Lucinda has three packages of baseball cards. the first package has thirteen cards. the second package has twenty-six cards, and the third package has twenty-two cards. using front end estimation, what is the best estimate for the total number of baseball cards she has? a. 30 b. 40 c. 50 d. 60

De Morgan's laws are two rules in formal logic that involve negating statements. The first law states that the negation of a conjunction (an "and" statement) is equivalent to the disjunction (an "or" statement) of the negations of the individual components.

The second law states that the negation of a disjunction is equivalent to the conjunction of the negations of the individual components.

Therefore, the negation of the original statement is "She does not make the bed, and I make the bed." This means that both she does not make the bed and I make the bed must be true in order for the negation to be true.

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Answer: To check a solution, you can substitute the solutions into the equations and verify that both equations are true.

Step-by-step explanation:

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Answer:

The equation of perpendicular bisector of QR is:

y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322

Step-by-step explanation:

Given points are:

Q(-2,0)\ and\ R(6,12)Q(−2,0) and R(6,12)

First of all, we have to find the slope of the given line

So,

m = \frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1

Here

(x1,y1) = (-2,0)

(x2,y2) = (6,12)

Let m1 be the slope of QR:

Then

\begin{gathered}m_1 = \frac{12-0}{6+2}\\= \frac{12}{8}\\= \frac{3}{2}\end{gathered}m1=6+212−0=812=23

Let m2 be the slope of perpendicular bisector

We know that the product of slopes of two perpendicular lines is -1

\begin{gathered}m_1.m_2 = -1\\\frac{3}{2}.m_2 = -1\\m_2 = -1 * \frac{2}{3}\\m_2 = -\frac{2}{3}\end{gathered}m1.m2=−123.m2=−1m2=−1∗32m2=−32

The bisector will pass through the mid-point of QR

\begin{gathered}M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\M = (\frac{-2+6}{2}, \frac{0+12}{2})\\M = (\frac{4}{2}, \frac{12}{2})\\M = (2,6)\end{gathered}M=(2x1+x2,2y1+y2)M=(2−2+6,20+12)M=(24,212)M=(2,6)

Slope-intercept form of equation is:

y = m_2x+by=m2x+b

Putting the value of slope

y = -\frac{2}{3}x+by=−32x+b

Putting (2,6) in the equation

\begin{gathered}6 = -\frac{2}{3}(2)+b\\6 = -\frac{4}{3}+b\\b = 6+\frac{4}{3}\\b = \frac{18+4}{3}\\b = \frac{22}{3}\end{gathered}6=−32(2)+b6=−34+bb=6+34b=318+4b=322

So,

y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322

Hence,

The equation of perpendicular bisector of QR is:

y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322

a. The perimeter of the first triangle is and the perimeter of the second triangle is

b. The difference between the perimeters is

c The perimeter of the triangles when x is 3 are

Perimeter is a math concept that measures the total length around the outside of a shape.

The perimeter of a triangle = a+b+c

1. 4x+2 + 7x+7 + x+3

= 4x+7x+ x +2+7+3

= 12x +12

Perimeter of the second triangle

= 2x-5+x+7+5x-4

= 2x+5x+x-5+7-4

= 8x-2

2. The difference of the perimeters

= 12x+12 -( 8x-2)

= 12x-8x +12+2

= 4x +14

3. when x is 3

The perimeter of the first triangle

= 12(3) +12

= 36+12

= 48 units

The perimeter of the second triangle

= 8(3)- 2

= 22 units

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the equation of the line will be x + y = 0 and it is being graphed.

Point on the line = (1, -1)

Slope of the perpendicular line = 1

So, the slope of the line will be

m × 1 = - 1

m = - 1

Equation of the line will be given by:

y - y₁ = m (x - x₁)

y - (- 1) = (- 1) (x - 1)

y + 1 = - x + 1

x + y = 0

We have graphed the equation.

Therefore, we get that, the equation of the line will be x + y = 0 and it is being graphed.

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9514 1404 393

Answer:

  47 -6√10

Step-by-step explanation:

As you know, the area of a square is the square of the side length. It can be helpful here to make use of the form for the square of a binomial.

  (a -b)² = a² - 2ab + b²

  (√2 -3√5)² = (√2)² - 2(√2)(3√5) + (3√5)²

  = 2 - 6√10 + 3²(5)

  = 47 -6√10

__

Check

  √2-3√5 ≈ -5.29399 . . . . . . . . note that a negative value for side length makes no sense, so this isn't about geometry, it's about binomials and radicals

  (√2-3√5)² ≈ 28.02633

  47 -6√10 ≈ 28.02633

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

The equation can be rewritten to make use of the graphing calculator's ability to identify function zeros:

  x(x -2)(x +3) -18 = 0

The attached shows x = 3 is the only real solution.

_____

We're not sure what "system of equations" is intended. Perhaps it is ...

  y = 18

  y = x(x -2)(x +3)

To create the expression we graphed, we effectively subtracted the first equation from the second.

The average rate of change of f(x) in 2 ≤x ≤8 is r = -6.

An average rate of change tells us how a function changes in a given interval.

If we have a function y = f(x) and we want to find the average rate of change on an interval [a, b], then we need to use the formula:

r = ( f(b) - f(a))/(b - a)

Here the function is defined by a table, and the interval in which we want to find the average rate of change is [2, 8]

using the table we can see that f(2) =42

f(8) = 6

Then we will get:

r = (6 - 42)/(8 - 2) = -36/6

r = -6

That is the average rate of change on the given interval.

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a) Yes, by multiplying both sides by 1/8.

b) The inequality is false, thus, there is nothing to solve.

Yes, you can.

There is a property that says that if you perform the same operation (multiplicating by 1/8 in this case) in both sides, then the truth value of the inequality does not change.

8m > -1/10

So,  if we multiply both sides by 1/8, we will get:

8m/m > -1/(10*8)

m > -1/80

The inequality is solved.

There is nothing to really solve here, as you can see, the inequality says that a negative number is larger than a positive number, so the inequality is clearly false, and thus, there is nothing to solve.

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Answer:

Check the answer below.

Step-by-step explanation:

This is a very trivial but professional question. Note that all of millimetre, centimetre and metres are acceptable metric units but the millimetre is more preferable by builders and architects because:

1. It is easier to work with integer values on building and architectural plans, an advantage given by measuring and recording in millimetre.

2. working in millimetre allows for precision. The builder will record values that are very close to the true value

3. The measurement will be easily readable by anybody that sees it.

The space curves r1(t) and r2(t) intersect at two points.

To find the points of intersection between the space curves r1(t) and r2(t), we need to set their corresponding components equal to each other and solve for t. The curves are defined as follows:

r1(t) = (ht^2, 1 - t^2, t)

r2(t) = (1 - t^2, t, t)

Setting the x-components equal to each other, we have:

ht^2 = 1 - t^2

Simplifying, we get:

h = (1 - t^2) / t^2

Next, we set the y-components equal to each other:

1 - t^2 = t

Rearranging the equation, we have:

t^2 + t - 1 = 0

Solving this quadratic equation, we find two values for t: t ≈ 0.618 and t ≈ -1.618.

Substituting these values of t back into either of the equations, we can find the corresponding points of intersection in 3D space.

Therefore, the space curves r1(t) and r2(t) intersect at two points.

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The record of the vote in the 435-member House is a descriptive statistical study, as it describes the actions and decisions of the members of the House. The study asking 435 citizens whether they want the tax cut bill passed is also a descriptive statistical study, as it describes the opinions and preferences of the citizens who were polled.

The record of the vote in the 435-member House is a descriptive statistical study because it is a report on what happened in the specific group (i.e., the House of Representatives) and does not involve making inferences about a larger population beyond the House members.

The poll asking 435 citizens whether they want the tax cut bill passed is an inferential statistical study because it aims to make inferences about a larger population beyond the 435 citizens who were polled. The poll results would be used to estimate the proportion of all citizens who want the bill passed, based on the assumption that the sample of 435 citizens is representative of the larger population. This involves making inferences and generalizations beyond the specific sample of 435 citizens who were polled.

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The time taken to traveled the van and the tornado before they  meet as per the speed of the van and the tornado is equal to 2.6 minutes.

As given in the question,

Speed of the van along the straight road = 94 kilometers per hour

After travelling distance of 7 kilometers

Speed of the tornado along the same road = 69 km/hour

Total relative speed of van and tornado = 94 + 69

                                                                  = 163km/hour

Distance travelled between two different speed = 7km

Time used to traveled before they meet = distance / speed

                                                                   = 7 / 163

                                                                   = 0.043 hours

                                                                   = 2.58minutes

                                                                   = 2.6minutes

Therefore, the time required to traveled the van and the tornado before they   meet is equal to 2.6 minutes.

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a. The price of the consol is approximately $133.33.

b. The new price of the consol would be $100. The price of the consol falls by 24.99% and the interest rate rises by 1%.

c. Your holding period return is approximately -49.99%.

a. The price of the consol can be calculated using the formula for the present value of a perpetuity:

Price = Annual Payment / Interest Rate

In this case, the annual payment is $4 and the interest rate is 3%. Substituting these values into the formula:

Price = $4 / 0.03 ≈ $133.33

Therefore, the price of the consol is approximately $133.33.

b. To calculate the new price of the consol if the interest rate rises to 4%, we use the same formula:

New Price = Annual Payment / New Interest Rate

Substituting the values, we get:

New Price = $4 / 0.04 = $100

The percentage change in the price of the consol can be calculated using the formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

Substituting the values, we have:

Percentage Change in Price = ($100 - $133.33) / $133.33 * 100 ≈ -24.99%

The percentage change in the interest rate is simply the difference between the old and new interest rates:

Percentage Change in Interest Rate = (4% - 3%) = 1%

Comparing the two percentages, we can see that the price of the consol falls by approximately 24.99%, while the interest rate rises by 1%.

c. The holding period return can be calculated using the formula:

Holding Period Return = (Ending Value - Initial Value) / Initial Value * 100

The initial value is the purchase price of the consol, which is $133.33, and the ending value is the price of the consol after one year with an interest rate of 6%. Using the formula for the present value of a perpetuity, we can calculate the ending value:

Ending Value = Annual Payment / Interest Rate = $4 / 0.06 = $66.67

Substituting the values into the holding period return formula:

Holding Period Return = ($66.67 - $133.33) / $133.33 * 100 ≈ -49.99%

Therefore, the holding period return is approximately -49.99%.

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The error made in solving the equation is in the step where ln(4x) is incorrectly rewritten as e ln⁴x. This step is not valid and leads to an incorrect solution.

To find the correct solution, let's start from the equation ln(4x) = 5:

So, the correct solution to the equation ln(4x) = 5 is x = e^5/4.

In concluding remraks , the error made in solving the equation ln(4x) = 5 was incorrectly applying exponential operations. The correct solution is x = e^(5/4).

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Answer:

The angle is 53.13 degrees

Step-by-step explanation:

In this question, we are to calculate the angle to which a ladder is to be set to get to a window.

Now, looking at this, we can picture a triangle where the length of the ladder represents the the hypotenuse while the angle we are considering makes the height of the room from the floor.

Please check attachment for picture of triangle

Since we are considering the hypotenuse and the opposite, the mathematical term we would be using is the sine.

Sine of an angle = length of opposite/length of hypotenuse

Sine angle = 8/10

since angle = 8/10

angle = arc sin 0.8

angle = 53.13 degrees

Answer:

See explanation

Step-by-step explanation:

f(g(13))=

f(16)=32

**The diagram is the only reference to solving  f(g(13)). f(x) or g(x) isn't provided for you, so just use the diagram.

Answer:

g(x) = 2ˣ⁻¹ + 3

Step-by-step explanation:

f(x) = 2ˣ

Translated 1 unit right

Translated 3 units up

Answer:

Well if its a translation on the x-axis  the formula would be g(x) = -2×

Although Functions are not my strong suit

I hope i got this right!

As D is the centroid of triangle ABC, we know that the line segment DE is one-third the length of the median from vertex A. CD = 15.4 and CE = 15.4.

Since D is the triangle ABC's centroid, we know that line section DE is one-third the median distance from vertex A.

Let CD and CE be the other two medians from vertices C and E, respectively, and let M be the middle of side BC. Next, we have

DM = EM (by specification of the centroid) (by definition of the centroid)

DE = (1/3) * AM (by specification of the centroid) (by definition of the centroid)

AM = 2 * DM (by meaning of the median) (by definition of the median)

Inputting the final solution into the second one results in:

DE = (1/3) * 2 * DM

DE = (2/3) * DM

As a result, we have:

(3/2) * DE = (3/2) * 11 = 16.5 DM

We know that CD and CE split the median BM into equal-sized segments because D is the centroid. As a result, we have:

BM/2 = CD = CE

The Pythagorean formula allows us to determine BM:

BM**2 = BC**2/4 + DM**2

BM**2 = 26**2/4 + 16.5**2

BM**2 = 676 + 272.25

BM**2 = 948.25

BM = sqrt(948.25)

BM = 30.8 (rounded to one decimal point)

As a result, we have:

BM/2 = CD = CE

CD = CE = 30.8/2

CD = CE = 15.4

Consequently, CD = 15.4 and CE = 15.4.

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Max heaps that follow the binary tree structure are popularly utilized in sorting methods such as heap sort and priority queues.

The correct answer is B.

A complete binary tree-based data structure known as a binary max heap exists.

The following attributes can be attributed to it:

The binary max heap is a complete binary tree that's completely filled at all levels except for the last level, which may not be completely filled and is filled from left to right.

The Heap Property is defined as follows: the value of any node must be equal to or greater than that of its children. Simply put, the highest value is stored in the root node of the heap.

Max heaps that follow the binary tree structure are popularly utilized in sorting methods such as heap sort and priority queues.

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Answer:

$2.28

38x.06

Brainlyest Pls

Step-by-step explanation:

TRUE. We can observe n coin flips, record each heads as 1, and each tails as 0. Then, sum up all of our 1s and 0s, divide by n (in other words, we calculate the sample mean), and we have just calculated the sample proportion p-hat. This is a method used to find the probability of an event.

The sample proportion is known as p-hat. The proportion of successes in the sample is denoted by the p-hat symbol. The sample proportion is a statistic that estimates the actual proportion of the population. The proportion of successes in a sample is referred to as the sample proportion.

When sample proportion represents a percentage, it is indicated as a percentage (x%). So, sample proportion p-hat is a statistical term that provides us with an estimate of the actual proportion of the population from the sample proportion.

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Answer:

Step-by-step explanation:

This is a combination of 6 out of 15

Correct choice is C

Answer:

C right?

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

tan < XYZ = opposite/adjacent

= 8/20  = 0.4.

XYZ = 21.8 degrees to 3 s f.

The argument is valid. The argument is valid based on the direct truth-table method.

To test the validity of the argument, we can use the direct truth-table method. Let's break down the argument and construct the truth table for the given premises and the conclusion:

Premises:

G ⊃ H

R ≡ G

~H v G

Conclusion:

R • H

Constructing the truth table:

We have three propositions: G, H, and R. Each proposition can have two truth values, true (T) or false (F). Therefore, we need 2^3 (8) rows in the truth table to evaluate all possible combinations.

By evaluating the truth table, we find that in all rows where the premises (1, 2, 3) are true, the conclusion (R • H) is also true. There is no row where the premises are true, but the conclusion is false. Therefore, the argument is valid.

The argument is valid based on the direct truth-table method. This means that if the premises (G ⊃ H, R ≡ G, ~H v G) are true, then the conclusion (R • H) must also be true.

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The correct answer is d. Chi-square. The chi-square method for finding confidence intervals should be used only when the population distribution is chi-square.

The method for finding confidence intervals with the chi-square distribution is specifically designed for situations where the data follows a chi-square distribution.

The chi-square distribution is a probability distribution that arises in inferential statistics, particularly in hypothesis testing and constructing confidence intervals for categorical data.

When the data does not follow a chi-square distribution, such as when the distribution is normal, skewed, or bimodal, using the chi-square distribution for constructing confidence intervals may lead to incorrect results.

In those cases, other methods appropriate for the specific distribution should be used. The correct answer is d. Chi-square.

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Solution

For this case we have the following info :

l= 18.5 ft

D= 20 ft

r= 20/2 = 10 ft

The surface area is given by;

Then the answer is:

581 ft^2