Expand: f(x) = x4 − x3 + x2 + x −

Divide any number by 9. Then then ur answer times 1 then times 8.

Example 9:9=1 1 and 8

36:9=4. 4 and 32

This problem is about the rule of three.

The given ratio is 20 minutes for 3 tasks done. We need to find the number of taks done after 8 hours.

First, we know that 1 hour is 60 minutes, so the total number of minutes is

Now, the rule of three is about the total number of tasks done after 480 minutes, if three tasks take 20 minutes only.

The equation could be described by "the product of three and the reciprocal of four divided by three"

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

To solve this problem we must perform the corresponding algebraic operations with mixed fraction.

Original equation:

4 / (1 1/3)

A mixed operation is solved as follows:

For the denominator: the same denominator is placed.

For the numerator:

We transform the mixed fraction into improper fraction and we have:

1 1/3 = [(3*1) + 1)] /3  = [3+ 1] /3 = 4/3

Now, describing the equation with the improper fraction we get:

4 / (4/3)

Solving the division with fractions we have:

(4*3) / 4

This means that "the product of three and the reciprocal of four divided by three"

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Answer(s):

3. Option B

4. Option D

Step-by-step explanation:

Question 3:

Question 4:

Answer:

y=2/3x-7

Step-by-step explanation:

For lines to be parallel, they must have the same slope which is 2/3. However, they can't have the same y-intercept.

By using compatible numbers, the estimate is 900

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

92 x 12

From the question, we are to make use of compatible numbers

This means that we have the following approximation

92 = 90

12 = 10

Next, we estimate the product using approximated values

i.e.

Product = Approximation of 92 x Approximation of 12

Substitute the known values in the above equation, so, we have the following representation

Product = 90 x 10

Evaluate the products

Product = 900

Using a calculator, we have

Product = 92 * 12

Evaluate the products

Product = 1104

900 is less than 1104

Hence, the estimate is less than the actual product

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Answer:

$4.16

Step-by-step explanation:

To find out how much 8 ounces of frozen yogurt costs if each ounce costs $0.52, we can use an equation that looks like this:

Therefore, for 8 ounces of yogurt is will cost $4.16.

The distance between two cities is

75

k

m

s

.

Explanation:

As a road of

4

c

m

.

on road map indicates a road of length equal to

30

k

m

.

Each

c

m

.

on map indicates

30

4

=

7.5

k

m

s

.

Hence a distance of

10

c

m

.

between two cities on the map indicates

7.5

×

10

=

75

k

m

s

Answer:

The formula you are referring to is the quadratic formula, which is used to solve quadratic equations of the form ax^2 + bx + c = 0. The formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a, b, and c are coefficients of the quadratic equation.

The length of this cable to the nearest tenth of a block will be 6.3 blocks. Then the correct option is C.

Let one point be (x, y) and another point be (h, k). Then the distance between the points will be

D² = (x - h)² + (y - k)²

A map of a small town identifies the town square as the origin (0,0). Each block along a street is represented by one unit along the x- or y-axis. The ice cream shop is at (5. 4) and the grocery store is at (3.-2).

To speed up deliveries, the grocer plans to set up an overhead delivery wire that runs directly between the grocery store and the ice cream parlor.

The length of this cable to the nearest tenth of a block will be

D² = (5 - 3)² + (4 + 2)²

D² = 2² + 6²

D² = 4 + 36

D² = 40

D = 6.3 blocks

The length of this cable to the nearest tenth of a block will be 6.3 blocks. Then the correct option is C.

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The answer of the given question based on right angle triangle is

∠H = 53.13° , and ∠J ≈ 66.42°.

Trigonometric ratios are ratios of  lengths of sides of right triangle. They are used to relate the angles of the triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent, often abbreviated as sin, cos, and tan, respectively.

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse, the cosine of an angle is ratio of the length of adjacent side to length of the hypotenuse, and tangent of an angle is ratio of the length of opposite side to the length of adjacent side.

To find ∠H and ∠J, we can use the trigonometric ratios sine, cosine, and tangent.

Let's start with ∠H:

sin(∠H) = opposite/hypotenuse = IH/HJ = 12/13

∠H = sin⁻¹(12/13) ≈ 53.13°

Now let's find ∠J:

cos(∠J) = adjacent/hypotenuse = IJ/HJ = 5/13

∠J = cos⁻¹(5/13) ≈ 66.42°

Therefore, ∠H ≈ 53.13° and ∠J ≈ 66.42°.

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Answer:

\(-\frac{5}{2}\)

Step-by-step explanation:

Step 1: Put this into an equation

\(-\frac{5}{3} - x = \frac{5}{6}\)

Step 2: Solve for x

\(-x = \frac{5}{6} + \frac{5}{3}\)

\(-x = \frac{5}{2}\)

\(x =- \frac{5}{2}\)

Therefore you need to subtract \(-\frac{5}{2}\) from \(-\frac{5}{3}\) to get \(\frac{5}{6}\)

Answer:i don’t know

Step-by-step explanation:I’m sorry dude I have no idea I tried doing it in the browser and I could not find an answer sorry

Step-by-step explanation:

It is given that,

The height of the sail on a boat is 7 feet less than 3 times the length of its base.

Let the length of the base is x.

ATQ,

Height = (3x-7)

Area of the sail is 68 square feet.

Formula for area is given by :

\(A=lb\\\\68=x(3x-7)\\\\3x^2-7x=68\\\\3x^2-7x-68=0\)

x = 8 feet and x = -3.73 feet

So, length is 8 feet

Height is 3(8)-7 = 17 feet.

So, its height and the length of the base is 17 feet and 8 feet respectively.

To find the unit tangent vector T(t) and the principal unit normal vector N(t) at each point on the graph of the vector function R(t) = (3sin(t), 4t, 3cos(t)), we need to calculate the first derivative vector R'(t) and then normalize it to obtain T(t). Then, we calculate the second derivative vector R''(t) and normalize it to obtain N(t).

Calculate the first derivative vector R'(t):

R'(t) = (3cos(t), 4, -3sin(t))

Normalize R'(t) to obtain the unit tangent vector T(t):

T(t) = R'(t) / ||R'(t)||

T(t) = (3cos(t), 4, -3sin(t)) / sqrt((3cos(t))^2 + 4^2 + (-3sin(t))^2)

Calculate the second derivative vector R''(t):

R''(t) = (-3sin(t), 0, -3cos(t))

Normalize R''(t) to obtain the principal unit normal vector N(t):

N(t) = R''(t) / ||R''(t)||

N(t) = (-3sin(t), 0, -3cos(t)) / sqrt((-3sin(t))^2 + 0^2 + (-3cos(t))^2)

Therefore, the unit tangent vector T(t) is T(t) = (3cos(t) / sqrt((3cos(t))^2 + 4^2 + (-3sin(t))^2), 4 / sqrt((3cos(t))^2 + 4^2 + (-3sin(t))^2), -3sin(t) / sqrt((3cos(t))^2 + 4^2 + (-3sin(t))^2)), and the principal unit normal vector N(t) is N(t) = (-3sin(t) / sqrt((-3sin(t))^2 + 0^2 + (-3cos(t))^2), 0, -3cos(t) / sqrt((-3sin(t))^2 + 0^2 + (-3cos(t))^2)).

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Answer:

y=4/3x+11

Step-by-step explanation:

To calculate the slope do difference in y divided by difference in x. Notice the different scales on the x and y axis.

The y intercept is where the line cuts through the y axis, (11)

No, the function y=2sin(2x) is not a solution of the differential equation y'''-8y=0.

To determine whether a function is a solution to the differential equation, we have to first find the derivatives of the function. The derivatives of y=2sin(2x) are y'=4cos(2x), y''=-8sin(2x) and y'''= -16cos(2x).

Next, we have to substitute the derivatives of the given function into the differential equation. When we substitute the derivatives of y=2sin(2x) into the differential equation, we get -16cos(2x) - 8×2sin(2x) = 0. This is not equal to 0, so y=2sin(2x) is not a solution to the differential equation y'''-8y=0.

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The analysis of the data set with 222 observations on the salaries of university professors and a few explanatory variables will involve the use of inferential Statistics, descriptive statistics, and regression analysis to obtain insights into the data set and its variables.

When analyzing a data set with 222 observations on the salaries of university professors and a few explanatory variables, the variables involved in the data set are as follows:

Response Variable - Salary Explanatory Variables -There are a few explanatory variables involved in the data set such as:

Years of ExperienceGenderDepartmentDegree typeNumber of publicationsThe analysis of the data set should be done through statistical methods to obtain insights into the data set and its variables. The statistical methods involve the use of inferential statistics, descriptive statistics, and regression analysis to obtain information on the data set.The use of descriptive statistics will provide an overview of the data set through the use of measures of central tendency and measures of dispersion. The measures of central tendency include the use of mean, median and mode to describe the center of the data set while the measures of dispersion include the use of range, variance and standard deviation to describe how spread out the data set is.

Inferential statistics will provide insights into the variables in the data set by analyzing a sample from the population of the data set. This will involve the use of hypothesis testing and confidence intervals to obtain information on the variables in the data set.

Regression analysis will help determine the relationship between the response variable and the explanatory variables. In this case, multiple linear regression analysis will be employed to determine the factors that affect the salaries of university professors. This method will involve the use of a regression model to determine the relationship between the response variable and the explanatory variables.

In conclusion, the analysis of the data set with 222 observations on the salaries of university professors and a few explanatory variables will involve the use of inferential statistics, descriptive statistics, and regression analysis to obtain insights into the data set and its variables.

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Answer:

0.6 servings

Step-by-step explanation:

division. divide 3/5.

Answer: 3/2

Step-by-step explanation: y2-y1/ x2- x1

Answer:

628ft²

Step-by-step explanation:

From the diagram, we are given the following

diameter of the semicircles

2semi circles  = 1 circle

Area of 2semicircles = πd²/4

Area of 2semicircles = 3.14(20)²/4

Area of 2semicircles = 3.14*400/4

Area of 2semicircles = 3.14*100

Area of 2semicircles = 314ft²

Area of the quarter circle =  πd²/4 * 1/4

Area of the quarter circle =  πd²/16

d = 2r

d = 2*20

d = 40ft

Area of the quarter circle  = 3.14(40)²/16

Area of the quarter circle = 3.14*1600/16

Area of the quarter circle = 3.14*100

Area of the quarter circle = 314ft²

Area of the fountain = 314ft²+314ft²

Area of the fountain = 628ft²

y intercept is where x=0 or the initial value

which is 60 because we gots

y=60(1)

y=60

y intercept is at y=60

8 years is x=8

y=82.114

round

y=82.11

answer:

y intercept is y=60

after 8 years, has $82.11

Danielle earned $951.25

Step-by-step explanation:

Multiply her commission by her sales and add her base rate

x=7.25%($4500)+625 or x=0.0725(4500)+625

distribute

x=326.25+625

simplify

x=951.25

Answer:

The smaller number is 27 and the larger number is 44

Step-by-step explanation:

Let x = the larger number

Let y = the smaller number

x + y = 71

x = y + 17  Substitute in y + 17 for x in the first equation.

x + y = 71

y +17 + y = 71  Combine the y's.

2y + 17 = 71  Subtract 17 from both sides of the equation

2y = 54  Divide both sides of the equation by 2

y = 27.  Plug 27 in for y for either of the two original equation to find x

x + y = 71

x + 27 = 71  Subtract 27 from both sides of the equation

x = 44

According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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A type of quantitative analysis in which the amount of a species in a material is determined by converting the species to a product that can be isolated completely and weighed is "gravimetric analysis."

Gravimetric analysis is a quantitative chemical analysis method in which the contribution sought is transformed into a material (of different compositions) that can be separated and weighed from the sample.

Some key features regarding the gravimetric analysis are-

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A Voronoi diagram is a division of a plane into areas near each of a given set of objects in mathematics. These things are just infinitely many points in the plane in the simplest scenario (called seeds, sites, or generators). There is a region, known as a Voronoi cell, for each seed that is made up of all points in the plane that are closer to that seed than to any other point. A set of points' Voronoi diagram and Delaunay triangulation are identical.

We are aware that any intersection of half-planes results in a convex region bordered by a collection of linked line segments. Voronoi edges are the line segments that define the limits of Voronoi regions. These edges' termini are known as Voronoi vertices.

Voronoi diagram:

A Voronoi diagram in mathematics is a division of a plane into areas near to each of a given set of objects. These things are simply infinitely many plane points in the most basic scenario (called seeds, sites, or generators).

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