(Photo attached) Trig question. Please explain and thanks in advance! :)

Answer:2

4 th root of 1024 is 5

Since 4 x4x4x4x4=1024

So 1+2x=5

-1 PN both sides

2x= 4

Divide by 2

X=2

Step-by-step explanation:

Answer:

The 98% confidence interval for the average credit card balance is

(564.04, 635.96).

Step-by-step explanation:

We have to calculate the 98% confidence interval on the average credit card balance.

The sample will consist of the n=30 customers that have credit card.

The sample has a mean of $600 and a standard deviation of $80.

As the population standard deviation is estimated from the sample standard deviation, we will use a t statistic.

The degrees of freedom are:

[tex]df=n-1=30-1=29[/tex]

The critical value for a 98% CI and 29 degrees of freedom is t=2.463 (this can be looked up in a t-table).

Then, the margin of error is:

[tex]E=t\cdot s/\sqrt{n}=2.463*80/\sqrt{30}=197.04/5.48=35.96[/tex]

Then, the upper and lower bounds of the confidence interval are:

[tex]LL=\bar X-E=600-35.96=564.04\\\\UL=\bar X+E=600+35.96=635.96[/tex]

Median: 133.5

Lower/First quartile: 128

Upper/Third quartile: 139

Interquartile range: 139 - 128 = 11

so your interquartile range is 11

Answer:

1  1/10 gallons

Step-by-step explanation:

Add 4/5 gallon + 3/10 gallon

Get a common denominator of 10

4/5*2/2  + 3/10

8/10 +3/10

11/10

Change from an improper fraction to a mixed number

10/10 + 1/10

1 1/10 gallons

Answer:

1.1

Step-by-step explanation:

If she added the first 4/5 then she added the 3/10 then you have to add them to figure out how much water is in the bucket.

Answer:

[tex]n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92[/tex]

So the answer for this case would be n=92 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

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

[tex]\mu[/tex] population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =1.5 and we are interested in order to find the value of n, if we solve n from equation (b) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for 92% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.04;0;1)", and we got [tex]z_{\alpha/2}=1.75[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.75(8.2)}{1.5})^2 =91.52 \approx 92[/tex]

So the answer for this case would be n=92 rounded up to the nearest integer

Answer:

She would have to sell 44 cookies or more.

Step-by-step explanation:

Answer:

She would have to sell 44 cookies or more

Step

Answer:

d

Step-by-step explanation:

C is the center of a circle. Find the length of arc AB to two decimal points

Answer:

d

Step-by-step explanation:

s=13.68

Answer:

The risk consequence of both activities is 1.6 months.

Step-by-step explanation:

We can define a randome variable D: total delay time for the project, and calculate its expected value.

This would be the risk consequence of both activities.

The expected delay time for the project is the sum of the expected delay for task A plus the expected delay for task B. It is assumed the likelihood of a problem in any task is independent of the other.

Then, each expected delay for a task is equal to the probability of a problem multiplied by the consequence (delay time).

[tex]E(D)=E(D_a)+E(D_b)=p_aT_a+p_bT_b\\\\E(D)=0.5*2+0.2*3=1+0.6=1.6[/tex]

The risk consequence of both activities is 1.6 months.

Answer:

It is A,B,and E.

I just did the question and it was right

The true statements about the dot plots are (A) Both have the same number of data points, (B) Both means are between 3 and 4. and (C) Westwood has less variability than Middleton.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Given are two plots, Middleton and Westwood.

Data points in plot 1 are 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 9

Total number of data points in plot 1 or Middleton = 20

Data points in plot 2 are 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6

Total number of data points in plot 2 or Westwood = 20

So, both have the same number of data points.

Mean of Middleton = Sum of the data points / Total number of data points

                                = [1 + (4×2) + (5×3) + (4×4) + (4×5) + 6 + 9] / 20

                                = 75/20

                                = 3.75

Similarly,

Mean of Westwood = 77/20 = 3.85

So both means are between 3 and 4.

Median is the exact middle element when arranged in increasing or decreasing order.

Exact middle point is the average of 10th and 11th element.

Median of Middleton = (3 + 4)/2 = 3.5

Median of Westwood = (4 + 4)/2 = 4

Both have different medians.

Range of the data set is the difference of maximum point and minimum point.

Range of Middleton = 9 - 1 = 8

Range of Westwood = 6 - 2 = 4

Both have different ranges.

Range is a measure of variation.

Range of Westwood is less than range of Middleton.

So, Westwood has less variability than Middleton.

Hence the true statements are A, B and C.

Learn more about Mean and Median here :

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There are 54 two-digit numbers greater than 45. This is calculated by finding the range of valid two-digit numbers (46 to 99) or carefully counting possible combinations without including 45.

The two-digit numbers greater than 45 are any numbers from 46 to 99. We can find the amount of these numbers by subtracting 45 from 99. So, there are 54 two-digit numbers greater than 45.

Another way to visualize this is by considering the two-digit possibilities. The first digit can range from 4 to 9 (six possibilities), and the second digit can range from 0 to 9 (ten possibilities). However, since 40-45 are not included, we subtract 5 from the total possibilities, resulting in 60 (=6*10) -5 = 55. Therefore, it seems that we have one number too many, but we must not forget that 45 itself is not included, hence the total numbers exceeding 45 are 54 (55-1).

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Answer:

3

Step-by-step explanation:

0 indicates no relationship. must be full number.

Answer:

(0.339, 0.391)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1295, \pi = \frac{473}{1295} = 0.365[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.365 - 1.96\sqrt{\frac{0.365*0.635}{1295}} = 0.339[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.365 + 1.96\sqrt{\frac{0.365*0.635}{1295}} = 0.391[/tex]

So the correct answer is:

(0.339, 0.391)

Answer:

1/3

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

took a test and its correct.

Answer:

A, E

Step-by-step explanation:

brainliest please

Answer:

The 95% confidence (and interpret) the proportion of all American adults of European an- cestry who dislike the taste of cilantro

(  0.2552  , 0.2709)

b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is  0.2552

Step-by-step explanation:

Explanation:-

Given data a survey of 12087 American adults of European ancestry asked whether they like or dislike the taste of cilantro.

large sample size 'n' = 12087 American adults

in survey A total of 3181 said that they dislike the taste of cilantro.

so The sample proportion 'p' = [tex]\frac{3181}{12087} = 0.2631[/tex]

a) Estimate with 95% confidence (and interpret) the proportion of all American adults of European ancestry who dislike the taste of cilantro.

[tex](p - 1.96 \sqrt{\frac{pq}{n} } ,p + 1.96\sqrt{\frac{pq}{n} } )[/tex]

[tex](0.2631 - 1.96 \sqrt{\frac{0.2631 X 0.7369}{12087} } ,0.2631 + 1.96\sqrt{\frac{0.2631 X 0.7369 }{12087} } )[/tex]

(0.2631 - 0.00784 , 0.2631 + 0.00784 )

(  0.2552  , 0.2709)

b) The lower bound for the proportion of all American adults of European ancestry who dislike the taste of cilantro is  0.2552

We are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%, and at least 25.5% dislike the taste.

This question is related to confidence intervals in statistics. To compute a confidence interval for a population proportion, we mainly need the sample proportion and the size of the sample. Here, the proportion is the number of respondents that dislike cilantro (3181) divided by the total number of respondents (12087).

Thus, the sample proportion (value of p) is 3181/12087 = 0.263 or 26.3%.

The formula for a confidence interval is:

CI = p +/- Z * sqrt[ (p(1-p)) / n ],

where Z is the Z-score (for 95% confidence, Z = 1.96), p is the sample proportion, and n is the sample size.

Applying the values, we get:

CI = 0.263 +/- 1.96 * sqrt[ (0.263)(1 - 0.263) / 12087 ]

After calculation, the 95% confidence interval is about (0.255, 0.271). This means we are 95% confident that the proportion of all American adults of European ancestry who dislike the taste of cilantro is between 25.5% and 27.1%.

For the lower bound, we can take the lower limit of our confidence interval, which is 0.255 or 25.5%. This means we are 95% confident that at least 25.5% of all American adults of European ancestry dislike the taste of cilantro.

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Answer:

9100

Step-by-step explanation:

I=Prt

I=7,000(.06)5

I=420(5)

I=2,100

2,100+7,000=9,100

Answer:

A. Brand A has a higher average price than brand B.

D. Brand A's prices are less spread out than brand B's prices.

Step-by-step explanation:

We are given the means and standard deviations for samples of prices from two  different brands of shoes below;

 Brand A                                                                  Brand B

Mean : $50                                                           Mean : $40

Standard deviation : $5                                  Standard deviation : $8    

Now, from the given statements;

Statement A is correct that Brand A has a higher average price than brand B because as given above Mean of Brand A ($50) > Mean of Brand B ($40).

Also, Statement D is correct that Brand A's prices are less spread out than brand B's prices because the Variance of Brand A is less than the variance of Brand B, i.e.;

    Variance of Brand A = [tex]5^{2}[/tex] = $25

    Variance of Brand B = [tex]8^{2}[/tex] = $64

Clearly, $25 < $64, so statement D is also correct.

Therefore, the two true statements are Statement A and Statement D.

Final answer:

A. Brand A has a higher average price than brand B.

D. Brand A's prices are less spread out than brand B's prices.

Explanation:

The true statements are that Brand A has a higher average price and less variability in prices than Brand B, which is represented by a lower standard deviation for Brand A.

To expand on these points:

Brand A has a mean price of $50 which is higher than Brand B's mean price of $40, confirming that Brand A has a higher average price (Statement A).

Brand A's standard deviation is $5, while Brand B's standard deviation is $8. A standard deviation is a measure of spread or variability in a set of data. The fact that Brand A's standard deviation is lower indicates that its prices are less variable and more closely clustered around the mean, hence less spread out compared to Brand B (Statement D).

Answer:

use 6cm twice and that adds up to 12cm .six is the minimal possible number

A ruler designed to measure lengths from one unit to twelve units with the minimum number of marks would only have marks at every unit. This results in only eleven markings (from 1 to 11), as the 0 marks the start and the twelfth unit marks the end.

The subject of the student's question pertains to the design of a ruler with the minimum possible number of marks that can measure lengths from one to twelve units. To achieve this, the ruler should only be marked at every unit. This way, there would be only eleven marks (1-11), as the 0 marks the start of the ruler and the twelfth unit is considered the end of the ruler but does not require a mark. Therefore, only the spaces between these numbers need to be marked to enable measurement all the way up to twelve units.

In practice, such a ruler is less precise than a ruler with more marks as the latter can measure smaller lengths more accurately. However, the task demands the bare minimum for a measure from 1 to 12, thus we have eleven marks.

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5 times,I hoped this helped you out,if not sorry

[tex]\[ s = kt^5 \][/tex]

This equation represents the model for the statement "s is directly proportional to the fifth power of t".

When two variables [tex]\( s \)[/tex] and [tex]\( t \)[/tex] are directly proportional to each other, it means that as one variable increases, the other variable also increases by a constant factor. Mathematically, we can express this relationship as:

[tex]\[ s = kt^n \][/tex]

Where:

- [tex]\( s \)[/tex] is the dependent variable.

-[tex]\( t \)[/tex] is the independent variable.

- [tex]\( k \)[/tex] is the constant of proportionality.

- [tex]\( n \)[/tex] is the exponent representing the power to which the independent variable is raised.

In this case, the statement says that  s is directly proportional to the fifth power of t . So, we have:

[tex]\[ s = kt^5 \][/tex]

This equation represents the model for the statement "s is directly proportional to the fifth power of t".

Complete correct question:

Write a model for the statement

s is directly proportional to the fifth power of t.

QUESTION BEGINNING

Given a snail is traveling along a straight path. The snail’s velocity can be modeled by [tex]v(t)=1.4ln(1+t^2)[/tex] inches per minute for 0 ≤ t ≤ 15 minutes.

Answer:

B=22.35 Inches per minutes

Step-by-step explanation:

If the snail's velocity is [tex]v(t)=1.4ln(1+t^2)[/tex] per minute, its displacement for             0 ≤ t ≤ 15 minutes is given by the integral:

[tex]\int v(t) dt=\int (1.4ln(1+t^2))dt=76.04307[/tex]

The constant acceleration of the ant is 2 Inches per minute.

The velocity of the ant therefore, twill be:

[tex]\int 2 dt=2t+K, $where K is a constant of integration$[/tex]

For the interval, 12≤t≤15, the displacement of the ant is:

[tex]\int_{12}^{15}(2t+K) dt=81+3K[/tex]

Since the snails displacement and that of the ant are equal in 12≤t≤15.

81+3K=76.04307

3K=76.04307-81

3K=-4.95693

K=-1.65231

At t=12, the velocity of the ant  is therefore:

2t+K=2(12)-1.65231=22.348 Inches per minutes

B=22.348 Inches per minutes

Final answer:

The question examines a scenario involving an ant accelerating to catch up with a snail, focusing on determining the ant's velocity at the catch-up point. Utilizing the principle of kinematics and acceleration, the answer lies in relating the acceleration to the final velocity, dependent on the time variable, which underscores the direct relationship between acceleration and velocity increase.

Explanation:

The question essentially deals with kinematics, specifically with the scenario of an ant accelerating from rest to catch up with a snail. Given the ant accelerates at 2 inches per minute per minute, and eventually matches velocities with the snail, the goal is to find the ant's velocity (B inches per minute) at the moment it catches up.

Firstly, we know the acceleration (a) is 2 inches/minute2. From kinematic equations, specifically v = u + at, where 'u' is the initial velocity (0 in this case since the ant starts from rest), 'a' is acceleration, and 't' is time, we can plug in our values. The time variable 't' here represents the duration from when the ant starts until it catches up with the snail, which is not explicitly given but is critical in understanding the rate of acceleration's contribution to velocity.

For the purpose of solving this problem, without explicit time or distances, we focus on the principle that the ant's final velocity (B) is a product of its acceleration over a given period: B = 0 + (2)t. Thus, the value of 'B' entirely depends on the time 't', demonstrating a direct correlation between acceleration duration and velocity increase.

Answer:

13%

Step-by-step explanation:

There are 100 squares and 13 are shaded so

13/100=

13%

Answer:

13%

Step-by-step explanation:

Answer:

The probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches is 0.5319.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard-deviation σ and appropriately huge random-samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the distribution of sample mean is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

[tex]\mu=200\\\sigma=22\\n=83[/tex]

Since n = 83 > 30, the Central Limit Theorem can be used to approximate the sampling distribution of sample mean diameter of the shafts.

Then:

Mean: [tex]\mu_{\bar x}=\mu=200[/tex]

Standard deviation: [tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{22}{\sqrt{83}}=2.415[/tex]

Compute the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches as follows:

[tex]P(\bar X-\mu_{\bar x}<0.20)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{0.20}{2.415})[/tex]

                            [tex]=P(Z<0.08)\\=0.53188\\\approx0.5319[/tex]

*Use a z-table.

Thus, the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches is 0.5319.

Answer:

1,0

Step-by-step explanation:

Answer:

1,0

Step-by-step explanation:

Answer:

a, -b

Step-by-step explanation:

When x is a, the function becomes

[tex]f(a)=3(a-a)(a+b)[/tex]

as you see, a-a is 0, and as your whole function is multiplied by this, it makes it 0.

[tex]f(-b)=3(-b-a)(-b+b)[/tex]

As you see -b+b is 0, and once again, this would make the whole function 0.

Answer:

The standard error of the sample proportion is closest to 1%

Step-by-step explanation:

Standard error of the sample proportion is given as

σₓ = √[p(1-p)/n]

where

p = sample proportion = estimated to be 23% = 0.23

n = Sample size = 2500

σₓ = √[p(1-p)/n]

σₓ = √[0.23×0.77/2500]

σₓ = 0.0084166502 = 0.00842

σₓ = 0.00842 = 0.842%

Hence, it is easy to see that the standard error of the sample proportion is closest to 1%.

Hope this Helps!!!

Answer:

Experiement lacked blindness concept

Step-by-step explanation:

In good experiments, the results are totally unbiased and unknown to anyone, even to those conducting the experiment.

In the given case, the interviewer had an idea about which group had gone for meditation so it was obvious that they would yield less anxiety.

Here the concept of blinding was missing, which is essential for a good and fair experiment. A good experiemnt is a double blinded experiement or atleast it should be single blinded

Answer:

(a)Mean=9

(b)Median=9.5

(c)Mode=12

(d)Standard Deviation=2.53

Step-by-step explanation:

The sample of the number of vehicles that proceeded through the intersection after the light changed for 6 days during a 1 month period is given below:

6 12 7 12 8 9

(a)Mean

[tex]Mean=\frac{6+12+ 7+ 12+ 8+ 9}{6} \\=\frac{54}{6} \\Mean=9[/tex]

(b)Median

First, arrange in ascending order

6,7,8,9,12,12

Since we have two terms in the middle, we take the average.

[tex]Median=\frac{8+9}{2}\\Median=8.5[/tex]

(c)Mode

The mode is the number with the highest frequency. The mode number of cars is 12.

(d)Standard Deviation

[tex]S.D.=\sqrt{\dfrac{\sum_{i=1}^{n}(x-\bar{x})^2}{n-1}}[/tex]

[tex]S.D.=\sqrt\frac{(6-9)^2+(7-9)^2+(8-9)^2+(9-9)^2+(12-9)^2+(12-9)^2}{6-1}[/tex]

[tex]=\sqrt{6.4} \\S.D.=2.53[/tex]

Answer:

i believe it is 4 but i'm not so sure

Step-by-step explanation:

:)

The graph of g(x)=(x-2)^2+3 compared to the graph of f(x)=x^2 is translated 2 units to the right and 3 units upwards.

To understand the transformation of graphs in mathematical terms, consider the initial function f(x) = x^2. The transition to the new function g(x)=(x-2)^2+3 is a result of a shift or translation of the graph. This transformation behaves as per the following rule: g(x) = f(x-h)+k where 'h' units is the horizontal displacement and 'k' units is the vertical displacement.

In the function g(x), x shifts two units to the right (as indicated by (x-2)) and three units upward (as indicated by +3).

So, the correct answer is 2 units right and 3 units up.

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Answer:

see explanation

Step-by-step explanation:

(a)

For the graph to display direct proportion it must pass through the origin.

The graph shown does not pass through the origin thus does not represent direct proportion.

(b)

Given that q is directly proportional to r then the equation relating them is

q = kr ← k is the constant of proportion

To find k use the condition q = 76 when r = 20, thus

76 = 20k ( divide both sides by 20 )

3.8 = k

q = 3.8r ← equation of proportion

When r = 45, then

q = 3.8 × 45 = 171