Mr. Jones needs to build a fence in his backyard to keep their dog safe. The length of the fence should be at least 60 ft, and the distance around should be no more than 260 ft. Which system of inequalities and graph represent the possible dimensions of the pen?

Answer:

yes

Step-by-step explanation:

2x+4=3x-2

4=x-2

6=x

x=6

Answer:

Yes, It equals 6.

On an average, 1.67 people will have to be stopped by the reporter before he finds his first democrat.

A supporter of democracy, Democratic Party subscriber, a democratic government, or a system of government where the people rule, may be referred to as a Democrat, Democrat, or Democratic.

The central value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a given set of numerical data.

For instance, (2+3+4)/3 = 9/3 = 3 is the average of 2, 3, and 4. As a result, in this instance, 3, which also includes 2, 3, and 4, serves as the central value. Finding the average value of a group of numbers is what average means, then.

Average is calculated by dividing the total number of values by the sum of the individual values.

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The flux of the vector-field F = 4i + 4j + 1k across the surface S is 63/4. We find out the flux of the vector-field using Green's Theorem.

Flux form of Green's Theorem for the given vector-field

φ = ∫ F.n ds

= ∫∫ F. divG.dA

Here G is equivalent to the part of the plane = 3x+2y+z = 3.

and given F = 4i + 4j + 1k

divG = div(3x+2y+z = 3) = 3i + 2j + k

Flux = ∫(4i + 4j + 1k) (3i + 2j + k) dA

φ = ∫ (12 + 8 + 1)dA

= 21∫dA

A = 1/2 XY (on the given x-y plane)

3x+2y =3

at x = 0, y = 3/2

y = 0, x = 1

1/2 (1*3/2) = 3/4

Therefore flux = 21*3/4 = 63/4

φ = 63/4.

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The numbers in the increasing order are:

(x-1)>(x+1)>(x+2)

In mathematics, factorization is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. The factorization of the integer 12, for instance, might be represented as 3 times 4. In the context of integers, factorization was first studied by Greek mathematicians. They established the basic theorem of mathematics, which states that every positive integer can be factored into a product of prime numbers but cannot be factored further into integers larger than 1. Up to the order of the factors, this factorization is also distinct.

It has also been studied for ages how to factor polynomials.

The given equation is:

x³+2x²-x-2

Now, we have to do factorization for the given equation.

(x+1)(x²+x-2)

(x+1)(x²+2x-x-2)

(x+1)(x(x+2)-1(x+2))

(x+1)(x-1)(x+2)

This is the factorized form of the given equation.

Therefore, the numbers in the increasing order are:

(x-1)>(x+1)>(x+2)

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The price of new car is reduced by $825 from the original price $12,500 which implies the price of car after reduction is $11,625 i.e

The percentage reduction is 7 .

Percentage is calculated by dividing the value by total value and then multiply with 100.

We have given that,

The price of a new car = $12,500

After the some reduction in price

then the price of car = $11,625

The reduction in total price of car = original price - price after reduction

= $12,500 - $11,625

= $875

Now, we have to calculate the reduction of price in percentage.

Using the percentage reduction formula,

P% = (original price - price after reduction )× 100 /original price

=> percentage reduction = ( 875/12500)×100

=> percentage reduction = 875/125 = 7

Hence, the reduction is 7% .

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Answer:

[tex]\frac{x}{3} \leq 5[/tex]

Hope this helps! :)

The area of the trapezium, if  CD = 8 cm, BD = 6 cm, AE = 9 cm, is  30 cm².

The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given:

CD = 8 cm,

BD = 6 cm,

AE = 9 cm,

Here you can see that the triangle AEC and triangle BDC are similar, so the ratio of sides of a triangle are also equal,

BD / AE = CD / CE

6 / 9 = 8 / CE

CE = 9 × 8 / 6

CE = 12 cm

Thus, DE = CE - CD.

DE = 12 - 8 = 4 cm

Calculate the area as shown below,

[tex]Area = (BD+AE) / 2 \times DE[/tex]

Area = (6 + 9) / 2 × 4

Area = 15 / 2 × 4

Area = 30 cm²

Therefore, the area of the trapezium, if  CD = 8 cm, BD = 6 cm, AE = 9 cm, is  30 cm².

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Answer:

Answer choice (C) -$19.56 is your answer. After the check was cashed she had negative -19.56

Step-by-step explanation:

Kathy had $45.67 in her checking account. She wrote a check for $65.23. What was her balance after the check was cashed? A. $110.90 B. $39.56 C. -$19.56 D. -$110.90

The line of fit for the coordinate points (1960, 23) and (2000, 32) is y=9/40 x+418.

The given coordinates are (1960, 23) and (2000, 32).

The line of best fit calculates a straight line that minimises the separation between itself and the locations of the observations in a given data collection. A trend or correlation between the dependent variable and the independent variable is depicted using the line of best fit (s). It can be expressed mathematically or graphically.

In the coordinate points (1960, 23) and (2000, 32)

In (1960, 23), 1960 is x-coordinate and 23 is y-coordinate

In ((2000, 32), 2000 is x-coordinate and 32 is y-coordinate

Here, Slope =(y2-y1)/(x2-x1)

= (32-23)/(2000-1960)

= 9/40

Substitute m=9/40 and (x, y)=(1960, 23) in y=mx+c, we get

23= 9/40 (1960)+c

23= 9×49+c

c=23-441=418

Substitute m=9/40 and c=418 in y=mx+c, we get

y=9/40 x+418

Hence, the line of fit for the coordinate points (1960, 23) and (2000, 32) is y=9/40 x+418.

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The missing statement and reason to complete the given proof of parallelogram is Option A.

What is a parallelogram?

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of a polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.

Given, NL is a diagonal of parallelogram KLMN

Since KL || NM and LN is transversal

That implies, ∠KLN ≅∠MNL by alternate interior angles theorem

Again, KN || LM  and NL is transversal

That implies, ∠LNK ≅ ∠NLM by alternate interior angles theorem

Hence, Option A is the correct answer.

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Answer:

B.

∠KLN ≅ ∠MLN, and ∠KNL ≅ ∠MNL

by the alternate interior angles theorem

Step-by-step explanation:

Functions are expressions, rules, or laws that specify the relationship between an independent variable and a dependent variable

Given,

A function;

An expression, rule, or regulation that establishes the connection between an independent variable and a dependent variable is known as a function (the dependent variable).

A function called f is defined by the notation y=f(x). This should be understood as "y is a function of x." The input value, or independent variable, is represented by the letter x. The output value, also known as the dependent variable, is denoted by the letter y, or f(x).

Examples for function are;

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Answer:

top right graph

Step-by-step explanation:

Having a zero at 3 means that the y coordinate is 0 when the x-coordinate is 3.

A y-intercept of 9 means it includes the point (0, 9).

Answer: top right graph

The total amount they will pay = $95.557

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.

Cost of meal = $75.99

tax amount = 6.75% of 75.99

                   = ( 6.75/100 ) * 75.99

                   = $5.129

Tip amount = 19% of 75.99

                   = (19/100)*75.99

                   =  $14.438

Total amount they will pay = $75.99 + $5.129 + $14.438 = $95.557

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The exact circumference of the circle with radius 17 millimeters is 34π   millimeters , the correct option is (b) .

In the question ,

it is given that ,

the radius of the circle is given as = 17 millimeter

we have to find the exact circumference of the circle,

we know that the formula to find circumference of the circle is ;

circumference = 2×π×r

Substituting the value of radius in the circumference formula ,

we get ;

circumference = 2×π×17

Simplifying  further ,

we get ,

= 34π

Therefore , the exact circumference of the circle is = 34π .

The given question is incomplete the complete question is

What is the exact circumference of a circle with a radius of 17 millimeters ?

(a) 17π millimeters

(b) 34π millimeters

(c) 68π millimeters

(d) 8.5π millimeters

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The inequality represents a number no more than 5 is n < 5.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

We have to find which inequality represents a number no more than 5.

Consider, the first inequality n ≤ 5.

This inequality contain 5 and less numbers.

Consider the second inequality n ≥ 25

This inequality contain numbers 5 and more

For n > 5  

This inequality contain numbers more than 5.

For n < 5

This inequality does not contain number more than 5.

Hence, the inequality represents a number no more than 5 is n < 5.

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The earliest finish time for the activity 10-11(far right-hand side) is 23 if the earliest start time of activity 8-10 and activity -10 is 12 and 13 respectively.

The depicted graph represents the critical path method(CPM)

Given,

Earliest start time of 8-10 = 12

Earliest start time of 9-10 = 13

From the network, it is observed that at 10, two networks are connecting, we need to take the largest earliest finish time from both the activities as earliest start time for 10-11.

Earliest finish time = earliest start time + activity duration

Earliest finish time for 8-10 = 12+4=16

Earliest finish time for 9-10 = 13+2=15

From above two times, 8-10's earliest finish time is the greatest. So, consider 16 as earliest start time for 10-11.

Now,

Earliest finish time for 10-11= earliest start time + activity duration=16+7=23

Thus, the earliest finish time for 10-11 is 23.

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The mean of this sampling distribution is 1 cm, the standard deviation is 0.033, X-bar is called the sampling distribution of the sample mean

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.

The bigger the deviation within the data collection, the more the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.

Processor chips = 35

Let the x-bar be the sample mean

x-bar = 1 mm

Size of the processor chips = 0.2 mm

n = 35

Standard deviation = Size of the processor chips/[tex]\sqrt{n}[/tex]

= 0.2/[tex]\sqrt{35}[/tex]

= 0.2/5.9160

= 0.033

Standard deviation = 0.033

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After solving, she is 25 years old.

In the given question,

When he asked her age, She replied "If you take my age and square it and then subtract 22 time my age then the result is 75"

We have to find the age of she.

To find the age of she we we firstly simplify the given statement in the form of expression then we solve the expression.

To write the expression we clearly read then sentence and then write the expression.

Let the age of she is x.

So When we take the square of her age, it is x^2.

When we subtract 22 times her age then it is x^2-22x.

Then its is equal to the 75. Now the expression is;

x^2-22x=75

Subtract 75 on both side, we get

x^2-22x-75=0

Now we simplifying the equation by factoring it.

x^2-(25-3)x-75=0

x^2-25x+3x-75=0

x(x-25)+3(x-25)=0

(x+3)(x-25)=0

Now the factor of x is -3 and 25.

Age can not be negative. So the age of she is 25.

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The right question is;

When he asked her age, She replied "If you take my age and square it and then subtract 22 time my age then the result is 75"how old is she?

Answer: $91017.17865 / 12 = $7585.5987

Step-by-step explanation:

To solve this problem, we need to first determine the total interest that will be earned on the account over the 5-year period. We can do this by using the formula for compound interest, which is:

A = P (1 + r/n) ^ nt

where A is the total amount of money in the account after the interest has been compounded, P is the initial deposit, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years the money is deposited.

In this case, the initial deposit is $10,000, the interest rate is 2.05%, the number of times the interest is compounded per year is 12 (because the interest is compounded monthly), and the number of years the money is deposited is 5. Plugging these values into the formula, we get:

A = 10000 (1 + 0.0205 / 12) ^ (12 * 5)

A = 10000 (1.001708333) ^ 60

A = 10000 (1.101717865)

A = 101017.17865

Therefore, the total amount of money in the account after 5 years will be $101017.17865.

Since Monica wants to save up $10,000, we can subtract this amount from the total amount in the account to find out how much she needs to deposit each month in order to reach her goal:

101017.17865 - 10000 = 91017.17865

Therefore, Monica needs to deposit $91017.17865 each month in order to save up $10,000 in 5 years. This means that she will need to deposit $91017.17865 / 12 = $7585.5987 per month in order to reach her goal.

The answer to this Question based on Linear equation is 28 and 45

What is Linear Equation?

It is a equation in which the degree of each and every variable is 1 only is called linear equation

Solution:

Let the time taken to complete maths homework be x and time to complete science homework be y

first we know that total time taken was 1 hr 15 minutes means 75 minutes which in turn means x + y = 75

and from 2nd relation that we are given

x = 2y - 9

now we got the 2 linear equations now we just need to solve them to get our final answer

putting this equation in first equation we got we get

2y - 9 + y = 75

3y - 9 = 75

3y = 84

y = 28

and hence x = 2y - 9

x = 56  - 9

x = 45

hence time to complete maths was 45 minutes and time to complete science is 28 minutes

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Answer:

D. One solution

Step-by-step explanation:

6-3x=4-x-3-2x

Combine your like-terms.

6-3x=1-3x

Subtract 1 to both sides (on the right side it cancels out).

5-3x=3x

Add 3 on both sides (on the left side it cancels out).

5=6x

Divide both sides by 6.

x=0.83

A function that is used to find the maximum = MAX

We know that the MAX function in Excel returns the data's largest numeric value from a set of values.

MAX does not take into account empty cells, logical values TRUE and FALSE, or text values.

To find the  to find the maximum value in a set of values:

First select a cell below or to the right of the numbers you're looking for the smallest number for.

Then click the arrow next to AutoSum on the Home tab, in the Editing group, then click Min (calculates the smallest) or Max (calculates the largest), and then press ENTER.

MAX function is used to find the maximum.

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Answer: 216 times

Step-by-step explanation:

18 * 12

Answer:

Pick at least four pennies to be sure of getting at least four pennies from the same year.

Step-by-step explanation:

To be sure of getting at least four pennies from the same year, you would need to pick at least four 1967 pennies, four 1968 pennies, or four 1971 pennies. Since these are the three smallest groups of pennies, you would need to pick at least four pennies to be sure of getting at least four pennies from the same year.

Expected number of defectives is 3.

What do you mean by probability?

Simply put, probability is the likelihood that something will occur.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The likelihood or chance of an event happening is known as probability.

Probability =  (the number of ways of achieving success)/( the total number of possible outcomes)

It is given that there are total 50 computers and out of which 3 are defective. So , here atmost 3 can be  defective out of 7.So , out of 7 , one can be defevtive , 2 can be defective and 3 can be defective

Therefore, expected number of defectives is 3.

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The ven diagram from set theory must be used to determine the highest value and minimum value in a set.

We're using this as an illustration.

Let A and B represent two sets with 4 and 7 items, respectively. The maximum number of elements that A and B can have is then written.

So let's assume:

A's element count is equal to n. (A).

B's element count is equal to n. (B).

The sum of the elements of A and B is n (A and B).

Now, here is the equation for the components of A U B:

n(A∪B)=n(A)+n(B)−n(A∩B)

The answer to the question states that set A's element count is four, whereas set B's element count is seven. We can thus write:

The number of elements that are included in both sets A and B is represented by the numbers n (A) = 4 and n (B) = 7.

The maximum number of elements in n(A,B) must be determined. Therefore, when n(AB) is smallest and when n(AB) is zero, n(AB) is at its maximum.

n(A∪B)=n(A)+n(B)−n(A∩B)⇒n(A∪B)=4+7−0⇒n(A∪B)=11

Hence, the maximum number of elements in A∪B is 11.

You might be asking why n (AB) must be minimized in order to be maximized, and why the minimal value of n (AB) is 0.

In the formula for n (A∪B),

n(A∪B)=n(A)+n(B)−n(A∩B)

L.H.S will be maximized when in the R.H.S; the term after minus sign will be minimized. Hence, n (A∩B) must be minimized.

The fact that n (AB) can take on any value less than 0 indicates that there are no elements in sets A or B that are shared by both sets. Furthermore, it's possible that the two sets we have don't share any elements.

When no elements is common in both the sets, the n (A∩B) is ∅.

The set which has no element in it is called a null set or an empty set.

By this we can find maximum value in a set.

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Answer:

Class 1

Mean 78.83

Median 88

Mode 90

Class 2

Mean 79.42

Median 85.5

Mode 90

Class 3

Mean 79.42

Median 78

Mode 75 and 80

The [0.513,0.616] range is the 95% confidence interval for the percentage of all dies that pass the test.

Given,

Number of items inspected = 356

Number of items passed the test = 201

We have to calculate the 95% (two-sided) confidence interval for the proportion of all dies that pass the test;

Here,

p' = 201 / 356 = 0.56460

Now,

The 95% confidence interval for the percentage of all dies that pass the test;

p∈ [p' ± zα / 2√p' (1−p') / n]

p∈ [0.56460 ± 1.96 × √0.56460 (1 − 0.56460) 356]

p∈ [0.513, 0.616]

That is,

The 95% confidence interval for the percentage of all dies that pass the test is [0.513, 0.616]

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Answer:

4

Step-by-step explanation:

[tex]\frac{-3}{4}[/tex] m - [tex]\frac{1}{2}[/tex] = 2 + [tex]\frac{1}{4}[/tex] m  Multiply each term by 4

-3m - 2 = 8 + m  Add 3m to both side

-2 =  8 + 4m  Subtract 8 from both sides

-10 = 4m  Divide both sides by 4

[tex]\frac{-5}{2}[/tex] = m

Answer: Her brother is 5 years old.

Step-by-step explanation:

s = 2b

4b + 3b = 35

7b = 35

First, I used s to represent Sarah's age. We are told that she is twice her brother, I used b to represent her brother's age. The sum of twice her age is 4 times her brother's age (2b + 2b) and 3 times her brother's age is 3b.