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The laptop will be worth $0.001286 after 15 years if its worth becomes 1/3 each year.

We can solve this problem by using the formula for geometric sequences,

an = a₁r^(n-1), here in this case, an is the worth of the laptop after n years, r is the rate at which the worth is changing that 1/3 in this case and a₁ is the value of the laptop currently. Substituting the given values, we get:

a₁₅ = 600(1/3)¹⁵⁻¹

a₁₅ = 600(1/3)¹⁴

a₁₅ = 600x0.0000021433

a₁₅ = 0.001286

Therefore, after 15 years, the laptop is worth approximately $0.001286.

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Answer:

Solution,

Cost of one television=£196.50

cost of 31 televisions:

\( = 196.50 \times 31 \\ = 6091.5\)

Cost of one DVD player=£50.99

Cost of 19 DVD player:

\( = 50.99 \times 19 \\ = 968.81\)

Now,

Total cost

= cost of 31 televisions + cost of 19 DVD player

=6091.5+968.81

=£7060.31

Hope this helps...

Good luck on your assignment..

Answer:

Step-by-step explanation:

cost of 31 televisions.

\(196.50 \times 31 \\ = 6091.5 0\\ \)

cost of 19 DVD players

\(50.99 \times 19 \\ = 968.81 \\ \)

Now let's find the total cost

\(6091.50 + 968.81 \\ = 7060.31\)

a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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Complement of set A is the set of all elements in the universal set that are not in the set .

If there is a subset of the universal set (U) called A, then the complement of set A, denoted by the symbol A', is different from the elements of set A and contains the elements of the universal set but not the elements of set A.

In this case, A' = x U: x A.

In other words, the complement of a set A is the difference between the universal set and set A.

For example: U = {1, 2, 3, 5, 7, 9, 15 ,14, 13}, A = {1, 2, 3, 5,7,9}, find the complement of A.

A' = U - A = {1, 2, 3, 5, 7, 9, 15,14,13} - {1, 2, 3, 5,7,9} = {15,14, 13}

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolised by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

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Answer:

$2

Step-by-step explanation:

if you divide 10 by 5 you get 2

Answer:

Each vase would cost 2$. 10 divided by 5 is 2 therefore each vase is 2$.

Step-by-step explanation:

Answer:

the like terms were not grouped together.

Answer:

First, we can simplify the left side of the equation by distributing 1/4:

1/4 (x - 2/5) = 1/4 x - 1/5

Now the equation becomes:

1/4 x - 1/5 = -1 1/2

We can convert the mixed number on the right side to an improper fraction:

-1 1/2 = -3/2

Adding 1/5 to both sides, we get:

1/4 x = -3/2 + 1/5

Combining the fractions on the right side:

1/4 x = -13/10

Multiplying both sides by 4:

x = -13/10 * 4 = -26/5

We can convert this to a mixed number in simplest form by dividing the numerator by the denominator:

x = -5 1/5

The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

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The group of volunteers can make a total of 200 masks out of 25 yards of fabric.

To calculate the number of masks that can be made, we divide the total amount of fabric (25 yards) by the amount of fabric required per mask (1/8 yard). To do this, we first convert the fraction 1/8 to decimal form, which is 0.125. Then, we divide the total fabric (25 yards) by the fabric required per mask (0.125 yards). This can be done by dividing 25 by 0.125, which equals 200. Therefore, the group of volunteers can make a total of 200 masks out of 25 yards of fabric. Each mask requires 1/8 yard of fabric, so dividing the total fabric by the fabric required per mask gives us the total number of masks that can be made.

Calculation steps:
1. Convert the fraction 1/8 to decimal form: 1/8 = 0.125.
2. Divide the total fabric (25 yards) by the fabric required per mask (0.125 yards):
  25 / 0.125 = 200.


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Answer:

It should be 2

Step-by-step explanation:

I searched it up

The value of the g(f(-5)) is -1 f(x)=2x+7 and g(x)= x^2-4/2x+1 then g(f(-5)) option (c) is correct.

It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) = 2x+7  and

\(\rm g(x) = \frac{x^2-4}{2x+1}\)

First calculating f(-5)

f(-5) = 2(-5) + 7 = -3

Putting x = -3 in the g(x)

\(\rm g(-3) = \frac{-3^2-4}{2(-3)+1}\)

g(-3) = 5/(-5)

g(-3) = -1

Thus, the value of the g(f(-5)) is -1 f(x)=2x+7 and g(x)= x^2-4/2x+1 then g(f(-5)) option (c) is correct.

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The derivative dz/dt can be found by applying the chain rule. Let's first substitute the given expressions for x and y into the equation for z:

z = (x + y)e^y

z = (3t + 1 - t^2)e^(1 - t^2)

Now, we can differentiate z with respect to t using the chain rule. The chain rule states that if u = f(g(t)), then du/dt = f'(g(t)) * g'(t).

Applying the chain rule to the given equation, we have:

dz/dt = d((3t + 1 - t^2)e^(1 - t^2))/dt

To differentiate this expression, we need to consider the derivative of each term. Let's break it down:

1. The derivative of 3t with respect to t is simply 3.

2. The derivative of 1 with respect to t is 0 since it is a constant.

3. The derivative of -t^2 with respect to t is -2t.

4. The derivative of e^(1 - t^2) with respect to t can be found using the chain rule again.

For the fourth term, let's define u = 1 - t^2. The derivative of u with respect to t is du/dt = -2t. Now, we have:

dz/dt = (3 + 0 - 2t)e^(1 - t^2) + (3t + 1 - t^2)d(e^(1 - t^2))/dt

Using the chain rule once more, we differentiate e^(1 - t^2) with respect to u:

d(e^(1 - t^2))/du = e^(1 - t^2) * d(1 - t^2)/dt

The derivative of 1 - t^2 with respect to t is -2t. Substituting this back into our expression, we get:

dz/dt = (3 + 0 - 2t)e^(1 - t^2) + (3t + 1 - t^2)(-2t)e^(1 - t^2)

Simplifying the expression, we have:

dz/dt = (3 - 2t)e^(1 - t^2) - 2t(3t + 1 - t^2)e^(1 - t^2)

Therefore, the derivative dz/dt is given by (3 - 2t)e^(1 - t^2) - 2t(3t + 1 - t^2)e^(1 - t^2), where e represents the exponential function.

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Other things being equal, the width of a confidence interval gets smaller as the sample size increases.

The width of a confidence interval gets smaller as:

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I believe that it is 31.4, but please correct me if I'm wrong.

The required area of the sculpture that is shaped like a circle is \(78.5m^{2}\).

Given that,

Jessie designed a sculpture that is shaped like a circle,

The circumference of the sculpture is 10π meters.

We have to determine,

Which measurement is closest to the area of the sculpture in square meters.

According to the question,

Circumference of the circle = \(2\pi r\)

Where, circumference = \(10\pi\)

Then,

\(10\pi =2\pi r \\\\r = \dfrac{10\pi }{2\pi }\\\\r = 5m\)

Therefore,

Jessie designed a sculpture that is shaped like a circle.

Area of the circle = \(\pi r^{2}\)

Where, r = 5m

Then,

Area of the circle is given by,

\(= \pi r ^{2}\\\\= 3.14 \times (5)^{2}\\\\= 3.14 \times 25\\\\= 78.5m^{2}\)

Hence, The required area of the sculpture that is shaped like a circle is \(78.5m^{2}\).

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Answer:

the third one

Step-by-step explanation:

a linear function is information that is increasing or decreasing at a steady rate, in that specific set of data their decreasing at a rate of 2

Answer:

W = x^2 - 2yz / - w

0 = x^2 - 2yz - w / +2yz

2yz = x^2 - w // 2z

y = (x^2 -w ) / 2z

So correct answer is D

Answer:

Everything is being timesed by 6 So 6/1?

Step-by-step explanation:

Supervisor can choose 6435 different such 8 people committees from 15 call center agents.

We know that we can choose ' r ' number elements or persons from ' n ' number of elements or persons respectively in C(n, r) ways if we do not replace once chosen elements.

Here the total number of staff of call center agent is = 15

So n = 15.

And supervisor of the call center has to choose 8 agents from that group of 15 agents.

So, here r = 8.

Here as supervisor chooses a person he or she cannot be selected as two people.

So the event is without replacement.

Thus by the combination formula, the number of different such committees can be chosen by supervisor is = C(15, 8) = 6435.

Hence, supervisor can choose 6435 different such 8 people committees from 15 call center agents.

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The percent of students scored between 460 and 480 is 19%. The Option B.

To get percentage of students who scored between 460 and 480, we need to calculate z-scores for these values and then find the corresponding area under the normal distribution curve.

We will calculate the z-score for 460:

z = (x - μ) / σ

z = (460-450)/35

z = 10/35

z = .2857

P(z < .2857) = 0.6124

P(z < .2857) 61.24%

We will calculate the z-score for 480:

z = (480-450)/35

z = 30/35

z = .8571  

P(z < .8571) = .8040

P(z < .8571) 80.40%

The difference between the scores is:

= 80.40% - 61.24%

= 19.16%

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Gerard concluded that triangle with given sides cannot be used as  building-frame support because it is not right triangle, he come to this conclusion because the Pythagoras-theorem is not satisfied.

In order to check if a triangle is "right-triangle", Gerard used the Pythagorean theorem. According to this theorem, in right triangle, the square of length of hypotenuse (the side opposite the right angle) is equal to sum of squares of other two sides,

So, the squares of the given sides are :

Square of √95 feet = (√95)² = 95 feet

Square of 8 feet = 8² = 64 feet

Square of √150 feet = (√150)² = 150 feet

We see that, 95 feet + 64 feet = 159 feet ≠ 150 feet,

Since the square of the longest side (√150) is not equal to the sum of the squares of the other two sides (√95 and 8), the Pythagorean-theorem is not satisfied.

Therefore, Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 feet is not a right triangle.

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The given question is incomplete, the complete question is

Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 cannot be used as a building frame support on the house because it is not a right triangle. How did Gerard come to that conclusion? explain.

The roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987

Quadratic equations are equations that have a second degree and have the standard form of ax^2 + bx + c = 0, where a, b and c are constants and the variable a does not equal 0

The equation of the function is given as:

f(x) = x^2 - 93987

The above equation is a quadratic equation

Express the equation as a difference of two squares

f(x) = (x - √93987)(x + √93987)

Set the equation of the function to 0

(x - √93987)(x + √93987) = 0

Split the factors of the above function equation as follows

x - √93987 = 0 and x + √93987 = 0

Solve for x in the above equations

x = √93987 and x = -√93987

Hence, the roots of the equation f(x) = x^2 - 93987 are x = √93987 and x = -√93987

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Answer:

Step-by-step explanation:

1. (3/4)^2 = 3/4 * 3/4

2. numerator * numerator so 3 * 3 = 9

3. denominator * denominator so 4 * 4 = 16

Hence, the answer is 9/16

Step-by-step explanation:

(3/4)² = 3²/4² = 9/16

(a×b×c×d×...×z)² = a²×b²×c²×d²×...×z²

Answer:

21 pencils for Nick and 63 pencils for Lance

Step-by-step explanation:

Now let's make an equation out of the information above:

3x + x = 84

Now solve for x.

3x + x = 84

4x = 84

x = 84/4

x = 21

So Nick has 21 pencils

Now for Lance:

3x

3 * (21) = 63

So Lance has 63 pencils

63 + 21 = 84 pencils

Answer:

Nonlinear.

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

We notice that if the line is linear, x will NOT go over a degree of 1.

x² is a quadratic function, and its slope is not proportional like a linear line.

Answer:

  Any of {412, 523, 634, 745, 856, 967, 1078, 1189}

Step-by-step explanation:

Relations are given between the number of 10-clip boxes, the number of 100-clip boxes, and the number left over. We assume there are at least one of each size box, and that there are fewer than 10 clips left over. (10 could be put into another box.)

__

Let h represent the number of 100-clip boxes. Then h-3 is the number of 10-clip boxes, and h-2 is the number of clips left over. The total number of paperclips is ...

  10(h -3) +100h +(h -2) = 111h -32

In addition, we require ...

  h -3 > 0 and h-2 < 10

  3 < h < 12 . . . . . . . rearranging these inequalities

So, Brian could have 111h -32 paper clips, where 3 < h < 12. That could be any of {412, 523, 634, 745, 856, 967, 1078, 1189} paper clips.

The equation representing the relationship between dy/dt and dx/dt that is rate at which the length of the woman's shadow is changing is equal to option C. dy/dt =4× (dx/dt).

Woman is walking towards the street lamp.

Rate at which the length of her shadow is changing as she walks.

Let us consider the height of the street lamp as h = 20 feet.

Height of the woman be w = 5 feet.

And the distance between the woman and the street lamp be x.

Length of the woman's shadow be y.

Triangles formed by the woman, the street lamp, and their shadows are similar.

Sides of similar triangles are in proportion,

This implies,

h / y = (h + w) / (x + y)

Solving for y we get,

⇒h(x + y) = y(h + w)

⇒hx + hy = hy + wy

⇒y = hx / w

Rate at which the length of the woman's shadow is changing by differentiating both sides of this equation with respect to time,

⇒ dy/dt = h(dx/dt) / w

Substitute in the values for dx/dt = 3 ft/s, h and w we get,

⇒dy/dt = (20)(3) / 5

⇒dy/dt = 60 /5

⇒dy/dt =12

⇒dy/dt = 4(3)

⇒dy/dt =4× (dx/dt)

Therefore, the rate at which the length of the woman's shadow is changing is given by option C. dy/dt =4× (dx/dt) .

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Answer:

8 ounces of honey

Step-by-step explanation: