-5 is reduced by 2, the result is 26 less than twice the opposite of the number. What is the number

David's demand curve for gasoline is given by q1 = Y / p1, where q1 represents the quantity of gasoline consumed, Y represents income, and p1 represents the price of gasoline.

To derive David's demand curve for gasoline, we need to find the quantity of gasoline that David will consume at different prices.

David's utility function is given as U(q1, q2) = 90q1^0.8q2^0.2, where q1 represents the quantity of gasoline consumed and q2 represents the quantity of bread consumed.
To find David's demand for gasoline, we can use the concept of utility maximization. According to this concept, consumers will allocate their income in a way that maximizes their overall utility.

Let's assume David's income is Y, the price of gasoline is p1, and the price of bread is p2.

The total expenditure (TE) for David can be calculated as:
TE = p1 * q1 + p2 * q2
To maximize utility, we need to differentiate the utility function with respect to q1 and set it equal to zero:
dU/dq1 = 0

Differentiating the utility function, we get:
dU/dq1 = 90 * 0.8 * q1^(-0.2) * q2^0.2 = 0
Simplifying the equation, we have:
72 * q2^0.2 = 0

Since q2 is positive, we can divide both sides of the equation by 72 to solve for q2:
q2^0.2 = 0
Taking both sides to the power of 5, we have:
q2 = 0

This implies that David's demand for bread is zero, which means he does not consume any bread.
Substituting this value into the total expenditure equation, we have:
TE = p1 * q1
To find the demand curve for gasoline, we need to solve for q1 in terms of p1 and Y. Rearranging the equation, we get:
q1 = TE / p1 = Y / p1

Therefore, David's demand curve for gasoline is given by q1 = Y / p1, where q1 represents the quantity of gasoline consumed, Y represents income, and p1 represents the price of gasoline.

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Answer:

Step-by-step explanation:

Same tape length measures 63 units on top and 7 times m on bottom.

Make an equation and solve for m:

Count the boxes noted with m

Now

Boxes are equal

\(\\ \sf\longmapsto 7m=63\)

\(\\ \sf\longmapsto m=63/7\)

\(\\ \sf\longmapsto m=9\)

a. Pair 2 is selected.

b. Respiratory system, its function is to breathe. Digestive system, its function is to break down food into nutrients.

c. The two systems work together by sharing the region of the mouth and upper throat.

First picture in Pair 2 is Respiratory system, which its function is to breathe. Second picture in Pair 2 is Digestive system, which its function is to break down food into nutrients such as carbohydrates, fats and proteins. The respiratory system takes in oxygen from the air, and also gets rid of carbon dioxide. The digestive system absorbs water and nutrients from the food we consume.

The respiratory system is mainly used to transport air, whilst the digestive system is used to transport fluids and solids, from water and food we eat. The respiratory and the digestive systems share the area of the mouth and upper throat, in which air, fluids, and solids can be mixed.

The digestive system does homeostasis by ensuring that the stomach area has the right pH balance. The body uses both positive and negative mechanisms to perform homeostasis. If the body detects an imbalance, the other systems work together to counterbalance and restore the right equilibrium.

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The expression for a cubic function f will be \(f(x)=-3x^{3}+3x^{2}+6x\).

It is given that,

f(1) = 6

f(-1) = f(0) = f(2) = 0

We have to find the cubic function f which satisfies the given equations.

Let the cubic function f be:-

\(f(x)=ax^{3}+bx^{2}+cx+d\)

Where,

x is the variable

a, b, c, and d are constants

Putting f(0) = 0 in f(x), we get,

\(f(0)=a(0)^{3}+b(0)^{2}+c(0)+d=0\\\)

f(0) = 0 + 0 + 0 + d = 0

d = 0

Putting f(1) = 6 in f(x), we get,

\(f(1)=a(1)^{3}+b(1)^{2}+c(1)+d=6\\\)

f(1) = a + b + c + d = 6

a + b + c + d = 6

We know that, d = 0,

Hence,

a + b + c  + 0 = 6
a + b + c = 6   ....(1)

Putting f(-1) = 0 in f(x), we get,

\(f(-1)=a(-1)^{3}+b(-1)^{2}+c(-1)+0=0\\\\\)

f(-1) = -a + b - c =0

b = a + c  ...(2)

Putting (2) in (1), we get

(a + c) + b = 6

b + b = 6

2b = 6

b = 6/2

b = 3

Hence,

a + c = 3  ... (3)

Putting f(2) = 0 in f(x), we get,

\(f(2)=a(2)^{3}+b(2)^{2}+c(2)+0=0\\\)

f (2) = 8a + 4b + 2c =0

2(4a + 2b + c) = 0

4a + 2b + c = 0

4a + 2*3 + c = 0

4a + c + 6 = 0  

4a + c = -6 ...(4)

(4) - (3)

(4a + c - a - c) = (-6 - 3)

3a + 0 = -9

3a = -9

a = -9/3

a = -3

Hence,

-3 + c = 3

c = 3 + 3

c = 6

We have found:-

a = -3

b = 3

c = 6

d = 0

So the equation \(f(x)=ax^{3}+bx^{2}+cx+d\) becomes \(f(x)=-3x^{3}+3x^{2}+6x\)

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The value of the definite integral of the function is -9/2

The region beneath a curve between two set limits is a definite integral. The symbol for the definite integral is

\(\int\limits^a_b {x} \, dx\)

The area inside bounds is determined using definite integrals, which are defined as the sum of the areas.

a. The definite integral for this function is

\(\int\limits^1_ {-2} (-x^5 + 4x^3 - 4x - 2 \, dx\\= -\frac{9}{2}\)

b. The value of the definite integral of the function is;

\(\int\limits^\frac{3x}{4} _\frac{-x}{3} {-2sinx \, dx = no solution\)

The definite integral has no solution

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The information makes sense in different scenarios like manufacturing, baking, researching survey, etc.

A sample is a portion of a population that is used to represent the full population in statistics. Researchers frequently utilise samples to draw conclusions about the population since it might be difficult or impossible to collect data from the complete population. In order for the conclusions made from the sample to be applicable to the entire population, it is important to pick a sample that is representative of the wider population. Many techniques, such as cluster sampling, stratified sampling, and random sampling, can be used to choose samples.

The knowledge of biscuit preferences may come in handy in a variety of situations. Here are three potential instances:

A biscuit manufacturer wants to launch a brand-new taste. They may opt to create a chocolate chip or peanut butter flavor as those are the most popular ones based on the preferences data.

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Complete question -

A national sampling of cookie preferences showed that 75% of people like chocolate chip, 50% like peanut butter, and only 3% like coconut. The use of this information makes sense in which of the following scenarios? A. The school cafeteria decides to make 3 coconut cookies for each 100 students who buy lunch, even though it puts them over budget for desserts. B. A national cookie company is thinking of changing the recipe in their peanut butter cookies. C. A national cookie company decides to spend $5 million in advertising to convince people to eat coconut cookies. D. Tom is about to open a small bakery and is using the result of the sampling to decide what kind of cookies to offer.

The probability of a bill exceeding $300 is 0.0091.

A probability distribution that is symmetric about the mean is the normal distribution, also referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

For normal distribution z score = (X-μ)/σ

here mean= μ = 196

std deviation  = σ = 44.0000

probability of a bill exceeding

$300  = P(X>300)

          =P(Z>(300-196)/44)  

          =P(Z>2.36)

          =0.0091

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Step-by-step explanation:

this is the ans in my view

The average speed required to reach the concert in time is 61 miles per hour.

The average speed required to reach school in time is 27.567 miles per hour.

What is the average speed?

The average speed of an object is defined as the total distance travelled by an object in a particular interval of time or average time. Mathematically, average speed = total distance / total time taken. Its SI unit is m/s.

Calculation of the average speed

We are given that a concert starts in 5 hours and is 305 miles away from the house, i.e. time = 5 hours and distance  305 miles

Then the average speed in miles per hour is given by total distance / total time

Average speed = 305 / 5

= 61 miles per hour

Further, the time taken to reach school is 37 minutes which when converted to hours becomes 37 / 60 hour

The distance between school and home is 17 miles

So, the average speed = total distance / total time

= 17 / (37 / 60)

= (17 × 60) / 37

= 27.567 miles per hour

Hence, the average speed required to reach the concert in time is 61 miles per hour.

The average speed required to reach school in time is 27.567 miles per hour.

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the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13.

In a standard deck of 52 cards, there are four jacks and four 4s, for a total of 8 cards that are either a jack or a 4. The probability of selecting a jack or 4 can be found by dividing the number of favorable outcomes (8) by the total number of possible outcomes (52): P(jack or 4) = 8/52. This fraction can be reduced by dividing both the numerator and denominator by 4: P(jack or 4) = 2/13. Therefore, the probability of randomly selecting a jack or 4 from a standard deck of 52 cards is 2/13. Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in a wide range of fields, from gambling and sports to scientific research and data analysis. Understanding probability is important for making informed decisions, predicting outcomes, and assessing risks.

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Answer:

Step-by-step explanation:

w/8-4=20

add 4 to each side

w/8=24

multiply by 8 to clear out the w on one side

w=192

Answer: Choice B.

ln(3) + ln(4) + ln(5) + ln(6)

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

Explanation:

Refer to the diagram below. It shows four rectangles each of base 1. Their height varies depending on the output of the natural log function.

More specifically the heights are ln(3), ln(4), ln(5) and ln(6) from left to right. Note how this corresponds exactly to the points on the y = ln(x) curve such that they are the upper right corners of the Riemann Sum rectangles. These corner points are points A,B,C,D.

Since each base is 1 unit wide, this means each rectangle's area is equal to the height. More thoroughly, we say that

area = base*height = 1*f(x) = f(x), where x takes on the values from {3,4,5,6}

Side note: As the diagram shows, we have an overestimate of the actual area under the curve from x = 2 to x = 5.

Answer:

\(\huge\boxed{\sf x = 85}\)

Step-by-step explanation:

0.2x - 6 = 11

0.2x = 11 + 6

0.2x = 17

x = 17/0.2

\(\rule[225]{225}{2}\)

Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \purple {━━━━━━━━━━━━━━━━━━━━━━━━━━━━}\)

hope it helps!

The function is not normalizable and cannot be a wave function.

A wave function must satisfy two important conditions. First, it must be normalizable, meaning its integral over all space is finite.

Second, it must be single-valued and continuous.

(i) The function Ψ1​(x) = \(e^{-x^{5} }\) is acceptable as a wave function, since it is continuous everywhere and decays to zero as x → ±∞.

However, we must check if it is normalizable. The normalization condition for a one-dimensional wave function Ψ(x) is:

∫(-∞) to ∞ |Ψ(x)|²dx = 1

In this case, we have:

∫(-∞) to ∞ |Ψ₁(x)|² dx

= ∫(-∞) to ∞ \(e^{-2x^{5} }\) dx

This integral can be quite challenging to evaluate, but we can see that the integrand goes to zero faster than any power of x as x → ±∞.

Therefore, the integral is convergent and the function is normalizable.

Therefore, Ψ₁(x) is an acceptable wave function.

(ii) The function Ψ₂​(x) = cos(x - 2π/3) is not acceptable as a wave function, since it is not normalizable.

The normalization condition for a one-dimensional wave function Ψ(x) is:

∫( -∞) to ∞ |Ψ(x)|² dx = 1

In this case, we have:

∫(-∞) to ∞ |Ψ₂​(x)|² dx = ∫(-∞)to∞ cos²(x - 2π/3) dx

This integral is not convergent, since the integrand oscillates between 0 and 1 over an infinitely repeating interval.

Therefore, the function is not normalizable and cannot be a wave function.

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According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7

Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.

Given,

n = 66

We know that,

According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:

\(k=1+log_{2} n\)

Here, n is equal to 66 and by substituting the value to the equation we get:

\(k=1+log_{2} (66)\)

k = 7.0444

k ≈ 7

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The similarity lies in the fact that both lists contain the same set of numbers, but their order is determined by different criteria - one based on magnitude and the other based on distance from zero.

Let's order the numbers -3, 5, -10, and 16 as requested.

From least to greatest:

-10, -3, 5, 16

The ordered list from least to greatest is: -10, -3, 5, 16.

Now let's order the same numbers from closest to zero to farthest from zero:

-3, 5, -10, 16

The ordered list from closest to zero to farthest from zero is: -3, 5, -10, 16.

Regarding the similarity between the two lists, both lists contain the same set of numbers: -3, 5, -10, and 16. However, the ordering criteria are different in each case. In the first list, we order the numbers based on their magnitudes, whereas in the second list, we order them based on their distances from zero.

By comparing the two lists, we can observe that the ordering changes since the criteria differ. In the first list, the number -10 appears first because it has the smallest magnitude, while in the second list, -3 appears first because it is closest to zero.

Overall, the similarity lies in the fact that both lists contain the same set of numbers, but their order is determined by different criteria - one based on magnitude and the other based on distance from zero.

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The appropriate distribution to use in this case is the discrete probability distribution since the number of missed days of employees at the shoe store is limited to specific values with associated probabilities.

In a discrete probability distribution, the random variable can only take on specific, separate values with associated probabilities. In this scenario, the number of missed days of employees at the shoe store can only take values from 0 to 10, which are distinct and separate values.

To construct the discrete probability distribution, we need to know the probabilities associated with each possible number of missed days. These probabilities will determine the likelihood of each outcome occurring. The sum of all probabilities should be equal to 1, as it represents the total probability of all possible outcomes.

Once we have the probabilities for each possible number of missed days, we can plot the distribution and analyze the likelihood of different outcomes. The distribution will provide insights into the frequency and probability of various levels of employee absenteeism at the shoe store.

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Jorge will receive 9 hours in time off from work.

How many hours will Jorge get to take time off?

It is given that, Jorge has done overtime for 6 hours in this week. As per the Fair Labor Standards Act, for 6 hours of overtime work, he must be paid one and a half times the pay he gets per hour.

Instead of receiving an overtime pay for working 6 hours extra, Jorge decides to receive paid leaves from work, that is, he will get one and a half of the total hours for which he worked overtime.

As a result, the time off he receives from work = \(1\frac{1}{2} (6)\) hours

\(=\frac{3}{2}(6) = 9 hours\)

Thus, Jorge gets 9 hours in time off from work in return. The time that he earns for the overtime is equivalent to the pay he was supposed to receive for the overtime work.

What is Fair Labor Standards Act?

The Fair Labor Standards Act (FLSA) specifies standards for minimum wage, over-time compensation, recordkeeping, and youth employment that are applicable to workers in the private sector and in federal, state, and municipal governments.

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The probability that either event will occur is 0.83

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

Event A = 18

Event B = 12

Other Events = 6

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 18 + 12 + 6

Evaluate

Total = 36

So, we have

P(A) = 18/36

P(B) = 12/36

For either events, we have

P(A or B) = 30/36 = 0.83

Hence, the probability that either event will occur is 0.83

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Answer:

9 : 2 : 4

Step-by-step explanation:

Given

72 : 16 : 32 ( divide each part of the ratio by 8, the LCM of 72, 16, 32 )

= 9 : 2 : 4

This approximates to roughly 6/7 = 0.8571

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

Explanation:

Let's define the following

There are 30 students in the class total. This must mean A+B+C+D = 30.

We know that "There were 7 students who failed the test and also did not complete the assignment", meaning we can say D = 7.

We can also say A+B = 21 because this is the entire group of people who passed the test (whether they did the hw or not).

This means:

A+B+C+D = 30

(A+B)+C+D = 30

(21) + C + 7 = 30

C+28 = 30

C = 30-28

C = 2

We have 2 people who failed the test, but did the hw.

Because 20 students did the hw, we know that

A+C = 20

A+2 = 20

A = 20-2

A = 18

We have 18 students who passed the test and did the hw. This is out of 21 students who passed. From here on out, we only focus on this group of students because of the phrasing "given that they passed the test". This means we know 100% that whoever we picked, they passed the test.

The probability we're after is therefore:

18/21 = (3*6)/(3*7) = 6/7

Side note: It might help to sort the data into a table as shown below. Start with table 1, and the goal is to replace the placeholder letters with the proper numbers, to arrive at table 2. You'll have to use algebra as shown earlier to fill out the table.

Answer:

6/7

Step-by-step explanation:

It's correct trust me.

(a) A basis for R4 that includes v0 and v1 can be found by adding two linearly independent vectors to {v0, v1}.

To find a basis for R4 that includes v0 and v1, we need to add two linearly independent vectors to the set {v0, v1}. Let's call these vectors v2 and v3. As long as v2 and v3 are linearly independent from v0 and v1, they will form a basis for R4.

The choice of v2 and v3 can vary, but they must be chosen carefully to avoid linear dependence. Once v2 and v3 are determined, we will have a basis {v0, v1, v2, v3} for R4 that includes v0 and v1.

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The results indicate that encountering sales clerks who smile could potentially increase customer purchases.

From the information given, we have that;

The four stores in the smile condition were 36, 40, 36, and 44;

To determine the t-value, we need to first calculate the mean for the control condition, we have;

Mean = 36 + 40 + 36+ 44/4

Mean =126/4

Mean = 32

Mean for the smile condition;

Mean = 39

One can employ a t-test to compare the average values of the two situations in order to scrutinize the outcomes. With a significance level of 0. 05, a two-tailed test with six degrees of freedom would require a critical t-value of around 2. 447

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The answer to the question "difference of -72 and a product of -720?" is -9.

To find the sum of the two numbers, we can set up the following equations based on the given information:

Let the two numbers be x and y, where x > y.

x - y = -72 (since the difference between the numbers is -72)

xy = -720 (since the product of the numbers is -720)

We can solve these equations simultaneously using algebraic methods. One way to do this is to isolate one of the variables in one of the equations and substitute it into the other equation. For example, we can isolate y in the first equation by rearranging it to y = x + 72, and then substitute this into the second equation:

x(x + 72) = -720

Expanding the left-hand side, we get:

x^2 + 72x = -720

Rearranging the equation, we get:

x^2 + 72x + 720 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 1, b = 72, and c = 720. Plugging in these values, we get:

x = (-72 ± √(72^2 - 4(1)(720))) / (2(1))

Simplifying further, we get:

x = (-72 ± √(5184 - 2880)) / 2

x = (-72 ± √2304) / 2

x = (-72 ± 48) / 2

Now we have two possible values for x:

x1 = (-72 + 48) / 2 = -12

x2 = (-72 - 48) / 2 = -60

Since x > y, we take x = -12 and y = -72 - (-12) = -60 + 12 = -48.

Thus, the sum of the two numbers is -9, which is obtained by adding x and y:

-12 + (-48) = -9.

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Answer:

x={-2,-5,4}

Step-by-step explanation:

Isolate the X

Divide both sides by the coefficient: x= -2,-5,4

If Hanna is recovering hundreds of treasure chests from an ancient shipwreck. The ratio of chests recovered to time is always 3:1, since Hanna recovers 9 chests every 3 hours.

The table showing the number of treasure chests recovered by Hanna over time, assuming she can recover 9 chests every 3 hours:

Time (hours)     Number of Treasure Chests

3                              9

6                              18

9                              27

12                              36

15                              45

18                              54

21                              63

24                              72

27                              81

30                              90

33                              99

36                              108

39                              117

42                              126

45                              135

48                              144

51                              153

54                              162

57                              171

60                              180

As you can see, the ratio of chests recovered to time is always 3:1, since Hanna recovers 9 chests every 3 hours.

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Answer:

D

Step-by-step explanation:

This is because if u subsitute x with 17, 17x5 is 85 and 85+95= 180

\(\color{plum}\tt\bold{(D) \: 17}\)

Given :

▪︎Angle (5x)° and angle 95° are supplementary angles.

Which means :

\( = \tt5x + 95 = 180\)

\( = \tt5x = 180 - 95\)

\( = \tt5x = 85\)

\( \hookrightarrow\tt \color{plum}x = 17\)

Thus, the value of x = 17

Let us check whether or not we have found out the correct value of x by placing 17 in the place of x:

\( =\tt5 \times 17 + 95 = 180\)

\( =\tt 85 + 95 = 180\)

\( =\tt 180 = 180\)

Since the sum of both angles is equivalent to 180[85+95=180], we can conclude that we have found out the correct value of x.

Therefore, the correct option is (D) 17

\(\\ \sf\longmapsto 6x-4+x+17=90\)

\(\\ \sf\longmapsto 7x+13=90\)

\(\\ \sf\longmapsto 7x=90-13=77\)

\(\\ \sf\longmapsto x=11\)

Answer:

\(62 \degree\)

Step-by-step explanation:

Complementary Angles are added up to 90°

Therefore,

\(6x - 4 + x + 17 = 90 \\ 7x + 13 = 90 \\ 7x = 90 - 13 \\ 7x = 77 \\ \frac{7x}{7} = \frac{77}{7} \\ x = 11\)

So,

\(ZA = 6x - 4 \\ = 6 \times 11 - 4 \\ = 66 - 4 \\ = 62 \degree\)

Hope this helps you.

Let me know if you have any other questions :-)