A particle moves along a line so that its velocity is given by v(t)=-t^3+2t^2+2^-t for t>0. For what values of t is the speed of the particle increasing? The answer is (0.177,1.256) and (2.057, infinity).

Henry's chances of getting a second turn when he rolls the number cubes are 1/9 or approximately 11/18.

To find Henry's chances of getting a second turn when he rolls the number cubes, we need to find the probability of rolling an even number less than 10.

First, let's find the total number of possible outcomes when rolling two number cubes. Each cube has 6 possible outcomes (1, 2, 3, 4, 5, or 6), so the total number of possible outcomes is 6 x 6 = 36.

Next, let's find the number of outcomes that meet the criteria for a second turn (even number less than 10). We can list out all the possible outcomes that meet these criteria:

2 (1+1)

4 (1+3 or 2+2)

6 (1+5 or 2+4 or 3+3)

8 (2+6 or 3+5 or 4+4)

So, there are 4 outcomes that meet the criteria for a second turn.

To find the probability, we divide the number of favourable outcomes (4) by the total number of possible outcomes (36).

4/36 = 1/9

So Henry's chances of getting a second turn when he rolls the number of cubes are 1/9 or approximately 11/18.

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The slope of the table is 2.

What is slope?

An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). The ratio of how much y grows as x grows by a certain amount is known as the slope of a line. A line's slope, or the amount by which y rises as x rises, indicates how steep a line is. The slope is constant (the same) along the line.

Here using given table we can find slope by taking any two points then,

[tex](x_1,y_1)=(6,0) and (x_2,y_2)=(4,-4)[/tex]

Now using slope formula m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> m = [tex]\frac{-4-0}{4-6}[/tex]

=> m = [tex]\frac{-4}{-2}[/tex]

=> m = 2

Hence the slope of the given table is 2.

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The slope of points that are given on the table is 2.

The slope of a line indicates how steep it is. "rise over run" is used to calculate slope mathematically (change in y divided by change in x). The slope of a line is the ratio of how much y grows as x grows by a certain amount. The slope of a line, or the amount by which y rises as x rises, indicates the steepness of the line. Along the line, the slope is constant (the same).

Using the given table, we can find the slope by taking any two points and then,

(x1,y1) = (6,0) and (x2,y2) = (4,-4)

Using the slope formula m = y2-y1/x2-x1,

Then,

m = -4-0/4-6

m = -4 /-2

=> m = 2

As a result, the slope of the given table is 2.

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The value of x is equal to 3

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here

[tex]y=x^{2}/3+1 \\y=2x-2[/tex]

 Solving these two equations we get

[tex]y=1x^{2} /3+1=2x-2\\1x^{2}/3-2x+3=0\\x^{2} -6x+9=0\\(x-3).(x-3)=0\\x=3,3[/tex]

Hence, the value of x is equal to 3

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Answer: The distance of the ship from the lighthouse is 546.4 feet.

Step-by-step explanation:

What is the angle of elevation?

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

The beacon light is 126 feet high, the angle of elevation to the beacon is 13° and the distance from the lighthouse to the ship = x

These from a right-angled triangle,

from trigonometry

tan 13 = 126/x

making x the subject of the equation we have

x tan 13 = 126

x = 126/tan 13

but tan 13 = 0.2308

x = 126/0.2308

x = 546.4 feet

In conclusion, the ship's distance from the lighthouse is 546.4 feet.

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Yes, based on the interval (0.59, 0.606), it reasonable to conclude that more than 50 percent of all U.S. adults would say they take part in some form of daily activity to keep physically fit.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

Given that, 60 percent of 1,000 randomly selected U.S. adults say that they take part in some form of daily activity to keep physically fit.

The 95% confidence interval for the Population proportion is given as:

(p-z×√(p×(1-p)/n), (p-z×√(p×(1-p)/n)

Here, p=0.60

n = 1000

Now, 0.60-z×√0.60(1-0.60)/1000), 0.60+z×√0.60(1-0.60)/1000)

z is the upper 0.025 point of a standard normal distribution which is 1.96

(0.60-1.96×√0.60(1-0.60)/1000, 0.60+1.96×√0.60(1-0.60)/1000)

(0.59, 0.606)

Yes, based on the interval (0.59, 0.606), it reasonable to conclude that more than 50 percent of all U.S. adults would say they take part in some form of daily activity to keep physically fit.

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The solutions to the exponential equation [tex]12^{x^2 + 5x - 4} = 12^{2x + 6}[/tex] are given as follows:

x = 2 and x = -5.

The exponential equation for this problem is defined as follows:

[tex]12^{x^2 + 5x - 4} = 12^{2x + 6}[/tex]

The n^x function is an injective function, which means that if they are equal, and have the same base, than their exponents are equal.

Thus the equation can be simplified as follows:

x² + 5x - 4 = 2x + 6.

x² + 3x - 10 = 0.

The coefficients of the quadratic function are given as follows:

a = 1, b = 3, c = -10.

Hence the discriminant is given as follows:

D = 3² - 4(1)(-10)

D = 49.

The first solution is given as follows:

x = (-3 + 7)/2 = 2.

The second solution is given as follows:

x = (-3 - 7)/2 = -5.

Meaning that the third option is the correct option in the context of this problem.

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Answer:

c

Step-by-step explanation:

Answer:

The gallons of water being pumped out each hour is -350 gallons/hour.

To find the gallons of water being pumped out each hour, we need to look at the coefficient of T in the equation W = -350 (T – 4). This coefficient is -350, which represents the rate of change of water in the pool with respect to time, and thus the gallons of water being pumped out each hour.

When the pump is placed in the pool, the time that has passed is 4 hours.

The pool contained 1400 gallons of water when the pumping started.

The pump will take 4 hours to empty the pool.

You can distribute the -350, the new equation will be W = -350T + 1400

The equation W = -350T + 1400 represents the amount of water in the pool (W) at any time (T), where the amount of water in the pool decreases linearly with time with a rate of -350 gallons/hour and the initial water in the pool is 1400 gallons.

Step-by-step explanation:

1. 350 gallons of water are being pumped out each hour.

2. Answer 1 can be found with the slope.

3. When, the pump is placed in the pool,  Time passed = zero.

4. Water in the pool when the pumping started = 1400 gallons

5. Time for the pump to empty the pool = 4 hours

6. Equation that is equivalent to W = -350(T – 4) is T = -W/350 + 4

7. New equation represents A line with slope = -1/350 that is time per gallon and intercept equal to 4 that is total time.

The slope-intercept form of a straight line is used to find the equation of a line. For the slope-intercept formula, we have to know the slope of the line and the intercept cut by the line with the y-axis. Let us consider a straight line of slope 'm' and y-intercept 'b'. The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as:

y = mx + b.

Given,

The amount of water in the pool(W, measured in gallons) at any time (T, measured in hours) is

W=-350(T-4).

1. How many gallons of water are being pumped out each hour?

Ans: That would be the slope: 350 gallons per hour

2. Explain how you found the answer.

Ans: Comparing the given equation to equation y = mx + b.

3. When the pump is placed in the pool, how much time has passed?

Ans: Since pump is just started time T = 0

4. How much water was in the pool when the pumping started?

Ans: that would be W(0) = -350(0-4) = 1400 gallons

5. How long will it take for the pump to empty the pool completely?

Ans: Let W(T) = 0 and solve for T:

T = 4

6. Write an equation that is equivalent to W=-350(T-4). What does this second equation tell you about the situation?

T = -W/350 + 4

Time per gallon = -1/350 and intercept = 4, that is total time in hours.

7. What does your new equation tell you about the situation?

Ans: Time per gallon = -1/350 and intercept = 4, that is total time in hours.

Hence,

1. Amount of water pumped out each hour = 350 gallons

2. The slope represents amount of water pumped out each hour.

3. Zero time was passed when the pump is placed in the pool.

4. 1400 gallons of water was in the pool when the pumping started.

5.  It will take 4 hours for the pump to empty the pool.

6. T = -W/350 + 4 is equivalent to W = -350(T – 4).

7. Slope = -1/350 represents the time per gallon, 4 is total time in hours that is y - intercept.

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Answer B)

Step-by-step explanation:

( x + 2 )² + ( y - 1 )² = r²

( - 4 + 2 )² + ( 1 - 1 )² = r²

4 = r², than we will plug in to a formula:

( x + 2 )² + ( y - 1 )² = 4

x² + 4 x + 4 + y² - 2 y +1 = 4

x² + y² + 4 x - 2 y + 1 = 0

(-14)+(-8) is expression has the same value as(-14)-8 as positive and negative signs cancel each other and becomes negative.

To determine whether a number is positive or negative, always pay attention to the sign before it. There is no positive or negative in zero. A positive number is equal to an addition of a negative number when it is subtracted from a negative number. In other words, it intensifies the negative value.

Negative numbers cancel out their negative signs when subtracted from positive numbers, making addition simple. It increases the positive number's positivity.

A plus sign is created when you subtract one negative number from another negative number because the negative signs once again cancel each other out. The response bears the larger number's sign.

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Answer:

[tex]\textrm {D. The derivative is }\dfrac{x^{3}\cdot(\boldsymbol{9x^{8}})-x^{9}\cdot(\boldsymbol{3x^{2}})}{x^{6}}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \dfrac{u(x)}{v(x)}[/tex]

the derivative of f(x) wrt x is

[tex]f'(x) = \dfrac{u'(x)v(x) - u(x)v'(x)}{[v(x)]^2}[/tex]

[tex]u(x) =x^9 \;so \; u'(x) = 9x^8[/tex]

[tex]v(x) = x^3 , v'(x) = 3x^2\\\\\[v(x)\]^2 = [x^3]^2 = x^6[/tex]

Putting all these together we get

[tex]f'(x)=y'=\dfrac{x^{3}\cdot(\boldsymbol{9x^{8}})-x^{9}\cdot(\boldsymbol{3x^{2}})}{x^{6}}[/tex]

Missing entries are in bold

B, $3.75 is less than or equal to $20

$3.75 is the price per pack

if he has a budget of $20, then the sum of $3.75x cannot be above it.

$3.75x <(or equal to) $20

AKA, B.

Answer:

Step-by-step explanation:

Total budget = $ 20

Cost 1 pack of paper = $3.75

Let the number of pack of papers Mr. Cooper can buy = x

Total cost of buying x packs of paper = $ 3.75x

The total cost of paper pack cannot exceed the total budget.

$3.75x <= $ 20

Answer:

8 pages is 32% of 25

Step-by-step explanation:

Change 32% to a decimal.

32% = .32

Multiply by 25

.32 * 25

8

8 pages is 32% of 25

Answer:

8 pages

Step-by-step explanation:

Now we have to,

→ find the 32% of 25 pages.

Let's solve the problem,

→ 32% of 25

→ (32/100) × 25

→ 0.32 × 25

→ 8 pages

Hence, answer is 8 pages.

The required special segment in triangles that are matched in the triangles is given as perpendicular bisector, altitude, median, and midsegments.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

The question seems to be incomplete, so we assume that there are two congruent triangles.
For the congruent triangles, special segments in triangles are congruent to each other.

Thus, the required special segments in triangles that are matched in the triangles is given as perpendicular bisector, altitude, median, and midsegments.

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Trisha is not correct in claiming that these mathematical expressions 4(3s + 2) and 5(7s + 3) both equal 20 when s = 1.

Mathematical expressions are the combinations of variables, numbers, and arithmetic operators without the equation symbol (=).

The basic mathematical or arithmetic operators are addition, subtraction, division, and multiplication.

Mathematical expressions are not the same as equations.  Equations show that two or more mathematical expressions are equal or equivalent.

In this situation, the equality of the two expressions can be proved by substituting s with 1, as follows:

Let s = 1

4(3s + 2) = 4(3 + 2) = 4 x 5 = 20

5(7s + 3) = 5(7 + 3) = 4 x 10 = 40

We know that 20 ≠ 40.

Thus, Trisha is not correct in claiming that the two mathematical expressions are equal when s = 1.

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Answer:

5, 9, 13, 17, 21, 25, 29, 33, 37, 41

Step-by-step explanation:

every time you go up one number, there is a 4 matchstick difference

the ninth figure therefore would be using 37 matchstick squares (:

hope this helped have a good day!

Answer:

The answer should be 7 [tex]cm^{2}[/tex]

Step-by-step explanation:

If I make a 4 by 4 rectangle around the figure, I will have a 4 by 4 square.

The area will be 16.  Now subtract out the triangle on the bottom left and top right.

The triangles have a length and a height of 3.

a = 1/2 (lxh)

1/2(3x3) + 1/2(3x3) = 9

Subtract 9 from 16

16-9 = 7

Answer:

-----------------------------

Slope-intercept form:

Use two points on the line:

The first point is the y-intercept:

Find the slope:

The line is:

Based on the information provided, the probability that Julia will land on a 1 and an A is 1/6 or 0.166.

The probability can be described as the likelihood of an event happening. In most cases, the probability depends on the ratio of the desired event and all possible outcomes. For example in a bag with a total of 6 red balls and 4 black balls the probability of getting a red ball is 6/10.

To find out the total probability, we need to calculate the two probabilities involved and mutiply them.

Probability spinner 1 lands = 1/3 as there are three spinners

Probability A lands = 1/4 as there are 4 possible outcomes A, B, C, D

This means the probability of this event happening is 1/6, which can be simplified as 0.166 or 16%.

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Answer:

i will take risk and do it an any situation to growth equation

The polygons with the specified vertices and their graphs are as follows;

2. The polygon is a rectangle

Please find attached the graph of polygon 2, a rectangle, created with MS Excel

3. The polygon is an irregular octagon

Please find attached the graph of the polygon, an octagon, created with MS Excel

A polygon is a closed plane figure with three or more linear sides and interior angles.

2. The vertices of the polygon are; (-3, 8), (5, 8), (-3, -5), (5, -5)

The number of vertex points indicates that the polygon is a quadrilateral.

The vertices indicates that the vertical lines x = -5, and x = 8, are lines that form the sides of the quadrilateral

Similarly, the horizontal lines y = -3, and y = 5 are boundaries of the quadrilateral

The distance between the vertical lines = 8 - (-5) = 13

The distance between the horizontal lines = 5 - (-3) = 8

The quadrilateral is therefore a rectangle

The graph of the rectangle, created with MS Excel is attached

3. The vertices of the polygon are; (4, 3), (3, 3), (2, 2), (2, 1), (3, 0), (4, 0), (5, 1), and (5, 2)

The number of vertex points are 8 indicating that the polygon is an octagon.

The length of the sides are;

(4 - 3) = 1

√((3 - 2)² + (3 - 2)²) = √2

(2 - 1) = 1

√((3 - 2)² + (0  - 1)²) = √2

4 - 3 = 1

√((5 - 4)² + (1 - 0)²) = √2

2 - 1 = 1

The lengths of the sides of the octagon are alternating therefore, the figure is an irregular octagon.

Please find attached the graph of the octagon, created with MS Excel

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The expression for each values of {a} and {c} are calculated below..

Given are the expressions as -

3a + 6 + 5a - 2

5c - 4c + c - 3

For the expression -

3a + 6 + 5a - 2

8a + 4

For {a} = 2, we can write -

8 x 2 + 4

20

for {a} = 5, we can write -

8 x 5 + 4

44

for {a} = -3, we can write -

8 x -3 + 4

-20

For the expression -

5c - 4c + c - 3c

- c

For {a} = 2, we can write -

- 2

for {a} = 5, we can write -

- 5

for {a} = -3, we can write -

3

Therefore, the expression for each values of {a} and {c} are calculated above.

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The final statement is: A rigid creates figure that are congruent.

A rigid motion is when an object is moved from one location to another and the size and shape of the object have not changed. Two figures are congruent if and only if there exists a rigid motion that sets up a correspondence of one figure as the image of the other.

Given here: A rigid motion

Rigid Motion and Congruence-Two figures are congruent if and only if there exists one, or more, rigid motions which will map one figure onto the other. (thus maintaining the conditions for the figures to be congruent)

Hence, The right option is A.Congruent.

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Answer:

A

Step-by-step explanation:

The probability of randomly selecting a spool of blue thread from the basket is P = 1/5 = 0.2

We know that there are:

25 spools each of:

blue, green, red, white, and yellow thread in the basket.

So there are a total of:

25*5 = 125 spools in total.

If the probability is evenly distributed, then the probability of randomly selecting a spool of color blue is equal to the quotient between the number of blue spools and the total number of spools, we will get:

P = 25/125 = 1/5 = 0.2

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Answer:

$81.19

Step-by-step explanation:

8.25% x 75 = 8.19

75 + 8.19 = $81.19

True, The notation "f(x)" (f of x) is another way of representing y-values in a function.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We know that;

When we write a function, then the notation "f(x)" (f of x) is another way of representing y-values in a function.

Hence, It is true, notation "f(x)" (f of x) is another way of representing y-values in a function.

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If pentagon ABCDE is rotated 180° around the origin to create pentagon A′B′C′D′E′, the ordered pair of point A′ is equal to (2, -4).

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

By applying a rotation of 180° to the ordered pair of point A in pentagon ABCDE, the coordinates of its image (pentagon A′B′C′D′E′) can be calculated as follows:

(x, y)                                                   →               (-x, -y)

Ordered pair of points A = (-2, 4)    →     Ordered pair of points A' = (-(-2), -(4)) = (2, -4).

Therefore, the coordinates of points A' is equal to (2, -4).

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Answer:

The answer is  A) (2, −4)

Step-by-step explanation:

The rotation rule for 180° is (x, y) → (−x, −y) so wll use this rule to find the ordered pair of A′.

A = (-2,4)

(x, y) → (−x, −y)  → (−(-2), −(4)) Change the sign of both coordinates (2, −4)

so, the answer is (2, −4)

Answer: C

Step-by-step explanation:

It's actually quite easy.

The problem says that the value of b is 0.5 and the value of c is 0.75

Substitute these values for both variables, and you see that

5b+c = 0.5*5+0.75 = 2.5+0.75 = 3.25

Final Answer = C

The complete statement is -

This equation will have infinitely many solutions when h = 4 because you get infinite solutions when you have the same number of x's on each side and the same constant.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the equation as -

4x + 4 = 4x + h

Now, for h = 4, the equation will become -

4x + 4 = 4x + 4

4x = 4x

x = x

x - x = 0

0 = 0

We can fill in the blank as -

This equation will have infinitely many solutions when h = 4 because you get infinite solutions when you have the same number of x's on each side and the same constant.

Therefore, the complete statement is -

This equation will have infinitely many solutions when h = 4 because you get infinite solutions when you have the same number of x's on each side and the same constant.

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