Find the equation (in terms of x) of the line through the points (-4,-6) and (3,8).
y=

The ratio of apple oranges and bananas cannot be calculated with the given information

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

Fruits = Orange, Bananas and Apple

Total number of fruits = 48

The available parameters is not enough to determine the ratio

Assuming that we have

Banana = 10

Orange =  20

Apple = 18

Then the ratio would be:

Apple : oranges : bananas = 18 : 20 : 10

Simplify

Apple : oranges : bananas = 9 : 10 : 5

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Answer:

90 children's tickets and 200 adult tickets were sold.

Step-by-step explanation:

Let's use the variables c and a to represent the number of children's and adult tickets sold, respectively.

From the problem, we know that:

The total number of tickets sold is 290: c + a = 290

The total revenue from ticket sales is $2250: 5c + 9a = 2250

We now have two equations with two unknowns. We can use substitution or elimination to solve for c and a. Here's one way to use elimination:

Multiply the first equation by 5 to get 5c + 5a = 1450

Subtract the above equation from the second equation to eliminate c: 5c + 9a - (5c + 5a) = 2250 - 1450

Simplify: 4a = 800

Solve for a: a = 200

Substitute a = 200 into the first equation to solve for c: c + 200 = 290

Simplify: c = 90

Therefore, 90 children's tickets and 200 adult tickets were sold.

(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.

(ii) The axioms of probability are:

the non-negativity (that the probability of an event is greater than or equal to zero), and

the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).

(iii) When two fair dice are thrown the probability of getting:

a) The sum of 9 = 1/9

b) Two odd numbers = 1/4

c) two prime numbers = 1/9

d)  two factors of 12 = 1/9

(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.

To find probability when two dice are thrown, we have:

(a) The sum of 9:

We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways

A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.

(b) Two odd numbers:

We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).

possible outcomes = 9,

So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.

(c) Two prime numbers

We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)

possible outcomes = 4,

So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.

(d) Two factors of 12:

We count the number of ways and divide by the total possible outcomes.

The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways

possible outcomes = 6

Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12

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Answer:

Think about the PEMDAS rules for order of operations.

Multiplication comes before addition or subtraction, so first we have "the product of a number and 5" - that's 5x. Then "six more" than that would be 5x + 6. "Equals" means the "=" sign, so the final answer is 5x + 6 = 8.

The proof for  AB ≅ CD is:

Step                 Statement                                Reason

 1              ∠B ≅ ∠D, BC || AD                          Given

 2               ∠BCA ≅ ∠CAD                Alternate Interior angles

 3                      AC ≅ AC                             common side

 4                 ΔABC ≅ ΔADC         Angle-Angle-Side rule of congruency

 5                   AB ≅ CD            Corresponding sides of congruent triangle

Consider triangle ABC and triangle ADC.

Here, side BC is parallel to side AD.

From the attached figure we can observe that AC is a transversal.

so, ∠BCA and ∠CAD would be alternate angles formed by two parallel lines and transversal.

By property of  Alternate Interior angles,

∠BCA ≅ ∠CAD

Also, we can observe that side AC is common side to ΔABC and ΔADC.

We rewrite this proof as,

Step                 Statement                                Reason

 1              ∠B ≅ ∠D, BC || AD                          Given

 2               ∠BCA ≅ ∠CAD                Alternate Interior angles

 3                      AC ≅ AC                             common side

 4                 ΔABC ≅ ΔADC         Angle-Angle-Side rule of congruency

 5                   AB ≅ CD            Corresponding sides of congruent triangle

This is the required proof.

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From the data given, we can see that as you move upward in the atmosphere from sea level, the temperature generally decreases such as from 28 degree to negative degree.

This is because earth atmosphere is heated from bottom-up by the Earth's surface, so, the nearest air to the ground is warmer than the air at higher altitudes. When we climb higher, the air pressure decreases and this causes the air to expand and cool.

This decrease in temperature with increasing altitude is known as the adiabatic lapse rate, but this is known to vary depending on factors such as humidity and atmospheric conditions.

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187, 500 ml are needed to prepare 750 mg from 1:250.

We have to find amount in ml to prepare 750 mg from 1:250.

let the amount needed in ml be x.

Using proportion

1/750 = 250 / x

x= 750 . 250

x= 187, 500 ml

Thus, to prepare 750 mg 187,500 ml is needed.

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The measures of the angles are ∠1 = 35 and ∠2 = 30

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

The figure

Using the sum of opposite internal angles in a triangle, we have

∠1 + 80 = 115

Subtract 80 from both sides

So, we have

∠1 = 35

Using the same theorem of sum of opposite internal angles in a triangle, we have

∠2 + 85 = 115

Subtract 85 from both sides

So, we have

∠2 = 30

Hence, the angles are ∠1 = 35 and ∠2 = 30

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Answer:

Step-by-step explanation:

The population density of the neighborhood is 12000 people per square mile.

Total number of people = 1250

Number of city blocks = 30

Length of the block, l = 1/16 mile

Width of the city block, w = 1/18 mile

Area of one block, A = l x w

A = (1/16) x (1/18)

A = 1/288 square mile

Total area of all the 30 blocks, A' = 30 x A

A' = 30/288 square mile

So, the population density,

D = Total no.of people/A'

D = 1250/(30/288)

D = 1250 x 288/30

D = 12000 people per square mile.

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The statements can be arranged correctly as follows:

1. Word Form shows a number written in words.

2. Standard form shows a number written using digits.

3.  Digit is one of the numerals from 0 to 9

4. Place value the position of a digit in a number, which determines its value.

5.  Period each three-digit part of a whole number, separated by commas

6. Expanded form shows a number written as an addition statement

We can determine the terms by first understanding the mathematical meanings. Word form is a term used in math to denote expressions written in word B.

Also, the standard form is a way of shortening large numerical values using digits. Digits are single numbers that run between 0 to 9 and they make up the higher values of numbers.

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The value of f(j) when

1. j = -1 is 11

2. j = 0 is 10

3. j = 1 is 11

4 . j = 2 is 14

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

For example, here j is a variable and f(j) is the function of 'j'.

f(j) = j²+10

Therefore , when j = -1

f(j) = -1)² + 10

f(j) = 1+10 = 11

When j = 0

f(j) = 0²+10

= 0+10 = 10

when j = 1

f(j) = 1²+10

= 1+10 = 11

When j= 2

f(j) = 2²+10

= 4+10

= 14

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Answer: (f+g)(x) = x² + 3x - 10

Step-by-step explanation:

The equivalent value of the expression is A = 12 + 6x + 6x + 6y

Given data ,

Let the expression be represented as A

Now , the value of A is

A = 6(2 + x + x + y)

On simplifying the equation , we get

A = 6 ( 2 ) + 6x + 6x + 6y

On further simplification , we get

A = 12 + 6x + 6x + 6y

Hence , the expression is A = 12 + 6x + 6x + 6y

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The complete question is attached below :

which expression uess exactly terms and is equivalent to 6(2 + x + x + y)

Yes , y varies directly with x as a proportion of k = 2.5

Given data ,

Let the values of x = { 2 , 6 , 18 }

Let the values of y = { 5 , 15 , 45 }

Now , the proportion equation is y = kx

On simplifying , we get

k = 5/2

k = 2.5

Therefore , the proportionality constant is k = 2.5

Hence , the proportion is y = 2.5 ( x )

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The pattern that can be used to represent a triangular number is T(n) = 1 + 2 + 3 + ... + n.

A number that can take the form of an equilateral triangle is called a triangular number. By definition, it represents the sum of positive integers up to n consecutive natural numbers. The pattern for such a calculation is expressed as follows:

T(n) = 1 + 2 + 3 + ... + n.

Triangular numbers exhibit many engaging properties and are applicable across various mathematical and real-world contexts.

In conclusion, the pattern used to represent a triangular number is T (n) = 1 + 2 + 3 + ... + n.

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The quantity of cats that will be in the pet daycare when there are 40 dogs would be = 120 cats.

Ratio can be defined as the comparison of two values that shows the amount of one value that can be found in the other value.

The initial amount of dogs = 20

The initial amount of cats = 60

The final amount of dog = 40

The final amount of cats = ?

That is;

20 dogs = 60 cats

40 dogs = X cats

make X the subject of formula;

X = 40×60/20

= 2400/20

= 120 cats

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Answer:

Step-by-step explanation:

True

The value of the expression is 2x³ + 3x² - 27x + 40

It is important we know that algebraic expressions are described as expressions that are composed of factors, constants, variables, coefficients and terms.

Algebraic expressions are also made up of arithmetic operations, such as;

From the information given, we have;

1. (x + 5)(2x² -7x + 8)

expand the bracket

2x³ - 7x² + 8x + 10x² -35x + 40

collect like terms

2x³ - 7x² + 10x² + 8x - 35x + 40

Add the like terms

2x³ + 3x² - 27x + 40

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The calculated surface area of the triangular prism is 976 square meters

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

The dimensions of the triangular prism

The surface area of the triangular prism is the sum of the individual shapes

So, we have the following formula

Surface area = Area of rectangle + Area of the 2 triangles + Area of the 2 rectangles

Using the dimensions, we have

Surface area = 10 * 14 + 2 * 1/2 * 24 * 14 + 2 * 25 * 10

Evaluate

Surface area = 976

Hence, the surface area is 976

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Answer:

The answer would be 3.5 in decimal form.

Answer:

The answer is 55/12

Step-by-step explanation:

8-41/12

(8×12+1×(-41))/12

(96-41)/12

55/12

The volume of the pyramid is  9333 cubic centimetres

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

Base dimensions = 40 cm by 20 cm

Height = 35 cm

The volume of the pyramid is calculated as

Volume = Product of Base dimensions and Height/3

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

Volume = 40 * 20 * 35/3

Evaluate

Volume = 9333

Hence, the volume is 9333

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Answer:

The correct answer is C

Step-by-step explanation:

The value of c as per the law of cosines, to the nearest tenth, is 5.1 units.

Given information:

a = 8, b = 9 C = 34°.

To find the value of C:

According to the Law of Cosines, for any triangle ABC:

c² = a² + b² - 2ab cos(C)

Substituting the given values:

c² = 8² + 9² - 2(8)(9) cos(34°)

c² = 64 + 81 - 144 cos(34°)

c² = 145 - 144 cos(34°)

Taking the square root of both sides:

c = √(145 - 144 cos(34°))

Using a calculator:

c ≈ 5.1 units (rounded to the nearest tenth)

Therefore, the value of c is approximately 5.1 units.

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Answer:

Hii^^ Here's your answers:
5 hrs=$150 earned
7 hrs=$210 earned
9 hrs=$270 earned

Step-by-step explanation:

30x = amount earned
x = hours

Answer:(5,150) (7,210) (9,270)

Step-by-step explanation: For each hour she works, she earns 30 dollars.

Number of hours: Money she earns

1:30

X stands for the amount of money she earns. So for 5 hours, we can write this:

5:X

To get from 1:30 to 5:x, you multiply by 5. 1x5=5. So you multiply 30x5 and get 150. Do the same for the other situations, and you get:

5:150

7:210

9:270

To plot them on the graph, the number of hours she works is x, and the money she earns is y.

So, put these on the graph:

(5,150)

(7,210)

(9,270)

The requried measure of the side QT in triangle SQT is 59 units.

A figure is shown with two triangles, SQT and SQR.

Since in the question we are given to RS = ST 81, QR = v + 33, and QT = 3v 19,

As RS = St and SQ is a common side both the triangle are congruent, QT = QR

v + 33 = 3v - 19
52 = 2v
v = 26

Now,
QT = 3(26) - 19
QT = 59

Thus, the requried measure of the side QT in triangle SQT is 59 units.

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The solution is,  $ 12833 .59 will he have in the account after 5 years.

Compound interest is a type of interest that is calculated not only on the principal amount of a loan or investment, but also on any interest that has previously accrued. In other words, it is interest that is earned on both the initial principal and any interest that has been added to it over time.

by the question.

We can use the formula for compound interest to solve the problem:

A = P

where:

A = final amount (x in this case)

P = principal or initial amount ($10,000.00)

r = annual interest rate (5% in this case)

n = number of times the interest is compounded per year (12, since it's compounded monthly)

t = time in years (5, since Tyrone opened the account 5 years ago)

Substituting the values given, we get:

A = $ 12833 .59

The solution is,  $ 12833 .59 will he have in the account after 5 years.

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The mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.

To calculate the mean excess return of the value-weighted index portfolio, we need to first calculate the total market capitalization of the three stocks:

Total Market Cap = $3,000 + $2,000 + $1,500 = $6,500

Next, we can calculate the weight of each stock in the index portfolio as follows:

Weight of Stock A = $3,000 / $6,500 = 0.4615

Weight of Stock B = $2,000 / $6,500 = 0.3077

Weight of Stock C = $1,500 / $6,500 = 0.2308

The capitalization-weighted beta of the portfolio can then be calculated as the sum of the product of each stock's weight and its beta:

Beta of Index Portfolio = (0.4615 x 0.15) + (0.3077 x 0.95) + (0.2308 x 1.7) = 1.081

The mean excess return of the index portfolio can be calculated using the single-index model as:

Mean Excess Return = Beta of Index Portfolio x Standard Deviation of Market-Index Portfolio

= 1.081 x 18%

= 19.458%

Finally, we need to adjust for the risk-free rate to obtain the actual mean return of the index portfolio. If the risk-free rate is 2%, then the mean return of the index portfolio would be:

Mean Return = Mean Excess Return + Risk-Free Rate

= 19.458% + 2%

= 21.458%

Therefore, the mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.

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Yes , Han is correct as the a circle with a longer arc length has a larger central angle

Given data ,

Let the arc length of the circle A = 6π units

Let the radius of the circle A = 15 units

Let the arc length of circle B = 2π units

Let the radius of the circle B = 5 units

Now , The length of an arc in a circle is determined by both the radius of the circle and the central angle that subtends the arc. The formula for calculating the length of an arc in a circle is given by:

Arc length = (Central angle / 360 degrees) x (2πr)

Though two circles' radii differ, they may nevertheless have distinct arc lengths even though their centre angles are the same. Similar to this, if the radii of two circles are adjusted properly, two circles with differing central angles can nevertheless have the same arc length.

Hence , the central angle is solved

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