According to the synthetic division below, which of the following statements
are true?
Check all that apply.
5 /4 -17 -15
20 15
4 3 0
□ A. (4x²-17x-15) ! (n-k)! (x+5) = (4x+3)
B. (x+5) is a factor of 4x²-17x-15.
C. (4x²-17x-15) n(n-k)! (x-5) = (4x+3)
D. (x-5) is a factor of 4x² - 17x-15.
E. The number 5 is a root of F(x) = 4x² - 17x-15.
F. The number -5 is a root of F(x) = 4x² - 17x-15.

The probability that Ali's sum at least 6 is 0.996.

Sample space of rolling four fair six-sided dice:

= {(1, 1, 1, 1), (1, 1, 1, 2), ….., (6, 6, 6, 6)}

= 6^4

= 1296 ways

Favourable cases = {sum at least 6}

So, now we need to find the sums less than 6, which means the sum is either 4 or 5. Then, we will get:

(1, 1, 1, 1)

(1, 1, 1, 2)

(1, 1, 2, 1)

(1, 2, 1, 1)

(2, 1, 1, 1)

From above we know that only 5 ways will have the sums less than 6. So, the possible way of the sums at least 6 is:

= {sample space} – {the sums less than 6}

= 1296 – 5

= 1291

Thus, the probability P (sum at least 6) will be:

= 1291 / 1296

= 0.996

Hence, the probability that Ali's sum at least 6 is 0.996.

A fair sided dice means that each of the faces has the same probability of landing facing up. A standard six-sided die can be considered as fair if each of the faces has the same probability of 1/6.

Learn more about probability at: https://brainly.com/question/30034780

#SPJ4

The number of trees on each acre of land, given that the trees are evenly spaced out, is 101 trees per acre

To find out how many trees are on each acre of land, we need to divide the total number of trees by the number of acres. This is given that the trees are spread out evenly as is the case here.

The number of trees per acre of land is therefore:

= Number of trees in total / Number of acres

= 3, 434 / 34

= 101 trees per acre

Find out more on acres at https://brainly.com/question/19783923

#SPJ1

The polynomial functions f(x) = x³-2x²-3x+6

To solve this question, we use the factor theorem, and using it, the polynomial function is: f(x) = x³-2x²-3x+6

The factor theorem means that if k is a root of f(x), f(k) = 0.

Thus, applying the factor theorem for this question, we have to choose the function for which:

f(2) =0, f(√3) =0, f(-√3) = 0

Function 1:

f(x) = x³-2x²-3x+6

Testing the values:

f(2( = 2³-2(2)²-3(2) +6

= 8--6+9 = 0

f(√3) = √3³-2(√3)²-3√3 +6

=3√3-3√3 = 0

f(-√3) = -√3³-2(-√3)²-3(-√3) +6

= -3√3-√3 = 0

Thus, since all three conditions are satisfied,  is the polynomial function.

Learn more about polynomial functions on https://brainly.com/question/12976257

#SPJ

Complete question:

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2x2 – 3x + 6, f (x)= x3 – 2x2 + 3x + 6, f (x) = x3 + 2x2 – 3x + 6, f (x) = x3 + 2x2 – 3x – 6

The slope of the given equation is -1/5 and the y - intercept is -1.

What is slope and y - intercept?

This procedure determines how quickly the value of the function's dependent variable, y, changes in relation to the independent variable, x. (independent variable). The slope itself identifies the slope and direction of the line.

the y-coordinate of a point on a surface, curve, or line where they cross the y-axis.

Consider, the given equation

p(x) = -1 - 1/5x

We have to find the slope and y - intercept of the given equation.

Rewrite the equation as,

y = -1/5x - 1

Compare this equation with

y = mx + c

where

m is the slope and

c is the y - intercept

So, from above equation, we get

m = -1/5 and c = -1

Hence, the slope of the given equation is -1/5 and the y - intercept is -1.

To know more about slope and y - intercept, click on the link

https://brainly.com/question/25722412

#SPJ1

The derivatives of b(t) with respect to t will be d(b(t))/dt = - ωacos(kx - ωt)

We have been given b(t) = asin(kx - ωt)

Hence, we need to find db(t)/dt

We will treat a, k, x, and ω as constants since no information is provided.

We will be using the chain rule to find the derivative

First, we consider sin as an individual term to get-

a______

Next, we know that the derivative of sin is cos Hence we get

acos(kx - ωt)______

Now we will move on to the terms in the brackets

Here kx is a constant so the derivative of this will be 0.

Hence we get left with - ωt

here the differentiation will clearly be - ω

Hence we get the final derivative

d(b(t))/dt = - ωacos(kx - ωt)

To learn more about Differentiation visit

https://brainly.com/question/28144387

#SPJ4

Correct Question

what is the derivative of b(t) with respect to t for b(t) = asin(kx - ωt)

Answer:

52.393

the square root of 2745 is 52.393

The equation that represent the total number of vehicles is x + y = 45

The equation that represent the total number of wheels is 4x + 2 y = 130

The total number of motocycles are 25 and number of ATVs are 20.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

A linear equation is expressed using the linear equation formula. There are several ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form.

Let y represent the motorcycles and x represent

The equation that represent the total number of vehicles is

x + y = 45       (i)

The equation that represent the total number of wheels is

4x + 2 y = 130

⇒ 2x + y = 65  (ii)

Subtracting equation (i) from (ii) we get ,

2x + y - x - y = 65 - 45

x = 20

putting x = 20 in equation (i) we get

y = 45 - 20 = 25

The total number of motocycles are 25 and number of ATVs are 20.

To learn more about Linear equation refer to :

https://brainly.com/question/30267028

#SPJ1

If the average price of regular unleaded gasoline excluding taxes was $3.06 per gallon then the percentage of gasoline stations had prices within 3 standard deviations of the mean is 99.74%  .

The Average Price of the gasoline (μ) is = $3.06 per gallon ;

the standard deviation price per gallon (σ) is = 0.06  ;

we have to find the percent of gasoline that had prices within 3 standard deviations of the mean ;

the the 3 standard deviation is calculated by :

⇒ [tex](\mu \pm 3\sigma )[/tex]

On substituting the values ,

we get ;

⇒ [tex](\mu - 3\sigma , \mu +3\sigma)[/tex]

⇒ [tex](3.06 - 3\times 0.06 , 3.06 + 3\times 0.06)[/tex]

= (2.88 , 3.24) ;

Step two ;

Now , We have to calculate P(2.88 < X < 3.24)

= [tex]P(\frac{2.88-3.06}{0.06} < Z < \frac{3.24-3.06}{0.06} )[/tex]

= [tex]P(-3 < z < 3) ;\\[/tex]

which means , [tex]P(z < 3) - P(Z < -3)[/tex] ;

= 0.9987 - 0.0013 ;

= 0.9974  ≈ 99.74% .

Therefore , the required percent of gasoline is 99.74%  .

The given question is incomplete , the complete question is

In December 2010, the average price of regular unleaded gasoline excluding taxes in the United States was $3. 06 per gallon according to the Energy Information Administration. Assume that the standard deviation price per gallon is $0.06 per gallon .

What percentage of gasoline stations had prices within 3 standard deviations of the mean ?

Learn more about Standard Deviation here

https://brainly.com/question/14815147

#SPJ4

All real numbers make up the domain, and all positive real numbers, or (0, ∞) in interval notation, make up the range.

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).

The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in. They are the y values.

An exponential function is a mathematical function of the following form: f ( x ) = ax. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828

To know more about exponential function on brainly : brainly.com/question/10541709

#SPJ4

The value of X² will always be positive, whether the value of "X" is positive or negative.

X² will always be positive because the square of any number, whether positive or negative, will always be positive.

For example, (-1)² = 1, which is a positive number. Therefore, regardless of the sign of X, X² will always be positive. Then we can conclude The value of X² will always be positive, regardless of the sign of X.

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. It can be solved using the quadratic formula, which is: x = [-b ± √(b2 - 4ac)] / 2a. This formula gives the two solutions to the equation.

Learn more about quadratic equation:

https://brainly.com/question/1214333

#SPJ4

Answer: 40

Step-by-step explanation: y=4x so if there is 10 strawberries the 10x4=40 so there would need to be 40 grapes to make a fruit salad.

The medians from a vertex, altitudes, and angle bisectors all coincide for an equilateral triangle. As a result, an equilateral triangle has the same orthocenter O, centroid G, and incenter I.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

The medians from a vertex, altitudes, and angle bisectors all coincide for an equilateral triangle.

As a result, an equilateral triangle has the same orthocenter O, centroid G, and incenter I.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer: 13/1560 (The distance flown in 13 hours is 1560 miles)

Step-by-step explanation: Rate X Time = distance

Therefore:

    r (rate) X 5 (hours) = 600 (distance)

    r = 600/5

    r = 120 miles per hour

    The rate of speed of the jet is 120 mph.

Then, to find out the distance flown in 13 hours:

    120 (rate) X 13 (time) = d (distance)

    120 X 13 = d

    1560 = d

    The distance flown in 13 hours is 1560 miles.

On solving the provided question we can say that from the graphs  y=e^-x+x => y = -3

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

from the graphs

y=e^-x+x

for(-3,6)

y = e^-3 -3

y = -3

To know more about graphs visit:

https://brainly.com/question/11950136

#SPJ1

Answer: Answer is D and B

Step-by-step explanation:

Answer:

Right and isosceles

Step-by-step explanation:

There is a marked right angle in the diagram of the triangle. Two side lengths are the same, meaning it is isosceles.

The process of plotting the graph a quadratic equation using the vertex and intercepts is explained below.

The term quadratic equation is defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.

Here we have given the vertex and intercepts.

And now we have to explain the process of plotting the graph through this.

As we all know that when you graph a quadratic then there are a couple of things you need to consider that will make your life easier.

The first thing that you need to find the vertex .

And that one is derived through  vertex form by using the equation y=a(x−h)² + k here the point (h,k) defines the vertex.

Where as it can be either the highest or lowest point on your graph and it is the first thing you need to graph.

Then the next steps is use the intercept that can be obtained by plug in 0 for y in the equation and then we have to solve is  for x then you will find the coordinates of the two intercepts.

To know more about Equation here.

https://brainly.com/question/10413253

#SPJ4

Answer:

For 1st both both a and b lies on the graph but for 2nd only a lies on the graph

Step-by-step explanation:

Since the Pennsylvania lottery was rigged, the probability of drawing a 666 in the April 24th, 1980 drawing is 100%. The probability of drawing a 666 in the September 19th, 1980 Connecticut lottery, however, is extremely low, as it was not rigged and the odds of picking a specific 6-digit combination are 1 in 1 million.

To calculate this probability, you would take 1 divided by 1 million, which would be 0.000001. This means that the probability of drawing a 666 in the Connecticut lottery is 0.000001.   In conclusion, the probability of drawing a 666 in the April 24th, 1980 Pennsylvania lottery is 100%, while the probability of drawing a 666 in the September 19th, 1980 Connecticut lottery is 0.000001.

To  know more about  probability  refer to the link  brainly.com/question/11034287

#SPJ4

The missing numbers for the respective rows are:

row 1: -0.5

row 2: -0.3 and -0.1

row 3: -0.2

The 3rd column to the right have a total of:

0 + 0.1 + (-0.4) = -0.3

Missing number for row 1(top row):

-0.2 - 0 - 0.3 = -0.5

Missing number for the diagonal from top left:

0.4 - 0.2 - 0.3 = -0.1

Missing number for row 2 (2nd number for 1st column):

0.1 - 0.1 - 0.3 = -0.3

Missing number for row 3 (bottom row):

0.4 - 0.3 - 0.3 = -0.2.

Therefore, row 1 have the missing number; -0.5. Row 2 missing numbers from left; -0.3 and -0.1. Row 3 missing number is -0.2.

Know more about missing numbers here:https://brainly.com/question/23171011

#SPJ1

The required value of k for the linear system is consistent is 2.

If and only if a linear system's coefficient matrix and augmented matrix have the same rank, the system is said to be consistent (the coefficient matrix with an extra column added, that column being the column vector of constants).

6x+2y=8

-9x+ky=-11

simplify by dividing all terms by 2

3x+y=4

multiply all terms by -3

-9x-3y=-12

-9x+ky=-11 (this is eq2)

The system won't be consistent if k=-3 because you'll have...

-9x-3y=-12

-9x-3y=-11

Because these lines are parallel, there is no way to solve them.

The following could have also been done by you.

6x+2y=8

2y=-6x+8

y=-3x+4

-9x+ky=-11

ky=9x-11

y=(9/k)x-(11/k)

(9/k)=-3

9=-3k

k=9/(-3)

k=-3

To know more about Consistency visit:

brainly.com/question/22566197

#SPJ4

Complete question:

Find the value of k such that the system of linear equations is inconsistent.

6x + 2y = 8

−9x + ky = −11

Give the unknowable quantity a variable in step 1. Let z be the undetermined number. Finding two verbal expressions with the same value is the second step. Use fractions when creating a mathematical equation from the phrase "quotient" Step four is to solve the equation.

To learn more about equation refer to:

https://brainly.com/question/2972832

#SPJ1

The correct statement regarding the sign of the reciprocal function is given as follows:

C. The function is positive when x > 0.

The intervals for which a function is positive are the intervals for which the function graph lies above the x-axis.

The intervals for which a function is negative are the intervals for which the function graph lies below the x-axis.

Hence the positive and negative intervals for this problem are given as follows:

Meaning that the correct option is given by option c.

More can be learned about functions at brainly.com/question/24808124

#SPJ1

The solution to the system of equations y equals negative 5x3 and Y equal one is x = ∛  - ( 1 - y) / 5 and y = 1 + 5x³  .

The given equation is -5x³ + y = 1.

now , the solution for x can be said as ,

x³  = - ( 1 - y) / 5

x = ∛  - ( 1 - y) / 5

and the solution for y can be given as ,

y = 1 + 5x³  .

An equation is a mathematical expression which is written in terms of constants , variables and are connected with each other with the help of operators.

The equations can be linear , quadratic , cubic etc.

example, 6x + 3y = 12.

To learn more about equations

brainly.com/question/9677341

#SPJ4

Answer: 476.9 x 100 = 47690

Step-by-step explanation: When you multiply a number by 100, you are simply adding two zeroes to the end of the number.

So, for example, to find 476.9 x 100, you can simply add two zeroes to the end of 476.9, giving you 47690.

Another way to think about it is to move the decimal point 2 places to the right.

476.9 -> 476.90

Therefore 476.9 x 100 = 47690

The thing that should be done for the game to be fair is 2. Add 2 cards with stars.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.

Since Four of the cards have stars on them and the other 6 are blank and you win if you draw a card with a star, it's important to add 2 cards with stars.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:

It is 276474

Step-by-step explanation:

The cost function, c(x), includes the point (40, 390)

A function is a rule that maps input variables to output variables, with each input producing exactly one output.

The cost functions the chef uses to estimate the cost of the fixed price menu for x guest are ppresented as follows;

The function for the anticipated cost of appetizers, a(x) = 3.25·x

The function for the anticipated cost for the main course, m(x) = 5.25·x

The cost function for the anticipated cost of the desert, d(x) = 1.25·x

The function for the combined function, which is the cost of the fixed price menue is therefore;

c(x) = a(x) + m(x) + d(x)

The po

The point included in the function, c(x) (40, can be found by plugging in the value, x = 40 in the cost function c(x) = a(x) + m(x) + d(x). as follows;

The point on the cost function is; (40, (c(40))

c(40) = a(40) + m(40) + d(40)

c(40) = 3.25 × 40 + 5.25 × 40 + 1.25 × 40 = 390

Learn more funtions here: https://brainly.com/question/10989920

#SPJ1

The smallest value of x for which the following inequality holds true is 7.

We are given

1/2 + 1/3 +...+ 1/x > 3/2

Here we will keep on assuming values of x till we get the first value of x for which LHS > RHS

manipulating the inequality we get

1/3 +... + 1/x > 1

or, 1/4 + ... + 1/x > 2/3

or, 1/5 + .... + 1/x > 5/12

or, 1/6 + ... > 13/60

or, 1/7 + ... > 3/60

or, 1/7 +... > 1/20

We know that when the numerator is the same, the denominator with the smaller value is the larger fraction.

Hence with the addition of the series till 1/7, we get a value larger than 3/2

Hence the smallest value of x is 7.

To learn more about Inequalities visit

https://brainly.com/question/26176716

#SPJ4

Correct Question

suppose 1/2 + 1/3 +...+ 1/x > 3/2. what is the smallest possible value for x?

The statement " Greatest common divisor of two or more numbers is the largest number that divides evenly into each of the given numbers" - True

In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y The greatest common factor (GCF) that divides two or more integers is known as the greatest common divisor (GCD). It is also known as the highest common denominator (HCF).

Thus, the given statement is true.

To know more about Greatest common divisor refer to:

https://brainly.com/question/219464

#SPJ1

The value of log 7 base 343 is 1/3.

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.

When there is no possibility of mistake or when the base is irrelevant, as in big O notation, the logarithm of x to base b is written as [tex]log_b (x)[/tex], [tex]log_b x[/tex], or even without the explicit base, log x.

[tex]log_{343}(7)[/tex] = x

Step1:Rewrite in exponential form first.

[tex]343^{x}[/tex] = 7

Step 2:Take the log from both sides .

log [tex]343^{x}[/tex] = log 7

Step 3: Use the log rule log [tex]a^x[/tex]=x log a

x log 343=log 7

x = log 7/log 343

Now use a calculator.

x = 1/3

The value of log 7 base 343 is 1/3.

To learn more about log rule link is here

brainly.com/question/16140433

#SPJ4