how many ping pong balls do you need if you want to arrange them in the shape of an equilateral triangle with 23 rows

Hello!

miles driven = x

the initial cost = 29

f(x) = 29 + 0.35x

The statements regarding matrix are a) True b) True c) True d) False e) True.

In mathematics, a matrix refers to a rectangular array or table of numbers, expressions, or symbols which are arranged in rows and columns. It is used to represent a mathematical object or a property of mathematical object. There are a number of basic operations that are used to modify matrices such as matrix addition, scalar multiplication, transposition, matrix multiplication, row operations, and submatrix.

a) The given statement “every matrix equation Ax = b corresponds to a vector equation with the same solution set” is true as the matrix equation Ax=b is simply another notation for the vector equation x1 a1 + x2 a2 +... + xn * an, are the columns of A.

b) The given statement “if the equation Ax = b is consistent, then b is in the set spanned by the columns of A” is true as the equation Ax = b has a nonempty solution set if and only if b is a linear combination of the columns of A.

c) The given statement “any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x” is true as the matrix A is the matrix of coefficients of the system of vectors.

d) The given statement “if the coefficient matrix A has a pivot position in every row, then the equation Ax = b is inconsistent is false as if A has a pivot position in every row, the echelon form of the augmented matrix could not have a row such as [0 0 0 1], and Ax = b must be consistent.

e) The given statement “the first entry in the product Ax is a sum of products” is true as the first entry in Ax is the sum of the products of corresponding entries in x and the first entry in each column of A.

Note: The question is incomplete. The complete question probably is: Determine whether each of statements below are true or false. a) Every matrix equation Ax = b corresponds to a vector equation with the same solution set. b) If the equation Ax = b is consistent, then b is in the set spanned by the columns of A c) Any linear combination of vectors can always be written in the form Ax for a suitable matrix A and vector x d) If the coefficient matrix A has a pivot position in every row, then the equation Ax = b is inconsistent. e) The first entry in the product Ax is a sum of products.

Learn more about Matrix:

https://brainly.com/question/2456804

#SPJ4

Answer:

no because these "imaginary numbers" can have the same value as 2 real numbers that add up to a real number. Example:7 3+4=7    x+y (Algebra so not real numbers)= infinite possibilities

Step-by-step explanation:

The value of the function f(-1) is 1/3. Option D

A function can be defined as a law, an expression or rule that is used to show the relationship between two variables.

These variables are listed as;

From the information given, we have the function written as;

f(x) = 3ˣ

To determine the function f(-1), we need to substitute the value of the variable x as -1 in the function f(x)

Substitute the values, we have;

f(-1) = 3⁻¹

Take the inverse of the value, we get;

f(-1) = 1/3

Learn more about functions at: https://brainly.com/question/11624077

#SPJ1

Answer:

q=6

Step-by-step explanation:

8-2 = q

q=6

Answer:

q = 6

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

q+2=8

Step 2: Subtract 2 from both sides.

q+2−2=8−2

q=6

Answer:

q=6

Answer:

The population density is 618.93 per square mile.

Step-by-step explanation:

It is given that,

No. of people, N = 70,000

The radius of a city's town hall, r = 6 miles

We need to find the population density. It can be calculated by the formula i.e. number of people divided by area of land such that,

\(P=\dfrac{N}{A}\\\\P=\dfrac{N}{\pi r^2}\\\\P=\dfrac{70000}{\pi (6)^2}\\\\P=618.93\ \text{per square mile}\)

So, the population density is 618.93 per square mile.

Seriously dude, c'mon

The percentage decrease is 43.75%

Initial volume = 3.2 millimeters

After experiment volume = 1.8 millimeters

Reduction = 3.2 - 1.8 = 1.4 millimeters

Therefore the percentage decrease will be:

= Reduction/Initial value × 100

= 1.4/3.2 × 100

= 43.75%

Therefore, the percentage decrease is 43.75%

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

At the beginning of a chemistry experiment, the volume of liquid in a container was 3.2 milliliters. During the experiment, the volume dropped to 1.8 milliliters. Find the percent of decrease.

Answer:

$544

Step-by-step explanation:

To determine the original price of the DVD player considering that you know that it had a 75% reduction, you can use a rule of three as the price of $136 represents 25% of the original price and with this you can calculate the price that represents 100%:

$136 → 25%

  x    ← 100%

x=(136*100)/25=$544

According to this, the answer is that the original price of the DVD player was $544.

The value of c that satisfies the condition a + b = 10 is 10.

To find the value of c such that the sum of the x- and y-intercepts of any tangent line to the curve √x + √y = √c is equal to 10, we can use the fact that the x-intercept occurs when y = 0, and the y-intercept occurs when x = 0.

First, let's find the x-intercept. When y = 0, we can substitute this value into the equation:

√x + √0 = √c

Simplifying, we have:

√x = √c

Squaring both sides of the equation, we get:

x = c

So, the x-intercept is given by (c, 0).

Next, let's find the y-intercept. When x = 0, we can substitute this value into the equation:

√0 + √y = √c

Simplifying, we have:

√y = √c

Squaring both sides of the equation, we get:

y = c

So, the y-intercept is given by (0, c).

Since we want the sum of the x- and y-intercepts to be equal to 10, we have:

c + 0 = 10

Simplifying, we find:

c = 10

For more such questions on condition visit:

https://brainly.com/question/24020391

#SPJ8

Answer:

he can rent the camera for 5 days and will have $5 left over

Step-by-step explanation: he only has $50 , and he has to pay 15 to register which will leave him with 35 left over and then he pays $6 each day and it would be 5 days of renting.

50-15+35

6x5=30 which means he pays $6 everyday for 5 days

which will leave $5 left over

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

Let's denote the original scholarship amount as "P."

According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.

Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).

Now, we can sum up all the shares to equal the original scholarship amount:

Ron's share + Nick's share + Mary's share + Margaret's share = P

(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P

To simplify the equation, we can combine like terms:

(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P

Combining the fractions and constants:

(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P

16P/12 - $48,000 = P

Multiplying both sides of the equation by 12 to eliminate the denominator:

16P - $576,000 = 12P

Subtracting 12P from both sides of the equation:

4P = $576,000

Dividing both sides of the equation by 4:

P = $144,000

Therefore, the original scholarship amount is $144,000.

Ron's share: (1/3)($144,000 - $72,000) = $24,000

Nick's share: (1/4)($144,000 - $72,000) = $18,000

Mary's share: (1/4)($144,000 - $72,000) = $18,000

Margaret's share: $72,000

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

For more questions on share

https://brainly.com/question/30319374

#SPJ8

Answer:

$218.10

Step-by-step explanation:

He made 4.95 per hour for 36 hours. Multiply.

36 × 4.95 = 178.2

For his commission, he earned 6% of 665. Change the percent to a decimal:

6% is .06

and then multiply.

665 × .06 = 39.9

Add together his hour pay with his commission earnings.

178.2 + 39.9

= 218.1

He made $218.10

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1

Answer:

B

Step-by-step explanation:

Most reasonable

Answer:

60

Step-by-step explanation:

Answer:

- 0.125

Step-by-step explanation:

Given the equation :

(0.020(5/4) + 3 ((1/5) – (1/4)))

0.020(5/4) = 0.025

3((1/5) - (1/4)) = 3(1/5 - 1/4) = 3(-0.05) = - 0.15

0.025 + - 0.15 = 0.025 - 0.15 = - 0.125

Answer: 64 degrees

Step-by-step explanation:

NCA and FCB are vertical angles so theyre the same measurement

Answer:

Step-by-step explanation:

vertical angles = ∠FCB = ∠NCA = 64°

Answer:

1) \(\dfrac78\)

2) \(\dfrac{17}{12} = 1 \frac{5}{12}\)

3) \(\dfrac{53}{12}=4 \frac{5}{12}\)

Step-by-step explanation:

1)

\(\dfrac38+\dfrac12=\dfrac38+\dfrac{1 \times4}{2 \times 4}=\dfrac38+\dfrac48=\dfrac78\)

2)

\(\dfrac23+\dfrac34=\dfrac{2 \times 4}{3 \times 4}+\dfrac{3 \times3}{4 \times3}=\dfrac8{12}+\dfrac{9}{12}=\dfrac{17}{12}=1 \frac{5}{12}\)

3)

First convert mixed number into improper fraction:

\(4 \frac23=\dfrac{3\times4+2}{3}=\dfrac{14}{3}\)

\(\implies 4 \frac23-\dfrac{3}{12}=\dfrac{14}{3}-\dfrac{3}{12}=\dfrac{14\times4}{3\times4}-\dfrac{3}{12}=\dfrac{56}{12}-\dfrac{3}{12}=\dfrac{53}{12}=4 \frac{5}{12}\)

Answer:

-i

Step-by-step explanation:

We are to find the value of i^31

Note that i^2 = -1

Expanding i^31

i^31 =

= (i^2)15 * i

= (-1)^15 * i

= -1 * i

= -i

Hence the equivalent is -i

Answer:

$43.05

Step-by-step explanation:

Add $28.66 and $19.39, after that you get 48.05. Then subtract 5 from it and you get $43.05

Answer:

30%

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

(% of drums÷100%) x 30

(30÷100) x 30

0.3 x 9

9

Answer:

Step-by-step explanation:

Since we are given two points in the graph, we can use the slope equation shown below:

(y2-y1)/(x2-x1)

reading the graph left from right (1,11) will be the first point and (3,1) the second. plug in and solve!

(1-11)/(3-1) = -10/2 = -5

The slope is -5

a negative slope makes sense since the graph is leaving the first quadrant.

hope this helps!

Answer: A) -5. Graph slope.

Step-by-step explanation:

The formula to calculate the slope of the line is:

\(\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff m=\dfrac{x_2-x_1}{y_2-y_1} }}\)

We have that the points are:

We substitute these points in the previous formula and solve:

     \(\boldsymbol{\sf{m=\dfrac{x_2-x_1}{y_2-y_1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{1-11 }{3-1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{-10}{5} }}\\ \\ \\ \boxed{\boldsymbol{\sf{m=-5}}}\)

well, if take a year to be 365 days so hmmm 150 days is really just 150/365 of a year, so let's use that.

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$11000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\to \frac{150}{365}\dotfill &\frac{30}{73} \end{cases} \\\\\\ A=11000[1+(0.09)(\frac{30}{73})]\implies A=11000\left( \frac{757}{730} \right)\implies A\approx 11406.85\)

Answer:

  (c)  8

Step-by-step explanation:

Your figure shows DS is the radius of a sphere with radius 4 inches. It also shows SI and SE are other radii of the sphere. Each of those is also 4 inches, as the radius of a sphere is the same in every direction from the center.

  DS +SI = (4 in) +(4 in) = 8 in

Answer:

8

Step-by-step explanation: