in this problems you will consider paths on the integer grid that start at (0,0) in which every step increments one coordinate by 1 and leaves the other unchanged. a) (4 points) how many such paths are there from (0,0) to (85, 65)?

After 15 more years of contributions of $4,000 at the end of each quarter, the retirement account will be worth approximately $760,514.47.

To calculate this, we need to use the formula for the future value of a lump sum. A lump sum is a one-time payment made at the beginning or end of a specific period. In this case, we're looking at the future value of the retirement account after 15 more years of contributions.

Using the given information, we can plug in the values and solve for FV:

PV = $150,000

Pmt = $4,000

r = 10%

n = 4 (since interest is compounded quarterly)

t = 15 years

First, we need to calculate the future value of the current investment of $150,000:

FV1 = $150,000 x (1 + 0.1/4)⁴ ˣ ¹⁵ = $548,534.24

Then, we can calculate the future value of the quarterly contributions of $4,000 over 15 years:

FV2 = $4,000 x [(1 + 0.1/4)⁶⁰ - 1] / (0.1/4) = $211,980.23

Finally, we can add FV1 and FV2 to get the total future value of the retirement account after 15 more years:

Total FV = FV1 + FV2 = $548,534.24 + $211,980.23 = $760,514.47

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Answer:

Step-by-step explanation:

the slope is uphill.. so we know it's positive

I can also see that that it's 1 up and 1 over so the slope is 1

the line also hits at -9   on the y axis

so

y = x - 9

Answer:

d

Step-by-step explanation:

The dimensions that yield the box with the largest volume are 5√2 inches by 5√2 inches by 5√2 inches.

To maximize the volume of the box, we need to determine the dimensions that will use up all 100 square inches of material while maximizing the volume of the box. Let the length, width, and height of the box be denoted by x, y, and z, respectively.

From the given information, we know that the surface area of the box is 2(xy + xz + yz) = 100, which simplifies to xy + xz + yz = 50.

The volume of the box is V = xyz, so we need to find the maximum value of V subject to the constraint xy + xz + yz = 50.

We can use Lagrange multipliers to solve this optimization problem. Let

f(x, y, z) = xyz

g(x, y, z) = xy + xz + yz - 50

The Lagrangian function is

L(x, y, z, λ) = f(x, y, z) - λg(x, y, z) = xyz - λ(xy + xz + yz - 50)

Taking partial derivatives with respect to x, y, z, and λ and setting them equal to zero, we get the following system of equations:

yz - λ(y + z) = 0

xz - λ(x + z) = 0

xy - λ(x + y) = 0

xy + xz + yz - 50 = 0

Solving this system of equations yields

x = y = z = 5√2

Therefore, the dimensions that yield the box with the largest volume are 5√2 inches by 5√2 inches by 5√2 inches.

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Answer: mutually exclusive are:

ii. Sit down and stand up

ii. Sit down and stand upiii. Two dice: Odd and Even

because they can not occur same time

Mutually exclusive events don't occur at same ineterval and are not dependent upon each other

Here

They are

the answer is 17 boards

Step-by-step explanation:

25+18=43

60-43=17

13. M=4/3

14. m=-6

Step-by-step explanation:

The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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Out of the three given options, option a) is the most appropriate definition of an experiment in the context of probability.

The term "experiment" in the context of probability refers to a process or activity that involves observing or measuring an outcome that is subject to chance or uncertainty. The outcome of an experiment is not necessarily predictable with certainty, and it may depend on various factors such as the conditions under which the experiment is conducted and the randomness inherent in the process.

Out of the three given options, option a) is the most appropriate definition of an experiment in the context of probability. An experiment is essentially a process that leads to one of several possible outcomes, and the probability of each outcome can be calculated or estimated based on the underlying assumptions and factors involved. Examples of experiments in probability include rolling a die, tossing a coin, drawing a card from a deck, or conducting a clinical trial to test a new drug.

Option b) is not an appropriate definition of an experiment because it suggests that the outcome can be predicted with certainty based on mathematical analysis, which is not always the case in experiments involving chance or uncertainty.

Option c) is also not an appropriate definition of an experiment because it suggests that an experiment is conducted to confirm a hypothesis, which may or may not be true. While experiments can be used to test hypotheses and provide evidence to support or refute them, the primary goal of an experiment in the context of probability is to observe or measure the outcome and calculate the probability of each possible outcome.

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Answer:

A reflection over line y=x.

Step-by-step explanation:

Answer:

C. Rotation of 180° about the origin

Step-by-step explanation:

A(-2,4) B(-4,2) C(-7,2) D(-4,7)

A'(2,-4) B(4,-2) C(7,-2) D(4,-7)

(x , y) ---> (-x , -y)

The value of angle 2 will be equal to 132°.

The distance between two intersecting lines or surfaces at or around the point where they meet (typically measured in degrees) is called an angle.

Given that:-

A line is intersecting two parallel lines and making angles one angle is 132 and another angle is need to be found.

We can see that the two angles are exterior opposite angles so the angle 2 will be 132

Hence the value of angle 2 will be equal to 132°.

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Answer:

54

Step-by-step explanation:

Answer:

y = 1/2x - 1

Step-by-step explanation:

The easiest was you do this is to first rearrange the equation into slope-intercept form (y = mx + b).  After rearranging, you can find the slope (m).

2x + y = -5

y = -2x - 5

The slope is -2.  Since the line we are trying to find is perpendicular, find the inverse and multiply it by -1.

-2  =>  1/2

Now use the point-intercept form to find the new equation.  Use the slope (1/2) and the given point (-1, -2).

y - y₁ = m(x - x₁)

y - (-2) = 1/2(x - (-2))

y + 2 = 1/2(x + 2)

y + 2 = 1/2x + 1

y = 1/2x - 1

The equation of the line perpendicular to line WX is  y = 1/2x - 1.

The equation is y = (1/2)x -(3/2) ; y = one half x − three halves.

The correct option is D.

What is the equation of a Straight Line?

An equation of the straight line is given by y = mx+c,

Here m is the slope and c is the intercept on y-axis.

The equation of the line WX is 2x+y = -5

y = -2x -5

The product of the slopes of the line and the line perpendicular to this line will be -1

Therefore the slope of the line perpendicular to the line WX is -2 * m = -1,

m = 1/2

y = (1/2)x +c

The line passes through the points (-1, -2)

-2 = (1/2) (-1) +c

c = -2 +(1/2)

c = (-4 +1) /2

c = -3/2

Therefore, the equation is y = (1/2)x -(3/2) ; y = one half x − three halves.

The correct option is D.

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The output values of f(2), f(4) and f(-3) in the function f(x) = x² - 2x - 4 are -4, 4 and 11 respectively.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

To determine the output value of f(2), f(4) and f(-3), replace all the occurrence of x with 2, 4, and -3 in the function and simplify.

For f(2),

f(x) = x² - 2x - 4

f(2) = (2)² - 2(2) - 4

f(2) = 4 - 4 - 4

f(2) = -4

For f(4),

f(x) = x² - 2x - 4

f(2) = (4)² - 2(4) - 4

f(2) = 16 - 8 - 4

f(2) = 16 - 12

f(2) = 4

For f(-3),

f(x) = x² - 2x - 4

f(-3) = (-3)² - 2(-3) - 4

f(-3) = 9 + 6 - 4

f(-3) = 9 + 2

f(-3) = 11

The output values of f(2), f(4) and f(-3) in the function f(x) = x² - 2x - 4 are -4, 4 and 11 respectively.

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Answer:

The answer is C. $56.00
Hazel earned $56.00 in interest after one year.

Step-by-step explanation:

700 x 6.5% =
700 x 0.065 = 45.5

300 x 3.5% =
300 x 0.035 = 10.5

45.5 + 10.5 = 56.00

The correct answer is a countable variable is characterized by infinitely uncountable values and can take any value within interval.

A random variable is with an unknown value or a function that gives values to each of the results of an experiment.

Random variables are frequently identified by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.

Continuous random variables have an endless number of possible values and can represent any value that falls within a given range or interval.

An experiment that measures the amount of rain that falls in a city over the course of a year or the average height of a random group of 25 people are two examples of continuous random variables.

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Answer:

Step-by-step explanation:

a:

21 49 70

46 34 80

67 83 150

b: 34+49=83

c:

total no. of students = 150

no of boys who disapproved = 46

probability = 150/46 = 75/23

hope that helps!

Three cards are drawn from a standard deck. Thus, the probability to get an ace, followed by a king, and then a queen, is  16/34,425

The formula for conditional probability is:

P(A∩B) = P(B|A) . P(A)

In the given problem:

P(ace) = 4 / 54

After an ace was drawn, the number of cards now is 51.

Hence,

P(king | ace) = 4/51

After the second drawn, the remaining cards is 50. Hence,

P(queen | (king | ace)) = 4/50

Therefore,

P(ace,king,queen) = 4/54 x 4/51 x 4/50 = 64 / 137,700 = 16/34,425

Thus, the probability to get an ace, followed by a king, and then a queen, is  16/34,425

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Answer:

D

Step-by-step explanation:

Answer:

Your blood carries oxygen and nutrients to all of the cells in your body. Blood cells also fight infection and control bleeding. Most blood cells are made in your bone marrow. They are constantly being made and replaced.

Step-by-step explanation:

Hope this helps!

Brainliest please.

Answer: It carries oxygen. Red blood cells also remove carbon dioxide from your body, transporting it to the lungs for you to exhale. Red blood cells are made in the bone marrow. They typically live for about 120 days, and then they die.

Answer:

6-2=3

Step-by-step explanation:

5234.9

Answer:

x = 9

Step-by-step explanation:

3.1= -5.9+x

x - 5.9 = 3.1

x - 5.9 + 5.9 = 3.1 + 5.9

x = 9

area of a circle = πr²

22/7 × 692/100 × 692/100

150.50011

Step-by-step explanation:

The length of any side of a triangle must be less than the sum of the other 2 sides of the triangle.

Let x be the length of the 3rd side. Then we have constraints 5 + 12 > x and 5 + x > 12.

This gives 17 > x and x > 7, hence the answer is 7 < Length of the 3rd side < 17.

Answer:

Length of DE = 7.5 units

Length of DB = 9.2 units

Measure of ∠FED = 82°

Step-by-step explanation:

In ΔABC,

AD ≅ BD and CE ≅ BE [Given]

By the theorem of mid-segments,

DE = \(\frac{1}{2}(AC)\)

     = \(\frac{1}{2}(15)\)

DE = 7.5 units

Since AD ≅ FE ≅ 9.2 [By midpoint theorem in ΔACB]

Therefore, length of DB = 9.2 units

[Although it's not given in the question, but we assume FE║AB]

Since FE║AB and DE is a transverse,

Therefore, m(∠FED) ≅ m(∠BDE) ≅ 82° [Interior alternate angles]

Answer:

Triangle

Step-by-step explanation:

It forms a triangle because when you plot the points and connect a dot its a triangle

\(XX, ¯xx¯ and ∑x∑x\) distribution for a 5K fun runGiven the below information:Mean of 5K fun run\(= μ = 21\)minutesStandard Deviation of 5K fun run\(= σ = 2.2\) minutesNumber of runners selected\(= n = 49\)

Random variable of 5K fun run = XXDistribution of \(XX: XX ~ N(μ,σ^2) = N\)(21, 2.2^2)

Distribution of \(¯xx¯: ¯xx¯ ~ N(μ, σ^2/n) = N(21, 2.2^2/49) = N\)(21,0.0976)Distribution of\(∑x∑x: ∑x∑x ~ N(nμ, nσ^2) = N(49×21, 49×2.2^2) = N\) (1029, 1085.96)

Therefore, the distribution of XX is N(21, 2.2^2), the distribution of\(¯xx¯ is N(\) 21,0.0976) and the distribution of ∑x∑x is N(1029, 1085.96).

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Answer:

C. 10.5(12 + x) square feet

E. (126 + 10.5x) square feet

Step-by-step explanation:

A. 10.5(12x) square feet

B. (10.5 + 12 + x) square feet

C. 10.5(12 + x) square feet

D. 126x square feet

E. (126 + 10.5x) square feet

F. (22.5 + x) square feet

length of a living room = 12ft

width = 10 1/2 ft

The length of the living room is being expanded by X feet

New length of a living room = 12ft + x feet

new area of the living room = length × width

= 12ft + x feet × 10 1/2 ft

= (12 + x) 10 1/2

Note: 10 1/2 is equivalent to 10.5

= (12 + x) 10.5

= (126 + 10.5x) square feet

Options that applies

C. 10.5(12 + x) square feet

E. (126 + 10.5x) square feet

Answer:

x = 30

y = 115

Step-by-step explanation:

Suppose line m is parallel to line n:

65+y = 180 because they are supplementary angles

subtract 65 from both sides

y = 115

angle represented by y and the angle represented by 3x + 25 are alternate angles and their measure is equal, so to find the value of x we can write the following equation:

3x + 25 = 115 subtract 25 from both sides

3x = 90 divide both sides by 3

x = 30

The dimension of rectangular piece of land is 17 x 12 square units in size.

The space surrounding a shape is known as its perimeter. It is the length of the shape's sides taken together.

The space occupied by a flat shape or an object's surface can be referred to as the area.

What is the rectangular area formula?

Rectangle area equals length x width

Let the rectangle plot's length and breadth be x and y, respectively.

Juliet has a 58-meter fence.

The rectangular piece of land's perimeter is 58 meters.

2(length + width) = 58

x + y = 58\2

⇒ x + y = 29

Moreover, the plot's total area is 204 square units.

x × y = 204

⇒ x × (29 - x) = 204

\(29x-x^{2} =204\\x^{2} -29x+204=0\\x^{2} -12x-17x+204=0\)

(x-12) (x-17) = 0

x = 12, x = 17

When, x= 17

y = 29 - 17 = 12m

when x = 12

y = 29 - 12 = 17m

As a result, the rectangular land parcel has dimensions of 17 x 12 square units.

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