Please help me with the math question

Answer:

The best point of estimate for the true mean is:

[tex]\hat \mu = \bar X = 2.55[/tex]

[tex]2.55-1.96\frac{12}{\sqrt{76}}=-0.148[/tex]    

[tex]2.55+1.96\frac{12}{\sqrt{76}}=5.248[/tex]    

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

Step-by-step explanation:

Information given

[tex]\bar X=2.55[/tex] represent the sample mean for the late time for a flight

[tex]\mu[/tex] population mean

[tex]\sigma=12[/tex] represent the population deviation

n=76 represent the sample size  

Confidence interval

The best point of estimate for the true mean is:

[tex]\hat \mu = \bar X = 2.55[/tex]

The confidence interval for the true mean is given by:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The Confidence level given is 0.95 or 95%, th significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. If we look in the normal distribution a quantile that accumulates 0.025 of the area on each tail we got [tex]z_{\alpha/2}=1.96[/tex]

Replacing we got:

[tex]2.55-1.96\frac{12}{\sqrt{76}}=-0.148[/tex]    

[tex]2.55+1.96\frac{12}{\sqrt{76}}=5.248[/tex]    

Since the time can't be negative a good approximation for the confidence interval would be (0,5.248) minutes. The interval are tellling to us that at 95% of confidence the average late time is lower than 5.248 minutes.

The inverse of the function is logx/log12

Given the function expressed as:
y = 12^x

To find the inverse, switch the variables to have:

x = 12^y

Take the log of both sides

logx = y log 12

y = logx/log12

Hence the inverse of the function is logx/log12

Learn more on inverse of a function here: https://brainly.com/question/2873333

Answer:

Corresponding Angles.

Step-by-step explanation:

When two lines are crossed by another line (called the Transversal): The angles in matching corners are called Corresponding Angles.

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

Simple

x + 6 < - 8

x < - 8 - 6

x < - 14

x + 4 > - 8

x > - 8 - 4

x > - 12

Option B is the correct answer

Answer:

  -4

Step-by-step explanation:

Use the given value of f(1) to find f(2):

  f(2) = f(1) · (-1/2) = (-16)(-1/2) = 8

Now, we can find f(3) using f(2):

  f(3) = f(2) · (-1/2) = (8)(-1/2)

  f(3) = -4

Step-by-step explanation:

There are a total of 16 marbles, 8 of which are green.

(a) The probability the first marble is green is 8/16.

The marble is replaced, so there are still a total of 15 marbles, 8 of which are green.  The probability the second marble is green is 8/16.

The probability of both events is (8/16) (8/16) = 1/4 = 0.2500.

(b) The probability the first marble is green is 8/16.

The marble is not replaced, so there are now a total of 15 marbles, 7 of which are green.  The probability the second marble is green is 7/15.

The probability of both events is (8/16) (7/15) = 7/30 = 0.2333.

Final answer:

The probability of selecting a green marble, then another green marble from a bag of marbles is 0.25 when the first marble is replaced and 0.2333 when the first marble is not replaced.

Explanation:

To find the probability of selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles, we need to consider two scenarios: (a) replacing the first marble before drawing the second, and (b) not replacing the first marble.

a) If the first marble is replaced before drawing the second, the probability of selecting a green marble on the first draw is 8/16, and the probability of selecting a green marble on the second draw is also 8/16. We can multiply these probabilities together to get the overall probability: 8/16 × 8/16 = 16/64 = 0.25.

b) If the first marble is not replaced, the probability of selecting a green marble on the first draw is 8/16. However, since the first marble is not replaced, there are only 15 marbles left in the bag for the second draw, with 7 green marbles remaining. The probability of selecting a green marble on the second draw is 7/15. We can multiply these probabilities together to get the overall probability: 8/16 × 7/15 = 56/240 = 0.2333 (rounded to four decimal places).

Comparing the probabilities, we can see that the probability in scenario (a) when the first marble is replaced is higher than the probability in scenario (b) when the first marble is not replaced.

Answer:

440 square inches

Step-by-step explanation:

10x10x2=200

10x6x4=240

240+200=440

Answer:

x=\frac{-3}{2}

Step-by-step explanation:

We have been given with the expression (1/3)^x=(27)^x+2

Now, to solve the equation firstly we have to make the base same on both sides

(1/3)^x=3^{-x}

27 can be written as 3^3

27^x=(3^3)^x=3^{3x}

Hence, given expression can be rewritten as

3^{-x}=3^{3(x+2)}

Now since, base is same we can equate the powers on both sides

-x=3(x+2)\\ \Rightarrow-x= 3x+6\\ \Rightarrow -x-3x=6\\-4x=6\Rightarrow x=\frac{-3}{2}

Therefore given expression (1/3)^x=(27)^x+2 is equivalent to x=\frac{-3}{2}

Equivalent means the simplified form of any given expression

The equation is equivalent to [tex]\(\boxed{3^x = 3^{-3x+2}}\)[/tex]

To solve the equation [tex]\((\frac{1}{3})^x = 27^{(x+2)}\)[/tex], we first need to express [tex]\(27\)[/tex] as a power of [tex]\(3\)[/tex], as [tex]\(27 = 3^3\)[/tex]. Then, we rewrite the equation as:

[tex]\[\left(\frac{1}{3}\right)^x = (3^3)^{(x+2)}\][/tex]

Now, we apply the properties of exponents, specifically the power of a power rule which states [tex]\((a^m)^n = a^{m \times n}\)[/tex], to simplify the expression:

[tex]\[\left(\frac{1}{3}\right)^x = 3^{3(x+2)}\][/tex]

Now, we have the same base on both sides of the equation. We can set the exponents equal to each other:

[tex]\[x = 3(x+2)\][/tex]

Now, let's solve for [tex]\(x\)[/tex]:

[tex]\[x = 3x + 6\][/tex]

[tex]\[x - 3x = 6\][/tex]

[tex]\[-2x = 6\][/tex]

[tex]\[x = \frac{6}{-2}\][/tex]

[tex]\[x = -3\][/tex]

Complete correct question:

Which equation is equivalent to [tex]( 1/3 )^x=27^{x+2}[/tex] ?

[tex]3^x=3^{-3x+2}[/tex]

[tex]3^x=3^{3x+6}[/tex]

[tex]3^{-x} =3^{3x+2}[/tex]

[tex]3^{-x} =3^{3x+6}[/tex]

Answer:

60 students

Step-by-step explanation:

The confidence interval of a proportion is given by:

[tex]p\pm z*\sqrt{\frac{p*(1-p)}{n} }[/tex]

Where 'p' is the proportion of students who responded 'yes', 'z' is the z-score for a 95% confidence interval (which is known to be 1.960), and 'n' is the number of students in the sample.

If the confidence interval is from 0.584 to 0.816, then:

[tex]p=\frac{0.584+0.816}{2}=0.7 \\0.816-0.584=2*(1.96*\sqrt{\frac{p*(1-p)}{n}}) \\0.116=1.96*\sqrt{\frac{0.7*(1-0.7)}{n}}\\n=16.8966^2*(0.7*0.3)\\n=60\ students[/tex]

60 students were in the sample.

Final answer:

To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher used a random sample and calculated a 95 percent confidence interval. Using the formula for the confidence interval for proportions, we can determine that the teacher selected approximately 223 students for the survey.

Explanation:

To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher selected a random sample of students and surveyed them one at a time, asking them if they regularly recycle plastic bottles. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816).

To find out how many students were in the sample selected by the teacher, we need to use the formula for the confidence interval for proportions:

n = (Z^2 * p * (1-p)) / (E^2)

Where:

n is the sample size,

Z is the Z-score corresponding to the desired level of confidence (in this case, 95 percent),

p is the estimated proportion of students who recycle plastic bottles (we can use the midpoint of the confidence interval, which is (0.584 + 0.816) / 2 = 0.7),

E is the margin of error (in this case, half the width of the confidence interval, which is (0.816 - 0.584) / 2 = 0.116).

Plugging in the values, we get:

n = (1.96^2 * 0.7 * (1-0.7)) / (0.116^2)

n = 2.992 / 0.013456

n ≈ 222.38

Since the sample size must be a whole number, we round up to the nearest whole number.

Therefore, the teacher selected approximately 223 students for the survey.

Answer:

86362600

Step-by-step explanation:

We want to round to the hundreds place

We look at the 7 in the tens place.  Since it is 5 or greater we round up

86,362,575 round to 86362600

Answer:

86,362,600

Step-by-step explanation

Answer:

about $982.20

Step-by-step explanation:

Formula = P(1+I)^T

T =18/12 because its in months not years, so 1.5 years

1+I = 1 + 54/900 or 1.03

P = 900

Plug those in and you get about 982.20

Answer:

4%

Step-by-step explanation:

For the simple interest rate,

I=P(i)t

54=900(i)(18/12)

i=54/900*(12/18)=4% annually

Answer:

y = 3x - 4

Step-by-step explanation:

Start with your point-slope formula which is shown at the

top of the image that is provided below.

Then, plug in your appropriate values for the ordered pair (4, 2).

Now, simplify.

First distribute.

Then add 2 to both sides.

This leaves you with y = 3x - 10.

All my work is in the image attached.

Answer:

Discrete(b,c and d)

Continuous (a and e)

Step-by-step explanation:

Discrete

Discrete Random variables are variables that can only take on integer values. Therefore the following are discrete variables.

b. The number of fish caught during a fishing tournament. e.g. 6 fishes

c. The number of statistics students now reading a book. e.g. 12 Students

d. The number of textbook authors now sitting at a computer. e.g. 9 Authors

Continuous

Continuous random variables can take on an uncountable number of values.

a. The time it takes for a light bulb to burn out. e.g.178.897 seconds

e. The height of a randomly selected giraffe. e,g 16.67 feet

Answer:

C) Descend 84 feet

Step-by-step explanation:

162+207=369

369-285=84ft above starting point, this means that he must descend 84 feet to reach the starting point.

Answer:

because your just adding a zero at the end.

Step-by-step explanation:

Adding 6+3 is like adding 60+30 because both utilize the place value system and the commutative property of addition where units are added to units and tens to tens, respectively.

The question of adding 6+3 is similar to adding 60+30 due to the property of place value and the commutative property of addition. In both cases, you are adding units that are consistent within their respective places. In single-digit addition, such as 6+3, you are adding units to units. Similarly, in the addition of multi-digit numbers like 60+30, you are adding tens to tens. This is much like the property A+B=B+A, which holds true for ordinary numbers, meaning you'll get the same result regardless of the order in which you add them.

Final answer:

To find the area of the rectangular field in square meters, convert the dimensions from kilometers to meters and then multiply them together, resulting in 45,000 square meters.

Explanation:

To calculate the area of a rectangular field that is 0.3 kilometers long and 0.15 kilometers wide, use the following steps:

The factorization of 121b^4 - 49 is (11b^2 + 7)(11b^2 - 7).

The given expression is 121b^4 - 49. We can recognize that it is a difference of squares, which can be factored using the formula (a^2 - b^2) = (a + b)(a - b). In this case, a is 11b^2 and b is 7.

Therefore, the factorization of 121b^4 - 49 is (11b^2 + 7)(11b^2 - 7).

https://brainly.com/question/33624529

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Answer:

x=32, y=36, and z=25

Step-by-step explanation:

There are only two sums the equations can all add up to, 67 degrees and 113 degrees. I know that to the equation with x is equal to 67 degrees.

2x+3=67

2x=64 (subtract 3)

x=32 (divide by 2)

Now to find the measurement of the other angle, we subtract 180 and 67 since the measurement of a line is 180 degrees.

180-67=113

The equations of y and z are both equal to 113.

3y+5=113                                 4z+13=113

3y=108 (subtract 5)                 4z=100 (subtract 13)

y=36 (divide by 3)                   z=25 (divide by 4)

Answer:oh yeah I remember that

Step-by-step explanation:

That’s tuff

Answer:

We conclude that the new technique is not an improvement over the old technique at 5% level of significance.

Step-by-step explanation:

We are given that the average speed of a baseball line drive is 83 miles per hour.  

His coach recorded the speed of 42 random hits during practice and found that his average speed using the new technique was 84.2 miles per hour, with a standard deviation of 4.7 miles per hour.

Let [tex]\mu[/tex] = true average speed using the new technique.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 83 miles per hour     {means that the new technique is not an improvement over the old technique}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 83 miles per hour     {means that the new technique is an improvement over the old technique}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                           T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average speed using the new technique = 84.2 mph

            s = sample standard deviation = 4.7 mph

            n = sample of hits = 42

So, the test statistics  =  [tex]\frac{84.2-83}{\frac{4.7}{\sqrt{42} } }[/tex]  ~ [tex]t_4_1[/tex]

                                     =  1.655

The value of t test statistics is 1.655.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of 1.6832 at 41 degree of freedom for right-tailed test.

Since our test statistic is less than the critical value of t as 1.655 < 1.6832, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the new technique is not an improvement over the old technique.

Answer :

11.45

step-by-step explantion :

4.25=17/4

when we add 41/5 and 17/4, we get

41×4+17×5/4×5

164+65/20

229/20

11.45 Ans

:

Answer:

C = πd or 2πr

Step-by-step explanation:

2r equals d

2r = d

Answer:

  (x +1)(x +24)

Step-by-step explanation:

Factors of 24 that have a sum of 25 are 1 and 24. These are the constants you need in the binomial factors:

  x^2 +25x +24 = (x +1)(x +24)

Final Answer:

The test statistic for the difference in proportions between the metropolitan area and the U.S. population is approximately ( -0.11 ). Since this value does not exceed the critical value of [tex]\( \pm 1.96 \)[/tex] at the 0.05 significance level, there is insufficient evidence to conclude a significant difference. Therefore, we fail to reject the null hypothesis.

Step-by-step explanation:

To determine whether there is sufficient evidence to conclude that a difference exists between this metropolitan area and the larger U.S. population, we can perform a hypothesis test for the difference in proportions.

Let:

[tex]\( p_1 \)[/tex]  be the proportion of women in the metropolitan area.

[tex]\( p_2 \)[/tex] be the proportion of women in the larger U.S. population.

The null hypothesis [tex](\( H_0 \))[/tex] is that there is no difference between the proportions, and the alternative hypothesis [tex](\( H_1 \))[/tex] is that there is a significant difference.

The formula for the test statistic for the difference in proportions ( z ) is given by:

[tex]\[ z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{p(1-p)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} \][/tex]

Where:

[tex]\( \hat{p}_1 \)[/tex]  and [tex]\( \hat{p}_2 \)[/tex] are the sample proportions of women in the metropolitan area and the U.S. population, respectively.

( p ) is the combined sample proportion.

[tex]\( n_1 \)[/tex]  and [tex]\( n_2 \)[/tex] are the sample sizes for the metropolitan area and the U.S. population, respectively.

First, let's calculate [tex]\( \hat{p}_1 \)[/tex], [tex]\( \hat{p}_2 \)[/tex], ( p ), and then plug them into the formula to find the test statistic.

[tex]\[ \hat{p}_1 = \frac{112}{150} = 0.7467 \][/tex]

[tex]\[ \hat{p}_2 = \frac{150}{200} = 0.75 \][/tex]

[tex]\[ p = \frac{112 + 150}{150 + 200} = \frac{262}{350} = 0.7486 \][/tex]

Now, we can calculate the test statistic:

[tex]\[ z = \frac{(0.7467 - 0.75)}{\sqrt{0.7486(1-0.7486)\left(\frac{1}{150} + \frac{1}{200}\right)}} \][/tex]

Calculate the values and round the test statistic to two decimal places. If the absolute value of the test statistic is greater than the critical value for a two-tailed test at the 0.05 significance level, we reject the null hypothesis.

Note: The critical value for a two-tailed test at the 0.05 significance level is approximately [tex]\( \pm 1.96 \)[/tex].

Answer:

Step-by-step explanation:

Hello!

a)

An observational study is one where the investigator has no control or intervenes on it. He just defines the variable of interest and merely collects and documents the information. These types of studies are usually made as precursors to a more formal experimental study, to have an idea of what's to be expected from the population.

An experimental study or experiment is one where the investigator intervenes by defining the variable of interest and artificially manipulates the study factor. It is also one of its characteristics the randomization of cases or subjects in groups (two or more, depending on what is the hypothesis of study).

In this example, the investigators used a randomized block design with "Bag" as the blocking factor and assigned the bags randomly to the students of the statistic class.

The researchers manipulated all confounding factors in this experiment leaving only "the number of candies per color per bag" as the only random variable. This is an experimental study.

b)

This is an ANOVA with two factors, "Bag" and "Colour" and the treatments are all possible combinations between these two factors.

Correct Option A.

c) The response variable is the "number of candies per color per bag"

Colors: Blue, Red, Orange, Green, Brown and Yellow.

I hope you have a nice day!

Answer:

[tex]7[/tex]

Step-by-step explanation:

[tex] \frac{b}{2.4} \\ \frac{16.8}{2.4} \\ = 7[/tex]

Final answer:

The total sales five months after the beginning of the campaign is approximately 72 million dollars.

Explanation:

To find the total sales five months after the beginning of the campaign, we need to calculate the definite integral of the sales rate function from t=0 to t=5. The sales rate function can be expressed as S'(t) = 10 - 10e^(-0.2t).

First, let's find the antiderivative of the sales rate function. The antiderivative of 10 is 10t, and the antiderivative of -10e^(-0.2t) is 50e^(-0.2t). Therefore, the indefinite integral of S'(t) is S(t) = 10t - 50e^(-0.2t) + C, where C is the constant of integration.

Next, we evaluate the definite integral over the interval t=0 to t=5. Substituting the upper and lower limits into the antiderivative, we get S(5) - S(0) = (10(5) - 50e^(-0.2(5))) - (10(0) - 50e^(-0.2(0))) = (50 - 50e^(-1)) - (0 - 50e^0) = 50 - 50e^(-1) + 50 = 100 - 50e^(-1) million dollars.

Rounding the answer to the nearest million, the total sales five months after the beginning of the campaign is approximately 72 million dollars.

Answer:

The Linear programming problem has 3 constraints :- Milling time, Inspection time, Drilling time constraints.

Step-by-step explanation:

Product A : 9 minutes milling, 7 minutes inspection, 6 minutes drilling Product B : 10 minutes milling, 5 minutes inspection, 8 minutes drilling Product C  : 7 minutes milling, 3 minutes inspection, 15 minutes drilling

Total milling time available  = 20 hours = (20 x 60) i.e 1200 minutes Total inspection time available = 15 hours = (15 x 60) i.e 900 minutes Total drilling time available = 24 hours = (24 x 60) i.e 1440 minutes

Let QA, QB, QC be quantities of product A, B, C respectively

Answer:

[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]

The degrees of freedom are given by:

[tex] df =n-1=25-1=24[/tex]

And the p value would be given by:

[tex] p_v = P(t_{24}>2) =0.0285[/tex]

And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate      

Step-by-step explanation:

Data provided

[tex]\bar X=4.2[/tex] represent the sample mean for the weigths

[tex]s=0.5[/tex] represent the sample standard deviation

[tex]n=25[/tex] sample size      

[tex]\mu_o =4[/tex] represent the value that we want to analyze

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

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

System of hypothesis

We want to conduct a hypothesis in order to check if the true mean weigth is less than 4 or not, the system of hypothesis would be:      

Null hypothesis:[tex]\mu \leq 4[/tex]      

Alternative hypothesis:[tex]\mu > 4[/tex]      

The statistic for this case is given by:

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

Replacing the info given we got:

[tex]t=\frac{4.2-4}{\frac{0.5}{\sqrt{25}}}=2[/tex]  

The degrees of freedom are given by:

[tex] df =n-1=25-1=24[/tex]

And the p value would be given by:

[tex] p_v = P(t_{24}>2) =0.0285[/tex]

And since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case is significantly hiher than 4. And the claim for this case is not appropiate