I am pretty sure it's A but I can't risk it so someone plzz help. Its not really hard.

Dan will have £25783.21 after 7 years by investing £18790 at a simple interest rate of 5.3% per year.

The question concerns how much money Dan will have after 7 years with an investment of \£18790\ at a \simple interest rate\ of 5.3% per year. We can calculate the total amount in Dan's bank account using the formula for simple interest:

Total amount = Principal + (Principal × rate × time)

Where:

Principal (P) is the initial amount invested, which is £18790.

Rate (r) is the annual interest rate, which is 0.053 (5.3% expressed as a decimal).

Time (t) is the number of years the money is invested, which is 7 years.

Now, let's do the calculation:

Total amount = £18790 + (\£18790 * 0.053 * 7\)

Total amount = £18790 + £6993.21

Total amount = £25783.21

Thus, Dan will have \£25783.21\ in his bank account after 7 years.

Answer:

New Average of New List = 87.5

Step-by-step explanation:

Average is the arithmetic mean (M) of observations.

M = ΣX / N

where ΣX = sum of all observations , N = number of observations

Given : M = 90 ; N = 40

M = ΣX / N

90 = ΣX / 4

ΣX  = 90 x 4

ΣX  = 360 [ Of Old List of 4 numbers ]

New ΣX  of new list of 4th new number = Old ΣX - Old 4th No. + New 4th No.

New ΣX   = 360 - 90 + 80

New ΣX   = 350

New Average (Mean M) = New ΣX / N

New M = 350 / 4

New M = 87.5  

Answer:

a.   0.71

b.   0.9863

Step-by-step explanation:

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

-To estimate the probability that a randomly selected house  has a value less than $500,000:

[tex]P(X<500,000)=P(X=0)+P(X=500)\\\\=0.34+0.37\\\\=0.71[/tex]

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume normal distribution.

-The probability can therefore be calculated as:

[tex]P(\bar X)=P(z<\frac{\bar X-\mu}{\sigma/\sqrt{n}})\\\\=P(z<\frac{500-403}{278/\sqrt{40}})\\\\=P(z<2.2068)\\\\=0.986336\\\\\approx 0.9863[/tex]

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

To estimate the probability that a house is valued less than $500,000, we count the bars below that value on the histogram. To estimate the probability that the mean value of 40 houses is less than $500,000, we use the Central Limit Theorem to calculate the z-score.

(a) To estimate the probability that the selected house is valued at less than $500,000, we need to find the area under the histogram below the value of $500,000. Looking at the histogram, we see that there are 3 bars below $500,000. Each bar represents a count of houses, so we add up the counts of those 3 bars. The estimated probability is given by:

Estimated Probability = (Count of houses valued less than $500,000) / (Total count of houses)

(b) To estimate the probability that the mean value of the 40 houses is less than $500,000, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. We can then calculate the z-score for $500,000 using the formula:

z = (x - mean) / (standard deviation / sqrt(sample size))

Once we have the z-score, we can find the estimated probability using a standard normal distribution table or calculator.

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Answer:

(C) The first is a premise supporting the argument's main conclusion; so is the second.

Step-by-step explanation:

The two sections in boldface are "Supplies in local freshwater reservoirs have been declining for years" and "few users have bothered to adopt even easy conservation measures"

In the economist's argument, both highlighted sections are premises giving the reason why the price of tap water should be drastically raised.

The conclusion of the argument is that the supply of water be drastically raised, the two boldfaced sections are just premises on which the conclusion is based.

Answer:

The correct answer is 63 cubic inches.

Step-by-step explanation:

Dali rolled up his painting and placed it in a cylinder 2 inches diameter.

Diameter of the painting is 2 inches. This also implies diameter of the cylinder is 2 inches.

Radius of the cylinder is 1 inch.

Length of the cylinder is 20 inches.

Volume of the cylinder is given by π × [tex]r^{2}[/tex] × h =  π × [tex]1^{2}[/tex] × 20 = 20π = 62.85 cubic inches ≈ 63 cubic inches.

Therefore the volume of the cylinder in which Dali placed his painting is given by 63 cubic inches.

Given:

Given that the figure DEFG with vertices D(1,2), E(2,6), F(6,7) and G(5,3)

We need to determine the perimeter of DEFG.

The length of the sides can be determined using the formula,

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Length of DE:

Substituting the coordinates D(1,2), E(2,6) in the formula, we get;

[tex]DE=\sqrt{(2-1)^2+(6-2)^2}[/tex]

[tex]DE=\sqrt{(1)^2+(4)^2}[/tex]

[tex]DE=\sqrt{17}[/tex]

Length of EF:

Substituting the coordinates E(2,6), F(6,7) in the formula, we get;

[tex]EF=\sqrt{(6-2)^2+(7-6)^2}[/tex]

[tex]EF=\sqrt{(4)^2+(1)^2}[/tex]

[tex]EF=\sqrt{17}[/tex]

Length of FG:

Substituting the coordinates F(6,7), G(5,3) in the formula, we get;

[tex]FG=\sqrt{(5-6)^2+(3-7)^2}[/tex]

[tex]FG=\sqrt{(-1)^2+(-4)^2}[/tex]

[tex]FG=\sqrt{17}[/tex]

Length of DG:

Substituting the coordinates D(1,2), G(5,3) in the formula, we get;

[tex]DG=\sqrt{(5-1)^2+(3-2)^2}[/tex]

[tex]DG=\sqrt{(4)^2+(1)^2}[/tex]

[tex]DG=\sqrt{17}[/tex]

Perimeter of DEFG:

The perimeter of DEFG can be determined by adding the side lengths DE, EF, FG and DG.

Thus, we have;

[tex]Perimeter=DE+EF+FG+DG[/tex]

Substituting the values, we have;

[tex]Perimeter=\sqrt{17}+\sqrt{17}+\sqrt{17}+\sqrt{17}[/tex]

[tex]Perimeter=4\sqrt{17}[/tex]

Thus, the perimeter of DEFG is 4√17

Hence, Option b is the correct answer.

Answer:

-5

Step-by-step explanation:

Answer:

The answer is -5

Step-by-step explanation:

Answer: a=-1

Step-by-step explanation: -3+1=-2 and 1-3also equals -2

Answer:

[tex]T \approx 3.967\,^{\textdegree}C[/tex]

Step-by-step explanation:

The density of water is given by the following definition:

[tex]\rho = \frac{m}{V(T)}[/tex]

[tex]\rho = \frac{1000\,g}{999.870.06426\cdot T + 0.0085043\cdot T^{2}-0.0000679\cdot T^{3}}[/tex]

The density is maximum when volume is minimum, which can be found by First and Second Derivative Tests:

First Derivative

[tex]V' = -0.06426 +0.0170086\cdot T -0.0002037\cdot T^{2}[/tex]

Second Derivative

[tex]V'' = 0.0170086 - 0.0004074\cdot T[/tex]

Critical values from the first derivative are:

[tex]T_{1} \approx 79.531\,^{\textdegree}C[/tex] (absolute maximum) and [tex]T_{2} \approx 3.967\,^{\textdegree}C[/tex] (absolute minimum).

The temperature at which water has its maximum density is:

[tex]T \approx 3.967\,^{\textdegree}C[/tex]

We have been given that last month, Belinda worked 160 hours at a rate of $10.00 per hour.

Let us find amount earned by Belinda last month as:

[tex]\text{Amount earned in 160 hours}=\$10\times 160[/tex]

[tex]\text{Amount earned in 160 hours}=\$1600[/tex]

We are also told that Belinda's employer retains 9% of her gross salary. This means that Belinda's net income will be 91% of $1600. [tex](100\%-9\%=91\%)[/tex].

[tex]\text{Belinda's net income would be}=\$1600 \times \frac{91}{100}[/tex]

[tex]\text{Belinda's net income would be}=\$16\times 91[/tex]

[tex]\text{Belinda's net income would be}=\$1456[/tex]

Upon rounding $1456 to nearest hundred, we will get:

[tex]\text{Belinda's net income would be}\approx \$1500[/tex]

Therefore, $1500 is a reasonable estimate of her net salary.

Final answer:

After calculating the gross salary at $1,600 and then determining the tax retained, Belinda's net salary would be $1,456. Hence, $1,500 is not a reasonable estimate for her net salary.

Explanation:

Let's first calculate the gross salary that Belinda earned. She worked for 160 hours at a rate of $10.00 per hour, so her gross salary can be calculated by multiplying the number of work hours by the rate per hour:

Gross Salary = 160 hours * $10.00 per hour = $1,600

The employer retains 9% of her gross salary, so let's find out how much that amounts to:

Tax = 9% of $1,600 = 0.09 * $1,600 = $144

Now, to obtain the net salary, we subtract the tax from the gross salary:

Net Salary = Gross Salary - Tax = $1,600 - $144 = $1,456

Therefore, $1,500 is not a reasonable estimate of her net salary, as the exact calculation shows that her net salary is $1,456.

Answer:

x = 3

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

x + 6 = 18/2

x+6=9

x=9-6

x=3

Answer:

The correct option is;

D. This method uses the binomial probability distribution with the P-value method ans uses the value of p assumed  in the null hypothesis

Step-by-step explanation:

Here we have the binomial probability distribution is used to test claims about a proportion then the requirement is np > 5 and nq >5

In a left-tailed test, the P value is the probability of getting x or fewer successes among n trials while in a right tailed test, the P-value is the probability of getting x or more successes among n trials

However, the P-value where a binomial distribution is used to test a claim about a proportion is derived from the z score of the parameters of the statistic and not from the p assumed in the null hypothesis.

The incorrect statement is option B. A left-tailed test in binomial probability distribution does not correspond to the probability of getting x or fewer successes among n trials.

The statement among the given options that is NOT true of using the binomial probability distribution for testing claims about a proportion is option B. A left-tailed test does not entail the probability of getting x or fewer successes in the n trials. Instead, it approximates the probability of observing a value as extreme as the test statistic or even more extreme, which leans to the left or lower end of the distribution. Thus, the P-value in a left-tailed test corresponds to the total probability of the shaded region of the curve that falls to the left of observed value or test statistic. The remainder of the options (A, C, and D) are accurate statements.

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Answer:

Step-by-step explanation:

a) Consider the sequence [tex]a_n =1 [/tex] if n is odd, and [tex] a_n= -1[/tex] if n is even. So, the sequence diverges (since as n tends to infinity the sequence doesn't approach any particular number), but the subsequence of the even integers is convergent to -1 since it is constant.

b) consider the sequence [tex] a_n = -e^{-n}[/tex]. The function f(x) = [tex] e^{-x}[/tex] when x is real is a monotolically decreasing function and tends to 0. Then, when multiplying by a minus sign, it becomes a monotonically increasing function that tends to 0. Hence, the given sequence is monotonically increasing and converges to 0.

c) Suppose that the sequence [tex]a_n[/tex] converges to a. So, from an specific n and on, the values of [tex]a_n[/tex] are really close to a. So, for almost all the value of the sequence, they are less than a+1 and greater than a-1. Hence it must be bounded.

d) It is a theorem that a monotonically decreasing/increasing sequence that is bounded must converge, so such a sequence can't exist.

In mathematics, various types of sequences can be studied. Examples of sequences satisfying certain conditions are presented in this solution.

(a) An example of a divergent sequence {an} such that {a2n} converges is the sequence {1, -1, 1, -1, ...}. The terms of the sequence alternate between positive and negative 1, so the sequence does not converge. However, the subsequence {a2n} consists of only positive 1's, which converges to 1.

(b) An example of a monotonically increasing sequence that converges to 0 is the sequence {1/n} for n = 1, 2, 3, ... Each term of the sequence is smaller than the previous term, and as n approaches infinity, the terms get closer and closer to 0.

(c) It is not possible for a convergent sequence to be unbounded. By definition, a convergent sequence approaches a specific limit, which means it cannot go beyond a certain value. If a sequence is not bounded, it cannot converge.

(d) An example of a monotonically decreasing bounded sequence that diverges is the sequence {(-1)^n/n} for n = 1, 2, 3, ... The terms of the sequence alternate between positive and negative values, but as n approaches infinity, the terms get smaller and smaller, converging towards 0. Therefore, the sequence is bounded. However, the sequence does not converge to a specific value, so it diverges.

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Answer:

50% is equivalent to the unit fraction .answer:1/2

To find 50% of $72, divide 72 by . answer: 2

50% of $72 is .answer: $36

Step-by-step explanation:

just answered  :) good luck everyone

The sales price of the Bikes are obtained by finding the percent value as $36.

A percentage is a value that indicates 100th part of any quantity. It can be converted into a fraction or a decimal by dividing it by 100. The percent value is useful in representing the large data into a two digit number.

The sales percent is given as 505

And, the original price is $72.

The value of sales price is given as follows,

50% × Original price

⇒ 50/100 × 72

⇒ 1/2 × 72

⇒ 36

Hence, the sales price is obtained as $36.

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Answer:

12$

Step-by-step explanation:

Answer:

$375

Step-by-step explanation:

Sale price = original price - (markdown percentage)(original price), or

Sale price = (1 - markdown percentage)(original price

That 32% discount is equivalent to multiplying the original price by 0.32.

Here, $255 = (1 - 0.32)(original price), or

          $255 = 0.68(original price)

Then (original price) = $255/0.68 = $375

A 36 year old male will pay $4.55 per $1,000 for a 10 year policy,

He bought a $150,000 policy:

150,000 / 1000 = 150

Multiply the rate per 1000 by 150:

4.55 x 150 = 682.50

His annual premium is $682.50

Answer:

His annual premium is $682.50

Step-by-step explanation:

Answer:

A unit rate is something over a unit of something else.

Such as:  (50 miles) / hour

If you have (150 miles) / 3 hours

This is not a unit rate, therefore you have to divide the top and bottom by 3 to get the unit rate

(150/3 miles) / (3/3 hours)

(50 miles) / hour

Hope this helps :)

Answer:

The value of r to have maximum profit is 3/25 ft

Step-by-step explanation:

To find:

The size of the sphere so that the profit can be maximized.

Manufacturing cost of the solid sphere = $500/ ft^3

Selling price of sphere (on surface area) = $30 / ft^2

We see that the manufacturing cost dealt with he volume of the sphere where as the selling price dealt with the surface area.

So,

To maximize the profit (P) .

We can say that:

⇒ [tex]P(r)=(unit\ cost)\ (SA) - (unit\ cost)\ (Volume)[/tex]

⇒ [tex]P(r)=(30)\ (4 \pi r^2) - (500)\ (\frac{4\pi r^3}{3} )[/tex]

⇒ [tex]P(r)=(120)\ (2\pi r^2) - (\frac{500\times 4}{3} )\ \pi r^3[/tex]

⇒ [tex]P(r)=(120)\ (\pi r^2) - (\frac{2000}{3} )\ \pi r^3[/tex]

Differentiate "[tex]P[/tex]" and find the "[tex]r[/tex]" value then double differentiate "[tex]P[/tex]", plug the "[tex]r[/tex]" values from [tex]P'[/tex] to find the minimum and maximum values.

⇒ [tex]P(r)'=(120)\ 2\pi r - (\frac{2000}{3} )\ 3\pi r^2[/tex]

⇒ [tex]P(r)'=(240)\ \pi r - (2000)\ \pi r^2[/tex]

Finding r values :

⇒ [tex](240)\ \pi r - (2000)\ \pi r^2 =0[/tex]  

Dividing both sides with 240π .

⇒ [tex]r-\frac{25}{3} r^2 =0[/tex]    ⇒ [tex]r(1-\frac{25}{3} r) =0[/tex]

⇒ [tex]r=0[/tex] and [tex]r=\frac{3}{25}[/tex]  

To find maxima value the double differentiation is :

⇒ [tex]P(r)'=(240)\ \pi r - (2000)\ \pi r^2[/tex]     ...first derivative

Double differentiating :

⇒ [tex]P(r)''=(240\pi) - (2000\pi)\ 2(r)[/tex]    ...second derivative

⇒ [tex]P(r)''=(240\pi) - (4000\pi)\ (r)[/tex]

Test the value r = 3/25 dividing both sides with 240π

⇒  [tex]1 - \frac{50\pi r}{3}[/tex]

⇒ [tex]1 - \frac{50\times \pi\times 3 }{3\times 25}[/tex]

⇒ [tex]-5.28 < 0[/tex]

It passed the double differentiation test.

Extra work :

Thus:

⇒ [tex]P(r)=(120)\ (\pi r^2) - (\frac{2000}{3} )\ \pi r^3[/tex]

⇒ [tex]P(r)=(120)\times (\pi (\frac{3}{25} )^2) - (\frac{2000}{3} )\times \pi (\frac{3}{25} )^3[/tex]

⇒ [tex]P(r) =1.8095[/tex]

Finally r =3/25 ft that will maximize the profit of the manufacturing company.

Final answer:

To calculate the total flour needed, simplify 2 6/8 cups to 2 3/4 cups and add it to 3 1/2 cups. Convert to a common denominator and sum up to get the total of 6 1/4 cups of flour.

Explanation:

To find the total amount of flour needed in the recipe, we will have to add the two quantities of flour given: 2 6/8 cups and 3 1/2 cups. First, we can simplify 2 6/8 cups to 2 3/4 cups by dividing the numerator by the denominator's GCD (Greatest Common Divisor), which is 2 in this case. Then, we can add the simplified amount to the 3 1/2 cups.

Adding the two amounts together, we have:

2 3/4 cups + 3 1/2 cups
= (2 + 3) + (3/4 + 1/2) cups
= 5 + (3/4 + 1/2) cups

To add fractions, we need a common denominator. Multiply the second fraction by 2/2 to get the same denominator:

5 + (3/4 + 2/4) cups
= 5 + (5/4) cups
= 5 + 1 1/4 cups
= 6 1/4 cups

Therefore, the total amount of flour needed for the recipe is 6 1/4 cups.

We want to find word problems that gives rise to the following systems of algebraic equations.

a)

x+y=13

x-y=1.

Answer: The sum of the ages of two students is 13. The difference between their ages is 1. Find the ages of the two students.

b)

3x-30y=15

2x+10y=40

Answer:

The difference between 3 times Dan's age and 30 times Mark's age is 15. If the sum of 2 times Dan's age and 10 times Mark's age is 40. Find the ages of Dan and Mark.

c)

8x+3y=37

8x-3y=50

Answer:

The sum of 8 times an eagle's distance above sea level in feet and a herring's distance below sea level is 37 feet. The difference between 8 times an eagle's distance in feet above sea level and 3 times the herring's distance below sea level is 50. Find the distance of the eagle and the herring relative to the surface of the sea.

d) x-5y=4

3x+5y=32

The difference between a pig's age and 5 times the age of a piglet is 4 years. If the sum of 3 times pigs and 5 times the piglet's age is 32 years, find the ages of the pig and its piglet.

Answer:

The perimeter is approximately 19.

Step-by-step explanation:

Three of the sides are roughly four segments long and two are around three and a half.

4 + 4 + 4 + 3.5 + 3.5 = 19

Answer:

Approximately 19 units.

Step-by-step explanation:

The question asks for an estimate, so this is an estimate.

The bottom side has a length of 4.

The two sides that go up from the bottom are diagonals in 1 by 3 rectangles.

Each side is between 3 and 4 units long. Call it approximately 3.5 units long each.

The two upper sides are diagonals in 3 by 3 rectangles.

Each side is approximately 4 units long.

4 + 3.5 + 3.5 + 4 + 4 = 19

Answer:

The median. 80 because the mean is 80.454545

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

If you plug it into desmos, this is the answer.

Answer:

x = 3

The number of games lost if 27 games are won = 3

Step-by-step explanation:

Complete question

Will records the wins and losses for his high school basketball team each year. He notices that the ratio of wins to losses has been consistent each year.

W | L

18 | 2

45 | 5

36 | 4

27 | x

Using the information in the table, how many losses should he predict for next year if the number of games won is 27?

1 3 6 9

The ratio of wins to losses each year has been consistent, in other words, the same. Hence, we can use this ratio to find x.

Ratio of wins to losses

18 : 2 = 9 : 1

45 : 5 = 9 : 1

36 : 4 = 9 : 1

Hence, 27 : x = 9 : 1

(27/x) = (9/1)

27 = 9x

x = (27/9) = 3

x = 3

Hope this Helps!!!

Answer: what there trying to say is x=3 and that's ur answer :)

Step-by-step explanation:

Answer:

The conditions that are not necessary to use the odd´s ratio to estimate the relative risk are a. Cases are representative of all cases and c. The exposure in question is rare in the population.

Step-by-step explanation:

Case-control studies are an example of observational studies. In this kind of studies, people are selected because of the presence or absence of a sisease, searching for the previous presence of the suspected cause (exposure).  The idea is to select a group of people that has a particular condition or disease (the group of cases) and compare it with a group of persons that does not have this disease (the control group). Reasearchers analyse both groups and compare them in order to find some information related with the presence of previous or present exposure to factors that are considered as the cause of the disease. The variable used to estimate the relationship between the exposure and the development of the disease is called odd ratio and it is an aproximation of another variable "relative risk".

The odd ratio is aproximately equal to the relative risk (it means it is a good estimator) when the disease is not frequent on the population (in other words, the event under study is rare in the population) and when controls are representative of the population that give rise to the cases.

The point a. Cases are representative of all cases is a dessirable condition but could it not be present.

Finally c. The exposure in question is rare in the population is not necessary, the only factor that must be rare in the population is the disease.

Summarizing, points b and d are strictly necessary, c. is a dessirable condition and a. is not necessary.  

Answer:

1, 4 and 6 are correct

Step-by-step explanation:

In answering this question, we shall be evaluating the validity of the options.

1 is correct

the total amount of money is 70+35 = 105

The percentage spent at pet store = 35/105 * 100 = 33 1/3 %

2. is wrong since 1 is correct

3 is wrong since 1 is correct

4. is correct

since she spent 33 1/3 at pet shop, what is spent at clothing store will be 100 - 33 1/3 = 66 2/3 %

5 is wrong

6 is correct

7 7 is wrong

Answer:

Step-by-step explanation:

Amount of Money spent by Annie

Total Amount Spent= 70+35=$105

Percentage Spent at each place

Clothing Store

[tex]\frac{70}{105}X100=66\frac{2}{3}\%[/tex]

Pet Store

[tex]\frac{35}{105}X100=33\frac{1}{3}\%[/tex]

Therefore the following applies:

Answer:

5 : 20 = 1 : 4

Step-by-step explanation:

Common multiple is 5 so divide each number bu five.

Answer:

B. No, the equation is not a good fit because the sum of the residuals is far from zero. Should be your answer

Step-by-step explanation:

Have a nice day :)

No, the equation is not a good fit because the sum of the residuals is far from zero.

Two or more expressions with an Equal sign is called as Equation. An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

An equation was created for the line of best fit from the actual enrollment data. which was used to predict the dance studio enrollment values shown in the table.

We need to check whether the equation that produced the predicted values represents a good line of best fit.

No, the equation is not a good fit because the sum of the residuals is far from zero.

A line of best fit is meant to compensate for positive and negative deviation in a matter that balances them. A large residual values' sum shows that they are not balanced.

Hence, No, the equation is not a good fit because the sum of the residuals is far from zero.

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Answer:

[tex]z=\frac{704-732}{\frac{65}{\sqrt{28}}}=-2.279[/tex]      

[tex]p_v =P(z<-2.279)=0.0113[/tex]  

If we compare the p value and the significance level given for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we can reject the null hypothesis, and the the true mean is significantly lower than 732 hours so we have enough evidence to reject the claim

Step-by-step explanation:

Data given and notation      

[tex]\bar X=704[/tex] represent the sample mean

[tex]\sigma=65[/tex] represent the standard deviation for the population      

[tex]n=28[/tex] sample size      

[tex]\mu_o =732[/tex] represent the value that we want to test    

[tex]\alpha[/tex] represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)      

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the true mean is at least 732 or no, the system of hypothesis would be:      

Null hypothesis:[tex]\mu \geq 732[/tex]      

Alternative hypothesis:[tex]\mu < 732[/tex]      

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:      

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)      

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic      

We can replace in formula (1) the info given like this:      

[tex]z=\frac{704-732}{\frac{65}{\sqrt{28}}}=-2.279[/tex]      

Calculate the P-value      

Since is a one-side lower test the p value would be:      

[tex]p_v =P(z<-2.279)=0.0113[/tex]  

Conclusion      

If we compare the p value and the significance level given for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we can reject the null hypothesis, and the the true mean is significantly lower than 732 hours so we have enough evidence to reject the claim

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≥ 732

For the alternative hypothesis,

µ < 732

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = lifetime of the bulb

µ = mean lifetime

σ = standard deviation

n = number of samples

From the information given,

µ = 732

x = 704 hours

σ = 65 hours

n = 28

z = (704 - 732)/(65/√28) = - 2.28

Looking at the normal distribution table, the probability corresponding to the z score is 0.011

Since alpha, 0.05 > than the p value, 0.011, then we would reject the null hypothesis. Therefore, At a 5% level of significance, there is enough evidence to reject the​ manufacturer's claim

Answer:

-707/704

Step-by-step explanation:

4x + 2 - 2116 - 2116x = 7

-2112x = 2121

x = 2121/-2112 = -707/704

Answer:

 x= 2121/-2112 = -707/704 = -1.00426136

Step-by-step explanation:

4x + 2 – 23(92 + 92x) = 7

               4x - 23(92+92x) = 5

    2. Discriminate by multiplying -23 with 92 and -23 with 92x

               4x - 2116 -2116x = 5

    3. Add 2116 both sides to eliminate -2116

              4x -2116x = 2121

    4. combine 4x-2116x together

             -2112x = 2121

    5. Divide both sides with -2112

              x= 2121/-2112 = -707/704 = -1.00426136