The interval [0,3] is partitioned into n equal subintervals, and a number xi is arbitrarily chosen in the ith subinterval for each i. Then lim n -> infinity n E i=1 (6xi-3)/n

Answers

Answer 1

The limit of the sum (6xi-3)/n as n approaches infinity is 9, which means that as the number of subintervals in the interval [0,3] becomes larger and larger, the sum of the values (6xi-3)/n approaches 9.

The limit is a concept in mathematics that helps us understand what happens as a function or a sequence approaches a certain value.

In this particular problem, we are looking at the limit of a sum of values as the number of subintervals in the interval [0,3] approaches infinity.

The interval [0,3] is divided into n equal subintervals and a number xi is chosen arbitrarily in the ith subinterval. We then look at the sum of the values (6xi-3)/n for all n subintervals.

Mathematically, we can write this sum as:

S = (6xi-3)/n for i = 1, 2, ..., n

And the limit of S as n approaches infinity can be written as:

lim n -> infinity S = lim n -> infinity (6xi-3)/n

Now, we use the concept of a Riemann Sum to evaluate the limit of this sum. A Riemann Sum is a way of approximating the area under a curve by breaking it down into rectangles and summing their areas.

In our case, we can think of the sum S as a Riemann Sum for the function f(x) = 6x-3 over the interval [0,3]. As n approaches infinity, the width of the subintervals approaches 0, and the sum S approaches the definite integral of f(x) over [0,3].

Using the fundamental theorem of calculus, we can find the definite integral of f(x) over [0,3] as:

∫f(x)dx = 6x^2/2 - 3x evaluated from 0 to 3

And this value is 9, so the limit of S as n approaches infinity is 9.

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Related Questions

Which set of words describes the end behavior of the function f(x)=−5x(x−4)(x+5)(2x+3)?

Answers

Answer:

Falls to the left and rises to the right

Step-by-step explanation:

because

degree =5

leading coefficient =4 and positive it will rise to the right

those are tips to use to determine it :

1. Even and Positive: Rises to the left and rises to the right.

2. Even and Negative: Falls to the left and falls to the right.

3. Odd and Positive: Falls to the left and rises to the right.

4. Odd and Negative: Rises to the left and falls to the right

Snowflake the snowman wants to buy new scarves if each scarf cost $4.27 how much did snowflake spend if he buys 5

Answers

Answer:

21.35

Step-by-step explanation:

4.27 * 5 i hope this is one of your answers

Find the value of x.

Plsss help

Find the value of x.Plsss help

Answers

Answer:

x=6

Step-by-step explanation:

7x+5+13x-8+11x-3=180

31x-6=180

31x=186

x=186÷31

x=6

I wrote the wrong answer so I erased it

Write 28.63 in expanded notation and word form.

Answers

Answer:

Answer below

Step-by-step explanation:

Expanded form : 20 + 8 + 0.6 + 0.03

Expanded form is a way of writing numbers to see the individual math value of digits.

Word form: twenty eight point six three.

HOPE THIS HELPED

A wholesaler gets 1.5% commision on the total annual sales and a bonus of 2% on the sales above Rs. 20,00,000. If, in a particular yearm the wholesaler recieved as bonus and commision the sum of Rs. 65000 in all, find the total sales of the year.

Answers

The total sales of the year after is Rs. 1857143

How to find the total sales after commission?

He gets 1.5% commission on the total annual sales and a bonus of 2% on the sales above Rs. 20,00,000.

Therefore, since he received a bonus, the sale is over Rs. 20,000.

Hence,

let

x = total sales

Therefore,

1.5% of x + 2% of x   = 65000

1.5 / 100 × x + 2 / 100 × x = 65000

0.015x +0.02x = 65000

0.035x = 65000

x = 65000 / 0.035

x = 1857142.85714

Therefore,

total sales = Rs. 1857143

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What is the volume of a sphere that has a diameter of 9 units

Answers

Answer:

V≈381.7

Step-by-step explanation:

Answer:

V≈381.7

Step-by-step explanation:

What is the volume of a sphere that has a diameter of 9 units

A runner sprinted 103.76 yd to finish a race.
Use the table of facts to find the distance she sprinted in feet.
Round your answer to the nearest tenth.

Answers

Answer:

311.3 feet

Step-by-step explanation:

1 yard = 3 feet

Therefore, 103.76 yards = 311.28 feet (by multiplying 103.76 by 3)

Rounding to the nearest tenth gives us 311.3 feet.

In a study of the relationship of the shape of a tablet to its dissolution time, 6 disk-shaped ibuprofen tablets and 8 oval-shaped ibuprofen tablets were dissolved in water. The dissolve times, in seconds, were as follows:
Disk: 269.0, 249.3, 255.2, 252.7, 247.0, 261.6
Oval: 268.8, 260.0, 273.5, 253.9, 278.5, 289.4, 261.6, 280.2 Can you conclude that the mean dissolve times differ between the two shapes? Conduct a hypothesis test at the
α = 5% level.
a. State the appropriate null and alternative hypotheses.
b. Compute the test statistic.
c. Compute the P-value.
d. State the conclusion of the test in the context of this setting.

Answers

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Let μ1 be the mean dissolution time for disk-shaped ibuprofen tablets and μ2 be the mean dissolution time for oval-shaped ibuprofen tablets.

The random variable is μ1 - μ2 = difference in the mean dissolution time for disk-shaped ibuprofen tablets and the mean dissolution time for oval-shaped ibuprofen tablets.

We would set up the hypothesis.

a) The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

For disk shaped,

Mean, x1 = (269.0 + 249.3 + 255.2 + 252.7 + 247.0 + 261.6)/6 = 255.8

Standard deviation = √(summation(x - mean)²/n

n1 = 6

Summation(x - mean)² = (269 - 255.8)^2 + (249.3 - 255.8)^2 + (255.2 - 255.8)^2+ (252.7 - 255.8)^2 + (247 - 255.8)^2 + (261.6 - 255.8)^2 = 337.54

Standard deviation, s1 = √(337.54/6) = 7.5

For oval shaped,

Mean, x2 = (268.8 + 260 + 273.5 + 253.9 + 278.5 + 289.4 + 261.6 + 280.2)/8 = 270.7375

n2 = 8

Summation(x - mean)² = (268.8 - 270.7375)^2 + (260 - 270.7375)^2 + (273.5 - 270.7375)^2+ (253.9 - 270.7375)^2 + (278.5 - 270.7375)^2 + (289.4 - 270.7375)^2 + (261.6 - 270.7375)^2 + (280.2 - 270.7375)^2 = 991.75875

Standard deviation, s2 = √(991.75875/8) = 11.1

b) Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

Therefore,

t = (255.8 - 270.7375)/√(7.5²/6 + 11.1²/8)

t = - 3

c) The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [7.5²/6 + 11.1²/8]²/[(1/6 - 1)(7.5²/6)² + (1/8 - 1)(11.1²/8)²] = 613.86/51.46

df = 12

We would determine the probability value from the t test calculator. It becomes

p value = 0.011

d) Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, we can conclude that at 5% significance level, the mean dissolve times differ between the two shapes

The area of a rectangle is 40 square inches. The rectangle is 8 inches long. How wide is the rectangle?

A. 3 inches
B. 32 inches
C. 5 inches
D. 13 inches

Answers

Answer:

C. 5 inches

Step-by-step explanation:

I’m area you have to multiply L • W

But since we don’t know the width we can divide the length by the area.


40/8 = 5

So the answer would be 5.

Another way to solve this problem is with using guess and check.


I hope it helps! Have a great day!

Anygays~

Answer:

C. 5 inches

Step-by-step explanation:

Use the numbers we have in the word problem, so you´d divide 40 by 8 since you´re trying to find the width. 40 is the area and 8 is the length so divide it tofind the width.

40/8 = 5

ANSWER: 5 inches

I hope it helps! Have a great day!

Andrea runs a fruit store. She started Sunday with 20 cherries in stock. During the day, she sold 17 cherries and got a shipment of fresh cherries. The shipment contained 4 times as many cherries as she started the day with. How many cherries does Andrea have in stock at the end off the day?


answer:


example ​

Answers

Answer:

Um.

Step-by-step explanation:

Could you give an example of what? Or no.?

3.
What is the value of the expression 2x^3y when
x=-2 and y = 32

IF YOU GET THIS RIGHT I WILL MARK BRAINLIEST

Answers

Answer:

The answer is 2^97

Step-by-step explanation:

I calculated it I am sure it is correct

Have a wonderful rest of your day,

Katharine Chavez

will give brainlisttttt for who first

will give brainlisttttt for who first

Answers

Answer:

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Help! Look at the figure. If mzJ = 55, find m
90

35

70

55

Help! Look at the figure. If mzJ = 55, find m90357055

Answers

The value of the required missing angle is;

m<JKM = 35°

How to find the missing angle of the triangle?

We know from geometry that the sum of angles in a triangle sums up to 180 degrees.

Now, we are trying told that in the given Triangle that the angle m<J = 55 degrees.

We also see that the angle <KMJ is equal to 90 degrees becasue it is a right angle.

Thus to find the angle m<JKM, we can write the name expression as;

m<JKM = 180 - (90 + 55)

m<JKM = 35°

Thus that's the value of the required missing angle.

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Reagan surveyed a number of her classmates about what time they usually go to bed. Of the fifteen classmates she asked, three said 9 p.m. What percent of the students is this? %

Answers

Answer:

Reagan surveyed a number of her classmates about what time they usually go to bed. Of the fifteen classmates she asked, three said 9 p.m. What percent of the students is this?

20%

Reagan surveyed a number of her classmates about what time they usually go to bed. Of the fifteen classmates she asked, three said 9 p.m. What central angle measure would you use to represent this group on a circle graph?

72°

Reagan surveyed a number of her classmates about what time they usually go to bed. Of the fifteen classmates she asked, nine said 10 p.m. What percent of the students is this?

60%

Step-by-step explanation:

help i tihnk i know the answers but unsure

help i tihnk i know the answers but unsure

Answers

Gender is categorical nominal, end-of-the-year stock classification is categorical and ordinal, and distance is quantitative and ratio.

What is the difference between quantitative and categorical variables?

Quantitative variables are measured with numbers. Some examples include:

Weight measured in kilos

The distance measured in meters or kilometers

Time measured in seconds or hours

On the other hand, a categorical variable is defined by features, categories, or concepts rather than numbers. Here is an example:

Breeds of dogs: Poodles, Boston Terriers, German shepherds, etc.

Moreover, variables can be classified as:

Nominal: Data can be categorized but not ranked.Ordinal: Data can be both categorized and ranked.Interval: Same properties as ordinal but can have values below zero.Ratio: Same properties as ordinal but does not have values below zero.

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The instructor noted the following scores on the last quiz of the semester for 8 students. Find the range of this data set 59,61,83,67,81,80,81,100

Answers

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

A pizza was divide
into 12 slices. Kesh
ate 2 slices. Jorge
ate 3 slices. What
fraction of the pizza
was left over?

Answers

Total number of slices = 12

No. of slices eaten by Kesh = 2

No. of slices eaten by Jorge = 3

No. of slices left

= Total number of slices - (No. of slices eaten by Kesh + No. of slices eaten by Jorge)

= 12 - (2 + 3)

= 12 - 5

= 7

Fraction of the pizza left

= No. of slices left/Total number of slices

= 7/12

Answer: 7/12

Find the total amount of pizza eaten.

Kesh = 2 slices

Jorge = 3 slices

Total eaten: 5/12

Subtract 5/12 from 12/12.

12/12 - 5/12 = 7/12

Answer = 7/12

Hope this answer helped!

Four boys compare the numbers on their football jerseys. Parker has the number 55. Nick has 49. Marshall has 57, and Leon has 59. Whose jersey has a prime number?

Answers

Leon- 59 is a prime number the rest are not

Answer:

Leon's jersey has a prime number

Step-by-step explanation:

Let f(x) = 5(3)x

The graph of f(x) is stretched vertically by a factor of 2 to form the graph of g(x).

Choose the equation of g(x).

Responses

g(x) = 10(3)xg(x) = 10(3)x

g(x) = 7(3)xg(x) = 7(3)x

g(x) = 2(3)xg(x) = 2(3)x

g(x) = 5(6)x

Answers

The required equation is g(x) = 10(3)x which is the correct answer would be an option (A).

The graph of g(x) is obtained by stretching the graph of f(x) vertically by a factor of 2.

Since the vertical stretch of a graph multiplies the y-coordinates of each point on the graph by a constant factor, the equation of g(x) must be obtained by multiplying the y-coordinate of each point on the graph of f(x) by 2.

In the given equation f(x) = 5(3)x, the y-coordinate of each point on the graph of f(x) is 5(3)x.

Thus, to stretch the graph of f(x) vertically by a factor of 2, we need to multiply this y-coordinate by 2 to get the y-coordinate of the corresponding point on the graph of g(x). This gives us the following equation for g(x):

⇒ g(x) = 2 × 5(3)x = 10(3)x

Therefore, the required equation is g(x) = 10(3)x.

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Hannah went shopping for a new phone. The listed price of the phone was $48, but
the price with tax came to $50.40. Find the percent sales tax.

Answers

Answer:

5%

Step-by-step explanation:

50.40 - 48 = 2.4.

The sales total sales tax was $2.40.

2.4 is 5% of the original $48 that was the listed price of the phone.

Use inductive reasoning to determine the next two terms in each sequence: a) 1, 3, 7, 15, 31 ....

Answers

Answer:

63,127

Step-by-step explanation:

the interval between each number is multiplied by 2

such as between 1 and 3 we have 2 so 2×2=4

the 4+3=7 and so on

Answer: 63, 127

Step-by-step explanation: 1+2=3; 3+4=7; 7+8=15; 15+16=31; 31+32=63; 63+64=127

Or, if we call the first value  a1 , the sequence is given by  an=2n−1

The first approach to analyzing almost any sequence is to look at the differences of successive elements. In this sequence, that’s 2, 4, 8, 16, 32. That makes the answers above pretty easy.

For a certain company, the cost for producing x items is 60x+300 and the revenue for selling x items is 100x−0.5x2 .



The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!



Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)



Part b: Find two values of x that will create a profit of $50 .



The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter. To enter a−−√ , type sqrt(a).

Answers

The equation for the profit from selling the items is P =  40x-0.5x²-300. The values of x are 10 and 70.

How to solve for the expression

We have the cost function in this question to be

Cx = 60x+300

Revenue = 100x−0.5x²

A. The revenue function is stated as the revenue - cost

= (100x−0.5x²)-60x+300

We have to open the equation

40x-0.5x²-300

B. when profit is 50 dollars

50 = 40x-0.5x²-300

We have to multiply both sides by 10

500 = 400x - 5x² - 3000

We have to collect like terms and form a quadratic equation

5x² - 400x - 3500 = 0

We have to solve the quadratic equation above using a quadratic calculator.

Hence

x = 10, 70

So the two values that would create a profit of 50 dollars is 10 and 70.

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In Rebecca's neighborhood, 89% of the houses have garages and 48% have a
garage and a pool. What is the probability (in percent) that a house in her
neighborhood has a pool, given that it has a garage? Round your answer to 1
decimal place.

Answers

why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

What multiply 12 and add to get -7

Answers

The answer is 3
Explantion:

I will give extra points please help

I will give extra points please help

Answers

Answer:

14.2

Step-by-step explanation:

The error function, or erf, is defied as x
erf(x)=2/π ∫ e^-u^2 du
0
The error function cannot be written in terms of elementary functions; this is the simplest way to write it. Do a substitution, changing the limits of integration, to write the following integral as aerf(bx), where a and b are constants. Fill in the blanks with these constants. x
∫ e^-5t^2 dt =| ___ erf ( ___ x)|
0

Answers

As per the error function, \(\int e^{-5t^2} dt\) is a erf(bx) | = 0

To illustrate this concept, let us consider the integral ∫ e^(-5t²) dt with limits of integration from 0 to x. We can rewrite this integral in terms of the error function by making the substitution u = √5t, which gives us du/dt = √5 and dt = du/√5. Thus, the integral becomes ∫ (e^-u²) (du/√5), with limits of integration from 0 to √(5x²).

Next, we can express the integrand as e^(-u²) = (2/√π) ∫ e^(-v²) dv, which follows from the standard result that ∫ e^(-x²) dx = √π/2. Substituting this expression into our integral, we obtain:

∫ (e^-u²) (du/√5) = (2/√(5π)) ∫ ∫ e^(-v²) du dv,

with limits of integration from 0 to √5x and 0 to u, respectively. Interchanging the order of integration, we get:

∫ (e^-u²) (du/√5) = (2/√(5π)) ∫ ∫ e^(-v²) dv du

= (2/√(5π)) ∫ e^(-v²) (u=0 to u=√5x) dv

= (2/√π) ∫ e^(-5x²) dx.

Therefore, we have shown that the integral ∫ e^(-5t²) dt with limits of integration from 0 to x can be expressed as:

| (2/√π) ∫ e^(-5x²) dx = a erf(bx) |,

where a = √(2/π) and b = 1/√5. Here, erf(bx) denotes the error function evaluated at the argument bx.

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Three blocks are shown. Which statement is correct?
A. Block A has the greatest density
B. Block B has the greatest density
C. The density of Block A is equal to the density of Block B
D. The density of Block B is equal to the density of Block C

Three blocks are shown. Which statement is correct?A. Block A has the greatest densityB. Block B has

Answers

Answer:

Block A has greatest density because it also the biggest.

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Please look at photo. Thank you!
Polynomial and rational functions:

A) Find all x and y intercepts. Check all that apply:
X intercepts: 4, 0, 1, and/or none.
Y intercepts: 1, 4, 0 and/or none.

B) write the equations for all vertical and horizontal asymptotes. Enter the equations by writing “and” or “none” when necessary.

C) find the domain and range of f. Write each answer as an interval or union of intervals.

Please look at photo. Thank you! Polynomial and rational functions:A) Find all x and y intercepts. Check

Answers

A) All x- and y-intercepts include the following:

x-intercepts: none.

y-intercept: 1.

B) The equation for vertical asymptote is x = 4 and the equation for horizontal asymptote is y = 0.

C) The domain and range of f are:

Domain = [-∞, 4) U [4, ∞]

Range = [0, ∞]

What is the x-intercept?

In Mathematics, the x-intercept is the point at which the graph of a function crosses or touches the x-coordinate and the y-value or value of "y" is equal to zero (0).

Part A.

Based on the graph of this rational function, the x-intercept and y-intercept include the following:

x-intercept: none.

y-intercept: 1.

Part B.

An equation that represents the vertical asymptote is x = 4 while the equation represents the horizontal asymptote is y = 0 because the line does not cross those points.

Part C.

By critically observing the graph of this rational function, we can logically deduce the following domain and range:

Domain = [-∞, 4) U [4, ∞] or {x|x ≠ 4}.

Range = [0, ∞] or {y|y ≥ 0}.

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(-5)*8 using commutative property of multiplication

Answers

Using the commutative property for (-5) * 8, we can say that;  (-5) * 8 = 8 * (-5)

What is Commutative Property of Algebra?

The commutative property of algebraic multiplication states that changing the order of factors does not change the product. For example:

4 × 3 = 3 × 4

Similarly, 5 * 6 = 6 * 5

Now, we want to use commutative property to use (-5) * 8. Thus, we can say that;  (-5) * 8 = 8 * (-5)

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Suppose that you want to begin saving money to buy a house valued at $300,000. The bank recommends that you have a 20% down payment before it approves a loan for the remaining difference. How much money do you need to save before you will be approved for a loan? What is the remaining difference that you will need to borrow?

Answers

Answer:

$60,000 as down payment and remaining difference for loan is 300,000 - 60,000 = $240,000.

The money you need to save before you will be approved for a loan is $60,000 and the remaining difference that you will need to borrow is $2,40,000

What is a percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100.

What is a loan?

A loan is money, property, or other material goods given to another party in exchange for future repayment of the loan value amount with interest.

Given value of the house is $300,000.

The bank recommends that you have a 20% down payment before it approves a loan i.e. is $300,000× 20% = $60,000

The remaining difference that you will need to borrow is $300,000 - $60,000= $2,40,000

Thus the money you need to save before you will be approved for a loan is $60,000 and the remaining difference that you will need to borrow is $2,40,000

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The Consumer Price Index (CPI) is a measure of the average change in price over time from a designated reference period, at which it equals 100. The index is based on prices of basic consumer goods and services. The table provided lists the CPI for several years from 1960 to 2012. If the price change in cars parallels the change in the CPI, what would a car sell for (to the nearest dollar) in 2012 if a comparable model sold for $13,000 in 1999? Which line below fromBradstreet's poem containsinverted syntax?A. "Framed by that mighty Architect,"B. "No candle e'er shall shine in thee,"C. "Nor bridegroom's voice e'er heard shallbe." How does not having an education affect the economy of South Sudan A natural increase in population occurs when the - of nation is greater than its death Write x^2 - 8x + 10 in the form (x + a)^2 + B Place the events leading up to the French Revolution in order.first event: second event: third event: fourth event: fifth event: sixth event: final event:Answer choices: 1) King Louis XVI is captured and then executed2) the king asks that the estates general convene3) the king's financial experts come up with ideas to relieve national debt4) the declaration known as the tennis court oath is sworn5) the hated royal political prison, The bastille is captured6) the third estate forms the national assembly7) the national assembly passes the declaration of the rights of man and the citizen in 1789 What is the solution to use the following equation 5(2x-6)+20=10 On average, Gil reads 57 pages in a book each week.How many pages des Gil read in 12 weeks? Find any rational number between -5.25 and -5.26 What is the main conflict of thisstory? Turn to a partner andsummarize "The Dog and the Wolf." I need help on this!!I dont see the lateral height, how do I solve for this?? What is the value of n in the equation 60+n\3=84+n/15 you need to use a gauge to figure out how much_ is in your tires How are extremists better than moderates? if you have a complaint about a bank in connection with any of the federal credit laws, who should you contact? icd 10 anemia: ______ 1. What are the names of the two major political parties in the United States today? 5. Which of the following can produce a therapeutic response? A drug that is:Bound to plasma albuminConcentrated in the bileNot absorbed from the GI tractUnbound to plasma proteins will someone also please check these answers, thanks.If a stock-market crash lowers people's wealth, what would be the effect on the market for minivans? A Demand increases Demand decreases Supply increases Supply decreases Question 10 8 Points Two driv A positively charged subatomic particle in the nucleus of an atomAtomProtonsElectronsNeutronsElectrical charge