Suppose f(x) is a polynomial of degree 4 or greater such that f(1) = 2, f(2) = 3, and f(3) = 5. Find the remainder when f(x) is divided by (x-1)(x-2)(x-3).

Answer:

Basically 30% of $15,000 is $5,000 so each year, 1/3 of the car is taken from the original price. I think its 1/3 sorry if its wrong.

Answer:

A

Step-by-step explanation:

Hello There!

This is the formula for volume of a cylinder

\(V=\pi r^2h\)

where r = radius and h = height

we are given the height and diameter height - 10 ft diameter - 22 ft

we are not give the radius directly but we can easily convert the diameter to the radius by dividing by 2

22/2=11 so the radius is 11

now having found the radius and height we plug in the values into the formula (note: it says leave answer in terms of pi so we will not apply pi to the final answer.)

\(V=\pi 11^210\\11^2=121\\121*10=1210\\V=1210\pi\)

so we can conclude that the answer is A

Answer:

Mark as BRAINLIEST plz

|x-323|<50: answer

Step-by-step explanation :

For water to be a liquid, the temperature must be within 50 Kelvin of 323 K.

So, the range of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323.

The equation that can be used to determine the maximum temperature at which water is a liquid can be given by :  x < 323 + 50

The equation that can be used to determine the minimum temperature at which water is a liquid can be given by : x > 323 - 50

So the resultant equation can be written as :

|x-323|<50

The solution of inequality equation is  | x - 323 | < 50

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the temperature of the water be = x Kelvin

Now , the equation will be

For water to be in the liquid state, the temperature must be within 50 kelvin (K) of 323 K

So , the value of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323

Substituting the values in the inequality equation , we get

For maximum temperature ,

x should be 50 more than 323 and

For minimum temperature ,

x should be 50 less than 323

So ,

The inequality relation is

x > 50 + 323   be equation (1)

x < 323 - 50   be equation (2)

So , the modulus function is expressed as

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

Therefore , the value is | x - 323 | < 50

Hence , The solution of inequality equation is  | x - 323 | < 50

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The largest integer less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13. is 1440

Given, a number less than 2010 that has a remainder of 5 when divided by 7, a remainder of 10 when divided by 11, and a remainder of 10 when divided by 13.

On using the Chinese remainder theorem. As, the numbers 7, 11, 13 are pairwise coprime.

Firstly, an integer  m  such that  m−5  is divisible by 7 and  m−10  is divisible by 11 .

The Chinese remainder theorem says that all integers that work will be of the form  54+7⋅11⋅k=54+77k  for any integer  k .

Next an integer  n  such that  n−10  is divisible by 13 and  n−54  is divisible by 77.

Then, by the Chinese remainder theorem, all the integers that also work are of the form  439+13⋅77⋅k=439+1001k .

Hence, the positive integers satisfying the condition are: 439, 439 + 1001 = 1440, 1440 + 1001 = 2441, and so on.

The largest integer less than 2010 is 1440.

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The value of data that might affect the statistical measures of spread and center is B. There is a high data value that causes the data set to be asymmetrical for the males.

Outliers stretch out the data further, resulting in a wider range and a higher standard deviation. On the other hand, eliminating outliers reduces data spread, resulting in a lower range and standard deviation.

When an outlier is present, it might change the way the graph looks since it raises the mean. From the chart, there is a high data value in the males which will therefore make the data to be asymmetrical for the males as the larger spread for the males means the data set tilts towards them.

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Answer:

its just rhombus and trapezoid i think.

Step-by-step explanation:

A total of 23, 950, 080 results are possible.

We are given;

10 women

12 men

5 men and 5 women, chosen and pared off, how many results in total?

Thus;

[10 choose 5] x [12 choose 5]=252 x 792 = 199584 ways

We then need to know how many ways there could put into pairs i.e. For the first woman, there will be 5 choices of men. For the second woman, there will be 4 choices remaining of men. For the third woman, there will be 3 choices remaining. For the fourth woman, there will be only 2choices remaining, and only 1 choice left for the last woman.

Therefore, there are 5x4x3x2x1 = 120 ways.

 In total there are 199584x120 = 23950080 total  ways

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The probability that exactly 3 jellies selected are yellow is 0.2149.

Given that the box contains 19 yellow, 31 green, and 32 red jelly beans. Therefore, the probability of getting a yellow jelly bean is,

Probability of Yellow jelly beans

= Number of Yellow jelly beans / Total number of jelly beans in the box

= 19 / (19 + 31 + 32)

= 19 / 82

= 0.2317

Now, as per the binomial probability distribution:

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Therefore, the probability of getting exactly 3 yellow jelly beans is:

P(x=3) = ⁹C₃ (0.2317³) (1-0.2317)⁽⁹⁻³⁾

           = 84 × 0.012438 × 0.205676

           = 0.2149

Hence, the probability is 0.2149.

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Answer:

The difference in square feet is 75 square feet.

Step-by-step explanation:

Formula for area of a rectangle: Area = length x width

Current measurements: 12 by 10, so

A = 12 x 10 = 120 square feet

New measurements: 15 by 13 (adding 3 feet to each)

A = 15 x 13 = 195 square feet

Subtract to find the difference:

195-120 = 75

Please let me know if you have questions.

Answer:

19-22= -3

Step-by-step explanation:

Please give brainliest :)

Step-by-step explanation:

XY^2=8^2+15^2 ... (Theorem of Pythagoras)

XY^2=64+225

XY^2=289

XY=17 units

Therefore:

SinX=15/17

CosX=8/17

TanX=15/8

The cost of the brick walkway would be $8164.To calculate the cost of the brick walkway surrounding the social area, we need to determine the area of the walkway and then multiply it by the cost per square yard.

The social area has a diameter of 24 yards, so its radius is half of that, which is 12 yards. The area of the social area is given by the formula for the area of a circle: A = πr^2, where π is approximately 3.14.

Area of social area = 3.14 * (12^2) = 3.14 * 144 = 452.16 square yards

To find the area of the walkway, we need to subtract the area of the social area from the area of the larger circle formed by the outer edge of the walkway. The radius of this larger circle is the sum of the radius of the social area and the width of the path.

Width of the path = 2 yards

Radius of larger circle = 12 yards + 2 yards = 14 yards

Area of walkway = 3.14 * (14^2) - 452.16 = 3.14 * 196 - 452.16 = 615.44 - 452.16 = 163.28 square yards

Finally, we can calculate the cost of the walkway by multiplying the area of the walkway by the cost per square yard, which is $50.

Cost of the walkway = 163.28 * $50 = $8164

Therefore, the cost of the brick walkway would be $8164.

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Answer:

the domingo of a grapa consiste of all the input vales show on the x-axis the rango is the set of posible output vales which are show on the y-axis

Answer:

2/5

Step-by-step explanation:

We can represent the probability that the spinner lands on purple as:

\(\dfrac{\# \text{ purple spins}}{\#\text{ total spins}}\)

\(=\dfrac{80}{40 + 80 + 80}\)

\(= \dfrac{80}{200}\)

\(\boxed{=\dfrac{2}{5}}\)

So, the probability of this spinner landing on purple is 2/5.

Answer:

The perimeter of the square is;

Explanation:

Given the square RSTV with the coordinates given the question.

Let us find the length of the sides of the square.

Using the formula for distance between two points;

Recall that the perimeter of a square can be calculated using the formula;

Therefore, the perimeter of the square is;

angle of F is 134, why? Because each triangle is 180 degrees altogether.

Step-by-step explanation:

In a 2 x 2 between-subjects factorial experiment, there are a total of four treatment conditions in the experiment, and each participant serves in one condition(s).

In a 2 x 2 between-subjects factorial experiment, there are a total of four treatment conditions in the experiment, and each participant serves in one condition. The four conditions in a 2 x 2 between-subjects factorial experiment are created by manipulating two independent variables, each with two levels.

The levels of these independent variables are crossed together to create four unique conditions.The factorial experiment design is used to analyze the effect of multiple independent variables on a dependent variable. When the levels of each independent variable are combined in a factorial design, this results in treatment conditions.

Each participant serves in one condition in a between-subjects design. Because each condition represents a distinct treatment in a factorial design, each participant serves in one treatment condition only. Therefore, in a 2 x 2 between-subjects factorial experiment, each participant serves in one of the four treatment conditions.

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Given:

Equation of line \(7x-4y=-12\).

To find:

The equation of line  that goes through the point ( − 21 , 2 ) and is perpendicular to the given line.

Solution:

The given equation of line can be written as

\(7x-4y+12=0\)

Slope of line is

\(\text{Slope}=-\dfrac{\text{Coefficient of x}}{\text{Coefficient of y}}\)

\(m_1=-\dfrac{7}{(-4)}\)

\(m_1=\dfrac{7}{4}\)

Product of slopes of two perpendicular lines is -1. So, slope of perpendicular line is

\(m_1m_2=-1\)

\(m_2=-\dfrac{1}{m_1}\)

\(m_2=-\dfrac{4}{7}\)           \([\because m_1=\dfrac{7}{4}]\)

Now, the slope of perpendicular line is \(m_2=\dfrac{4}{7}\) and it goes through (-21,2). So, the equation of line is

\(y-y_1=m_2(x-x_1)\)

\(y-2=-\dfrac{4}{7}(x-(-21))\)

\(y-2=-\dfrac{4}{7}x-\dfrac{4}{7}(21)\)

\(y-2=-\dfrac{4}{7}x-12\)

\(y=-\dfrac{4}{7}x-12+2\)

\(y=-\dfrac{4}{7}x-10\)

Therefore, the required equation in slope intercept form is \(y=-\dfrac{4}{7}x-10\).

Answer:

A) the fraction of the week that Jamaar spent in this garden.

Answer: slope is 4, y intercept is ( 0,8) , x intercept is (-2,0)

Step-by-step explanation: graph the line using the slope and and y intercept.

9514 1404 393

Answer:

  (a) All three pyramids have the same volume

Step-by-step explanation:

The triangular base has an area of ...

  B = 1/2bh . . . . where b is the base of the triangle and h is its height.

The volume of the pyramid is ...

  V = 1/3BH . . . . where B is the area of the base, and H is the height of the pyramid.

Combining these equations gives ...

   V = 1/3(1/2bh)H = 1/6bhH

__

Pyramid 1 volume

  V1 = 1/6(12 m)(2 m)(10 m) = 40 m³

Pyramid 2 volume

  V2 = 1/6(6 m)(4 m)(10 m) = 40 m³

Pyramid 3 volume

  V3 = 1/6(12 m)(4 m)(5 m) = 40 m³

All three pyramids have the same volume.

The simplified product of - (2/5).(2/5) is equal to - 4/25.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

A product of two fractions - 2/5 and 2/5 is given.

We know in the product of fractions numerator is multiplied by the numerator and the denominator is multiplied by the denominator.

Therefore, - (2/5).(2/5).

= - (2×2)/(5×5).

= - 4/25.

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Answer:

13#

Step-by-step explanation:

5 cakes equal to 65$

1 cake equals ?

1/5×65

13$

Answer:

Each cake is $13

Step-by-step explanation:

If each cake costs the same and you bought 5, spending a total of $65, you would simply divide the $ you spent by the amt. of cakes to find how much each cake is. Let's assume x is how much each cake is, and 5 is the number of cakes you buy, so 5 (The amount of cakes) multiplied by x (how much each cake costs) must give you 65.

Equation:

5x=65

x=65/5

x=13

Answer: Each cake is $13.

Answer:

A. Pink 0.3 Green 0.2 Yellow 0.05 Blue 0.45

Step-by-step explanation:

Adding up the total number of values:

\(6+4+1+9=20\)

Then, finding the probability of each color:

Pink: \(6/20=0.30\)

Green: \(4/20 = 0.20\)

Yellow: \(1/20=0.05\)

Blue: \(9/20=0.45\)

The problem is asking for two function equations of the "quadratic" graph, the factored form equation and the vertex form equation.

Vertex form equation) This functional equation has always the form

It is called vertex form for (h,k) is the vertex of the parabola. Intuitively, the vertex of a parabola is its "starting" point, the point from where the parabola opens its "arms".

In this case, as you can see in the picture above, the vertex is

Then,

Thus our equation becomes

Our task now is to find the constant a. Note that the origin (0,0) is part of our function, that is

This (equality) is the same as

Then

Factored form equation) This equation is easier. It has the form

where r_1 and r_2 denote the roots of the parabola. They are just the x-intercepts of the function.

In this case, as you can see in the picture above,

Then, our equation becomes

For the vertex of the parabola is clearly a point of the function, we have

So

Let's solve this for b:

The vertex form equation of f(x) is

(Be careful! In the third box, you must put -8 not just 8. In the second one, you must put just 2 without the minus sign)

The factored form equation of f(x) is

Answer:

Step-by-step explanation:

9.7 = \(\frac{97}{10}\)

Count the number of places in the decimal number after the decimal point.

Here , there is only one place.

So, multiply and divide by 10. 9.7 *10/1*10 = 97/10

There are ²⁰С₁₀ × 10!  × 10! ways to divide the class and line up the groups.

Number of students in the class = 20

Selection of group one = ²⁰С₁₀ ways

Selection of group two = 1 way

Number of ways to arrange 10 students in a group = 10!

So, Total number of ways = ²⁰С₁₀ × 10!  × 10! ways.

Hence there are  ²⁰С₁₀  × 10!  × 10! ways to divide the class and line up the groups.

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The given sequence 16, 7, -2 is arithmetic progression with a common difference of -9. The next term in the sequence is found by adding the common difference. Therefore, the complete sequence is 16, 7, -2, -11, ....

To determine whether the sequence 16, 7, -2, ... is arithmetic, we need to check if there is a common difference between consecutive terms.

The common difference (d) between consecutive terms of an arithmetic sequence is given by:

d = a(n) - a(n-1)

where a(n) is the nth term of the sequence.

From the given terms, we can see that:

a(1) = 16

a(2) = 7

a(3) = -2

Using the formula for the common difference, we have:

d = a(2) - a(1) = 7 - 16 = -9

d = a(3) - a(2) = -2 - 7 = -9

Since the common difference is the same for both pairs of consecutive terms, we can conclude that the sequence is arithmetic with a common difference of -9.

To find the next term in the sequence, we can add the common difference to the previous term:

a(4) = a(3) + d = -2 - 9 = -11

Therefore, the complete sequence is:

16, 7, -2, -11, ..

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Answer:

100

Step-by-step explanation:

25% can also be converted to 0.25

if you want to INCREASE it by 25%, you're adding 25% to your current 100% to get 125% of 80

125% is the same as 1.25, so you multiply 80 by 1.25

80 * 1.25 = 100

Answer:

100

Step-by-step explanation:

To increase 80 by 25%, you need to add 25% of 80 to 80.

First, we find what 25% of 80 is.

To find a percent of a number, multiply the percent by the number.

Change the percent to a decimal by dividing the percent by 100.

25% of 80 = 25% × 80 = 25/100 × 80 = 0.25 × 80 = 20

25% of 80 is 20.

Now we add 20 to 80.

80 + 20 = 100

Answer: 100