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Graph the following system of inequalities.

Y ≥ 1/3x - 2

Y ≤ -4x - 2


A. Z

B. X

C. W

D. Y

The stated combination of coins is not possible as the number of quarters are highly more than the number of dimes and nickels.

Let the number of dimes be x. So, the number of an nickels will be 2x. The number of quarters will be (30 - 3x). As per the known information, the one nickel is 0.05 dollars, one dime is 0.1 dollars and one quarter is with 0.25 dollars.

Now forming the expression -

x×0.1 + 2x×0.05 + (30-3x)×0.25 = 3

Performing multiplication on Left Hand Side of the equation

0.1x + 0.1x + 7.5 - 0.75x = 3

Performing addition on Left Hand Side of the equation

0.2x - 0.75x = 3 - 7.5

On subtraction we will find the value on Left Hand Side will be negative. Thus, the stated combination is not possible.

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The required simplified value of the given expression is given as 11/12x² + 7/15x - 1/3.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= (11/12x-5/6) (x-2/5)
= 11/12x (x - 2/5) + 5/6 (x - 2/5)
= 11/12x² - 11/30x + 5/6x - 1/3
= 11/12x² + 7/15x - 1/3

Thus, the required simplified value of the given expression is given as 11/12x² + 7/15x - 1/3.

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Original Equation:

[tex]\frac{3}{4} + x < \frac{1}{6}[/tex]

1) Subtract 3/4 from both sides:

[tex](\frac{3}{4}+x)-\frac{3}{4} < \frac{1}{6}-\frac{3}{4}[/tex]

2) Simplify:

[tex]x < \frac{1}{6}-\frac{3}{4}[/tex]

Find a common denominator for both fractions (I will use 12)

[tex]x < \frac{2}{12} -\frac{9}{12}[/tex]

Simplify:

[tex]x < \frac{-7}{12}[/tex]

We cannot simplify the expression anymore, therefore this is the answer!

Answer: You should buy 7.5 pounds of pecan.

Step-by-step explanation: Each pecan pie needs 1.5 pounds each and 1.5 x 5 = 7.5

Answer:6

Step-by-step explanation:

The quarter mile grounding rule for rural electric utilities for direct-buried jacketed distribution cables says that they must have at least 4 grounds per mile.

A utility cooperative is a specific kind of cooperative that is responsible for providing its members with a public utility, such as power, water, or telecommunications. Profits are either distributed to members as "patronage" or "capital credits," which are dividends paid on a member's investment in the cooperative, or they are reinvested for infrastructure. 

Every consumer is a shareholder and a member of the company. This means that, in contrast to investor-owned utilities where the amount of individual authority is determined by the number of shares held, all members have the same level of personal authority. Many utility cooperatives operate their business in accordance with a set of ideals based on the Rochdale Principles, just like cooperatives active in other industries.

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Answer:

90 is 150% of 60

OR

90 is 50% greater than 60

Step-by-step explanation:

To find the percentage increase between two values, the first step is to find the difference between the final and initial value.

Final value: 90cm

Initial value: 60cm

Difference = 90 - 60 = 30cm

Next, you need to divide the difference between the two values by the initial value.

30 / 60 = 0.5

Lastly, you need to take the value previously found and multiply it by 100 to convert it from a decimal to a percentage.

0.5 * 100 = 50%

This value will be your percentage increase.

If you want to know what percentage the final value is of the initial value, you can take the percentage you have and add 100% to it.

50% + 100% = 150%

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Answer: 150%

Step-by-step explanation:

First, ask yourself what the difference between the two is: 90-60=30.

Secondly, 30 is 1/2 of 60. 1/2=50%.

You also need to add the hundred percent because we are adding 60 and 60 is 100% of 60. It increases by 50 and then 100. so 150%.

50% + 100% = 150%

The measure of value of x for the given set of parallel lines is found as:

x = 34.

From the definition of  alternate exterior angles:

3x + 1 = 103°

3x = 103 - 1

3x = 102

x = 34

Thus, the measure of value of x for the given set of parallel lines is found as: x = 34.

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The two integers required in the question are; 16 and 12

We are told that the sum of two positive integers is 28. Now, if the two integers are x and y, then we have;

x + y = 28   ------(1)

When the smaller integer is subtracted from three times the larger, the result is 36. Thus;

3x - y = 36  ------(2)

Add eq 1 and eq 2 to get;

4x = 64

x = 64/4

x = 16

16 + y = 28

y = 28 - 16

y = 12

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The value of k = −8 for which AB = BA.

[tex]A = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right][/tex]

Now,

[tex]AB = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right] \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right] = \left[\begin{array}{ccc}-7&18+3k\\2&-9-k\end{array}\right][/tex]

[tex]BA = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right] \left[\begin{array}{ccc}2&3\\-1&-1\end{array}\right] = \left[\begin{array}{ccc}-7&-6\\-6-k&-9-k\end{array}\right][/tex]

Thus, in order for AB = BA, we must have that

[tex]\left[\begin{array}{ccc}-7&18+3k\\2&-9-k\end{array}\right] = \left[\begin{array}{ccc}-7&-6\\-6-k&-9-k\end{array}\right][/tex]

Equate the values, and we get

18 + 3k = -6

3k = -6 - 18

3k = -24

k = -8

and 2 = -6 - k

k = -6 - 2

k = -8

Therefore we can say that it is easy to see that these equations are satisfied if and only if k = −8, and thus k = −8 is the (unique) value for which AB = BA.

--The given question is incomplete; the complete question is

"Let [tex]A = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right][/tex]. What value(s) of k, if any, will make AB = BA?"--

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The circumference of the circle with radius 3 miles is 18.85 miles.

All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The following are some of the circle's crucial characteristics:

The radius of the circle is 3 miles

Circumference of the circle 2π(radius) = 2*π*3 = 18.85 miles.

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On solving the provided question, we can say that here, the function is f(x) = 1/5(15^x) and growth factor is 15.

What is function?

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

For given question

the function is

f(x) = 1/5(15ˣ)

when f(x) = aˣ

then the growth factor of function = a

Then for f(x) = 1/5(15ˣ)

Growth factor = 15

Therefore the growth factor of function is 15.

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If $450.46 were invested at 2% interest that is compounded annually, it would be worth after 6 years.

The future value of a loan or investment may be determined using the formula FV = P*(1+R/N)(N*T), where FV is the future value, P is the original principal, R is the annual interest rate, N is the number of times interest is compounded annually, and T is the amount of time in years.

A = P(1+r/n)ⁿ

From the question, we have

P = $400

t = 6 year

r = 2%

r = 0.02

n = 1

A = P(1+r/n)ⁿ

A = 400(1+0.02/1)⁶

A = 400(1.02)⁶

A = $450.46.

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The probability that both the father and mother are current smokers is 0.12.

The probability that the mother is a current smoker is, 0.3 and the father is a current smoker is, 0.4.

The events are independent, the probability that both the events will occur is the multiplication of probability of individual events.

Therefore, the required probability is product of probability that mother is a current smoker with the probability that father is a current smoker.

P(Father and Mother are current smokers) = P(Father is a current smoker) × P(Mother is a current smoker)

P(Father and Mother are current smokers) = 0.4 × 0.3

P(Father and Mother are current smokers) = 0.12

The required probability is 0.12.

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A stratified random sample size is being used by Donald. He is segmenting the population into groups and choosing a representative sample of pupils from each category at random.

To examine the eating patterns of all pupils attending his school, Donald is utilising stratified random sampling. In this kind of sampling, the population is divided into strata, or groups, and a proportionate number of people from each category are randomly chosen to make up the sample. To make sure the sample is representative of the total community, Donald in this instance is grouping the pupils by grade level. Then he gathers information from the sample in order to make generalisations about the eating patterns of all the pupils enrolled in his school. A representative sample can be obtained and reliable population inferences can be made using stratified random sampling

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If 29 student tickets were sold, then all possible values for the number of adult tickets that the drama club must sell in order to meet the show's expenses are 54 and 55 .

the price for each student ticket is $4.50 and adult is $8 ;

The number of people auditorium can hold is = no more than 84 people ;

the number of children tickets sold is = 29 tickets ;

Let "x" be number of adult tickets sold.

The total revenue from ticket sales = $4.50×29 + $8×(x)

⇒ $130.5 + $8x.

The total revenue must be at least $560,

So , $130.5 + $8x ≥ $560.

Subtracting $130.5 from both sides, we get $8x ≥ $429.5   ;

Dividing both sides by 8, we get x ≥ 53.69    ;

Since the number of adult tickets sold must be an integer, the minimum number of adult tickets that must be sold is 54.

The maximum number of people allowed in the auditorium is 84, so the maximum number of adult tickets that can be sold is 84 - 29 = 55.

Therefore, the possible values for the number of adult tickets that must be sold are 54, 55.

The given question is incomplete , the complete question is

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4.50 and each adult ticket sells for $8. The auditorium can hold no more than 84 people. The drama club must make at least $560 from ticket sales to cover the show's costs. If 29 student tickets were sold, determine all possible values for the number of adult tickets that the drama club must sell in order to meet the show's expenses.

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The mean and median number of times a face will appear are 100 and 99.5. The mean and median face value of the 600 rolls of the die are 96.2 and 94.5

a) Mean number of appearances of each face = [tex]\frac{107+120+84+110+92+87}{6}[/tex]

                                                                             = 100

Median number of appearances of each face = Average of middle two values when arranged in ascending order

Ascending order: 84, 87, 92, 107, 110, 120

Average of middle two values = [tex]\frac{92+107}{2}[/tex]

                                                  = 99.5

b) Mean and Median face values of the 600 rolls of the die:

Mean = [tex]\frac{107\times1+120\times2+84\times3+110\times4+92\times5+87\times6}{21}[/tex]

         = [tex]\frac{2021}{21}[/tex]

         = 96.2

Median = [tex]\frac{92\times5+107}{2}[/tex]

            = [tex]\frac{567}{6}[/tex]

            = 94.5

The question is incomplete. The complete question is

"The following represents the outcomes of rolling a die 600 times

Face       1      2     3     4     5     6

Number 107 120  84  110   92   87

a. What are the mean and median numbers of appearances of each face?

b. What are the mean and median face values of the 600 rolls of the die?"

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Answer:

40,28,16,4, -8,-20... keep going

Step-by-step explanation:

use 40-12, then 40-2*12, so forth

The weight of gift is 5 pound extra with medium size of box.

In science and engineering, the weight of an object is the force acting on the object due to gravity.

Let the weight is W

The first company charged “$15 to ship a medium box, plus an additional $1 per pound”.

So, that the amount of certain weight is F =  $15 + $1*W

The second company charged “$10 to ship a medium box, plus an additional $2per pound”.

So, that the amount of certain weight is S  =  $10 + $2*W

The two shipping methods will cost the same amount

so that, F = S

$15 + $1*W = $10 + $2*W

$5  =  $1*W

W = 5 pound.

So that the weight of gift is 5 pound extra with medium size of box.

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Tomatoes are typically lighter than cucumbers since the mean weight for tomatoes is less than the mean weight for cucumbers.

Answer:

Lighter, less

Step-by-step explanation:

The mean is also known as the average. This means that it is the sum of all values divided by the total number. Therefore it is said that on average, tomatoes weigh less than cucumbers.

The probability of getting at least 14 heads when flipping a fair coin 20 times is 0.25.

This can be calculated using the binomial distribution formula which states that the probability of obtaining exactly x successes in n trials is given by

P(x) = (n choose x) * p^x * (1-p)^(n-x),

where n is the total number of trials, p is the probability of success, and x is the number of successes.

For this problem, n=20, p=0.5, and x=14, so the probability of getting at least 14 heads is P(x) = (20 choose 14) * 0.5^14 * 0.5^6 = 0.25.

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Answer:

Step-by-step explanation:

sin(YZX)=opposite/hypotenuse

sin(YZX)=7.5/22.3

then apply sin inverse to find angle Z

Answer:

2.5

Step-by-step explanation:

The minimum is the smallest value taken by the function.

The recommended behavior that Nina is practicing is ethical social media usage.

Ethical social media usage refers to responsible and respectful behavior when using social media platforms. This includes respecting others' privacy, avoiding the spread of false information, not engaging in cyberbullying or harassment, and being mindful of one's own digital footprint.  This is what Nina is doing by making sure what she shares is accurate.

Additionally, ethical social media usage also involves being transparent about one's identity and intentions, and recognizing the power of one's words and actions in the digital world.

.

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Answer:

x greater-than-or-equal-to negative 9.2

Step-by-step explanation:

Step by step in math notation here is what Marquis solved

Starting with -5.6 ≥ x + 3.6

Step 1

Step 2: Interpret the results

Since the question is asking only for the first step where the error was made, the rest of the actions taken have no relevance

Answer:

Step-by-step explanation:

P = x

The probability that a resident of this city who is 60 years old will survive until they are 80 will be 0.54 l.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.

In this case, in the city of exactly 100,000 people, 90% can expect to live to (at least) age 60 and 60% can expect to live to (at least) age 80.

The probability that a resident of this city who is 60 years old will survive until they are 80 will be:

= 90% × 60%

= 0.54

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The rule that describes the composition transformation that maps ABCD to A''B''C''D'' is;

''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

The given coordinates of parallelogram ABCD are;

⇒ (3, 5), (6, 5), (4, 1), (1, 1)

The coordinates of the parallelogram A'B'C'D' are;

⇒ A'(3, -5), B'(6, -5), C'(4, -1), D(1, -1)

The coordinates of the parallelogram A''B''C''D'' are;

⇒ D(-5, 0), C''(-2, 0), A''(-3, -4), B''(0, -4)

The image of the point (x, y), following a reflection about the x-axis is the point (x, -y).

And, The difference in the coordinates of the parallelogram ABCD and A'B'C'D' is the change in the sign of the y-coordinates

Therefore, the transformation that gives the parallelogram A'B'C'D' from the parallelogram ABCD is a reflection about the x-axis

Thus, The difference between the coordinates of the vertices of the parallelogram A'B'C'D' and the parallelogram A''B''C''D'', is a change in the x-value by (-6), and a change in the y-value by (+1)

Therefore, the parallelogram A''B''C''D'' can be obtained from parallelogram A'B'C'D', by a translation of -6 units (left) in the x-direction and a translation of 1 unit, x in the y-direction.

Which gives;

The composition transformation that maps the pre-image ABCD to the final image A''B''C''D'', (given that in a composition transformation, the transformation to the right is done first) are; which is the option;

''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.

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Answer: 13.2%

Step-by-step explanation:

To find the percentage we need to use the formula: (original cost-new cost)/original cost *100

Plugging in the numbers: (38-33)/38*100=0.131578947368421*100=13.2%

The equation for your savings account can be represented as:

y = 50 + 10x

The equation for your friend's savings account can be represented as:

y = 25 + 10x

where x is the number of weeks and y is the total amount of money in the account.

The equation for the savings account can be determined by taking the initial amount of money and adding the weekly deposit over a certain number of weeks. The initial amount of money in your savings account is $50, and you plan to deposit $10 each week, so each week your balance will increase by $10.

Starting from the initial balance, after the first week, the balance will be $50 + $10 = $60. After the second week, the balance will be $60 + $10 = $70, and so on. We can represent this pattern using an equation:

y = 50 + 10x

where y is the balance after x number of weeks.

Similarly, for your friend's savings account, the initial balance is $25 and the weekly deposit is $10. So, each week the balance will increase by $10. Using the same pattern, the equation for your friend's savings account can be represented as:

y = 25 + 10x

where y is the balance after x number of weeks.

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