To conserve water, many communities have developed water restrictions. the water utility charges a fee of $29, plus an additional $1.41 per hundred cubic feet (hcf) of water. the recommended monthly bill for a household is between $54 and $82 dollars per month. if x represents the water usage in hcf in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (round your answer to one decimal place.) 54 ≤ 1.41x 29 ≤ 82; to stay within the range, the usage should be between 17.7 and 37.6 hcf. 54 ≤ 1.41x 29 ≤ 82; to stay within the range, the usage should be between 17.7 and 58.2 hcf. 54 ≤ 1.41x − 29 ≤ 82; to stay within the range, the usage should be between 38.2 and 78.7 hcf. 54 ≤ 1.41x − 29 ≤ 82; to stay within the range, the usage should be between 58.9 and 78.7 hcf.

The branch of mathematics that analyzes situations in which players must make decisions and then receive payoffs most often used by economists is "game theory". So, option C is the correct answeer.

Game theory is a branch of mathematics that studies how people or organizations interact in situations where there are choices to be made and where the outcome of each choice depends on the choices made by others. It is often used in economics to model the behavior of firms and consumers in markets, and to analyze strategic interactions between competitors in oligopolistic industries.

One of the most famous examples of game theory is the prisoner's dilemma, which is a simple model that illustrates how two individuals might not cooperate, even if it appears that it is in their best interest to do so.

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The new account balance of Clare is calculated as $127.38 by using the given data.

A mathematical operation is a mathematical action. A mathematical operation includes addition, subtraction, multiplication, division, and computing the root.

In math, a word problem is a question expressed in one or more sentences that asks learners to apply their arithmetic skills to a'real-life' scenario. This implies that in order to understand the word problem, students must be conversant with the terminology linked with the mathematical symbols to which they are used.

Given:

Clare has a savings account balance of $102.38. She uses the ATM to deposit three cheques she received for her birthday. Each check was made out for $15.00. She then takes out $20 in cash.

Amount in her savings account = 102.38

Amount after depositing 3 checks = 102.38 + 3(15)

                                                         = 147.38

Amount after withdrawing $20 in cash = 147.38 - 20

                                                                = 127.38

Therefore, the new account balance of Clare is calculated as $127.38 by using the given data.

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Answer:

1,3,5,9,15,45

Step-by-step explanation:

All factors of 45 to get a whole number

Answer:

90, 135, 180, 225, 270... ∞

Step-by-step explanation:

All multiples of 45 are divisible by n

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Answer:

c ≈ 9.1 m

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

c² = 4.1² + 8.1² = 16.81 + 65.61 = 82.42 ( take square root of both sides )

c = \(\sqrt{82.42 }\) ≈ 9.1 m ( to the nearest tenth )

Answer:

-3.646 and 1.646

Step-by-step explanation:

Additionally, make sure to double check your math as that always helps.

Answer:

\(\sf Total \ amount \ of \ walnuts \ and \ pecans \ needed = \dfrac{7}{12}\)

Step-by-step explanation:

    \(\sf Amount \ of \ walnut \ needed = \dfrac{1}{4}\)

    \(\sf Amount \ of \ pecans \ needed =\dfrac{2}{6} =\dfrac{1}{3}\)

To find the total amount of walnut and pecans, we have to add the fractions.

LCM of 4 & 3 = 12

Equivalent fractions:

      \(\sf \dfrac{1}{4}=\dfrac{1*3}{4*3}=\dfrac{3}{12}\\\\\dfrac{1}{3}=\dfrac{1*4}{3*4}=\dfrac{4}{12}\)

Now, add

   \(\sf \dfrac{3}{12}+\dfrac{4}{12}=\dfrac{3+4}{12}\)

                  \(\sf = \dfrac{7}{12}\)

False. Calculating standard error is indeed important in statistics, as it serves a different purpose than the regular standard deviation of a single data set.

While standard deviation measures the variability or dispersion within a data set, standard error is used to measure the accuracy of a sample mean as an estimate of the true population mean.
1. Standard deviation measures the dispersion or spread of data points in a single data set. It helps you understand how much the individual data points deviate from the mean (average) of that data set.
2. Standard error, on the other hand, is a measure of how accurate a sample mean is in estimating the true population mean.

It is calculated by dividing the standard deviation of the sample by the square root of the sample size (n).
Standard Error (SE) = Standard Deviation (SD) / √n
3. As the sample size increases, the standard error decreases, indicating that the sample mean becomes a more accurate estimate of the population mean.

This is because larger sample sizes tend to have a smaller sampling error.
4. In hypothesis testing and confidence interval estimation, standard error plays a crucial role.

It helps to determine the margin of error and to assess the significance of differences between sample means.
5. While standard deviation is a useful measure for understanding variability within a single data set, standard error is essential for making inferences about the population based on the sample data.
In conclusion, both standard deviation and standard error are important in statistics as they serve different purposes. Ignoring standard error would lead to inaccurate conclusions about the population mean based on sample data.

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Answer:

the unit price on is $2.50

Step-by-step explanation:

61.5÷24.60

Assuming Ryan buys 61.5 ounces of lemonade for $24.60. The unit price is: $0.4.

Using this formula

Unit pice=Cost price/ Ounces of lemonade

Where:

Cost price=$24.60

Ounces of lemonade=6.15 ounces

Let plug in the formula

Unit price=$24.60/6.15

Unit price=$0.4

Therefore the unit price is: $0.4.

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Given :

The Dobson exit is halfway between the Mt. Airy exit and the Elkin exit. If the Elkin exit is located at (-5,-2) and the Dobson exit is located at (-1,4).

To Find :

How far is it from the Elkin exit to the Mt. Airy exit.

Solution :

E(-5,-2) , D(-1 ,4 ) .

It is also given that Dobson exit is halfway between the Mt. Airy exit and the Elkin exit.

Let , location of Elkin exit is A(h,k) .

So , point D in terms of A and E is given by :

\((\dfrac{h-5}{2},\dfrac{k-2}{2})\) .

Comparing it with given D :

\(\dfrac{h-5}{2}=-1\\\\h=3\) \(\dfrac{k-2}{2}=4\\\\k=10\)

Therefore , the location of Mt. Airy exit is ( 3, 10 ) .

Distance between Elkin exit to the Mt. Airy exit.

\(D=\sqrt{(5-3)^2+(-2-10)^2}\\\\D=12.17\ units\)

Therefore , distance between Elkin exit to the Mt. Airy exit is 12.17 units .

Hence ,this is the required solution .

Answer:

a= 50

Step-by-step explanation:

Divide 100 by the amount of variable which in this case is 2

100/2 = 50

Answer:

Hy

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Answer:

22x

Step-by-step explanation:

2x 2(6x+3)

2x 12x+6x

22x

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

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Answer:

Domain:  { 2 ,  3 ,  − 1 ,  6 }

Range: { 9 ,  4 ,  2 ,  1 }

Step-by-step explanation:

Answer:

Decimal value is 99

Step-by-step explanation:

To convert 01100011 to decimal, we use the zero index method by counting from the last digit

0 = 7

1 = 6

1 = 5

0 = 4

0 = 3

0 = 2

1 = 1

1 = 0

Then we proceed by multiplying the binary digits by 2 and raising them to the power of their zero-index equivalent

(0*2^7) + (1*2^6) + (1*2^5) + (0*2^4) + (0*2^3) + (0*2^2) + (1*2^1) + (1*2^0)

  =(0*128) + (1*64) + (1*32) + (0*16) + (0*8) + (0*4) + (1*2) + (1*1)

      =0 + 64 + 32 + 0 + 0 + 0 + 2 + 1

         = 64 + 32 +3

             =99

Answer:

H=horse

H=4(21-7)

Step-by-step explanation:

H=4(21-7)

H=4(14)

There were 56 horses.

The true comparison is 2/3 > 3/10.

Option (C) is correct.

What is a fraction?

A fraction is a mathematical representation of a part of a whole. It is written as two numbers separated by a slash (/) and represents the number of parts being considered out of the total number of parts in a whole. The number on the top is called the numerator and the number on the bottom is called the denominator.

To compare the amounts of water the scientist poured, we need to compare the fractions 2/3 and 3/10. To do this, we can convert both fractions to have a common denominator, which is the least common multiple of the denominators.

The least common multiple of 3 and 10 is 30. So, we can convert both 2/3 and 3/10 to 30 as the denominator:

2/3 = 20/30

3/10 = 9/30

Comparing the two fractions with a common denominator, we see that 20/30 is greater than 9/30. Therefore, the comparison that is true is:

C) 2/3 > 3/10

Hence, the true comparison is 2/3 > 3/10.

Option (C) is correct.

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Answer:

C cannot make a triangle

Step-by-step explanation:

One of these choices does not have 3 angles adding to 180.

A) adds to 180 degrees

B) B also adds to 180 degrees.

C) Adds to 169 degrees, so this set of 3 does not make a triangle.

D) Adds to 180

Answer:

3

Step-by-step explanation:

45/15 = 3

There are 3 touchdowns per 1 game

Answer:

the awnser should be. c

Step-by-step explanation:

because shes cutting them which divides them

Answer:

26

Step-by-step explanation:

f(x) = -9x + 8

f(-2)

______________

When we have a function f(x), x can be plugged in with anything, when plugged, the equation the function f(x) is tied too will also have x replaced with the value.

Therefore, if f(x) equals f(-2), -9(-2) + 8

Multiply :

-9(-2) + 8

18 + 8

26

The data sufficiency question if t and x are integers, so on finding the value of x both the given statements are not sufficient.

It is given that t and x are integers

Statement 1: x²/t² = 4/9

Let us test some values. There are many values of x and t that satisfy statement 1.
Here are two cases:

Case a: Taking x = 2 and t = 3. Noticing that x²/t² = 2²/3² = 4/9. So, here in this case x = 2

Case b: Taking x = 20 and t = 30. Noticing that x²/t² = 20²/30² = 400/900 = 4/9. So, here in this case x = 20

Since we cannot answer the given question with certainty, so statement 1 is NOT SUFFICIENT

Statement 2: It is given that x > 0 and t > 0 Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined

There are many values of x and t that satisfy BOTH statements. Here are two cases:

Case a: Taking x = 2 and t = 3. Noticing that x²/t² = 2²/3² = 4/9. So, here in this case x = 2

Case b: Taking x = 20 and t = 30. Noticing that x²/t² = 20²/30² = 400/900 = 4/9. So, here in this case x = 20

Since we cannot answer the given question with certainty, the combined statements are NOT SUFFICIENT

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To construct a proof with the specified premises and conclusion, we can utilize the three inference rules: → E (modus ponens), ∧ E (conjunction elimination), and ∧ I (conjunction introduction).

The goal is to prove the statement ∧ given the premises , T, → , and (( → ) ∧ T).

To prove ∧ , we can start by using the → E rule on the premises → and , which gives us . Next, we can apply the ∧ E rule on the obtained expression and the premise T to obtain . Now, we have two separate statements: and .

From the premise (( → ) ∧ T), we can use the ∧ E rule to obtain → and T. Finally, we can apply the ∧ I rule on the statements and to conclude the proof with the desired result ∧ . Therefore, we have successfully constructed a proof using the given premises and inference rules.

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1) Let's pick the 2nd equation and to eliminate the x variable, multiply by -2 then add both equations like this

2x+ 4y=10

-2X+ -2y=-30

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

2y = -20

y = -10

2) Now let's plug that y=-10 into one equation, usually the simpler one.

x +y = 15

x -10 = 15 add 10 to both sides

X = 15 +10

x=25

3) So the solution is S ={25, -10}

Answer:

10

Step-by-step explanation:

sqrt(100) is 10

Replace x and y with their values:

Sqrt (2 -14(-7))

Multiply 14 and -7

Sqrt(2 - -98)

Add

Sqrt(100)

Simplify to get 10

Answer = 10

True statements:

A)

It's true, because if we apply the horizontal line test to the graph, it passes. It is in fact a function

C)

It's true because the graph intercepts the y- axis for x = 0

F)

It´s true because the number of cars washed does relate to the amount of money in the band fundraiser account via a function.

The length of the radius of the circle is 4.9cm.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Calculation for the length of the radius of the circle-

In order to overcome this issue, we must first translate the angle from radians to degrees.

The central angle of circle is 7/6π rads = 210 degrees.

Length of the arc is 18 cm.

The formula of length of an arc is given as-

\(l_{a r c}=\frac{\theta}{360} * 2 \pi r\)

Let's change the values and find the solution.

\(\begin{aligned}&18=\frac{210}{360} * 2 \pi r \\&18=3.663 r \\&r=\frac{18}{3.663} \\&r=4.9 \mathrm{~cm}\end{aligned}\)

Therefore, the length of the radius of the circle is 4.9 cm.

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