It takes seven cows 30 days to graze a plot of land how long will it take 21 cows to graze the same plot of land

Answer:

It has no solution within Real numbers. Its solutions are Complex/imaginary, since its discriminant is negative (-64).

Step-by-step explanation:

The normalized form of the equation

(x+2)^2= - 16

x^2 + 4x + 4 = - 16

x^2 + 4x + 20 = 0

We have in the form ax^2 + abx + c = 0

a = 1

b = 4

c = 20

Discriminant is b^2 - 4ac = 4^2 - 4*1*20 = 16 - 80 = - 64

Discriminant is negative, therefore, no Real solutions.

Answer:

$508.79 .............................................................

Answer:

Step-by-step explanation:

L = 3*w + 1                      Given

P = 2*(L + w)                   Formula for Perimeter. Substitute for L    

P = 2*(3w + 1 + w)           Combine

P = 2*(4w + 1)                  

P = 58                             Given

58 = 8w + 2                    Remove the brackets

58 - 2 = 8w                     Subtract 2

56 = 8*w                         Divide by 8

56/8 = w

7 = w

================

Find L

L = 3*w + 1

L = 3*7 + 1

L = 22

================

Check

2L + 2W  = 58

2*22 + 2*7 =? 58

44 + 14 = ? 58

58 = 58

The answer checks.

Answer:

  4.6 km

Step-by-step explanation:

You want to know how many kilometers east Santos walked to end up 5 km from his starting position after walking 2 km south.

The distance Santos is from his starting position will be the hypotenuse of a right triangle with one leg 2 km. Using the Pythagorean theorem, we can find the length of the other leg.

  c² = a² + b²

  5² = 2² + b²

  21 = b²

  b = √21 ≈ 4.583

Santos walked about 4.6 km east.

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Answer: (-7,4]

Step-by-step explanation: okay so the domain is the word they use to chart everything along the x-axis, where the range is to chart everything on the y-axis. So since we’re looking for domain, I started looking from left to right for the first point which is at -7, and since the circle is open this means that you want to put a ( on the outside of it instead of a [. So then I looked along the line to the end of it, and saw that the furthest point to the right on the x-axis was at 4. With this one though we want to put a ] on it because the circle is closed. I hope this is helpful!

Solution

Given a triangle XYZ on the graph

The coordinates of points X, Y and Z are

To find the approximate length of the sides, we apply the formula to find the distance, d, between two points which is

To find the approximate length of side XY, substitute the coordinates of points X and Y into the formula to find the distance, d, between two points

Hence, the approximate length of side XY is 3.16 units (option b)

The throw of the dice or the drawing of a card is known as random behavior.

Random behavior refers to events that occur by chance, without any predictability or pattern. These events cannot be influenced or controlled, and their outcomes are determined by the laws of probability. In games such as dice and card games, the outcomes are determined by random variables, such as the position of the dice or the shuffle of the deck.

Random behavior can also occur in other contexts, such as weather patterns or the stock market, where events are subject to unpredictable fluctuations. Understanding random behavior is important in many fields, including mathematics, statistics, and economics, as it can help us make informed decisions based on the probability of different outcomes.

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This is a good example of confirmation bias.

Confirmation bias refers to the tendency of individuals to seek and interpret information in a way that confirms their existing beliefs or preconceptions. In this scenario, the individual has a strong belief that cigarette smoke does not increase the probability of getting cancer. They selectively search for and rely on information from the internet that supports their belief, disregarding or downplaying any conflicting evidence. This bias can prevent individuals from considering alternative perspectives or evaluating evidence objectively, potentially leading to an inaccurate or skewed understanding of the topic.

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Answer:

D

Step-by-step explanation:

cos 30 = 9/x

x = 9/(\(\sqrt{3}/2\)) = 6\(\sqrt{3}\)

(6\(\sqrt{3}\))² - 9² = x²

x² = 27

x = 3\(\sqrt{3}\)

The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.

A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.

The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.

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Answer:

14.6

Step-by-step explanation:

Subtraction is a mathematical operation that reflects the removal of things from a collection. The number of students who climbs the rock wall is 4.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The total number of students in the class is 48, out of these 48 students, 24 students choose to play volleyball. Therefore, the remaining students are 24 (48-24).

Students remaining after volleyball

  = Total number of students - Number of students who play volleyball

  = 48 - 24 = 24

Now, The teacher then divides the remaining students into as many groups of 5 as possible to shoot baskets. Therefore, the teacher divides the remaining 24 students into 4 groups of 5 people. After this, the number of students that are remaining is 4(24-20).

Students remaining after basketball

  = Total number of students - Number of students who shoot basketball

  = 24 - (4x5)

  = 24 - 20 = 4

Further, the remaining students go for climbing the rock wall.

Hence, the number of students who climbs the rock wall is 4.

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Answer:

y = 4, x=1 or x=110

Step-by-step explanation:

1. 4y-2=18                      2. x/2+5=11

       -2  -2                         x/10=11

4y = 16                               x=1

4y/4 = 16/4                         or

y=4                                  x/10=11

                                       0.1x=11

                                        0.1x/0.1 = 11/0.1

                                         x=110

Factor by grouping: 16x³ +28x² - 28x - 49 = 0 is  (4x² - 7) (4x - 7) = 0

Large polynomials can be divided into groups based on a common factor. As a result, we may factor each distinct group and then merge like words. We refer to this as factoring by grouping.

We have the equation,

16x³ +28x² - 28x - 49 = 0

In order to solve the equation by using factor by grouping:

We find common terms in between,

So, we arrange the terms,

16x³ +28x² - 28x - 49 = 0

4x² (4x - 7) -7 (4x - 7) = 0

Here, we have common term (4x-7).

Factor out the common binomial.

(4x² - 7) (4x - 7) = 0

Therefore, (4x² - 7) (4x - 7) = 0 is the factor.

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Answer:

its 3.05

Step-by-step explanation:

The coordinates of A will be at (-10, -5) when the transformation (x,y) → (x + 10, y + 5) is  performed on point A.

Given the coordinate of the resulting image after the transformation is A'(0, 0). We need to get the coordinate of the original image A.

Since the transformation (x,y) → (x + 10, y + 5) is performed on A.

A = (0 - 10, 0 - 5)

If we are going from the pre-image to the image, we will translate to the left and downwards

A = (-10, -5)

Hence the coordinates of A will be at (-10, -5)

Learn more here:

An expression is defined as a set of numbers, variables, and mathematical operations. The correct options are B and D.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that are equivalent to -4/3p - 2/5 are:

Hence, the correct options are B and D.

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The probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item is 0.68.

Given data ,

According to store records, approximately  1/ 4 of all customers who go to the service department ask for help finding an item.

All the  customers who go to the service department will not ask for help.

Now, the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item is

P(X>=1)   = 1 - P(X<1)

               = 1 - (1/4)⁰ (3/4)⁴

               = 1 - (3/4)⁴

               = 0.68

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced to predict how likely events are to happen.

The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment.

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Answer:

Two events that are mutually exclusive when rolling two number cubes are:

Getting an odd number on the first cube and getting an even number on the second cube.

Getting a 1 on the first cube and getting a 2 on the second cube.

Two events that are not mutually exclusive when rolling two number cubes are:

Getting a 4 on the first cube and getting a 3 on the second cube.

Getting a 5 on the first cube and getting an odd number on the second cube.

Step-by-step explanation:

First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

The sampling technique used in the first scenario is stratified random sampling. Where as for the second and third scenario convenience sampling and systematic sampling are used.

i) In the first scenario, where 20 randomly selected households are interviewed from every grid in a disaster area, the sampling technique employed is stratified random sampling. The area is divided into 100 equal grids, and households are randomly selected from each grid. This approach ensures representation from each grid and provides a comprehensive view of the residents' needs.

ii) In the second scenario, where students are questioned as they leave the university's computer lab, the sampling technique used is convenience sampling. The researcher selects students conveniently available in the lab without following a specific randomization process. While this approach is convenient and easily accessible, it may introduce bias since it relies on the availability and willingness of students to participate.

iii) In the third scenario, where a researcher draws a sample from sequentially numbered invoices by selecting a random starting point and then drawing every 50th invoice, the sampling technique employed is systematic sampling. This technique involves selecting elements at fixed intervals from an ordered list. By randomly choosing a starting point and sampling every 50th invoice, the researcher ensures a systematic and evenly spaced sample.

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Answer:

D

Step-by-step explanation:

To evaluate p(- 7) substitute x = - 7 into p(x) , that is

p(- 7)

= - 4((- 7)² + 8) - 9

= - 4(49 + 8) - 9

= - 4(57) - 9

= - 228 - 9

= - 237 → D

A correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.

A correlation can be defined as the relationship that exists between two variables when one of them is related to the other in some way.

It is also a measure that expresses the extent to which two variables are closely or linearly related which entails that they change together at a constant time.

Hence, correlation is a statistical relationship between two variables, such that knowing one of the variables makes it possible to predict the other.

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Answer:

C) 20 Speeders

Step-by-step explanation:

5 divided by 2 is 2.5

there are 2.5 speeders per hour

over the span of 8 hours just multiply

8x2.5=20

The graph of the proportional relationship is (c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

From the question, we have

It costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry

This means that

(x, y) = (20.70, 23) and (34.20, 38)

Where

x = Weight and y = Cost

From the question, we understand that

The graph is a proportional graph

This means that the line passes through the origin

So, we have

(x, y) = (0, 0), (20.70, 23) and (34.20, 38)

Remove one of the points

(x, y) = (0, 0) and (34.20, 38)

Hence, the graph of the proportional relationship is (c)

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Answer:

The graph of the proportional relationship is (c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)

Step-by-step explanation:

I took the exam and got it right

The width of the rectangle is 7m and the length of the rectangle is 10m.

A rectangle is a quadrilateral that is a four sided polygon with two opposite sides parallel and equal.

Let the width of the rectangle be x.

Therefore the length of the rectangle = x + 3.

Area of a rectangle = length * width

Area = (x + 3) (x)

Open bracket;

Area = x² + 3x

We are given the area = 70 m².

Therefore,

70 = x² + 3x

x² + 3x - 70 = 0

Solve quadratically using the factorization method by finding two factors of -70 that add up to give 3 the coefficient of x.

Factors = 10 and -7 which add up to 3.

Rewrite the equation;

x² + 10x - 7x - 70 = 0

x( x + 10) - 7 ( x + 10) = 0

(x - 7) (x + 10) = 0

x - 7 = 0 or x + 10 = 0

x = 7 or x = -10

x = 7m because the width can't be negative.

Therefore,

Length = x + 3 = 7 + 3 = 10 m

Therefore, the width of the rectangle is 7m and the length of the rectangle is 10m.

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Answer:

b I think it' hope I helped

Answer:

\(\lim_{x\to 1^+} f(x)=5\)

Step-by-step explanation:

So we have the function:

\(f(x) = \left\{ \begin{array}{ll} x+2 & \quad x \leq 1 \\ x^2+2x+2 & \quad x > 1 \end{array} \right.\)

And we want to evaluate:

\(\lim_{x\to 1^+} f(x)\)

In other words, we want to evaluate the limit for f(x) as x approaches 1 from the right.

Since our x is approaching from the right, this means that we need to use the second equation. This is because the second equation is defined for all values greater than 1. So, if we approach from the right, we are using all values greater than 1. Therefore:

\(\lim_{x\to 1^+} f(x)\)

Replace f(x) with the second equation:

\(=\lim_{x\to 1^+} (x^2+2x+2)\)

Evaluate. Use direct substitution:

\(=(1)^2+2(1)+2\)

Square:

\(=1+2(1)+2\)

Multiply:

\(=1+2+2\)

Add:

\(=5\)

Therefore:

\(\lim_{x\to 1^+} f(x)=5\)

And we're done!

In the given experiment x is the independent variable.

Given that, professor Jones found that the students in the experimental group scored on average 10 points higher than the students in the control group.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the average score of control group be x and the average score of experimental group be y.

Now, y=x+10

Therefore, in the given experiment x is the independent variable.

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