For each of the values a=1, a=2,a=4, and a=6

The polynomial function of least degree possible using the given information is: f(x) = -7/3 (x+1)(x-1)(x-3)

What is polynomial function?

A polynomial function is a type of mathematical function that consists of one or more terms, each of which is a constant multiplied by a variable raised to a non-negative integer power.

To construct a polynomial function of least degree possible using the given information, we need to use the fact that the function has real roots at -1, 1, and 3. This means that the function can be factored as follows:

f(x) = a(x+1)(x-1)(x-3)

where a is a constant coefficient that we need to determine.

Next, we need to use the fact that the function passes through the point (2, 7) to determine the value of a. We substitute x=2 and f(x)=7 into the above equation and solve for a:

7 = a(2+1)(2-1)(2-3)

7 = -3a

a = -7/3

Therefore, the polynomial function of least degree possible using the given information is:

f(x) = -7/3 (x+1)(x-1)(x-3)

Note that this function has real roots at -1, 1, and 3, and passes through the point (2, 7).

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Check the picture below.

[tex]\sin(43^o )=\cfrac{\stackrel{opposite}{y}}{\underset{hypotenuse}{18}}\implies 18\sin(43^o )=y\implies 12.28\approx y[/tex]

Make sure your calculator is in Degree mode.

Answer:

NO

Step-by-step explanation:

First, we should simplify both fractions to the most simple form.

4/14=2/7

12/40=6/20=3/10

A proportion means that it is equal. 2/7 does not equal 3/10, so the answer is no.

The area of the semicircle that has a radius of 3 kilometers is calculated as: 14.13 square kilometers.

To find the area of a semicircle, you can follow these steps:

The semicircle's area = 1/2(πr²) = 1/2 * (3.14 * 3²)

= 14.13 square kilometers.

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The domain of this function can be expressed as (-∞,0) U (0,∞).

The interval on which the function is decreasing is

(-∞,0) U (0,∞).

The interval on which the function is increasing is none.

The interval on which the function is constant is (0,0).

The domain of a function is the set of all acceptable inputs for the function. In other words, it is the set of all values for which the function is defined.

The domain of the given function is all real numbers, excluding 0.

This can be seen by observing that the denominator in the fraction is the absolute value of t, which is always positive.

Therefore, the domain of the function is all real numbers except 0, which can be expressed as (-∞,0) U (0,∞).

The function is decreasing over all intervals in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.

Therefore, the interval on which the function is decreasing is

(-∞,0) U (0,∞).

The function is constant over the interval (0,0) since the absolute value of 0 is 0 and thus, the denominator in the fraction is equal to 0.

Therefore, the interval on which the function is constant is (0,0).

Finally, the function is not increasing over any interval in its domain since the negative sign preceding the fraction indicates that the value of the function is always negative.

Therefore, the interval on which the function is increasing is none.

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A. The mean age of the team rounded to 1 decimal place is 20.9 years

B. The age of the new player is 23.1 years

The mean age of the team can be obtained as illustrated below:

Mean age = ∑fx / ∑f

Mean age = [(19 × 2) + (20 × 3) + (21 × 1) + (22 × 4) + (23 × 1)] / (2 + 3 + 1 + 4 + 1)

Mean age = 230 / 11

Mean age = 20.9 years

Thus, the mean age of the team is 20.9 years

The age of the new player can be obtained as follow:

New mean = (mean of previous + age of new player) / 2

22 = (20.9 + age of new player) / 2

Cross multiply

22 × 2 = 20.9 + age of new player

44 = 20.9 + age of new player

Collect like terms

44 - 20.9 = Age of new player

Age of new player = 23.1 years

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Complete question:

Pleas attached photo

the correct answer is a. SAS congruency theorem can be used to prove that ABD =DCA.

In this question we accept two angles is given that is:

two triangles ∠ABD and

In this, an angle is common that is,

AD = AD

AB = CD

∠A is equal = ∠A (which is given)

That is the reason the SAS rule is right.

SSS is a geometric term that stands for "side-side-side." It refers to a congruence condition in which three sides of one triangle are equal to three corresponding sides of another triangle, making the two triangles congruent. Congruent triangles have the same size and shape, so if two triangles are congruent, all corresponding angles and sides are equal.

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the complete question is:

Which congruency theorem can be used to prove

that ABD =DCA?

a. SAS

b. Not enough information

c. SSS

d. AAS

Ms. Maynard grates 23/30 of a block of cheese, leaving the fraction of 7/30 of the cheese. Mr. Connor then eats 3/30 of the cheese, leaving the fraction of 4/30 of the cheese remaining.

Let us suppose the total block of cheese as 1.

If Ms. Maynard grates 23/30 of a block of cheese, then the fraction of cheese left is:

Remaining cheese = 1 - 23/30 = 7/30

After Mr. Connor eats 3/30 of the cheese, the fraction of cheese left is:

Remaining cheese = 7/30 - 3/30 = 4/30

Therefore, 4/30 of the cheese is left over after grating by  Ms. Maynard and  Mr. Connor respectively.

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Answer: required ratio is 1;3

Step-by-step explanation:

Since we have given that

Ratio of the number of 5 p coins to the number of 10 p coins = 2:3

So, the number of 5p coins be '2x'

Let the number of 10p coins be '3x'.

Value of 5p coins = 5p x 2x =10px

Value of 10p coins = = 10p x 3px=30px

So, the ratio of value of 5p coins to the value of 10p coins is given by

10px:30px

1:3

The equatiοn οf the circle will be [tex]x^{2}+y^{2} -6x-16=0[/tex]

A clοsed rοund shaped figure which cοntains nο cοrners is called circle. It has center called (h, k)  and radius r. Rοund clοck, car tire, wheels are the examples οf circle.

If the center and radius is given then the equatiοn οf circle is:

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex] ------------- (1) where (h, k) centre and r radius.

Here center οf the circle is (3,0) and radius οf the circle is 5

putting h= 3 , y=0  and r=5 in equatiοn (1) we get

    [tex](x-3)^{2} + (y-0)^{2} =5^{2}[/tex]

⇒ (x²- 6x+9) +y²=25

⇒ x²+y²-6x+9-25=0

⇒x²+y²-6x-16=0

Hence the equatiοn οf circle is x²+y²-6x-16=0.

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The values of the inequalities are -5 ≤ x ≤ 1 and 2/3 ≤ x ≤ 1

What are inequalities?

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Here, we have

Inequality 1: f(4x - 3) ≥ f(2 - x²), Df = (-8 , 4)

The function increases at (-8,4).

So, we have:

4x - 3 ≥ 2 - x²

Rewrite as:

x² + 4x - 2 - 3 ≥ 0

Evaluate the like terms

x² + 4x - 5 ≥ 0

Expand

x² + 5x - x - 5 ≥ 0

Factorize the expression

x(x + 5) - 1(x + 5) ≥ 0

Factor out x + 5

(x - 1)(x + 5) ≥ 0

Solve for x

x ≥ 1 or x ≥ -5

Rewrite as:

-5 ≤ x ≤ 1

Inequality 2: g(3x² - 2x) ≥ g(3x - 2), Dg = all real numbers

g(3x² - 2x) ≥ g(3x - 2)

(3x² - 2x) ≥ (3x - 2)

Evaluate the like terms

3x² - 2x -3x + 2 ≤ 0

3x² - 5x + 2 ≤ 0

3x² - 3x -2x + 2 ≤ 0

3x(x-1) -2(x-1) ≤ 0

Solve for x

x≤1 or x≤2/3

Hence, the values of the inequalities are -5 ≤ x ≤ 1 and 2/3 ≤ x ≤ 1

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Answer:

-18x + 54y + 60

Step-by-step explanation:

you get this answer by distributing the -6 to all 3 properties.

-6 x 3x = -18x

-6 x -9y = 54y

-6 x -10 = 60

The surface area of a cylinder is given by the formula:

A = 2πrh + 2π[tex]r^{2}[/tex]= 2*3.14*4.8*19.1= 575.504 square ft.

Surface area is the measure of the total area that the surface of an object occupies. It is the sum of all the areas of the individual faces or surfaces of the object. For example, if you have a cube, the surface area would be the sum of the areas of all six faces of the cube. The surface area is usually measured in square units, such as square meters, square centimeters, or square feet, depending on the system of measurement used. Surface area is an important concept in many fields of study, including mathematics, physics, chemistry, and engineering.

by the question.

The surfaces area of a cylinder is given by the formula:

[tex]A = 2πrh + 2πr^2[/tex]

where r is the radius of the circular base of the cylinder, and h is the height of the cylinder.

If a=9.6ft and b=19.1ft, we need to determine the values of r and h before we can calculate the surface area.

Since the cylinder has a circular base, we know that the diameter of the base is equal to b, or 19.1ft. Therefore, the radius of the base is half the diameter, or:

r = b/2 = 19.1/2 = 9.55ft

we know that the radius of the cylinder is = diameter/2

= 9.6/2

= 4.8

The surfaces area of a cylinder= [tex]A = 2πrh + 2πr^2[/tex]

A = 2πrh + 2π[tex]r^{2}[/tex]= 2*3.14*4.8*19.1= 575.504 square ft.

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the area of the equilateral triangle with a side length of 15 is approximately 97.4279 square units.

A regular triangle is also known as an equilateral triangle, which means all of its sides are equal in length. To find the area of an equilateral triangle with a side length of 15, we can use the following formula:

Area = (√(3) / 4) × side²

where "side" is the length of one side of the triangle.

Let's plug in the given value of side length, which is 15, into the formula:

Area = (√(3) / 4) × 15²

Area = (√(3) / 4) × 225

Area = 97.4279 (rounded to 4 decimal places)

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Therefore, when y = 10 and z = 5, the value of the expression 0.3y + y/z is 5.

In mathematics, an expression is a combination of numbers, variables, and operators that are grouped together to represent a mathematical quantity or relationship. Expressions can be simple, such as a single number or variable, or they can be more complex, involving multiple operations and variables. Expressions are often used in mathematics to represent relationships between variables, to evaluate quantities, and to solve equations.

Here,

Substituting y = 10 and z = 5 in the given expression, we get:

0.3y + y/z = 0.3(10) + 10/5

= 3 + 2

= 5

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Answer:

that question is incomplete

Answer:3.14sq^2

Step-by-step explanation:b x c x a = 3.14

Any number that is strictly greater than 11/16 and strictly less than 15/16 belongs to this interval.

In mathematics, inequalities are statements that cοmpare twο values and indicate whether οne value is greater than, less than, οr equal tο the οther value.

Tο find the numbers that are greater than 11/16 and less than 15/16, we need tο cοnsider all numbers between these twο values, excluding the endpοints. That is,

11/16 < x < 15/16

where x represents the number we are looking for. We can also write this using interval notation as:

(11/16, 15/16)

Hence, any number that is strictly greater than 11/16 and strictly less than 15/16 belongs to this interval.

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Answer:

The constant of variation in the given problem is 9.8

GIVEN

w = 2,116.8

m = 120

h = 1.8

SOLUTION

w=kmh

2116.8 = k(120)(1.8)

2116.8=216k

9.8=k

Answer:

a. 250,000

b. 450,000

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Both 8 and 1/32 are powers of 2.

2³ is 8, since 2*2*2=8.

2^-5 is 1/32.

2^5 is 2*2*2*2*2, and the negative sign in front of the 5 flips the answer to be 1/32

Answer:

First, we need to find the area of one block:

Area of one block = length x width = (1/10) mile x (1/10) mile = 1/100 square mile

Since there are 500 blocks in the town, the total area of the town is:

Total area of town = 500 blocks x (1/100) square mile/block = 5 square miles

To find the population density, we divide the population by the total area:

Population density = population / total area

Population density = 80,250 / 5 = 16,050 people per square mile

Therefore, the population density of the town is 16,050 people per square mile.

The exact value of x is 12.97.

In geometry, a bisector refers to a line or plane that divides a geometric figure into two equal parts. Specifically, a bisector divides an angle into two equal angles, a line segment into two equal parts, or a plane figure into two equal areas.

There are two types of bisectors:

Angle bisector: A line or ray that divides an angle into two equal angles is called an angle bisector. The point where the bisector intersects the angle is known as the vertex of the angle.

Segment bisector: A line, ray, or line segment that divides a line segment into two equal parts is called a segment bisector. The point where the bisector intersects the line segment is known as the midpoint of the line segment.

We can use the angle bisector theorem to find the value of x. According to the angle bisector theorem, the length of the segment bisecting an angle in a triangle is proportional to the lengths of the two sides adjacent to that angle.

Let's call the point where ST intersects QS point U. Then, by the angle bisector theorem, we have:

QU / QR = SU / SR

Substituting the given values, we get:

QU / 20 = x / 16

Multiplying both sides by 20, we get:

QU = (20x) / 16 = (5x) / 4

Similarly, we have:

SU / QS = TU / TR

Substituting the given values and simplifying, we get:

SU / 12 = x / 20

Multiplying both sides by 12, we get:

SU = (12x) / 20 = (3x) / 5

Now, we can use the fact that QRS is a triangle to find the remaining side length:

QR + RS = QS

20 + 16 = 12 + SU + QU

36 = 12 + (3x/5) + (5x/4)

Multiplying both sides by 20, we get:

720 = 240 + 12x + 25x

720 = 37x + 240

37x = 480

x = 480/37

So the value of x is approximately 12.97 (rounded to the nearest hundredth).

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Answer:

Step-by-step explanation:

10 percent of 3000 = 300

3000+300=3300

3300+300=3600

3600+300=3900

interest = 3900-3000

= R900

he will pay R900 interest over 3 years.

i think this is the answer.

Answer:

18%

Step-by-step explanation:

first you divide 97,200 from 540,000= 0.18 x 100=18%

Therefore, the coordinates of A are (1, 3) and (2, 4). Therefore, the area of the shaded region is (1/2) square units.

In mathematics, area is the measure of the amount of surface enclosed by a two-dimensional shape or object. It is the size of a surface, and is typically measured in square units such as square meters (m²), square centimeters (cm²), square feet (ft²), or square inches (in²).

Here,

First, we need to find the coordinates of the point where the line and the curve meet (point A).

Substituting y = x(4 – x) into y + 2x = 5, we get:

x(4 – x) + 2x = 5

Simplifying and rearranging, we get:

x² – 3x + 2 = 0

Factoring, we get:

(x – 1)(x – 2) = 0

Therefore, x = 1 or x = 2.

When x = 1, y = 3, and when x = 2, y = 4. Therefore, the coordinates of A are (1, 3) and (2, 4).

To find the area of the shaded region, we need to find the integral of the curve y = x(4 – x) between x = 1 and x = 2, and subtract the area under the line y + 2x = 5 between the same limits.

The equation y + 2x = 5 can be rewritten as y = -2x + 5.

Integrating y = x(4 – x) between x = 1 and x = 2, we get:

∫(1 to 2) x(4 – x) dx = (8/3) – (2/3)

= 2

Integrating y = -2x + 5 between x = 1 and x = 2, we get:

∫(1 to 2) (-2x + 5) dx = (3/2)

Therefore, the area of the shaded region is:

=2 - (3/2)

= (1/2) square units

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The probability that a randomly selected athlete uses a stair climber for,

(a) P(X < 18) = 0.2514

(b) P(22 < X < 31) = 0.4332

(c) P(X > 30) = 0.0918

Let X be the amount of time an athlete uses a stair climber. Then, X ~ N(22, 6^2) represents a normal distribution with mean 22 and standard deviation 6.

(a) To find the probability that a randomly selected athlete uses a stair climber for less than 18 minutes, we need to calculate P(X < 18).

Z-score for 18 minutes = (18 - 22) / 6 = -0.67

Using a standard normal table or calculator, we find that P(Z < -0.67) = 0.2514.

Therefore, P(X < 18) = P(Z < -0.67) = 0.2514.

(b) To find the probability that a randomly selected athlete uses a stair climber for between 22 and 31 minutes, we need to calculate P(22 < X < 31).

Z-score for 22 minutes = (22 - 22) / 6 = 0

Z-score for 31 minutes = (31 - 22) / 6 = 1.5

Using a standard normal table or calculator, we find that P(0 < Z < 1.5) = 0.4332.

Therefore, P(22 < X < 31) = P(0 < Z < 1.5) = 0.4332.

(c) To find the probability that a randomly selected athlete uses a stair climber for more than 30 minutes, we need to calculate P(X > 30).

Z-score for 30 minutes = (30 - 22) / 6 = 1.33

Using a standard normal table or calculator, we find that P(Z > 1.33) = 0.0918.

Therefore, P(X > 30) = P(Z > 1.33) = 0.0918.

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T3=R1

T4=R2}==>TUR=TSR

RT=RT

so: S=U

Number of ways that the researcher can select 4 boxes, consisting of 2 boxes of regular and 2 boxes of diet, for a quality control test is 441

To select 4 boxes consisting of 2 regular and 2 diet from 7 boxes of each, we need to use combinations.

The number of ways to select 2 regular boxes out of 7 is

C(7,2) = 21

Similarly, the number of ways to select 2 diet boxes out of 7 is also 21.

Now we need to choose 2 regular boxes out of 2 and 2 diet boxes out of 2, which can only be done in one way.

So the total number of ways to select 4 boxes consisting of 2 regular and 2 diet is

21 x 21 x 1 x 1 = 441

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Answer:

[tex]85 + 8h = 125[/tex]