Solve the system using elimination.


6x-y=6
3x-4y = -18

Answer:

-2 1/2 is the correct answer

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The probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

The given data is

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

(a) calculate mean value of x:

μ = E(x)

  = ∑(xi.P(xi))

 = 4.13

(b)  calculate variance of x:

σ² = ∑(xi - E(x))².P(xi)

   = 1.81331

(c)  calculate standard deviation of x:

σ = √σ²

σ = √1.831

σ = 1.3539

The likelihood that the quantity of systems sold will be within one standard deviation of the its mean:

P(μ  - σ < x < μ  + σ ) = P(4.13 - 13539 < x < 4.13 + 1.3539)

                                = P(2.7761 < x < 5.4839)

                                = P(x = 3) + P(x = 4) + P(x = 5)

                                = 0.13 + 0.30 + 0.31

                                = 0.74

Thus, the probability that now the number of sold will not deviate more than 1 standard deviation from the average is 0.74.

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The complete question is-

Suppose that for a given computer salesperson, the probability distribution of x = the number of systems sold in one month is given by the following table.

x 1 2 3 4 5 6 7 8

p(x) 0.04 0.10 0.13 0.30 0.31 0.10 0.01 0.01

What is the probability that the number of systems sold is within 1 standard deviation of its mean value?

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

The half-life period of a radioactive element is 7 days. The fraction of the radioactive element that disintegrates in 21 days is 0.406.

The half-life period of a radioactive element is 7 days.

Fraction of the sample will remain after 21 days:

The decay constant \(\lambda\) = \(\frac{0.693}{t_{1/2} }\)

= \(\frac{0.693}{7} = 0.099\)/ hour

t = 21 days

t = \(\frac{2.303}{\lambda} log\frac{a}{a-x}\)

21 = \(\frac{2.303}{0.099}log\frac{a}{a-x}\)

0.9028 = \(log\frac{a}{a-x}\)

2.466 = \(\frac{a}{a-x}\)

\(\frac{a-x}{a} =0.406\)

Hence,

The half-life period of a radioactive element is 7 days. The fraction of the radioactive element that disintegrates in 21 days is 0.406.

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Answer: the measures of the angles of polygon ABCD are equal to the measures of the corresponding angles of both translated images. this means that the angles of the polygon are preserved as the figure is translated in any direction

Answer:

The opposite sides of quadrilateral ABCD have equal slopes, which means the opposite sides are parallel. Therefore, by definition, quadrilateral ABCD is a parallelogram.

Plato

The warranty period is approximately 4.6 years (rounded to one decimal place).

The question tells us that replacement times are normally distributed with a mean of 7.7 years and a standard deviation of 1.8 years.

The company wants to offer a warranty that ensures only 4.4% of the DVD players are replaced before the warranty expires.

We want to know the length of this warranty period.

\(To find the warranty period, we will use the z-score formula.z=(x−μ)/σ\)

Here, x is the time length of the warranty, μ is the mean, and σ is the standard deviation.

We want to find x such that the area to the left of x on the standard normal distribution is 0.044 (since we want only 4.4% of DVD players to be replaced before the warranty expires).

Using a z-score table, we can find the z-score that corresponds to this area.

The z-score that corresponds to an area of 0.044 is approximately -1.75.

\(Now we can substitute the values we know into the formula and solve for x.-1.75=(x−7.7)/1.8\)

\(Solving for x:x=7.7−1.75(1.8)x=4.629\)

Therefore, the length of the warranty period that ensures only 4.4% of DVD players will be replaced before the warranty expires is approximately 4.6 years (rounded to one decimal place).

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This question was not properly written

Complete Question

Choose the letter of the correct answer Write the chosen letter on a separate sheet of

1. The measure of the volume of a rectangular solid is a²b - 63b²-9ab³? Find the dimensions of the

solid

A.(a + 3b). (a - 3b), and (ab + 7)

C. (a + 3b). (3a - 3b), and (ab + 3 )

B.(3a+ 3b). (a - 3b), and (ab + 7)

D. (a + 3b). (a-3b), and (ab + 3)

2. The floor plan for a rectangular building states that the length of the building is to be 8 meters more than

times its width. If the floor area is to be 256 square meters, what must be the length and width of the building?

A.6 meters long and 16 meters wide C. 8 meters long and 32 meters wide

B.30 meters long and 10 meters wide D. 32 meters long and 8 meters wide

3. The area of the dining room is 130 square units. If the width is 3 meter less than its length what is the weidin

of the room?

A. 10 units

B. 11 units

C 12 units

D. 13 units

4. One of the factors of 2b2 + 15b-50 is b +10. What is the other factor?

A.2b - 10

B. 2-5

C. 2b +5

D. 2b + 10

5. The area of the nachos is 15x² - 10x square centimeters. If the base is 5x centimeters, which is the length of

the height?

A. 3x - 2 cm.

B. 3x + 2 cm

C. 6x-4 cm

D. 6x + 4 cm

Answer:

1 A.(a + 3b). (a - 3b), and (ab + 7)

2 D. 32 meters long and 8 meters wide

3 A. 10 units

4 B. 2b -5

5. C. 6x - 4 cm

Step-by-step explanation:

Choose the letter of the correct answer Write the chosen letter on a separate sheet of

1. The measure of the volume of a rectangular solid is a²b - 63b²-9ab³? Find the dimensions of the

solid

We pick the options one after the other

A.(a + 3b). (a - 3b), and (ab + 7)

(a² -3ab + 3ab -9b²)(ab + 7)

(a² - 9b²) (ab + 7)

a²b - 9ab³ - 63b²

C. (a + 3b). (3a - 3b), and (ab + 7 )

(3a² - 3ab + 3ab -9b³)(ab + 3)

(3a² - 9b³)(ab + 3)

3a³b + 21ab² - 9b⁴a - 27b³

B.(3a+ 3b). (a - 3b), and (ab + 7)

(3a² - 9ab + 3ab - 9b²)(ab + 7)

(3a² - 6ab - 9b²)(ab + 7)

3a³b +21a² - 6a²b² + 42ab - 9ab³ - 63

D. (a + 3b). (a-3b), and (ab + 3)

(a² -3ab + 3ab - 9b²)(ab + 3)

(a² - 9b²) (ab + 3)

a³b + 3a² - 9ab³ - 27b²

Therefore, option A.(a + 3b). (a - 3b), and (ab + 7) is the correct option

2. The floor plan for a rectangular building states that the length of the building is to be 8 meters more than 3 times its width . If the floor area is to be 256 square meters, what must be the length and width of the building?

Area of a rectangle = Length × Width

Length of the building is to be 8 meters more than times its width.

= Length = 3W + 8

Area = 256m²

Hence:

256 =( 3W + 8 )× W

256 = 3W² + 8W

= 3W² + 8W - 256

Factorise

= 3W(W - 8) + 32(W - 8)

= (3W + 32) ( W - 8)

W - 8 = 0

W = Width = 8m

Length = 3W + 8

Length = 3(8) + 8

= 24 + 8

= 32m.

D. 32 meters long and 8 meters wide

3. The area of the dining room is 130 square units. If the width is 3 meter less than its length what is the width

of the room?

A. 10 units

B. 11 units

C 12 units

D. 13 units

Area = Length × Width

The width is 3 meter less than its length

W = L - 3

Area = 130 square units

Hence:

130 = L (L - 3)

130 = L² - 3L

L² - 3L - 130

= L² + 10L - 13L - 130

= L(L + 10) - 13(L + 10)

= (L - 13) (L + 10)

L - 13 = 0

L = Length = 13 units

L + 10 = 0

L = -10 units.

W = L - 3

L = 13 units

W = 13 - 3

W = 10 units

Therefore, the width of the room is 10 units

A. 10 units

4. One of the factors of 2b² + 15b-50 is b + 10. What is the other factor?

A.2b - 10

B. 2b -5

C. 2b +5

D. 2b + 10

2b² + 15b -50

One of the factors is b +10.

We factorise

2b² + 15b - 50

= 2b² + 20b - 5b - 50

= 2b(b + 10) - 5(b + 10)

= (2b - 5) (b + 10)

The other factor is 2b - 5

B. 2b -5

5. The area of the nachos is 15x² - 10x square centimeters. If the base is 5x centimeters, which is the length of

the height?

A. 3x - 2 cm.

B. 3x + 2 cm

C. 6x-4 cm

D. 6x + 4 cm

Nachos are triangular in shape

Area of a triangle = 1/2 × Base × height

A = 1/2 bh

A = bh/2

2A = bh

h = 2A/b

The area of the nachos is 15x - 10x square centimeters. If the base is 5x centimeters,

h = 2(15x² - 10x)/5x

h = 30x² - 20x/5x

h = 30x²/5x - 20x/5x

= 6x - 4 cm

the length of the height is:

C. 6x - 4 cm

Answer:

54 words per minute

Step-by-step explanation:

36/(2/3)

= (36/2)×3

= 18 ×3

= 54

The surface area of the rectangular pyramid is approximately 567.9 in².

What is rectangular pyramid?

A rectangular pyramid is a type of pyramid that has a rectangular base and four triangular faces that meet at a common vertex. The rectangular base of a rectangular pyramid can be any rectangle, meaning that the length and width can be different. The four triangular faces of a rectangular pyramid are congruent, which means they are the same size and shape. The height of the rectangular pyramid is the distance between the vertex and the center of the base. The surface area of a rectangular pyramid can be calculated by finding the area of each face and adding them together.

To find the surface area of the rectangular pyramid, we need to find the area of each face and add them together.

First, let's find the area of the rectangular base:

Area of base = length x width = 13 in x 17 in = 221 in²

Next, let's find the area of the larger triangular faces:

Area of each larger triangular face = (1/2) x base x height = (1/2) x 17 in x 11 in = 93.5 in²

Total area of both larger triangular faces = 2 x 93.5 in² = 187 in²

Finally, let's find the area of the smaller triangular face:

Area of smaller triangular face = (1/2) x base x height = (1/2) x 13 in x 12.3 in = 79.95 in²

Now, we can find the total surface area of the rectangular pyramid by adding the areas of all the faces:

Total surface area = area of base + area of both larger triangular faces + area of smaller triangular face

Total surface area = 221 in² + 187 in² + 79.95 in²

Total surface area = 488.95 in²

Therefore, the surface area of the rectangular pyramid is approximately 567.9 in².

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In a Venn diagram, we illustrate the relationships between sets a, b, and c, specifically the relationships a ⊂ b (a is a subset of b) and a ⊂ c (a is a subset of c).

A Venn diagram is a visual representation of sets using overlapping circles. In this case, we have three sets: a, b, and c. To illustrate the relationship a ⊂ b, we draw a circle representing set b and a smaller circle inside it representing set a. This indicates that every element in a is also an element of b, but b may contain additional elements that are not in a. The subset a is completely contained within set b. Similarly, to represent the relationship a ⊂ c, we draw a circle representing set c and a smaller circle inside it representing set a. This indicates that every element in a is also an element of c, but c may contain additional elements that are not in a. The subset a is completely contained within set c. By using the Venn diagram, we visually demonstrate the relationships between sets a, b, and c. The diagram clearly shows that a is a subset of both b and c, indicating that all elements of a are also elements of b and c. However, b and c may have additional elements that are not in a.

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The length of the ramp is approximately 20.433 feet.

To find the length of the ramp, we can use trigonometric functions.

Let's consider a right triangle formed by the ramp, the ground, and the vertical line from the top of the ramp to the ground. The length of the ramp is the hypotenuse of this triangle.

Given:

Height of the tailgate (opposite side) = 4.25 feet

Angle of inclination (angle opposite to the height) = 12 degrees

Using the sine function, we can write the following equation:

sin(12°) = opposite/hypotenuse

Rearranging the equation to solve for the hypotenuse, we get:

hypotenuse = opposite / sin(12°)

Substituting the values into the equation:

hypotenuse = 4.25 / sin(12°)

Using a calculator to compute the value of sin(12°) approximately as 0.208, we have:

hypotenuse = 4.25 / 0.208

Calculating the result, we find:

hypotenuse ≈ 20.433

Therefore, the length of the ramp is approximately 20.433 feet.

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Answer:

d Because I just took the test and got it right

Answer:

20 gallons.

Step-by-step explanation:

The given points (2, 44) and (5, 80) represent two points on the linear function that relates the total amount of water in the pool to the time since Jabari turns on the hose. We can use these points to find the equation of the function in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Using the two given points, we get:

m = (80 - 44) / (5 - 2)

m = 12

To find the y-intercept, we can use the point-slope form of the equation and substitute one of the given points, say (2, 44), for x and y, and the slope we just found for m:

y - y1 = m(x - x1)

y - 44 = 12(x - 2)

y - 44 = 12x - 24

y = 12x + 20

So the equation of the function that relates the total amount of water in the pool to the time since Jabari turns on the hose is:

y = 12x + 20

When Jabari turns on the hose, the time since he turns on the hose is 0 minutes. Substituting a = 0 into the equation we just found, we get:

y = 12(0) + 20

y = 20

Therefore, when Jabari turns on the hose, there is already 20 gallons of water in the pool.

Answer:

7.5 in

Step-by-step explanation:

Alejandro's current age is 17 years old.

Let's assume that Wilfredo's current age is 42 years. According to the given information, Wilfredo is 8 years older than twice Alejandro's age.

Let's represent Alejandro's age as 'x'. Therefore, twice Alejandro's age would be 2x. According to the information, Wilfredo is 8 years older than twice Alejandro's age, so we can form the equation:

42 = 2x + 8

To find the value of 'x', we can subtract 8 from both sides of the equation:

42 - 8 = 2x

34 = 2x

Next, we can divide both sides of the equation by 2 to solve for 'x':

34/2 = 2x/2

17 = x

Therefore, Alejandro's current age is 17 years old.

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Answer:

Area of the triangle = 12.92 cm²

Step-by-step explanation:

Area of a triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

From the figure attached,

Length of base of the triangle = 7.6 cm

Length of the height of the triangle = 3.4 cm

Area of the triangle = \(\frac{1}{2}(7.6)(3.4)\)

                                 = 12.92 square cm

Answer:

(0,0) and (2,12)

Step-by-step explanation:2x=8x-x^2

8x -2x -x^2 = 0

6x-x^2 =0 factor out common x

x(6-x)=0

x=0 or 6

y = 0 or 12

After 35 minutes there will be 40 bacteria remaining.

The process of a constant percentage rate decrease in an amount over time is referred to as "exponential decay." The formula to calculate exponential decay is given as, \(N_t=N_0\left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}\). Here, Nt is the quantity after time t, N0 is the initial quantity, t1/2 is the half-life, and t is time.

For the first situation, Nt=360, N0=900, t=10 minutes. Therefore, substituting the given values get the value of t1/2. So,

\(\begin{aligned}360&=900\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}} \\\frac{360}{900}&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\0.4&=\left(\frac{1}{2}\right)^{\frac{10}{t_{1/2}}}\\ \ln(0.4)&=\frac{10}{t_{1/2}}\ln(0.5)\\t_{1/2}&=10\times\frac{\ln(0.5)}{\ln(0.4)}\\&=7.6\end{aligned}\)

Now, for the second situation,  Nt=40.  We have to find the time at which there will be 40 bacteria remaining. Then,

\(\begin{aligned}40&=900\left(\frac{1}{2}\right)^{t/7.6}\\0.04&=\left(\frac{1}{2}\right)^{t/7.6}\\\ln(0.04)&=\frac{t}{7.6}\ln(0.5)\\t&=7.6\times\frac{\ln(0.04)}{\ln(0.5)}\\&=7.6\times4.64\\&=35.26\\&\approx35\end{aligned}\)

The answer is 35 minutes.

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Total surface area of cylinder is 303.34 \(cm^{2}\)

A cylinder is a 3D solid shape made up of two bases that are parallel and identical and are connected by a curved surface. These bases resemble spherical disks. The axis of the cylinder shape is a line drawn through the center or connecting the centers of two circular bases.

The surface area of a cylinder is

SA = \(2\pi r^{2}\) + 2πrh

where:

r = radius

h = height

This formula comes from adding the areas of the surfaces of the cylinder.  It has two flat circular faces and a rounded face.

If we cut the cylinder from the circular face symmetrically, the surface area for one piece will be

SA = 2[\(\frac{\pi r^{2} }{2}\)]  +  (\(\frac{2\pi r}{2}\))h  +  2rh

We will have 2-half flat circular faces, a flat rectangular surface, and half of the rounded surface.

Simplify the SA formula.

SA = \(\pi r^{2}\) + πrh + 2rh

SA = r(πr + πh + 2h)

Substitute the values into this formula.

SA = 3(3π + 8π + (2×8))

SA = 3(11π + 16)

SA = 33π + 48

SA = 151.67\(cm^{2}\)

Since we have 2 pieces, multiply this result by 2.

2(151.67\(cm^{2}\)) = 303.34\(cm^{2}\)

Total surface area is 303.34\(cm^{2}\)

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Answer:

B

Step-by-step explanation:

Hey There!

In order for two equations to be parallel they have to have the same slope

The only answer with equation that have the same slope is b

They both have a slope of 2

Hope this helps :)

Answer:

B.

Step-by-step explanation:

If two lines are parallel, that means that their slopes are the same.

If they're perpendicular, their slopes would be the negative reciprocal of the other.

For example, if line 1's slope was 5 and line 2 was parallel to it, that means that line 2's slope must be 5 as well. If line 3 was perpendicular to line 1, that meant that line 3's slope would be -1/5.

The best estimate of the number of raccoons in the area is approximately 71.

The best estimate of the number of raccoons in the area can be obtained using the mark and recapture method, also known as the Lincoln-Petersen index.

The formula for the Lincoln-Petersen index is:

Estimated population size = (Number of marked individuals in first sample * Total number of individuals in second sample) / Number of marked individuals recaptured in second sample

In this case, 16 raccoons were initially captured and tagged, and in the subsequent sample of 40 raccoons, 9 were found to be tagged.

Using the formula, the estimated population size would be:

Estimated population size = (16 * 40) / 9 = 71.11

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The solution to the initial value problem is y = -(4/3)x3 + (4/2)x2 + c

To solve this initial value problem, use the following steps:

Separate the variables:
y' = (x y - 4)2

Integrate with respect to x:
y' dx = (x y - 4)2 dx

Solve the integral:
y' dx =  (x3 y/3 - 4x2/2) + C

Substitute the initial value y(0) = 0 and solve for C:
0 =  (x3 y/3 - 4x2/2) + C
C = -4/2

Putting the constant back into the equation and solve for y:
=>y' dx =  (x3 y/3 - 4x2/2 - 4/2 )
=>y = -(4/3)x3 + (4/2)x2 + c Where c is an arbitrary constant.

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Answer:

A. -6 - 15 = - 21

Step-by-step explanation:

-3(x+8)=-21

open the bracket

-3x-24=-21

-3x=-21+24

-3x=3

x=-3/3

x=-1

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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Using the cosine law, the measure of angle R is calculated as approximately: a. 44.5°.

The cosine law is expressed as follows:

cos R = [s² + q² – r²]/2sq

Given the following side lengths of triangle QRS:

Side q = 11,

Side r = 17,

Side s = 23.

Plug in the values into the cosine law formula:

cos R = [23² + 11² – 17²]/2 * 23 * 11

cos R = 361/506

Cos R = 0.7134

R = cos^(-1)(0.7134)

R ≈ 44.5°

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