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The value of k is given as follows:

k = 2.

The polynomial for this problem is defined as follows:

P(p) = p^4 + p² + p - k.

We have that p - 1 is a factor of the polynomial, meaning that according to the Factor Theorem, P(1) = 0.

Hence, considering that when p = 1, P = 0, the value of k is obtained as follows:

1^4 + 1² + 1 - k = 1

3 - k = 1

k = 3 - 1

k = 2.

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Answer:

That is true!

\(1,200 * 11 = 13,200\)

Let me know if you need more help with multiplication. I may be able to help.

Have a great day.

There is no elementary matrix e such that ea = b for this pair of matrices.

To find an elementary matrix e such that ea = b, we need to perform the same elementary row operation on a that was performed on the identity matrix to obtain e. We can then multiply e by a to obtain b.

1. a = [1 3; 2 4], b = [4 10; 2 4]

To get from the identity matrix to a, we need to subtract 2 times the first row from the second row. The elementary matrix e is therefore:

e = [1 0; -2 1]

We can check that ea = b:

e * a = [1 0; -2 1] * [1 3; 2 4] = [1 -3; 0 -2]

ea = [1 -3; 0 -2] = b

2. a = [2 1; 3 2], b = [4 3; 5 3]

To get from the identity matrix to a, we need to subtract 3 times the first row from the second row. The elementary matrix e is therefore:

e = [1 0; -3 1]

We can check that ea = b:

e * a = [1 0; -3 1] * [2 1; 3 2] = [2 1; 0 1]

ea = [2 1; 0 1] = b

3. a = [1 0; 0 -1], b = [-1 0; 0 1]

To get from the identity matrix to a, we need to multiply the second row by -1. The elementary matrix e is therefore:

e = [1 0; 0 -1]

We can check that ea = b:

e * a = [1 0; 0 -1] * [1 0; 0 -1] = [1 0; 0 1]

ea = [1 0; 0 1] ≠ b, so there is no elementary matrix e such that ea = b for this pair of matrices.

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The correct relative frequency and the conclusion based on the table is B. The relative frequency for traveling out of state for longer than a week is 48%. This could be high because people want to spend more time if they have traveled farther.

Given a table.

Relative frequency of a data set is defined as the ratio of the number of outcomes that occured by the total number of trials.

Total number of surveys = 100

Relative frequency for traveling in state for longer than a week is,

10/100 = 10%

Relative frequency for traveling out of state for longer than a week is,

48/100 = 48%

This must be true since people will be more likely to spend more time if they travelled farther.

Hence the correct option is B.

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approximately 95% of female university students will have a height no more than 174.87 cm (rounded to two decimal places).

To determine the height at which 95% of female university students will have a height no more than, we can use the properties of the normal distribution and the concept of z-scores.

In a normal distribution, approximately 95% of the data falls within 1.96 standard deviations from the mean (assuming a symmetric distribution). This is often referred to as the 95% confidence interval.

To calculate the specific height, we need to find the value that corresponds to the z-score of 1.96, given the mean and standard deviation of the distribution.

The formula to calculate the specific value (height) is:

Specific value = Mean + (Z-score * Standard Deviation)

In this case:

Mean = 165 cm

Standard Deviation = 6 cm

Z-score = 1.96

Plugging in these values, we get:

Specific value = 165 + (1.96 * 6)

Specific value ≈ 165 + 11.76

Specific value ≈ 176.76 cm

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Answer:48

Step-by-step explanation:

The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

The probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/4.A spinner is a gambling tool used for games and competitions. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result.

When it stops, a pointer will land on one of many different numbered segments of the spinner, each of which corresponds to a particular reward or consequence. Spinning games are frequently based on chance, and players frequently wager money or other objects on the result. Probability is the study of the likelihood of events taking place.

Probability is expressed as a fraction, decimal, or percentage and is always between 0 and 1. The probability of an event can be calculated using the following formula: Probability = number of favorable outcomes / total number of possible outcomes. Given the spinner has a polka-dot section, 2 white sections, and 1 shaded section, it has a total of 4 sections.

Therefore, the probability of the spinner stopping at a polka-dot section is 1/4.Also, after the first spin, the spinner still has 2 white sections. Therefore, the probability of stopping at a solid white section is 2/4 or 1/2 (since there are only 2 possible outcomes after the first spin).

To determine the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section, we must multiply the probability of each event.1/4 × 1/2 = 1/8

Hence, the probability of the spinner stopping at a polka-dot section and then stopping at a solid white section is 1/8.

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Answer:

Use a graphing calc and plug in the equation.

Step-by-step explanation:

Answer:

It's C on EDGE

Step-by-step explanation:

Answer:

Zack = x

Tony = x + 6

x + x + 6 = 42

2x + 6 = 42

2x = 36

x = 18

So,

Zack = x = 18

Tony = x + 6 = 18 + 6 = 24

Answer:

hello :

Step-by-step explanation:

x(x+3)(x+3)=0  means : x=0 or x+3=0 or x+3=0

x=0 or x=-3 or x=3

To find the absolute value of the determinant of the Jacobian for the change of coordinates T: R² → R² given by x = e^(-2u)cos(4v) and y = e^(-2u)sin(4v), we need to compute the Jacobian matrix and then evaluate its determinant.

The Jacobian matrix J is defined as:

J = [∂(x)/∂(u)  ∂(x)/∂(v)]

   [∂(y)/∂(u)  ∂(y)/∂(v)]

Let's calculate the partial derivatives:

∂(x)/∂(u) = -2e^(-2u)cos(4v)

∂(x)/∂(v) = -4e^(-2u)sin(4v)

∂(y)/∂(u) = -2e^(-2u)sin(4v)

∂(y)/∂(v) = 4e^(-2u)cos(4v)

Now, we can construct the Jacobian matrix:

J = [ -2e^(-2u)cos(4v)  -4e^(-2u)sin(4v) ]

   [ -2e^(-2u)sin(4v)   4e^(-2u)cos(4v) ]

The determinant of the Jacobian matrix is:

|J| = (-2e^(-2u)cos(4v))(4e^(-2u)cos(4v)) - (-4e^(-2u)sin(4v))(-2e^(-2u)sin(4v))

   = 8e^(-4u)(cos²(4v) + sin²(4v))

   = 8e^(-4u)

Therefore, the absolute value of the determinant of the Jacobian for the given change of coordinates is |J| = |8e^(-4u)| = 8e^(-4u).

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For seven hours of landscaping, Company B would be less expensive than Company A.

An equation is defined as any pair of expressions that both contain the equal sign.

Because of this, Company charges $35 per hour and a $250 equipment fee, compared to Company B's $25 per hour and $300 equipment fee.

For t hours of landscaping, Company A will bill the following:

A = 35t + 250 (1) (1)

In a similar vein, Company B bills the following sum for t hours of landscaping:

B = 25t + 300 (2) (2)

Solve equation (1) now with t = 7:

A = 35 (7) + 250

A = 245 + 250

A = 495

So, for 7 hours of landscaping, business A would bill $495.

Similarly, when equation (2) is resolved for t = 7,

B = 25(7) + 300

B = 175 + 30

B = 475

So, for 7 hours of gardening, business B would bill $475.

Therefore, for seven hours of landscaping, Company B would be less expensive than Company A.

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The compound inequality which represents the range of possible values of x for the given triangle is  8<x<34.

What is triangle?

A triangle is a specific type of polygon which consists of three sides, three angles and three vertices. There are different types of triangle based on different types of base and angles.

In triangle ABC, the side lengths are AB = 13, AC=21, and BC = x.

Here we use the theorem of triangle that describes , the sum of the length of any two sides of a triangle is always greater than the third side.

So at first considering BC as longer side we get,

AB+AC>BC

putting the values we get,

13+21> x

34>x

34>x

Again considering AC as the longer side and again applying the same argument of triangle we get,

AB+BC>AC

13+x>21

x>21-13

x>8

Hence, the compound inequality which represents the range of possible values of x for the given triangle is  8<x<34.

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Answer:

I wanna say $5,970.26

Step-by-step explanation:

To find the PDF (Probability Density Function) of the duration of the trip, we need to determine the distribution of the speed and calculate the corresponding duration.

Given that the speed of John Slow is uniformly distributed between 30 and 60 miles per hour, we have a continuous uniform distribution over this interval.

The duration of the trip can be calculated by dividing the distance (180 miles) by the speed (v) since speed = distance/time, rearranging the equation gives time = distance/speed.

Let's denote the duration of the trip as T. We can express T in terms of the speed (v) as follows:

T = 180 miles / v

To find the PDF of T, we need to determine the probability density function of v. Since v is uniformly distributed between 30 and 60 mph, its PDF is a constant over this interval.

The width of the interval is (60 - 30) = 30 mph, and since it is a uniform distribution, the height of the PDF is 1/30 mph^(-1) to ensure the total area under the PDF equals 1.

Therefore, the PDF of T is given by:

PDF(T) = PDF(v) * |dt/dv|

Since v = 180/T, we can differentiate this equation with respect to T to find |dt/dv|:

|dt/dv| = |-180/T²|

Substituting the PDF of v and |dt/dv| into the PDF of T:

PDF(T) = (1/30 mph^(-1)) * |-180/T²|

Simplifying further, we have:

PDF(T) = 6/T² mph^(-1)

Therefore, the PDF of the duration of the trip is 6/T² mph^(-1).

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Answer:

a³²

Step-by-step explanation:

the law of exponents states that when raising a power to another power multiply the exponents

our answer will go like this:

(a⁸)⁴

a⁸*⁴

a³²

The illustration of 10 sided polygon is attached below.

Polygons are closed geometric figures made up of line segments that are connected end-to-end. The number of sides of a polygon determines the polygon's name.

In mathematical terms, a decagon is a 10-sided polygon with 10 vertices and 10 angles.

To draw a decagon, we need to start by drawing a circle. We can use a compass to draw a circle of any size we want. The radius of the circle will determine the size of the decagon.

Next, we need to draw a horizontal line through the center of the circle. This line will be the base of the decagon, and it will divide the circle into two equal halves.

Since a decagon has 10 sides, we need to divide the circle into 10 equal parts.

We can then use these lines as guides to draw the sides of the decagon. We start at one of the points where the lines intersect the circle, and draw a line segment to the next point.

We can label the vertices of the decagon with numbers, starting with 1 and going clockwise, as shown in the diagram.

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Answer:

4 tiles are added to each figure in the tile pattern.

Answer: do 8 x 12

Step-by-step explanation:

Answer:

48cm^2

Step-by-step explanation:

(b*h)/2 -> (8*12)/2 -> 96/2 = 48 cm^2

Answer:

Break-even point is at quantity 220.

Step-by-step explanation:

Given the rent amount that is fixed cost for the store = $550

The average cost of the goods = $3

The average price of the goods = $5.50

Let the total number of break-even items = Q

Thus, total revenue = 5.50 x Q = 5.50Q

At break-even, TR = TC

5.50Q = FC + VC

5.50Q = 550 + 3Q

5.50Q - 3Q = 550

2.50Q = 550

Q = 550 / 2.50

Q = 220

Thus break-even point is at quantity 220.

Answer:

In geometry, a Chittagong or 1000-hon is a polygon with 1,000 sides. Philosophers commonly ... The measure of each internal angle in a regular Chittagong is 179.64°. ... Rene Descartes uses the Chittagong as an example in his Sixth Meditation to ... uses the Chittagong as evidence that "intuition is not necessarily founded

Step-by-step explanation:

Answer:

3= A

2=A or D I am not sure

Step-by-step explanation:

Answer:

1/20

Step-by-step explanation:

3/10 - 1/4

First, convert the fractions to a common denominator:

3/10 *2/2 = 6/20

1/4 * 5/5 = 5/20

Now put them back into the equation and solve:

6/20 - 5/20 = 1/20

Another way to do this:

3/10 - 1/4

Convert the fractions into decimals:

3/10 = 0.3

1/4 = 0.25

substitute back into the equation and solve:

0.3 - 0.25 = 0.05

convert back into fractions:

0.05 = 1/20

Answer:

3.5

Step-by-step explanation:

b divided by 10 is A

35 divided by 10 is 3.5

Answer: The domain is all values of x that make the expression defined. The range is the set of all valid y values

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be Domain: (-∞, ∞) and   Range: (0,∞).

Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.

Here,

Given :  f(x)=\(2^{x}\)+1

If a value has not been added, an exponential function's curve normally approaches a horizontal asymptote at y=0 or the x-axis. The curve changes if it has.

The asymptote is unaffected by this function's addition on the exponent because it does not apply to the entire function.

The values of its y-axis remain between 0 and. This is the set of y values, or the range.

However, depending on the leading coefficient, the range of exponentials can vary. If the value is negative, the graph turns inside-out and the range reaches -. It's also lacking in this.

The exponent's addition to 1 moves the function to the left without changing the range.

The x values in exponential functions are often unaffected and all are taken into account in the function. The domain stays the same even while it changes. Its range is (0,∞)

 Range: (0,∞)

Therefore , the solution of the given problem of function comes out to be

Domain: (-∞, ∞) and   Range: (0,∞).

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The area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To solve this problem, we can use the formula for the volume of a hexagonal prism:

V = (3√3/2) * a^2 * h

where V is the volume, a is the length of one side of the hexagonal base, and h is the height of the prism.

We are given that the height of the prism is 4 units and the volume is 98 units^3. Plugging these values into the formula, we can solve for the length of one side of the base:

98 = (3√3/2) * a^2 * 4
a^2 = 98 / (12√3)
a ≈ 2.95

Now that we know the length of one side of the base, we can find the area of the hexagon by using the formula:

A = (3√3/2) * a^2

where A is the area of one of the bases. Plugging in the value we found for a, we get:

A = (3√3/2) * (2.95)^2
A ≈ 7.39

Therefore, the area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

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