b) p is directly proportional to the square of q. p is 3825 when q is 15. Work out p when q is 20.​

Answer:

f(y - 3) = y - 2

Step-by-step explanation:

to find f(y - 3) , substitute x = y - 3 into f(x) , that is

f(y - 3) = y - 3 + 1 = y - 2

To use substitution to determine which value of x makes the inequality true, we need to have an inequality with x as one of the variables. Without more information on the inequality, it is not possible to determine which value of x makes the inequality true. The set {10, 18, 21} does not contain any variable x.

By using trigonometric relations, we can see that the angle x on the right triangle is:

x = 62.96°

On the image, we can see a right triangle, and we want to find the value of x, which is the measure of an angle on the right triangle.

On the given triangle we can see that the hypotenuse measures 77 units, and the adjacent cathetus to the angle has a measure of 35.

Then we can use the trigonometric relation:

cos(x) = (adjacent cathetus)/(hypotenuse)

Replacing the values that we know:

cos(x) = 35/77

Now we can apply the inverse cosine function in both sides:

Acos(cos(x)) = Acos(35/77)

x = Acos(35/77) = 62.96°

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Answer:

Sin A / A = Sin B / B         Law of Sines

Sin 73 / X = Sin 59 / 18     Application of Law of Sines

X = Sin 73 / Sin 59 * 18 = .956 / .857 * 18 = 20.1

A quadratic equation has two roots.

A function can have two roots. A root of a function is a point at which the function's value is equal to zero. This means that the function crosses the x-axis, and two roots means that it crosses the x-axis twice. Depending on the type of function, these two points can be either real or complex numbers. For example, the quadratic equation x2-3x+2 has two real roots, namely x = 1 and x = 2.A quadratic polynomial may have one, two, or zero roots. Quadratic polynomials have a degree of two.

Let's consider a quadratic polynomial

[tex]ax^2+bx+c=0[/tex]

where [tex]a\neq 0[/tex]

The quadratic polynomial is of degree two. Therefore, a quadratic equation has no more than two roots.

There is a formula to find the roots of quadratic polynomials, which is called the quadratic formula.

[tex]x=\frac{-b\frac{+}{-}\sqrt{b^2-4ac} }{2a}[/tex]

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Simplest radical form means the radical form of a number or algebraic expression in simplest terms.

The simplest radical form of the square root of 16 is √16. Generally, the radical form of the square root of a number can be written, if we know the prime factorization of a number. Thus, the prime factorization of 16 is 2×2×2×2.

Square root of 16 is +4 or -4. Since -4 is not a natural number, the square root can be described as an integer.

16 (sixteen) is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4.

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The age of my sister and her three children in 4 years will be 70 years

The age is added in 6 years to get 90 years> the addition is done as follows

Sister + 6 + Child1 + 6 + Child2 + 6 + Child3 + 6 + Child4 + 6 = 90 years

Sister + Child1 + Child2 + Child3 + Child4 + 6 + 6 + 6 + 6 + 6 = 90

Sister + Child1 + Child2 + Child3 + Child4 + 6 * 5 = 90

Sister + Child1 + Child2 + Child3 + Child4 = 90 - 30

Sister + Child1 + Child2 + Child3 + Child4 = 60

In 4 years the age will be

Sister + Child1 + Child2 + Child3 + Child4 + 4 * 5 = 90

Sister + Child1 + Child2 + Child3 + Child4 = 90 - 20

Sister + Child1 + Child2 + Child3 + Child4 = 70

in 4 years the ages will be 70 years

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[tex] \sf \frac{2x}{5} = 4 \\ \sf \: 2x = 4 \times 5 \\ \sf \: 2x = 20 \\ \sf \therefore \: x = 10[/tex]

Answer: X stands for 10

Step-by-step explanation:

If we subsitute X for 10, and convert 2/5 to 0.4 we get, 10x0.4 = 4

To convert a fraction to a decimal, you simply divide the numerator by the denominator.

Calculate the length of the longest side of the triangle use following methods :

Pythagoras theorem : (hypotenuse)² = (Base)² + (altitude)²

Sine rule : AB/sin C = AC / sin B = BC / sin A.

As given in the question,

To find the length of the longest side of a triangle use following methods:

a. Triangle is right angle triangle.

In the right angle triangle ,

Hypotenuse is the longest side.

To find the length of the hypotenuse use Pythagoras theorem:

(Hypotenuse)² = (Base)² + (Altitude)²

b. Triangle is not right angle triangle.

Use sine rule:

AB be the longest side in triangle ABC.

Side opposite to ∠A , ∠B , ∠C in ΔABC are BC, AC,AB respectively.

If measure of angles and other sides are given apply sine rule:

 AB/sin C = AC / sin B = BC / sin A.

Therefore, the measure of the longest side of the triangle is calculated by :

Pythagoras theorem : (hypotenuse)² = (Base)² + (altitude)²

Sine rule : AB/sin C = AC / sin B = BC / sin A.

The above question is incomplete , the complete question is :

How do you find the long side of the triangle?

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Points P and Q are 3/8 unit away from 0, and because absolute values cannot be zero, the absolute values are the same. Tim is the correct one here, and the correct argument is the second answer option.

Absolute values are numbers that are either zero or positive. They can never be negative, since it is the very definition of absolute values. If a given number is negative, then you only need to change the sign to positive so that you get the absolute value of the number. For example, the absolute value of - 0.001 is 0.001.

Points P and Q are equally 3/8 unit away from 0, but P is negative and Q is positive. The distance of both are not 3/8 unit but twice as that. Even though - 3/8 and 3/8 are not the same because of the different signs, they have the same absolute value, which is 3/8. Therefore, Tim is the correct one.

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b. Total Sample = 300 college students

The question is asking how many people were in the sample of 300 college students that were asked if they were interested in playing video games. The answer is option B: 300.

To answer this question, we must first understand the context of the question. It is asking about the number of English-speaking people on the planet who want to play a new kind of online video game. To answer this, 300 college students were asked if they were interested in playing video games. Of those 300 students, 100 said yes, and 20 of those students preferred this new game to an existing game that is widely used. Therefore, the sample size was 300.

The sample size is 300 college students. From the 300 college students, 100 said yes to playing video games. Of these 100, 20 preferred the new game to an existing game. Therefore, the sample size is 300 college students.

Total Sample = 300

No. of Yes = 100

No. of Prefers new game = 20

So, Total Sample = 300 college students

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Answer:

tenth

Step-by-step explanation:

Note that after the expression 2x³-5x²-19x+42, has been factorized, we have (x−2)(x+3)(2x−7).

Factorization or factoring in mathematics is the process of expressing a number or any mathematical object as a product of numerous factors, generally smaller or simpler objects of the same sort.

The polynomial 2x³-5x²-19x+42 can be factorized by using the rational root test. To apply this test first we need to find at least one rational zero.

In this case one rational zero is x=2.

This means that we can divide polynomial 2x³-5x²-19x+42 by x−2 (the factor theorem)

That is:

2x³-5x²-19x+42/ x-2

= 2x² - x - 21, this means that

2x³-5x²-19x+42 =  (2x² - x - 21) * (x-2)

From the above, our constants are given as:

a = 2, b = -1 and c = 21

Multiply the constant terms by the leading coefficient.

a *x = -42

Find out two number that multiply to a*c = -42 and add b = -1

Next we identify all pairs of numbers with a product of -42. They are:

Next we find all factor pair that sum up to b = -1. It is given as 6 +-7 which is identical to item 8 above.

Next, replace the middle term -1x with 6x-7x to get:

(2x²  −x−21) * (x-2) =(2x²  +6x−7x−21) * (x-2)

If we thus apply factoring by grouping, and factor 2x out of the first group and -7 out of the second group, we have: (2x-7) (x+3) (x-2).

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Full Question:

Factorise 2x³-5x²-19x+42

The rate of change of the angle of elevation is -2π/3 radians/second.

We can use the tangent ratio to solve this problem. Since the rope is attached to the boat, we can draw a right triangle with the rope as the hypotenuse. The angle of elevation is the angle formed by the rope and the horizon.

The pulley is 5 feet above the water level, so the length of the opposite side (the side adjacent to the angle) is 5 feet. The length of the hypotenuse is 12 feet, since the boat is 12 feet from the dock.

Using the tangent ratio, we can calculate the angle of elevation:

tan(θ) = opp/hyp = 5/12

θ = arctan(5/12) = 0.927 rad

Now, since the rope is being pulled in at 3 ft/sec, the length of the hypotenuse is decreasing at a rate of 3 ft/sec. Therefore, the rate of change of the angle of elevation is:

rate of change of θ = -(3 ft/sec) / (12 ft) = -2π/3 radians/second

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Answer:

b. |−37| + |−28|

Step-by-step explanation:

The absolute value of a number is its distance from 0 on the number line. Since the divers are below sea level, both 37 and 28 will be negative numbers.

To find the distance between the two divers, we need to add the absolute values of their depths.

The first diver is at -37 ft and the second diver is at -28 ft, so we can calculate the distance between them as |-37| + |-28| = 37 + 28 = 65 ft

By using the properties of real numbers the given expression can be written as  -8y.

What is solving an expression?

Another word for "solving a math problem" is "simplifying an expression." When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.

Given:

The given expression is, [tex]\frac{4}{3}(-6y)[/tex]

According to the distributive property of real numbers, if a, b, c are three real numbers the,

a(bc) = (ab)c

Using the associative property of multiplication, the given expression can be written as,

[tex]\frac{4}{3}(-6y) = (\frac{4}{3}*(-6))*y \\\frac{4}{3}(-6y) = (\frac{-24}{3} )*y\\\frac{4}{3}(-6y) = -8y[/tex]

Hence, by using the properties of real numbers the given expression can be written as  -8y.

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Answer:

Step-by-step explanation:

x=#of minutes

y= cost

Laceys equation: y=3x+398

Sebastions equation: y=x+466              

intersection (34, 500)

itll take 34 minutes and cost $500

Answer: We can find the inequalities. One inequality has a line with y-intercept 2 and slope -1. The inequality is y >= -x + 2.

Step-by-step explanation:

a) The velocity and position functions are given as follows:

b) The particle is at rest when: t = kπ, k = ± 1, ± 2, ± 3, ...

The acceleration function for this problem is defined as follows:

a(t) = cos(t).

The velocity function is the integral of the acceleration function, hence it is given as follows:

v(t) = sin(t).

(as the integral of cos(t) is sin(t).)

The particle will be at rest when:

v(t) = 0.

Hence:

sin(t) = 0

t = arcsin(0)

t = kπ, k = ± 1, ± 2, ± 3, ...

The position function is the integral of the velocity function, hence it is given as follows:

s(t) = -cos(t) + 3.

As:

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Answer:

Step-by-step explanation:

The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the polynomial is 4w - 1. The highest power of the variable w is 1, so the degree of the polynomial is 1.Therefore, the correct answer is A) 1

Answer:

Here are the answers in fraction form.

[tex]x > \frac{1.7}{0.7}[/tex]

[tex]x < - \frac{11.7}{0.7}[/tex]

Here are the answers in decimal form.

[tex]x > 2.43[/tex]

[tex]x < -16.71[/tex]

Step-by-step explanation:

We will have 2 answers.

Answer 1

[tex]0.7x+5 > 6.7[/tex]

Move all terms not containing [tex]x[/tex] to the right side of the inequality.

[tex]0.7x > 6.7-5\\0.7x > 1.7[/tex]

Divide both sides by [tex]0.7[/tex].

[tex]\frac{0.7x}{0.7} > \frac{1.7}{0.7}\\[/tex]

[tex]x > \frac{1.7}{0.7}[/tex]

[tex]x > 2.43[/tex]

Answer 2

[tex]-0.7x-5 > 6.7[/tex]

Move all terms not containing [tex]x[/tex] to the right side of the inequality.

[tex]-0.7x > 6.7+5\\-0.7x > 11.7[/tex]

Divide both sides by [tex]-0.7[/tex].

When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

[tex]\frac{-0.7x}{-0.7} < \frac{11.7}{-0.7}[/tex]

[tex]x < \frac{11.7}{-0.7}[/tex]

[tex]x < -16.71[/tex]

The surface area of the hemispherical vessel is 715.92 square centimeter and the cost to paint is Rs. 3579.62.

An object's surface area is the total area that all of its surfaces occupy. Different 3D shapes in geometry have various surface areas. There are two groups for the surface area:

Surface area of the lateral Surface that is curved Surface area overall.

Given that the external diameter of the hemispherical vessel is 16cm, hence the radius is 8cm.

The internal diameter of the hemispherical vessel is 12cm, hence the radius is 6cm.

The total surface area of the vessel is given by the following formula:

[tex]SA= 2\pi R^2 + 2\pi r^2 + \pi (R^2 - r^2)\\\\SA= 2(3.14)(8)^2 + 2(3.14)(6)^2 + (3.14)(8^2 - 6^2)\\\\SA= 401.92 + 226.08 + 87.92\\\\SA= 715.92[/tex]

The total surface area of the vessel is 715.92 square centimeters.

The cost to paint 1 square centimeter is Rs. 5, hence the cost to paint 715.92 square centimeters is:

C = (715.92)(5)

C = 3579.6

Hence, the cost to paint 715.92 square centimeters is Rs. 3579.62.

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The weighted average of the numbers −1 and 1 is 0.3. Hence option A is the correct option.

What is the weighted average?

A weighted mean is similar to an average. Rather than contributing equally to the final mean, some data points contribute more "weight" than others. If all of the weights are equal, the weighted mean equals the arithmetic mean (the familiar "average").

Given numbers are  -1 and 1.

The first number is -1 and the second number is 1.

Two third of the first number is

= -1 × (2/3)

= -2/3

The one third of second number is

= 1 × (1/3)

= 1/3

The average weight is the sum of two third of the first number and one-third of the second number is -2/3 + 1/3 = -1/3 = -0.33.

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The sample correlation coefficient, is represented as  r, measures the strength of correlation  and direction of the linear relationship between two variables. It ranges from -1 to 1. The closer the coefficient is to -1, the stronger the negative correlation, the closer it is to 1, the stronger makes the  positive correlation reach towards its closer and the closer towards to the expectancy to 0, the weaker the correlation.

The correlation coefficient does not indicate the cause and effect relationship between the variables, just the association between them.

A positive correlation tells us  that as one variable increases with respective its the other variable also increases, and a negative correlation means that as one variable increases with respective to its the other variable decreases.

So, the value of the sample correlation coefficient between the  rates of admit and the -yr grad rate . rate can indicate if these variables are positively or negatively done as  correlated and how strong is this correlation occurs.

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The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

Given that,

Mean = 195

Standard deviation = 14

Thus, the probability between 183 and 218 is the ρ value of z when x = 195

Subtracting by the ρ value of z when x = 183

so, x = 218

z = 218-195/14 = 1.64

when x = 183

z = 183-195/14= -0.85

Thus, z value is 1.64 then the probability is 0.94950 and when z value is -0.85 then the probability is 0.21886

Now, 0.94950 - 0.21886 = 0.73064

Therefore, The probability that in the next game of serenity bowls, her score will be between 183 and 218 is 73.14%

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The true statement is:

The asymptote of g(x) is the asymptote of f(x) shifted three units down.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = [tex](2/5)^x[/tex]

and, g(x) ==  [tex](2/5)^x[/tex] - 3

Now, Using translation the '-3' in g(x) shows the Vertical Translation down by 3 units.

Hence, The asymptote of g(x) is the asymptote of f(x) shifted three units down.

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The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

An official list of the players who will take part in the event when the game starts is known as a starting lineup in sports. The players who are in the starting lineup are frequently referred to as starters, while the rest are known as bench players or replacements.

Case 1: Bob starts (and Yogi doesn't). In this case, the coach must choose 4 more players from the 10 remaining players (remember that Yogi won't play, so there are only 10 players left to select from). Thus there are 10C4 lineups that the coach can choose.

⇒ ¹⁰C₄ = 10!/4!(10-4)! = 10!/4!6!

⇒ ¹⁰C₄ = (10*8*9*7)/(4*3*2*1)

⇒ ¹⁰C₄ = 210

Case 2: Yogi starts (and Bob doesn't). As in Case 1, the coach must choose 4 more players from the 10 remaining players. So there are 10C4 lineups in this case.

⇒ ¹⁰C₄ = 210

Case 3: Neither Bob nor Yogi starts. In this case, the coach must choose all 5 players in the lineup from the 10 remaining players. Hence there are 10C5 lineups in this case.

⇒ ¹⁰C₅ = 10!/5!(10-5)! = 10!/5!5!

⇒ ¹⁰C₅ = (10*8*9*7*6)/(5*4*3*2*1)

⇒ ¹⁰C₅ = 252

To get the total number of starting lineups, we add the number of lineups in each of the cases:

Case 1 + Case 2 + Case 3

= 210 + 210 + 252 = 672

The total number of starting lineups (of 5 players) can coach yells lot make, if the starting lineup can't contain both bob and yogi is 672.

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The quadratic equation written in the vertex form is:

y = 2*(x - 3)^2 - 1

We know that for a leading coefficient a, and a vertex (h, k), we can write the quadratic equation as:

f(x) = a*(x - h)^2 + k

Here we know that the leading coefficient is 2, and the vertex of our quadratic equation is (3, -1)

Then the values that we have are:

a = 2

h = 3

k = -1

Then we can write the quadratic equation in the vertex form as:

y = 2*(x - 3)^2 - 1

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Answer: the answer is negative  5

Step-by-step explanation: