6) Sam bought 9 new baseball trading cards to add to his collection. The next
day his dog ate half of his collection. There are now only 46 cards left.
How many cards did Sam start with ?

Option C provides evidence in favor of OLS assumption (1).

OLS assumption (1) states that the conditional distribution of the error term u given the independent variable X has a mean of zero, E(u|X) = 0. In other words, the error term is not systematically related to the independent variable.

In option C, if the correlation between intelligence and education is not equal to zero (i.e., correlation(intelligence, education) ≠ 0), it suggests that there is a systematic relationship between the unobservable variable intelligence and the independent variable education. This violates OLS assumption (1) because intelligence is affecting both wage and education, making the error term u correlated with the independent variable X. Therefore, option C provides evidence against OLS assumption (1).

Options A, B, and D do not directly address the relationship between the error term u and the independent variable X. Option A refers to the confidence interval of intelligence and education, which does not provide information about the conditional mean of the error term. Option B refers to the covariance between intelligence and education, which does not capture the conditional relationship between the error term and the independent variable. Option D compares the expected values of intelligence and education, which also does not provide evidence about the conditional mean of the error term.

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Given the transformation I: R2 → R3 that takes any vector in 2-space and views it as a vector sitting in the xy-plane in 3-space.

(a) The algebraic formula for the transformation I: R2 → R3 that takes a vector [x, y] in 2-space and views it as a vector in the xy-plane in 3-space can be written as I([x, y]) = [x, y, 0].

(b) The range of I represents all possible outputs of the transformation. Since the third component of the resulting vector is always 0, the range of I is the xy-plane in 3-space. Therefore, the equation of the range is z = 0.

(c) To determine if I is a linear transformation, we need to check if it satisfies two properties: preservation of vector addition and preservation of scalar multiplication. In this case, I preserve both vector addition and scalar multiplication, so it is a linear transformation.

(d) For a linear transformation to be one-to-one (or injective), each input vector must map to a distinct output vector. However, in this transformation, multiple input vectors [x, y] can map to the same output vector [x, y, 0]. Therefore, I is not one-to-one.

(e) To determine if I is onto (or surjective), we need to check if every vector in the range of the transformation is reachable from some input vector. Since the range of I is the xy-plane in 3-space, and every point in the xy-plane can be reached by setting the third component to 0, I is onto.

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Answer: the answer is 0.51

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Answer:

Area = 20 in^2

Step-by-step explanation: 20/4=5  100/5=20

Answer:

20 inches squared

Step-by-step explanation:

20 ÷ 4 = 5

100÷5 = 20

I'm guessing that you want to simplify \(67.6^2\)

The two above the 67.2 is a square or a power.

Usually when you take something to a power, you mutiply the number of time by the power:

Examples:   \(78^2\) would be 78*78

                   \(23^5\) would be 23*23*23*23*23

Questions?

67.6² would simply be 67.6*67.6.

So therefore it is 4569.76

Answer:

A: 236 sqaure ft.

B: 4 cans

Step-by-step explanation:

Sure, I can help you with that.

Part A:

The total surface area of a rectangular prism is calculated using the following formula:

Total surface area = 2(lw + wh + lh)

where:

In this case, we have:

Plugging these values into the formula, we get:

Total surface area = 2(8*6+6*5+8*5) = 236 square feet

Therefore, the total surface area of the doghouse is 236 square feet.

Part B:

Since the bottom of the doghouse will not be painted, we only need to paint the top, front, back, and two sides.

The total surface area of these sides is 236-6*8 = 188 square feet.

Therefore,

we need 188 ÷ 50 = 3.76 cans of paint to paint the doghouse.

Since we cannot buy 0.76 of a can of paint, we need to buy 4 cans of paint.

Answer:

A)  236 ft²

B)  4 cans of paint

Step-by-step explanation:

The given diagram (attached) shows the doghouse modelled as a rectangular prism with the following dimensions:

The formula for the total surface area of a rectangular prism is:

\(S.A.=2(wl+hl+hw)\)

where w is the width, l is the length, and h is the height.

To find the total surface area of the doghouse, substitute the given values of w, l and h into the formula:

\(\begin{aligned}\textsf{Total\;surface\;area}&=2(6 \cdot 8+5 \cdot 8+5 \cdot 6)\\&=2(48+40+30)\\&=2(118)\\&=236\; \sf ft^2\end{aligned}\)

Therefore, the total surface area of the doghouse is 236 ft².

\(\hrulefill\)

As the bottom of the doghouse will not be painted, to find the total surface area to be painted, subtract the area of the base from the total surface area:

\(\begin{aligned}\textsf{Area\;to\;be\;painted}&=\sf Total\;surface\;area-Area\;of\;base\\&=236-(8 \cdot 6)\\&=236-48\\&=188\; \sf ft^2\end{aligned}\)

Therefore, the total surface area to be painted is 188 ft².

If one can of paint will cover 50 ft², to calculate how many cans of paint are needed to paint the doghouse, divide the total surface area to be painted by 50 ft², and round up to the nearest whole number:

\(\begin{aligned}\textsf{Cans\;of\;paint\;needed}&=\sf \dfrac{188\;ft^2}{50\;ft^2}\\\\ &= \sf 3.76\\\\&=\sf 4\;(nearest\;whole\;number)\end{aligned}\)

Therefore, 4 cans of paint are needed to paint the doghouse.

Note: Rounding 3.76 to the nearest whole number means rounding up to 4. However, even if the number of paint cans needed was nearer to 3, e.g. 3.2, we would still need to round up to 4 cans, else we would not have enough paint.

Answer:

D(may not be D for everyone)

Step-by-step explanation:

The given statement is 2x + 5 = 11 :)

Answer:

answer is B

or

[  6  2  |  618  ]

[  1  1  | 165  ]

Step-by-step explanation:

did the test and got it right

The augmented matrix represents the situation is given as, \(\begin{bmatrix}6 & 2 | & 618 \\1 & 1 |& 165 \\\end{bmatrix}\). Then the correct option is B.

A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.

Let x be the number of the adults and y be the number of the children.

Adults were charged $6, and children were charged $2.

The total amount of money collected was $618.

6x + 2y = 618

A total of 165 people attended the opening night of a school play.

x + y = 165

The equation can be written in the form of matrix form. Then

\(\begin{bmatrix}6 & 2 | & 618 \\1 & 1 |& 165 \\\end{bmatrix}\)

Then the correct option is B.

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Answer: To find out how many days it will take for the family to pay off their credit card balance, we can use the following equation:

Days = (-300) / 33

Solving for Days gives us:

Days = (-300) / 33 = -9

So it will take the family 9 days to pay off their credit card balance, assuming they only spend money on essential items and don't add any more to their debt.

Step-by-step explanation:

Answer:

The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1) . This video shows you how to solve a quadratic equation by factoring.

Step-by-step explanation:

ANSWER:

D. 44

STEP-BY-STEP EXPLANATION:

The percentage of a number is calculated by multiplying the percentage number in its decimal form by the number whose percentage is to be calculated.

A percentage number is converted to a decimal by dividing that number by 100, so it would finally look like this:

So the correct answer is D. 44

Given:

Given a rectangle with coordinates A(-5, 6), B(3, 6), C(3, -1) and D(-5, -1).

Required: Area of rectangle ABCD

Explanation:

First, find the length and width of the rectangle.

The are of the rectangle is

Option C is correct.

Final Answer: Rectangle ABCD has area 56 square units.

Answer:

\(81.2\:\mathrm{ft}\)

Step-by-step explanation:

We can form a right triangle and use basic trig for a right triangle to solve this problem:

\(\tan33^{\circ}=\frac{h}{125}\), where \(h\) is the height of the tree.

Solving, we get:

\(h=125\cdot \tan 33^{\circ},\\h\approx \fbox{$81.2\:\mathrm{ft}$}\).

Answer:

$ 56.34

Step-by-step explanation:

    height = h = 2. 1m

    diameter = 0.7m

            radius = diameter ÷2

                    r  = 0.7 ÷ 2 = 0.35 m

Substitute the values of r and h in the below mentioned formula and find the surface area of the tank.

\(\boxed{Area \ of \ cylindrical \ tank = 2\pi r((r + h)}\)

                                            = 2 * 3.14 * 0.35 (0.35 + 2.1)

                                            = 2 * 3.14 * 0.35 * 2.45

                                            = 5.39 square meter

To find the cost of painting the surface area of tank, multiply the cost of painting per square meter by the total surface area of tank.

Cost of painting = 5.93 * 9.50

                           = $ 56.34

The given information describes a monopolist's price and cost functions:

Price function: p = 1200 - 4q

Cost function: c = 8600 + 24q - q^2

To analyze the monopolist's behavior and determine various quantities, we can use these functions.

(a) To find the monopolist's revenue function, we multiply the price by the quantity sold:

Revenue (R) = p * q

R = (1200 - 4q) * q

R = 1200q - 4q^2

(b) The monopolist's profit function is calculated by subtracting the cost function from the revenue function:

Profit (Π) = Revenue - Cost

Π = R - c

Π = (1200q - 4q^2) - (8600 + 24q - q^2)

Π = 1200q - 4q^2 - 8600 - 24q + q^2

Π = -3q^2 + 1176q - 8600

(c) To find the quantity that maximizes the monopolist's profit, we can take the derivative of the profit function with respect to q and set it equal to zero:

Π' = -6q + 1176 = 0

-6q = -1176

q = 196

Therefore, the quantity that maximizes the monopolist's profit is q = 196.

(d) To find the price at the profit-maximizing quantity, we substitute the value of q into the price function:

p = 1200 - 4q

p = 1200 - 4(196)

p = 1200 - 784

p = 416

Therefore, the price at the profit-maximizing quantity is p = 416.

(e) To find the monopolist's maximum profit, we substitute the profit-maximizing quantity (q = 196) into the profit function:

Π = -3q^2 + 1176q - 8600

Π = -3(196)^2 + 1176(196) - 8600

Π = -1176 + 229696 - 8600

Π = 220920

Therefore, the monopolist's maximum profit is $220,920.

Note: The above calculations assume that the monopolist operates in a single period and faces no capacity constraints or other market considerations.

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we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

===============================================

Explanation:

If we replace x with 0, then we get...

f(x) = 3x^2-8x+2

f(0) = 3(0)^2 - 8(0) + 2

f(0) = 3(0) - 8(0) + 2

f(0) = 0 - 0 + 2

f(0) = 2

Showing that the input x = 0 leads to the output y = f(x) = 2

The answer is between choice A and choice D because of this. Something like choice B is eliminated because this table shows x = 0 leading to y = -3 which is not correct.

-----------

Let's plug in x = 1

f(x) = 3x^2-8x+2

f(1) = 3(1)^2 - 8(1) + 2

f(1) = 3(1) - 8(1) + 2

f(1) = 3 - 8 + 2

f(1) = -5 + 2

f(1) = -3

So x = 1 leads to y = -3. We can rule out choice D and confirm it is choice A.

We don't need to try other x values since we have the answer, but I recommend practicing with other x values to help confirm that the first table is the answer.

The time it takes both train to be 312 miles apart is 2.4 hours.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

To calculate how long it will take the two trains to be 312 miles apart, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the time it takes is 2.4 hours.

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Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.

Start with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.

Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.

Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.

Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.

Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.

Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.

Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.

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Given the surface integral ∬ S (x+y+z)dS and the parallelogram S with parametric equations x=u+v,

y=u−v,

z=1+2u+v, 0≤u≤9,0≤v≤.

Let us evaluate the surface integral:

We know that the surface integral is given by the formula:

∬Sf(x,y,z)dS∬ S (x+y+z)dS= ∬ S x dS+ ∬ S y dS + ∬ S zdS..........(1)

Here, the parametric equation of the surface S is given as x=u+v,

y=u−v, and

z=1+2u+v

∴x+y+z = (u+v) + (u-v) + (1+2u+v)

=4u + 1 + 2v

On differentiating the given equations we get, dx/dv = 1,

dy/du = 1 and

dy/dv = −1,

dz/du = 2 and

dz/dv = 1

Also, we know that

dS= ∣∣(∂(x,y) / ∂(u,v) × ∂(x,y) / ∂(u,v) × ∂(x,z) / ∂(u,v) )∣∣ du dv

So, we have,  (∂(x,y) / ∂(u,v))²  + (∂(x,z) / ∂(u,v))² + (∂(y,z) / ∂(u,v))²

= (1+1)² + (2+1)² + (1-1)²

= 3²

=9

On evaluating the integral in (1) with the help of the above values, we get,

∬ S (x+y+z)dS

=∫ 0 9∫ 0 1 4u + 1 + 2v 9 dvdu

= (1161/2) unit²

Hence, the required value of the surface integral is (1161/2) unit².

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Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

Answer:

\(\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4\)

Step-by-step explanation:

Given

\(Dividend = 125x^3 - 8\)

\(Divisor = 5x - 2\)

Required

Determine the quotient

See attachment for complete process.

First, divide 125x^3 by 5x

\(\frac{125x^3}{5x} =25x^2\)

Write \(25x^2\) at the top

Multiply \(5x - 2\) by \(25x^2\)

\(= 125x^3 - 50x^2\)

Subtract from 125x^3 - 8

i.e.

\(125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8\)

Step 2:

Divide 50x^2 by 5x

\(\frac{50x^2}{5x} = 10x\)

Write \(10x\) at the top

Multiply \(5x - 2\) by \(10x\)

\(= 50x^2 - 20x\)

Subtract from 50x^2 - 8

i.e.

\(50x^2 - 8 - (50x^2 - 20x) = 20x - 8\)

Step 3:

Divide 20x by 5x

\(\frac{20x}{5x} = 4\)

Write \(4\) at the top

Multiply \(5x - 2\) by \(4\)

\(= 20x - 8\)

Subtract from 20x - 8

i.e.

\(20x - 8 - (20x - 8) = 0\)

Hence:

\(\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4\)

Answer:

C

Step-by-step explanation:

5 times a number is the 5n and the four less is the - 4 so that makes 5n-4

Therefore , the solution of the given problem of function comes out to be it is compatible with P(J(y)) = 1/3J(y) +4.

Math is a science that studies numbers, their variants, math and the tissues in the area, shapes, and both their real and possible locations. 'Function' refers to the relationship between a set of inputs, which each have a corresponding output. A function is a relationship between inputs in which each input yields a single variable, distinct output.

Here,

Given:

The quantity of paintings is returned by the function P, which accepts a number of months as an argument.

The function J returns the number of weeks in a year after accepting an undefined parameter.

P(weeks annually) = P(J(y)) seems to be the composites function that will provide the annual number of paintings.

Choice C is compatible with P(J(y)) = 1/3J(y) +4.

Therefore , the solution of the given problem of function comes out to be it is compatible with P(J(y)) = 1/3J(y) +4.

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The statement "A necessary condition for an integer to be divisible by 6 is that it be divisible by 3" is true.

To determine the correctness of the given statement, we need to analyze the conditions and provide supporting evidence. In this case, the statement states that for an integer to be divisible by 6, it must also be divisible by 3. By examining the provided sentences, we can arrange them in the correct order to construct a logical argument.

The first sentence presents a proof by supposing that n is any integer divisible by 6. It states that n can be expressed as n = 6r for some integer, and since 2r is a product of integers, it is also an integer. Consequently, n can be represented as n = 3(2r), demonstrating that n is divisible by 3.

The second sentence concludes that the above proof shows the truth of the statement. It establishes the validity of the necessary condition for an integer to be divisible by 6, which is being divisible by 3.

Lastly, the third sentence introduces a counterexample where n is set to 15. This counterexample demonstrates a situation where n is divisible by 3 but not divisible by 6, thus refuting the statement.

By organizing the sentences in this order, we can see that the statement is false, as evidenced by the counterexample.

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Answer:

y=-5x+2

Step-by-step explanation:

rise/run

or

y2-y1/x2-x1

-8-(-3)/2-1

-8+3/2-1

-5/1=m=slope

Slope intercept formula:y=mx+b

use point (1,-3)

-3=-5(1)+b

-3=-5+b

+5 +5

2=b

Final Answer: y=-5x+2

9514 1404 393

Answer:

  g(x) = 3x^2 -2

Step-by-step explanation:

Reflection in the y-axis replaces x with -x.

  g(x) = f(-x) = 3(-x)^2 -2

  g(x) = 3x^2 -2

_____

The given function is symmetrical about the y-axis, so its reflection is itself.

Answer:

$16.50

Step-by-step explanation:

$27.50/5=5.5

5.5*3=16.5

Answer:

What we can do is calculating what one bag cost. If we know that 5 cost 27.50 dollars, to know how much does one cost we only divide:

27.50/5 = 5.50 dollars

Now, we know how much does one bag cost, so we multiply it by three:

5.50 * 3 = 16.50

Now, we know 3 bags cost 16.5 dollars

The reason for 1/2 and not 5/10 is it is a norm in math to  reduce fractions to the least terms

This is a term used to refer to fractions that are equal even though they have different values in both he numerator and the denominator

Fractions are class of numbers that are of two parts the upper part is the numerator while the lower part is called the denominator.

In the given problem, 1/2

5/10 is an equivalent form of 1/2, this means that they are equal.

5/10 is shown to be equal to 1/2 by dividing by 5, this reduces the fraction to the least term which is 1/2. Using calculator can still show it that both numbers equal 0.5

In mathematics, it is preferred to reduce fractions to it's least form except it was stated.

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