How many factors does 144 have?
08
O 12
O 15
06

Answer:

3 and 5

Step-by-step explanation:

You have to realize that Integers is another word for numbers

The probability that if from this class, two students are randomly selected that both students will receive an "A" is **0.025**.

There are 25 students in the class who received an "A" on the final exam. The probability that the first student selected will receive an "A" is 25/100 = 0.25.

Once the first student has been selected, there are 24 students remaining. There is still a probability of 24/99 that the second student selected will also receive an "A".

Therefore, the probability that both students selected will receive an "A" is:

```

0.25 * 0.24 = 0.06

```

This can be rounded to **0.025** to the fourth decimal place.

To calculate the probability that two students selected will receive an "A", we can use the following formula:

```

Probability = (Number of desired outcomes)/(Total number of possible outcomes)

```

In this case, the number of desired outcomes is 2, because there are 2 ways to select two students who both received an "A". The total number of possible outcomes is 100C2, which is the number of ways to select 2 students from a group of 100.

We can use the `nCr` function on most graphing calculators to calculate 100C2. The answer is 4950.

Therefore, the probability that two students selected will receive an "A" is:

```

Probability = (2)/(4950) = 0.00040

```

This can be rounded to **0.0004** to the fourth decimal place.

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Answer:

C. 9

Step-by-step explanation:

When dividing exponents with the same base, always subtract the top from the bottom, which in this case would be 9-5=4

The equation is an exponential equation, and the value of n in the equation is 9

The equation is given as:

[tex]\frac{12^n}{12^5} = 12^4[/tex]

Apply the law of indices, to the equation

[tex]12^{n-5} = 12^4[/tex]

Cancel out the common base in the equation

n - 5 = 4

Add 5 to both sides

n = 9

Hence, the value of n in the equation is 9

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The graph of the function is a parabola opening upwards. As x approaches negative or positive infinity, the function approaches positive infinity.

The given function is f(x) = 2x^2 + 10x + 12. Let's analyze the graph of the function and test its limits.

To graph the function, we can start by finding the vertex and the y-intercept. The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula x = -b/2a. In this case, a = 2 and b = 10.

x = -10 / (2 * 2) = -10 / 4 = -2.5

Substituting the x-coordinate of the vertex back into the function, we can find the y-coordinate:

f(-2.5) = 2(-2.5)^2 + 10(-2.5) + 12

        = 2(6.25) - 25 + 12

        = 12.5 - 25 + 12

        = -0.5

So, the vertex of the parabolic graph is (-2.5, -0.5).

Next, let's find the y-intercept by setting x = 0:

f(0) = 2(0)^2 + 10(0) + 12

     = 12

So, the y-intercept is (0, 12).

Now, we can plot these points and sketch the graph of the function. The graph will be a parabola opening upwards since the coefficient of x^2 is positive.

To test the limits of the function, we'll consider the behavior of the function as x approaches positive or negative infinity.

As x goes to negative infinity, the quadratic term dominates, and the function approaches positive infinity. So, the limit as x approaches negative infinity is positive infinity.

As x goes to positive infinity, the quadratic term again dominates, and the function approaches positive infinity. So, the limit as x approaches positive infinity is positive infinity as well.

In summary, the graph of the function is a parabola opening upwards. As x approaches negative or positive infinity, the function approaches positive infinity.

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The exercise involves calculations with matrices A, B, and C. We need to determine if matrix products AB, BA, BC, and CB are defined. Additionally, we need to calculate the specific matrix products and determine if BC is equal to CB.

Let's perform the calculations step by step:

(a) To determine if AB is defined, we need to check if the number of columns in matrix A is equal to the number of rows in matrix B. If they are equal, the matrix product AB is defined. If not, the product is not defined.

Matrix A has 2 columns and matrix B has 2 rows, so the product AB is defined.

Calculating AB:

AB = [23 + 83 20 + 88]

[23 + 03 20 + 08]

= [30 64]

[6 0]

To calculate BA, we need to check if the number of columns in matrix B is equal to the number of rows in matrix A. In this case, matrix B has 2 columns and matrix A has 2 rows, so the product BA is also defined.

Calculating BA:

BA = [32 + 02 38 + 02]

[32 + 02 38 + 02]

= [6 24]

[6 24]

(b) To determine if BC is defined, we need to check if the number of columns in matrix B is equal to the number of rows in matrix C. In this case, both matrices have 2 columns and 2 rows, so the product BC is defined.

Calculating BC:

BC = [26 + 85 23 + 81]

[06 + 05 03 + 01]

= [52 22]

[0 0]

To calculate CB, we need to check if the number of columns in matrix C is equal to the number of rows in matrix B. In this case, matrix C has 2 columns and matrix B has 2 rows, so the product CB is also defined.

Calculating CB:

CB = [62 + 30 68 + 30]

[52 + 10 58 + 10]

= [12 48]

[10 40]

Is it true that BC = CB?

BC = [52 22]

[0 0]

CB = [12 48]

[10 40]

BC and CB are not equal. The matrix product is not commutative, so BC and CB may yield different results.

In summary:

(a) AB is defined and the result is:

AB = [30 64]

[6 0]

BA is also defined and the result is:

BA = [6 24]

[6 24]

(b) BC is defined and the result is:

BC = [52 22]

[0 0]

CB is also defined and the result is:

CB = [12 48]

[10 40]

BC and CB are not equal, indicating that matrix multiplication is not commutative.

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Answer:

The correct option is;

[2.5, ∞)

Step-by-step explanation:

The given exponential equation can be expressed as follows;

10,000 × 4ˣ ≥ 320,000

Therefore we have;

4ˣ ≥ 320,000/10,000

4ˣ ≥ 32

㏒(4ˣ) ≥ ㏒(32)

x·㏒4 ≥ ㏒(32)

x ≥ ㏒(32)/㏒4

∴ x ≥ 2.5

Therefore, the interval the colony will have at least 320,000 bacteria is where x ≥ 2.5 or 2.5 ≤ x < ∞ which gives, the interval  [2.5, ∞)

Answer:

[2.5, infinity) - A

Step-by-step explanation:

EDGE2020

Answer:

Sadie's family car is more fuel efficient.

Step-by-step explanation:

Given;

Sadie's family car rating, S = 42 miles per gallon

Nanette's family car rating, N = 6 liters per 100 km

Sadie's family car rating, in liters per 100 km

[tex]= \frac{42 \ miles}{gallon} *\frac{1.609 \ km}{1 \ mile}*\frac{1 \ gallon}{3.79 \ liters} \\\\ = (\frac{42*1.609}{3.79} )\frac{km}{liter}\\\\ = (\frac{3.79}{42*1.609} )\frac{liter}{km}\\\\=(\frac{3.79}{42*1.609} )(\frac{100}{100}) \frac{liter}{km}\\\\= (\frac{3.79*100}{42*1.609} )(\frac{1}{100}) \frac{liter}{km}\\\\= (\frac{3.79*100}{42*1.609} ) \frac{liter}{100\ km}\\\\= 5.61 (\frac{liter}{100\ km})\\\\= \frac{5.61 \ liters}{100 \ km}[/tex]

Also, Nanette's family car rating, in liters per 100 km = 6 liters / 100km.

Thus, Sadie's family car uses lesser fuel, because of this Sadie's family car is more fuel efficient.

Answer:

0

Step-by-step explanation:

7x - 4 = -4

add 4 to both sides

7x = 0

x = 0

Answer:

x = 0

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 4 to both sides of the equation:

7x - 4 (+4) = -4 (+4)

7x = -4 + 4

7x = 0

Next, divide 7 from both sides of the equation:

(7x)/7 = (0)/7

x = 0/7

x = 0

0 is your answer.

~

Answer:

15c = m

Step-by-step explanation:

for every car she washes she learns 15 dollars. So you would multiply the number of cars she washes by 15 to get the amount she earns

The total surface area of the right trapezoidal prism is 536 square feet. Therefore, the approximate surface area of sphere is 1,256.6 square inches. The surface area of  right trapezoidal prism is 1,485 square feet.

Surface area of the sphere:

The formula for the surface area of a sphere is given by A = 4πr², where r is the radius of the sphere. Substituting the given radius of 10 inches, we have A = 4π(10)² = 400π square inches. The exact value is 400π square inches. To approximate it to the nearest tenth we can use the value of π as approximately 3.14159. Therefore, the approximate surface area is 400π ≈ 400(3.14159) = 1,256.6 square inches.

Surface area of the right trapezoidal prism:

The total surface area of a right trapezoidal prism can be calculated by adding the areas of all its faces. The formula is A = 2h(b₁ + b₂) + (b₁ + b₂)(x + y), where h is the height of the prism, b₁ and b₂ are the lengths of the parallel bases, and x and y are the lengths of the non-parallel sides.

Substituting the given dimensions, we have A = 2(16)(16 + 11) + (16 + 11)(12 + 11) = 2(27)(16) + (27)(23) = 864 + 621 = 1,485 square feet.

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Answer:

Step-by-step explanation:

Given data

speed v= 13 miles per hour

time taken t= 20min to hour 0.3 hours

the distance D

We know that the relationship between speed, time, and distance

speed=distance/time

13=D/0.3

(the expression above describes the relationship between  distance, speed, and time)

making D subject of formula we have

D= 0.3*13

D= 3.9 miles

hence the distance is 3.9miles

Answer:

If your looking for the equation it will be

D = 13 · 1/3

And the answer to this equation is 3.9 miles

Hope this helps

To calculate a three-month moving average for monthly forecasting, you need to follow these steps: Gather the historical data, Determine the time period, Calculate the moving average, Repeat the process.

Gather the historical data: Collect the monthly data for the specific variable you want to forecast. For example, if you want to forecast sales, gather the sales data for the past several months.

Determine the time period: Decide on the time period for your moving average. In this case, it is three months.

Calculate the moving average: Add up the values for the variable you are analyzing over the past three months and divide the sum by three to get the average. This will be your moving average value for the third month.

Repeat the process: Shift the time period by one month and calculate the moving average for the new three-month period. Continue this process for each subsequent month, updating the time period and calculating the moving average accordingly.

For example, let's say you have the following sales data for the past six months:

Month 1: 100 units

Month 2: 120 units

Month 3: 110 units

Month 4: 130 units

Month 5: 140 units

Month 6: 150 units

To calculate the three-month moving average for Month 4, you would add up the sales values for Month 2, Month 3, and Month 4 (120 + 110 + 130 = 360) and divide it by three to get an average of 120 units. Repeat this process for each subsequent month to obtain the moving average values for your forecast.

Note that the number of data points you include in the moving average calculation and the frequency of the data (monthly in this case) can be adjusted based on your specific needs and the nature of the data.

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Answer: C. 13/24 i hope it help you out

The market price per ordinary share is $ 266.67 given that the profit is $ 2,000,000 and there are 150,000 ordinary shares while the price earnings ratio is 1.2.

Below is the solution:
Formula used: Market price per share = (Profit/Number of ordinary shares) * Price earnings ratio
Calculation: Market price per share = (2,000,000/150,000) * 1.2
Market price per share = 13.33 * 1.2
Market price per share = $ 16
Given that the profit is $ 2,000,000 and there are 150,000 ordinary shares while the price earnings ratio is 1.2, this question is asking about the market price per ordinary share. To find this, we need to use the formula of market price per share, which is (Profit/Number of ordinary shares) * Price earnings ratio. Applying the given values, the answer would be:
Market price per share = (2,000,000/150,000) * 1.2
Market price per share = 13.33 * 1.2
Market price per share = $ 16
Therefore, the market price per ordinary share is $ 266.67 ($ 16 * 16.67). Hence, option D is the correct answer.

The market price per share is calculated as (Profit/Number of ordinary shares) * Price earnings ratio. Given the values, the answer would be $ 16. Therefore, the market price per ordinary share would be $ 266.67.

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a. R3 = {(a, a), (a, b), (a, c), (a, d), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (d, a), (d, b), (d, d)}.

b. S3 = {(a, a), (a, c), (a, d), (b, a), (b, c), (b, d), (d, a), (d, c)}.

c. R ∪ S = {(a, b), (a, d), (a, c), (b, c), (c, c), (d, a), (b, d)}

d. S - R = {(a, c), (b, d)}

To find the given operations on relations R and S, let's start with the definitions of each operation:

a. R3: This represents the composition of relation R with itself three times.

To find R3, we need to perform the composition operation on R three times:

R3 = R ∘ R ∘ R

Calculating R ∘ R:

R ∘ R = {(a, c), (a, a), (b, a), (c, c), (d, b), (d, d)}

Now, let's calculate R ∘ R ∘ R:

R ∘ R ∘ R = R ∘ (R ∘ R)

= R ∘ {(a, c), (a, a), (b, a), (c, c), (d, b), (d, d)}

= {(a, a), (a, b), (a, c), (a, d), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (d, a), (d, b), (d, d)}

Therefore, R3 = {(a, a), (a, b), (a, c), (a, d), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (d, a), (d, b), (d, d)}.

b. $3: This represents the composition of relation S with itself three times.

To find S3, we need to perform the composition operation on S three times:

S3 = S ∘ S ∘ S

Calculating S ∘ S:

S ∘ S = {(a, a), (a, d), (b, a), (d, c)}

Now, let's calculate S ∘ S ∘ S:

S ∘ S ∘ S = S ∘ (S ∘ S)

= S ∘ {(a, a), (a, d), (b, a), (d, c)}

= {(a, a), (a, c), (a, d), (b, a), (b, c), (b, d), (d, a), (d, c)}

Therefore, S3 = {(a, a), (a, c), (a, d), (b, a), (b, c), (b, d), (d, a), (d, c)}.

c. R ∪ S: This represents the union of relations R and S.

R ∪ S = {(a, b), (a, d), (a, c), (b, c), (c, c), (d, a), (b, d)}

d. R ∩ S: This represents the intersection of relations R and S.

R ∩ S = {(d, a)}

e. S - R: This represents the set difference of relation S and relation R.

S - R = {(a, c), (b, d)}

Therefore:

a. R3 = {(a, a), (a, b), (a, c), (a, d), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c), (d, a), (d, b), (d, d)}.

b. S3 = {(a, a), (a, c), (a, d), (b, a), (b, c), (b, d), (d, a), (d, c)}.

c. R ∪ S = {(a, b), (a, d), (a, c), (b, c), (c, c), (d, a), (b, d)}

d. S - R = {(a, c), (b, d)}

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Answer:

-3

Step-by-step explanation:

All you have to do is graph it... and to get from negative one to negative four you add -3   so -3 would be my best guess... if this a multiple choice and -3 is not on there then do -4 as the answer.

Answer:24

Step-by-step explanation:

3 times 8 is 24

Answer:

24°F

Step-by-step explanation:

It's pretty simple. All you need to know is simple math.

First of all take away the °F. Then do the multiplcation.

3 x 8 = 24

Then add the °F  back and that's your answer.

Answer:

it would be 10.

Step-by-step explanation:

you have to reflect the quadrilateral to Q over x-axis then the Y-axis, and you would see that 10 is on the same side of ST.

It's given to prove that, for every positive integer n, there exist two regular polygons with the property that the ratio of the measure of an interior angle of one of the polygons to the measure of an interior n + 1 angle of the other equals n + 1/ n.

We know that for a regular polygon with n sides, the measure of each interior angle is given by:

(n-2)×180°/n

That is to say, each interior angle of a regular polygon with n sides is equal to (n-2)×180/n degrees.

Suppose P and Q are two regular polygons with P having n sides and Q having n+1 sides. Then, measure of each interior angle of polygon P is given by: (n-2)×180/n degrees

Similarly, the measure of each interior angle of polygon Q is given by: (n-1)×180/(n+1) degrees

Thus, the ratio of the measure of an interior angle of one of the polygons (say P) to the measure of an interior n+1 angle of the other (say Q) is given by:

(n-2)×180/n ÷ (n-1)×180/(n+1) = (n+1)/n

Therefore, we can conclude that for every positive integer n, there exist two regular polygons with the property that the ratio of the measure of an interior angle of one of the polygons to the measure of an interior n+1 angle of the other equals n+1/n.

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Answer:

12 bouquets, each having 6 red roses, 5 pink roses, and 4 yellow roses.

Step-by-step explanation:

The Greatest Common Multiple is 12

72/12 = 6

60/12 = 5

48/12 = 4

Answer:

7n - 6 = -20

Step-by-step explanation:

To prove that quadrilateral is a parallelogram using the Distance & Slope Formulas D(-5, -6), E(5, 2), F(4, -4), G(-6, -12), follow these steps

:Step 1: Plot the points in a coordinate plane: (D) (-5,-6), (E) (5,2), (F) (4,-4), (G) (-6,-12)

Step 2: Find the distance of all sides using distance formula.

Distance Formula =sqrt((x2 - x1)² + (y2 - y1)²)DE

                              = sqrt((5 - (-5))² + (2 - (-6))²)

                              =sqrt(10²+8²)

                              =sqrt(164)

                              = 2 sqrt(41)EF

                              = sqrt((4 - 5)² + (-4 - 2)²)

                              =sqrt((-1)²+(-6)²)

                              =sqrt(37)FG

                              = sqrt((-6 - 4)² + (-12 - (-4))²)

                              =sqrt((-10)²+(-8)²)

                              = 2sqrt(41)DG

                              = sqrt((-6 - (-5))² + (-12 - (-6))²)

                              =sqrt((-1)²+(-6)²)

                              =sqrt(37)

Since the opposite sides are equal, we can say that DE = FG and DG = EF.

Step 3: Find the slope of all sides using slope formula.

Slope Formula = (y2-y1)/(x2-x1)DE

                         = (2-(-6))/(5-(-5))

                         =8/10=4/5FG

                         = (-12-(-4))/(-6-4)=-8/-10=4/5DG = (-6-(-12))/(-5-(-6))=6/1=6EF = (-4-2)/(4-5)=-6/-1=6

Since opposite sides have the same slope, DE // FG and DG // EF. Therefore, we can conclude that the quadrilateral is a parallelogram.In conclusion, the quadrilateral is a parallelogram because opposite sides are parallel.

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The minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board is 11.

In order to find the minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board, we need to calculate the time taken by each method and then compare it. Let's say the minimum number of carrots is x.

Here's how we can calculate the time taken to chop x carrots:

Time taken using knife and cutting board = 45x + 25 (25 is added for the time taken to clean the knife and board)

Time taken using food processor = 12x + 360 (360 is added for the time taken to clean the food processor)

Now, we need to find the value of x for which the time taken using the food processor is less than the time taken using the knife and cutting board.

So,12x + 360 < 45x + 2512x - 45x < 25 - 360-33x < -335x > 10.15

Therefore, the minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board is 11.

Thus, the minimum number of carrots to cut up for which it will be faster to use a food processor than the knife and cutting board is 11.

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The Composite Trapezoidal rule is used to approximate the given integrals. In part (a), the integral [tex]\( \int_{1}^{2} x \ln x \, dx \)[/tex] is approximated using [tex]\( n = 4 \)[/tex]subintervals. In part (b), the integral[tex]\( \int_{2}^{2} x^{3} e^{x} \, dx \)[/tex] is given with incorrect limits, so it cannot be evaluated.

To approximate [tex]\( \int_{1}^{2} x \ln x \, dx \)[/tex] using the Composite Trapezoidal rule, we divide the interval [tex]\([1, 2]\) into \( n = 4 \)[/tex] subintervals. The step size, [tex]\( h \)[/tex], is calculated as[tex]\( h = \frac{b-a}{n} = \frac{2-1}{4} = \frac{1}{4} \)[/tex]. Then, we evaluate the function [tex]\( x \ln x \)[/tex]at the endpoints of each subinterval and sum the areas of the trapezoids formed. The approximation formula for the Composite Trapezoidal rule is: [tex]\[\int_{a}^{b} f(x) \, dx \approx \frac{h}{2} \left[ f(a) + 2\sum_{i=1}^{n-1} f(x_i) + f(b) \right]\][/tex]

Using this formula, we can calculate the approximation for the given integral. The limits of the integral [tex]\( \int_{2}^{2} x^{3} e^{x} \, dx \)[/tex] are given as [tex]\( 2 \)[/tex] to 2 which indicates an interval of zero length. In this case, the integral cannot be evaluated since there is no interval over which to integrate.

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Answer:

Jamie read 0.75 pages a minute

Step-by-step explanation:

1 hour is 60 minutes. 2 hours is 120 minutes. Now, you divided 90 by 120. so 0.75

Answer:

0.75

Step-by-step explanation:

[tex]90 \div 120 = \frac{3}{4} [/tex]

Answer:

The horizontal line on a graph.

Step-by-step explanation:

Answer:

The horizontal value in a pair of coordinates: how far along the point is.

The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5).

I hope this help you out

Answer:

A [2.5, ∞)

Step-by-step explanation:

Answer:

A, 1st option

Step-by-step explanation: