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Daisy is studying an ant population. On the first day, there are 10 ants. A week later, there are 100 ants. After the third week, there are 1,000 ants. Assuming the ant growth continues at this rate, how many ants would there be after 5 weeks?

Statement A is the Associative Property of Addition. Statement B is the Multiplicative Property of Equality. Statement C is the Commutative Property of Multiplication. Statement D is the Additive Identity Property.

Arithmetic properties are fundamental principles that govern the behavior of arithmetic operations such as addition, subtraction, multiplication, and division. These properties determine how numbers interact with each other and help us to simplify and manipulate mathematical expressions.

A. 2x-2y=2(z-y)

This statement is true because of the distributive property: if a(b + c) = ab + ac, then multiplying both sides of an equation by a scalar will not change the equality of the equation.

B. 4x/3 x 3/4x=1

This statement is true because of the property of multiplication of inverse elements: if a x 1/a = 1, then multiplying both sides of an equation by the reciprocal of a variable will not change the equality of the equation.

C. -9 x 5a²=5a² x -9

This statement is true because of the commutative property of multiplication: if a x b = b x a, then rearranging the terms of an equation will not change the equality of the equation.

D. √10 + 0 = √10

This statement is true because of the identity property of addition: if a + 0 = a, then adding zero to both sides of an equation will not change the equality of the equation.

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The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.

To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:

Step 1: Find the mean (average) of the data set.

Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5

Step 2: Calculate the difference between each data point and the mean.

Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|

Step 3: Calculate the absolute value of each difference.

Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10

Step 4: Find the average of the absolute differences.

MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20

The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.

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Answer:

This is an percentage change question, by any chance you have a maths textbook, search for units that contains the topic: Percentage Change/Percentage. Now, let's get solving! :D

Step-by-step explanation:

First of all, you multiply 7% with $778,095 which gives: $54,466.65 (This is your commission/Answer)

Most currency questions use 1 decimal place, so I recommend you to use this answer: $54,466.7

Stay safe and Merry Christmas! :)

Answer:

he received commission amount =7% of $778,095=$54466.65

Step-by-step explanation:

commission =7%

marked price=$778,095

commission amount =7% of $778,095=$54466.65

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Step-by-step explanation:

Pitchers(p) = 12

Infielders(i) = 5

Others(o) = 8

Total players = 25

Probability(2p and 1i) =

\(( \frac{2}{25} ) \times ( \frac{1}{25} ) = ( \frac{2}{625} )\)

The expression that is equivalent to the given value would be = 18-i . That is option C.

An equivalent expression is defined as the type of expression that is similar to a given value when simplified.

The given expression = ( 3 + 4i) ( 2 - 3i)

Expand the given expression by removing the brackets as follows:

= =2(3+4i)−3i(3+4i)

=(6+8i)−(9i−12)

= (6+12)+i(8−9)

=18−i.

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Answer:

28.52

Step-by-step explanation:

105.87 - 77.35 = 28.52

The measure of the unknown sides is equivalent to 12.6

The given figure is a circle geometry with the perpendicular lines intersecting both segments of the circle.

We need to determine the measure of x. Since the measure of the perpendicular lines are equal, hence the measure of the line of the segments will also be equal.

Hence:

x = 6.3 + 6.3

x = 12.6

Therefore the measure of x from the given diagram is equivalent to 12.6

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The formula for nCk is ...

  nCk = n!/(k!(n -k)!)

It always works out that nC0 = 1 and nC1 = n, and the sequence of numbers across a row of the diagram is symmetrical about the center.

This means you only need to calculate one value to finish filling your diagram.

  4C2 = 4!/(2!(2!)) = (4·3)/(2·1) = 6

You will find the pattern to be ...

  each element in the diagram is the sum of the two above  it.

The slope of the line passing through points A and B is 1/3.

The formula for the slope of a line to find the slope passing through points A and B. The formula is:

slope = (change in y) / (change in x)

Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).

Then, substitute the values and calculate the slope:

slope = (y₂ - y₁) / (x₂ - x₁)

slope = (3 - 2) / (3 - 0)

slope = 1 / 3

Therefore, the slope of the line passing through points A and B is 1/3.

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Answer:

the answer is b, c, d, a, respectively

The photos are similar because the enlarged photo is 1.5 times the size of the original photo.

What is meant by similarity transformations?

Similarity transformations turn items in space into similar objects. If two items have the same shape or have the same shape as their mirror images, they are said to be similar. More specifically, by uniformly scaling (enlarging or decreasing), maybe with additional translation, rotation, and reflection, one can be created from the other. This indicates that one object may be properly aligned with the other object by rescaling, moving, and reflecting it. When two things are comparable to one another, one is consistent with the outcome of a specific uniform scaling of the other.

Here the initial dimension of the photo is  5" by 7" and after enlarging it has dimensions 7.5" by 10.5".

The scale factor is = 7.5/5 = 10.5/7 = 1.5

Since the scale factor is constant for all sides, the pictures before and after enlargement are similar.

Therefore the photos are similar because the enlarged photo is 1.5 times the size of the original photo.

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Answer:

9/41

Step-by-step explanation:

Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side)  which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.

Answer:

V= -25

Step-by-step explanation:

5 = V+30

-30          - 30

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

-25 = V

so, you have to figure out 5-30 which gets you -25 and you want to get the variable by itself so you do -30 and do the inverse operation and what you do to one side has to be done to the other so when you do +30-30 it gets you nothing so those cancel

Hope this helped u sorry if incorrect and welcome to Brainly

Answer:

X= 52

2X+24 =128

Step-by-step explanation:

128+52= 180

Answer:

A = 16000(1+0.14)^12 = 77086.4777

Answer:

12 22 23 24 25 26 2u 28 ug6fyd

Answer:

Annette should plan to spend 2.25 hours walking back.

Step-by-step explanation:

To solve this problem, we can use the formula:

Time = Distance / Speed

Let's assume the distance of the race is D miles.

Annette spends her time running the distance of the race, which takes:

Time running = D / 9 hours

She then walks back the same distance, which we need to find the time for:

Time walking = D / 3 hours

Since Annette has a total of 3 hours for her training, the sum of the running time and walking time should equal 3 hours:

D / 9 + D / 3 = 3

To simplify the equation, we can multiply all terms by 9 to eliminate the denominators:

D + 3D = 27

Combining like terms:

4D = 27

Dividing both sides of the equation by 4:

D = 6.75

So, the distance of the race is 6.75 miles.

To find the time Annette should spend walking back, we substitute the distance into the time-walking formula:

Time walking = D / 3 = 6.75 / 3 = 2.25 hours

Therefore, Annette should plan to spend 2.25 hours walking back.

Answer:

m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Step-by-step explanation:

2m³ - 5m² - 7m = 0 ← factor out common factor m from each term

m(2m² - 5m - 7) = 0

factorise the quadratic 2m² - 5m - 7

consider the factors of the product of the coefficient of the m² term and the constant term which sum to give the coefficient of the m- term

product = 2 × - 7 = - 14 and sum = - 5

the factors are + 2 and - 7

use these factors to split the m- term

2m² + 2m - 7m - 7 ( factor the first/second and third/fourth terms )

2m(m + 1) - 7(m + 1) ← factor out (m + 1) from each term

(m + 1)(2m - 7)

then

2m³ - 5m² - 7m = 0

m(m + 1)(2m - 7) = 0 ← in factored form

equate each factor to zero and solve for m

m = 0

m + 1 = 0 ( subtract 1 from both sides )

m = - 1

2m - 7 = 0 ( add 7 to both sides )

2m = 7 ( divide both sides by 2 )

m = \(\frac{7}{2}\)

solutions are m = - 1 , m = 0 , m = \(\frac{7}{2}\)

Answer:

x = 18

Step-by-step explanation:

Missing Components of triangle for angles:

A=39

B=51

C=90

Missing Components of triangle for sides:

a=11.3

b=14

x=18

Answer:

growth rate: 4

y-value: 19

equation: y=4x+19

Step-by-step explanation:

Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.

For the question:
The change in y-values is 11-7=4,

and the change in x-values is +1.

Therefore, the growth rate is 4.

\(\hrulefill\)

Initial Value: The initial value of a linear function is the value of the function when x is 0.

In this case, the initial value is 19.

This can be found by looking at the y-value of the point where x is 0.

In this case, the y-value is 19.

\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Using the table you provided, we can find the slope by using two points on the line.

Let’s use (-3, 7) and (1, 23).

The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4

Now,

Taking 1 point (-3,7) and slope 4.

we can find the equation by using formula:

y-y1=m(x-x1)

y-7=4(x+3)

y=4x+12+7

y=4x+19

Therefore, the equation of the given table is y=4x+19\(\hrulefill\)

Answer:

Growth rate:  4

Initial value:  19

Equation:  y = 4x + 19

Step-by-step explanation:

The slope of a linear function represents its growth rate.

Therefore, the growth rate of a linear function can be found using the slope formula.

Substitute two (x, y) points from the table into the slope formula, and solve for m.  Substituting points (0, 19) and (1, 23):

\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)

Therefore, the growth rate of the linear function is 4.

The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.

From inspection of the given table, y = 19 when x = 0.

Therefore, the initial value of the linear function is 19.

To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.

As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:

\(\boxed{y=4x+19}\)

The total number of coins that were in Kay's bank are 137 coins.

In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Since she has 11 less dimes than nickels, an equation which models this situation is given by;

n = d + 11     ....equation 1.

Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.

Additionally, the coins are worth 10 dollars;

0.1d + 0.05n = 10 ....equation 2.

By solving both equations simultaneously, we have:

0.1d + 0.05(d + 11) = 10

0.1d + 0.05d + 0.55 = 10

0.15d = 9.45

d = 63 dimes.

For nickels, we have:

n = d + 11

n = 63 + 11

n = 74

Now, we can determine the total number of coins;

Total number of coins = n + d

Total number of coins = 74 + 63

Total number of coins = 137 coins.

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The proper steps for the construction are given as 1, 2 4, and then 3.

The proper steps for the construction are;

1. Place the compass needle on the external point R. Make the compass width greater than the distance from R to the given line.

2. Draw an arc cutting the given line at two points. Mark and label the points of intersection P and Q.

3. Move the compass needle to P and make an arc below the line. Keep the compass width, and move the compass needle to Q. Draw an arc below the line crossing the other arc. Mark and label the point of intersection S.

4. Draw a line from the external point R to the points where the arcs intersect, S. Line RS is perpendicular to line PQ and passes through the external point R.

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Answer:

Step-by-step explanation:

Cost of 3 oranges = cost of 54 oranges / 18

The median is 5.

The median is 11.

The data set is bimodal.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(13 + 13 −5 −5 + 13 + 11 −5) / 7 = 35/7 =5

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

-5, -5, -5, 11,  13,13, 13

Median = 11

A bimodal data set is a distribution with two clear most frequent values.

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Answer:

what's that

Step-by-step explanation:

Answer:

cs sometimes we needa pass a test n dis is the only shi dat b righh fr

Step-by-step explanation:

Answer:

\(x=(x-3)^{\frac{9}{5}}\)

Step-by-step explanation:

The first thing we are going to do is change both sides of the equation to be base (x-3):

\((x-3)^{log_{(x-3)}(x)}=(x-3)^{\frac{9}{5}}\).

Now, since the log is in base (x-3), the base (x-3) and the log cancel out:

\(x = (x-3)^\frac{9}{5}\)

This is the final answer.

Answer:

the radius of the circular target in the center is 2.12 feet

Step-by-step explanation:

the total area of the dartboard is

π x r² = π x 3² = 9π  (28.27 ft²)

The area of the actual target in the center needs to be half of the dartboard (4.5 π)  (14.14 ft²)

(Small area :  4.5π =  π x r²

                      Divide both sides by  π

        4.5 = r²

       √4.5 = r

      r= 2.12132034.......  (2.12 feet)

Answer:

Nominal.

Step-by-step explanation:

The option that is NOT a level of measurement is qualitative.

With qualitative, numbers are not assigned to the measurement.

A level of measurement classifies and relates values to variables.  Four levels of measurement have been identified as nominal, ordinal, interval, and ratio.

Ordinal can be quantitative or qualitative, while interval and ratio are always quantitative, and nominal has non-quantitative values assigned as measurements.

Thus, qualitative is not a recognized level of measurement.

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