Find a polynomial function of degree 4 with the zeros -3 (multiplicity 2) and 3 (multiplicity 2), whose graph passes through the point (-4,245).

The possible equation of the parabola is y = (x - 5)^2 - 4

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

Vertex = (5, -4)

The vertex form of a parabola is given by:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.

We are given that the vertex of the parabola is (5,-4). Substituting these values into the vertex form, we get:

y = a(x - 5)^2 - 4

Let a = 1

So, we have

y = (x - 5)^2 - 4

Hnce, the possible equation is y = (x - 5)^2 - 4

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Liters of 10% solution = 1 liters

Liters of 70% solution = 5 liters

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x +3 = 8 is an equation.

We have,

10% solution = x

70% solution = y

Now,

A 10% antifreeze solution is to be mixed with a 70% antifreeze solution to get 6 liters of a 20% solution.

This means,

We can make two equations.

0.10x + 0.70y = 6 x 0.20

0.10x + 0.70y = 1.2 ______(1)

x + y = 6 ______(2)

Solve for x and y.

From (2),

x = 6 - y

Substituting in (1) we get,

0.10x + 0.70y = 1.2

0.10 (6 - y) + 0.70y = 1.2

0.6 - 0.10y + 0.70y = 1.2

0.6 + 0.60y = 1.2

0.60y = 1.2 - 0.6

0.60y = 0.6

y = 1

And,

x = 6 - y

x = 6 - 1

x = 5

Thus,

10% solution = 1 liter

70% solution = 5 liters

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On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:

weight

x = 15bags X 28/1 X 0.453

x = 258.21 kg

volume

x = 15 X 4/27 = 2.222 yd

15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

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On solving the provided question we can say that 15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

In terms of dimensions, a pound is equivalent to 0.453 kilos and a cubic yard is equivalent to 27 cubic feet. We next continue to get the weight and volume of 15 bags using the conversions below:

weight

x = 15bags X 28/1 X 0.453

x = 258.21 kg

volume

x = 15 X 4/27 = 2.222 yd

15 bags total 258.21 kilos in weight. 15 bags have a volume of 2.222 cubic yards.

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Answer:

D

Step-by-step explanation:

It's the most random and produces no bias.

Answer:

D

Step-by-step explanation:

300.5 ml of antihistamine is needed for a 100​-pound person to take in a​ week

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

1 day = 24 hours

1 week = 7 days = 24 hours per day * 7 days = 168 hours

A typical dose for a 100​-pound person is 22 mg every six hours. Hence for one week:

Dosage in one week = (22 mg per 6 hours) * 168 hours = 616 mg

Antihistamine also comes in a liquid form with a concentration of 12.3 ​mg/ 6 mL. For 616 mg:

Amount of antihistamine = 616 mg / (12.3 ​mg/ 6 mL) = 300.5 ml

300.5 ml of antihistamine is needed

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An equation to show the sequence is -25n.

When all the terms of the geometric sequence are added, than that expression is known as geometric series.

The sum of terms of a geometric sequence;

Now, lets suppose its initial term is   , multiplication factor will be r

and let it has total n terms, then, its sum is given as:

[tex]S_n = \dfrac{a(r^n-1)}{r-1}[/tex]

(sum till nth term)

We are given that;

The first term of sequence=-25

D= -50-(-25)

=-25

Now,

an = a + (n-1)d

=-25+(n-1)-25

=-25-25n+25

=-25n

Therefore, the answer of the sequence will be -25n.

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The probability that the hiker will reach his destination is, 1/2

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Since the hiker chooses one of the four trails with equal probability by rolling a fair 4-sided die,

the probability of taking any one trail is 1/4.

Once the hiker is on a trail, there are two sub-trails, and the hiker chooses one of them by flipping a fair coin.

The probability of taking the correct sub-trail is 1/2.

P(reaching destination) = P(trail 1) x P(correct sub-trail on trail 1) + P(trail 2) x P(correct sub-trail on trail 2) + P(trail 3) x P(correct sub-trail on trail 3) + P(trail 4) x P(correct sub-trail on trail 4)

P(reaching destination) = (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2) + (1/4) x (1/2)

P(reaching destination) = 4/8

P(reaching destination) = 1/2

Therefore, the probability that the hiker will reach his destination is 1/2, or 50%.

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Answer:

Step-by-step explanation:

When we use the distance formula for two points ( x, y ) and ( x', y¹ ) Then formula is (distance)² = (x - x¹)² + (y - y¹)² This is quite similar to the formula used in a right angle triangle

Answer:

Step-by-step explanation:

The y-intercept b of the equation of the line is 30.

The graph represent a linear relationship between the temperature in degree farad and time in minutes.

Therefore, let's find the y-intercept b of the equation.

Hence, using slope intercept form,

y = mx + b

where

Therefore,

y = 20x + b

where

Using (6, 150) let's find b as follows:

y = 20x + b

150 = 20(6) + b

150 - 120 = b

Therefore,

b = 30

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The equation of the polynomial function graphed is given as follows:

y = -0.125(x³ + x² - 14x - 24).

From the graph, the roots of the polynomial are given as follows:

Considering the roots, the linear factors of the polynomial are given as follows:

Applying the Factor Theorem, the function, as a product of it's linear factors, is given as follows:

y = a(x + 3)(x + 2)(x - 4).

y = a(x² + 5x + 6)(x - 4)

y = a(x³ + x² - 14x - 24).

When x = 0, y = 3, hence the leading coefficient a is obtained as follows:

-24a = 3

a = -0.125.

Hence the function is:

y = -0.125(x³ + x² - 14x - 24).

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His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

Two or more expressions with an Equal sign is called as Equation.

Sheldon wants to buy two shirts at the store.

They were each originally $14.99, but one of the shirts is on sale this week for 10% off.

A 6% sales tax is applied to the total cost of the shirts.

0.90 • 14.99 + 14.99 • 1.06 = n

The first term in the equation, 0.90 • 14.99, represents the cost of the shirt that is on sale.

The 10% discount is applied to the original price of $14.99, which is why we multiply by 0.90.

This term calculates the discounted price of the first shirt.

The second term in the equation, 14.99 • 1.06, represents the cost of the second shirt, plus the 6% sales tax that is applied to both shirts.

This term calculates the total cost of the second shirt with sales tax.

Hence, His equation correctly represents the total cost of his order is the statement describes Sheldon’s equation

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Given,

y=55cm
w=73 cm

Using Pythagoras Theorem,

[tex]w^{2}[/tex] = [tex]y^{2} + x^{2}[/tex]

73² = 55² + x²

x= √3025

x = 48cm

Answer= 48cm

Answer: x ≅ 11.2

Step-by-step explanation:

We can set up two equations:

Let y = measure of <BAD = measure of <CAD

then:

sin y = x/23

sin y = (20-x)/18

Since both of these are sin y, we can set them equal to each other:

x/23 = (20-x)/18

.: 18x = 460 - 23x

41x = 460

.: x ≅ 11.2

Answer:

x = 11.2

--------------------

Use angle bisector theorem. It states that:

Apply this to the given triangle:

Cross-multiply and solve for x:

Answer:

2,19/3 this is answer this is correct

In this question you're given that a coin is flipped 12 times. Now I'll make some assumption here. The first assumption is that the coin is fair. That means the probability of getting ahead in a trial in the toss is the same as probability of getting a deal in the toss and that would be half And second. The all the 12 flips or tosses are independent of each other. And thirdly that the probability of getting ahead, it's the same in each toss and you can see that in each talks there's only two outcomes ahead or not ahead which is a so this is considered a success and this is a failure. It just happened to be the probability of the success and the probability of failure is the same at heart. So this actually follows a binomial distribution model. But in the event that you have not learned by normal distribution we can just go by simple probability multiplication rule. So in probability and it's times or is plus. But the assumption of independent trials and the coin is fair is still the same whether you're using binomial distribution or just simple probability multiplication rule, no Probability of obtaining 12 heads in a row when flipping a coin would be the first pulse, you get a hit. And the second course you also get ahead. And the third toss you get ahead. So on so forth. Up to the last toss, which is the 12th toss, you also get a hit. So it's hit for every toss. So what this means is that probability of first courses ahead is half so that's half now. N and in probability means multiple execution. So just times and second hand is second thoughts is also ahead. So there's a half and so N. S. A. Terms enter is ahead, so that's another half, so so on, so forth. All the way to the last end here. Mr toms And the 12 is also a hit. So this times, how so what we have here is half to the power of 12 since half is multiplying itself 12 times. And so the answer is 1/4 oh 96 Or 0.0002, 44 six, decimal places. Now, if you are using binomial distribution to solve this problem, you will be after this part here. You will be letting X be the number of heads. Oh 12 courses. Right, So X follows the binomial distribution Number of trials is 12, 12 horses. And probability of success in this case is probability of getting ahead in a in a toss is half, so probability of X equals two. R. Where r is the number of heads in 12 courses will be 12, choose our half to the power of our and one minus half is also half To the power of 12 minus are so probability of obtaining 12 heads in a role. So we will be looking at probability of X equals 2, 12. So just suck 12 into the arm. So is this and you will get the same answer of 0.000244

Answer: 68.82

Step-by-step explanation:

74 * (1- 7%) and solve

= 68.82

Answer:

RJ and his 2 brothers are given a weekly allowance of PHP 2,000. They have allocated 60% for food, 8% for fare, 15% for school needs, and 17% for savings.

For food, the allocation would be: PHP 2,000 x 60% = PHP 1,200.

For fare, the allocation would be: PHP 2,000 x 8% = PHP 160.

For school needs, the allocation would be: PHP 2,000 x 15% = PHP 300.

For savings, the allocation would be: PHP 2,000 x 17% = PHP 340.

So, for food, the allocation is PHP 1,200, for fare, it's PHP 160, for school needs, it's PHP 300, and for savings, it's PHP 340

Answer:

[tex]\mbox{\large \textsf{Timothy bought 14 books}}[/tex]

Step-by-step explanation:

Let's use first letters of names to represent the number of books bought by that person. This makes it easier to explain.

Therefore, the books bought by each of the three persons are T(imothy), L(aurence) and M(ike)

We will now convert each of the word description into math equations and solve

We are given that the ratio of the number of books bought by Laurence and Mike were 2: 7

We can write this as:
[tex]\dfrac{L}{M} = \dfrac{2}{7}\\\\[/tex]

Multiplying both sides by M:
[tex]L = \dfrac{2}{7}M\cdots\cdots(1)[/tex]  

Timothy and Laurence bought a total of 20 books can be represented as
[tex]T + L = 20\cdots\cdots(2)[/tex]

Timothy and Mike bought a total of 35 books can be represented as
[tex]T + M = 35\cdots\cdots(3)[/tex]

Eq (3) - Eq (2):

[tex]T + M - (T + L) = 35 - 20\\\\T + M - T - L = 15\\\\M - L = 15 \cdots\cdots (4)[/tex]

Substituting for [tex]\displaystyle L = \frac{2}{7}M[/tex]  from equation (1) into equation (4) we get

[tex]M - \dfrac{2}{7}M = 15\\\\\dfrac{5}{7}M = 15\\\\M = \dfrac{7}{5} \times 15\\\\M = 21\\\\[/tex]

Given [tex]\displaystyle M = 21[/tex] using equation (3), [tex]\displaystyle T + M = 35[/tex] we get

[tex]T + 21 = 35\\\\T = 35 - 21\\\\\textrm{or}\\\\T = 14[/tex](Answer)

If we wanted to find out how many books Laurence bought use Eq(1)
[tex]L = \dfrac{2}{7}M\\\\L = \dfrac{2}{7} \times 21\\\\L = 6\\\\[/tex]

From given quadratic equation:

Exact Cost of 31st food processor = $15.6

Approx. cost of 31st food processor  =  $15.2

What is a quadratic equation?

The polynomial equations of degree two in one variable of type f(x) = ax2 + bx + c = 0 and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f. (x).

It is given that the quadratic equation has two roots. Roots might have either a real or imaginary nature.

The given quadratic equation for the cost of producing x food processors is:

 C(x) = 2400 + 40x - 0.4x²

a) The exact cost of producing the 31st food PROCESSOR is:

cost of 31 food processors - cost of 30 food processors = C(31) - C(30)

= (2400 + 40*31 - 0.4*31²) - (2400 + 40*30 - 0.4*30²)

= 3255.6 - 3240 = $15.6

b) The marginal cost at x = 31

Differentiate the quadratic equation

C'(x) = 40 - 0.8x

Marginal cost = C'(31) = 40 - 0.8*31 = $15.2

So the cost of producing the 31st food processor is approx $15.2.

Therefore from the given quadratic equation:

Exact Cost of 31st food processor = $15.6

Approx. cost of 31st food processor  =  $15.2

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Answer:

16

Step-by-step explanation:

As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16

Answer:

46.21%

Step-by-step explanation:

The area of the table top is 1.3 x 1.3 = 1.69 m²

The area of the circular tablecloth is given by πr² where r is the radius of the table cloth

Give diameter of tablecloth is 2m, radius r = 2/2 = 1 m

Area of tablecloth = π · 1² = π

So the excess area of the tablecloth which overhangs

= π - 1.69 = 1.45 m²  (taking π = 3.14)

So the fraction of the tablecloth that overhangs
= Excess area of tablecloth ÷ total area of tablecloth
= 1.45 /π

= 0.4621

As a percentage this would be
0.4621 x 100

= 46.21%

The equation that represents the graph of a line passing through the points (0, -1) and (1, -4) is y = -3x - 1.

What is graph?

A graph is a visual representation of data or information that shows the relationship between different variables or quantities. Graphs can take many forms, including bar graphs, line graphs, scatterplots, and pie charts, among others. They are widely used in many fields, including mathematics, science, economics, and social sciences, to help visualize and analyze data, identify patterns, and communicate findings to others in a clear and concise manner. By representing complex information in a simple, easy-to-understand format, graphs can provide valuable insights and help us make informed decisions.

The equation that represents the graph of a line passing through the points (0,-1) and (1,-4) is:

y = -3x - 1

To find the equation of a line given two points, you can use the slope-intercept form:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the given points.

First, we can find the slope of the line:

m = (y2 - y1) / (x2 - x1)

= (-4 - (-1)) / (1 - 0)

= -3

Next, we can choose one of the given points and substitute its coordinates and the slope into the slope-intercept form:

y - (-1) = -3(x - 0)

y + 1 = -3x

y = -3x - 1

Therefore, the equation that represents the graph is y = -3x - 1.

Option A, y = -1/3x - 1, has a slope of -1/3, which is not the slope of the line passing through the given points.

Option C, y = -1/3x + 1/3, also has an incorrect slope of -1/3, and it also does not pass through the point (0,-1).

Option D, y = -3x + 1/3, has the correct slope of -3, but it does not pass through the point (0,-1).

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The sample distribution of (PM-PB) will not be normal, because w expect fewer than 10 electric cars in both samples.

There are two types of data sets are collected for the research. They are population and sample. Population includes all the elements from the data set. Sample is a part of population.

The company planned to take survey from the employees from both the main office and the branch office.

For this, the company took 100 employees from main office and 50 employees from a branch office.

We expect at least 10 successes and at least 10 failures in both samples, then the sampling distribution of [tex]p_{1 }and p_{2}[/tex] will be approximately normal.[tex]n_{1}p_{1}\ge 10 and n_1(1-p_1)\ge10[/tex]

[tex]n_{2}p_{2}\ge 10 and n_2(1-p_2)\ge10[/tex]

Let [tex]x_{1} and x_2[/tex] denotes the number of persons in the sample.

[tex]x_{1} =100\\n_{2} =50[/tex]

Also given 1.5% of employees at the main office have electric cars and 2% of employees at the branch office have electric cars.

so, [tex]p_{1}=0.015, p_{2}=0.02[/tex]

Combining this values we have,

[tex]n_1p_1=100(0.015)=1.5\le10[/tex] and

[tex]n_1(1-p_1)=100(1-0.015)=98.5 > 10[/tex]

Similarly, [tex]n_2p_2=50(0.02)=1\le10[/tex] and

[tex]n_2(1-p_1)=50(1-0.02)=49\ge10[/tex]

Hence, the sample distribution of PM-PB will not be normal, because w expect fewer than 10 electric cars in both samples.

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x^2 - 2x + 1 is the required quadratic equation using the completing the square

Given the quadratic expression below

x^2 - 2x

We need to determine the constant that will make the expression a perfect square.

The constant will be the half of the square of coefficient of 'x'

Coefficient of 'x' = -2

Half of the coefficient of 'x' = -2/2 = -1

Square of the coefficient = (-2/2)^2

Square of the coefficient = 1

Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1

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Answer:

f(-2) = 46

f(-1) = 17

f(0) = 2

f(1) = 1

f(2) = 14

Step-by-step explanation:

F(-2) = 46

F(-1)= 17

F(0)= 2

F(1)= 1

F(2)= 14

In the equation, the number 5,000 represents the initial value of the motorcycle. The value of the motorcycle is increasing at a rate of 3% per year.

Exponential functions are functions where the independent variable, x is in the exponent.

The given exponential equation is,

V = 5,000 (1.03)^t

Here V represents the value of the motorcycle in t years.

When t = 0,

V = 5000 (1.03)⁰ = 5000

So 5000 represents the initial value of the motorcycle.

V = 5,000 (1 + 0.03)^t

At t = 0, V = 5000

At t = 1, V = 5000 (1.03)¹ = 5150

At t = 2, V = 5000 (1.03)² = 5304.5

So the value of the motorcycle is increasing.

The rate is 0.03 or 3%.

Hence, 5,000 represents the initial value of the motorcycle and the value of the motorcycle is increasing at a rate of 3% per year.

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The true statements are

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

The sequence:

640, 160, 40, 10, ...

Because the current term is less than the previous term, then it represents a decay function

And also, the domain will be the set of natural numbers

This is so because the input values are 1, 2, 3 and so on

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Complete question

Which statements correctly describe how the graph of the geometric sequence below should appear?

640, 160, 40, 10, ...

Select two options.

The graph will show exponential growth.

The graph will appear linear.

The domain will be the set of natural numbers.

The range will be the set of natural numbers.

The graph will show exponential decay.

Answer:

C & D

Step-by-step explanation: