ken bought a bike that was priced at $450.He was offered a 25% discount what was the discount on the bike.

"79 % of all students at the local university voted in the last election" the numerical value describes a population parameter.

Population Parameter is a quantity/measurement that can be used as material for follow-up on population management activities.

 Population is a generalized area consisting of: objects/subjects that have certain qualities and characteristics determined by the researcher to be studied and then drawn conclusions.

The population or universe is the total number of units or individuals whose characteristics are to be studied. And these units are called units of analysis, and can be people, institutions, things, etc.

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we can conclude that the value of n for which [tex]t_n[/tex] = 0.3325 is between 3 and 4 and the value of n for which [tex]S_n[/tex]= -6 is 6.

A) To find the value of n for which [tex]t_n[/tex] = 0.3325, we can use trial and error method.

Starting with n=1, we have:

[tex]t_1 = (1^2 - 1)/(3 * 1^2) = 0[/tex]

For n=2, we have:

[tex]t_2 = (2^2 - 1)/(3 * 2^2) = (3)/(12) = 0.25[/tex]

For n=3, we have:

[tex]t_3 = (3^2 - 1)/(3 * 3^2) = (8)/(27) = 0.296296...[/tex]

Continuing in this way, we find that t_3 < 0.3325 < t_4, where

[tex]t_4 = (4^2 - 1)/(3 * 4^2) = (15)/(48) = 0.3125[/tex]

Thus, we can conclude that the value of n for which [tex]t_n[/tex] = 0.3325 is between 3 and 4, and it can be found more accurately by using numerical methods such as bisection or Newton's method.

B) To find the sum of the arithmetic series 16 + 13 + 10 + ..., we can use the formula for the sum of an arithmetic series:

[tex]S_n = n/2 * (a_1 + a_n),[/tex]

where n is the number of terms in the series, [tex]a_1[/tex] is the first term (16 in this case), and a_n is the nth term.

Let's assume that the nth term is represented by [tex]a_n = 16 - 3 * (n - 1),[/tex] so that a_1 = 16 and a_n = 16 - 3 * (n - 1).

Then, we have:

S_n = n/2 * (16 + 16 - 3 * (n - 1)) = n/2 * (16 + 16 - 3n + 3) = n/2 * (16 + 16 - 3n + 3) = n/2 * (32 - 3n + 3) = 16n - (3/2)n^2 + (3/2)n

We want to find the value of n for which S_n = -6, so we can substitute the value of S_n into the equation and solve for n:

[tex]S_n = n/2 * (16 + 16 - 3 * (n - 1)) = n/2 * (16 + 16 - 3n + 3) = n/2 * (16 + 16 - 3n + 3) = n/2 * (32 - 3n + 3) = 16n - (3/2)n^2 + (3/2)n[/tex]

[tex]-6 = 16n - (3/2)n^2 + (3/2)n[/tex]

Expanding the equation and solving for n, we find that n = 6.

Thus, the value of n for which [tex]S_n[/tex]= -6 is 6.

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The coordinates of the triangle when translated 2 units left are A'(-3, -1), B'(-3, -5) and C'(-1.5, -5).

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

The given triangle has the coordinates A(-1, -1), B(-1, -5) and C(0.5, -5).

Translation is done 2 units left.

A(-1, -1) becomes A(-1 - 2, -1) = (-3, -1)

B(-1, -5) becomes B(-1 - 2, -5) = (-3, -5)

C(0.5, -5) becomes C(0.5 - 2, -5) = (-1.5, -5)

Hence the coordinates are A'(-3, -1), B'(-3, -5) and C'(-1.5, -5).

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(a) The value of E(Y) will be = 0.8

(b)  The expected amount of the surcharge is $165.

(a) The expected value of Y is given by:

E(Y) = 0(0.5) + 1(0.25) + 2(0.2) + 3(0.05)

= 0.25 + 0.4 + 0.15

= 0.8

Therefore, the expected number of moving violations for which the individual was cited during the last 3 years is 0.8.

(b) The amount of the surcharge for an individual with Y violations is $110[tex]y^{2}[/tex]. The expected surcharge is given by:

E($110[tex]y^{2}[/tex]) = $110 * E([tex]y^{2}[/tex])

To calculate E([tex]y^{2}[/tex]), we use the formula:

E([tex]y^{2}[/tex]) = Σ [tex]y^{2}[/tex] p(y)

where the sum is taken over all possible values of Y.

E([tex]y^{2}[/tex]) = [tex]0^{2}[/tex](0.5) + [tex]1^{2}[/tex](0.25) + [tex]2^{2}[/tex](0.2) + [tex]3^{2}[/tex](0.05)

= 0 + 0.25 + 0.8 + 0.45

= 1.5

Therefore, the expected surcharge is:

E($110[tex]y^{2}[/tex]) = $110 * E([tex]y^{2}[/tex])

= $110 * 1.5

= $165

So, the expected amount of the surcharge for an individual with moving violations is $165.

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The equation of line in standard form is  y = -146x + 69.

A line equation is an algebraic way of representing a set of points that together form a line in a coordinate system. The various points that together form a line of axes can be represented as a set of (x,y) variables and form an algebraic equation, also called the line equation. You can use the straight line equation to determine if a given point lies on a straight line.

Each row of equations is a linear equation of degree 1. Read the entire article to learn about the different forms of linear equations and how to determine them. A line segment can be defined as a connection between two points. Any two points in a 2D geometry can be connected by a line segment or a simple straight line. The equation of a straight line can be obtained in three ways:

slope intercept method

point slope method

Standard method

Given two points lying on a given line, we usually follow the point-gradient method.

The equation for a straight line is y−y1=m(x−x1)

where y1 is the Y-axis coordinate, m is the tilt, x1 Coordinates on the x-axis.  m = y2-y1/x2-x1

eqn = y +4 = (-36/1/4)(x-1/2)

y +4 = -146x + 73

y = -146x + 69

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The total amount of cash collected is $10,418.6.

A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.

The amount of cash collected at the time of making a cash sale of $9,220 worth of merchandise subject to 13 % HST is,

Rate of interest on the sales amount is 13%

13% of 9220 = [tex]\frac{13}{100}*9220=1198.6[/tex]

Here, sales price = $9,220

The total amount of cash collected = 1198.6+9220

                                                          = 10,418.6

Hence, the total amount of cash collected is $10,418.6.

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Without knowing the specific ingredients and proportions used in a smoothie, it is impossible to definitively say whether any ingredients make up an equal amount. However, it is likely that the proportions of ingredients in a smoothie vary based on the desired taste, texture, and nutritional content.

For example, a smoothie may have more fruit than liquid to create a thicker consistency, or more liquid than fruit to create a thinner consistency. Additionally, the amount of sweeteners, such as sugar or honey, may vary based on personal preference and the natural sweetness of the fruit used.

In conclusion, without more specific information about the ingredients and proportions used in a particular smoothie, it is not possible to determine whether any ingredients make up an equal amount. The proportions of ingredients in a smoothie are likely to vary based on various factors and personal preference.

Answer:

1 - 3i, 4

Step-by-step explanation:

The polynomial has real coefficients, so if it has a complex root, it must have at least two complex roots which are complex conjugates.

Since 1 + 3i is a root, then 1 - 3i is also a root.

Two of the factors of the polynomial are:

x - (1 + 3i) and x - (1 - 3i)

Simplify the factors above:

x - 1 - 3i and x - 1 + 3i

Find their product:

(x - 1 - 3i)(x - 1 + 3i) =

Rewrite them showing we have the product of  a sum and a difference.

= [(x - 1) - 3i][(x - 1) + 3i]

Multiply the factors above noticing they are a sum and a difference which follows the pattern (a + b)(a - b) = a² - b².

= (x - 1)² - (3i)²

= x² - 2x + 1 - 9(-1)

= x² - 2x + 10

Now we divide the original polynomial by the product we just found using long division.

                                        x - 4

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

         x² - 2x + 10      |    x³ - 6x² + 18x - 40

                                  -   x³ - 2x² + 10x

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

                                            -4x² + 8x - 40

                                      -     -4x² + 8x - 40

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

                                                0 +    0  + 0

Now we know that x³ - 6x² + 18x - 40 factors into (x² - 2x + 10)(x - 4).

(x² - 2x + 10)(x - 4) = 0

From x² - 2x + 10, we have roots x = 1 + 3i and x = 1 - 3i.

x - 4 = 0

x = 4

From x - 4, we have root x = 4.

Answer: 1 - 3i, 4

By using fundamental theorem of calculus  The exact value of the definite integral [tex]\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx[/tex] is 6(√(π) - 1).

First, we can find an antiderivative of the integrand by using the power rule and the constant multiple rule of integration:

∫(3x^(-1/2)) dx = 3 ∫(x^(-1/2)) dx = 3 (2x^(1/2)) + C = 6√(x) + C

where C is the constant of integration.

Now, we can use the fundamental theorem of calculus to evaluate the definite integral \int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx. The theorem states that if f(x) is continuous on the interval [a, b] and F(x) is an antiderivative of f(x), then

∫[a, b] f(x) dx = F(b) - F(a)

In this case, f(x) = 3x^(-1/2) and F(x) = 6√(x) + C. Therefore,

∫{1}^{π} (3x^(-1/2)) dx = F(π) - F(1) = 6√(π) + C - 6√(1) - C = 6√(π) - 6√(1) = 6(√(π) - 1)

So the exact value of the definite integral [tex]\int {1}^{\pi}\left(3x^{-1} \sqrt{x}\right)\ dx[/tex] is 6(√(π) - 1).

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Answer:

120

Step-by-step explanation:

18 = .15x  Divide both sides by .15 (15% as a decimal is .15)

[tex]\frac{18}{.15}[/tex] = [tex]\frac{.15x}{.15\\}[/tex]

120 = x

Answer:

13.3 miles

Step-by-step explanation:

Picture a right triangle with legs of 3 and 13.  The hypotenuse is the straight line distance back to the starting point.  Use the Pythagorean theorem to find the hypotenuse (c):

c² = 13² + 3² = 178

c = √178 = 13.3 miles

If the chute does not open until 1 min after he leaves the helicopter, then the equation to calculate the seconds it will he hit the ground is (1/2)mv² + ∫ F(v) dv = 0

The force due to air resistance is assumed to be proportional to the velocity of the parachutist, and we will use this information to determine the time it takes for the parachutist to reach the ground with and without a chute.

The force of air resistance is proportional to the velocity of the parachutist. This means that the larger the velocity, the larger the force of air resistance.

As the velocity increases, the force of air resistance also increases, which reduces the kinetic energy. When the chute opens, the force of air resistance increases even more, which further reduces the kinetic energy and slows down the parachutist.

To determine the time it takes for the parachutist to hit the ground, we can use the following equation:

PE + KE + work done by air resistance = PE + KE

where PE is the gravitational potential energy, KE is the kinetic energy, and work done by air resistance is the work done by the force of air resistance.

When the chute is closed, we can write:

mgh = (1/2)mv² + ∫ F(v) dv

where m is the mass of the parachutist, g is the acceleration due to gravity, h is the height of the helicopter above the ground, and the integral is taken over the velocity range from 0 to v.

Similarly, when the chute is open, we can write:

mgh = (1/2)mv² + ∫ F(v) dv

where b = b4 and the integral is taken over the velocity range from 0 to v.

To solve for the time it takes for the parachutist to hit the ground, we need to determine the velocity at which he hits the ground. This is the velocity where KE = 0, and we can find it by equating the expressions for KE and work done by air resistance when the parachutist hits the ground:

(1/2)mv² + ∫ F(v) dv = 0

We can solve these equations numerically to find the time it takes for the parachutist to hit the ground with and without the chute.

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Answer:

z = 50°

Step-by-step explanation:

We know that,

→ Sum of all sides of triangle is 180°.

Formula we use,

→ <A + <B + <C = 180°

Forming the equation,

→ 60° + 70° + z = 180°

Now the value of z will be,

→ 60° + 70° + z = 180°

→ 130° + z = 180°

→ z = 180° - 130°

→ [ z = 50° ]

Hence, the value of z is 50°.

Answer:

The function g(x) is the derivative of the function sin(x). So, g(x) = cos(x).

Therefore, the instantaneous rate of change of g with respect to x at x = π/3 is cos(π/3), which is approximately equal to 0.5.

Step-by-step explanation:

np and pls mark brainlist:)

a) The factors that impact a person's credit score and history include:

b) To raise or improve a credit score and history, you must undertake the following actions:

A credit score is a numerical rating or expression of an individual's credit history to determine their creditworthiness.

Credit scores are presented on credit reports, which are regularly prepared by credit bureaus.

On the other hand, a credit history is an official record of an individual's credit management.

Thus, one must understand the credit history and meet payment obligations to improve a person's credit score.

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The rod's linear density at 1 metre from the left end and a point x meters to the right is 8 x 3 kg is = 8(1)2 = 8 kg/m.

We can start by using the definition of linear density, which is the mass per unit length of a rod or wire. Let's assume that the linear density of the rod at a distance of 1 meter from the left end is ρ kg/m.

Then, the mass of the part of the rod that lies between 0 meters and 1 meter to the right is:

m1 = ρ * 1 kg

Similarly, the mass of the part of the rod that lies between 0 meters and x meters to the right is:

m2 = 8x^3 kg

The mass of the part of the rod that lies between 1 meter and x meters to the right is:

m2 - m1 = (8x^3 - ρ) kg

Since we know that this mass is equal to ρ times the length of the rod segment, which is (x-1) meters, we can write:

ρ * (x-1) = 8x^3 - ρ

By condensing this solution, we obtain:

ρ * (x-1+1) = 8x^3

ρ * x = 8x^3

ρ = 8x^2 kg/m

As a result, the rod's linear density at 1 metre from the left end is = 8(1)2 = 8 kg/m.

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Answer:

4 to the 4th power is 256

Explanation:

4 to the 4th power is a mathematical expression indicating that the number 4 is multiplied by itself four times. Mathematically, it is represented as 4^4.

To calculate 4^4, you would multiply 4 by itself four times: 4 x 4 x 4 x 4.

The result of this multiplication is 256, which means that 4 to the 4th power is equal to 256.

The number 4 to the 4th power is equal to 256.

When you raise a number to a power, it means multiplying that number by itself the specified number of times.

In the case of 4⁴, you are multiplying 4 by itself four times:

4⁴ = 4 × 4 × 4 × 4

When you perform the multiplication, you get:

4 × 4 = 16

16 × 4 = 64

64 × 4 = 256

Therefore, 4 to the 4th power is equal to 256.

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The volume of the parallelepiped is 190.

The volume V of a parallelepiped with adjacent edges pq, pr, and ps can be found using the scalar triple product as:

V = |pq · (pr x ps)|

where · denotes the dot product and x denotes the cross product.

pq = q - p = (-1-3, 2-0, 5-1) = (-4, 2, 4)

pr = r - p = (5-3, 1-0, -1-1) = (2, 1, -2)

ps = s - p = (0-3, 4-0, 2-1) = (-3, 4, 1)

pr x ps = det([i, j, k; 2, 1, -2; -3, 4, 1]) = i(-4) - j(7) + k(10) = (-4, -7, 10)

V = |(-4, 2, 4) · (-4, -7, 10)| = 190

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Company A will charge $7 more than company B.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.

Given that a family wants to rent a car to go on vacation. Company A charges ​$55.50 and 16 cents per mile. Company B charges ​$50.50 and 9 cents per mile.

The expression for the charges by company A is,

C = 16x + 55.50

The expression for the charges by company B,

C = 9x + 55.50

The amount of company A more than company B is calculated as:-

Amount = ( 16 + 55.50) - ( 9 + 55.50 )

Amount = 71.50 - 64.50

Amount = $7

Hence, company A will charge $7 more.

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Answer:

= 11x + 20.

Step-by-step explanation:

2x + x + x+2x+3x+30+(2x-10)

= 2x+x+x+2x+3x+30+2x-10

=2x + x + x + 2x + 3x + 2x + 30 - 10

=11x + 20.

If y+3=-4/3(x-1) and y=-4/3x-1 are two lines then these are parallel.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The two equations are

y+3=-4/3(x-1)

y=-4/3x-1

When we compare both the equations to slope intercept form.

we get slope -4/3 for both the equations.

If the lines have same slope then the lines are parallel.

Hence, the two lines are parallel lines.

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The cost for each person is $12.

So, each person paid $12 for a movie ticket.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

The cost of going to the movie theater for Elissa and 11 of her friends is $144.

The total cost is divided equally among each person.

The number of total people is 12.

So, the cost of each person,

= total cost/ the number of total people

= 144/12

= 12

Therefore, 12 is the required value.

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∫1.5 T(h) dh = 9.573, rounded to three decimal places. (a) To evaluate ∫1.5 T(h) dh, we need to integrate T(h) with respect to h from 0 to 1.5: ∫1.5 T(h) dh = ∫0.1.5 (9.43h^3 - 15.41h^2 + 17.34h - 9.83) dh

Using the power rule of integration, we can integrate each term of the polynomial: ∫0.1.5 (9.43h^3 - 15.41h^2 + 17.34h - 9.83) dh

= (9.43/4)h^4 - (15.41/3)h^3 + (17.34/2)h^2 - 9.83h |0.1.5

= [(9.43/4)(1.5)^4 - (15.41/3)(1.5)^3 + (17.34/2)(1.5)^2 - 9.83(1.5)] - [(9.43/4)(0)^4 - (15.41/3)(0)^3 + (17.34/2)(0)^2 - 9.83(0)] = 9.573

Therefore, ∫1.5 T(h) dh = 9.573, rounded to three decimal places.

(b) The answer to part (a) represents the total change in temperature during the hour and a half after the beginning of the thunderstorm. This means that the temperature increased by an average of 9.573 degrees per hour during this time period.

This integral gives us a measure of the total effect of the thunderstorm on the temperature, which is useful for predicting the weather and understanding the behavior of natural phenomena.

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Answer:

Jakaur7889 on inta

Step-by-step explanation:

Babahaja

The fourth number ​is equal to -6.

Mathematically, the arithmetic average for a given data set can be calculated by using this formula:

Average = [F(x)]/n

Next, we would calculate the arithmetic average for the four numbers (data set) as follows:

Let the fourth number be represented by the variable n.

Total numbers = 17 + 13 + 16 + n

Total numbers = 46 + n

10 = 46 + n/4

40 = 46 + n

n = 40 - 46

n = -6

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u is the slope of the line passing through the points (1, -3) and (1, 0).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope of the line passing through the points (1, -3) and (1, 0)

m=0-(-3)/1-1

=3/0

Undefined

Hence, the slope of the line passing through the points (1, -3) and (1, 0) is u.

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The volume of the parallelepiped formed by the adjacent edges u=i+j, v=j+k, and w=i+k is: 1.

The triple scalar product can be used to find the volume of the parallelepiped formed by three non-coplanar vectors u, v, and w. The triple scalar product is defined as:

where × represents the cross product and · represents the dot product.

Given that u=i+j, v=j+k, and w=i+k, we can first find the cross product of v and w as:

= i x (j+k) + k x (j+k)

= i x j + i x k + k x j + k x k

= -k + i -j

Next, we can find the dot product of u with the cross product of v and w as:

= i · (-k) + i · i + i · (-j) + j · (-k) + j · i + j · (-j)

= -ik + i^2 - ij - jk + ji - j^2

= i^2 - j^2 - k(i+j)

= 1 - 0 - (1+0)

= -1

The absolute value of this result gives the volume of the parallelepiped, so the volume is:

Therefore, the volume of the parallelepiped formed by the adjacent edges u=i+j, v=j+k, and w=i+k is 1.

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Answer:

Robin.

Step-by-step explanation:

Clinton scored 24% of his attempts which means 24/100.

Then Katniss scored 6/25 of his attempts which means 24/100.

After that Robin scored 0.26 of his attempts which means 26/100.

Finally William scored 1/5 of his attempts which means 20/100.

Therefore, Robin has the highest score and wins the competition.

The difference of  8/3x+5 -2x/3x+5 is (8 - 2x) / (3x+ 5).

The correct option is (A).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

We have the Expression as:

8/3x+5 -2x/3x+5

Now, Simplifying the expression as:

=  8/3x+5 -2x/3x+5

= (8 - 2x) / (3x+ 5)

= 8/(3x+ 5) - 2x/ (3x+ 5)

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