P(x) = 3x3 - 3x2 + x - 1?​

λ is nullhomotopic in A ∩ B as well, using the fact that λ is nullhomotopic in both A and B.

To show that λ is nullhomotopic in A ∩ B, we can use the Seifert-Van Kampen theorem.

First, let's consider A. Since λ is nullhomotopic in A, there exists a continuous map h: S^1 × I -> A such that h(x, 0) = λ(x) and h(x, 1) is a constant map for all x in S^1.

Next, let's consider B. Similarly, since λ is nullhomotopic in B, there exists a continuous map g: S^1 × I -> B such that g(x, 0) = λ(x) and g(x, 1) is a constant map for all x in S^1.

Now, let's define a map f: S^1 × I -> A ∩ B by f(x, t) = h(x, t) = g(x, t) for all x in S^1 and t in I.

Since h and g are both continuous and agree on the intersection A ∩ B, the map f is well-defined. Moreover, f is continuous as it is the restriction of both h and g to A ∩ B.

Furthermore, f(x, 0) = h(x, 0) = λ(x) and f(x, 1) = g(x, 1) = constant map for all x in S^1.

Therefore, we have shown that λ is nullhomotopic in A ∩ B as well, using the fact that λ is nullhomotopic in both A and B.

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Answer:

Step-by-step explanation:

\((3x+4)(x^2+px+5) \\=3x^3+3px^2+15x+4x^2+4px+20\\=3x^3+(3p+4)x^2+(15+4p)x +20\)

since we know that \(x^2\)  in this expansion is \(-23x^{2}\)

thus \(3p+4=-23\\3p=-27\\p=-9\)

Hope that helps!

Answer:

l = 32.57, w = 24.43, h = 8.14

Step-by-step explanation:

volume = l*w*h

l = 4x

w = 3x

h = x

540 = 4x * 3x * x

540 = 12x^3

\(\sqrt[3]{540}\) = 8.14

l = 4x = 4(8.14) = 32.57

w = 3x = 3(8.14) = 24.43

h = x = 8.14

hope it helps :)

mark brainliest!!

The problem is asking us to calculate the probability that less than 200 of 500 cell phone calls selected at random will be spam, given that First Orion estimates 45% of all cell phone calls in 2019 will be spam. To solve this problem, we can use the normal approximation to the binomial distribution.

First, we need to find the mean and standard deviation of the binomial distribution. The mean is given by:

μ = n * p

where n is the number of trials (500) and p is the probability of success (i.e., a cell phone call is spam) on a single trial (0.45):

μ = 500 * 0.45 = 225

The standard deviation is given by:

σ = sqrt(n * p * (1 - p))

σ = sqrt(500 * 0.45 * (1 - 0.45)) = 11.79

Next, we can use the normal approximation to calculate the probability that less than 200 of the 500 cell phone calls selected at random will be spam. We need to standardize the value of 200 using the mean and standard deviation of the binomial distribution:

z = (x - μ) / σ

where x is the number of successes (i.e., spam calls) we're interested in (200):

z = (200 - 225) / 11.79 = -2.12

We can use a standard normal distribution table or calculator to find the probability that a standard normal random variable is less than -2.12. This probability is approximately 0.017.

Therefore, the probability that less than 200 of the 500 cell phone calls selected at random will be spam is approximately 0.017 or 1.7%.

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Answer:

-2x^2+10x-8

Step-by-step explanation:

(2x-2)(-x+4)

-2x^2+8x+2x-8

Answer:

FOR ALL MY POINTS write an argumentative essay on why dog parks are "helpful or harmful"

READ PROMPT

Step-by-step explanation:

Answer:

Formula for the circumference of a circle =2pir

Since the diameter is 10m the radius is half of that which is 5m.

2×3.14×5=31.4m

Step-by-step explanation:

I hope this helps.Have a great day♡

Answer:

y = 6 when x = 18

Step-by-step explanation:

The appropriate formula for this direct proportion is y = kx, where k is the constant of proportionality.

We know y = 3 when x = 9:  3 = k(9)

This yields k = 3/9, or k = 1/3

Then the formula is y = (1/3)x

and when x = 18, y = (1/3)(18) = 6

y = 6 when x = 18

Answer:

  1 = 1; 2 = 3 -1; 3 = 3; 4 = 3 +1; 5 = 9 -3 -1;

  6 = 9 -3; 7 = 9 -3 +1; 8 = 9 -1; 9 = 9; 10 = 9 +1

  11 = 9 +3 -1; 12 = 9 +3; 13 = 9 +3 +1

Step-by-step explanation:

You want the numbers 1 – 13 expressed in terms of the digits 1, 3, 9 using operations +, -, and ×.

The digits 1, 3, 9 represent the place values of numbers in base 3. This means we can use the base-3 representation of a number to give a clue as to how to represent it using these digits.

The digits of a base 3 number are 0, 1, 2. We don't have a 2 to work with, but we know that 2 = 3 -1, so we can use that fact. Here is an example:

  5 = 12₃ = 1×3 + (3 -1)×1 = 3 +3 -1

  = 20₃ -1 = (3 -1)×3 -1 = 9 -3 -1

After writing a few numbers, we notice the signs go in the progression +, -, 0 where 0 means the digit is not included. The attachment shows the sums that make the numbers 1–13.

__

Additional comment

We could, of course, use the allowed "other digits" to include 2. For example, ...

  5 = 3 + 2×1

  6 = 2×3

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Step-by-step explanation:

30%=0.3

3%=0.03

1/300=0.003333

30000/100=300

Therefore the order is:

0.003;1/300;3%, 30%;1.3;30;30000/100

Answer:

Step-by-step explanation:

30%=0.3

3%=0.03

1/300=0.003333

30000/100=300

Therefore the order is:

0.003;1/300;3%, 30%;1.3;30;30000/100

Answer:

You are right

Step-by-step explanation:

80% of a number is always going to be less than 100% of a number. Assuming the numbers positive, which it said

Answer: its >

Step-by-step explanation: beacuse80% x .01 =0.008 and 0.008= 0.8%

Answer:

1. 89 2. 91

Step-by-step explanation:

180-29-62=118-29=89

180--89=91

Answer:

91 and 89 degrees respectively

Step-by-step explanation:

Sooooo, the exterior angle of any angle in a triangle is equal to the sum of the  2 other adjacent interior angles in a triangle. Therefore, we just need to do 29+62, which is 91 degrees, so the Exterior angle is 91 degrees. Next, to find the last unknown angle of a triangle, we can take the sum of the 2 other interior angles and subtract it from 180. Doing this here, we get 180-91, which is 89 degrees.

The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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The time taken by cook to make one sandwich is equals to forty-five seconds.

let "x" be the time (in seconds) to make 1 sandwhich and " y " be the time (in seconds) to make 1 salad. Now, it takes 3 min 45 sec to make 3 sandwiches and 3 salads.

time in seconds , 3 min 45 sec = 225 sec

so, 3x + 3y = 225

=> x + y = 75 --(1)

Also, it takes 8 min 30 sec to make 6 sandwiches and 8 salads, i.e ,8min 30sec = 510 sec

so, 6x + 8y = 510

=> 3x + 4y = 255--(2)

We have a system of linear equations consists equation (1) and (2). We solve this system of equations by using Substitution,

Substitute the value of x = 75 - y in equation (2),

3x + 4y = 255

=> 3(75- y) + 4 y = 255

=> 225 - 3y + 4y = 255

=> y = 255 - 225 = 30

from equation (1) , x = 75 - 30 = 45.

So, it takes 45 seconds to make one sandwich and 30 seconds for one salad .

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The definition and explanation of an equation are given below with an example.

in mathematics, an equation is defined as an expression that expresses equality between 2 quantities or expressions. We use equations quite a lot in our daily lives whenever we have to equate two quantities and find out how they are equal. These are used in all branches of science because of the huge purpose they serve.

in simple words it tells what we have on the Left-Hand Side of the "=" sign is the same as what we have on the right-hand side of the statement. Some examples of equations are-

E²=m²c⁴+p²c²

x²+3x-1=0

70 oranges= 7 oranges × 10 oranges

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Answer:

7 1/8 is your answer

Step-by-step explanation:

He needs to fill the 1/3 cup 7 1/8 times, not sure if you have answer choices or if your teacher is expecting a whole number, the right answer is 7 1/8 but if your teacher wants a whole number as an answer, you might want to round up or down.

Answer:

i keep getting different stuff

Step-by-step explanation:

4 x − 5 + y = 0

x + 6 y = 5

6 x − 3 y =12

3 x + y = 16

6 x − 3 y = 12

3 x + 4 y = − 5

Answer:

one proportion is 15 miles over 2.5 hours -  yesterday is M miles over 4 hours (?)

Step-by-step explanation:

Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

Answer: False

Step-by-step explanation: On the X-axis would be (0,A)

Answer:

I think it's 2.5 million liters

Step-by-step explanation:

I asked  my mom. And sister but my sister got a different answer but I took my mom answer.

There is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.

In two- or three-dimensional space, a curve is a mathematical object that symbolises a continuous, smooth path. Curves can be derived from geometric operations, parametric equations, or mathematical equations. They are commonly used to simulate real-world processes in physics, engineering, mathematics, and many other disciplines.

To find the level curve of value c for the given surface \(z = f(x, y) = (x^2/4) + (y^2/25) = c\), where c < 0, follow these steps:

Step 1: Write down the equation of the surface.
\(z = f(x, y) = (x^2/4) + (y^2/25)\)

Step 2: Replace z with the constant c.
\(c = (x^2/4) + (y^2/25)\)

Step 3: Rearrange the equation to isolate \(y^2\).
\(y^2 = 25(c - (x^2/4))\)

However, note that we're given that c < 0. This means that the value inside the parentheses (c - (\(x^2/4\))) must also be negative. Since y^2 can't be negative, there's no real solution for this equation.

In conclusion, there is no curve that describes the level curve of value c for the given surface, as the condition c < 0 makes it impossible to find a real solution.

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Answer:

The answer is -1.088

Step-by-step explanation:

Multiply  − 13.6  by  0.08 .

Hoped this helped!

Rounded to the nearest tenth, the greatest possible length of the longest side is 25.4 mm, which corresponds to option (C)

Since the triangle is acute, the sum of the squares of the two shorter sides must be greater than the square of the longest side. Using this fact, we can set up the inequality:

$19^2 + (2x)^2 > (3x)^2$

Simplifying, we get:

$361 + 4x^2 > 9x^2$

$5x^2 < 361$

$x^2 < 72.2$

Since x must be positive, we take the square root of both sides:

$x < 8.5$

Therefore, the longest side has a maximum length of:

$3x < 3(8.5) = 25.5$

Rounded to the nearest tenth, the greatest possible length of the longest side is 25.4 mm, which corresponds to answer choice (C).

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To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.

Here,

4 is a root/zero of polynomial

P(x)  =   (k-2) x²  - 2 x  - (k+5)

P(4) = 0

(k - 2) 4²  - 2 * 4 - (k+5)  = 0

15 k - 45 = 0  

k = 3

The value of k if 4 is one of the zeros of the quadratic polynomial is 3.

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Complete question:

If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.

The experimental probability of landing on A is 0.3 and the experimental probability of landing on C is 0.4.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To find the experimental probability of landing on A or C, we need to add up the number of times the spinner landed on A and C, and then divide that by the total number of spins.

From the table, we can see that the spinner landed on A 30 times and on C 40 times. Therefore, the total number of times the spinner landed on either A or C is:

30 + 40 = 70

So the experimental probability of landing on A or C is:

70/100 = 0.7

However, we need to find the experimental probability of landing on A or C separately. To do that, we need to divide the number of times the spinner landed on A or C individually by the total number of spins:

Experimental probability of landing on A = 30/100 = 0.3

Experimental probability of landing on C = 40/100 = 0.4

Therefore, the experimental probability of landing on A is 0.3 and the experimental probability of landing on C is 0.4.

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The two limits when x tends to zero are:

\(\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0\)

Notice that we have a jump at x = 0.

Then we can take two limits, one going from the negative side (where we will go along the blue line)

And other from the positive side (where we go along the orange line).

We will get:

\(\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0\)

Notice that the two limits are different, that means that the function is not a continuous function.

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SOLUTION

(c) The values of x for which f(x) = -1

Looking from the graph, this does not exist.

Hence the answer is "None"

(d) The values of x for which f(x) = -3

Looking form the graph, this is between 0 and 1

So we have this as

So in interval notation, the answer is

(e) The x-intercept is where the graph cuts the x-axis

The graph cuts the x-axis at -1

Hence the answer is (-1, 0)

Here are the Laplace transforms of the given functions:

(a) The Laplace transform of the function te^(-at)u(t - a) is:

L{te^(-at)u(t - a)} = 1/(s + a)^2

(b) The Laplace transform of the function (ta)e^(-at)u(t - a) is:

L{(ta)e^(-at)u(t - a)} = 2a/(s + a)^3

(c) The Laplace transform of the function 8δ(t) + (a - b)e^(-bt)u(t) is:

L{8δ(t) + (a - b)e^(-bt)u(t)} = 8 + (a - b)/(s + b)

(d) The Laplace transform of the function (t^3 + 1)e^(-2t)u(t) is:

L{(t^3 + 1)e^(-2t)u(t)} = (6/s^4) + (8/s^3) + (2/s^2) + (1/(s + 2))

Note: In the Laplace transform, u(t) represents the unit step function, and δ(t) represents the Dirac delta function.

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