Please help, I’m very confused !

Answer:

its b

Step-by-step explanation:

i took the test

Answer: its b cause i took the test and got it right

They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.

The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23.  however amount is represented by a number.

It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.

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Answer:

2,184

Step-by-step explanation:

linear equation

hope it helps

The way to compare the value of the exponent is

C. Write each power as repeated multiplication. Then, evaluate and compare their values.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number

Based on the information given, it should be noted that the numbers given are 7² and 2^7.

7² = 7 × 7 = 49

2^7 = 2 × 2 × 2 × 2 × 2 × 2 × 2 = 128

Therefore, 2^7 is more than 7² after evaluation.

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Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.

We can use the following formula to calculate ROI:

ROI = (gain from investment - cost of investment) / cost of investment

where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.

Using the values given in the question, we can calculate the ROI as:

ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000

ROI = 0.16 or 16%

Therefore, the return on the investment is 16%.

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Answer:

7.5% compounded continuously yields the greatest return after 9 years

Step-by-step explanation:

Compounded interest = P(1+r/n)^(nt), where P is the principle, r is the rate of interest, n is the number of times compounded annually, and t is the time of the investment.

7.6% compounded semiannually:

I = 11000(1+0.076/2)^(2*9) --> 11000(1.038)^18 ~ $21525.09

7.5% compounded continuously:

Since it is compounded continuously, we use the mathematical constant e.

I = 11000e = $29901.01

Answer:

  $142.32, profit on sale of the policy

Step-by-step explanation:

You want to know the expected value of a $280,000 life insurance policy sold for $270, if the probability the insured will live for the year is 0.999544.

The insurance company expects to have to pay the $280,000 death benefit for 0.000456 of the policies issued. That means their expected payout on any one policy is ...

  0.000456 × $280,000 = $127.68

The company gets a premium of $270 for the policy, so the expected value of the policy to the company is ...

  $270 -127.68 = $142.32

The expected value of the policy to the company is $142.32.

This represents its profit from sale of the policy.

__

Additional comment

Of course, the company has expenses related to the policy, perhaps including a commission to the agent selling it, and expenses related to handling claims. That is to say that not all of the difference between the premium and the average death benefit is actually profit. It is what might be called "contribution margin."

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Answer:

5.33

Step-by-step explanation:

Answer:

The area of the fenced yard is 48 feet sq. and the perimeter is 32 feet.

Step-by-step explanation:

I hope this helps! Have a great rest of your day!

Answer:

You begin with 1 bacteria, and after 1 hour it has tripled so you now have 1 x 3=3.

Next hour, it triples again so you now have 1 x 3 x 3=9

You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 34 means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).

Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:

n x 324 where n is the number of bacteria you begin with.

Since you begin with 1 bacteria, the solution is 1 x 3 to the power 24 and u will get ur answer

Ciana should purchase the skirt at the store across town because the total economic cost will be lowest.

Ciana makes $30 per hour at her work, and her purchase decision includes the opportunity cost of lost wages:

Total economic cost:

Local store = $114 + [1/4 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $144

Across town = $86 + [1/2 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $131

Neighboring city = $60 + [1 hour x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $135

Ciana should buy a skirt at the store across town. Because it has the lowest total economic cost ($131).

Opportunity cost is the lost benefit or additional cost of choosing one activity or investment over another. Economic costs include both accounting costs and opportunity costs.  

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To draw a distance vs time graph for this problem, we would plot the distance on the y-axis and time on the x-axis. We would start at time t = 0, which is 8:59 am, and plot the distance that Suzette has traveled up to that point.

How to do?

For the first hallway, Suzette runs 35.0 m at a speed of 3.50 m/s. This means she covers this distance in 10 seconds (35.0 m / 3.50 m/s). So at t = 10 seconds, we would plot a point on the graph at a distance of 35.0 m.

For the second hallway, Suzette covers 48.0 m at an average speed of 1.20 m/s. This means it takes her 40 seconds (48.0 m / 1.20 m/s) to cover this distance. So at t = 50 seconds, we would plot a point on the graph at a distance of 83.0 m (35.0 m + 48.0 m).

For the final hallway, Suzette covers 60.0 m at a speed of 5.00 m/s. This means she covers this distance in 12 seconds (60.0 m / 5.00 m/s). So at t = 62 seconds, we would plot a point on the graph at a distance of 143.0 m (35.0 m + 48.0 m + 60.0 m).

To determine if Suzette makes it to class on time, we need to find how many seconds she arrives before or after the bell, which rings at t = 60 seconds. Suzette arrives at t = 62 seconds, which means she is 2 seconds late for class.

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To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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Answer:  A  129

Step-by-step explanation:

Because the 2 chords are the same (lines in the circle), the 2 arcs are the same  create an equation that makes them equal

3x+24 = 4x -11             >bring x to one side by subtracting both sides by 3x

24 = x -11                     > add both sides by 11

35 = x

Now that we have solved for x you need to plug that back into the equation for BC

BC= 4x-11

BC = 4(35) - 11

BC =  140 - 11

BC = 129                   >A

Answer:

7/2 = 35/10

3/5 = 6/10

Step-by-step explanation:

To get a common denominator of 10, simply multiply the current denominator by any number to equal 10. The first fraction has a denominator of 2. If we divide 10 by 2, we get the answer 5. This means 2 can be multiplied by 5 to get a denominator of 10. However, what we do to the denominator we must also do to the numerator (multiply by 5).

7/2

7 × 5 / 2 × 5

35/10

3/5

3 × 2 / 5 × 2

6/10

Answer:

7/2 = 35/10

3/5 = 6/10

Step-by-step explanation:

\(\frac{7}{2}\cdot \frac{5}{5}=\frac{35}{10}\)

\(\frac{3}{5}\cdot \frac{2}{2}=\frac{6}{10}\)

The numbers can be a solution for the inequality 32+a>44 is 13 and 14.

If the equation or inequality have variable terms, than there might be some values of those variables for which the equation or inequality might be correct. Such values are known as solution to that equation or inequality. To set of such values are called solution set to be considered equation or inequality.

Given that;

The inequality= 32+a>44

To solve the inequality 32 + a > 44, we need to isolate the variable "a" on one side of the inequality.

32 + a > 44

Subtract 32 from both sides:

a > 44 - 32

a > 12

This means that any number greater than 12 can be a solution to the inequality.

Therefore, the inequalities numbers 13 and 14 can be solutions, but 11 and 12 cannot.

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The solution to the inequality expression is n < -9

The inequality expression is given as

4n - 6(n + 1) > 12

Open the bracket in the above inequality expression

4n - 6n - 6 > 12

Evaluate the like terms

-2n > 18

Divide both sides by -2

n < -9

Hence, the solution to the inequality expression is n < -9

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Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

The only matrix that is certainly symmetric is a)\((a^2 - b^2).\)

We know that a matrix A is symmetric if it is equal to its transpose, that is \(A = A^T.\)

a) \((a^2 - b^2)\)

We can write the transpose of this matrix as

\((a^2 - b^2)^T = (a^2)^T - (b^2)^T = a^2 - b^2\), which is equal to the original matrix. Therefore, this matrix is symmetric.

b) (A+B)(A-B)

Expanding this expression, we get \((A+B)(A-B) = A^2 - AB + BA - B^2.\)

Taking the transpose of this, we get \((A^2)^T - (AB)^T + (BA)^T - (B^2)^T = A^2 - BA + AB - B^2.\)

Since AB and BA may not be equal, we cannot say for certain that this matrix is symmetric.

c) ABA

Taking the transpose of this matrix, we get\((ABA)^T = A^T B^T A^T\). Since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

d) ABAB

Taking the transpose of this matrix, we get \((ABAB)^T = B^T A^T B^T A^T\). Again, since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

Therefore, the only matrix that is certainly symmetric is a) \((a^2 - b^2).\)

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Answer:

3x^2 -20x-32

Step-by-step explanation:

(3x + 4)(x − 8)

Foil

First: 3x*x = 3x^2

outer: -8*3x = -24x

inner: 4x

last: -8*4 =-32

Add them together

3x^2 -24x+4x -32

Combine like terms

3x^2 -20x-32

Standard form is ax^2 +bx+c

Answer:

\(3 {x}^{2} + 20x - 32\)

Step-by-step explanation:

\((3x + 4)(x - 8) \\ 3x(x - 8) + 4(x - 8) \\ 3 {x}^{2} - 24x + 4x - 32 \\ = 3 {x}^{2} + 20x - 32\)

Answer:

false

Step-by-step explanation:

(123+54)•4= 708

123+(54•4)=339

Answer:

A. Associative property of addition

Step-by-step explanation:

The associative property is about the grouping of terms/numbers in parentheses in an equation.

As group size increases, the complexity of the group increases (option A).

What is group size?

Even within the same species, group size can vary greatly, so we frequently need statistical tests to evaluate these measurements between two or more samples as well as statistical measures to quantify group size. Since group sizes typically follow an aggregated (right-skewed) distribution, where most groups are small, few are large, and a very small number are very large, group size measures are infamously challenging to handle statistically.

As group size increases, the complexity of managing and coordinating the group also increases.

The larger the group, the more difficult it is to communicate effectively, to make decisions, and to ensure that everyone is working towards a common goal.

This is why larger organizations often have more complex hierarchies and more formalized communication and decision-making processes.

Therefore, the correct option is A.

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Answer:

D, E, and F

Step-by-step explanation:

✔️Statement D is true:

Rationale: m<4 is more than 90°, while m<2 is less than 90°. Therefore m<4 is greater than m<2

✔️Statement E is true:

Rationale: m<4 is more than 90°, while m<1 is less than 90°. Therefore m<4 is greater than m<1

✔️Statement F is true:

Rationale:

m<4 is an external angle of the triangle.

m<1 and m<2 are interior angles that are opposite to m<4. Therefore, based on the external angle theorem of a triangle,

m<4 = m<1 + m<2

Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that come together at a point in the middle known as the angle's vertex. An angle that is in the plane where the rays are placed can be created by two rays. An angle is also produced when two planes collide. They are known as dihedral angles. In planar geometry, an angle is the form produced by two rays or lines that share a termination. The English word "angle" comes from the Latin word "angulus," which means "horn." The vertex, also known as the sides of the angle, is where the two rays' common terminals meet.

given

m∠V + m∠W + m∠X + m∠Y = 360

10x -27 + 2x + 19 = 180

12x - 8 = 180

188 = 12x

x = 15.66

m∠V + m∠X = 180

2x = 180

x = 90

Since the total of the inner angles of the rhombus is 360 degrees, the angle mV has a value of 90.

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Answer:

The maximum rate of change of the given function is equal to 3√2.

The direction at which the vector points is given by the unit vector \(\displaystyle \frac{\sqrt{2}}{2} \hat{\i} + \frac{\sqrt{2}}{2} \hat{\j}\).

General Formulas and Concepts:
Pre-Calculus

Vectors

Calculus

Differentiation

Derivative Property [Addition/Subtraction]:
\(\displaystyle (u + v)' = u' + v'\)

Derivative Rule [Basic Power Rule]:

Multivariable Calculus

Partial Derivatives

Gradient:
\(\displaystyle \nabla f(x, y, z) = \frac{\partial f}{\partial x} \hat{\i} + \frac{\partial f}{\partial y} \hat{\j} + \frac{\partial f}{\partial z} \hat{\text{k}}\)

Gradient Property [Addition/Subtraction]:
\(\displaystyle \nabla \big[ f(x) + g(x) \big] = \nabla f(x) + \nabla g(x)\)

Step-by-step explanation:

Step 1: Define

Identify given.

\(\displaystyle f(x, y) = x^2y^2 + xy - 10\)

\(\displaystyle \text{Point} \ (1, 1)\)

Step 2: Find Maximum Rate of Change

∴ the maximum rate of change of the given function f(x, y) is equal to 3√2.

Step 3: Find Direction

∴ we have found the direction of the gradient.

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Topic: Multivariable Calculus

Unit: Directional Derivatives

Answer:

x=3

Step-by-step explanation:

7x+9=30

   7x=30-9

       =21

     x=21÷7

       =3