Consider the function f(x)=x^(3)-6x^(2)-49x+294. When f(x) is divided by x+7, the remainder is 0. For which other binomial divisors is the remainder 0?

Answer:

3y + 42 -4x

Step-by-step explanation:

3y +6 -4(x-9) distribute -4 through the  ( )

3y + 6 -4x + 36   calculate add the numbers

3y + 42 -4x

The set of all symmetric 3x3 matrices satisfies all three conditions for a subspace, it is indeed a subspace of M33

To determine whether the set of all symmetric 3x3 matrices is a subspace of M33, we need to check if it satisfies the three conditions for a subspace:

Closure under addition: If A and B are both symmetric 3x3 matrices, then A+B will also be a symmetric 3x3 matrix since \((A+B)^T = A^T + B^T = A + B\). Therefore, the set is closed under addition.

Closure under scalar multiplication: If A is a symmetric 3x3 matrix and c is a scalar, then cA will also be a symmetric 3x3 matrix since \((cA)^T = cA^T = cA\). Therefore, the set is closed under scalar multiplication.

Contains the zero vector: The zero vector in M33 is the matrix of all zeroes. This matrix is also a symmetric 3x3 matrix since all its entries are equal. Therefore, the set contains the zero vector.

Since the set of all symmetric 3x3 matrices satisfies all three conditions for a subspace, it is indeed a subspace of M33.

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ascending order is being small number and ends with greatest number

your answer is:-11,-9,-3,+5

Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

Answer:

2 out of 11

Step-by-step explanation:

hope this helps

Answer: 5:1

Step-by-step explanation:

25:5

Divide by 5 both sides

5:1

Answer:

12x^5 +28X^4 + 20x^3 + 27x^2 + 63x + 45

Step-by-step explanation:

(4x^3)(3x^2) + (4x^3)(7x) + (4x^3)(5) + (9)(3x^2) + (9)(7x) + (9)(5) =

12x^5 +28X^4 + 20x^3 + 27x^2 + 63x + 45

Answer:

Either B or C

Step-by-step explanation:

The factored form of the quadratic equation is given as follows:

y = 3(x + 0.6667)(x - 6).

The quadratic equation for this problem is defined as follows:

3x² - 16x - 7 = 5.

3x² - 16x - 12 = 0.

The coefficients are given as follows:

a = 3, b = -16, c = -12.

Hence the discriminant is of:

D = (-16)² - 4(3)(-12)

D = 400.

Then the roots are of:

Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:

y = 3(x + 0.6667)(x - 6).

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The probability that out of four residential fires who independently reported on a single day, two are in family homes, one is in an apartment, and one is in another type of dwelling is 0.0895 or 8.95%.

The multinomial distribution deals specifically with events that have multiple discrete outcomes. The multinomial distribution is not limited to events with only discrete outcomes.

We have given that

The National Fire Incident Reporting Service stated, among all residential fires.

Let consider the number of events ,

X₁---> fires residential who are in home

X₂--> fires residential who are in appartment

X₃--> fires residential who are in another type of dwelling

The probability of ae X₁ occured (p₁)

= 73% = 0.73

The probability of event X₂ occured (p₂) = 20% =0.20

The probability of event X₃ occurred (p₃) = 7% = 0.07

Four residential fires are independently reported on a single day.

we have to calculate probability that two are in family homes, one is in an apartment, and one is in another type of dwelling?

Now, Using the Multinomial distribution,

X₁= 2 , X₂= 1, X₃ = 1 and n = 4

P( X₁, X₂,-----,Xₙ ) =( n!/(X₁! X₂! ----Xₙ!) )( p₁ˣ₁ × p₂ˣ₂ × ----× pₙˣₙ)

P( 2,1,1) = 4!/2! 1! 1! ( 0.73² × 0.2× 0.07¹)

= 12 ( 0.014 × 0.5329)

= 0.0895272

Hence, the required probability is 0.089..

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Complete question:

The National Fire Incident Reporting Service stated that, among residential fires, 73% are in family homes, 20% are in apartments, and 7% are in other types of dwellings.

a) If four residential fires are independently reported on a single day, what is the probability that two are in family homes, one is in an apartment, and one is in another type of dwelling?

Answer:

The month will be October again lol :)

Step-by-step explanation:

You can use the factored form of the quadratic polynomial and then find the simplified sum.

The numerator of the simplified sum of the given expression is \(4x + 6\)

Quadratic polynomial with single variables are expressible in the form

\(ax^2 + bx + c\) where x is the variable and a,b,c are constants.

Its factored form is

\(\dfrac{1}{4a^2} \times (2ax +b-\sqrt{b^2 - 4ac})(2ax +b+ \sqrt{b^2 - 4ac})\)

The given expression is

\(\dfrac{x}{x^2 + 3x + 2} + \dfrac{3}{x + 1}\)

Factorizing \(x^2 + 3x +2\) using the aforesaid method, as we have got

a = 1, b = 3, c = 2,

thus, we have

\(ax^2 + bx + c = \dfrac{1}{4a^2} \times (2ax + b-\sqrt{b^2 - 4ac})(2ax +b + \sqrt{b^2 - 4ac})\\\\\begin{aligned}x^2 + 3x + 2 &= \dfrac{1}{4}(2x + 3 - \sqrt{9-8})(2x + 3 + \sqrt{9-8})\\\\&= \dfrac{1}{2}(2x+2) \times \dfrac{1}{2}(2x+4)\\&= (x+2)(x+1)\end{aligned}\)

Thus, the given sum is

\(\begin{aligned}\dfrac{x}{x^2 + 3x + 2} + \dfrac{3}{x + 1} &= \dfrac{x}{(x+2)(x+1)} + \dfrac{3}{x + 1} \times \dfrac{(x+2)}{(x+2)}\\\\&= \dfrac{x + 3(x+2)}{(x+1)(x+2)} \\&= \dfrac{4x + 6}{(x+1)(x+2)}\\\end{aligned}\)

Thus, the numerator of the simplified sum is \(4x + 6\)

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Answer:

4x+6

Step-by-step explanation:

C on edge 2022

Yuki would have typed more than Neil at 10:30 AM and the inequality is 45×90+45 × x < 90 × x

We know that Neil started 90 minutes earlier than Yuki by subtracting the time difference So that tells us that

at 10:30 AM Neil would have typed 45 times 90. After x minutes he would have typed 45*90+45*x and Yuki would have typed 60*x.

Words typed by Yuki will be greater than those that will be Words typed by Neil

45×90+45 × x < 90 × x

When we will try in  Solving the above inequality would give us

x >90

it means that 90 minutes after 10:30 AM

Yuki would type more than Neil.

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Answer:

7

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an

exterior angle that's complementary to the third interior angle

60 + 4 + 8x = 8 + 16x add like terms

8x + 64 = 16x + 8

64 - 8 = 16x - 8x

56 = 8x divide both sides by 8

7 = x

Answer:

D

Step-by-step explanation:

A is not right as we don't know the formula used so we cant say the x intercept

B is not right as the function is not liner

C The function is not liner

That leaves D!

hope this helps!

Answer:

D

Step-by-step explanation:

Answer:

65/139 fraction form

0.47 decimal form

Answer:

Step-by-step explanation:

Total sample space , n (s) = 139

no of green candies , n (g) = 45

no. of yellow candies , n (y) = 20

Probability that is green or yellow is

P( g or y) = P(g) + P(y)

               = n(g) / n(s) + n (y) / n(s)

               = 45 / 139 + 20 / 139

               = 65 / 139

hope it will help :)

Removing the electric car from the data set will reduce the standard deviation as the extreme value of 112 mpg is taken out, resulting in a decrease in the spread of the data. The interquartile range (IQR) will also be affected as the extreme outlier is taken out, will decrease the spread of the data in the boxplot.

The electric car with a rating equivalent to 112 miles per gallon is an extreme outlier, which means it is very far from the rest of the data. Therefore, removing this outlier from the data set will decrease the variability and, consequently, decrease the standard deviation. The extreme outlier with the rating equivalent to 112 miles per gallon is outside of the whiskers of the boxplot, which means it is beyond the range of the middle 50% of the data. Therefore, removing this outlier from the data set will decrease the spread of the data in the boxplot and, consequently, decrease the IQR.

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To find the area of a rectangle, we need to determine the length and width of the rectangle using the coordinates of its vertices. The formula for calculating the area of a rectangle is "Area = length × width."

Given the coordinates of two vertices of the rectangle, (1, 1) and (5, 6), we can determine the length and width of the rectangle. The length is the horizontal distance between the x-coordinates of the two vertices, which is 5 - 1 = 4 units. Similarly, the width is the vertical distance between the y-coordinates of the two vertices, which is 6 - 1 = 5 units.

Now, we can use the formula for the area of a rectangle, "Area = length × width," and substitute the values we found. Plugging in the values, we get "Area = 4 units × 5 units," which simplifies to "Area = 20 square units."

Therefore, the area of the rectangle with vertices located at (1, 1) and (5, 6) on the coordinate plane is 20 square units.

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Answer:

B. {all real numbers less than 2}

Step-by-step explanation:

Subtracting 5 from both sides yields x<2.

Answer:

x=\(\sqrt{55}\) or about 7.4

Step-by-step explanation:

Use the Pythagorean Theorem:

8^2=3^2+x^2

64=9+x^2

55=x^2

x=\(\sqrt{55}\) or about 7.4

Answer:

7.42 feet

Step-by-step explanation:

.

Answer:

hajskshsjakalskksks

The equation for the cost of ticket 13.50 = 1.5m is and the price for a matinee movie ticket is $9.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's use "m" to represent the price of a ticket to a matinee movie.

From the given information, we know that the cost of a ticket to an evening movie is 1.5 times more than a ticket for a matinee movie.

This means that -

Cost of an evening movie ticket = 1.5 × Cost of a matinee movie ticket

We also know that the cost of a ticket to an evening movie is $13.50.

Substituting this value into the equation above, we get -

$13.50 = 1.5m

To solve for "m", we can divide both sides of the equation by 1.5 -

$13.50 / 1.5 = m

m = $9

Therefore, the price of a ticket to a matinee movie is $9.

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True. If the zero conditional mean assumption holds, the coefficients can be given a causal interpretation.

True. If the zero conditional mean assumption, also known as the exogeneity assumption or the assumption of no omitted variables bias, holds in a regression model, then the coefficients can be given a causal interpretation.

The zero conditional mean assumption states that the error term in the regression model has an expected value of zero given the values of the independent variables. This assumption is important for establishing causality because it implies that there is no systematic relationship between the error term and the independent variables.

When this assumption is satisfied, we can interpret the coefficients as representing the causal effect of the independent variables on the dependent variable, holding other factors constant. However, if the zero conditional mean assumption is violated, the coefficients may be biased and cannot be interpreted causally.

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There are 49 distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000.

The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm, is the smallest positive integer that is divisible by both a and b.

Given that, how many distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000,

1000 = 10³ = 2³×5³

Therefore, we get:

x = 2ᵃ×5ᵇ

y = \(2^c\)×\(5^d\)

where

0 ≤ a, b, c, d ≤ 3

a or c = 3

b or d = 3

To figure out the number of distinct ordered pairs  (x, y), we need to find the distinct number of ordered quadruples  (a, b, c, d)

there are.

Case  1 : Exactly  2 of  a, b, c, d = 3

a = b = 3, c = 0, 1, 2, d = 0,1,2

a = d=3, b = 0, 1, 2, c = 0,1,2

c = b = 3, a = 0, 1, 2, d = 0, 1, 2

c = d = 3, a=0, 1, 2, b = 0, 1, 2

4(1×1×3×3) = 36

Case 2 : Exactly 3 of  a, b, c, d = 3

a = b = c = 3, d = 0, 1, 2

a = b = d = 3, c = 0, 1, 2

a = c = d = 3, b = 0, 1, 2

b = c = d = 3, a = 0, 1, 2

4(1×1×1×3) = 12

Case 3 : Exactly 4 of a, b, c, d = 3

a = b = c = d = 3

1(1×1×1×1) = 1

Total  =36+12+1=49

Hence. there are 49 distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000.

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1. The volume of the given solid is ∫[0,1] (3 - tan^(-1)(-x))² dx. 2. The volume of the given solid is (√3/4) × (b - a)³. 3. The volume of the given solid is (π/12) × [(8 - b)³ - (8 - a)³].

1. To find the volume of the solid with square cross sections, we need to integrate the area of the square cross sections over the interval from x = 0 to x = 1.

The equation y = tan⁻¹(-x) bounds the upper side of the square, while the line y = 3 bounds the lower side. Since each cross section is a square, the side length of the square is given by the difference between these two y-values.

The height of the square cross section is dx, as the cross sections are perpendicular to the x-axis.

Therefore, the volume (V) of the solid can be calculated by integrating the area of the square cross sections:

V = ∫[0,1] (3 - tan⁻¹(-x))² dx

Simplifying the integral is not straightforward, and there isn't a closed-form solution. However, you can approximate the integral using numerical methods such as the trapezoidal rule or Simpson's rule.

2. To find the volume of the solid with equilateral triangle cross sections, we need to integrate the area of the equilateral triangles over the given region.

The equation y = 2x - x² bounds the upper side of the equilateral triangle, while the x-axis bounds the lower side. The height of the equilateral triangle is the y-value of the curve at a given x.

The base of the equilateral triangle is given by the difference between the x-values of the region.

Therefore, the volume (V) of the solid can be calculated by integrating the area of the equilateral triangle cross sections:

V = ∫[a,b] [(side length)² × (√3)/4] dx

The side length of the equilateral triangle can be determined by taking the difference between the x-values of the region

side length = b - a

Substituting the values into the equation, we have:

V = ∫[a,b] [(b - a)² × (√3)/4] dx

= (√3/4) × (b - a)² × (b - a)

Therefore, the volume of the solid is (√3/4) × (b - a)³ cubic units.

3. Since the cross sections perpendicular to the x-axis are semicircles, the volume of the solid can be calculated by integrating the area of the semicircle cross sections over the given region.

The equation x + 2y = 8 can be rewritten as y = (8 - x)/2, which represents the upper boundary of the semicircle.

The x-axis represents the lower boundary of the semicircle.

The radius of the semicircle at a given x is given by the y-value of the upper boundary.

Therefore, the volume (V) of the solid can be calculated by integrating the area of the semicircle cross sections:

V = ∫[a,b] [(π × r²)/2] dx

The radius of the semicircle can be determined by taking the y-value of the upper boundary:

r = (8 - x)/2

Substituting the values into the equation, we have:

V = ∫[a,b] [(π × (8 - x)²)/4] dx = (π/4) × [(8 - x)³/3] evaluated from a to b = (π/4) × [(8 - b)³/3 - (8 - a)³/3]

Therefore, the volume of the solid is (π/12) × [(8 - b)³ - (8 - a)³] cubic units.

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-- The given question is incomplete, the complete question is

"1. The base of a solid is the region in the first quadrant bounded by the y-axis, the graph of

The expression that shows how many cupcakes the baker decorated is:

c/2.

A mathematical expression is a combination of numbers, symbols, and/or variables that represents a mathematical relationship or operation. It can be written using various mathematical symbols and notation to convey a specific meaning or instruction.

Mathematical expressions can also include functions, exponents, logarithms, and other mathematical operations that represent specific relationships or computations. They are commonly used in algebra, calculus, geometry, and other branches of mathematics to represent and solve mathematical problems.

The number of cupcakes the baker decorated can be found by dividing the total number of candy eyes by the number of candy eyes needed per cupcake.

If the baker used c candy eyes in total and each cupcake needed 2 candy eyes, then the expression that shows how many cupcakes the baker decorated is:

c/2

Dividing c by 2 gives the number of cupcakes the baker decorated, since each cupcake required 2 candy eyes.

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The number of cupcakes is the total number of candy eyes divided by 2.

What is equation?

A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra.

The number of cupcakes decorated is equal to the total number of candy eyes divided by the number of candy eyes used per cupcake. So, if c is the number of candy eyes, then the expression that shows how many cupcakes the baker decorated is:

c/2

This is because each cupcake needs 2 candy eyes.

Therefore, the number of cupcakes is the total number of candy eyes divided by 2.

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The slope field shown in the question is that of a differential equation of the form y'= f(x,y).

The solutions of this equation are the curves in the slope field that emanate from each point and that have the same slope as the line at that point. Thus, for each point (x,y) in the slope field, it is possible to calculate the particular solution that passes through that point.

The first statement is false because it involves the second derivative of the particular solution, which cannot be determined from the slope field. The second statement is false because a concave up graph requires that the derivative of the solution be increasing at x=0, but the slope field does not indicate the sign of the derivative of the particular solution. The third statement is false because a concave up graph requires that the derivative of the solution be decreasing at x=-1, which cannot be determined from the slope field. The fourth statement is false because a concave down graph requires that the derivative of the solution be increasing at x=0, which cannot be determined from the slope field.

In summary, none of the statements can be determined to be true or false from the slope field shown.

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Answer:

Linear model

Step-by-step explanation:

A linear model models a real-life situation y = mx + b (m will be the constant rate of change and b is the initial or starting value)

A linear function that mimics a real-world scenario is known as a linear model.

A continuous response variable is described by a linear model as a function of one or more predictor variables. They can assist you in analyzing experimental, monetary, and biological data or in understanding and predicting the behavior of complex systems. A statistical technique used to build a linear model is called linear regression.

It is called a linear model because the formula indicates a link between the left and right sides that is established by "linear" or "constant" parameters for each term, which are then solved for to reduce the overall divergence of the data from the model.

By using a linear combination of predictor variables, linear models can be used to describe a response variable.

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Answer:

1=1/3p

Step-by-step explanation: