The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39. 48, 56, 95, 81 and 75. Find the

Range of the marks obtained

Mean marks obtained by the group

The length of the base, x, of the larger flag is 6.25 ft.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

The two flags are similar using the AA criteria.

Thus, the ratio of the segments of the two triangle are equal.

4/5 = 5/x

4x = 25

x = 25/4

x = 6.25 ft

Hence, the length of the base, x, of the larger flag is 6.25 ft.

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The exponential equation is y=2,642(2.5)ˣ. x represents the number of days.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

Given that a video was released to the public, it already had 2,642 views.

One day later, the number of views increased to 3,963.

The number of viewers after one day is ( 3,963 + 2,642 ) = 6,605

Assume that the exponential function y = a(b)ˣ represents the number of viewers. x represents the number of days.

Putting x = 0 and  y = 2,642 in y = a(b)ˣ:

2,642 = a(b)⁰

a = 2,642

Putting x = 1 and  y = 6,605 in y = a(b)ˣ:

6,605 = a(b)¹

Putting a = 2,642:

6,605 = 2,642(b)¹

b = 6,605/2,642

b = 2.5

Therefore, an exponential equation is y=2,642(2.5)ˣ.

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The number of which 3.92 is 56 percent, is 7.

A percentage of an object is how many parts of it there are out of 100 equal parts. For example, if you split a shape into 100 parts, 20 of the parts make 20%.

Given that, 3.92 is what number's 56%,

Let the number be x,

Therefore, by the definition of percentage,

56% of x = 3.92

56/100 × x = 3.92

x = 3.92 × 100/56

x = 392/56

x = 7

Hence, the number of which 3.92 is 56 percent, is 7.

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The most likely explanation for the inconsistency between the first and second studies is that the initial findings were a false positive, meaning that the effect observed was not actually present in the population being studied.

In the given scenario, the researcher tested a new laparoscopic treatment for chronic shoulder dislocation and found statistically significant results compared to an older treatment. This means that the difference between the two treatments was not due to chance and is likely to be a real effect.

However, a replication study failed to show statistical significance, which means that the difference between the two treatments could have been due to chance. This can happen even if the sample sizes were sufficient in all four studies. A lack of statistical significance in a replication study indicates that the effect observed in the first study may not be as strong or consistent as previously thought.

The fact that the third and fourth studies produced the same effects as the second could be attributed to random variation or other factors such as study design, sample selection, or measurement methods.

Statistical significance is a crucial concept in research as it helps to establish the credibility of a study's findings. However, it is important to understand that statistical significance alone does not necessarily mean that the effect observed is meaningful or important in practical terms.

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Answer:

Tje answer is 36

Step-by-step explanation:

16-30=14

24+14=-36

For the given data, the cutoff point using the upper fence is 791.25 minutes.

To find the cutoff point using the upper fence, we need to first calculate the lower and upper fences.

The lower fence is given by the formula:

Lower fence = Q1 - 1.5 x IQR

where Q1 is the first quartile and IQR is the interquartile range.

The upper fence is given by the formula:

Upper fence = Q3 + 1.5 x IQR

where Q3 is the third quartile and IQR is the interquartile range.

To find these values, we first need to order the data:

307 311 322 321 354 363 377 406 410 425

435 461 464 474 499 505 513 534 548

The first quartile (Q1) is the median of the lower half of the data:

Q1 = (354 + 363) / 2 = 358.5

The third quartile (Q3) is the median of the upper half of the data:

Q3 = (513 + 534) / 2 = 523.5

The interquartile range (IQR) is the difference between the third and first quartiles:

IQR = Q3 - Q1 = 523.5 - 358.5 = 165

Now we can calculate the lower and upper fences:

Lower fence = Q1 - 1.5 x IQR = 358.5 - 1.5 x 165 = 91

Upper fence = Q3 + 1.5 x IQR = 523.5 + 1.5 x 165 = 791.25

Therefore, the cutoff point using the upper fence is 791.25 minutes. Any customer who uses more than 791.25 minutes in a month should be contacted by the phone company as part of the fraud prevention program.

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The number of tons required when the central HVAC unit will be installed is 1. 73 tons

For the HVAC unit to be installed, the three separate incubation rooms will have to be installed.

This means that the tons required for the central HVAC unit would be the total sum of the three requirement for the other incubation rooms.

The sum would be :

= 1 / 5 + 5 / 6 + 25 / 36

= 0. 2 + 0. 8333 + 0. 69444

= 1. 72774

= 1. 73 tons

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Answer:

7% sales tax

Step-by-step explanation:

If the pencils cost $6, then the sales tax costs $6.42 - $6 = $0.42. To find the rate, we must divide $0.42 by $6. $0.42/$6 = 0.07. 0.07 is 7%.

Answer:

x = 8

Step-by-step explanation:

AB/AC = BD/DC

2x/12 = x+4/x+1

12x + 4 = 2x² + 2x

2x² - 10x - 48 = 0

x² - 5x - 24 = 0

(x-8) (x+3) = 0

x = 8 (or) x= -3 (impossible)

x = 8

Answer:

c=8p

Step-by-step explanation:

c=8p

Mr. Durant has 5.75 acres of lawn, therefore he was charged $125

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The slope intercept form of an equation is:

y = mx + b

where m is the rate of change and b is the y intercept.

Let y represent the total cost of charging  for mowing x acres.

He charges a flat rate of $10 plus $5 per quarter acre of lawn. Therefore:

$5 = quarter acre; $(5 * 4) = $20 is for one acre.

y = 20x + 10

He made a total of $125; hence:

125 = 20x + 10

115 = 20x

x = 5.75 acres

Mr. Durant has 5.75 acres of lawn.

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The equation connecting y and x when y is directly proportional to x and y = 30 when x = 6 is y = 5x.

If y is directly proportional to x, we can write the equation in the form:

y = kx

where k is the constant of proportionality.

To find k, we can use the values of y and x given:

y = 30, x = 6

When we enter these values into the formula above, we obtain:

30 = k * 6

Solving for k, we get:

k = 30/6 = 5

Therefore, the equation connecting y and x when y is directly proportional to x is:

y = 5x

When two variables are directly proportional, it means that when one variable increases or decreases, the other variable changes in the same proportion. In this scenario, we are given that y is directly proportional to x and we are also given a specific point on the line, (6, 30). Using this information, we can solve for the constant of proportionality k and write the equation connecting y and x as y = kx, where k is 5.

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The maximum number of points on the circles that a line passing through all three circles can touch is 36.

Two circles may cross in two points, one point, or no points on a aeroplane, digression circles are coplanar circles that cross at a single point.Concentric circles are coplanar circles that share a common centre.

You can select any two circles in (₂³) ways and each pair will intersect at 2 points. Therefore total 3*2=6 points.

Similarly, 4 lines will intersect at (₂⁴)=6

points.

Now each line will intersect at 2 points with a circle. And since we can select a circle in (³₁) ways and a line in (₁⁴) ways, therefore total (₁³)∗(₁⁴)∗2=24 points they will intersect.

Therefore, total number of intersection points = 6 + 6 + 24 = 36 points.

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The function that can be used to find the total height, h, of the building in feet, including the antenna is h = 6.8n + 13.5.

A builder is constructing an office building with n floors that will have an antenna 13.5 feet tall on its roof. Each floor of the building will be 6.8 feet high.

Therefore, the function that can be used to find the total height of the building in feet including the antenna can be calculated as follows:

Therefore,

n = numbers of floors in the building.

h = total height of the building

Hence, the function is as follows

h = 6.8n + 13.5

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The closest answer to initial value of the account is $538,021.66

It is given that the money Seth withdraws was compounded every quarter for 35 years. So, we get,

Amount withdrawn every quarter, P = $4567

Rate of interest, r  =  = 0.002525

Time period, n = 35 × 4 = 140

Now, as we know the formula for annuity as,

[tex]PV = PMT[(1 - (1 / ( 1 + r)^n)) / n][/tex]

where P = installments, PV = present value, r = rate of interest and n = time period.

This gives,[tex]PV = PMT[(1 - (1 / ( 1 + r)^n)) / n]= 4567[1 - (1 / 1.00253^40)) / 0.00253][/tex]

= 4567[(1 - 0.70254) / 0.00253]

= 4567[117.80636]

= $538,021.66

So, the closest answer to initial value of the account is $538,021.66

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By using line of best fit, the time for a trip of 6 miles long is 11.96 minutes.

A line of best fit is a graphical representation of straight line which gives  the best approximation of the given data set.

A taxi driver records the time required to complete various and the distance for each trip.

The best-given fit line by the equation y=0.467x + 0.417.---(1)

where y represents the distance miles, and x represents the time for the trip in minutes.

To find the time for a 6 miles:

i.e., substitute y=6 in the equation(1)

6=0.467x+0.417

⇒x=11.96 minutes.

Hence, by using line of best fit, the time for a trip of 6 miles long is 11.96 minutes.

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Since the chance that the interval contains the actual value of the population parameter is what we put the confidence level 1 - alpha near to 1 when creating confidence intervals for parameters. false

Parameters are a value or set of values that can be used to define or characterize a certain system, model, or process. It is a variable that can be changed to affect how the system or process to which it is connected functions. In mathematics, a parameter is a variable that is used to describe the overall properties of a function or equation. In computer programming, it refers to a value or variable that is passed to a function or procedure. The function or method can then use these parameters to perform a specific operation or calculation.A parameter in statistics is a number that characterizes a population or a sample of data. They help to specify the characteristics.

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240

Step-by-step explanation:

12-8+4+[(6+2)-3]2×3

= 4+4[(6+2)-3]2×3

= 8[(6+2)-3]2×3

= 8[(8)-3]2×3

= 8[5]2×3

= 8[5]6

= 40(6)

= 240

The ratio of girls to boys in the class is 1:3, meaning that for every one girl there are three boys.

There are 10 girls and 30 boys in the class.

The ratio of girls to boys can be expressed as a fraction: 10/30.

To make the fraction easier to understand, we can simplify it to its lowest form: 1/3.

The ratio of girls to boys in the class is therefore 1:3, meaning that for every one girl there are three boys.

The ratio of girls to boys in a class can be determined by dividing the number of girls by the number of boys. In this case, there are 10 girls and 30 boys, so the ratio is 10/30. This fraction can be simplified to its lowest form, 1/3. This means that for every one girl there are three boys in the class. Knowing the ratio of girls to boys can be helpful in a variety of situations, such as organizing activities or determining the number of supplies needed. This ratio can also be expressed as a percentage, with 10% of the class being girls and 30% being boys. Knowing the ratio of girls to boys can also be a useful tool in understanding the demographics of the class.

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Answer:

C 11

Step-by-step explanation:

you have 1 less penny than dimes which is 10 pennies

you have 2 less nickels than dimes which is 9

11+10+9=30

The valid names for the given triangle are options:

B.  ΔMLZ

D.  ΔLMZ

E. ΔZML

A triangle is a two-dimensional shape that is formed by three line segments that are connected end-to-end. It is a fundamental shape in geometry, and its properties and uses are numerous.

Therefore, The triangle in the picture has three vertices labeled L, M, and Z. To name the triangle, we use the labels of the vertices and write them in capital letters. It doesn't matter which vertex we start with, as long as we keep the letters in order as we go around the triangle. So, the names for the triangle in the image can be : ΔLMZ, ΔLZM, ΔMLZ, ΔMZL, ΔZLM, and ΔZML.

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The measure of x in the figure is 180 degrees

From the question, we have the following parameters that can be used in our computation:

The circle and the intersecting chords

The value of x represented by ? is then calculated as

120 = 1/2(x + 60)

Cross multiply the equation

This gives

x + 60 = 240

Subtract 60 from both sides

x = 180

Hence, the measure of x is 180 degrees

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The scale to figure out the heavier stack 2 gram higher.

To determine the heavier stack of coins, you will need to use the electronic scale. However, since you cannot weigh all the coins at once, you will have to use the concept of unitary method.

Based on this, you can calculate the total weight of the coins on the scale. Since each coin weighs 1 gram, the total weight of the coins should be equal to the sum of the natural numbers from 1 to 10, which is 55.

Next, you need to compare the weight of the coins on the scale to the expected weight of 55 grams. If the weight on the scale is less than 55 grams, then the stack of coins that you did not weigh is the heavier stack.

However, if the weight on the scale is more than 55 grams, you need to use the concept of unitary method again. Suppose the weight on the scale is 56 grams. This means that the heavier stack has one coin that weighs 2 grams, and the other stack has 10 coins that weigh 1 gram.

To determine which stack is heavier, you can subtract the expected weight of 55 grams from the weight on the scale (56 grams). The difference is 1 gram.

Now you need to divide the difference by 2 (since one coin weighs 2 grams). This gives you 0.5. This means that the heavier stack has 0.5 coins that weigh 2 grams.

Since you cannot have half a coin, this means that the stack with one coin that weighs 2 grams is the heavier stack.

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Step-by-step explanation:

To find a percentage, it's the portion divided by the total. 100% represents the total between the children or adults respectively in the maintee and evening.

So, to answer, let's find the total of children and adults.

34+27 = 61 is the total for children.

38+46 = 84 is the total for adults.

Now, to find each percentage, take one of the numbers (Children-Maintee, Children-Evening) and divide it by the total we found.

34/61 = 0.557 or 55.7%

27/61 = 0.442 or 44.2%

I'm leaving it in fractional form in case you need a specific decimal answer.

As for adults, it's the same procedure.

38/84 = 0.452 or 45.2%

46/84 = 0.548 or 54.8%

Answer: There would be a higher rate on the 2250 labels on 150 sheets.

Step-by-step explanation:

1080/90 = 12

2250/150 = 15

There would be a higher rate on the 2250 labels on 150 sheets.

Option A: The probability of rejecting H_o, whether it's true or not, best describes the notion of the P-value of a hypothesis test.

The level of marginal significance within the hypothesis test that represents the probability of occurrence of a given event is referred to as its P-value. In order to provide the least significance at which the null hypothesis would be rejected, it is utilized as a choice for the rejection point. This signifies that the option A is correct.

The P-value is known as the probability value. It can be defined as the probability of getting a result that is either the same or more advanced than the actual observations. There is more support for the alternative hypothesis when the P-value is low.

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Correct way to ask the question is:

Which one of the following best defines the notion of the P-value of a hypothesis test?

The probability of rejecting H_o, whether it's true or not

The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.

The probability of the type I error

The probability of the type II error

Answer:

C

Step-by-step explanation:

This would represent the point (0,3)  You would move 5 units to the right of where x is 5.