the class average on a statistics test is 62 marks with a standard deviation of 12 marks. what minimum mark must a student obtain to be in the top 9% of the class?

Answer:

The constraints are:

Plot the graphs of the constraints

From the graph (see attachment), the only optimal point is (3,4)

Substitute 3 for x and 4 for y in the objective function.

So, we have:

Hence, the maximum value of C is 17

Step-by-step explanation: Hope this helps!!!

You need 1.8 lbs of the type of chocolate that sells for $2.50/lb and 6.6 lbs of the type of chocolate that sells for $3.60/lb.

A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these problems. The intersection of two lines represents the system of equations' solution.

let

x = lbs of the type of chocolate that sells for $2.50/lb

y = lbs of the another type of chocolate that sells for $3.90/lb

You would like to have 8.4 lbs of a chocolate mixture that sells for $3.60/lb

x + y = 8.4

2.50x + 3.90y = 8.4 x 3.60

2.50x + 3.90y = 30.24

Putting the value of x = 8.4 - y in equation 2.

2.50( 8.4 - y) + 3.90y = 30.24

21 - 2.5y + 3.9 y = 30.24

1.4y = 9.24

y = 6.6

Putting y in x equation we get,

x = 1.8

by solving the above system of equations we find:

x = 1.8 lbs

y = 6.6 lbs

Therefore, each chocolate will you need to obtain the desired mixture is 1.8 lbs and 6.6 lbs.

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The result of the two-sided test with the null hypothesis of the population mean equaling 43, based on the 95% confidence interval that ranges from 35 to 45, would be rejecting the null hypothesis.

The 95% confidence interval that ranges from 35 to 45 suggests that we are 95% confident that the true population mean falls between those values.

To conduct a two-sided test with the null hypothesis of the population mean equaling 43, we can use the confidence interval to see if the null hypothesis falls within the range of the confidence interval or not.

Since the null hypothesis of 43 is not within the confidence interval of 35 to 45, we can reject the null hypothesis at the 0.05 level of significance, which means we have evidence to suggest that the true population mean is not 43.

Therefore, the likely result of our test would be rejecting the null hypothesis.

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The height of the trapeziod is 7 feet

The formula used for calculating the area of a trapezoid is expressed with the equation;

A = (a + b)/2 h

Such that the parameters in the equation are;

Substitute the values, we have;

24. 5 = (3 + 4)/2 h

add the values

24. 5 = 7//2 h

Divide the values

24.5 = 2.5 h

Make 'h' the subject of formula by dividing both sides by 3.5, we get;

h = 24.5/3.5

h = 7 feet

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Answer: x = 24

Step-by-step explanation:

21 + 3= 24

Diego can make 56 bags with each bag containing 8 brownies and 12 cookies.

To package both items, he can divide the items into groups of 8 brownies and 12 cookies. He will then make 56 of these groups, ensuring each bag contains 8 brownies and 12 cookies.

Diego has 48 brownies and 64 cookies to package. To make the same combination of items in each bag, he needs to group the items into groups of 8 brownies and 12 cookies.

This can be done by dividing the 48 brownies into 6 groups of 8, and the 64 cookies into 5 groups of 12. He then needs to combine these two groups together, making 56 total bags.

Each of these bags will contain 8 brownies and 12 cookies. This is one way of packaging both items so that each bag has the same combination.

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Answer:

the amswer is five apples

From the given information provided, the surface area and volume of cylinder is 1130.97 and 3816.85 respectively.

To find the surface area and volume of the cylinder, we can use the following formulas:

Surface Area = 2πr² + 2πrh

Volume = πr²h

Substituting the given values, we get:

Surface Area = 2π(9)² + 2π(9)(15) = 1130.97 square inches (rounded to the nearest tenth)

Volume = π(9)²(15) = 3816.85 cubic inches (rounded to the nearest tenth)

Therefore, the surface area of the cylinder is approximately 1130.97 square inches, and the volume is approximately 3816.85 cubic inches, both rounded to the nearest tenth.

Question - A cylinder has a height of 15 in and a radius of 9 in. Find area and volume. Round to the nearest tenth.

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Answer: it should be 17.5

15+20 = 35

35/2 = 17.5 -----> mean of the two numbers

so, the BEST supported conclusion is option D: "A majority of visitors had a favorite attraction."

Percentage is a way of expressing a number as a fraction of 100. The symbol used to represent percentage is "%". For example, if we say that 75% of students passed a test, it means that 75 out of every 100 students passed the test.

To calculate a percentage, you can use the following formula:

[tex]percentage = (part/whole) * 100[/tex]

Here, "part" refers to the number that is being expressed as a percentage of the "whole" number. For example, if we want to find out what percentage of 80 is 20, we can use the formula as follows:

percentage = (20/80) x 100 = 25%

So, 20 is 25% of 80.

According to the results of the sample, 40% of the visitors responded that they had no favorite attraction, while the remaining 60% did have a favorite. Among those who had a favorite attraction, the percentages for each attraction were: 15% safari, 20% aquarium, and 25% panda bears. Therefore, no conclusion can be made about which attraction was the most popular among all visitors. However, it is possible to conclude that a majority of visitors (60%) had a favorite attraction, so the BEST supported conclusion is option D: "A majority of visitors had a favorite attraction."

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The greatest integer m for which n is an integer is 40.

This is because the product of all multiples of 3 between 1 and 100 (n) is equal to the product of all integers from 3 to 99, which is equal to 3^39*2^20.

By using the prime factorization of n, we can see that the greatest integer m is equal to the sum of the exponents of the prime factors, which is 39 + 20 = 40.

To solve this problem, we must first factor n, which is the product of all multiples of 3 between 1 and 100. n can be expressed as a product of prime factors 3^39*2^20.

This can be further expressed as 3^39*2^20 = (3*2)^39*2^20 = 6^39*2^20. To find the greatest integer m for which n is an integer, we must add the exponents of the prime factors, which gives us 39 + 20 = 40. Therefore, the greatest integer m for which n is an integer is 40.

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The equation of the circle is with the diameter given is x² + y² = 9.

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

We can quickly determine the circle's centre and radius thanks to this form. We must first square the x and y terms before rearranging the components in order to transform a circular equation into standard form.

The endpoints of the diameter is (-3,0) and (3,0).

Now, using the section formula the coordinates of radius are:

((-3+3)/2, (0+0)/2) = (0,0

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h,k) is the center of the circle.

Substituting the values:

(x - 0)² + (y - 0)² = 3²

Hence, the equation of the circle is x² + y² = 9.

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The table showing the distance traveled by the boat at various times should be completed as follows;

Time (h)                  0      0.5     1      1.5     2     2.5      3

Distance (mi)          0       1        2      3       4      5        6

In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in the table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 3/1.5

Constant of proportionality, k = 2.

When x = 0.5, the distance is given by;

y = 2x

y = 2(0.5) = 1 mile.

When x = 1, the distance is given by;

y = 2x

y = 2(1) = 2 miles.

When x = 2, the distance is given by;

y = 2x

y = 2(2) = 4 miles.

When x = 2.5, the distance is given by;

y = 2x

y = 2(2.5) = 5 miles.

When x = 3, the distance is given by;

y = 2x

y = 2(3) = 6 miles.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

At alpha equal to 0.01 there is enough evidence to reject the claim that is the chance of a false positive.

When reducing the alpha from 0.05 to 0.01 reduces the chance of a false positive also called a Type I error, it makes it harder to detect differences with a t-test and with any significant results one might obtain would be more trustworthy but there would probably be less of them.

We know that:

probability > 0.1: no evidence,

then, probability between 0.05 and 0.1: weak evidence

then, probability between 0.01 and 0.05: evidence

then, probability between 0.001 and 0.01: strong evidence

and probability < 0.001: very strong evidence

The alpha level set relates to the formal decision made rather than this informal interpretation, but both can be reported together.

Lower alpha levels are sometimes used while carrying out multiple tests at the same time and a common approach is to divide the alpha level by the number of tests being carried out.

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So the coordinates of point X' after dilation are (15, 11).

Polygon WXYZ is dilated by a scale factor of 3, with vertex W as the center of dilation. This means that the distances from vertex W to the other vertices are multiplied by 3, while W remains unchanged. Given the coordinates of point W are (3,2) and point X are (7,5), we can find the coordinates of point X' after dilation.

To do this, first determine the change in the x and y coordinates from point W to point X:

Δx =[tex]7 - 3 = 4\\[/tex]
Δy =[tex] 5 - 2 = 3[/tex]

Now multiply these changes by the scale factor of 3:

Δx' =[tex] 4 * 3 = 12[/tex]
Δy' =[tex] 3 * 3 = 9[/tex]

Now add these new changes to the original coordinates of point W to get the coordinates of point X':

X'(x) =[tex] W(x) + Δx' = 3 + 12 = 15[/tex]
X'(y) = [tex]W(y) + Δy' = 2 + 9 = 11[/tex]

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Answer:

Step-by-step explanation:

9to12

Answer:

b = 12 units

Step-by-step explanation:

In a right angled triangle,

Base² + Perpendicular² = Hypotenuse²

b² + 16² = 20²

b² = 20² - 16²

b² = 400 - 256

b² = 144

b = √144

b = 12 units

Answer:

Step-by-step explanation:

To find the percentage of the original amount that Dylan has remaining on his gift card, we can divide the remaining amount by the original amount and then multiply by 100 to express it as a percentage.

The original amount on the gift card was $20.00, and the remaining amount is $0.06, so the percentage of the original amount that Dylan has remaining on his gift card is:

($0.06 ÷ $20.00) x 100% =

0.003 x 100% =

0.3%

Therefore, Dylan has 0.3% of the original amount remaining on his gift card.

Answer:

Step-by-step explanation:

The total surface area includes:

The area is:

Answer:

There is a [tex]\frac{1}{24}[/tex] chance that Sara will be picked.

There is a 4.16% chance that Sara will be picked.

Step-by-step explanation:

there are 12 boys + 12 girls in Mooney's class => 24 total students

Sara is ONE out of those students

Sara is [tex]\frac{1}{24}[/tex].

[tex]\frac{1}{24}[/tex] as a percent is 4.16%.

Using the identity sin² 0 + cos² 0 = 1, the value of cos 0 is 0.951 (to the nearest hundredth)

Using the identity sin² 0 + cos² 0 = 1, we can solve for cos 0:

cos² 0 = 1 - sin² 0

cos² 0 = 1 - (-0.31)²

cos² 0 = 1 - 0.0961

cos² 0 = 0.9039

Taking the square root of both sides, we get:

cos 0 ≈ ±0.951

Since 0 is in the interval ³ < 0 < 2π, we know that cos 0 must be positive. Therefore, to the nearest hundredth, cos 0 ≈ 0.95.

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Glenn orders the same drink every time. This can be answered by the Simple intelligence.

The logic behind this conclusion is as follows:

Brian orders tea: In this case, John must order the same drink as Glenn. According to statement 4, if Brian orders tea, John orders the drink that Glenn orders. However, Glenn's choice is not dependent on Brian's choice, so Glenn will always order the same drink. Therefore, Glenn is the only person who orders the same drink every time.

Therefore, Glenn orders the same drink every time.

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The frequency table would have three classes, one for each digital music player option.

When summarizing the consumer responses with a frequency table, the frequency table would have 3 classes.

Frequency table:

A frequency table is a statistical tool that is used to organize raw data in a clear and concise manner.

It is a way of representing the information contained in the data so that it can be easily interpreted and analyzed.

A frequency table is often used to summarize categorical data, such as the data collected in a marketing study like the one mentioned in the question.

The marketing study in this question involved asking 100 consumers to select the best digital music player from three options:

the iPod Touch, Sony Walkman, and Zune HD.

To create a frequency table from this data, we would need to count the number of times each option was chosen by the consumers.

This can be done by grouping the data into classes, which are categories that are created based on the values in the data.

For this particular study, there are only three options to choose from, so there are only three possible classes:

iPod Touch, Sony Walkman, and Zune HD. We would simply count the number of times each option was chosen and record it in the appropriate class.

The resulting frequency table would look something like this: Digital Music Player Frequency i Pod Touch 45 Sony Walkman 28 Zune HD27

Total 100

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The probability of drawing a second card as an ace after drawing one card and putting it aside without looking at it depends on the outcome of the first draw and whether the card was replaced or not.

The possibility of drawing an ace from a general deck of 52 playing cards is 4/52, or 1/13. But, the probability of drawing an ace as the second card relies upon whether or not the first card drawn turned into an ace or now not, in addition to whether the first card was replaced lower back into the deck or no longer.

If the primary card becomes an ace and it was now not replaced, then there are only three aces left inside the deck out of fifty-one cards, so the opportunity of drawing another ace as the second card could be 3/51.

However, if the primary card becomes an ace and it is turned into changed, then the opportunity of drawing any other ace as the second one card would nonetheless be 4/52, or 1/13 because the deck could be efficiently reset.

Then again, if the primary card was now not an ace, then there might be 4 aces left inside the deck out of fifty-one cards. Consequently, the opportunity of drawing an ace as the second card could be 4/51.

In precis, the opportunity of drawing a 2nd ace from a well-known deck of cards could rely on the outcome of the primary draw and whether the cardboard was replaced or no longer.

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The expense of 1.5 lbs of bananas and 1 gallon of apple juice, according to the provided statement, is $7.45.

Multiplication is one of the four basic operations in mathematics, along with adding, subtracting, and division. Multiply in mathematics refers to the continual adding of sets of identical size.

The cost of 1.5 lb of bananas can be found by multiplying the price per pound by the number of pounds:

Cost of 1.5 lb of bananas = 1.5 x $1.97 = $2.96 (rounded to the nearest cent)

The cost of 1 gallon of apple juice is $4.49.

So, the total cost of 1.5 lb of bananas and 1 gallon of apple juice is:

Total cost = Cost of bananas + Cost of apple juice

Total cost = $2.96 + $4.49

Total cost = $7.45

Therefore, the cost of 1.5 lb of bananas and 1 gallon of apple juice is $7.45.

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It would be: D) Increased recycling of waste

Your Welcome

A = P(1 + r/n)^(nt)

Where:

A = the amount of money after t years

P = the principal amount (in this case, $4000)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year (in this case, twice a year, so n = 2)

t = the number of years

Plugging in the given values, we get:

A = 4000(1 + 0.02/2)^(2t)

Simplifying, we get:

A = 4000(1.01)^2t

Therefore, the function that models the situation is:

A = 4000(1.01)^(2t)