What is the sum of the series?
Σ (2k2 – 4)
k=1

We will have that Sarah's function is the correct one, since each hour she will get $9, then when we multiply will give us the amount of money she makes in the number of hours.

H = 9h

Answer:

Tamara earns $2,050 each month.

She spends 65% of that, so the amount that she spends is:

S = (65%/100%)*$2,050 = 0.65*$2,050 = $1,332.50

Then the amount that she has left is:

R = $2,050 -  $1,332.50 = $717.50

Now she divides that in half, and deposits those amounts in two separate accounts.

She deposits $717.50/2 = $358.75 in each acount.

Then she deposits $358.75 per month, so after x months she has:

x*$358.75 in each of those accounts, so one of the accounts will have more than $2,500 when:

x*$358.75 = $2,500

x = $2,500/$358.75 = 6.96

So after 6.96 moths she will have more than $2,500 in one of her accounts, we can round it to:

After 10 months Tamara has deposited more than 2,500 in one of her accounts.

Answer:

\(62 in^2\)

Step-by-step explanation:

\(===========================================\)

Formulas:

Area of a rectangle/square:

\(A=lw\)

\(===========================================\)

Big Rectangles (2):

7*3=21

Multiply by 2

21*2= 42 in

Long rectangles (2)

7*1=7

Multiply by 2

7*2= 14 in

Short rectangles (2):

3*1=3

Multiply by 2

3*2= 6 in

Total:

Add.

42+14+6= 62 in2

Answer: {0, 5, 7}

Step-by-step explanation:

{0, 5, 7}

Answer:

0,5,7

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

given

tanΘ = \(\frac{3\sqrt{5} }{2}\) = \(\frac{opposite}{adjacent}\)

this ratio relates to a right triangle, with hypotenuse h and

legs 3\(\sqrt{5}\) and 2

using Pythagoras' identity in the right triangle

h² = (3\(\sqrt{5}\) )² + 2² = 45 + 4 = 49 ( take square root of both sides )

h = \(\sqrt{49}\) = 7

then

cosΘ = \(\frac{adjacent}{hypotenuse}\) = \(\frac{2}{7}\)

In the case of the electronic chess game, with a useful life that follows an exponential distribution with a mean of 30 months, we need to determine the length of service time after which the percentage of failed units will approximately equal 50 percent. The options provided are 9 months, 16 months, 21 months, and 25 months.

For the major television manufacturer, the service life of its 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. We are asked to calculate the probability of service lives of at least five years.

1. Electronic Chess Game:

The exponential distribution is characterized by a constant hazard rate, which implies that the percentage of failed units follows an exponential decay. The mean of 30 months indicates that after 30 months, approximately 63.2% of the units will have failed. To find the length of service time when the percentage of failed units reaches 50%, we can use the formula P(X > x) = e^(-λx), where λ is the failure rate. Setting this probability to 50%, we solve for x: e^(-λx) = 0.5. Since the mean (30 months) is equal to 1/λ, we can substitute it into the equation: e^(-x/30) = 0.5. Solving for x, we find x ≈ 21 months. Therefore, the length of service time after which the percentage of failed units will approximately equal 50 percent is 21 months.

2. LED Televisions:

The service life of 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. To find the probability of service lives of at least five years, we need to calculate the area under the normal curve to the right of five years (60 months). We can standardize the value using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. Substituting the values, we have z = (60 - 72) / 0.5 = -24. Plugging this value into a standard normal distribution table or using a calculator, we find that the probability of a service life of at least five years is approximately 1.0000 (or 100% with four digits after the decimal point).

Therefore, the probability of service lives of at least five years for 50-inch LED televisions is 1.0000 (or 100%).

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Based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

To solve the problem using the determinant method (Cramer's rule), we need to set up a system of equations based on the given information and then solve for the unknowns, which represent the number of 0.5 litre bottles and 0.7 litre bottles.

Let's denote the number of 0.5 litre bottles as x and the number of 0.7 litre bottles as y.

From the given information, we can set up the following equations:

Equation 1: 0.5x + 0.7y = 16.5 (total volume of moonshine)

Equation 2: 8x + 10y = 246 (total earnings from selling moonshine)

We now have a system of linear equations. To solve it using Cramer's rule, we'll find the determinants of various matrices.

Let's calculate the determinants:

D = determinant of the coefficient matrix

Dx = determinant of the matrix obtained by replacing the x column with the constants

Dy = determinant of the matrix obtained by replacing the y column with the constants

Using Cramer's rule, we can find the values of x and y:

x = Dx / D

y = Dy / D

Now, let's calculate the determinants:

D = (0.5)(10) - (0.7)(8) = -1.6

Dx = (16.5)(10) - (0.7)(246) = 150

Dy = (0.5)(246) - (16.5)(8) = -18

Finally, we can calculate the values of x and y:

x = Dx / D = 150 / (-1.6) = -93.75

y = Dy / D = -18 / (-1.6) = 11.25

However, it doesn't make sense to have negative quantities of bottles. So, we can round the values of x and y to the nearest whole number:

x ≈ -94 (rounded to -94)

y ≈ 11 (rounded to 11)

Therefore, based on the calculation, it appears that Matti had approximately 94 bottles of 0.5 litres and 11 bottles of 0.7 litres in the last patch of moonshine that he sold.

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Question

Matti is making moonshine in the woods behind his house. He’s selling the moonshine in two different sized bottles: 0.5 litres and 0.7 litres. The price he asks for a 0.5 litre bottle is 8€, for a 0.7 litre bottle 10€. The last patch of moonshine was 16.5 litres, all of which Matti sold. By doing that, he earned 246 euros. How many 0.5 litre bottles and how many 0.7 litre bottles were there? Solve the problem by using the determinant method (a.k.a. Cramer’s rule).

Answer:

a, \(Books = 315\)

b, \(Total = 20s + 45l\)

Step-by-step explanation:

Given

\(Small\ Box = 20\)

\(Large\ Box = 45\)

Solving (a): Books using 5 small and 7 large boxes;

This is calculated as follows

\(Books = Size * quantity\)

For Small box

\(Books = 20 * 5\)

\(Books = 100\)

For large box:

\(Books = 45 * 7\)

\(Books = 315\)

\(Total = 100 + 315\)

\(Total = 415\ books\)

Solving (b): s small and l large

We use the same concept as (a) above:

For Small Box

\(Books = 20 * s\)

\(Books = 20s\)

For large box

\(Books = 45 * l\)

\(Books = 45l\)

\(Total = 20s + 45l\)

Answer:

x = 3

x = (-1)/2

x = 13/4

Step-by-step explanation:

Solve for x:

(2 x)/3 + 15 = 17

Put each term in (2 x)/3 + 15 over the common denominator 3: (2 x)/3 + 15 = (2 x)/3 + 45/3:

(2 x)/3 + 45/3 = 17

(2 x)/3 + 45/3 = (2 x + 45)/3:

1/3 (2 x + 45) = 17

Multiply both sides of (2 x + 45)/3 = 17 by 3:

(3 (2 x + 45))/3 = 3×17

(3 (2 x + 45))/3 = 3/3×(2 x + 45) = 2 x + 45:

2 x + 45 = 3×17

3×17 = 51:

2 x + 45 = 51

Subtract 45 from both sides:

2 x + (45 - 45) = 51 - 45

45 - 45 = 0:

2 x = 51 - 45

51 - 45 = 6:

2 x = 6

Divide both sides of 2 x = 6 by 2:

(2 x)/2 = 6/2

2/2 = 1:

x = 6/2

The gcd of 6 and 2 is 2, so 6/2 = (2×3)/(2×1) = 2/2×3 = 3:

Answer:  x = 3

______________________________________________________

Solve for x:

3 x - x + 8 = 7

Grouping like terms, 3 x - x + 8 = (3 x - x) + 8:

(3 x - x) + 8 = 7

3 x - x = 2 x:

2 x + 8 = 7

Subtract 8 from both sides:

2 x + (8 - 8) = 7 - 8

8 - 8 = 0:

2 x = 7 - 8

7 - 8 = -1:

2 x = -1

Divide both sides of 2 x = -1 by 2:

(2 x)/2 = (-1)/2

2/2 = 1:

Answer: x = (-1)/2

_______________________________________

Solve for x:

4 (2 x - 6) = 2

Divide both sides of 4 (2 x - 6) = 2 by 4:

(4 (2 x - 6))/4 = 2/4

4/4 = 1:

2 x - 6 = 2/4

The gcd of 2 and 4 is 2, so 2/4 = (2×1)/(2×2) = 2/2×1/2 = 1/2:

2 x - 6 = 1/2

Add 6 to both sides:

2 x + (6 - 6) = 1/2 + 6

6 - 6 = 0:

2 x = 1/2 + 6

Put 1/2 + 6 over the common denominator 2. 1/2 + 6 = 1/2 + (2×6)/2:

2 x = 1/2 + (2×6)/2

2×6 = 12:

2 x = 1/2 + 12/2

1/2 + 12/2 = (1 + 12)/2:

2 x = (1 + 12)/2

1 + 12 = 13:

2 x = 13/2

Divide both sides by 2:

x = (13/2)/2

2×2 = 4:

Answer: x = 13/4

Answer:

41/81

Step-by-step explanation:

There are a total of 4 blue marbles, 5 red marbles giving 9 total number of marbles

Let P(B₁) =Probability of getting a blue marble on the first draw

Let P(B₂) =Probability of getting a blue marble on the second draw

Let P(R₁) =Probability of getting a red marble on the first draw
Let P(B₂) =Probability of getting a red marble on the second draw

P(B₁) = Number of blue marbles ÷ total number of marbles = 4/9

Since the marble is replaced before the second draw, the total number of blue marbles and total number of both marbles is the same as for the first draw

P(B₂) = P(B₁) = 4/9 also

Probability of getting 2 blue marbles on 2 consecutive draws= P(B₁B₂)
= 4/9 x 4/9 = 16/81

P(R₁) = Number of red marbles ÷ total number of marbles = 5/9

P(getting a red marble on the second draw) = P(R₁R₂) = 5/9

Probability of getting 2 red marbles on 2 consecutive draws = P(R₁R₂)
= 5/9 x 5/9 = 25/81

Since we are asked the probability of getting 2 of the same color we can rephrase the same question as

P(two of same color) = P(B₁B₂ ∪ R₁R₂) = P(B₁B₂) + P(R₁R₂) = 16/81 + 25/81 = 41/81

The statement which is given as , "The product of permutation matrices is again a permutation matrix." is True.

A permutation matrix is a square matrix whose entries are either 0 or 1 and has exactly one "1" in each row and each column. In other words, it is a matrix that represents a permutation of the rows (or columns) of the identity matrix.

When two permutation matrices are multiplied, the result is another square matrix with exactly one "1" in each row and each column. To see why this is true, consider two permutation matrices, A and B. Suppose that A is a m x m matrix and B is a m x m matrix. The product of these two matrices is another m x m matrix, C = AB.

Each entry in the matrix C is given by the dot product of the corresponding row in A and the corresponding column in B. If the row in A has a "1" in the i-th position and the column in B has a "1" in the j-th position, then the i,j-th entry in C will be "1".

Since both A and B are permutation matrices, each row in A and each column in B has exactly one "1". This means that each row in C will have exactly one "1", and each column in C will also have exactly one "1". Hence, C is also a permutation matrix.

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Answer:

a) -0.4

b) 2.5

c) 0.125

d) 1.5

Step-by-step explanation:

given set satisfies all three conditions, it is a subspace of Ph for n = 2.The set of polynomials Ph is a vector space. To determine if a subset of Ph is a  subspace.

, we need to check if it satisfies the three conditions for a subspace:

1. Contains the zero vector: the zero vector of Ph is the polynomial p(t) = 0, which is of the form p(t) = 0 + t^2. This polynomial is in the given set, so it contains the zero vector.

2. Closed under addition: Let p1(t) = a1 + t^2 and p2(t) = a2 + t^2 be two polynomials in the given set. Then, their sum is p1(t) + p2(t) = (a1 + a2) + 2t^2. Since a1 and a2 are real numbers and the sum of real numbers is also a real number, the sum of p1 and p2 is of the form p(t) = a + t^2, where a is a real number. Therefore, the given set is closed under addition.

3. Closed under scalar multiplication: Let c be a scalar and let p(t) = a + t^2 be a polynomial in the given set. Then, the product cp(t) = ca + ct^2 is also of the form p(t) = a + t^2, where a and c are real numbers. Therefore, the given set is closed under scalar multiplication.

Since the given set satisfies all three conditions, it is a subspace of Ph for n = 2.

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Answer:

8 square units

Step-by-step explanation:

Area of the shaded shape = sum of shaded squares × 1 square unit

= 8 × 1 = 8 square units

The proportion of candy bars with fewer than 200 calories cannot be determined without additional information.

To calculate the proportion of candy bars with fewer than 200 calories, we need to know the total number of candy bars and the number of candy bars that have fewer than 200 calories.

Without this information, we cannot determine the proportion. The number of candy bars with fewer than 200 calories could vary greatly depending on the specific dataset or context.

The proportion of candy bars with fewer than 200 calories cannot be determined without additional information regarding the total number of candy bars and the number of candy bars that fall into that category.

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The required length of each piece is 18 inches.

How to find HCF?

The highest common factor (HCF) is found by listing all the common factors of two numbers and choosing the highest one. The required length of each piece is 18 inches.

Given that,

Length of red ribbon spool = 22,608 in

Length of blue ribbon spool = 10,206

To find the required length of each piece we should find the highest common factor (HCF) of the length of a piece of both ribbons.

22, 608 = 1,2,3,4,5,6,8,9,12,16,18,24,36,48,72 .....

10,206 = 1,2,3,6,7,9,14,18,21,27,42,54,63 .......

Common factors are 1,2,3,6,9,18

Therefore, HCF = 18

Hence, the required length of each piece is 18 inches.

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Yes, this shape belong in a group of shapes that have more than one perpendicular sides because its sides meet at a right angle.

In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles) as shown in the image (see attachment) attached below.

However, it should be noted that it is not all intersecting lines that are perpendicular to each other because the lines may intersect at different angles other than 90 degrees (90°).

By critically observing the geometric shape, we can reasonably infer and logically deduce that it has more than one perpendicular sides.

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Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15

x = arctan (8/15)

x = 28.1° (rounded)

Step-by-step explanation:

we know that

The x-intercepts are the values of x when the value of y is equal to zero

so

in this problem

x-intercepts are

(-5,0) and (5,0)

the y-intercepts are the values of y when the value of x is equal to zero

in this problem

y-intercept is (0,7)

Answer:

a = 1.125

is your compleate full answer

Answer:

the factorised form is 4(8a+9)

Answer: yes, they are congruent they are just rotated

Step-by-step explanation:

Given that the opposite sides of a parallelogram are congruent, a diagonal

of the parallelogram forms two congruent triangles.

The correct options to complete the proof are;

Reasons:

The completed two column proof is presented as follows;

Statement  \({}\)                                  Reason

1. ABCD is a parallelogram  \({}\)       1. Given

2. \(\overline{AB}\) ≅ \(\overline{DC}\) and \(\overline{BC}\) ≅ \(\overline{DA}\)  \({}\)      2. Opposite sides of a parallelogram

3. \(\overline{AC}\) ≅ \(\overline{CA}\)    \({}\)                             3. Reflexive property of congruency

4. ΔABC ≅ ΔCDA     \({}\)                   4. SSS

The correct options are therefore;

Opposite sides of a parallelogram; ABCD is a parallelogram

Reflexive property of congruency

SSS;

Reason 2. Opposite sides of a parallelogram, which is based on the

properties of a parallelogram and that ABCD is a parallelogram.

Reason 3. The reflexive property of congruency, states that a side is

congruent to itself.

Reason 4. SSS is an acronym for Side-Side-Side, which is a congruency

postulate that states that if the three sides of one triangle are equal to the

three sides of another triangle, then the two triangles are congruent.

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Answer:

360-137+x+y

Step-by-step explanation:

Answer:

12x + 50 =210

Step-by-step explanation:

Given the data on the world problem, we know that one of our terms will be 12x because it says "each month" in the problem. If his mom is going to give him 50 dollars, and the Jordans cost 210, then we can write  a simple equation.

x = number of months it will take him

\(12x+50=210\)

Answer: 5.8=x

Step-by-step explanation:

$210=Price

$12=Each Month

$50=From Mom

120-50=70

70/12=5.8 Months

Answer: x=+2

Step-by-step explanation:2x-6=12x-26

We move all terms to the left:

2x-6-(12x-26)=0

We get rid of parentheses

2x-12x+26-6=0

We add all the numbers together, and all the variables

-10x+20=0

We move all terms containing x to the left, all other terms to the right

-10x=-20

x=-20/-10

x=+2

The angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

In this question,

A normal vector to the plane is any vector that starts at a point in the plane and has a direction that is orthogonal (perpendicular) to the surface of the xy plane .

The magnitude of the xy plane, hypotenuse = 25 units

The x component of the xy plane, base = 12 units

Let θ be an angle, then the angle it makes with the positive x axis is

\(\theta = cos^{-1}(\frac{base}{hypotenuse} )\)

⇒ \(\theta = cos^{-1}(\frac{12}{25} )\)

⇒ \(\theta = cos^{-1}(0.48)\)

⇒ \(\theta = 61.3145\)

Hence we can conclude that the angle it makes with the positive x axis in the xy plane is 61.3145 degrees.

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Answer:

Step-by-step explanation:

When you multiply radicals together, the only rule that needs to be followed is that the index is the same on both. These are both square roots (so the index is a 2 on each radical) so we can multiply the radicals together to get 5√66.  That does not simplify at all and is irrational (since the decimal goes on without repeating)

The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.

If the probability of making a sale is 0.03 then the probability of not making a sale must be 1-0.03 which is 0.97.

So looking at contacting 100 prospects, you could say there are two general outcomes. Either the salesman makes no sales at all, or he makes at least one sale. There are no other possible outcomes, so the probability of those two outcomes must add up to 1.

So the probability of making of at least one sale is 1 minus the probability of making no sales.

The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.

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The Area of the Faces are:

Face A: 93.5 square inches

Face B: 93.5 square inches

Face C: 46.75 square inches

Face D: 46.75 square inches

Face E: 93.5 square inches

Face F: 93.5 square inches

Face A:

Since the dimensions of the base sheet are 8.5 inches by 11 inches, the area of Face A is:

Face A = 8.5 inches x 11 inches

= 93.5 square inches

Face B:

Since the dimensions of the whole sheet are 8.5 inches by 11 inches, the area of Face B is:

Face B = 8.5 inches x 11 inches

= 93.5 square inches

Face C:

Since the dimensions of the half sheet are 8.5 inches by 5.5 inches (half of 11 inches), the area of Face C is:

Face C = 8.5 inches x 5.5 inches

= 46.75 square inches

Face D:

It has the same dimensions as Face C, so the area is also:

Face D = 8.5 inches x 5.5 inches = 46.75 square inches

Face E:

They have the same dimensions as the whole sheet, so the area of Face E is:

Face E = 8.5 inches x 11 inches = 93.5 square inches

Face F: This is the top face of the prism, which is the same as Face B. So the area of Face F is also:

Face F = 8.5 inches x 11 inches = 93.5 square inches

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