A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship. graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 3 comma 7 Find and interpret the slope and y-intercept in this real-world situation. The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour. The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour. The slope is 9, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 9 inches every hour. The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.

If sentence 6 states that ¬C is true, and sentence 7 presents a conditional statement with C as the antecedent and Q as the consequent, we can use modus ponens to infer that Q is false.

Modus ponens is a deductive reasoning rule that allows us to derive a conclusion from a conditional statement and its antecedent. Therefore, we can apply modus ponens to sentence 7 given that we know ¬C from sentence 6.
Since from sentence 6 we know ¬C, we can apply modus ponens to sentence 7. To do this, follow these steps:
1. Identify the premises: One premise is sentence 6, which states ¬C. The other premise should be a conditional statement, such as "If ¬C, then P" (replace P with the relevant proposition).
2. Apply modus ponens: Modus ponens is a rule of inference that allows us to deduce a conclusion from the given premises. If we have the premises "If ¬C, then P" and "¬C", we can conclude "P" using modus ponens.
3. State the conclusion: After applying modus ponens, we can conclude "P" based on the given premises, which include sentence 6 (¬C) and the conditional statement.

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Answer:196

Step-by-step explanation:

Answer:

196

Step-by-step explanation:

Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor. So in the case of 32, it can be written as 2 × 2 × 2 × 2 × 2=25, where 2 is the “base” and 5 is the “exponent”. We read this expression as “two to the fifth power”.

Answer:

Area of a circle

=πr^2

therefore...

radius r =13

but π =22/7

so..

=22/7 × 13^2

=22/7 ×169

=531.14m

Area of circle

Answer:

The answer is B. For rectangle, the sides have different lengths.

The rest of the options, applies to all squares and rectangles.

Answer:

24.5 inches

Step-by-step explanation:

The ratio of the length of the toucan’s bill to the length of its body can be expressed as

(1: 3.5)

Then if the bill is 7 inches, then the Length of the body will be X

1: 3.5

7: X

If we cross multiply, we have

X= 7×3.5

X= 24.5

Hence, the Length of the body is 24.5 inches

Answer:

the reciprocal of 1 is 1

Step-by-step explanation:

1/1 flipped is still equal to 1

Answer:

10 square units.

Step-by-step explanation:

Area of Polygon C = 40 square units.

Scale factor used in obtaining polygon D = \(\dfrac12\)

To obtain the area of the new polygon, we multiply the area of the polygon from which it was derived by the square of the scale factor.

Therefore:

Area of Polygon D

\(=40 \times (\frac12)^2\\\\=40 \times \frac14\\\\=10$ square units\)

The area of polygon D is 10 square units.

Answer:

X= 10/3y + -4/3                

Step-by-step explanation:

Step One: add -5y to both sides

Step two: divide both sides by -3

Answer:

-x=1 1/3

Step-by-step explanation:

x-(4x-5y)=(5y+4)

x-4x+5y=5y+4

-3x+5y=5y+4

5y-5y=0

-3x=4

x=4÷3

4÷3=1 1/3

Answer:

72

Step-by-step explanation:

The interior angles of a 6 sided figure add to (n-2) * 180

where n is the number of sides

(6-2) *180

4*180

720

2x+4x+4x+4x+4x+2x = 720

20x = 720

Divide by 20

20x/20 = 720/20

x =36

We want <F

<F = 2x = 2*36 = 72

Answer:

Step-by-step explanation:

Reason given:

Required information:

Information given:

Addition information needed, the other side, adjacent to given angle:

On a standardized exam, the scores are normally distributed with a mean of 140 and a standard deviation of 20. The z-score of a person who scored 140 on the exam is 0

The z-score of a person who scored 140 on an exam can be calculated using the formula z = (x - μ) / σ

where x is the exam score, μ is the mean of the exam scores, and σ is the standard deviation of the exam scores.

In this case, x = 140, μ = 140, and σ = 20.

Plugging these values into the formula, we get z = (140 - 140) / 20 = 0

Therefore, the z-score of a person who scored 140 on the exam is 0.

The z-score represents the number of standard deviations away from the mean that a particular value falls. A z-score of 0 indicates that the value is equal to the mean, which is 140 in this case. If a z-score is positive, it means that the value is above the mean, and if it is negative, it means that the value is below the mean. For example, a z-score of 1 indicates that the value is one standard deviation above the mean, and a z-score of -1 indicates that the value is one standard deviation below the mean.

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Answer:

2 + 1 = 3

Step-by-step explanation:

You have 2 toy cars in your possession, and a friend gives you 1 more, now you have 3.

Hope this was the answer you were looking for.

:)

If the original price of the radio is 2,400 Naira and it is reduced by one third, then the discounted price is 1,600 Naira.

A store usually provides discount of some items to attract more customers and make greater sales.

Suppose the original price is p, the discount rate is d%, and the discounted price is q, then the discounted price can be calculated as:

q = (1 - d%) x p

Parameters given in the problem:

p = 2,400 Naira

d = 1/3

Hence,

q = (1 - 1/3) x 2400

q = 2/3 x 2400 = 1600

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Minimization of  f(x) = |x+3| + x^3 at the endpoints (-2 and 6)  the minimum value of the function is approximately 3.84, which occurs at x= \sqrt{1/3}

within the given interval.

To minimize the function subject to the constraint f(x) = |x+3| + x^3 that x lies in the interval [-2, 6], we need to find the value of x that minimizes f(x) within that interval.

First, let's analyze the function f(x). The absolute value term |x+3| can be rewritten as:

|x+3| =

x+3 if x+3 >= 0

-(x+3) if x+3 < 0

Since the interval [-2, 6] includes both positive and negative values of x+3, we need to consider both cases.

Case 1: x+3 >= 0

In this case, f(x) = (x+3) + x^3 = 2x + x^3 + 3

Case 2: x+3 < 0

In this case, f(x) = -(x+3) + x^3 = -2x + x^3 - 3

Now, we can find the minimum of f(x) within the given interval by evaluating the function at the endpoints (-2 and 6) and at any critical points within the interval.

Calculating the values of f(x) at x = -2, 6, and the critical points, we can determine the minimum value of f(x) and the corresponding value of x.

Since the equation involves both absolute value and a cubic term, it is not possible to find a closed-form solution or an exact minimum value without numerical methods or approximation techniques.

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The probability that neither of the two individuals has some college or a college degree is (1 - P(college))^2.

To calculate the probability that at least one of the two individuals chosen at random from the population will have some college or a college degree, we need to consider the complement of the event, which is the probability that none of the individuals have a college degree.

Let's assume that the population size is N, and the number of individuals with a college degree is C. The probability that an individual does not have a college degree is (N - C) / N.

When choosing the first individual, the probability that they do not have a college degree is (N - C) / N.

When choosing the second individual, the probability that they do not have a college degree is also (N - C) / N.

Since these events are independent, we can multiply the probabilities together:

P(no college degree for either individual) = (N - C) / N * (N - C) / N = (N - C)² / N².

Now, to find the probability that at least one of the individuals has a college degree, we subtract the probability of none of them having a college degree from 1:

P(at least one with a college degree) = 1 - P(no college degree for either individual) = 1 - (N - C)² / N².

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The possible dimensions (length and width) of the field are:(10 m × 13 m) or (13 m × 10 m) and (11 m × 12 m) or (12 m × 11 m).

Given that Aaron has 47m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. The fourth side of the enclosure would be the river.

The area of the land is 266 square meters.To find the possible dimensions (length and width) of the field, we can use the given information.The length of fencing required = 47 m.

Since the fence needs to be built on three sides of the rectangular plot, the total length of the sides would be 2l + w = 47.1. When l = 10 and w = 13, we have:

Length of the field, l = 10 m Width of the field, w = 13 mArea of the field = l × w = 10 × 13 = 130 sq. m2. When l = 11 and w = 12,

we have:Length of the field, l = 11 m

Width of the field, w = 12 m

Area of the field = l × w = 11 × 12 = 132 sq. m

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The numbers whose sum is 26 are 15, 3, 8 .

Given data of matrix ,

First number is three times the difference between the second and the third.

The second number is two more than twice the third.

Now according to the given data,

Let the three numbers be x, y , z.

Then,

x = 3(y-z).......(1)

y = 2 + 2z

z = z

So,

The summation of all the three numbers is 26, then

3(y-z) + 2 + 2z + z = 26

z = 3

Substitute the value of z in 2,

y = 8

Substitute the value of y and z i 1,

x = 15.

Hence the values are:

x= 15

y = 8

z = 3

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Answer:

Step-by-step explanation:

1. 10^2+7^2=x^2

x=sqrt(149)

2. 21^2-19^2=x^2

x=sqrt(80)

3. This is all pythagorean theorem busywork, a^2+b^2=c^2 where c is the hypotenuse of the triangle.  I think from my examples you should be able to figure the rest out.

In order to solve this system using the inverse of a matrix, first let's put the system in the matrix form:

Now the system is in the form AX = B, where A, X and B are matrices.

To solve this system, we can do the following:

So we need to calculate the inverse matrix of A. We can do this as follows:

Now we have:

So the solution of this system is x = -2.5 and y = 0.5

Given data:

The given equations are x - 2y = -1 and 2x + 3y = 12.

The given point of intersection is the solution of the equation which is (3, 2).

Thus, the solution of the given equations is (3, 2).

The real root of the equation x - sin(x) - 0.25 = 0, obtained using the Successive Approximation method, is approximately x = 0.732.

The Successive Approximation method is an iterative numerical technique used to approximate the roots of an equation. In this case, we are solving the equation x - sin(x) - 0.25 = 0 to three significant digits.

Step 1: Start with an initial guess for the root, let's say x0 = 0.

Step 2: Substitute x0 into the equation to calculate the next approximation, x1, using the formula x1 = sin(x0) + 0.25.

Step 3: Repeat step 2, using x1 as the new approximation, until the desired level of accuracy is achieved.

By applying the Successive Approximation method, we iterate the calculations and obtain the following results:

x1 = sin(0) + 0.25 = 0 + 0.25 = 0.25

x2 = sin(0.25) + 0.25 ≈ 0.247

x3 = sin(0.247) + 0.25 ≈ 0.248

x4 = sin(0.248) + 0.25 ≈ 0.248

x5 = sin(0.248) + 0.25 ≈ 0.248

After five iterations, we reach a value of x = 0.248, which is the real root of the equation x - sin(x) - 0.25 = 0 to three significant digits.

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\(\displaystyle\\\\ Answer: A=\frac{2P}{xV^3}\)

Step-by-step explanation:

\(\displaystyle\\P=\frac{1}{2} xAV^3\\\)

Multiply both parts of the equation by 2:

\(2P=xAV^3\)

Divide both parts of the equation by xV³:

\(\displaystyle\\\frac{2P}{xV^3} =A\)

\(\displaystyle\\\\Thus,\ A=\frac{2P}{xV^3}\)

Answer:

f(x) = -x -4 or f(x) = (-x)-4

Step-by-step explanation:

Let the graph of g be a translation of 4 units down followed by a reflection in the y-axis of the graph of f(x)=x. Write a rule for g.

Transformations can be found using this general formula: f(x) = a(bx-h)+k

For this question, we want a translation down as well as a reflection.

The two values we need to use are for k, a vertical translation, and b, a reflection over the y-axis.

Since we are translating down 4 units, k = -4

Since we are reflecting across the y-axis, b = -1

So, f(x)=(-x)-4

or

f(x)= -x -4

The exponential function for this problem is defined as follows:

y = 0.5(2/3)^x + 2.

An exponential function is defined as follows:

y = a(b)^x + c.

In which:

From the graph of the function, the horizontal asymptote is at y = 2, hence the parameter c is given as follows:

c = 2.

When x increases by 1, y is multiplied by 2/3, hence the parameter b is given as follows:

b = 2/3.

When x = 0, y = 2.5, hence the parameter a is obtained as follows:

a + c = 2.5.

a + 2 = 2.5

a = 0.5.

Meaning that the function is defined as follows:

y = 0.5(2/3)^x + 2.

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After answering the presented question, we can conclude that Rounded area to the closest tenth, the basement floor area is 147.25 square yards

The size of a surface area can be expressed as an area. The surface area is the area of an open surface or the boundary of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a shape or flat layer. The area of an object is the entire amount of space occupied by a planar (2-D) surface or shape. Make a square with a pencil on a piece of paper. A two-dimensional character. On paper, the area of a shape is the amount of space it takes up. Assume the square is made up of smaller unit squares.

To calculate the size of the basement level, multiply the length and width of the rectangular floor by two. We can see from the measurements that the length is 15.5 yards and the width is 9.5 yards.

As a result, the basement floor area is:

Area = length x breadth = 15.5 yards x 9.5 yards

147.25 square yards is the area.

Rounded to the closest tenth, the basement floor area is 147.25 square yards.

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The points on the curve where the tangent is horizontal: (1, 0) & (-1, 0),  and where the tangent is vertical: (0, 1) & (0, -1)

To find the points on the curve x=cos(theta) where the tangent is horizontal or vertical, we need to find the derivative of x with respect to theta.

Taking the derivative of x with respect to theta, we get:

dx/dtheta = -sin(theta)

When the tangent is horizontal, the derivative is equal to zero. So we need to solve the equation -sin(theta) = 0 for theta.

This equation is true when theta = n*pi, where n is an integer. So the points on the curve x=cos(theta) where the tangent is horizontal are:

(1, 0) for n=2k, where k is an integer

(-1, 0) for n=2k+1, where k is an integer

When the tangent is vertical, the derivative is undefined. This happens when cos(theta) = 0, which is true when theta = (2k+1)*pi/2, where k is an integer.

So the points on the curve x=cos(theta) where the tangent is vertical are:

(0, 1) for n=2k+1, where k is an integer

(0, -1) for n=2k, where k is an integer

Therefore, the points on the curve where the tangent is horizontal are (1, 0) and (-1, 0), and the points on the curve where the tangent is vertical are (0, 1) and (0, -1).

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The value of the equation 6 + 3p = 4p + 7 is 1

Reorder the terms:

6 + 3p = 7 + 4p

Solving for the value of p by collecting like terms

6 + 3p = 7 + 4p

Move all terms containing p to the left, all other terms to the right.

Add '-4p' to each side of the equation.

-6 + 3p + -4p = -7 + 4p + -4p

Combine like terms: 3p + -4p = -1p

-6 + -1p = -7 + 4p + -4p

Combine like terms: 4p + -4p = 0

-6 + -1p = -7 + 0

-6 + -1p = -7

Add '6' to each side of the equation.

-6 + 6 + -1p = -7 + 6

Combine like terms: -6 + 6 = 0

0 + -1p = -7 + 6

-1p = -7 + 6

Combine like terms: -7 + 6 = -1

-1p = -1

Divide each side by '-1'.

p = 1

Simplifying

p = 1

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