The cubic polynomial x ^3 - 3x ^ 2 + ax + b is factor (x - 2)
(a)Find a linear relationship between a and b (b )Find the remainder when the polynomial is divided by
(a)(x-1)
(b)x-3)

Answer:

The total value of the account after 3 years will be $5,503.52.

Step-by-step explanation:

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Tyler's bank account pays a straightforward yearly financing cost of 3.25%. Assume he stores $5,000 in the record and sets aside no extra installments or withdrawals for a long time.

The total value of the account after 3 years will be calculated as,

A = $5,000(1 + 0.0325)³

A = $5,000 x (1.0325)³

A = $5,000 x 1.1007

A = $5,503.52

The total value of the account after 3 years will be $5,503.52.

f(x) = 4. 8x² function can be used to compute the approximate area, in square inches, of a stop sign if it has a side length of x inches.

A function, which produces single output from either a single input, is an illustration of a rule. Alex Federspiel was contacted to collect the image. An illustration of this is the equation y=x2. For each input of x, there is simply one output of y. Considering that x is actually the input value, we would claim that y is just a rational number.

area = (# of sides * side length^2) / [4 * tan (180/n)]

area = (8 * x^2) / 4 * tan (22.5)

area = 8 x^2 / (4 * 0.41421)

area = 8 x^2 / 1.65684

area = 4.8 x^2

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Answer:

Step-by-step explanation:

It is not possible to accurately compare the weight of 1 kilogram of corn to 1 cup of precooked corn because the weight of the corn will change after it is cooked. Corn is composed of water, starch, and other nutrients, and the weight of the corn will change depending on how much water is retained in the kernels.

For example, 1 cup of uncooked corn kernels (about 168 grams) will yield about 1 1/4 cups of cooked corn (about 210 grams), while 1 cup of precooked corn (about 160 grams) will yield about 1 cup of cooked corn (about 160 grams).

Therefore, the weight of 1 kilogram of corn (about 1000 grams) is significantly greater than the weight of 1 cup of precooked corn (about 160 grams). It is not possible to accurately compare the weight of these two quantities because they are in different states (raw versus cooked) and have different densities.

The most reasonable estimate of the gallons of gas in a tank if it has been 3 days since filling up is 17 gallons.

On plotting the graph we will get ,

The most reasonable value of y corresponding to x = 3 is approximately 17 gallons.

A plot is a graphical technique for representing a data set, typically in the form of a graph that depicts the relationship between two or more variables. The plot can be created either by hand or by computer. Previously, mechanical or electronic plotters were used.

Graphs are a visual representation of the relationship between variables that are very useful for humans because they allow them to quickly derive an understanding that would not have been possible from lists of values. Graphs can also be used to read off the value of an unknown variable plotted as a function of a known variable given a scale or ruler, but this can also be done with data presented in tabular form. Function graphs are used in mathematics, science, engineering, and technology.

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The distance between the two points is 10 units

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

A = (13, 2) and B =(7, 10)

The distance between the two points can be calculated using the following distance equation

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where

(x, y) = (13, 2) and (7, 10)

Substitute (x, y) = (13, 2) and (7, 10) in distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

distance = √[(13 - 7)² + (2 - 10)²]

Evaluate

distance = 10

Hence, the distance is 10 units

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Answer: need brainliest

Step-by-step explanation:

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-\frac{5}{2}})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{\left( -\frac{5}{2} \right)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-3)}}} \implies \cfrac{-8+\frac{5}{2}}{3+3}\implies \cfrac{~ \frac{ -16+5}{2 } ~}{6}\implies \cfrac{~ \frac{ -11}{ 2} ~}{6} \\\\\\ \cfrac{~ \frac{ -11}{ 2} ~}{\frac{6}{1}}\implies \cfrac{ -11}{ 2}\cdot \cfrac{1}{6}\implies -\cfrac{11}{12}[/tex]

Answer:

Below

Step-by-step explanation:

a)  there are 10 cards    only one '4'    so 1 out of 10 = 1/10

b)  there are 2 cards out of 10 with a '1' on them    2/10 = 1/5

c)  8 out of 10 = 8/10

The proportion that you use to derive the equation of the line is (y+2)/x=4/3.

So, option c is correct.

An equation is something like 3x - 5 = 16. By solving for x, we discover that x equals 7, which is the value for the variable. By deleting parentheses and merging like terms, you can simplify either side of an equation and find its solution.

Identify the variable term on one side of the equation by adding or subtracting. You can find the variable's value by multiplying or dividing. When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions. Depending on the language, the definition of the word equation and its cognates may alter slightly. For instance, an equation is what is meant in French.

Here,

In the given diagram:

The slope of the straight lines is constant

So, DE/AD=CB/AB

(y+2)/x=4/3

Therefore, option c is correct.

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Area will be 2[tex]r^{2}[/tex]

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form.

Given radius of circle is r

Then area of circle=π[tex]r^{2}[/tex]

The diagonal of the square is comparable to the diameter (2r) of the circle since two opposing corners of the square contact it.

Now, we will set up Pythagoras' Theorem to determine one side of the square:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

Since it is a square a=b which means all  the sides are same

∴2[tex]a^{2}[/tex] = [tex]c^{2}[/tex]

We know c, which is 2r, the diagonal.

∴2[tex]a^{2}[/tex] = [tex](2r)^{2}[/tex]

⇒[tex]a^{2}[/tex] = 2[tex]r^{2}[/tex]

We can leave it as [tex]a^{2}[/tex]

since a is one side of the square and [tex]a^{2}[/tex] would be the area of the square.

So the area of the square =2[tex]r^{2}[/tex]

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11.18033

let b=x

use pythag and rearrange for side b. Then simply maths.

The probability of randomly selected student who plays sport  given that student is senior is 0.04

P(A) denotes probability of occurring of  an event A

P(B) denotes probability of occurring of an event B

P(B/A)  is known as condition probability.

The dependent events are the only ones that give rise to the conditional probability P(B/A). The conditional probability of B given that A has happened is provided.

According to this question A denotes as student is senior

B denotes student plays sport.

What is the probability that a randomly selected  student plays a sport

given that the student is senior is same as conditional probability.

P(B/A) ->Condition probability of B given that A has happened.

Student is senior given we have to tell about student plays a sport.

P(B/A) = P(A∩B) / P(A)

Given that P(A∩B) = 0.10

P(A) = 0.25

P(B/A) = 0.10/0.25 = 0.4

Given Question is incomplete Complete Question here.

At a high school, the probability that a student is a senior is 0.25. The probability that a student plays a sport is 0.15. The probability that a student is a senior and plays a sport is 0.10. What is the probability that a randomly selected student plays a sport, given that the student is senior?

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Answer:

-2/5

Step-by-step explanation:

Answer:

-2/5

Step-by-step explanation:

get a calculator and click those numbers you will find out the answer

Answer:

Step-by-step explanation:

Given two inscribed quadrilaterals with various arcs and angles marked, you want to solve for specific unknown values.

The measure of an inscribed angle is half the measure of the arc it intercepts. The sum of arcs of a circle is 360°.

  Arc PSR = 2·∠PQR = 2·93° = 186°

  Arc RS = Arc PSR -Arc PS = 186° -90° = 96°

  Arc QR = 360° -126° -90° -96° = 48°

The unknown arcs are ...

Opposite angles in an inscribed quadrilateral are supplementary:

  105° +(7x +1)° = 180°

  7x = 74 . . . . . . . . . . . divide by °, subtract 106

  x = 74/7 = 10 4/7 . . . . . divide by 7

  (4y +14)° +(7y +1)° = 180°

  11y = 165 . . . . . . . divide by °, subtract 15

  y = 15 . . . . . . . . . divide by 11

The values of x and y are ...

The product of matrix A and matrix B is matrix C

a)  [tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]

b) [tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]

What is multiplication of matrices?

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix

Given data ,

a)

Let the first matrix be A

The value of A is

[tex]A = \begin{pmatrix}2&3\end{pmatrix}[/tex]

The value of second matrix B is

[tex]B = \begin{pmatrix}4\\ \:5\end{pmatrix}[/tex]

Now , the product of matrix A and matrix B is matrix C

The value of matrix C is

[tex]C = \begin{pmatrix}2&3\end{pmatrix}\begin{pmatrix}4\\ 5\end{pmatrix}[/tex]

On simplifying the value of matrix C , we get

[tex]C = \begin{pmatrix}2\cdot \:4+3\cdot \:5\end{pmatrix}[/tex]

[tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]

Therefore , the value of matrix C is [tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]

b)

Let the first matrix be A

The value of A is

[tex]A = \begin{pmatrix}1&2\end{pmatrix}[/tex]

The value of second matrix B is

[tex]B = \begin{pmatrix}-3\\ \:4\end{pmatrix}[/tex]

Now , the product of matrix A and matrix B is matrix C

The value of matrix C is

[tex]C = \begin{pmatrix}1&2\end{pmatrix}\begin{pmatrix}-3\\ 4\end{pmatrix}[/tex]

On simplifying the value of matrix C , we get

[tex]C =\begin{pmatrix}1\cdot \left(-3\right)+2\cdot \:4\end{pmatrix}[/tex]

[tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]

Therefore , the value of matrix C is [tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]

Hence , the matrix multiplication is

The product of matrix A and matrix B is matrix C

a)  [tex]C = \begin{pmatrix}23\end{pmatrix}[/tex]

b) [tex]C = \begin{pmatrix}5\end{pmatrix}[/tex]

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We know that each friend will pay $13.3 using simple mathematical operations.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition Subtraction (from left to right).

So, we know that:

There are 5 friends.

Each ticket costs $11.75.

They have a large popcorn for $7.75.

Then, the amount that each friend will pay:

[(11.75*5)+7.75]/5

[58.75+7.75]/5

66.5/5

$13.3

Therefore, we know that each friend will pay $13.3 using simple mathematical operations.

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Correct question:
Five friends go to a movie. Each movie ticket cost $11. 75. They have a large popcorn for $7. 75. If they divide the total cost equally, how much will each friend pay?

Answer:

Step-by-step

Each friend pays $3.9 each.  

1.   $11.75 + $7.75 = 19.50.

2. 19.50 divided by 5 (friends) is equal to 3.9.

Answer: 2. 55/8

Step-by-step explanation: Add the whole numbers first (5+1 = 6), then add the fractions (4/8 + 3/8 = 7/8). Now we have 6 7/8 and since they want the answer in fraction form we will multiply the 6 and the 8 (6x8=48) and then add the 7 to the 48 (7+48 =55) and we leave our answer over the denominator which is 8. This leaves us with the final answer of 55/8

a) The p-value indicates that it is very rare to observe a test statistics equally or more extreme when the null hypothesis is true.

A null hypothesis is a claim or presumption that there is no association between two observed variables or that observed differences between groups are the result of chance. It is frequently employed in statistical testing, and it is represented by the symbol "H0". The null hypothesis is often the inverse of the alternative hypothesis, which posits a link or difference between the variables. To reject the null hypothesis, the observed data must be statistically significant and unlikely to have occurred by chance. In scientific research, the null hypothesis is crucial because it enables researchers to assess the significance of their data and reach reliable conclusions.

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Answer:

6

Step-by-step explanation:

the hypotenuse of this special right triangle is twice the value of the leg near to the angle of 60°

x = 3 · 2 = 6

Answer:

2 quarts

Step-by-step explanation:

1 quart = 2 pints

4 pints × (1 quart)/(2 pints) = 2 quarts

Answer:

2 quarts

Step-by-step explanation:

1 quart=2 pints

2 quarts=4 pints

Have a great day

a) If N is the population of the city and is the time in years, N expressed as a function of t is; N(t) = N₀*e^(kt)

b) The population 2 years from now will be; 25198 people

The general formula for exponential growth model is;

N(t) = N₀*e^(kt)

where;

f(x) is exponential growth function

N₀ is initial amount

t is time

k is constant

a) We are told that;

N is the population of the city.

t is the time in years

Thus, N expressed as a function of t is;

N(t) = N₀*e^(kt)

b) We are told that the population doubled in size over an 18-month

period . Thus, the equation would now be;

N(t) = N₀*2^(t/18)

Thus,  if the current population is 10000, then it means that 2 years from now, we will have;

N(2) = 10000 * 2^(24/18)

I used 24 because 2 years is 24 months

Thus;

N(2) ≈ 25198 people

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The amount agency makes on the house is $16830 and the agent got $4207.5 based on the given rate or percentage.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

As per the given,

Total cost of house = $374,000

The commission rate of real estate = 4.5%

4.5% of $374,000 = (4.5/100)374000 = $16830

The commission rate of agent = 25 % of $16830

(25/100)16830 = $4207.5

Hence "The amount agency makes on the house is $16830 and the agent got $4207.5 based on the given rate or percentage".

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The amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of petrol in Spain be = A

Let the amount of petrol in Wales be = B

Now , the total amount Sam paid for 18 Liters of petrol in Spain = 27 euros

1 euro = 0.85 pounds

So ,

Total amount Sam paid for 18 Liters of petrol in Spain = 27 x 0.85 pounds

Total amount Sam paid for 18 Liters of petrol in Spain = 22.95 pounds

So ,

The amount for 1 Liter of petrol in Spain = Total amount Sam paid for 18 Liters of petrol in Spain / 18

Substituting the values in the equation , we get

The amount for 1 Liter of petrol in Spain = 22.95 / 18

The amount for 1 Liter of petrol in Spain = £ 1.275

And ,

Now , the total amount Sam paid for 8 gallons of petrol in Wales = £ 40.80

1 gallon = 4.5 Liters

8 gallons = 4.5 x 8 Liters

8 gallons = 36 Liters

So ,

Total amount Sam paid for 36 Liters of petrol in Wales = £ 40.80

So ,

The amount for 1 Liter of petrol in Wales = Total amount Sam paid for 36 Liters of petrol in Spain / 36

Substituting the values in the equation , we get

The amount for 1 Liter of petrol in Wales = 40.80 / 36

The amount for 1 Liter of petrol in Wales = £ 1.13

£ 1.13  <   £ 1.275

Therefore , the amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain

Hence , The amount for 1 Liter of petrol in Wales is less than the amount for 1 Liter of Petrol in Spain

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The sample size is necessary if the 95% ci for p is to have a width of at most 0.15 irrespective of p being 385 people.

In statistics, a confidence interval describes the likelihood that a population parameter will fall between a set of values for a given percentage of the time. Confidence intervals that include 95% or 99% of anticipated observations are frequently used by analysts.

The largest confidence interval occurs when p = .5

The standard error = [tex]\sqrt{\frac{(0.5)^{2} }{x} }[/tex]

The z* for a 95% confidence interval = 1.96

Setting up an equation,

[tex]1.96\sqrt{\frac{(0.5)^{2} }{x} } = 0.05[/tex]

Solving gives x=384.2.

So you need 385 people.

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Therefore ,the total number of days to rent a car at both locations for the same price is 11 days.

Two or more algebraic equations can be simultaneous if they share variables, such as x and y. Due to the simultaneous solution of the equations, they are known as simultaneous equations.

Here,

Let x be the number of days to repay after a down payment and y be the total amount due.

Consequently, equation 1 is 61+24x=y.

Eq. 2: 105 + 20x = y

Equation 1 minus equation 2

105-61+20x-24x= 0

44-4x= 0

4x = 44

multiply both sides by 4.

x= 44/4

x= 11 days

the total number of days to rent a car at both locations for the same price is 11 days.

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|20 - 25| • 2  and 33 - |6 + 17| are the following absolute value expressions are equal to 10.

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think of a number's absolute value is as its distance from zero on the real number line. A more general form of the equation is y=a| xh |+k for an absolute value function.

Here,

|20 - 25| • 2,

=5*2

=10

33 - |6 + 17|

=33-23

=10

The absolute value expressions |20 - 25| • 2 and 33 - |6 + 17| are both equal to 10.

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We are given the slope and the y-intercept so using the slope-intercept form:

Substitute values to get:

To graph a line we need two points, one is given, (0, - 7) - the y-intercept.

Find one more point,  take even value of x to cancel the fraction, let it be x = 4, find its y-coordinate:

So our points are:

Plot the points and connect to graph the line.

See below.

The graph of the linear equation:y = (3/2)*x - 7 can be seen in the image at the end.

A general linear equation is written as:y = a*x + b

Where a is the slope and b is the y-intercept. Then our linear equation is:y = (3/2)*x - 7

To graph it, we need to know two points in our line, to do so, we evaluate it in two different values of x. if x = 0y = (3/2)*0 - 7y = -7So we have the point (0, -7)

And if x = 2 then:y = (3/2)*2 - 7y = 3 - 7y = -4So we have the point (2, -4)

Now we just need to graph these two points and connect them with a line. You can see the graph below.

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The temperature of this object in degrees Celsius is equal to -270.65°C.

Temperature can be defined as a measure of either the degree of hotness or coldness of a physical body (object).

In Science and Mathematics, temperature is measured by using a thermometer and its units include the following:

In this exercise, you're required to convert the value of temperature in degree Fahrenheit (°F) to Celsius (°C). Therefore, we would use the following mathematical expression (formula) to perform the conversion:

C = K - 273.15

When t = 2.5 K, we have:

C = K - 273.15

C = 2.5 - 273.15

C = -270.65°C.

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The lowest integer value m can take in the inequality 7m + 5 > 49 - 3m is 5.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

In other words, Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's solve the inequality for the lowest integer value of m

7m + 5 > 49 - 3m

add 3m to both sides of the inequality

7m + 5 > 49 - 3m

7m + 3m + 5 > 49 - 3m + 3m

10m + 5 > 49

subtract 5 from both sides of the inequality

10m + 5 > 49

10m + 5 - 5 > 49 - 5

10m > 44

m > 44 / 10

m > 4.4

Hence,

lowest integer = 5

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