Consider U = {x|x is a positive integer greater than 1}.


Which is an empty set?


{x|x ∈ U and 1/2 x is prime}


{x|x ∈ U and 2x is prime}


{x|x ∈ U and 1/2 can be written as a fraction}


{x|x ∈ U and 2x can be written as a fraction}

Given is the Principal amount, P = 1600 dollars.

Given the Annual interest is 7% i.e. r = 0.07

Given the Compounding period is semi-annually i.e. n = 2.

Given is the Time of investment, t = 33 years.

It says to find the Final Value of invested amount in the account after 33 years.

We know the formula for Future Value of Money is given as follows :-

[tex] Future \;\;Value = P*(1+\frac{r}{n})^{nt} \\\\
Future \;\;Value = 1600*(1+\frac{0.07}{2})^{(2*33)} \\\\
Future \;\;Value = 1600*(1+0.035)^{66} \\\\
Future \;\;Value = 1600*(1.035)^{66} \\\\
Future \;\;Value = 1600*(9.684185201) \\\\
Future \;\;Value = 15494.69632 \\\\
Future \;\;Value = 15,494.70 \;\;dollars [/tex]

Hence, the final balance would be 15,494.70 dollars.

Answer:

After 33 years balance in the account  = A= $15494.696

Explanation:

We will applying the compound interest formula.

[tex] A =  P(1 +\frac{r}{n})^{nt} [/tex]  

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per year

t = the number of years

Given that,

P = $1,600

r = 7%  =  [tex] \frac{7}{100}  [/tex] = 0.07

n = 2 (because of twice in a year)

t = 33 years

A= [tex] 1600(1 + \frac{0.035}{2}) ^{2*33}  [/tex] 

A =[tex]  1600 (1.035)^{66}  [/tex] 

A= $15494.696

Answer:

3/23 x 5/23 = 15/529 = 2.84%

The other zero of the parabola with a vertex at (4, -2) and one zero at 1 is 7, determined by the symmetry of the parabola about its vertex.

If a parabola has its vertex at (4, -2) and one of its zeros is 1, we can find the other zero by using the concept of symmetry about the vertex. Since the axis of symmetry for a parabola with a vertical axis goes through the vertex, we know that the x-coordinate of the vertex will be exactly in the middle between the two zeros. The vertex form of a parabola's equation is typically written as y = a(x-h)² + k, where (h, k) is the vertex. In this case, the vertex is (4, -2).

Knowing that one zero is 1, we can determine that the other zero is equidistant from the vertex on the other side. This means that the distance from the vertex x-coordinate (4) to the known zero (1) is 3 units (4 - 1 = 3). So, counting 3 units in the other direction from the vertex's x-coordinate will give us the second zero: 4 + 3 = 7. Thus, the other zero of the parabola is 7.

If the x-coordinate is 7, representing 7 hexagons, the y-coordinate, representing the total number of sides, is 42. This is because each hexagon has 6 sides, and 7 hexagons have 7 * 6 = 42 sides.

To find the y-coordinate when the x-coordinate represents the number of hexagons, and the y-coordinate represents the total number of sides, we need to use the properties of a hexagon. A hexagon has 6 sides.

Given that the x-coordinate is 7, this means there are 7 hexagons. Each hexagon has 6 sides, so to find the total number of sides (which is the y-coordinate), you multiply the number of hexagons by the number of sides each hexagon has:

Thus,

y-coordinate = 7 hexagons * 6 sides per hexagon = 42 sides

Therefore, if the x-coordinate is 7, the y-coordinate is 42.

Answer:

[tex]12\frac{1}{6}[/tex] cups of punch

Step-by-step explanation:

Peter is making a punch. He mixes :

Orange juice  =  [tex]4\frac{1}{2}[/tex] cups

Ginger ale   =    [tex]1\frac{1}{3}[/tex]

Strawberry lemonade =  [tex]6\frac{1}{3}[/tex]

Now we will add all the mixes

[tex]4\frac{1}{2}[/tex] +  [tex]1\frac{1}{3}[/tex] +  [tex]6\frac{1}{3}[/tex]

Now first we convert all the mixed fractions to improper.

[tex]\frac{9}{2}+ \frac{4}{3}+ \frac{19}{3}[/tex]

Now take LCM of 2,3,3 = 6

= [tex]\frac{27+8+38}{6}[/tex]

= [tex]\frac{73}{6}[/tex] =  [tex]12\frac{1}{6}[/tex]

The total number of cups of puch that peter makes is  [tex]12\frac{1}{6}[/tex]

Peter makes a total of 12 cups and 1/6 cup (or approximately 2/3 cup) of punch by mixing 4 1/2 cups of orange juice, 1 1/3 cups of ginger ale, and 6 1/3 cups of strawberry lemonade.

To find the total number of cups of punch that Peter makes,

need to add together the quantities of orange juice, ginger ale, and strawberry lemonade.

Here are the quantities given:

Orange juice = 4 1/2 cups

Ginger ale = 1 1/3 cups

Strawberry lemonade = 6 1/3 cups

Now, add these quantities together:

4 1/2 cups + 1 1/3 cups + 6 1/3 cups

To add these mixed numbers together, it's helpful to first find a common denominator, which in this case is 6.

Convert 4 1/2 to an improper fraction: 4 1/2

= (2 × 4 + 1)/2

= 9/2

Convert 1 1/3 to an improper fraction: 1 1/3

= (3 ×1 + 1)/3

= 4/3

Keep 6 1/3 as it is since it's already in mixed fraction form.

Now, add the fractions:

(9/2) cups + (4/3) cups + (6 1/3) cups

To add the fractions, first, find a common denominator of 6:

(9/2) cups + (8/6) cups + (19/3) cups

Now, all fractions have a common denominator of 6:

(27/6) cups + (8/6) cups + (38/6) cups

Now, add the fractions:

(27/6 + 8/6 + 38/6) cups

Combine the numerators:

(27 + 8 + 38)/6 cups

Now, add the numerators:

(27 + 8 + 38) = 73

So, Peter makes a total of 73/6 cups of punch. You can also simplify this fraction:

73/6 = 12 1/6

Therefore, Peter makes 12 cups and 1/6 cup (or approximately 2/3 cup) of punch in total.

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Answer:

It’s y=-2 on edge

To solve the equation, we first distribute the 2 on the left, then collect like terms and finally isolate x. The solution to the equation 2(x + 3) = x + 10 is x = 4.

To solve the equation 2(x + 3) = x + 10, we will first distribute the 2 on the left-hand side of the equation to get 2x + 6. Therefore, the equation becomes: 2x + 6 = x + 10.

The next step is to collect like terms. To do this, we subtract x from both sides, which gives us: x + 6 = 10.

Finally, to solve for x, we subtract 6 from both sides of the equation: x = 4. Hence, the solution to the equation 2(x + 3) = x + 10 is x = 4.

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Final answer:

x = 4

Explanation:

To solve the equation 2(x + 3) = x + 10, we first expand the left side of the equation:

2 × x + 2 × 3 = x + 10

2x + 6 = x + 10

Now subtract x from both sides to move all x terms to one side:

2x - x + 6 = 10

1x + 6 = 10

Subtract 6 from both sides to solve for x:

x = 10 - 6

x = 4

Thus, the solution to the equation is x = 4. Checking the solution, we substitute x back into the original equation:

2(4 + 3) = 4 + 10

2(7) = 14

14 = 14

The mass of the fruit is 74 grams and the mass of the yoghurt is 111 grams.

Given :

Solution :

Now to form a linear equation first let x be the mass in gram. Than total mass of the desert is given by:

[tex]3x+2x=185[/tex]

[tex]5x = 185[/tex]

[tex]x = \dfrac{185}{5}[/tex]

x = 37 grams

Therefore the mass of the fruit = [tex]2 \times 37[/tex] = 74 grams and the mass of the yoghurt = [tex]3\times 37[/tex] = 111 grams.

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Area = (L1 + L2)*h/2

Area = 18

L1 + L1 = 6

h = ???

18 = (L1 + L2)*h/2

18 = (6) * h/2 Multiply both sides by 2

36 = 6h Divide by 6

36/6 = h

h = 6

So the square is 6 by 6

Area square = s^2 where s is the side of the square.

Area = 6^2 = 36 

so your answer will be 6^2 = 36 

Final answer:

The transformation is a translation where you subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate. Using this rule, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).

Explanation:

The student is asking about a translation transformation in a coordinate plane. Given the original and translated coordinates for point X, we can determine the translation rule by calculating the differences between the coordinates.

The x-coordinate has changed from 6 to 2.8, a decrease of 3.2, and the y-coordinate has changed from -2 to -1.3, an increase of 0.7. Thus, the translation rule is to subtract 3.2 from the x-coordinate and add 0.7 to the y-coordinate.

To find the translated coordinates for points Y and Z, we apply the same rule:

In summary, Y' is (4.3, 5.7) and Z' is (4.8, 4.7).

To find the translation rule, we used the given coordinates of X and X' to determine a translation vector of (-3.2, 1). Using this rule, the coordinates of Y' are (4.3, 6) and Z' are (4.8, 5).

Given the vertices of triangle XYZ: X(6, -2.3), Y(7.5, 5), and Z(8, 4), and knowing that vertex X when translated has coordinates X'(2.8, -1.3), we need to determine the translation rule.

Hence, the coordinates of the translated points are Y'(4.3, 6) and Z'(4.8, 5).

here is the complete question-Triangle XYZ has vertices X(6, -2.3), Y(7.5, 5), and Z(8, 4). When translated, X` has coordinates (2.8, -1.3). Write a rule to describe this transformation. Then find the coordinates of Y' and Z'.

The volume of the prism with the given dimensions is;

V = 12x³ - 30x²

We are given that the formula for the volume of a cube is;

V = Lwh

where;

L is length

w is width

h is height

We are given;

L = (24x² + 6x)/(x -1)

w = 2x - 5

h = (x² - x)/(4x + 1)

This means that;

V = [(24x² + 6x)/(x - 1)] × (2x - 5) × [(x² - x)/(4x + 1)]

Now, let us factorize the terms that can be factorized;

(24x² + 6x)/(x - 1) can be factorized into; [6x(4x + 1)/(x - 1)]

Similarly;[(x² - x)/(4x + 1)] can be factorized into [x(x - 1)/(4x - 1)]

Using the factorized terms to get the volume now;

V = [tex]\frac{6x(4x + 1)}{x -1} * (2x - 5) * \frac{x(x - 1)}{4x + 1}[/tex]

(x - 1) will cancel out and also 4x + 1 will cancel out to give;

V = 6x * x * (2x - 5)

V = 6x²(2x - 5)

V = 12x³ - 30x²

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Answer: C)  The range between the maximum and minimum values for taco truck 2 is greater than the range between the maximum and minimum values for taco truck 1.

Answer:

4mph

Step-by-step explanation:

Natasha can treat a maximum of 10 people to the movies.

To determine how many people Natasha can treat to the movies, we can set up an inequality equation.

Let's say she wants to treat x number of people.

The amount she spends on tickets is $11x, and the amount she spends on popcorn and candy is $21. Since she can spend under $131, the inequality equation would be:

11x + 21 < 131.

To find the maximum number of people Natasha can treat, we need to solve this inequality:

11x + 21 < 131

11x < 110

x < 10

Natasha can treat a maximum of 10 people to the movies.

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Final answer:

Using the Pythagorean theorem, it is determined that the ladder reaches 12 feet up the side of the house when the base is placed 5 feet away.

Explanation:

To solve for the height at which the ladder reaches the house, we can use the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

In this scenario, the ladder represents the hypotenuse (c), the distance from the base of the ladder to the house gives one leg of the triangle (a), and the height the ladder reaches up the side of the house is the other leg (b).

According to the Pythagorean theorem, a² + b² = c². Plugging in our known values allows us to solve for b²:

Therefore, the top of the ladder will be 12 feet above the ground.