Give a brief history about TRIANGLE NUMBERS, including Mathematicians that contributed for its development.

Answer:$6,000

Step-by-step explanation:

Answer:

The answer is going to be letter B.

Therefore, John is incorrect, as buying a 2-liter bottle of orange juice is actually slightly more expensive per liter than buying a 1.5-liter bottle of cola.

An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.

Here,

2.1.1 To determine how many packets of patties Julia should buy, we need to know the total number of patties needed for the school function. Let's assume that each person will eat one patty.

If there are 300 people attending the function, then Julia needs to buy:

300 x 1 = 300 patties

Each packet of patties contains 12 patties, so the number of packets needed can be calculated as follows:

300 patties ÷ 12 patties/packet = 25 packets

Therefore, Julia should buy 25 packets of patties.

2.1.2 To justify Julia's calculation, we can use algebra. Let's assume that the number of packets of patties she buys is x. We know that there are 12 patties in each packet, so the total number of patties is 12x. We also know that if she buys 42 packets, there will be a leftover of 4 patties.

This can be represented as the following equation:

12x + 4 = 42 x 12

Simplifying this equation:

12x = 500 - 4 = 496

x = 496/12 = 41.33 (rounded to two decimal places)

Since we can't buy a fractional number of packets, Julia would need to buy 42 packets of patties. This would give her a total of:

12 x 42 = 504 patties

She would then have 4 leftover patties, as calculated earlier. Therefore, Julia's calculation is correct.

2.2.1 To determine whether buying a 2-liter bottle of orange juice is cheaper than buying a 1.5-liter bottle of cola, we need to compare the price per liter of each drink.

For orange juice, the price per liter is:

R18.95 ÷ 2 liters = R9.475/liter

For cola, the price per liter is:

R14.50 ÷ 1.5 liters = R9.67/liter

To know more about equation,

https://brainly.com/question/2228446

#SPJ9

Answer:

\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)

Step-by-step explanation:

An exponential function of form f(x) = ba^(-x) + c has a horizontal asymptote of y = c as x approaches infinity, and a y-intercept of (0, b + c). We can use the given information to set up a system of equations and solve for the unknowns.

The horizontal asymptote is given as y = 33, so we have:

c = 33

The y-intercept is given as (0, 408), so we have:

b + c = 408

Substituting c = 33, we get:

b + 33 = 408

b = 375

So the function we're looking for is of the form:

\(\bold{f(x) = 375a^{-x}+ 33}\)

To find a, we use the fact that the function passes through P(2, 93):

93 = 375a^(-2) + 33

60 = 375a^(-2)

a^2 = 375/60

a^2 = 6.25

a = \(\sqrt{6.25 } =2.5\)

Therefore, the exponential function that satisfies the given conditions is:

\(\bold{f(x) = 375(2.5)^{-x}+ 33}\)

The system of linear equations that can be solved from the matrices is given as follows:

Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:

A = [-5 4; -8 1]

Hence the multiplication of matrices representing the system is given as follows:

[-5 4; -8 1][x; y] = [3; -6]

Applying the multiplication of matrices, the system of equations is given as follows:

More can be learned about a system of equations at https://brainly.com/question/13729904

#SPJ1

The change after buying the calculators is $204.12

Ms. Wood has a class of 18 students

She wants to spend $20 on each of her students

The total money she can spend can be calculated as follows

= 18 × 20

= 360

She buys the calculators for her students, everything costs $155.88

The money she has left to spend can be calculated as follows

= 360 - 155.88

= 204.12

Hence she has $204.12 left as the change she can spend on her students

Read more on change here

https://brainly.com/question/28779204

#SPJ1

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer:

x • (x - y) • (x^2 + xy + y^2 + 3y)

Step-by-step explanation:

The methods to reduce the risk of tuberculosis include Educating patients on respiratory hygiene

What is tuberculosis?

Mycobacterium tuberculosis is the bacteria that causes tuberculosis (TB). TB germs often attack the lungs, but they can attack any region of the body, including the kidney, spine, and brain.

When an infected individual coughs or sneezes, the germs that cause tuberculosis spread. The majority of people who are infected with the germs that cause tuberculosis do not show symptoms. When symptoms do appear, they are typically accompanied by a cough (sometimes blood-tinged), weight loss, night sweats, and fever.

Learn more about tuberculosis on:

brainly.com/question/18173152

#SPJ4

We cannot conclude that there are more than 70,000 defined words in the dictionary.

To test the claim that there are more than 70,000 defined words in the dictionary, we can set up the null and alternative hypotheses as follows:

Null Hypothesis (H0): The mean number of defined words on a page is 48.0 or less.

Alternative Hypothesis (H1): The mean number of defined words on a page is greater than 48.0.

So, sample mean

= (59 + 37 + 56 + 67 + 43 + 49 + 46 + 37 + 41 + 85) / 10

= 510 / 10

= 51.0

and, the sample standard deviation (s)

= √[((59 - 51)² + (37 - 51)² + ... + (85 - 51)²) / (10 - 1)]

≈ 16.23

Next, we calculate the test statistic using the formula:

test statistic = (x - μ) / (s / √n)

In this case, μ = 48.0, s ≈ 16.23, and n = 10.

test statistic = (51.0 - 48.0) / (16.23 / √10) ≈ 1.34

With a significance level of 0.05 and 9 degrees of freedom (n - 1 = 10 - 1 = 9), the critical value is 1.833.

Since the test statistic (1.34) is not greater than the critical value (1.833), we do not have enough evidence to reject the null hypothesis.

Therefore, based on the given data, we cannot conclude that there are more than 70,000 defined words in the dictionary.

Learn more about test statistic here:

https://brainly.com/question/31746962

#SPJ1

Answer:

Hi! The answer to your question is x = 12

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

The cost of one small box of fruit and the cost of one large box of fruit is $11.5 and $14.5 respectively.

Let

cost of one small box of fruit = x

cost of one large box of fruit = y

15x + 15y = 390

20x + 25y = 592.50

From (1)

x + y = 26

x = 26 - y

Substitute x = 26 - y into (2)

20x + 25y = 592.50

20(26 - y) + 25y = 592.50

520 - 20y + 25y = 592.50

- 20y + 25y = 592.50 - 520

5y = 72.50

divide both sides by 5

y = 72.50/5

y = 14.5

Substitute y = 14.5 into

15x + 15y = 390

15x + 15(14.5) = 390

15x + 217.5 = 390

15x = 390 - 217.5

15x = 172.5

divide both sides by 15

x = 172.5/15

x = 11.5

Therefore, small box cost $11.5 and large box cost $14.5

Read more on simultaneous equation:

https://brainly.com/question/16863577

#SPJ1

The quadratic regression equation is y = 1.38x^2 - 5.77x + 0.96

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

(-1,8), (5,-4), (7,8), (2,-6)

Using a graphing calculator, we have the following summary:

function value

mean of x 3.25

mean of y 1.5

correlation coefficient r 0.9990171837

A 1.380577428

B -5.769028871

C 0.9553805774

The equation is represented as

y = ax^2 + bx + c

So,, we habe

y = 1.38x^2 - 5.77x + 0.96

Hence, the equation is y = 1.38x^2 - 5.77x + 0.96

Read more about regression at

https://brainly.com/question/25987747

#SPJ1

Answer:

The amount is $8358.7 and the interest is $3858.7.

Step-by-step explanation:

The ordered pair that solves the system of equation is (0, 0).

To solve this system, we can substitute the first equation into the second equation to eliminate y:

x = 2x

Solving for x, we get x = 0.

Substituting x = 0 into the first equation, we get y = 0.

Therefore, the ordered pair that solves the system is (0, 0).

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

6.8333333333 or 41/6

Step-by-step explanation:

Answer:

L= 1/2 × 7.8×7

L=1/2×54.6

L=27.3

Answer:

191.1km

Step-by-step explanation:

½×7.8×7×7

This is the procedure used to get the answer above

Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

Answer:

No, the equation is not a linear equation.

Step-by-step explanation:

There is the x^2 thing that doesn't make it a linear equation.

Answer:

5,12

Step-by-step explanation:

because 7-2 is 5 and it would take 12 to get to 7

Answer:

\( \frac{3( {5}^{8} - 1) }{5 - 1} = 292968\)

If the streetlights are spaced in the same way, there will be 48 streetlights on the 4-mile road.

First, we know that there are 18 streetlights evenly spaced on a 1.5 mile road.

Then the space between consecutive streetlights is:

1.5mi/18 = (3/36) mi = (1/12) mi

Now, the number of streetlights that we will have on a 4-mile road is given by the quotient between the length of the road and the distance between consecutive streetlights, it is:

N = 4mi/(1/12 mi) = 12*4 = 48

There will be 48 streetlights on a 4 mile road.

Learn more about quotients at:

https://brainly.com/question/629998

#SPJ1

I recommend use of simple random sampling to determine the three possible toppings to be used for the vegetarian pizza.

It is a sampling technique in which each member of the population has an equal chance of being selected for the sample. Here, the population would be students who regularly eat at the school cafeteria.

By using the sampling, we make sure that each student has an equal chance of being selected to taste test the different pizza toppings. This will help to eliminate bias and provide a representative sample of the population's preferences. They will provide feedback which will be used to determine which topping should be used for the vegetarian pizza.

Read more about sampling technique

brainly.com/question/28292794

#SPJ1

Answer:

3b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perimeter formula:

Given:

Find the value of x:

BC is parallel side to AD and is:

BC must parallel to DA hence equal

Now

BC=2(6)=12units

Step-by-step explanation:

To multiply two numbers in scientific notation, you multiply their coefficients and add their exponents. Applying this rule, we get:

(4 x 10^11) (8 x 10^6) = (4 x 8) x (10^11 x 10^6) = 32 x 10^17

However, this result is not yet in scientific notation because the coefficient 32 is not between 1 and 10. To put it in scientific notation, we need to divide the coefficient by 10 and increase the exponent by 1. This gives:

32 x 10^17 = 3.2 x 10^18

Therefore, the product of (4 x 10^11) and (8 x 10^6) expressed in scientific notation is 3.2 x 10^18.