤ x ≤ -2, are the intervals in which the graph is constant.

So, from the shown graph, the horizontal line have the constant function which lies in the intervals -4 ≤ x ≤ -2.

Thus, in the intervals -4 ≤ x ≤ -2, the function is constant.

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1000 - 180x represents the remaining number of samples after x weeks.

What is exponents?

Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".

Main body:

Consider what is actually happening in the question.

You begin with 1000 samples,  after it decreases to

=1000-18% of 1000

= 820

You can see the pattern shows that the number of samples decreases 18% every week ,1000-18% of 1000 - 18% 0f 1000.

= 1000 - 180x where x denotes number of weeks.

Hence 1000 - 180x represents the remaining number of samples after x weeks.

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By solving a linear equation, we will see that they sold a total of 288 cookies.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

We know that Phil and Matt sell cookies for $0.25 each, so, if they sell x cookies, the total revenue is: R(x) = $0.25*x

Now, we know that they made a total of $72.00, so now we need to solve the linear equation:

$0.25*x = $72.00x

= $72.00/$0.25 = 288

They sold 288 cookies.

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slope formula  can be illustrated  as ,  (y₂ - y₁) / (x₂ - x₁)

It is given in question that-

x₁ = -1 and y₁ = 1

x₂ = -2and y₂ = -3

so by using given formula for slope

slope= (y₂ - y₁) / (x₂ - x₁)

slope = (-3- (1) / (-2 - (-1) = (-3 - 1) / (-2 + 1) = -4/-1 = 4

final answer , slope =4

What is slope ?

The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).

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Answer:

[tex] \sf \: slope(m) = 4[/tex]

Step-by-step explanation:

Now we have to,

→ find the required slope.

Formula we use,

→ Slope(m) = (y2 - y1)/(x2 - x1)

Then the slope will be,

→ m = (y2 - y1)/(x2 - x1)

→ m = (-3 - 1)/(-2 -(-1))

→ m = (-4)/(-2 + 1)

→ m = (-4)/(-1)

→ m = 4/1

→ [ m = 4 ]

Hence, the slope is 4.

The critical numbers of the function are; θ = π/6, 5π/6

We are given the trigonometric function as;

f(θ) =  6secθ + 3tanθ ; 0 < θ < 2π

The critical points of a function are defined as those points of the domain where the function is not differentiable or those points for which the derivative is equal to zero.

Let us find the first derivative;

f'(θ) = 6(-sin θ/cos² θ) + 3(1/cos² θ)

f'(θ) = (3 - 6sin θ)/cos² θ

At f'(θ) = 0, we have;

3 - 6sin θ = 0

θ = sin⁻¹(3/6)

Since sin is positive, then;

θ = π/6, 5π/6

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I will have the fraction of 1/6 cups of one cup, if 3 cups of half 2/6 fill is what I have.

We can solve word problems in mathematics using the 4 basic operations (addition, subtraction, multiplication and division) on fractions.

From the question, we are have 3 cups of half 2/6 filled cups, this implies that;

2/6 filled cups = 1/3

half 2/6 filled cups = (1/3)/2

half 2/6 filled cups = 1/3 × 1/2 {changing the division to multiplication}

half 2/6 filled cups = 1/6

Therefore, I have 1/6 for one cup and for 3 cups of half 2/6 filled cups, I will have 1/2.

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