Algebraically calculate the following limit exactly: lim ℎ→0

Hey there!

First, let's take all of the expenses and change the ones that aren't monthly into monthly.

Groceries: $800/month

Car insurance: $87.5/month

Gasoline: $100/month

Now, let's add together all of our expenses

1090+800+125+87.5+100+200+50=2452.5

Now, we subtract that from her salary.

2300-2452.5=-152.5

Therefore, Rebecca's net monthly cash flow is -$152.5. She should spend a bit less on groceries, not do so much miscellaneous, find a place that charges less rent, drive less, etc. so she isn't spending more than she earns.

I hope that this helps! Have a wonderful day!

Answer:

A sample size of at least 531 is required.

Step-by-step explanation:

We are lacking the confidence level to solve this question, so i am going to use a 90% confidence level.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Find the required sample size for the new study.

A sample size of at least n is required.

n is found when [tex]M = 0.05[/tex]

We have that [tex]\sigma = 0.7[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.05 = 1.645*\frac{0.7}{\sqrt{n}}[/tex]

[tex]0.05\sqrt{n} = 1.645*0.7[/tex]

[tex]\sqrt{n} = \frac{1.645*0.7}{0.05}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.645*0.7}{0.05})^{2}[/tex]

[tex]n = 530.4[/tex]

Rounding up

A sample size of at least 531 is required.

Answer:

Center line = 46

UCL = 46.84852

LCL = 45.15148

Step-by-step explanation:

Given:

Standard deviation = 0.8

Mean, u = 46

Sample size, n= 8

First calculate the estimated standard deviation:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{0.8}{\sqrt{8}} = 0.282843[/tex]

a) The center line, X', would be the average across all components. Here the average across all 960 bottles is 46

Therefore,

[tex] X' = 46 [/tex]

b) The upper control limit, UCL:

UCL = u + 3s

= 46 + 3(0.28284)

= 46 + 0.84852

= 46.84852

c) The upper control limit, LCL:

LCL = u + 3s

= 46 - 3(0.28284)

= 46 - 0.84853

= 45.15148

Answer:

I don't know

Step-by-step explanation:

but that looks like chemistry not biology

Answer: F.) 7 triangles

Step-by-step explanation:

Congruent means completely equal in side lengths and angles. Think of this weird figure like 4 triangles that are see through and are covering a diamond underneath

Of those 4 "see through triangles", there are 3 equal to ΔABC

Now on the diamond underneath, there is another 4. Its hard to actually explain what I mean, but take two triangles from that dimaond. Theyre gonna be congruent to ΔABC.

That's 4 + 3 = 7 total triangles

Answer:

A.

Step-by-step explanation:

Volume of cone = 1/3πr²h

= (1/3)(3.14)(1.5)²(5)

= (1/3)(3.14)(2.25)(5)

= (1/3)(35.3)

= 11.78

≈ 11.8 cubic inches

Answer:

9.72% probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.

Step-by-step explanation:

For each theft, there are only two possible outcomes. Either the need to buy drugs is the reason of the theft, or it is not. Each theft is independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

In a certain city district the need for money to buy drugs is stated as the reason for 70% of all thefts.

This means that [tex]p = 0.7[/tex]

Find the probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.

This is P(X = 3) when n = 7. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]

9.72% probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.

Answer:

q = 0.5 quarts of 100% antifreeze

Step-by-step explanation:

q = quarts of pure antifreeze

Set this up as a weighted combination of the mixtures.

(100%)(q) + (10%)(4) = (20%)(q + 4)

100q + 40 = 20(q + 4)

5q + 2 = q + 4

4q = 2

q = 0.5 quarts of 100% antifreeze

Answer:

8 hours

Step-by-step explanation:

Solve with a proportion

[tex]\frac{12}{5}[/tex] = [tex]\frac{19.20}{x}[/tex]

Multiply 5 by 1.6 to get x

5 x 1.6 = 8

Answer:

All college freshman is called Population and Right handed students are excluded is called sample from Population

Step-by-step explanation:

Explanation:-

Population:-  The total of the observations which we are concerned

given data all college freshman is called Population

Sample :-

A sample is a subset of a Population

Given data  all college freshman is called Population and Right handed students are excluded is called sample from Population

Answer:

  -3i +-12j

Step-by-step explanation:

P2 -P1 = (-1-2, -6-6) = (-3, -12)

In terms of unit vectors i and j, this is -3i -12j.

Answer:

Step-by-step explanation:

Rearranging the weights in ascending order, it becomes

5.4, 5.7, 5.7, 5.8, 6.0, 6.6, 7.1, 7.1, 7.5, 7.5, 8.1, 8.7, 9.3, 9.4, 9.4

The formula for determining the percentile is expressed as

n = (P/100)N

Where

n represents the value of the given percentile

P represents the given percentile

N represents the number of items(weights)

From the information given, the number of items, n is 15

P = 53

Therefore,

n = (53/100) × 15

n = 7.95

n = 8

Therefore, the weight that represents the 53rd percentile is the 8th value. It becomes 7.1

53rd percentile is 7.1

Answer:

-7,9

Step-by-step explanation:

x-1=-8

x=-7

x-1=8

x=9

Answer:

Option B is correct.

It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5

Step-by-step explanation:

Complete Question

Six measurements were made of the magnesium ion concentration (in parts per million, or ppm) in a city's municipal water supply, with the following results. It is reasonable to assume that the population is approximately normal.

170 201 199 202 173 153

Based on a 95% confidence interval for the mean magnesium ion concentration, is it reasonable to believe that the mean magnesium ion concentration may be greater than 199.5? (Hint: you should first calculate the 95% confidence interval for the mean magnesium ion concentration.)

A) The likelihood cannot be determined.

B) Yes

C) No

Solution

For this question, obtaining the confidence interval will give a clear solution to the problem.

Since the Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence, if the range obtained contains values greater than the standard we are comparing against (199.5), then the confidence interval proves that the mean magnesium ion may be greater than 199.5.

But to obtain the confidence interval, we need the mean and standard deviation for the sample.

170, 201, 199, 202, 173, 153

Mean = (sum of variables)/(total number of variables)

Sum of variables = 170+201+199+202+173+153 = 1098

Total number of variables = 6

Mean = (1098/6) = 183

Standard deviation = σ = √[Σ(x - xbar)²/N]

x = each variable

xbar = mean = 183

N = number of variables = 6

Σ(x - xbar)² = (170-183)² + (201-183)² + (199-183)² + (202-183)² + (173-183)² + (153-183)²

= 169 + 324 + 256 + 361 + 100 + 900

= 2110

σ = √(2110/6) = 18.75

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = 183

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population mean and standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 6 - 1 = 5.

Significance level for 95% confidence interval

(100% - 95%)/2 = 2.5% = 0.025

t (0.025, 5) = 2.57 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 18.75

n = sample size = 6

σₓ = (18.75/√6) = 7.656

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 183 ± (2.57 × 7.656)

CI = 183 ± 19.675

95% CI = (163.325, 202.675)

95% Confidence interval = (163.3, 202.7)

It is reasonable to believe that the mean magnesium ion concentration may be greater than 199.5 as the confidence interval obtained contains values that are greater than 199.5

Hope this Helps!!!

Answer:

answer is 2/3

Step-by-step explanation:

probability it is an eclair is 1/15=3/(3+2x+6+x)= 1/(x+3)

so x+3=15 and then x = 12

so the probability it is a humbug is (2*12+6)/(3*12+9) = 30/45 = 2/3

Answer:

The undefined term which is used to define an angle is line i.e., . Further explanation: In geometry the three terms which are considered to be undefined are line, point and plane.

Answer:

Line

Step-by-step explanation:

A line is a undefined term used to define a angle. An angle is the corner that is created where two non-parallel lines meet/ intersect

Answer:

a) 20.44% probability that none of the selected adults say that they were too young to get tattoos.

b) 35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) 56.34% probability that the number of selected adults saying they were too young is 0 or 1.

d) No

Step-by-step explanation:

For each adult, there are only two possible outcomes. Either they say they were too young when they got their tattoos, or they don't say that. Each adult is independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

18% say that they were too young when they got their tattoos.

This means that [tex]p = 0.18[/tex]

Eight adults who regret getting tattoos are randomly selected

This means that [tex]n = 8[/tex]

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{8,0}.(0.18)^{0}.(0.82)^{8} = 0.2044[/tex]

20.44% probability that none of the selected adults say that they were too young to get tattoos.

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{8,1}.(0.18)^{1}.(0.82)^{7} = 0.3590[/tex]

35.90% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

Either a. or b.

20.44 + 35.90 = 56.34

56.34% probability that the number of selected adults saying they were too young is 0 or 1.

d. It we randomly select 9 adults. Is 1 a significantly low number who day that they were too young to get tattoos?

Now [tex]n = 9[/tex]

It is significantly low if it is more than 2.5 standard deviations below the mean.

The mean is [tex]E(X) = np = 9*0.18 = 1.62[/tex]

The standard deviation is [tex]\sqrt{V(X)} = \sqrt{n*p*(1-p)} = \sqrt{9*0.18*0.82} = 1.15[/tex]

1 > (1.62 - 2.5*1.15)

So the answer is no.

Answer:

7x+6 = 6x-3

Step-by-step explanation:

2 (x + 3) + 5 x = 3 (2 x - 1)

Distribute

2x+6+5x = 6x-3

Combine like terms

7x+6 = 6x-3

Answer:

7x + 6 = 6x - 3                                  Option A

Step-by-step explanation:

Now Jalesa wants to simplify this equation.

Firstly applying the distributive property

Distribute the 2 over the parenthesis and distribute the over the parenthesis

that is,

2*x + 2*3 + 5x = 3*2x - 3*1

2x + 6 + 5x = 6x - 3

After that combine like terms

2x + 5x + 6 = 6x - 3

7x + 6 = 6x - 3

Result is:

7x + 6 = 6x - 3

That's the final answer.

Answer:

Step-by-step explanation:

Consider the augments matrix (the right most column is  the extra vector).

[tex]\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right][/tex]

By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix

[tex]\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right][/tex]

Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.

Answer:

(-3,2) is not a solution.

Step-by-step explanation:

The solution of a linear inequality in two variables like [tex]Ax + By > C[/tex] is an ordered pair [tex](x, y)[/tex] that produces a true statement when the values of x and y are substituted into the inequality.

To find if (-3,2) is a solution of [tex]7x+9y>-3[/tex], you must substitute this point into the inequality.

                                                 [tex]7\left(-3\right)+9\left(2\right)>-3\\\\-21+18>-3\\\\-3>-3[/tex]

Because -3 is not greater than -3, (-3,2) is not a solution.

Answer:

No

Step-by-step explanation:

Khan academy

Answer:  [tex]y=4x-35[/tex]

y = Sidney’s weekly salary

x = Casey’s weekly salary

Answer: y=4x-35

x is Casey's salary

Y is Sidney's salary

Step-by-step explanation:

Sidney makes a quarter of Casey,

y=4x,

Then it also states that he makes 35 less than the first equation.

Therefore,

Y=4x-35

Answer:

Population = 34.27336

Step-by-step explanation:

Given:

Population function (t) = 34(1.00804)^t

Number of year = 2000

Find:

Number of citizen in year 2000

Computation:

We know that, base year is 2000

So, t = 1

Population function (t) = 34(1.00804)^t

Population function (1) = 34(1.00804)^1

Population = 34(1.00804)

Population = 34.27336

Therefore, Population is 34.273636 million

Answer:

  (-2, 1)

Step-by-step explanation:

For a relation consisting of (x, y) pairs to be a function, all of the x-values must be unique. In the given relation, points (-2, -3) and (-2, 1) have the same x-value. Removing either point will make the relation a function.

Of these, the only one listed among answer choices is (-2, 1).

Answer:

-2 , 1

Step-by-step explanation:

good luck love

Answer:

3u-2v = [tex]\sqrt{505\\}[/tex]

5u-v = [tex]\sqrt{1,157}[/tex]

2u-3v = [tex]\sqrt{1,300}[/tex]

u+4v = [tex]\sqrt{4,505}[/tex]

Step-by-step explanation:

I just started by doing the results for each of the operations given.

3u-2v:

3u = (-9, 24)       2v = (-28, 12)

Do the operation of 3u-2v and you get a resultant vector of (19, 12).

You calculate this by doing the square root of 19^2 + 12^2, which is the square root of 505.

5u-v:

5u = (-15, 40)       v = (-14, 6)

Do the operation of 5u-v and you get a resultant vector of (-1, 34).

You calculate this by doing the square root of (-1)^2 + 34^2, which is the square root of 1,157.

2u-3v:

2u = (-6, 16)   3v = (-42, 18)

Do the operation of 2u-3v and you get a resultant vector of (36, -2).

You calculate this by doing the square root of 36^2 + (-2)^2, which is the square root of 1,300.

3u+2v:

3u = (-9, 24)       2v = (-28, 12)

Do the operation of 3u+2v and you get a resultant vector of (-37, 36).

You calculate this by doing the square root of (-37)^2 + 36^2, which is the square root of 2,665. This is not a given tile, so we can just ignore this one.

u+4v:

u = (-3, 8)       4v = (-56, 24)

Do the operation of u+4v and you get a resultant vector of (-59, 32).

You calculate this by doing the square root of (-59)^2 + 32^2, which is the square root of 4,505.

Since this is a given tile, I didn't do 7u-2v, but you would use the same methodology.

Answer:

C) The auditor may or may not achieve the desired risk of assessing control risk too low.

Step-by-step explanation:

In a concept of risk sampling, if the sample size is chosen randomly in accordance with random selection procedures, the auditor may or may not achieve the desired risk of assessing risk too low. In other words the auditor may or may not achieve desired precision. This is because a samole chosen randomly may not represent the true population.

This depends largely on the sample size. If the sample size selected is too small, the allowance for sampling risk will be larger than what is required because it will lead to a large standard error of the mean

Answer:

  On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5)

Step-by-step explanation:

The distinction between "straight line" and "blue diamonds" is that the straight line represents the relation for all possible values of x. The blue diamonds show the values of y for very specific values of x.

Since x is the amount of rice from a bulk bin, we assume it can take any non-negative value. Hence, the graphs with negative values or with "blue diamonds" are not appropriate.

The straight-line graph in the first quadrant is the best choice.

Answer:

The answer is graph 1

Step-by-step explanation:

On a coordinate plane, a straight line with a positive slope begins at point (0, 0), and ends at point (2.5, 5).

Answer:

  4 cm

Step-by-step explanation:

The side of the square will be the average of the two sides of the rectangle with the same perimeter.

Formulas for the perimeters are ...

  P = 2(L+W)

  P = 4s

Equating these gives ...

  4s = 2(L+W)

  s = (L +W)/2 . . . . . divide by 4

For the given side lengths, ...

  s = (2 cm +6 cm)/2 = (8/2) cm = 4 cm

The length of one side of the square is 4 cm.

Answer:

Step-by-step

The null and the alternative hypothesis can be define as  follows,

Null Hypothesis; There is no significance difference between the proportions of non participating athletes in 1999 and 2000

[tex]H_0:(p_1-p_2)\neq 0[/tex]

Alternative Hypothesis: The proportion of non participating  athletes in  2000 will be more than the proportion of non participating athletes in 1999

[tex]H_1:(p_1-p_2)<0[/tex]

The proportion of nonparticipating athletes in 1999 is given by

[tex]\hat p_1 = \frac{x_1}{n_1} \\\\=\frac{159}{830} =0.1916[/tex]

The proportion of nonparticipating athletes in 2000 is given by

[tex]\hat p_2 =\frac{x_2}{n_1} \\\\=\frac{133}{825} =0.1612[/tex]

The pooled proportion can be calculated using the following formula

[tex]\hat p = \frac{x_1+x_2}{n_1+n_2} \\\\=\frac{159+133}{830+825} =0.1764[/tex]

under the null hypothesis, the test statistics can be calculated as follows

[tex]Z=\frac{\hat p_1 - \hat p_2}{\sqrt{\hat p \hat q(\frac{1}{n_1}+\frac{1}{n_2} ) } }[/tex]

[tex]=\frac{0.1916-0.1612}{\sqrt{(0.1764)(0.8236)(\frac{1}{830} +\frac{1}{825} )} } \\\\=1.6257[/tex]

Determine the P-value using the following formula

P-value = Normdist(1.6257)

=0.947993

Here, it can be observed that the P-value is greater than the level of the significance,

Hence, the null hypothesis fails to be rejected

Therefore it can be concluded that there is insufficient evidence to support that the proportions of non participating athletes in 2000 will be more than the proportions of non participating athletes in 1999