(1) Complete the number sequences.

(a) 0.4, 0.2, 0.6, 0.4, 1.2, 1.0, 3.0,

Answer:

32°F

Step-by-step explanation:

The temperature conversion formulae for degrees Fahrenheit(F) to degrees Celsius (C)

C = (F - 32) x 5/9

F = 9/5 x C + 32

Specifically, 0° C which is the freezing point of water is 32° F

For 0°C, F = 9/5 x 0 + 32 = 32°F

ANSWER

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Note: 100° C is the boiling point of water and converts to 212°F

The summation notation for the series is given as follows:

C. [tex]\sum_{i = 1}^{8} \frac{(-1)^i}{2i}[/tex]

The summation series for this problem is defined as follows:

-1/2 + 1/4 - 1/6 + ... - 1/16.

For the numerator, which is the top term of the fractions, we have that:

The sign of each term is controlled by the numerator, which is defined as follow:

(-1)^i.

For the denominator, we have that it is multiplied by two for each new term, starting at two, hence the rule is given as follows:

2i.

This means that the summation notation for the series is given as follows:

[tex]\sum_{i = 1}^{8} \frac{(-1)^i}{2i}[/tex]

Meaning that the correct option is given by option C.

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The total value of the annuity in 26 years is $93,678.57.

An ordinary annuity is when a series of payments is made over a particular period at the end of each period.

The formula that can be used to determine the future value of the annuity is:

Future value = Quarterly deposit x annuity factor

Annuity factor = (1 + r)^n] - 1} / r

Where:

Annuity factor = [{(1 + 0.0175)^(104)} - 1 ] / 0.0175 = 290.02652

Future value = 290.02652 x 323 = $93,678.57

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The Pythagorean theorem can be used to find the length of the third side of a triangle if the lengths of the other two sides are known. The formula for the Pythagorean theorem is: c^2 = a^2 + b^2, where c is the length of the third side, and a and b are the lengths of the other two sides.

3) 17

4) 32

The mass of an object that is experiencing a net force of 200 N and an acceleration of 500 m/s² is 0.4kg.

We know that, according to newton's second law of motion

F = m×a

here, F: force, m: mass of the object, a: acceleration

200 N = m × 500 m/s²

m = 200/500 kg = 2/5 kg

or m = 0.4 kg

Therefore, the mass of an object that is experiencing a net force of 200 N and an acceleration of 500 m/s² is 0.4kg.

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Answer: 9.2

Explanation: The value of the square root of 85 lies between the whole numbers 9 and 10.

Step-by-step explanation:

plsssssssssssssssssssssssssssssssssssssssssssssssssssssssdssssssssssssssssssssssssssssssssssssssssss do it don't be lazy.

The coordinates of the equation are (-2, -7), (-1, -5), (0, -3), (1, -1) and (2, 1)

The value of x and y in the given equation or in the graph is together represented by (x, y) and called coordinates.

Given is an equation, y = 2x-3

And we have x values = -2, -1, 0, 1 and 2, To find the corresponding value of y, we will use one by one the values of x in the equations,

When, x = -2,

y = -2(2) - 3

y = -7

(-2, -7)

When x = -1

y = 2(-1) - 3

y = -5

(-1, -5)

When x = 0

y = 2(0) - 3

y = -3

(0, -3)

When x = 1

y = 2(1)-3

y = -1

(1, -1)

When x = 2

y = 2(2) - 3

y = 1

(2, 1)

Hence, the value of y are -7, -5, -3, -1 and 1

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Answer:

To reflect, place points at

5, -2

2, -2

2, -5

5, -5

Step-by-step explanation:

If weekday is true and miles is less than 10, then the Boolean variable available is set to true.

Step 1: Check if weekday is true

Step 2: Check if miles is less than 10

Step 3: If both conditions are true, then set the Boolean variable available to true

Step 1: Check if weekday is true. This is done by checking if the Boolean variable weekday is set to true. If it is, then proceed to the next step.

Step 2: Check if miles is less than 10. This is done by using the integer variable miles and checking if it is less than 10. If it is, then proceed to the next step.

Step 3: If both conditions are true, then set the Boolean variable available to true. This is done by setting the Boolean variable available to true if the conditions from the previous steps are both true. If not, then the Boolean variable available is set to false.

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The equation of the line as shown in the image above is: y = 3x.

Using the slope-intercept form we can write the equation of a line as y = mx + b, where we have:

To find the equation, use two points on the line, (0, 0) and (-2, -6) to find the slope:

Slope (m) = change in y / change in x = (-6 - 0) / (-2 - 0)

Slope (m) = -6/-2

Slope (m) = 3

The y-intercept (b) = 0

Substitute b = 0 and m = 3 into y = mx + b:

y = 3x + 0

y = 3x

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7

it could be 7 because if you think about it, 4 can't go into 7 evenly.

so the proper way to solve this would be by finding how many times 4 can go into 7 evenly

4 can go into 7 once evenly

3 times 1 is 3

so you would have 4 left over

1 r4

Ratio of lawns to hours is 6:5

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Frank mows the lawn constantly 6/5 per hour

But Rate is also equal to number of lawns mowed in a certain amount of time.

Since ratio should always be in terms of simple whole numbers.

If 6/5 lawns are mowed in 1 hour, then,

6 lawns will be mowed in:6/6/5

=5 hours

therefore, 6 laws will be mowed in 5 hours.

Hence, Ratio of lawns to hours is 6:5

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Answer:

Step-by-st(3 + x^3 + 3x^2) + (2x^3 - 2 - 4x^2)

= 3x^3 + x^2 + 3x^2 - 2 - 4x^2

= 3x^3 - x^2 - 2

So the final answer is 3x^3 - x^2 - 2ep explanation:

Answer:

a) y = 2,035(1.03)^t

b) 2,359

Step-by-step explanation:

a)

Exponential growth:

y = a(1 + r)^t

where

y = future vale

a = initial value

r = periodic rate of growth

t = number of periods

y = 2,035(1 + 0.03)^t

y = 2,035(1.03)^t

b)

Here we have a = 2,035; r = 3% = 0.03; t = 5

y = 2,035(1 + 0.03)^5

y = 2,359

2,359

Answer: C’(3,-4)

Step-by-step explanation: All you have to do is count how many blocks away is the point from the x axis and then count down the x axis where you stop counting and that is how you get your point.

In 8 1/2 hours, the candle would burn  6 3/8 inches.

A mixed number is a non-integer that is made up of a whole number and a proper fraction. An example of a mixed number is 8 1/4.

The first step is to determine how much of the candle burns in one hour.

Inches of candle that burns in 1 hour = 8 1/4 ÷ 11

33/4 x 1/11 = 3/4 inches

Now, multiply the inches of candle that burns in an hour by 8 1/2

Inches of candle that would burn in 8 1/2 hours = 3/4 x 8 1/2

3/4 x 17/2 = 51/8 = 6 3/8 inches

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For any real number c, it is calculated that √(c²) is; Option D: c

The set of real numbers is defined as the union of the set of Irrational numbers and the set of rational numbers.

Now, we are given the equation as;

√(c²)

Now, from definition of real numbers, it means that they are not imaginary and as such any value of c remains the same. Thus, we have;

√(c²) = c

Now, because c is not classified as an absolute value, and even if since it is square, will be surely positive and as such the final answer for every real number c in the square root will be c.

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Answer:

w = 3

Step-by-step explanation:

The total area of the shape is 129 square feet.

A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.

In the given diagram, there are two shapes,

One is rectangle whose sides are 16 feet and 5 feet.

And other is square whose side is 7 feet.

Since, the area of rectangle = length x width = 16 x 5 = 80 square feet.

And area of square = (side)² = (7)² = 49 square feet.

Total area of shape = area of rectangle + area of square

= 80 + 49

= 129 square feet.

The total area of the shape is 129 square feet.

Hence, the total area of the shape is 129 square feet.

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The pounds of expensive jelly beans that Mike should use, given the amount he wants to sell the mixture, is 30 pounds.

The total weight of the mixture is x + 10 pounds because Mike adding 10 pounds of the cheaper jelly beans while the cost of the expensive jelly beans would be:

= 5 x number of pounds

= 5x

The total cost of the cheaper jelly beans is :

= 10 pounds x 2

= $ 20

The total revenue from the mixture is therefore:

= 4.25x + 42.5

The total cost is :

= 5x + 20

Equating these would find the pounds of expensive jelly beans needed :

5x + 20 = 4.25x + 42.5

0.75x = 22.5

x = 30

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The number line graph for this inequality's resolution. 5/8z>5/6 is z > 4/3. Draw a rightward-pointing arrow and an open circle on 4/3.

Finding z ⇒ 5/8z > 5/6 ⇒ 8/5 z > 40/30 z > 4/3 multiplied by both sides. Create an open circle on 4/3 and a rightward pointing arrow. The values that an inequality represents can be seen when we plot inequality on a number line. By drawing a straight line and designating the end points with either an open circle or a closed circle, we can depict inequalities on a number line by illustrating the range of integers.

The collection of points that represents all possible solutions to a two-variable inequality is called its graph. The coordinate plane is split in half by a boundary line created by a linear inequality, with one half representing the solutions to the inequality.

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The particle increases its velocity in the following three subintervals:

In this question we find the case of the position of a particle (x) in versus time (t), whose graph is shown below. The velocity associated to a given time t is represented by the slope of the line tangent to that point. The velocity of a particle increases when the signs of function position and function velocity are the same.

By secant line formula, velocity can be approximated by this formula:

v ≈ Δx / Δt

Since time is a non-negative real number, the sign of velocity is derived by the following rules:

Then, the velocity of the particle increases in the following two cases:

The velocity is increasing in the following subinterval 0 < t < 2, 4 < t < 7 and 9 < t < 10.

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1) The investment's balance (future value) after 15 years, assuming no further deposits or withdrawals, for the first account modeled by the equationy=5000⋅1.05^x, is $10,395.

2) Assuming no other deposits or withdrawals occurred, the initial investment (present value) for the second account modeled by the equation 3257.79=p⋅1.05^10 is $2,000.

The future value is the present value or periodic investments compounded at an interest rate.

The future value can be computed using an online finance calculator or the FV factor.

The present value is the future value or periodic inflows discounted at an interest rate.

Similarly, the present value can be computed using an online finance calculator or the PV factor.

Equation 1: y=5000⋅1.05^x

Initial investment = $5,000

Annual interest rate = 5%

Investment period = 15 years

Future value factor for 15 years at 5% = 2.079

N (# of periods) = 15 years

I/Y (Interest per year) = 5%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

FV = $10,395 ($5,000 x 2.079)

Total Interest = $5,395

Equation 2: 3257.79=p⋅1.05^10:

Future value = $3,257.79

Annual interest rate = 5%

Investment period = 10 years

Present value factor for 10 years at 5% = 0.641

N (# of periods) = 10 years

I/Y (Interest per year) = 5%

PMT (Periodic Payment) = $0

FV (Future Value) = $3,257.79

Results:

PV (Present Value) = $2,000 ($3,257.79 x 0.641)

Total Interest = $1,257.79

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Step-by-step explanation:

to solve this problem we use the growth exponential formula: A=P(1+r%)^t

3000×(1+(r/100))^39=6000

by dividing both sides by 3000

(1+(r/100))^39=2

1+r/100=2^(1/39)

r/100=2^(1/39)-1

r=100(-1+2^(1/39))

r=1.79318

by multiplying by 1,000,000

r=1,793,18 approximately

The answer choice which represents why the given expression is a non-example of a polynomial as required is; The expression has a variable raised to a fraction.

It follows from the task content that the underlying reason why the given expression is not a fraction be identified.

Recall that an expression is termed a polynomial expression when the powers of variables in such expression are integers.

On this note; since the term; -35x^⅓y² has a variable raised to a fraction, it follows that the given expression is not a polynomial.

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Answer:

Step-by-step explanation:

graphs above x-axis are positive and below are negative.

(b). A(+), B(+), C(-),D (-)

A=(3-0)/(1-0)=3

B=(1-0)/(2-0)=1/2

C=(-6-0)/(1-0)=-6

D=(-1-0)/(4-0)=-1/4

(c). 3>1/2>-1/4>-1/6

so 3 is greatest value.

The inequality that represents the graph will be y ≤ -(3/4)x + 2.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The line is passing through points (0, 2) and (4, -1). Then the equation of the line is given as,

(y - 2) = [(- 1 - 2) / (4 - 0)](x - 0)

y - 2 = -(3/4)x

y = -(3/4)x + 2

The region below the line and points on the line is considered. Then the linear inequality is written as,

y ≤ -(3/4)x + 2

The inequality that represents the graph will be y ≤ -(3/4)x + 2.

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Answer:  3.0625

Step-by-step explanation:  math :}

Answer:

Step-by-step explanation:

25% = 25/100 = 0.25

Then:

Bounce 1:

160 - (160*0.25) = 160 - 40 = 120

Bounce 2:

120 - (120*0.25) = 120 - 30 = 90

Bounce 3:

90 - (90*0.25) = 90 - 22.5 = 67.5

Bounce 4:

67.5 - (67.5*0.25) = 67.5 - 16.875 = 50.625

The coordinates of the focus of the parabola is calculated as; (0, 2).

We are told that the shape of a satellite dish can be described as parabolic. This is due to the fact that radio waves are reflected from the surface of the dish and received into the focus.

The path of the object shown in a plane curve generated by a moving point is called a parabola.

The general equation of a parabola is;

x² = 4ay

Where a is the focus of the parabola.

The given equation of the parabola is;

x² = 8y

The coordinate of the focus of the parabola is of the form; (0, a).

Comparing both equations, we have that the focus of the parabola is;

4a = 8

a = 8/4

a = 2

Hence, we conclude that the coordinate of the focus of the parabola is (0, 2).

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