You are given 12 to 1 odds against drawing two hearts when two cards are selected at random from a standard deck of 52 cards (with replacement of the first card before the second card is drawn). This means that you win $12 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. Round to the nearest cent.

The amount of money he will have after eight years of savings would be = 15,600.

To calculate the total amount of money the skateboarder will have after the number of giveyears, the formula that should be used would be given below as follows:

Simple interest = Principal×time ×rate /100

Where:

principal = 10,000

Time = 8 years

Rate = 7%

Simple interest = 10,000×8×7/100

= 560000/100

= 5600

The total amount of money the skateboarder will have will be = 10,000+5600 = 15,600

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Answer:

14 students have to retake the test

Step-by-step explanation:

to calculate the mean mark as

sum of ( product of mark and frequency ) ÷ total

mean = [tex]\frac{14(2)+15(10)+16(2)+17(3)+18(13)}{30}[/tex]

        = [tex]\frac{28+150+32+51+234}{30}[/tex]

       = [tex]\frac{495}{30}[/tex]

      = 16.5

students who score less than 16.5 will retake the test , that is

2 scored 16 , 10 scored 15 , 2 scored 14

number who have to retake test = 2 + 10 + 2 = 14

This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.

The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:

∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))

The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.

The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.

The statement can be interpreted as follows:

"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."

In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.

It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.

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The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

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The expressions that are equivalent to 2c - 8. By applying algebraic properties and operations such as distribution, Simplification, addition, and subtraction its equivalence to the original expression.

To find expressions that are equivalent to 2c - 8, we can use the properties of algebraic operations to manipulate and simplify the expression. Here are a few examples:

1. 2(c - 4):

  By using the distributive property, we can distribute the 2 to both terms inside the parentheses:

  2c - 8.

  This expression is equivalent to 2c - 8 since it simplifies to the same value.

2. 2(c - 4) + 16:

  Adding 16 to the previous expression, we get:

  2c - 8 + 16.

  Combining like terms, we have:

  2c + 8.

  This expression is also equivalent to 2c - 8.

3. 4c - 16:

  By multiplying both terms in 2c - 8 by 2, we get:

  4c - 16.

  This expression is equivalent to 2c - 8 since it represents the same value.

4. 2(c - 3) - 2:

  By subtracting 2 from the previous expression, we have:

  2c - 8 - 2.

  Combining like terms, we get:

  2c - 10.

  This expression is equivalent to 2c - 8 as it simplifies to the same value.

These are just a few examples of expressions that are equivalent to 2c - 8. By applying algebraic properties and operations such as distribution, simplification, addition, and subtraction, we can manipulate the expression in various ways while maintaining its equivalence to the original expression.

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The system of equations that represents this is:

x + y = 144

x*23 + y*90 = 10347

Solving it, we conclude that they sold 39 of the Basic ones and 105 of the Super ones.

To do this, first we need to define the variables we will be using. Let's define:

x = number of basic graphers sold.

y = number of SuperGraphers sold.

They sold a total of 144 items, so x + y = 144

And they earned a total of $10347, then we can write:

x*23 + y*90 = 10347

Then the system of equations that represents this is:

x + y = 144

x*23 + y*90 = 10347

The graph of this system is on the image below, there we can see that the solution is (39, 105).

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let's keep in mind that an inverse function has the same x,y pairs as the original function but flipped sideways, another mouthful way to put it is, the domain of the original function is the range of the inverse and the range of the original is the domain of the inverse.

well, since that's the case for g(x), Check the picture below.

now let's check for h⁻¹(x)

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{h(x)}{h}~~ = ~~\cfrac{x-9}{7}\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~\cfrac{h-9}{7}} \\\\\\ 7x=h-9\implies 7x+9=h ~~ = ~~ h^{-1}(x)[/tex]

now, what's [tex]\left( h^{-1}\circ h \right)(-5) ~~ \implies ~~ h^{-1}(h(-5))\textit{\LARGE ?}[/tex]

we know that h(x) is a one-to-one function and its inverse is a function, since that's the case h⁻¹(  h(x)  ) = x.

what the heck all that means?  well, it simply means that

[tex]\left( h^{-1}\circ h \right)(-5) ~~ \implies ~~ h^{-1}( ~~ h( ~~ \text{\LARGE -5} ~~ ) ~~ )~~ = ~~\text{\LARGE -5}[/tex]

Answer:

Step-by-step explanation:

Calculating the area of a road involves considering the road's shape and cross-sectional profile. There are two common methods for calculating the area:

Cross-Sectional Area Method: This method involves measuring the width of the road at regular intervals along its length and taking elevation measurements. By dividing the road into sections and multiplying the width by the corresponding elevation difference, you can calculate the area of each section and sum them up to obtain the total road area.

Digital Terrain Model (DTM) Method: This method uses advanced surveying techniques to obtain a digital terrain model of the road surface. By applying surface area algorithms to the DTM, you can calculate the surface area of the road, considering the elevation data and interpolating the area between points.

The chosen method depends on available data, accuracy requirements, and project needs. It is essential to refer to engineering standards and guidelines specific to your region or project for accurate and appropriate road area calculations.

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Answer:

The percent of change in Anna's working hours is 22%, indicating an increase.

Step-by-step explanation:

Step 1: Calculate the difference:

Difference = 36 hours - 28 hours

Difference = 8 hours

Step 2: Calculate the percent change:

Percent Change = (Difference / Original Value) * 100

Percent Change = (8 hours / 36 hours) * 100

Percent Change ≈ 22.22%

Therefore, the percent change in Anna's working hours is approximately 22.22%, representing an increase.

The biconditional statement is: A rectangle is a parallelogram with four right angles if and only if a parallelogram has four right angles.

The term "if and only if" or biconditional statement refers to a compound statement composed of two conditional statements connected by a logical operator.

This definition is commonly utilized to describe the characteristics of a rectangle when it comes  to its correlation with a parallelogram. The opening section of the biconditional statement is comprised of a conditional statement indicating that a rectangle is defined as a parallelogram featuring four right angles.

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Write this definition as a biconditional statement.

A rectangle is a parallelogram with four right angles.

The translation pattern that took place is given as follows:

(x, y) -> (x + 2, y - 9).

The effect on the coordinates is given as follows:

The four translation rules are defined as follows:

Hence the composite translation rule from ABC to A'B'C' is given as follows:

(x, y) -> (x + 2, y - 9).

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Answer: -16

Step-by-step explanation:

The distance away from zero is 16 and -16 is negative + do u do rsm

The first quartile being 39 years old indicates a relatively younger age profile among the employees at CCNHS – Main Campus.

The first quartile (Q1) of the ages of the 256 employees of CCNHS – Main Campus being 39 years old implies that 25% of the employees have an age equal to or less than 39 years old.

To solve the problem, we need to understand the concept of quartiles. In statistics, quartiles divide a data set into four equal parts. The first quartile represents the point below which 25% of the data falls.

In this case, since the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

This information provides insight into the age distribution of the employees. It suggests that there is a significant proportion of younger employees within the institution. Understanding the age demographics can be important for various purposes such as human resources planning, identifying generational differences, and designing age-appropriate policies or programs.

Overall, the first quartile being 39 years old indicates a relatively younger age profile among the employees at CCNHS – Main Campus.

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Jasmine has 8 glasses of lemonade remaining in the pitcher.

Jasmine made a pitcher of lemonade, which contains 12 glasses of lemonade. She served 4 glasses of lemonade, and we need to determine how many more glasses she has left.

To solve this problem, we can subtract the number of glasses served from the total number of glasses in the pitcher:

12 (total glasses) - 4 (glasses served) = 8 (glasses remaining)

Therefore, Jasmine has 8 glasses of lemonade left in the pitcher after serving 4 glasses.

In terms of the equation, we have:

Total number of glasses - Number of glasses served = Number of glasses remaining

Or:

12 - 4 = 8

So, the correct equation and solution are:

12 - 4 = 8

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Answer:

Step-by-step explanation:

cos θ=0.58

[tex]\theta=cos^{-1} (0.58) \approx 54.55^\circ,(360-54.55)^\circ\\\theta=305.45^\circ[/tex]

∵ θ lies between 180° and 360°

Answer: 4032 cm^2.

Step-by-step explanation: The equation to find the surface area of a rectangular prism is SA=2(wl+hl+hw). Substitute the given values into the equation. SA=2(12x12+15x12+15x12). Simplify inside the parentheses. SA=2(144+180+180). SA=2(504). SA=1008 cm^2. This is the surface area for 1 box. Multiply the surface area by 4 to get the total surface area of 4 congruent boxes. 1008x4=4032 cm^2.

Kendra | | | |

Madison | | | | | | | | | | | | | | | | | | | | | | | |

Madison drew 24 dolphins.

To solve this problem, we need to use the information given in the problem and represent it in a bar model. Let's use the following bar model:

Kendra: 4 dolphins

Madison: 6 times as many dolphins as Kendra

Kendra | | | |

Madison | | | | | | | | | | |

From the model, we can see that Kendra drew 4 dolphins and we don't know how many dolphins Madison drew, which is represented by "d". The problem tells us that Madison drew 6 times as many dolphins as Kendra, so we can multiply Kendra's number of dolphins by 6:

Kendra: 4 dolphins

Madison: 6 x 4 = 24 dolphins

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Answer:

3

Step-by-step explanation:

tan(A) = y-coordinate / x-coordinate

tan(A) = -3 / -1

tan(A) = 3/1

tan(A) = 3

Therefore, the value of tan(A) is 3.

Answer:

$393,120

Step-by-step explanation:

To find the decrease in the house's value in dollars, we need to calculate 9% of the initial value:

Decrease in value = (Initial value) * (Percentage decrease) = $432,000 * 9%

Converting the percentage to a decimal:

Decrease in value = $432,000 * 0.09 = $38,880

The house's value decreased by $38,880.

Now, to find the current value of the house, we need to subtract the decrease in value from the initial value:

Current value = Initial value - Decrease in value = $432,000 - $38,880 = $393,120

The current value of the house is $393,120.

Hope this helps!

De acuerdo con la información, podemos inferir que un ejemplo de experimento aleatorio con orden y reemplazo: Lanzar un dado y registrar el resultado en cada lanzamiento.

Los experimentos aleatorios tienen diferentes formas de aplicación según su tipo, a continuación explicamos algunos:

De acuerdo con lo anterior, UN ejemplo de experimento aleatorio con orden y reemplazo: Lanzar un dado y registrar el resultado en cada lanzamiento.

Question in English

Give examples of randomized experiments with order, replacement, and no repetition.

Answer in English

Based on the information, we can infer that an example of a random experiment with order and replacement: Throw a die and record the result on each throw.

Random experiments have different forms of application depending on their type, some of which are explained below:

Order involve recording the results in sequence, while experiments. Orderless do not take into account the order in which the results occur. With replacement, items can be repeated in each selection, while in experiments. Without replacement, the selected items they are no longer available for subsequent selections.

Based on the above, ONE example of a random experiment with order and replacement: Roll a die and record the result on each roll.

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Covariance between two variables x and y is -9/56 (= -0.160). Option C

Covariance between two variables is a measure of how much the variables change together. It's calculated with the formula:

Cov(X, Y) = E[XY] - E[X]E[Y]

Where:

E[XY] is the expected value of the product of X and Y.

E[X] is the expected value of X.

E[Y] is the expected value of Y.

First, we need to calculate E[X], E[Y], and E[XY].

E[X] = ∑ x × g(x) for all x

= 0×(5/14) + 1×(15/28) + 2×(3/28)

= 15/28 + 6/28 = 21/28 = 0.75

E[Y] = ∑ y × h(y) for all y

= 0×(15/28) + 1×(3/7) + 2×(1/28)

=0.5

E[XY] = ∑∑ xyf(x, y) for all (x, y)

= 00(3/28) + 01(3/14) + 02(1/28) + 10(9/28) + 11(3/14) + 12(0) + 20(3/28) + 21(0) + 22(0)

= 0.2143

Now we can substitute these values into the formula for Cov(X, Y):

Cov(X, Y) = E[XY] - E[X]E[Y]

= 0.2143 - (0.75)×(0.5)

= -0.1607

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Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Statement 1, 2 and 3 are correct about using the distributive property.

Expanding is the same as using the distributive property. Factoring means going from ab + ac to a(b + c).Factoring can only be done when an expression has two terms.

Statement 1: Expanding is the same as using the distributive property. The distributive property states that a(b + c) = ab + ac. When we expand an expression, we are multiplying everything out. So, expanding an expression is the same as using the distributive property. Therefore, this statement is correct.

Statement 2: Factoring means going from ab + ac to a(b + c).When we factor an expression, we are essentially undoing the distributive property. In other words, we are going from a common factor in the two terms to a product. This is exactly what happens when we factor ab + ac to a(b + c). Therefore, this statement is correct.

Statement 3: Factoring can only be done when an expression has two terms. Factoring is the process of breaking down an expression into simpler factors. However, in order to do that, the expression needs to have two or more terms. If the expression only has one term, then we cannot factor it. Therefore, this statement is correct.

Statement 4: Factoring can only be done when an expression has plus signs. This statement is incorrect. Factoring can be done when an expression has either plus signs or minus signs. For example, we can factor x² - 4 to (x + 2)(x - 2). Therefore, this statement is incorrect.

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The measures of central tendency of the dataset, and the measurements in the dataset indicates;

(a) Mode

(b) Mean

(c) Mean, Median

(d) Roughly symmetrical

Measures of central tendency are descriptive statistical values that represent the typical value or centerpoint of a data set.

(a) The mean of a data set always has only one value. The mode of the dataset are 11 and 14. Therefore, the measure of central tendency that takes more than one value is the mode. The correct option is therefore;

Mode

(b) The mode will remain the same. The middle value or median will remain the same. The mean, which i the average value will increase. The correct option for measure of central tendency that will be affected by the change is therefore the mean.

Mean

(c) The smallest measurement which is 1, if removed, the mean will change and the median will change from 11 to (10 + 11)/2 = 10.5. The correct options for the measures of central tendency that will change are therefore;

Mean

Median

(d) The distribution of the original dataset can be presented as shown in the histogram, which is symmetrical about the class with one of the modes, indicating that the original data is roughly symmetrical about the class with the mode 11. The correct option is therefore;

Roughly symmetrical

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Step-by-step explanation:

I'm pretty sure you just use the law of cosines in this case.

c= sqrt(a^2+b^2﹣2ab (cos γ))
where a is a Side, b is a Side, γ is Gamma or the angle. Sqrt means square root

In your case, a is 20, b is 13, and  γ is 93. Just plug it into the formula now :). I got 24.41751 ish.

Answer:

$61.29 per day.

Step-by-step explanation:

Checking account balance on February 1st: $443

Checking account balance on February 7th: $872

Difference in balances: $872 - $443 = $429

Number of days between February 1st and February 7th: 7 days

Rate of change = Difference in balances / Number of days

Rate of change = $429 / 7 days

To find the rate of change per day, divide the difference in balances by the number of days:

Rate of change = $429 / 7 days ≈ $61.29 per day

Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.

The surface integral in terms of ρ and θ ∫∫S.((6y - 5)e^(x^2))

To evaluate ∬s.curl F•nds using Stokes' Theorem, we first need to find the curl of the vector field F and then compute the surface integral over the given surface S.

Given vector field F = (6yz)i + (5x)j + (yz(e^(x^2)))k, let's find its curl:

∇ × F = ∂/∂x (yz(e^(x^2))) - ∂/∂y (5x) + ∂/∂z (6yz)

Taking the partial derivatives, we get:

∇ × F = (0 - 0) i + (0 - 0) j + (6y - 5)e^(x^2)

Now, let's parametrize the surface S, which is the portion of the paraboloid z = (1/4)x^2 + y^2 for 0 ≤ z ≤ 4. We can use cylindrical coordinates for this parametrization:

r(θ, ρ) = ρcos(θ)i + ρsin(θ)j + ((1/4)(ρcos(θ))^2 + (ρsin(θ))^2)k

where 0 ≤ θ ≤ 2π and 0 ≤ ρ ≤ 2.

Next, we need to find the normal vector n to the surface S. Since S is oriented upward, the normal vector points in the positive z-direction. We can normalize this vector to have unit length:

n = (∂r/∂θ) × (∂r/∂ρ)

Calculating the partial derivatives and taking the cross product, we have:

∂r/∂θ = -ρsin(θ)i + ρcos(θ)j

∂r/∂ρ = cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k

∂r/∂θ × ∂r/∂ρ = (-ρsin(θ)i + ρcos(θ)j) × (cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k)

Expanding the cross product, we get:

∂r/∂θ × ∂r/∂ρ = (ρcos(θ)(1/2)(ρcos(θ)) - (1/2)(ρcos(θ))(-ρsin(θ)))i

+ ((1/2)(ρcos(θ))sin(θ) - ρsin(θ)(1/2)(ρcos(θ)))j

+ (-ρsin(θ)cos(θ) + ρsin(θ)cos(θ))k

Simplifying further:

∂r/∂θ × ∂r/∂ρ = ρ^2cos(θ)i + ρ^2sin(θ)j

Now, we can calculate the surface integral using Stokes' Theorem:

∬s.curl F•nds = ∮c.F•dr

= ∫∫S.((∇ × F)•n) dS

Substituting the values we obtained earlier:

∫∫S.((∇ × F)•n) dS = ∫∫S.((6y - 5)e^(x^2))•(ρ^2cos(θ)i + ρ^2sin(θ)j) dS

We can now rewrite the surface integral in terms of ρ and θ:

∫∫S.((6y - 5)e^(x^2))

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