A number cube with faces labeled 1 to 6 is rolled once. The number rolled will be recorded as the outcome. Consider the following events. Event A: The number rolled is even. Event B: The number rolled is less than 4.
a) Event "A or B":
b) Event "A and B":
c) The complement of the event B:

The different Algebraic Properties that were used are:

1) Associative Property

2) Commutative Property

3) Inverse Property

4) Identity Property

There are different Algebraic Properties such as:

Commutative Property

Associative Property

Inverse Property

Identity Property

1) A + (B + C) = (A + B) + C  

The algebraic property used here is referred to as: associative  property

2) A + B = B + A  

The algebraic property used here is referred to as: commutative  property

3) A + (−A) = 0  

The algebraic property used here is referred to as: inverse property

4) A + 0 = A  

The algebraic property used here is referred to as: identity  property

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The vertical angles among the given options are ∠CAB and ∠DAE.

In the given question, we have three lines. Let's call the line that contains points C, A, and E as Line 1. The line that intersects Line 1 at point A and contains points B and D is called Line 2. The line that extends from point A to point F and lies between points B, A, and E is called Line 3.
Now, let's look at the given angles. We have ∠CAB, ∠DAE, ∠DAC, and ∠DAE.
∠CAB refers to the angle formed by Line 1 and Line 2 at point A.
∠DAE is the angle formed by Line 2 and Line 3 at point A.
∠DAC is the angle formed by Line 2 and Line 1 at point A.
To find the value of ∠DAC, we need to use the fact that angles on a straight line add up to 180 degrees. Since Line 1 and Line 2 intersect at point A, ∠DAC and ∠CAB are supplementary angles. Therefore, ∠DAC + ∠CAB = 180 degrees.
To find the value of ∠DAE, we can use the fact that ∠DAC and ∠DAE are corresponding angles formed by a transversal cutting two parallel lines, Line 2 and Line 3. Hence, ∠DAC = ∠DAE.
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Answer:

b d

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

its the middle of the first half

Answer:

x² + y² = 74

Step-by-step explanation:

given

(x - y) = 8 ( square both sides )

(x - y)² = 8² ← expand left side using FOIL

x² - 2xy + y² = 64 ← substitute xy = 5

x² - 2(5) + y² = 64

x² - 10 + y² = 64 ( add 10 to both sides )

x² + y² = 74

The conclusion remains the same as mentioned earlier. Danielle's monthly payment for the entertainment center with the new plasma television is $115. She will make equal monthly payments of $115 for 1 year to pay off the remaining amount owed.

To find Danielle's monthly payment, we need to subtract the down payment from the total cost of the entertainment center with the new plasma television.

The total cost of the entertainment center with the new plasma television = $1680

Down payment = $300

The remaining amount to be paid off is $1680 - $300 = $1380.

Since Danielle pays off the remaining amount in equal monthly payments for 1 year, we need to calculate the number of months in a year. There are 12 months in a year.

To find Danielle's monthly payment, we divide the remaining amount by the number of months:

Monthly payment = Remaining amount / Number of months

= $1380 / 12

= $115

Therefore, Danielle's monthly payment is $115. She will make equal monthly payments of $115 for 1 year to pay off the rest of the amount owed for the entertainment center with the new plasma television.

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Given statement solution is :- It takes approximately 1.122 seconds for the ball to reach its maximum height.

To find the time it takes for the ball to reach its maximum height, we need to determine the vertex of the parabolic function given by the equation h(t) = [tex]-4.9t^2 + 11t + 7.[/tex]

The vertex of a parabola in the form y = [tex]ax^2 + bx[/tex] + c is given by the formula t = -b / (2a).

Comparing the equation h(t) = [tex]-4.9t^2 + 11t + 7[/tex] to the standard form, we have:

a = -4.9

b = 11

Using the formula for the vertex, we can calculate the time it takes to reach the maximum height:

t = -11 / (2 * -4.9)

t = -11 / -9.8

t ≈ 1.122

Therefore, it takes approximately 1.122 seconds for the ball to reach its maximum height.

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Answer:

(12, 11, 10)

(2, 3, 4)

(5, 7, 13)

(1, 1, 1)

(7, 10, 3)

(4, 6, 7)

(x, y, x + y) for any positive values of x and y

(x, y, x - y) if x is greater than y and x - y is greater than 0

(x, x, 2) for any positive value of x

Step-by-step explanation:

The given equation is:

4a + 3 = 7a - 2

To solve for a, we can start by simplifying both sides of the equation. First, we can combine the constants on the right side:

4a + 3 = 7a - 2

4a + 5 = 7a

Next, we can isolate the variable terms on one side of the equation and the constant terms on the other side. Let's subtract 4a from both sides:

4a + 5 = 7a

5 = 3a

Finally, we can solve for a by dividing both sides by 3:

5 = 3a

5/3 = a

Therefore, the solution is:

a = 5/3

We can check this solution by substituting it back into the original equation:

4a + 3 = 7a - 2

4(5/3) + 3 = 7(5/3) - 2

20/3 + 3 = 35/3 - 2

29/3 = 29/3

Since both sides of the equation are equal when we substitute a = 5/3, we can confirm that this is the correct solution.

C 3) 1) 2) B. triangle and a (X) if it does not form a triangle. Which of the following could be the lengths of the sides of a triangle. Put a () if it is forms 12, 11, 10 2, 3, 4 3, 2, 1 4) 5) 6) 7) 7, 13, 7 8) 13, 12, 5 F 9) 3, 7, 10 10) 4, 6, 7 11) x, y, x + y 1 12) x, y, x-y 13) 1, 1, 2 nd all possible value of x.​

To determine whether a set of lengths could form the sides of a triangle, we need to check if the sum of the two shorter sides is greater than the longest side. If it is, then the lengths can form a triangle; otherwise, they cannot.

Using this criterion, we can determine which sets of lengths form triangles:

(12, 11, 10) - (O) forms a triangle, since 10 + 11 > 12.

(2, 3, 4) - (O) forms a triangle, since 2 + 3 > 4.

(3, 2, 1) - (X) does not form a triangle, since 1 + 2 is not greater than 3.

(5, 7, 13) - (O) forms a triangle, since 5 + 7 > 13.

(1, 1, 1) - (O) forms a triangle, since all sides are equal.

(8, 8, 16) - (X) does not form a triangle, since 8 + 8 is not greater than 16.

(13, 12, 5) - (O) forms a triangle, since 5 + 12 > 13.

(7, 10, 3) - (X) does not form a triangle, since 3 + 7 is not greater than 10.

(4, 6, 7) - (O) forms a triangle, since 4 + 6 > 7.

(x, y, x + y) - (O) forms a triangle for any positive values of x and y, since x + y is always greater than x and y individually.

(x, y, x - y) - (O) forms a triangle if x is greater than y and x - y is greater than 0.

(1, 1, 2) - (X) does not form a triangle, since 1 + 1 is not greater than 2.

(x, x, 2) - (O) forms a triangle for any positive value of x, since x + x > 2.

Therefore, the sets of lengths that can form triangles are:

(12, 11, 10)

(2, 3, 4)

(5, 7, 13)

(1, 1, 1)

(7, 10, 3)

(4, 6, 7)

(x, y, x + y) for any positive values of x and y

(x, y, x - y) if x is greater than y and x - y is greater than 0

(x, x, 2) for any positive value of x

If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

C)  $2,443.71

Step-by-step explanation:

To calculate the amount of interest earned on the savings account, use the compound interest formula.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ I=P\left(1+\dfrac{r}{n}\right)^{nt}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued.\\ \phantom{ww}$\bullet$ $P =$ principal amount. \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form). \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year. \\ \phantom{ww}$\bullet$ $t =$ time (in years). \\ \end{minipage}}[/tex]

Given values:

Substitute the given values into the formula and solve for I:

[tex]I=4570.65\left(1+\dfrac{0.039}{12}\right)^{12\cdot 11}-4570.65[/tex]

[tex]I=4570.65\left(1+0.00325\right)^{132}-4570.65[/tex]

[tex]I=4570.65\left(1.00325\right)^{132}-4570.65[/tex]

[tex]I=4570.65\left(1.534653130...\right)-4570.65[/tex]

[tex]I=7014.362330...-4570.65[/tex]

[tex]I=2443.712330...[/tex]

[tex]I=\$2,443.71\[ \sf (nearest\;cent)[/tex]

Therefore, the amount of interest the account has earned is $2,443.71, rounded to the nearest cent.

Answer:

$2,443.71

Step-by-step explanation:

To calculate the interest earned, we can use the formula for compound interest:

[tex]\rm\implies A = P(1 + \frac{r}{n})^{(nt)}[/tex]

where:

Given:

Substitute the given values into the above formula:

[tex]\begin{aligned}\rm\implies A& =\rm 4570.65(1 + \frac{0.039}{12})^{(12 \cdot 11)}\\& \approx \rm{\$9,014.36}\end{aligned}[/tex]

To find the interest earned, we subtract the initial deposit from the final amount:

[tex]\begin{aligned}\rm\implies Interest& =\rm A - P\\& \approx \$9,014.36 - \$4,570.65\\& \approx \boxed{\rm{\$2,443.71}}\end{aligned}[/tex]

[tex]\therefore[/tex] The account has earned $2,443.71 in interest.

Answer:

d = [tex]\sqrt{89}[/tex]

Step-by-step explanation:

to calculate the distance d use the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 4, - 1 ) and (x₂, y₂ ) = (1, - 9 )

d = [tex]\sqrt{(1-(-4))^2+(- 9-(-1))^2}[/tex]

  = [tex]\sqrt{(1+4)^2+(-9+1)^2}[/tex]

  = [tex]\sqrt{5^2+(-8)^2}[/tex]

  = [tex]\sqrt{25+64}[/tex]

  = [tex]\sqrt{89}[/tex]

Answer:

scale factor = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original , that is

scale factor = [tex]\frac{ST}{AB}[/tex] = [tex]\frac{5}{15}[/tex] = [tex]\frac{1}{3}[/tex]

bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.

Let's assume the original price of an item is $100.

The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.

The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.

Therefore, the final price you end up paying after both discounts is $22.50.\

To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:

Percent of original price = (final price / original price) * 100

In this case, the final price is $22.50 and the original price is $100:

Percent of original price = ($22.50 / $100) * 100

                       = 0.225 * 100

                       = 22.5%

Therefore, you end up paying 22.5% of the original price after the discounts.

It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.

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Answer:

Step-by-step explanation:

Answer:

D)

Step-by-step explanation:

ΔSTU is translated to ΔS'U'T'

    (i) moved right by 1 unit. Horizontal displacement right is denoted positive number. So, x +1.

   (ii) moved down by 7 unit. Vertical displacement down is denoted by negative number. So, y - 7

(x, y)  --> (x + 1, y -7)

No, she is not correct because: The unit rate should be 1.5 teaspoons of nutmeg to 1 teaspoon of cinnamon.

A unit rate (or unit ratio) describes how many units of a quantity of the first type correspond to units of a quantity of the second type.

Now, the formula to find the un it rate of a linear graph like the one given in the attached file is:

Unit rate = y/x

We will make use of the coordinate as: (2, 3)

Thus, the unit rate is: 3/2 = 1.5 teaspoons of cinnamon to 1 teaspoon of nutmeg.

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Complete Question is:

Heidi looked at this graph and thought, “The first point I see is at 2 tsp of nutmeg and 3 tsp of cinnamon. The unit rate is 3 tsp of cinnamon for every 2 tsp of nutmeg.”

Is Heidi correct?

No. The unit rate should be 2 teaspoons of cinnamon to 3 teaspoons of nutmeg.

No. The unit rate should be 1.5 teaspoons of nutmeg to 1 teaspoon of cinnamon.

No. The unit rate should be 1.5 teaspoons of cinnamon to 1 teaspoon of nutmeg.

Yes. Heidi is correct.

The length of side a is approximately B. 24.3 (to the nearest tenth).

The correct answer is B. 24.3

To find the length of side a in triangle ABC, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

The Law of Sines can be expressed as:

a/sin(A) = c/sin(C)

where a is the length of side a, A is the measure of angle A, c is the length of side c, and C is the measure of angle C.

Angle A (m∠A) = 45°

Side c (c) = 17

Angle B (m∠B) = 25°

We need to find the length of side a.

Using the Law of Sines:

a/sin(45°) = 17/sin(25°)

To find a, we isolate it by multiplying both sides of the equation by sin(45°):

a = 17 * (sin(45°) / sin(25°))

Using a calculator to evaluate the expression:

a ≈ 24.3

Therefore, the length of side a is approximately 24.3 (to the nearest tenth).

The correct answer is:

B. 24.3

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The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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The expression 48 − 8 × 48−8x48 is factored to give an equivalent expression 8(6 − x) × 48, where 8, 6, and x are terms of the expression. Factoring is the method of expressing a polynomial as the product of other polynomials. The term minus refers to subtraction, and the operation of subtraction is used to subtract 8 × 48 from 48 to get a result of 16.

The expression to factor is 48 − 8 × 48−8x48. Factoring the expression 48 − 8 × 48−8x48 gives an equivalent expression 8(6 − x) × 48, where 8, 6, and x are terms of the expression.

In mathematics, factoring is the method of expressing a polynomial as the product of other polynomials. The factored expression 8(6 − x) × 48 can be expanded back to the original expression by multiplying the individual factors with each other.

The term minus refers to subtraction. In this context, the operation of subtraction is used to subtract 8 × 48 from 48, yielding a result of 16. This result is multiplied by 48 − 8x48 to get the original expression 48 − 8 × 48−8x48.

Therefore, the equivalent expressions are 48 − 8 × 48−8x48 and 8(6 − x) × 48, where 8, 6, and x are terms of the expression.

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The largest value for 60 such that 0 < x - c < 5 - f(x) < e is x < -5/7.

To determine the largest open interval about c on which the inequality f(x) - LI < e holds, we need to find the interval where the difference between f(x) and LI is less than e.

Given:

f(x) = 8x + 81

L = 11

c = 5

e = 0.04

We can start by substituting the values of L and c into the function f(x):

f(x) - LI = 8x + 81 - 11(5) = 8x + 81 - 55 = 8x + 26

Now we want to find the interval where 8x + 26 < e. Substituting e = 0.04, we have:

8x + 26 < 0.04

Subtracting 26 from both sides of the inequality, we get:

8x < -25.96

Dividing both sides by 8, we obtain:

x < -3.245

Therefore, the largest open interval about c = 5 on which the inequality f(x) - LI < e holds is (-∞, -3.245). In interval notation, this can be written as (-∞, -3.245).

Now let's determine the largest value for 60 such that 0 < x - c < 5 - f(x) < e.

Substituting the values of c and f(x) into the inequality, we have:

0 < x - 5 < 5 - (8x + 81)

Simplifying the inequality, we get:

0 < x - 5 < -8x - 76

Combining like terms, we have:

8x < x - 5 < -76

Adding 76 to all sides of the inequality, we obtain:

8x + 81 < x + 76 < 0

Subtracting x from all sides, we get:

7x + 81 < 76 < -x

Subtracting 81 from all sides, we have:

7x < -5 < -x

To isolate x, we need to multiply all sides by -1. Since we're looking for the largest value for 60, we will multiply all sides by -1 and reverse the inequality signs:

-x > 5 > 7x

Dividing all sides by 7 and flipping the inequality signs, we have:

x < -5/7 < -x/7

Since we want the largest value for 60, we need to maximize x. So, x must be less than -5/7.

Therefore, the largest value for 60 such that 0 < x - c < 5 - f(x) < e is x < -5/7.

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Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.

What theory directly contradicts concept of absolute zero?

All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).

Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.

Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.

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The range of the function on the graph is y > -6

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

The graph

The graph is an exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

In this case, it is -6 i.e. the point where it intersects with the y-axis

So, the range is y > -6

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The number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) is a number line from negative 5 to 5 in increments of 1, with an open circle at 3 and a bold line starting at 3 and pointing to the right.

To determine which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5), we need to solve the inequality and analyze its solution.

First, let's simplify the inequality:

3(8 – 4x) < 6(x – 5)

24 - 12x < 6x - 30

Next, let's bring all the terms involving x to one side of the inequality:

-12x - 6x < -30 - 24

-18x < -54

Now, divide both sides of the inequality by -18.

Since we are dividing by a negative number, we need to reverse the direction of the inequality:

x > -54/-18

x > 3

The inequality solution is x > 3, which means x is greater than 3. In interval notation, this can be represented as (3, +∞),

where the parentheses indicate that 3 is not included in the solution.

Now let's analyze the given options:

A number line from negative 5 to 5 in increments of 1.

An open circle is at 3 and a bold line starts at 3 and is pointing to the left: This option represents values less than 3, but we need values greater than 3.

A number line from negative 5 to 5 in increments of 1.

An open circle is at 3 and a bold line starts at 3 and is pointing to the right:

This option represents values greater than 3, which matches the solution set.

A number line from negative 5 to 5 in increments of 1.

An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left: This option does not match the given inequality.

A number line from negative 5 to 5 in increments of 1.

An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right:

This option does not match the given inequality.

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

let's relist the 10 names, as there was some "mixing" going on in your text :

Dorothy

Anthony

Harold

Margaret

Tiffany

Nancy

Angela

Paul

Patrick

Jeremy

so, whatever happens, the totally possible cases are 10 (as we are only taking about these 10 names, no other name can suddenly appear in all the scenarios).

in each scenario one student is randomly chosen.

a) the probabilty to pick a student with name ending "k".

we look through the list and find only 1 student, whose name ends with "k" : Patrick.

that means the number of desired cases is 1.

and the probabilty is therefore

1/10 = 0.1

b) the probability to pick a student with name beginning "C".

we look and look and look. none of the 10 names start with a "C".

that means the number of desired cases is 0.

and the probabilty is

0/10 = 0

c) the probability that the name of the picked student contains "m" or "M".

we find 2 names : Margaret and Jeremy.

that means that the number of desired cases is 2.

and the probabilty is therefore

2/10 = 1/5 = 0.2

d) in how many ways can we pick 7 elements out of 10, when the sequence of the pulled 7 elements does not matter (e.g. ... Nancy, Paul ... is the same as ... Paul, Nancy, ...). and no student can be pulled more than once (no repetitions).

that means we have to calculate the combinations of 7 items out of 10 without repetition :

C(10, 7) = 10! / (7! × (10-7)!) = 10! / (7! × 3!) =

= 10×9×8 / (3×2) = 5×3×8 = 120

there are 120 possibilities to build the math club.

e) now we pick 4 students out of 10. but as we give them prices based on ranking, the sequence matters (e.g. Nacy first, Paul second is different to Paul first, Nancy second).

but we still have no repetition, as nobody can win more than one price.

that means we need to calculate the permutations of 4 items out of 10 without repetition :

P(10, 4) = 10! / (10-4)! = 10! / 6! = 10×9×8×7 = 5,040

there are 5040 different ways to distribute the 4 prices among the 10 students.

We can conclude that Portland sales were 70.3125% of Seattle's.

Given that a company's sales in Seattle were $320,000 in 2012, while their sales in Portland were $225,000 for the same year, we are to complete the following statements:c. Portland sales were % of Seattle's.To find the percentage of Portland sales in relation to Seattle sales, we can use the formula: (Portland sales/Seattle sales) × 100%Substituting the given values, we get:(225,000/320,000) × 100% = 70.3125%

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Answer:

Length = 16 inches

Width = 7 inches

Step-by-step explanation:

Let "x" be the width of the rectangular piece of cardboard.

If the rectangular piece of cardboard is 9 inches longer than it is wide, then let "x + 9" be the length of the rectangular piece of cardboard.

As squares with side lengths of 2 inches are cut from each corner of the rectangle, the height of the open box will be 2 inches, and the width and length of the box will be 4 inches less than width and length of the rectangular piece of cardboard.

Therefore, the dimensions of the open box are:

Given the open box has a volume of 72 in³, substitute all the values into the formula for the volume of a cuboid and solve for x:

[tex]\begin{aligned}\textsf{Volume of a cuboid}&=\sf width \cdot length \cdot height\\\\72&=(x-4)\cdot (x+5)\cdot 2\\36&=(x-4)(x+5)\\(x-4)(x+5)&=36\\x^2+x-20&=36\\x^2+x-56&=0\\x^2+8x-7x-56&=0\\x(x+8)-7(x+8)&=0\\(x-7)(x+8)&=0\\\\x-7&=0 \implies x=7\\x+8&=0 \implies x=-8\end{aligned}[/tex]

As length cannot be negative, the only valid value of x is 7.

To find the length and width of the piece of cardboard, substitute the found value of x into their expressions:

[tex]\textsf{Length}=x+9=7+9=16\; \sf inches[/tex]

[tex]\textsf{Width}=x=7\; \sf inches[/tex]

Therefore, the dimensions of the rectangular piece of cardboard are:

Answer:

Length= 16 inches

Width= 7 inches

Step-by-step explanation:

Let's denote the width of the rectangular piece of cardboard as "w" inches.

According to the given information,

the length of the cardboard is 9 inches longer than its width, so the length can be represented as "w + 9" inches.

When the sides are folded up, the height of the box will be 2 inches.

After folding, the width of the base of the box will be "w - 4" inches, and the length will be "w + 9 - 4" inches, which simplifies to "w + 5" inches.

The volume of a rectangular box can be calculated as the product of its length, width, and height.

In this case, the volume is given as 72 in³:

Volume = Length*Width*Height

72 = (w + 5)*(w - 4) × 2

Simplifying the equation:

36 = (w + 5)*(w - 4)

Expanding the right side:

36 = w² - 4w + 5w - 20

Rearranging and combining like terms:

w² + w - 56 = 0

We can factorize by using middle term factorization:

w² + 8x-7x - 56 = 0

w(w+8)-7(w+8)=0

(w - 7)(w + 8) = 0

Setting each factor equal to zero:

either

w - 7 = 0

Therefore, w = 7

or

w + 8 = 0  

w = -8 (Discard since width cannot be negative)

Therefore, the width of the piece of cardboard is 7 inches.

Substituting this value back into the expression for the length:

Length = w + 9

Length = 7 + 9

Length = 16 inches

So, the length of the piece of cardboard is 16 inches, and the width is 7 inches.

The weight of one bucket of lobster is 18 pounds per bucket. Option b

To determine the weight of one bucket of lobster, we can use the given information about the rate of 450 pounds over 25 buckets.

The rate is defined as the amount of weight (in pounds) divided by the number of buckets. In this case, the rate is 450 pounds over 25 buckets.

To find the weight of one bucket of lobster, we can divide the total weight by the number of buckets:

Weight of one bucket = Total weight / Number of buckets

Weight of one bucket = 450 pounds / 25 buckets

Weight of one bucket = 18 pounds per bucket

Therefore, the weight of one bucket of lobster is 18 pounds per bucket.

The correct answer is option b) 18 pound per bucket.

It's important to note that this calculation assumes a constant weight per bucket throughout the given scenario. In reality, the weight of one bucket of lobster may vary depending on factors such as the size and type of lobsters being weighed. Additionally, it's possible that the weight per bucket may change over time or across different batches of lobsters.

Option B

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The true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

From the given options, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

Let's analyze each statement:

Its leading coefficient is positive:

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

From the graph, if the polynomial is going upwards on the right side, it indicates that the leading coefficient is positive.

It has an odd degree: The degree of a polynomial is the highest power of the variable in the polynomial expression.

If the graph has an odd number of "turns" or "bumps," it indicates that the polynomial has an odd degree.

None of the zeroes have even multiplicity:

The multiplicity of a zero refers to the number of times it appears as a factor in the polynomial.

In the given graph, if there are no repeated x-intercepts or no points where the graph touches and stays on the x-axis, it implies that none of the zeroes have even multiplicity.

The other statements (its leading coefficient is negative, it has an even degree, it has exactly two real zeroes, it has exactly three real zeroes, and none of the zeroes have odd multiplicity) cannot be determined based solely on the information given.

Therefore, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

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Answer:5

Step-by-step explanation:To find the first quartile (Q1) for a given dataset, you need to arrange the data in ascending order and determine the value that separates the lowest 25% of the data.

Arranging the dataset in ascending order:

2, 3, 5, 5, 6, 8, 8, 9, 10, 11, 11, 11, 12

To calculate Q1, you can use the formula:

Q1 = (n + 1) / 4

where n is the total number of data points.

In this case, n = 13, so:

Q1 = (13 + 1) / 4 = 14 / 4 = 3.5

Since Q1 is not exactly a data point in this dataset, we need to find the value that falls between the third and fourth data points. In this case, the third and fourth data points are both 5.

Therefore, the Q1 for this dataset is 5.

The equation (x+2)^2/64 + (y-1)^2/81 = 1 represents an ellipse.

To determine the coordinates of the foci of the ellipse, we need to find the square root of the denominators of x and y, which represent the lengths of the major and minor axes.

The square root of 64 is 8, and the square root of 81 is 9.

These values correspond to the lengths of the major and minor axes, respectively.

Since the major axis is in the x-direction (horizontal), the foci lie along the x-axis.

We can determine the center of the ellipse by identifying the values of (h, k) in the form (x - h, y - k). In this case, the center of the ellipse is (-2, 1).

The distance from the center of the ellipse to each focus is given by the formula c = sqrt(a^2 - b^2), where a is half the length of the major axis and b is half the length of the minor axis.

The formula to calculate the distance from the center to the foci is given by c = sqrt(a^2 - b^2), where a and b are the semi-major and semi-minor axes of the ellipse.

In this case, a = 8/2 = 4 and b = 9/2 = 4.5. Substituting these values into the formula, we have c = sqrt(4^2 - 4.5^2) = sqrt(16 - 20.25) = sqrt(-4.25).

Since the square root of a negative number is imaginary, we conclude that the ellipse does not have any real foci.

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The bank reconciliation shows an adjusted bank balance of Br.5,301.42 and an adjusted ledger balance of Br.4,173.83.

To prepare the bank reconciliation and journal entry for ABC Company based on the given information, we need to compare the transactions recorded in ABC's ledger with the transactions shown in the bank statement. Here's the bank reconciliation:

1. Bank Statement Balance:

Cash on deposit at July 31: Br.4,964.47

2. Adjusted Bank Balance:

Bank Statement Balance: Br.4,964.47

3. Deposit not on the statement: + Br.410.90

(Adjusted Bank Balance: Br.5,375.37)

Erroneously charged check: + Br.79

(Adjusted Bank Balance: Br.5,454.37)

Outstanding checks:

Check 801: - Br.100.00

Check 888: - Br.10.25

Check 890: - Br.294.50

Check 891: - Br.205.00

(Adjusted Bank Balance: Br.4,844.62)

4. Incorrectly charged check: + Br.90

(Adjusted Bank Balance: Br.4,934.62)

5. Collection of interest-bearing note: + Br.500

(Adjusted Bank Balance: Br.5,434.62)

6. Interest earned: + Br.24.75

(Adjusted Bank Balance: Br.5,459.37)

7. Incorrectly recorded check: - Br.90

(Adjusted Bank Balance: Br.5,369.37)

8. Collection fee: - Br.5.00

(Adjusted Bank Balance: Br.5,364.37)

9. NSF check: - Br.50.25

(Adjusted Bank Balance: Br.5,314.12)

10. Service charge: - Br.12.70

(Adjusted Bank Balance: Br.5,301.42)

Adjusted Ledger Balance:

Bank Balance in ABC's Ledger: Br.4,173.83

Reconciled Bank Balance: Br.5,301.42

Reconciled Ledger Balance: Br.4,173.83

Journal Entry:

To record the bank reconciliation, we make the following journal entry:

Debit: Cash (Ledger Balance adjustment) - Br.5,301.42

Credit: Cash (Bank Statement Balance adjustment) - Br.4,964.47

Credit: Miscellaneous Income/Expense - Br.336.95 (the difference between the two balances)

This journal entry ensures that the ledger balance matches the reconciled bank balance by adjusting for the discrepancies identified during the reconciliation process.

The journal entry reflects the necessary adjustments to reconcile the two balances, with a debit to Cash (Ledger Balance adjustment), a credit to Cash (Bank Statement Balance adjustment), and a credit to Miscellaneous Income/Expense to account for the difference.

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