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Answer:

Step-by-step explanation:

To find the total distance traveled in the first second, we need to find the distance traveled during the first half-second and then double it.

The particle starts 2 cm to the right of 0, so its position function is given by:

s(t) = t - t^2 + 2

The distance traveled by the particle during the first half-second (from t = 0 to t = 0.5) is given by:

distance = |s(0.5) - s(0)|

We have:

s(0.5) = 0.5 - (0.5)^2 + 2 = 2.25 cm

s(0) = 0 - 0^2 + 2 = 2 cm

So, the distance traveled during the first half-second is:

|2.25 - 2| = 0.25 cm

To find the total distance traveled in the first second, we double this distance:

total distance = 2 * 0.25 = 0.5 cm

Therefore, the total distance traveled in the first second is 0.5 cm.

The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

A Z-score is a statistical measurement that indicates how many standard deviations a data point is from the mean of a distribution.

It is calculated by subtracting the mean of the distribution from the data point and then dividing the result by the standard deviation of the distribution.

Here we have

The cumulative area is 0.3897

Using the standard normal table, we can find the z-score that corresponds to a cumulative area of 0.3897 as follows:

1. Locate the entry in the body of the table that is closest to 0.3897. In this case, the closest entry is 0.3897 in the body of the table.

2. Identify the corresponding row and column headers for this entry. The row header is 0.0 and the column header is 0.08.

3. The z-score that corresponds to the area of 0.3897 is the value at the intersection of the row and column headers. In this case, the value is 0.25.

Therefore,

The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

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Parabola intersects x-axis at two points: (-5,0) and (-4,0)

What does a parabola actually mean?

Each point on a parabola with a U-shape is equally spaced from both the focus, a fixed point, and the directrix, a fixed line. As the topic of conic sections depends heavily on the parabola, all of the parabola-related concepts are covered here.

The x-intercepts of a parabola are where the parabola intersects the x-axis on its graph. There are a number of ways to find the x-intercepts of a parabola, and each one is usually specific to each situation.

In the case, when you are given the graph, the easiest way to find x-intercepts is to identify points at which parabola intersects the x-axis.

From your graph, parabola intersects x-axis at two points: (-5,0) and (-4,0)

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A ratio that can be used to determine the slope of this line include the following: D. [tex]\frac{7\;+\;2}{-5\;+\;-8}[/tex]

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (7 - (-2))/(-5 - 8)

Slope (m) = (7 + 2)/(-5 - 8) ⇒ (Required ratio)

Slope (m) = 9/-13

Slope (m) = -0.6923.

In this context, we can reasonably infer and logically deduce that the slope of this line is equal to -9/13 or -0.6923.

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The value of the variable x for the similar triangles is equal to 25

The triangles BDR and QDC are similar, this implies that the length DC of the smaller triangle is similar to the length DR of the larger triangle

and the length DQ of the smaller triangle is similar to the length DB of the larger triangle

so;

x/(15 + x) = 40/64

64x = 40(15 + x) {cross multiplication}

64x = 600 + 40x

64x - 40x = 600 {subtract 40x from both sides}

24x = 600

x = 600/24

x = 25

Therefore, the value of the variable x for the similar triangles is equal to 25

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The value of the expression 34 - 9 x 2 is 16.

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. These rules help to ensure that mathematical expressions are evaluated correctly and consistently. The order of operations is typically summarized by the acronym PEMDAS, which stands for:

Parentheses: Perform operations inside parentheses first.

Exponents: Evaluate exponents (powers and square roots, etc.) next.

Multiplication and Division: Perform multiplication and division, from left to right.

Addition and Subtraction: Perform addition and subtraction, from left to right.

In the given questions,

In this case, there are no parentheses or exponents, so we move on to multiplication before subtraction.

We perform the multiplication first, following the rule of performing multiplication before addition or subtraction.

9 x 2 = 18

Then, we subtract the result from 34:

34 - 18 = 16

Therefore, the value of the expression 34 - 9 x 2 is 16.

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Answer: A.   -2√7

Step-by-step explanation:

3√7 - 5√7

= -2√7

The polynomial function f(x) which produced the graph shown is f(x) = -6(x - 1/2)²(x + 1)²(x - 2).

In Mathematics and Geometry, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

By critically observing the graph of the polynomial function shown above, we can logically deduce that its x-intercepts include the following;

x = -1 ⇒ x + 1 = 0.

x = 2 ⇒ x - 2 = 0.

Also, the graph has a zero of multiplicity 2 at x = 1/2;

x = 1/2 ⇒ x - 1/2 = 0.

(x - 1/2)²

In this context, an equation that represent the polynomial function is given by:

f(x) = a(x - 1/2)²(x + 1)²(x - 2)

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 3), we have;

3 = a(0 - 1/2)²(0 + 1)²(0 - 2)

3 = a(1/4)(-2)

3 = -a/2

a = -6.

Therefore, the required polynomial function is given by:

f(x) = -6(x - 1/2)²(x + 1)²(x - 2)

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Answer:

X is 4.

Step-by-step explanation:

Hope this helps!

Answer:

To determine the lowest amount that agent C could have earned in 2014, we need to know the number of tanks that agent C sold in 2014 and the commission rate per tank.

Let's assume that the commission rate per tank for agent C is R x. We need to find the lowest value of R that would result in the agent earning a minimum commission of R713.76 per tank.

We know that the commission earned per tank is the product of the commission rate and the selling price of the tank. Let's assume that the selling price of each tank is SP.

So, the commission earned per tank is R x SP.

We also know that the minimum commission per tank is R713.76. Therefore,

R x SP >= R713.76

Solving for R, we get:

R >= R713.76 / SP

This means that the commission rate per tank must be at least R713.76 / SP in order for the agent to earn a minimum commission of R713.76 per tank.

Now, let's assume that agent C sold a total of T tanks in 2014. The total commission earned by agent C in 2014 would be:

Total Commission = R x SP x T

From the above equation, we can see that the total commission earned by agent C depends on the commission rate per tank, the selling price per tank, and the number of tanks sold.

To find the lowest amount that agent C could have earned in 2014, we need to minimize the total commission earned by agent C subject to the constraint that the commission rate per tank is at least R713.76 / SP.

Assuming that the selling price per tank is fixed, the lowest amount that agent C could have earned in 2014 would be when the commission rate per tank is equal to R713.76 / SP. In this case, the total commission earned by agent C would be:

Total Commission = R713.76 x T

Therefore, the lowest amount that agent C could have earned in 2014 is R713.76 x T, where T is the number of tanks sold by agent C in 2014.

First, let's simplify the expression (4c + 8) + 3c - 2:

(4c + 8) + 3c - 2

= 4c + 3c + 8 - 2 (rearrange terms)

= 7c + 6 (combine like terms)

So the first expression simplifies to 7c + 6.

Next, let's simplify the expression 4c + 2(0.5c + 1):

4c + 2(0.5c + 1)

= 4c + 2(0.5c) + 2(1) (distribute the 2)

= 4c + c + 2 (simplify the parenthesis)

= 5c + 2 (combine like terms)

So the second expression simplifies to 5c + 2.

Now we can compare the two expressions:

7c + 6 vs. 5c + 2

These expressions are not equivalent because they do not have the same coefficients or constants.

Answer: Ace has 8 apples Christi has 4 and Pudge has 24

Step-by-step explanation:

Ace has 2 twice as much as Christi has, and 4 x 2 is 8. Pudge has 3 times more than Ace has and 8 x 3 is 24. Pudge has 12 more than Christi and Ace combined. 8 + 4 = 12. 12 + 12 = 24. I hope I explained it right.

Answer:

To calculate the payback period (PBP) for this project, we need to determine how long it will take for the initial cash outlay of $40,000 to be recovered from the after-tax cash flows.

Year 1 cash flow = $10,000

Year 2 cash flow = $12,000

Year 3 cash flow = $15,000

Year 4 cash flow = $10,000

Year 5 cash flow = $7,000

Total cash inflows for year 1 and year 2 = $10,000 + $12,000 = $22,000

Total cash inflows for year 3 = $15,000

Total cash inflows for year 4 = $10,000

Total cash inflows for year 5 = $7,000

Cumulative cash inflows for year 1 and year 2 = $22,000

Cumulative cash inflows for year 3 = $37,000

Cumulative cash inflows for year 4 = $47,000

Cumulative cash inflows for year 5 = $54,000

It can be seen that the cumulative cash inflows reach the initial cash outlay of $40,000 after year 2, and therefore the payback period for this project is 2 years. Since the payback period is less than the maximum PBP of 3.5 years set by management, this project can be considered acceptable.

So, Hodgman Honest should recommend that Basket Wonders should accept this project as it has a payback period of only 2 years, which is less than the maximum PBP of 3.5 years set by management.

Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

In mathematics, reflection is a transformation that flips a figure over a line called the line of reflection. This line acts like a mirror, reflecting the original figure onto the opposite side of the line.

Reflections, rotations, and translations are all transformations that change the position and/or orientation of a geometric figure.

Reflections (also known as flips) change the orientation of a figure by flipping it across a line of reflection, which acts like a mirror.

Rotations change the orientation of a figure by rotating it around a fixed point. The figure stays the same shape and size, but its position and orientation in space changes.

Translations (also known as slides) change the position of a figure by sliding it along a straight line without changing its orientation or shape.

All of these transformations are important in geometry and other fields, such as physics and computer graphics, and can be used to describe the motion and properties of geometric objects.

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Answer:

12.29 I thin

Step-by-step explanation:

The monthly periodic interest rate is 0.01%.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

APR=14.75%

Now,

The monthly periodic interest rate is the annual interest rate divided by 12 months. According to 1, the formula is:

r = (1 + i/m)^(m/n) - 1

Where:

r = periodic interest rate

i = nominal annual rate

m = number of compounding periods per year

n = number of payments per year

In this case, i = 14.75%, m = 12 and n = 12. Plugging these values into the formula, we get:

r = (1 + 0.1475/12)^(12/12) - 1

r = (1 + 0.012292) - 1

r = 0.012292 or 1.23%

Therefore, by the given APR the interest rate will be 0.01%, rounded to the nearest hundredth of a percent.

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Answer: the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.

Step-by-step explanation:

Let's assume that there are 100 people in the focus group. Then, the number of males in the focus group is 47 and the number of females is 53.

Out of 47 males, 40% said they would buy the fruit drink, which is 0.4 x 47 = 18.8 males (rounded to the nearest whole number). Out of 53 females, 54% said they would buy the fruit drink, which is 0.54 x 53 = 28.62 females (rounded to the nearest whole number).

The ratio of males who would buy the drink to females who would buy the drink is:

18.8/28.62 = 0.6560 (rounded to the nearest ten-thousandth)

Therefore, the ratio of males who would buy the drink to females who would buy the drink is approximately 0.6560.

The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.

What is a linear function?

A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.

We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:

D(x) = 65 - 0.8x

where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.

Therefore, the equation for the function is D(x) = 65 - 0.8x.

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Answer:7

Step-by-step explanation:

6.7 to the 10 is 7

Answer:

To calculate the surface area of an object, we need to know its shape. Please provide more information on the object's shape or context of the problem to calculate its surface area.

Answer:

28 units

Step-by-step explanation:

The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width.

Substituting l = 9 and w = 5, we get:

P = 2(9 + 5) = 2(14) = 28

Therefore, the perimeter of the rectangle is 28 units.

The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

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Answer: 6

Step-by-step explanation:

21 - 1 = 20

20 - 2 = 18

18 - 3 = 15

15 - 4 = 11

11 - 5 = 6

Answer:

1. is 10

2. is 4

3. is 2

?= is 2

Barbie should build a roof support that is 4√7 inches high to fit the slanted roof perfectly on her dream house.

The Pythagorean theorem is a fundamental theorem in mathematics that describes the relationship between the three sides of a right-angled triangle. It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, this can be expressed as:

a² + b² = c²

where a and b are the lengths of the two shorter sides of the triangle (called the legs), and c is the length of the hypotenuse.

The Pythagorean theorem has important implications in geometry, trigonometry, and other branches of mathematics. It is also widely used in a variety of real-world applications, such as architecture, engineering, and physics. For example, it can be used to calculate the distance between two points in a two-dimensional plane, the height of a building or a tree, or the length of a diagonal in a rectangle or a square.

To solve this problem, we need to use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse (the longest side).

In this case, the two legs of the right triangle are the height of the roof and half the width of the house (since the roof slants down from the center of the house). The hypotenuse is the length of the roof, which is 16 inches on both sides.

So, we can set up the equation:

(height)² + (12)² = (16)²

Simplifying and solving for the height:

(height)² = (16)² - (12)²

(height)² = 256 - 144

(height)² = 112

height = √112

Using a calculator or simplifying by hand, we find that:

height = 4√7 inches

Therefore, Barbie should build a roof support that is 4√7 inches high to fit the slanted roof perfectly on her dream house.

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The size of angle y in the quadrilateral is 130 degrees.

A quadrilateral is a polygon with 4 sides and angles. The quadrilateral above is a kite. The sum of angles in a quadrilateral is 360 degrees.

Therefore, let's find the angles in the quadrilaterals as follows:

y + y + 70 + 30 = 360(sum of angles in a quadrilateral)

2y + 100 = 360

2y = 360 - 100

2y = 260

divide both sides by 2

y = 260 / 2

y = 130 degrees

Therefore, the size of y is 130 degrees.

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Step-by-step explanation:

remember the trigonometric triangle inscribed in a circle (the norm circle with radius = 1).

for a larger system the leg lengths are sine and cosine multiplied by the radius (which is the Hypotenuse of the right-angled triangle).

the longer leg is opposite of the larger angle (60°).

the shorter leg is opposite of the smaller angle (30°).

what is the desired solution ? the length of the Hypotenuse ? or what ?

6 = sin(60)×Hypotenuse

Hypotenuse = 6/sin(60) = 6/(sqrt(3)/2) = 12/sqrt(3) =

= 6.92820323... ≈ 6.9

Answer:

4096/15625 or

0.262144 or

(4/5)^6

Answer:

The answer is 96

Step-by-step explanation:

2*(26+22)

2*48

96

Slope is zero and the y-intercept is (0,-5)

What is slope ?

In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.

In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.

The formula for calculating slope is:

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

where (x1, y1) and (x2, y2) are two points on the line.

According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Comparing the equation Y = -5 to y = mx + b, we can see that:

The slope, m, is 0, since there is no x-term in the equation.

The y-intercept, b, is -5, since that is the constant value in the equation.

Therefore, the correct answer is:

B. Slope is zero and the y-intercept is (0,-5)


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answer is

512

Step-by-step explanation:

1.6x80=128

128x4=512