class council is selling prom tickets for $55 per person.the senior class consists of 342 students,who are each allowed to bring one date from another school.complete the table(if needed) and answer the questions below

The proof of the diagonals of the rectangle are congruent, is given.

When two figures or objects in geometry have the same forms, sizes, or are mirror images of one another, they are said to be congruent.

We have the parallelogram SPQR.

And SQ is the diagonal.

d(S,P) = √(0-0)² + √(b-0)²

d(S,P) = √b²

d(S,P) = b

So, distance SP = b

d(P, Q) = √(a-0)²+ √(b-b)²

d(P, Q) = √a²

d(P, Q) = a

So, distance of  PQ = a

SQ = c²= a² + b²

SQ = √(a² + b²)

Similarly, for the other vertices.

Therefore, The diagonals are congruent.

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The length of the other leg of the triangle is 11.7 inches

Now, According to the question:

We have the right triangle

The length of the right triangle is 24 inches

The length of the hypotenuse is 26.7 inches

To find the length of the other leg of the triangle

We know that the Pythagorean theorem.

The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.

Let the length of the other leg of the triangle be 'x'

According to the information:

[tex]24^2 + x^2 = 26.7^2[/tex]

576 + [tex]x^{2}[/tex] = 712.89

[tex]x^{2}[/tex] = 712.89 - 576

[tex]x^{2}[/tex] = 136.89

x = [tex]\sqrt{136.89}[/tex]

x = 11.7

Hence, The length of the other leg of the triangle is 11.7 inches.

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0.117 Or 11.7% chance of n should the player choose in order to maximize the probability of winning a prize.

The probability of precisely x successes on n further trials in an experiment with two potential outcomes is referred to as the binomial probability (commonly called a binomial experiment).

When a procedure is performed a certain number of times (for example, in a group of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of witnessing a defined number of "successes."

The probability of winning a prize remains the same for. n = 10 or n=20 or n = 100; the probabilities are the same.

Given that,

p = 0.5, So, q = 1 - 0.5 = 0.5.

If 70% of 'n' games are won then 30% of n games must be lost.

Let n = 10.

Therefore, P ( x = 3) = [tex]^{10}C_3p^7q^3[/tex]

or, P ( x = 3) = [tex]^{10}C_3(0.5)^7(0.5)^3[/tex]

or, P (x = 3) = 120×0.0078×0.125.

or, P (x = 3) = 0.117 Or 11.7% chance.

Now, Changing the value won't have any effect as all the 'n's are multiple of 10 and we'll have same probability.

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the factor of the quadratic expression are:

1) x² - x - 30 = 0 : (x - 5)(x + 6) = 0

2) x² - 10x = -21 : (x - 7)(x + 3) = 0

3) x²= 10x - 9 : (x - 3)(x + 3) = 0

4) x – 5x =0 : x = 0

5) 10x - 24 = x² : (x - 6)(x - 4) = 0

6) x² = -12x : (x + 6)(x - 2) = 0

What is the factor of the quadratic expression?

Factorization of quadratic equations is the part of finding the roots of a quadratic equation. Factoring quadratic equations means converting the given quadratic expression into the product of two linear factors.

1) x² - x - 30 = 0

To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the constant term (-30) and add to give us the coefficient of the x term (-1). The two integers that fit this criterion are -6 and 5, so we can factor the expression as:

(x - 5)(x + 6) = 0

2) x² - 10x = -21

To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the constant term (-21) and add to give us the coefficient of the x term (-10). The two integers that fit these criteria are -7 and 3, so we can factor the expression as:

(x - 7)(x + 3) = 0

3) x²= 10x - 9

To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the constant term (-9) and add to give us the coefficient of the x term (10). The two integers that fit this criteria are -3 and 3, so we can factor the expression as:

(x - 3)(x + 3) = 0

4) x – 5x =0

To solve this equation, we can first combine like terms to get:

-4x = 0

Then, we can divide both sides by -4 to get:

x = 0

5) 10x - 24 = x²

To solve this equation, we can first move the x² term to the left side and the constant term to the right side to get:

x² - 10x + 24 = 0

To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the constant term (24) and add to give us the coefficient of the x term (-10). The two integers that fit this criteria are -6 and 4, so we can factor the expression as:

(x - 6)(x - 4) = 0

6) x² = -12x

To solve this equation, we can first move the constant term to the right side to get:

x² + 12x = 0

To factor this quadratic expression, we can use the method of finding the two integers that multiply to give us the coefficient of the x term (12) and add to give us 0. The two integers that fit this criteria are -6 and 2, so we can factor the expression as:

(x + 6)(x - 2) = 0

Hence, the factor of the quadratic expression are:

1) x² - x - 30 = 0 : (x - 5)(x + 6) = 0

2) x² - 10x = -21 : (x - 7)(x + 3) = 0

3) x²= 10x - 9 : (x - 3)(x + 3) = 0

4) x – 5x =0 : x = 0

5) 10x - 24 = x² : (x - 6)(x - 4) = 0

6) x² = -12x : (x + 6)(x - 2) = 0

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Answer:

D

Step-by-step explanation:

multiply by 8 and add 5.

so,

we need to do this for every unit value and see, if the result is the same as the listed output value.

5 -> 5×8 + 5 = 45

6 -> 6×8 + 5 = 53

7 -> 7×8 + 5 = 61

8 - > 8×8 + 5 = 69

9 -> 9×8 + 5 = 77

10 -> 10×8 + 5 = 85

so, D is the correct answer.

Solving this equation gives us a half-life of approximately 1.36 years. Rounded to two decimal places, the half-life of this substance is 1.36 years.

The half-life of a substance is the amount of time it takes for half of the atoms in a sample of the substance to decay.

To find the half-life, you can use the following formula:

half-life = (time) * ln(2) / ln(initial mass / final mass)

half-life = (1 year) * ln(2) / ln(32 mg / 25.5 mg)

Solving this equation gives us a half-life of approximately 1.36 years.

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Answer:

The cake cost $6.00

Step-by-step explanation:

Let c = the cost of the cake

Let t =  the cost of the tea

c = 2t

c + 5t = 21  Substitute 2t for c

2t + 5t = 21  Combine like terms

7t = 21  Divide both sides by 7

[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]

t = 3  

A cup of tea costs $3.00

c = 2t  Substitute 3 for t

c = 2(3)

c = 6

A cake costs $6.00

Answer:

Cake: £6

Step-by-step explanation:

1c = 2t             Eq. 1

1c + 5t = 21      Eq. 2

c = cost of a cake

t = cost of a cup of tea

Replacing Eq. 1 in Eq 2:

2t + 5t = 21

7t = 21

t = 21/7

t = 3

From Eq. 1:

c = 2t

c = 2*3

c = 6

Check:

From Eq. 2:

c + 5t = 21

6 + 5*3 = 21

6 + 15 = 21

Answer:3-4 times  but im not sure but here my logic

use it to your needs

Step-by-step explanation:

she has 5 shirts and 3 jackets right
so take the first shirt the third jacket then the fourth shirt the 2nd jacket
that 2 outfits then take the second shirt and the last remaining jacket then on the weekend wear one of the non-used shirts no jacket or the first jacket
-ElectricWolfieOnYT

The solution is

a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01

b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125

The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96

What is Compound Interest?

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

a)

Let the principal be P = amount after first period =  $ 402

Now , the rate of interest r = 6 %

The compound interest is calculated by compounding monthly

Now , the interest for the second period = ( PRT / 100 x 12 )

Substituting the values in the equation , we get

The interest for the second period = ( 402 x 6 x 1 ) / 1200

The interest for the second period = $ 2.01

The amount after the second period = amount after first period +  interest for the second period

The amount after the second period = 402 + 2.01

The amount after the second period = $ 404.01

b)

Let the principal be P = $ 18260

The rate of interest r = 2.5 %

The compound interest is calculated by compounding quarterly

Now , the interest for the first period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the first period = ( 18260 x 2.5 ) / 400

The interest for the first period = 45650 / 400

The interest for the first period = $ 114.125

The amount for the first period = 18260 + 114.125

The amount for the first period = $ 18,374.125

Now , the principal for the second period = interest + amount of first period

The principal for the second period = $ 18,374.125

The rate of interest = 2.5 %

The interest for the second period = ( PRT / 4 x 100 )

Substituting the values in the equation , we get

The interest for the second period = ( 18374.125 x 2.5 ) / 400

The interest for the second period = 45935.3125 / 400

The interest for the second period = $ 114.83828125

The amount for the second period = 18,374.125+ 114.84

The amount for the second period = $ 18,488.96

Hence , the amount and interest is calculated

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The length of the line segment with endpoints P(2, 1, -4) and Q(-1, 5, 3) is 8.60 units

To find the length of a line segment with endpoints P(x1, y1, z1) and Q(x2, y2, z2) in three-dimensional space, we can use the distance formula:

length = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

Substituting the coordinates of P and Q into the formula, we get:

length = √((-1 - 2))²  + (5 - 1))²  + (3 - (-4)))² )

          = √((-3))²  + (4))²  + (7))² )

         = √(9 + 16 + 49)

         = √(74)

        = 8.60 units

Therefore, the length of the line segment is 8.60 units

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Answer:

A. 36/5

Step-by-step explanation:

cross multiply

6/5 = x/6

5x = 36

x = 36/5

Answer:

A) [tex]\frac{36}{5}[/tex]

Step-by-step explanation:

[tex]\frac{6}{5}[/tex] = [tex]\frac{x}{6}[/tex]  Cross multiply and solve for x

36 = 5x  Divide both sides by 5

[tex]\frac{36}5}[/tex] = [tex]\frac{5x}{5}[/tex]

[tex]\frac{36}{5}[/tex] = x

When she uses 5 bags of coffee every day at her café, half of a bag of coffee lasts for 10 days.

Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The basic purpose of splitting is to determine how many equal groups develop or how many people are in each group when distributing equally. Division is a basic operation that divides an integer. It's best to imagine of it as a group of things being distributed among a group of individuals, as in the preceding example.

Here,

number of bags needed in a day=5

number of days 1/2 bag last,

=5÷1/2

=10 days

Half of bag of coffee last for 10 days when she uses 5 bags of coffee every day in her café.

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Answer:

The length of the sides of the second pentagon would be half of 5 inches, or 2.5 inches. This is because when you halve the length of a line, the new line is half as long as the original.

Shahina can make apple crumble for 6 people with 550g of apple

From the question, we have the following parameters that can be used in our computation:

For 8 people it is:

700g of apple, 40g butter, 240g sugar and 180g flour

This means that the grams of apple for 1 person is

Apple unit rate = 700g of apple/Number of people

Substitute the known values in the above equation, so, we have the following representation

Apple unit rate = 700g of apple/8

For 6 people, we have the following equation

Amount = Apple unit rate * Number of people

Substitute the known values in the above equation, so, we have the following representation

Amount = 6 * 700g of apple/8

Evaluate

Amount = 525g of apple

525g of apple is less than 550g of apple

Hence, she can make apple crumble for 6 people

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Domain: x > –6; range: all real numbers are the domain and range of f (x).

What is domain and range ?

The range of values that can be plugged into a function is known as its domain. The x values for a function like f make up this set (x).

                              The collection of numbers that the function assumes is known as its range. After we enter an x value, the function outputs this sequence of values.

we need to remove all the values of x such that

x + 6 ≤ 0

Solving for x, we get

x ≤ -6

So the only values of x allowed are the ones that make the next inequality true:

x > -6.

Thus we can write the domain as:

D {x | x ∈ R | x > -6}

Where the second part, x ∈ R, is usually ignored, as we assume that x is a real number .

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Answer:

2 or B

Step-by-step explanation:

The answer above is correct.

Answer:

y = 1/4x - 4

Step-by-step explanation:

4x + y = 3

y = -4x + 3

Perpendicular slope = 1/4

y = 1/4x + b

-3 = 1/4(4) + b

-3 = 1 + b

b = -4

y = 1/4x - 4

The angle 2 is 149° , angle 3 is 31° , angle 4 is 149°

What is the name for two opposing angles?

Angles where two lines cross that are directly opposite one another are known as opposing angles. The vertex, where the lines come together to produce the angle, is the location of the junction. Vertical angles are another name for opposite angles.

Given that :
Angle 1 is = 31°

Angle 2 is = 180 - 31 = 149° (As in a line total angle is 180°)

Angle 3 is = 31° (As equal opposite angle with angle 1)

Angle 4 is = 149°  (As equal opposite angle with angle 2)

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The value of the variable x is -2

An algebraic expression can be defined as an expression made up of terms, variables, coefficient, factors and constants.

These expressions are also made up of arithmetic or mathematical operations, which includes;

From the information given, we have;

2 ^ (x + 3) * 3 ^ (x + 4) = 18

Now, let's find the factors of 18 in 2's and 3's, we have;

2 ^ (x + 3) * 3 ^ (x + 4) = 2^1 × 3^ 2

Collect the common factors, we get;

x+ 3 + x + 4 = 1 + 2

collect like terms

2x = 3 - 7

2x = -4

make 'x' the subject of formula

x = - 2

Hence, the value is -2

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Answer:

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

Given:

Find y if x = a:

Correct choice is B.

The values of of the functions f(x)=3x+2 and g(x)=x²-x are: (14) 14, (15) 26, (16) -4, (17) 2, (18)12, (19) 42 (20)7, (21)2, (22)2, (23)5 (24) 3x+5 (25) 9b²-3b

We should know that in each of the functions, we have to substitute the given values

The given functions are

f(x)=3x+2

g(x)=x²-x

(14) f(x)=3x+2

Substitute for x

f(4)=3*4+2

f(x)=12+2=14

(15) f(8)=3x+2

f(8)=3*8+2

Substitute for x

f(x)=24+2 = 26

(16) f(-2)=3*-2+2

Substitute for x

f(-2)=-6+2

f(x)=-4

(17) g(2)=2²-2

Substitute for x

g(x)=4-2

g(x)=2

(18) g(-3)=3²-(-3)

Substitute for x

g(x)=9+3 = 12

(19)g(-6)=-6²-(-6)

g(x)=36+6 = 42

(20) f(2)+1

Substitute for x

=2*3+1

=6+1

=7

(21)  f(1)-1

3*1-1 = 2

(22) g(2) -2

2²-2

4-2=2

23 = g(-1)+4

-1²+4

1+5=5

(24) f(x+1)

Substitute for x

= 3(x+1)+2

=3x+3+2

=3x+5

(25) g(3b)

Substitute for x

=(3b)²-3b

9b²-3b

In conclusion, the values of the values of of the functions f(x)=3x+2 and g(x)=x²-x are: (14) 14, (15) 26, (16) -4, (17) 2, (18)12, (19) 42 (20)7, (21)2, (22)2, (23)5 (24) 3x+5 (25) 9b²-3b

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the value of y is 3 when the value of x is 8.

what is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.

Given y is inversely proportional to x

When x=3, y=1/x = 8

So when x = 8 the value of y =3

Hence the value of y is 3 when the value of x is 8.

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The time since dinosaurs became extinct is roughly equal to 10⁶ average human lifespans

From the question, we have the following parameters that can be used in our computation:

Rewrite the exponents properly

So, we have the following representation

This means that

Number of times = Time since dinosaurs became extinct/Average human lifespan

Substitute the known values in the above equation, so, we have the following representation

Number of times = 2.4 x 10¹⁰/2.4 x 10⁴

Evaluate the quotient

Number of times = 10⁶

Hence, the number of times is 10⁶

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Answer:

B

Step-by-step explanation:

970 + 2436 = 3406

The perimeter of the object is the sum of the lengths of all the sides

which is 302 units.

Perimeter is the sum of the lengths of all the sides of a planar two-dimensional figure.

In the case of a circle, we call it perimeter circumference it is the distance around the circle.

Given, A figure has side lengths EF = 71, FD = 80, ED = 74, IG = 40, and

HG = 37.

Now the perimeter of this figure is the sum of the lengths of all the sides which is,

= (EF + FD + ED + IG + HG).

= (71 + 80 + 74 + 40 + 37).

= 302 units.

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Answer:

Below

Step-by-step explanation:

m = slope = rise / run

m = 5 for this equation

rise /run = 5

15 / run = 5

run = 3

Answer:

A and D

Step-by-step explanation:

so sorry im in school

x+y=4

 -y.  -y

x=4-y

4-y-y=2

4-2y=2

-4      -4

-2y= -2

/-2.   /-2

y=1

x+1=4

  -1 -1

x=3

so A and D is correct

Answer:

1/64

Step-by-step explanation:

1/8 x 1/8 = 1/64

Answer:

Step-by-step explanation:

A linear equation has only more than one additional, that may be expressed as , and the further discussion can be defined as follows:

In this, No factor has been raised the power which is greater than one or utilized as the denominator of a fraction.  

When we discover pairs of values that satisfy a linear model and plot them on a coordinate grid, all the points fall on the same line.

Please find the attached file of the graph.