Which one of the following is a rule of multiplication?

A.The order in which you multiply two whole numbers
changes the product.

B.The product of a whole number and 1 is never the
same whole number.

C.The product of a whole number and zero is the same
whole number.

D.The way you group numbers in a series of
multiplication problems doesn't change the final
product.

If the line passes through the point (2,8) that cuts off the least area from the first quadrant, the slope is 8/3 and the y-intercept is 0.

To find the equation of the line that passes through the point (2, 8) and cuts off the least area from the first quadrant, we need to first determine the slope of the line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

We can use the point-slope form of the equation of a line to find the slope. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line. Plugging in (2, 8) as the point, we get:

y - 8 = m(x - 2)

Next, we want to minimize the area that the line cuts off in the first quadrant. Since the line passes through the origin (0, 0), the area cut off by the line in the first quadrant is equal to the product of the x- and y-intercepts of the line.

We can express the x-intercept in terms of y by setting y = 0 in the equation of the line and solving for x:

0 - 8 = m(x - 2)

x = 2 + 8/m

The y-intercept is simply the y-coordinate of the point where the line intersects the y-axis, which is given by:

y = mx + b

8 = 2m + b

b = 8 - 2m

We can now express the area cut off by the line as:

A = x*y

A = (2 + 8/m)*8 - (8 - 2m)*2/m

A = (16 + 64/m) - (16 - 4m)/m

A = 64/m + 4m/m

To minimize the area, we can take the derivative of A with respect to m and set it equal to zero:

dA/dm = -64/m² + 4/m² = 0

64 = 4

m = 8

Plugging m = 8 into the equation for the x-intercept, we get:

x = 2 + 8/8 = 3

So the equation of the line is y = 8x/3.

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Answer:

Step-by-step explanation:

8+(6-3)-9

The first action is addition in parentheses

(6-3) = 3

The second action is addition and then subtraction, you can subtract first and then add, it makes no difference because the answer will be the same in all cases

8 + 3 - 9 = 11 - 9 = 2

Answer:

Step-by-step explanation:

To calculate the mean (average) weekly earnings of workers in the occupations listed for 2010, we need to add up the earnings for each occupation and divide by the total number of occupations.

Forestry, logging and support: $971

Manufacturing: $977

Transportation and warehousing: $900

Construction: $1071

Retail trade: $501

Total earnings: $4,420

Total number of occupations: 5

Mean weekly earnings: $4,420 ÷ 5 = $884

Therefore, the mean (average) weekly earnings of workers in the occupations listed for 2010 is $884.

the limit expression gives the value of the derivative of a function at a specific point. where f'(x_0) denotes the derivative of f(x) at x = x_0.

what is derivative  ?

The derivative of a function is a measure of how the function changes as its input variable changes. It gives the instantaneous rate of change or slope of the tangent line of the function at a specific point.

In the given question,

The expression you provided represents the limit definition of the derivative of a function f(x) at the point x = x_0. The limit evaluates the instantaneous rate of change or slope of the tangent line of the function f(x) at the point x = x_0.

To evaluate the limit, substitute x = x_0 + h in the expression of the function f(x) and simplify:

[tex]lim h - > 0 [f(x_{0} + h) - f(x_{0})] / h = f'(x_{0})[/tex]

where f'(x_0) denotes the derivative of f(x) at x = x_0.

Therefore, the limit expression gives the value of the derivative of a function at a specific point.

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Answer:

x = - 9

Step-by-step explanation:

-48 - x = -39

Add 48 on both sides

-x = 9

Divided both sides by -1

x = - 9

So, the answer is x = - 9

Answer: 4.8 Inches

Step-by-step explanation:

6 is 60% of 10

Therefore  (60%*8 = 4.8)

*since they are similar, and therefore proportional

Answer:

Step-by-step explanation:

The speed in miles per hour is 111.2 and the direction angle in degrees is 260.2.

We are given the speed of a plane on a bearing of N [tex]75^\circ[/tex] E and its ground speed. We have to find its speed in miles per hour and the direction angle in degrees. We will apply the formula of projection for both the x-axis and y-axis.

As we know, projection, R = V + W

Now, the x-axis projection will be R cos[tex]15^\circ[/tex] according to the angle given to us. Therefore, R cos [tex]15^\circ[/tex] = V cos[tex]30^\circ[/tex] + [tex]W_{x}[/tex]

The y-axis projection,

R sin [tex]15^\circ[/tex] = V sin [tex]30^\circ[/tex] + [tex]W_{y}[/tex]

From here, now we will find [tex]W_{x}{[/tex] and [tex]W_{y}[/tex]

[tex]W_{x}{[/tex] = 330 cos[tex]15^\circ[/tex] - 390 cos[tex]30^\circ[/tex]

[tex]W_{x}[/tex] = -19 miles/hour

[tex]W_{y}[/tex] = 330 sin[tex]15^\circ[/tex] - 390 sin[tex]30^\circ[/tex]

[tex]W_{y}{[/tex] = -109.6 miles per hour

Now, W = [tex]\sqrt{(W_{x})^{2} + (W_{y})^{2{}}[/tex]

W = [tex]\sqrt{(-19.0)^{2} + (-109.6})^{2{}}[/tex]

W = 111.2 miles/hour

Now, we will find the angle with the help of tan θ.

tan θ = [tex]\frac{W_{y}}{W_{x}}[/tex]

tan θ = [tex]\frac{-109.6}{-19.0}[/tex]

θ =  [tex]tan ^{-1} (\frac{109.6}{19.0})[/tex]

θ = 260.[tex]2^\circ[/tex]

Therefore, the speed in miles per hour is 111.2 and the direction angle in degrees is 260.2.

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The side length x of the given right angle triangle is: 14.97

When two sides of a right-angled triangle are given and one side is to be found, we can do so using the Pythagoras theorem. In the given triangle the base is x, the perpendicular is 10 and the hypotenuse is 18.

According to the Pythagoras Theorem, the following equation can be written as:

x² = 18² - 10²

x = √224

x = 14.97

Thus, that is the missing length of the given right triangle

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Answer:

10 wax cubes

Step-by-step explanation:

the volume of the square pyramid can be found by using the following formula:

[tex]V = \frac{1}{3} * B * h[/tex]

where b is the base of the pyramid and h is the height of the pyramid

The area of the base of the pyramid is given as 12 in * 12 in = 144 in^2

So, the volume of the pyramid is:

V = (1/3) * 144 in^2 * 14 in = 2,016 in^3

Each wax cube has a volume of 6 in * 6 in * 6 in = 216 in^3.

To find the number of wax cubes needed, we can divide the volume of the pyramid by the volume of each wax cube:

Number of wax cubes = Volume of pyramid / Volume of each wax cube

Number of wax cubes = 2,016 in^3 / 216 in^3

Number of wax cubes = 9.33 (rounded to two decimal places)

Since we can't have a fraction of a wax cube, Josiah will need to use 10 wax cubes to make the candle.

The percentage rate of change per minute is approximately 0.98%

The mass of the sample decreases by 59% every hour, so we can write the following differential equation:

dm/dt = -0.59m

Rate of change of the mass (dm/dt) is equal to the mass (m) multiplied by the constant -0.59.

We can solve this differential equation using separation of variables:

dm/m = -0.59 dt

Integrating both sides, we get:

ln|m| = -0.59t + C

where C is the constant of integration.

To find C, we can use the initial condition that the mass of the sample is 530 grams at t=0:

ln|530| = C

C = ln(530)

So the solution to the differential equation is:

ln|m| = -0.59t + ln(530)

[tex]m(t) = 530 e^(^-^0^.^5^9^t^)[/tex]

This function represents the mass of the sample after t hours, where the rate of change per minute is given by the constant

k = -0.59/60 = -0.00983 (rounded to 5 decimal places).

To find the percentage rate of change per minute, we can multiply k by 100 to convert it to a percentage:

-0.00983 × 100 = -0.983%

Therefore, the percentage rate of change per minute is approximately 0.98%

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The probability that a single randomly selected value is greater than 31.9 is 0.511.

The probability that a sample of size 66 is randomly selected with a mean greater than 31.9 is 0.641.

Probability that a single randomly selected value is greater than 31.9:

z = (31.9 - 32) / 3.9 = -0.026

We can find the probability:

P(X > 31.9) = P(Z > -0.026) = 0.511

Also, μ = 32, σ = 3.9, n = 66

z = (31.9 - 32) / (3.9 / √66) = -0.363

Using a standard normal distribution table or calculator, we can find the probability:

P(M > 31.9) = P(Z > -0.363) = 0.641

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The vector v can be expressed as v = -0.161 i + 0.618 j, where i and j are the unit vectors

To express a vector v in terms of i and j, we need to find its x and y components. The magnitude ||v|| of a vector is given by:

||v|| = √(v₁² + v₂²)

where v₁ and v₂ are the x and y components of v, respectively.

The direction angle θ of a vector with respect to the positive x-axis is given by:

θ = atan(v₂/v₁)

where atan denotes the arctangent function.

In this problem, we are given that the magnitude ||v|| of the vector v is 2/3, and its direction angle θ with respect to the positive x-axis is 116 degrees. Therefore, we can write:

||v|| = √(v₁² + v₂²) = 2/3

θ = atan(v₂/v₁) = 116°

Solving for the x and y components, we get:

v₁ = ||v|| cos(θ) = (2/3) cos(116°) ≈ -0.161

v₂ = ||v|| sin(θ) = (2/3) sin(116°) ≈ 0.618

Therefore, the vector v can be expressed as:

v = -0.161 i + 0.618 j

where i and j are the unit vectors in the x and y directions, respectively.

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Answer:

We can use synthetic division to divide the polynomial 2x^3 + 522x^2 - 11x + 104 by x + 8, since x + 8 is a factor of the polynomial:

-8 | 2   522   -11   104

  |     -16   -412  2584

  |--------------------

  2   506   -423  2688

The numbers in the bottom row of the synthetic division represent the coefficients of the quotient polynomial, in order of decreasing degree. So the quotient polynomial is:

2x^2 + 506x - 423

Therefore, the other factor of the polynomial is 2x^2 + 506x - 423.

Answer: To evaluate this expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) and work from left to right:

(49)^(-2) * (34)^(-2)

First, we can simplify the exponents:

1/(49^2) * 1/(34^2)

Next, we can calculate the values of 49^2 and 34^2:

1/2401 * 1/1156

Then, we can multiply the fractions:

1/2785456

Therefore, the value of the expression (49)^(-2) * (34)^(-2) is approximately 0.000000359.

Step-by-step explanation:

Answer: A

Step-by-step explanation:

We can use the logarithmic identity logb(a^n) = n*logb(a) to solve this problem.

First, we need to express 4 as a power of 2. We know that 2^2 = 4, so we can write:

log4 = log2^2

Then we can use the identity to rewrite this as:

log4 = 2*log2

Now we can use the given approximation log2 ≈ 0.4307 to approximate log4:

log4 ≈ 2 * 0.4307

log4 ≈ 0.8614

Therefore, the answer is (A) 0.8614.

Answer: 0.12

Step-by-step explanation:

just divide whatever is under 5 with the total amount of frequency

so then you do 12/100 which is 0.12

The decimal 15.75 into a percentage is 1575%

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

Decimal = 15.75

This means that

Number = 15.75

Multiply the number by 1

so, we have the following representation

Number = 15.75 * 1

Express 1 as 100%

This gives

Number = 15.75 * 100%

Evaluate the products of 15.75 and 100

So, we have

Number = 1575%

Hence, the percentage is 1575%

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The solution is: the area of the shaded base in square centimeters is:

B= 15 cm²

Here, we have,

The base of the triangular shaped wedge of cheese is a right-triangle.To find the area of a right-triangle you apply the formula for half base by height.

A=1/2*b*h

 = base area

 = B

In this case, assume the sides of the triangle given are;

a=5 cm and b=6 cm,

thus area will be 1/2*6*5 =15 cm²

Hence, the area of the shaded base in square centimeters is :

B= 15 cm²

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complete question:

Evelyn cut a wedge of cheese into the shape of a triangular prism-like the one shown below. The shaded part represents one of the bases of the prism.

A formula for the volume of a triangular prism is v=Bh . Which equation can be used to find B , the area of the shaded base in square centimeters?

The probability of getting blue or green is 1/3, the probability of getting blue is 3/4 and there are 8 blue marbles.

a) If the probability of getting a yellow marble is 2/3, then the probability of getting a blue or green marble is:

P(blue or green) = 1 - P(yellow) = 1 - 2/3 = 1/3

b) If the probability of getting a green marble is 1/4, then the probability of getting a blue marble is:

P(blue) = 1 - P(green) = 1 - 1/4 = 3/4

c) The total number of marbles in the bag is 24. Let x be the number of blue marbles. Then the number of yellow marbles is 2x, and the number of green marbles is 24 - x - 2x = 24 - 3x. We know that:

2x/24 = 2/3 (probability of getting a yellow marble is 2/3)

=> x = 8

Therefore, there are 8 blue marbles in the bag.

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Answer:

60

Step-by-step explanation:

14 rounds to 10

23 rounds to 20

28 rounds to 30

10+20+30=60

The given function does not represent the curve passing through the given points. The multiplicative rate of change of the function is 5.

A curve is a continuous, smooth line that gradually alters direction. Rather than being straight line that follows a curve may be referred to as a curve line. A curve line can be made by connecting a number of non-straight-line-lying sites. In mathematics, a curve is a geometrical object that can be described by equations, such as parametric or function equations.

The rate of change of a function is the ratio of the change in the output (y) to the change in the input (x). In this case, we can calculate the rate of change between the first two points:

Changing at what rate between (1, 10) and (2, 50)?

Y change = 50 – 10 = 40

Variation in x = 2 - 1 = 1

Rate of change equals change in y/change in x, or 40/1, or 40.

In a similar manner, we can determine how quickly the second and third points will change:

The change between (2, 50) and (3, 250) is as follows:

Changing y by 250 - 50 equals 200

Variation in x = 3 - 2 = 1

Rate of change equals change in y/change in x, which is 200/1, or 200.

Now that we have the second rate of change, we can compute the multiplicative rate of change by dividing it by the first:

Multiplicative rate of change is equal to 200/40, or 5.

The function's multiplicative rate of change is thus 5.

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Answer: x=11, y=3

Step-by-step explanation:

x=y+8, name one x and one y, so x is 8 more than y

x+y=14, x plus y is 14

substitute x into second eqution, so (y+8)+y=14

simplify so 2y+8=14

y=3 and use that to find x

x=11

The value of x in the triangle to the nearest tenth is 2.6.

The figure in the image is a right triangle.

To solve for the missing side length x, we use the trigonometric ratio.

Note that: tangent = opposite / adjacent

Hence:

tan( H ) = opposite / adjacent

Plug in the given values and solve for x.

tan( 43° ) = x / 2.8

Cross multiply

x = tan( 43° ) × 2.8

x = 2.6 units

Therefore, the value of x is 2.6.

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Answer:

Step-by-step explanation:

We can use the formula for continuous compounding to determine how long it will take each account to reach $1,800.

For Michael's account, the formula is:

A = P*e^(rt)

where:

A is the amount in the account after t years

P is the principal

r is the annual interest rate

t is the time in years

Plugging in the values given, we get:

1,800 = 1,000*e^(0.0475t)

Taking the natural logarithm of both sides, we get:

ln(1,800/1,000) = 0.0475t

t = ln(1,800/1,000)/0.0475

t ≈ 8.55 years

So it will take approximately 8.55 years for Michael's account to reach $1,800.

Similarly, for Peter's account, the formula is:

A = P*e^(rt)

where:

A is the amount in the account after t years

P is the principal

r is the annual interest rate

t is the time in years

Plugging in the values given, we get:

1,800 = 1,200*e^(0.0425t)

Taking the natural logarithm of both sides, we get:

ln(1,800/1,200) = 0.0425t

t = ln(1,800/1,200)/0.0425

t ≈ 9.03 years

So it will take approximately 9.03 years for Peter's account to reach $1,800.

Therefore, Michael's account will grow to $1,800 first as it will take less time (8.55 years) compared to Peter's account (9.03 years).

The population of Greensville 10 years from now will be approximately 13,184.

To find the population of Greensville 10 years from now, we need to use the formula for compound interest:

A = P(1 + r)ᵗ

Where A is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.

In this case, the present value (P) is 8,000, the annual interest rate (r) is 5.6% or 0.056 as a decimal, and the time (t) is 10 years. Plugging these values into the formula, we get:

A = 8,000(1 + 0.056)¹⁰

A = 8,000(1.648)

A = 13,184

This calculation assumes that the population growth rate remains constant at 5.6% per year.

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An inequality to show the number of people  is  p ≥ 12

Let p be the number of people on the bus. We know that there are at least 12 people on the bus, so we can write:

p ≥ 12

This inequality means that the number of people on the bus, p, must be greater than or equal to 12.

To graph this inequality, we can draw a horizontal line at y = 12 on the y-axis, and shade the area above the line, since any value of p that is greater than or equal to 12 satisfies the inequality.

Here's a graph of the inequality attached

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Answer:

-[tex]\sqrt{3}[/tex]/2

Step-by-step explanation:

cos is negative in quad II

cos(210)= -cos(30) = -[tex]\sqrt{3}[/tex]/2

If we express the 9!  we have 9×8×7×6×5×4×3×2×1.

A factorial operation is described as  a mathematical formula represented by an exclamation mark. (!). This operation is carried out when a whole number is being multiplied by its successive smaller numbers until it gets to 1.

for Example

n! = n(n-1)(n-2)........(1)

From the question, it is are asked to evaluate 9!

9! = 9×8×7×6×5×4×3×2×1

Hence, when 9! is evaluated, we get 9×8×7×6×5×4×3×2×1.

#Probable complete question;

Use the factorial operation to evaluate 9!.

8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

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