8. A parabola has its focus at (1,2) and its directrix is y = -2. The equation of this parabola could be
1) y = 8(x + 1)²
2)y=1/8(x + 1)²
3)y =8(x-1)²
4)y=1/8(x-1)²

7,701 divided by 36 is 213.91

The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in mathematics. For example, we can divide a group of 20 members into 4 groups of 5 members

The number 7701 is called the numerator or dividend, and the number 36 is called the denominator or divisor.

The quotient of 7701 and 36, the ratio of 7701 and 36, as well as the fraction of 7701 and 36 all mean (almost) the same:

7701 divided by 36, often written as 7701/36

Therefore, 7701 divided 36 is 213.91

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The difference between the largest and the smallest fraction is 0.24.

A fraction is a component of a whole.

Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided.

In a simple fraction, both are integers.

In a complex fraction, a fraction can be found in either the numerator or the denominator.

A suitable fraction has a numerator that is less than its denominator.

So, first, we will figure out the smallest and the greatest fraction:

We have: 3/5, 5/6, 2/3, 9/8, 7/9 and 3/4

LCM of denominators: 2*2*2*3*3*5 = 360

216/360, 300/360, 240/360, 405/360 (Improper), 280/360, 270/360

Smallest: 216/360

Largest: 300/360

Subtract smallest from largest:

300/360 - 216/360

84/360

7/30

0.2333

Round off: 0.24

Therefore, the difference between the largest and the smallest fraction is 0.24.

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Answer:

1.2+2.56.7×3218°÷456.7820

The completed sentences that describe the height reached by the ball specified by the function, f(x), that indicates the balls height, based on the number of bounces, x, f(x) = 64·(0.75)ˣ, which is similar to a geometric progression, is presented as follows;

The variable, x, represents the number of times the ball bounces.

The variable f(x) represents the height of the ball after x bounces.

The parameter, 64, represents the initial height of the ball.

The parameter, 0.75, represent the percentage of height left from each previous bounce.

A geometric progression is a number sequence, arranged such that the ratio between a term and the previous term is a constant, known as the common ratio of the geometric progression.

The exponential function that models the specified situation of finding the height of the ball is presented as follows;

f(x) = 64·(0.75)ˣ

The initial height from which the student drops the ball = 64 feet

The height the ball reaches after one bounce = 48 feet

Height of the ball after 2 bounces = 36 feet

The exponential function, f(x) = 64·(0.75)ˣ, is similar to the equation for a geometric progression, aₙ = a₁·r⁽ⁿ⁻¹⁾

Where;

a₁ = The first term = The initial height

r = The common ratio = 48/64 = 36/48 = 0.75

n = The number of times the ball bounces, in addition to the time the ball is dropped from the initial height, therefore;

x = n - 1, therefore;

x = The number of times the ball bounces

n = x + 1

The terms that complete the sentences are therefore:

The variable that represents the number of time the ball bounces = x

The variable that indicates the height of the ball after x bounces = f(x)

The initial height of the ball = The parameter 64

The percentage of the height the ball bounces to after the previous bounce = 0.75

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Step-by-step explanation:

be a function, there needs to be one unique

value of +y+ for every +x+

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

The 1st set has 5 different values of +y+

for +x+=+1+ and violates definition

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

The 2nd set is a function

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

The 3rd set has

( 1,2 ) & ( 1,1 )

( 2,3 ) & ( 2,2 )

( 3,4 ) & ( 3,3 )

Each of these pairs violates the definition

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

The 4th set has ( 2,-7 ) & ( 2,0 ) which

violate definition

Answer:

The answer is 9

Step-by-step explanation:

The given triangle is equivalent triangle

We know that in equivalent triangle all angles are equal to 60°

So,

(7x - 3)° = 60°

7x - 3° = 60°

7x - 3° + 3° = 60° + 3°

7x = 63°

x = 63°/7°

x = 9°

Thus, The value of x is 9°

For Verification Only;

(7x - 3)° = 60°

[7(9) - 3]° = 60°

(63 - 3) = 60°

60° = 60°

Hence,

L.H.S = R.H.S

If each large truck $70,000. Past experience shows that they need twice as many vans as small trucks. The number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.

Since the company intends to purchase 320 vehicle, Let write this equation:

C + S + L = 320 (Eq. 1)

Total cost of the vehicles:

25C + 80S +70L = 16,000 (Eq. 2)  (Divided by 1000 to keep the numbers small)

Number of commercial vans is twice the number of small trucks,

C = 2S

Substituting 2S in place of C in Eq. 1 and Eq. 2

2S + S + L = 320

25(2S) +80S +70L = 16,000

130S + 70L = 16,000

Multiplying the first of those equations by 70

210S + 70L = 22,400

130S + 70L = 16,000

Subtracting the second equation from the first:

80S = 6400

Divide both  side by 80S

S = 6400/80

S = 80 (Small truck)

Then:

C = 2S

C= 2(80)

C= 160 (Commercial van)

So,

C + S + L = 320

160 + 80 + L = 320

L = 320 - 160 - 80

L =80 (Large van)

Therefore  the number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.

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Answer:

(a) A(w) = w(950-2w) = 950w-2w^2

(b) w = 237.5

(c) A = 112812.5

Step-by-step explanation:

First of all the maximum area is always a square. You can get the answer first to check your work later.

950/4 = 237.5

One side is not needed so add that length to the non-parallel side.

237.5+237.5=475 feet is the length and 237.5 feet is the width(s)

A=475*237.5

A=112812.5 square feet

Doing the algebra...

P=l+2w

950=l+2w

950-2w=l

A=lw

A=(950-2w)w

A=950w-2w^2

Answer: 5

Step-by-step explanation: To find the distance between 2 points, we should use this formula:

d=√((x_2-x_1)²+(y_2-y_1)²)

So, using that it would be written as:

[tex]\sqrt{9 + 16}[/tex] (after simplified)

Now, we need to find the square root of 25

The square root of 25= 5

So, that is how I got my answer.

The total years taken to double the money according to Compounding will be  12.5 years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $2500

Total amount = $5000

Compounded semi -anually,

so formula becomes,

Total amount = amount (1+r/200)^2t

T = [tex]A (1+\frac{r/2}{100})^{2t}[/tex])

5000 = 2500 (1+3/100)^2t

2 = [tex](1+0.03)^{2t}[/tex]

2 = [tex]1.03^{2t}[/tex]

taking log on both sides

log 2 = 2t *log 1.03

0.3/0.012 = 2t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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Answer:

$11.25

Step-by-step explanation:

If Stephen receives a 4.5% hourly pay increase each year, his hourly pay will be $10.30 + (4.5% * $10.30) = $10.30 + $0.465 = $10.765 after the first year.

In the second year, his hourly pay will be $10.765 + (4.5% * $10.765) = $10.765 + $0.486 = $11.251.

Therefore, in two years, Stephen's hourly pay will be $11.251. This is closest to the answer choice of $11.25, so it is the correct answer.

The equation of the total amount is A = 500 + 500 * 6% * 1 and the value is $530

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

Principal, P = $500

Rate, r =6%

Time = 1 year

The amount is calculated as

A = P + PRT

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

A = 500 + 500 * 6% * 1

The above represents the equation

So, we have

A = 530

Hence, the amount is $530

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The sampling distribution refers to the distribution of the sample mean (X-bar) computed from a set of n independent, normal random variables (X1,...,Xn).

The sampling distribution is a theoretical distribution that describes how the sample mean would vary if you were to take multiple samples from the population and compute the sample mean for each sample. It is based on the assumption that the X1,...,Xn are independently and normally distributed with a common mean and variance.

The sampling distribution is important because it allows us to make inferences about the population mean based on the sample mean. By understanding the properties of the sampling distribution, we can calculate confidence intervals and perform hypothesis tests to determine whether the sample mean is significantly different from the population mean.

In contrast, the distribution on the individual random variables (X1,...,Xn) is the distribution of the individual observations in the sample. The distribution on the means of the individual random variables (Xi) is the distribution of the mean of each individual random variable.

The frequency distribution obtained from a set of n experimental data values is the distribution of the observed data values in the sample.

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Answer:

(3+2)

Step-by-step explanation:

Perimeter of a square = 4L

L is the length of one side of the square

Given the expression 12 + 8 that represents the perimeter of a square, factoring out 4 from both terms;

12 + 8

= (4*3)+(4*2)

= 4(3+2)

Comparing with 4L

4L = 4(3+2)

Divide both sides by 4

4L/4 = 4(3+2)/4

L = (3+2)

Hence the expression that represents one side of the square is (3+2).

Hope this helps!!! :)

Step-by-step explanation:

I just answered this with all explanations.

Answer:

5

Step-by-step explanation:

In an isosceles triangle two of the angles are equal and the corresponding sides are also equal

Here ∠A = ∠B

AC = BC

3x + 4 = 10

3x = 6

x = 2

Side AB = x + 3 = 2 + 3 = 5

****

The bacteria after 24 hours will be equal to 450000.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria.

The number of bacteria will be calculated as,

N = 125×(60×60)

N = 125×3600

N = 450000

Therefore, the bacteria after 24 hours will be equal to 450000.

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5b+3.79 has two terms, 5b and 3.79.

The variable b seems to represent the cost of one bagel.  Since we know Gaspar bought 5 bagels, 5b would represent the cost of 5 bagels.

In 5b, 5 is the coefficient and b is the variable.

Since 5b represents the cost of the bagels, then 3.79 would appear to be the cost of the cream cheese.

Answer:

The variable "b" represents the cost of one bagel (in dollars).

The coefficient "5" represents the number of bagels purchased.

The constant "3.79" represents the cost of one container of cream cheese (in dollars).

Step-by-step explanation:

Given algebraic expression:

If the given algebraic expression represents the total cost, in dollars, of buying 5 bagels and a container of cream cheese, then:

1. d. 8/52 (Ace ∪ 5)

2. h. 0 (Ace ∩ 5)

3. b. 20/52 (Even')

4. c. 36/52 (Even ∪ black)

5. a. 3/52 (Face ∩ Diamond)

What is probability?

Probability means the quality or state of being the outcome; the extent to which something is likely to happen or take place. Probability means the possibility of any outcome which can take place in any event.

Solution:

1. Probability of Ace ∪ 5 = (No. of Aces + no. of cards with face value 5)/52 = 8/52

2. Probability of Ace ∩ 5 = (Intersection of Ace and face value of card 5)/52 = 0

∵ Intersection of ace and 5 is 0 as there is no intersection in between the 2 subevents.

3. Probability of Even complement = No. of cards with odd values/52                    

 {A,3,5,7,9,A,3,5,7,9,A,3,5,7,9,A,3,5,7,9}/52      =20/52

4. Probability of Even ∪ black = {(2,4,6,8, 10)×4 types of cards odd black spades + odd black clubs = 20+16/52

                                          = 36/52

5.  Probability of Face ∩ Diamond = No. of face cards in diamonds/52

                                                        = {Jack, Queen, King}/52

                                                        = 3/52

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The value of x= 35.5, y= 43.75 and z= 62.75

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the three angles are x, y and z.

x+ y + z = 180............(E3)

The sum of the measures of the second and third angles is three times the measure of the first angle.

So, y+ z = 3x

3x- y- z= 0.............(E1)

and, third angle is 19 more than the second

z= y+ 19

y- z= -19..........(E2)

So, E1+E2, and E3-E2,

3x- 2z= -19

x+ 2z= 161

Now, adding above

4x = 142

x= 35.5

and, y + z = 106.5, y- z = -19

Again, adding

2y= 87.5

y= 43.75

and, z= 62.75

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Answer:

960.00

Step-by-step explanation:

Interest = principle x rate x time

interest = 6000 x .04 x 4

960.00

Answer:

I = $ 960.00

Step-by-step explanation:

I = Prt

Since we are figuring out how much money was earned in interest, we will need to convert our R (which is the interest rate) into decimals, which will be, r = R/100 = 4%/100 = 0.04 per year.

Step 1. Divide R by 100, in this case, R is 4, so it will be 0.04.

Step 2. Times 6000 (the money that was deposited) by 0.04, then times it with 4 (the years) and you will get 960.

I = 6000 × 0.04 × 4 = 960

I = $ 960.00

I hope this helps you!

The inverse of y=-x²+9 is [tex]x=\sqrt{9-y}[/tex]

What is Inverse of a Function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

The output of a function is returned by the inverse function, which also returns the initial value.

If f and g are inverse functions, then f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.

For instance, f(x) = 2x + 5 = y

Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).

The relationship that results from swapping out an independent variable with a variable that depends on a given equation; the inverse may or may not be a function.

A function is said to be an inverse function if its own inverse is represented by the symbol f-1.

[tex]x^2=9-y\\\\\x=(9-y)^\frac{1}{2}\\\\ x=\sqrt{9-y}[/tex]  is the inverse of y=-x²+9

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Answer: 720.0 cm³

Step-by-step explanation:

To convert the volume of the die from millimeters to centimeters, we need to divide the volume by the conversion factor that relates millimeters to centimeters. Since 10 millimeters is equal to 1 centimeter, the conversion factor is 10.

To convert the volume to centimeters, we can divide it by the conversion factor:

7200 mm³ / 10 = 720 cm³

This means that the volume of the die is 720 cm³. Rounded to the nearest tenth, the volume of the die is 720.0 cm³.

Answer: 7% at 6 years would best fit their payment option. They would then be paying $238.69 monthly and which is under $250, I hope this helps!

Answer:

Rectangle

Step-by-step explanation:

Welcome to Brainly! :]

A rectangle uses A=lw to calculate area

Where l is length and w is width

Hope this helps,

:]

The inequality and statement about the possible amount of money in the other piggy bank is 0 ≤ PB₂ ≤ 2.69.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10.

∴ PB₁ + PB₂ ≤ 10.

One piggy bank has $7.31 in it.

∴ 7.31 + PB₂ ≤ 10.

PB₂ ≤ 2.69.

So, The amount in PB₂ can be  0 ≤ PB₂ ≤ 2.69.

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The value of x is 9 and the value of y is 4.

What is the congruent triangle?

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

The system of equations is

x + 3 = 3y ....(i)

x = y + 5 .....(ii)

Putting x = y + 5 in equation (i):

y + 5 + 3 = 3y

y + 8 = 3y

3y = y + 8

3y - y = 8

2y = 8

y = 4

Putting y = 4 in equation (ii)

x = 4 + 5 = 9

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The number of possible wins if the ball lands on red is  4.86 games.

Let there be 100 successive spins,

Random Variable (winnings): $1, -$1

Associated probabilities:

P($1) = 18/38 =9/19

P(-1) = 20/38 = 10/19

Expected winnings is (9/19)*1 + (10/19)*-1

= -1/19 on one spin.

= -2/19 on two spins

= -2/19 on a single spin for $2

= -100/19 on 100 successive spins

since there are 100 spins,  n =100

18 out of 38 spots are red, thus p=18/37 =0.486

expected number of wins = np

= 100* 0.486

=4.86

Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring. Probability is defined as the degree to which something is likely to occur.

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