Let f and g be polynomials of degree 3. Is it true that f ∘ g = g ∘ f?

A. Yes, always

B. No, it's only with polynomials with a degrees of 1

C. It is true in some cases

D. No, never

In response to the given query, the result we have is As a result, the expressions following statement may be used to explain how long Interstate 90 is: 2m + 153.5

Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.

Let L represent the length of I-90. We are informed that

L = 2m + 153.5

where m is Interstate 15's length.

As a result, the following statement may be used to explain how long Interstate 90 is:

2m + 153.5

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Answer:

A: x

Step-by-step explanation:

So with problems like this when it saids f(g(x) it wants you to plug those values in. In some cases you have a value where the x is but you don't so you can't solve g(x) so you move on to the next step. You plug in g(x)= x-1/2 everywhere there is a x in f(x). So our equation would be 2(x-1/2) + 1. Then you solve by canceling the 2 by dividing it out so we would have x-1 +1. Then you combine like terms which -1 +1 is 0 so our final answer would be x.

Step-by-step explanation:

Refer to pic...........

Answer:

Step-by-step explanation:

Here's the long division of (2x³ + 3x² + 4x + 2) ÷ (x + 2):

2x^2 - x + 6

x + 2 | 2x^3 + 3x^2 + 4x + 2

- (2x^3 + 4x^2)

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

- x^2 + 4x

- (- x^2 - 2x)

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

6x + 2

- (6x + 12)

--------

-10

Therefore, the quotient is 2x^2 - x + 6, and the remainder is -10.

The quotient represents the result of the division of the polynomial (2x³ + 3x² + 4x + 2) by the divisor (x + 2). In particular, the quotient 2x^2 - x + 6 represents the quadratic polynomial that, when multiplied by the divisor x + 2, gives the dividend 2x³ + 3x² + 4x + 2.

In other words, we have:

(2x³ + 3x² + 4x + 2) = (x + 2)(2x^2 - x + 6) - 10

The remainder -10 indicates that the division is not exact, and that there is a "leftover" term of -10 when we try to divide the polynomial (2x³ + 3x² + 4x + 2) by (x + 2).

Answer:

Option A.) 1055.66 lbs

Step-by-step explanation:

Carlota's rate on a bicycle who is 74 miles away is approximately 6.1667 miles per hour.

Carlota's rate can be found by using the formula: rate = distance ÷ time. To find her rate for the first part of the trip, we can plug in the given values:

To find her rate for the second part of the trip, we need to subtract the distance and time she had already traveled from the total distance and time:

Then we can plug these values into the formula:

Since Carlota's rate is the same for both parts of the trip, we can simply use the overall distance and time to find her rate:

Therefore, Carlota's rate is approximately 6.1667 miles per hour.

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Answer:

420mm^3

Step-by-step explanation:

10mm×10.5mm=105mm

105mm×8mm=840mm^3

840mm^3÷2=420mm^3

The volume of this prism is calculated by this equation:

V = (area of a triangle)(height)

So plugging in the numbers it looks something like this

V = (10 x 10.5 x 1/2)(8)

V = (105 x 1/2)(8)

V = (52.5)(8)

V = 420 mm^3

Answer: I remember this question very well. I believe that the correct answer is 99.7%

68% of data falls between 15 and 25.

95% of data falls between 10 and 30.

99.7% of data falls between 5 and 35.

The value of x on the straight line is 43 degrees

From the question, we have the following parameters that can be used in our computation:

The straight line

The sum of angles on a straight line is 180 degrees

Using the above as a guide, we have the following equation

3x + 51 = 180

Evaluate

3x = 129

Divide by 3

x = 43

Hence, the value of x is 43 degrees

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To solve the equation 1/2 + a = 1 3/4, we need to convert the mixed number 1 3/4 to an improper fraction:

1 3/4 = 4/4 + 3/4 = 7/4

Now we can rewrite the equation as:

1/2 + a = 7/4

To isolate the variable a, we need to subtract 1/2 from both sides:

a = 7/4 - 1/2

To add these two fractions, we need to find a common denominator, which is 4:

a = (7/4 - 2/4)

a = 5/4

Therefore, a = 5/4.

To solve the equation 1/2 + ? = 7, we can follow a similar approach. We need to isolate the variable on one side of the equation, so we need to subtract 1/2 from both sides:

? = 7 - 1/2

We need to find a common denominator to add these two fractions, which is 2:

? = (14/2 - 1/2)

? = 13/2

Therefore, the missing number is 13/2.

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The probability that there are not greater than 859 defective products in 359 packages is 0.9999.

We are given that;

Distribution: X 0 3 4 1 2 Р 0.02 0.14 0.34 0.36 0.14 1

0(X) = 0.9635 2

Now,

We need to know the probability of success for each package, which is the probability of having a defective product. Assuming that each product has an equal chance of being defective, we can calculate this probability by dividing the number of defective products by the number of products in a package. In this case, we have:

[tex]p = \frac{0.02 + 0.14 + 0.34 + 0.36 + 0.14}{4} = 0.25[/tex]

This means that each product has a 25% chance of being defective, and each package has a binomial distribution with n=4 and p=0.25.

To find the average and the standard deviation of the number of defective products in a package, we can use these formulas³:

[tex]$$E(X) = np$$$$\sigma(X) = \sqrt{np(1-p)}$$[/tex]

Plugging in the values of $n$ and $p$, we get:

[tex]$$E(X) = 4 \times 0.25 = 1$$$$\sigma(X) = \sqrt{4 \times 0.25 \times (1-0.25)} = \sqrt{0.75} \approx 0.866$$[/tex]

Therefore, the average number of defective products in a package is 1, and the standard deviation is 0.866.

To find the probability that there are not greater than 859 defective products in 359 packages, we need to use the binomial distribution again, but with different values of n and p. In this case, we have:

[tex]$$n = 359 \times 4 = 1436$$$$p = 0.25$$[/tex]

We want to find the probability that [tex]$X \leq 859$[/tex], where [tex]$X$[/tex] is the number of defective products in 1436 trials. We can use this formula:

[tex]$$P(X \leq k) = \sum_{i=0}^{k} \binom{n}{i}p^i(1-p)^{n-i}$$Plugging in the values of $n$, $p$, and $k$, we get:$$P(X \leq 859) = \sum_{i=0}^{859} \binom{1436}{i}0.25^i(1-0.25)^{1436-i}$$[/tex]

Therefore, by probability the answer will be 0.9999.

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The answer is \( f(3) = 5 \) with no spaces.

Given the function \( f(x) = \left\{ \begin{array}{llr} -x^2 & \text{for} & x < 0 \\ x+2 & \text{for} & x \ge 0 \end{array} \right. \), we need to evaluate \( f(3) \).

Since \( 3 \ge 0 \), we will use the second part of the function, which is \( f(x) = x + 2 \).

So, we plug in \( x = 3 \) into the function and get:

\( f(3) = 3 + 2 = 5 \)

Therefore, the answer is \( f(3) = 5 \) with no spaces.

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The measure of Angle D in a parallelogram is 88 degrees.

Explain about parallelogram ?

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure.

Properties of a parallelogram:

According to the question:
Since EFDM is a parallelogram, we know that opposite angles are equal. Therefore,

Angle E = Angle M

Angle D = Angle F

We're given:

Angle E = 16x + 12

Angle D = 18x - 2

So we have:

Angle M = 16x + 12

Angle F = 18x - 2

The sum of the angles in a parallelogram is 360 degrees. Therefore, we have:

Angle E + Angle F + Angle D + Angle M = 360

Substituting the given values, we get:

(16x + 12) + (18x - 2) + (16x + 12) + (18x - 2) = 360

72x + 20 = 360

72x = 340

x = 5

Now we can find the values of Angle E, Angle D, Angle F and Angle M:

Angle E = 16x + 12 = 16(5) + 12 = 92 degrees

Angle D = 18x - 2 = 18(5) - 2 = 88 degrees

Angle F = Angle D = 88 degrees

Angle M = Angle E = 92 degrees

Therefore, the measure of Angle D is 88 degrees.

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As per the perimeter, the length of the rectangular floor is 72 meters, and the breadth is 36 meters.

Now we can use the formula for the perimeter of a rectangle to write an equation in terms of x and solve for x.

Perimeter of the rectangle = 2(length + breadth)

Given that the perimeter is 216 m, we can substitute the values of length and breadth in terms of x to get:

216 = 2(2x + x)

Simplifying this equation, we get:

216 = 2(3x)

Dividing both sides by 2, we get:

108 = 3x

Solving for x, we get:

x = 36

Now that we have the value of x, we can use it to find the length and breadth of the rectangular floor.

Length = 2x = 2(36) = 72 m

Breadth = x = 36 m

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The given exponential functions are classified as exponential growth or exponential decay above.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is to check whether the given functions represent exponential growth or decay.

We can write the classified functions as -

{ 1 }.   y = 500(0.30)ˣ                     exponential decay

{ 2 }.  y = 500(1.70)ˣ                      exponential growth

{ 3 }.  y = 0.3(500)ˣ                       exponential growth

{ 4 }.  y = 500(0.30)ˣ - 6               exponential decay

{ 5 }.  y = 0.3(1.7)ˣ - 2                    exponential growth

{ 6 }.  y = 500(0.30)ˣ ⁺ ⁸               exponential growth

{ 4 }.  y = 500(0.30)ˣ ⁻ ⁶               exponential decay

Therefore, the given exponential functions are classified as exponential growth or exponential decay above.

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The Simple ratio and the ratio of the perimeters of two regular octagons are approximately 1.472

The formula for the area of the regular polygon is:

Area = (2 + 2[tex]\sqrt{2}[/tex]) × [tex]s^{2}[/tex]

Where, s = length of the side of a polygon

consider two equations for the two octagons,

48 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s1)^{2}[/tex]

147 = (2 + 2[tex]\sqrt{2}[/tex]) × [tex](s2)^{2}[/tex]

The length of each polygon is

s1 = [tex]\sqrt{\frac{48}{(2 + 2\sqrt{2} )} }[/tex] ≈ 3.079cm

s2 = [tex]\sqrt{\frac{147}{(2 + 2\sqrt{2} )} } }[/tex] ≈ 4.532cm

The similarity ratio is,

s2 ÷ s1 ≈ 1.472

The ratio of perimeters is,

8s2 ÷ 8s1 = s2 ÷ s1 ≈ 1.472

Therefore, the similarity ratio and the ratio of the perimeters are both approximately 1.472.

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Answer: you probly need to find the root of the number 8

Step-by-step explanation:

The correct domain for the function f(t)=(5)/(t^(2)+4) is {all reals}.

The domain of a function is the set of all possible inputs or values for the independent variable, t in this case. The function f(t)=(5)/(t^(2)+4) has a denominator of t^(2)+4. To find the domain, we need to determine the values of t that would make the denominator equal to zero, as those values would make the function undefined.

t^(2)+4=0
t^(2)=-4
t=±√(-4)

Since the square root of a negative number is not a real number, there are no real values of t that would make the denominator equal to zero. Therefore, the domain of the function is {all reals}.

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Kendra needs to have at least $7.35 in her purse and needs to accumulate at least $2.87 more to shop for the special bead.

To discover the total amount Kendra needs to shop for the special bead, we add the amount she already has in her purse to the amount she needs to shop for the bead:

x = $7.35 + $2.87

x = $10.22

Thus, Kendra needs a total of $10.22 to shop for the special bead.

To represent the scenario as inequalities, we can use the subsequent:

Let y be the amount Kendra wishes to buy the unique bead, then:

Kendra has at least $7.35: y + $7.35 ≥ y

Kendra needs at the least $2.87 more: y + $2.87 ≤ x

Combining these inequalities, we get:

y + $7.35 ≥ y

y + $2.87 ≤ x

Therefore, Kendra needs to have at least $7.35 in her purse and needs to accumulate at least $2.87 more to shop for the special bead.

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We can write the mean absolute deviation as -

1.63.

Absolute deviation or mean absolute deviation is the measure of how far a given data element is from a given mean value of the data.

Given is that Suzie's Desserts offers its customers 5 dessert options. The prices are: $5.00 $9.00 $9.00 $6.00 $6.00 $9.00 $9.00.

The formula for absolute deviation is -

[tex]$\frac {1}{n} \sum \limits_{i=1}^n |x_i-m(X)|[/tex]

We can calculate the mean as -

(5 + 9 + 9 + 6 + 6 + 9 + 9)/7 = 7.57

We can write the  absolute deviation as -

Absolute deviation =

1/7(5 - 7.57 + 9 - 7.57 + 9 - 7.57 + 6 - 7.57 + 6 - 7.57 + 9 - 7.57 + 9 - 7.57) = 1.63

Therefore, we can write the mean absolute deviation as -

1.63.

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Answer:

151 tables

Step-by-step explanation:

If 1 table is used for 6 guests then for 901 guest we need to divide 901 by 6

901÷6= 150.15

Rounding of the answer 151 tables needed

The equation that can be used to determine the area of the glass is A = 2 1/2 x 4.

A rectangle is a 2-dimensional quadrilateral with four right angles. A rectangle has two diagonals of equal length which bisect each other. The sum of interior angles is 360 degree and opposite sides are parallel

The area of the rectangle is the product of the length and the width.

Area of a rectangle = length x width

A = 4 x 2 1/2

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The value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.

The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.

The connection between the four edges of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem.

For the given figure we see the right triangle DHB.

Here, DH = 20 in and HB = 12 in.

Using the Pythagoras theorem we have:

DB² = DH² + HB²

DB² = 20² + 12²

DB² = 400 + 144

DB = 23.32

For the right triangle RHK we have:

HR = 16 and HK = 8.72

Using the Pythagoras theorem:

RK² = 16² + 8.72²

RK= 18.22

Also, KY = YK = 6.83 in.

Hence, the value of the segments DB = 23.32 in, RK = 18.22 in and YK = 6.83 in.

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{-2 2 22}

a) The characteristic polynomial of A is given by:
$$p_A(\lambda) = \lambda^3 - 5\lambda^2 + 18\lambda + 36$$
b) The two eigenvalues of A are:
$$\lambda_1=2, \lambda_2=-4, \lambda_3=9$$
c) A basis for the eigenspace corresponding to the smallest eigenvalue $\lambda_2=-4$ is given by the set of vectors:
$$\begin{bmatrix} 0\\1\\0 \end{bmatrix}, \begin{bmatrix} 2\\0\\1 \end{bmatrix}$$
d) A basis for the eigenspace corresponding to the largest eigenvalue $\lambda_3=9$ is given by the set of vectors:
$$\begin{bmatrix} 1\\0\\-4 \end{bmatrix}, \begin{bmatrix} -2\\2\\22 \end{bmatrix}$$

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The cubic inch value that most closely approximates the prism's volume is 12in³.

Any three-dimensional solid's volume is the area it takes up. The shapes of these solids include cubes, cuboids, cones, cylinders, and spheres.

Forms come in a wide range of volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylinders, cones, and more. We'll learn how to calculate the volumes of each of these forms.

To find the volume of the rectangular prism in the above problem, multiply its length, width, and height. The image reveals the rectangle's measurements to be around 5.5 inches long and 4 inches broad. Volume is calculated as follows: Volume = Length x Width x Height

= 5.5 inches x 4 inches x 218 inches

= 4 x 5.5 x 218

= 4 x 1199

= 4796

4796 cubic inches is the result.

When we round this response to the nearest whole number 12 in³ is the measurement that most closely approximates the prism's volume in cubic inches.

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The complete question is:

The rectangle shown represents the base of a rectangular prism. Use the ruler provided to measure the length and width of the rectangle to the nearest 14 inch. The height of the prism is 218inches. The dimensions are 5.5 inches and 4 inches. Which measurement is closest to the volume of the prism in cubic inches?

F.33 inches3

G.23 inches3

H.11 inches 3

J.12 inches 3

The cost of producing 2000 bagels is $796.8.

To determine the cost of producing 2000 bagels, we need to plug in the value of x into the given equation and solve for C(x).
C(x) = 300 + 0.25x - 0.4(x/1000)^3
C(2000) = 300 + 0.25(2000) - 0.4(2000/1000)^3
C(2000) = 300 + 500 - 0.4(2)^3
C(2000) = 300 + 500 - 0.4(8)
C(2000) = 300 + 500 - 3.2
C(2000) = 796.8

Therefore, the cost of producing 2000 bagels is $796.8.

In general terms, profit is nothing more than revenues minus costs. This mathematically expressed is:

Profit = Revenues - Costs

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The solution to the inequality 5(3y+1)<15 in interval notation is (-∞, 2/3).

To solve the inequality 5(3y+1)<15, we need to isolate the variable y on one side of the inequality. Here are the steps to do so:
1. Start with the given inequality: 5(3y+1)<15
2. Distribute the 5 on the left side: 15y+5<15
3. Subtract 5 from both sides: 15y<10
4. Divide both sides by 15: y<10/15
5. Simplify the fraction: y<2/3

Now, we can write the solution in interval notation. Interval notation uses parentheses or brackets to indicate the range of values that satisfy the inequality. In this case, the solution is all values of y less than 2/3, so we use the notation (-∞, 2/3).

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As our calculated t-value of 3.032 is greater than the critical value of ±1.645, we can reject the null hypothesis at the 0.1 significance level and conclude that the coefficient for the variable is statistically significant and different from zero.

The hypotheses that we want to test are:

H0: The coefficient for the variable is equal to zero.

H1: The coefficient for the variable is not equal to zero.

Using the given output, we can see that the coefficient for the variable is 15.509, and the standard error of the coefficient is 5.123. The t-value for the coefficient is calculated by dividing the coefficient estimate by its standard error, so:

t = 15.509 / 5.123 = 3.032

To test the hypothesis, we can compare the calculated t-value with the critical value of the t-distribution with n-k-1 degrees of freedom (where n is the sample size and k is the number of independent variables), at a significance level of 0.1 and using a two-tailed test.

Since the sample size and number of independent variables are not provided, we cannot determine the degrees of freedom or the critical value directly. However, we can use a t-distribution calculator or look up the critical value from a t-distribution table. For example, with n=50 and k=2 (based on the given output), the critical value for a two-tailed test at a significance level of 0.1 is approximately ±1.645.

Since our calculated t-value of 3.032 is greater than the critical value of ±1.645, we can reject the null hypothesis at the 0.1 significance level and conclude that the coefficient for the variable is statistically significant and different from zero. In other words, there is evidence to suggest that the variable has a significant effect on the outcome being predicted by the regression model.

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