A yogurt stand gave out 200 free samples of frozen yogurt, one free sample per person. The three sample choices were vanilla, chocolate, or chocolate & vanilla twist. 162 people tasted the vanilla and 115 people tasted the chocolate, some of those people tasted both because they chose the chocolate and vanilla twist. How many people chose chocolate and vanilla twist?

The solution to the proportion  4/(x+1) = 3/(x+2) is x = -5 and

The solution to the proportion  x/(x+3) = (x-2)/x is x = 2.

A quadratic polynomial is a polynomial of degree 2, which means that the highest power of the variable in the polynomial is 2. A quadratic polynomial can be expressed in the general form:

a[tex]x^2[/tex] + bx + c

where a, b, and c are constants, and x is the variable.

In this form, coefficient a is the leading coefficient, and it determines the concavity of the quadratic function. If a is positive, the function is concave up, meaning that it opens upward and has a minimum value. If a is negative, the function is concave down, meaning that it opens downward and has a maximum value.

The quadratic polynomial is named as such because it is a polynomial of degree 2, and the term "quad" means "square." The quadratic function is commonly seen in geometry, algebra, and physics, and it has many applications in real-life problems, such as finding the maximum or minimum values of a function, determining the trajectory of a projectile, and modeling certain natural phenomena.

Quadratic polynomials can be solved by various methods, including factoring, completing the square, and using the quadratic formula.

To solve the proportion 4/(x+1) = 3/(x+2), we can cross-multiply to get:

4(x+2) = 3(x+1)

Expanding the brackets gives:

4x + 8 = 3x + 3

Subtracting 3x from both sides gives:

x + 8 = 3

Subtracting 8 from both sides gives:

x = -5

To solve the proportion x/(x+3) = (x-2)/x, we can cross-multiply to get:

[tex]x^2[/tex] - 2x = (x+3)(x-2)

Expanding the brackets gives:

[tex]x^2[/tex]- 2x = [tex]x^2[/tex] + x - 6

Subtracting[tex]x^2[/tex] from both sides gives:

-2x = x - 6

Subtracting x from both sides gives:

-3x = -6

Dividing both sides by -3 gives:

x = 2

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The probabilities of winning are 1/6 and 2/9

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

Devices = Number cube and spinner

Using the above as a guide, we have the following sample space:

S = {(1, Red), (2, Red), (3, Red), (4, Red), (5, Red), (6, Red), (1, Yellow), (2, Yellow), (3, Yellow), (4, Yellow), (5, Yellow), (6, Yellow), , (1, Blue), (2, Blue), (3, Blue), (4, Blue), (5, Blue), (6, Blue)}

For Zeke, we have: Factor of 2 and Red

From the sample space, we have

P(Zeke) = 3/18

P(Zeke) = 1/6

For Erin, we have: 5 or 6 and Yellow or Blue

From the sample space, we have

P(Erin) = 4/18

P(Erin) = 2/9

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The circumstances in which the median is the preferred measure of central tendency is given as follows:

There are three measures of central tendency of a data-set, which are defined as follows:

The median represents the middle value of the distribution, hence it should be used in these following cases:

They should be used in this case as the median is less affected by outliers compared to the mean.

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The answers to each part is given below.

Given is that Greenville Fine Jewelry charges $12 per charm, plus $14 for the bracelet. Hanson Jewelers, in contrast, charges $11 per charm and $21 for the bracelet.

For the Greenville Fine Jewelry, we can write -

A{x} = 14 + 12x

For the Hanson Jewelers, we can write -

B(x) = 21 + 11x

To add a certain number of charms to her bracelet, the cost will not be same.

Therefore, the answers to each part is given above.

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Answer: 4[tex]\pi[/tex] m^2

Step-by-step explanation:

The formula to calculate the area of a circle:

[tex]\pi r^{2}[/tex]

Given that the diameter of a circle is 4, we can work out that r (the radius) is 2.

(The radius is half of the diameter)

Therefore we can plug in our values:

[tex]\pi 2^{2}[/tex]

[tex]2^{2}[/tex] = 4

Therefore your answer is:

[tex]4\pi[/tex] [tex]m^{2}[/tex]

(Remember your units!)

Answer: A=12.566

Step-by-step explanation:

A=πr^2

R=2

π*4=12.566

I don't know how you want the answer rounded so I just rounded it to the nearest thousandths

The option which is most appropriate for describing the number line below is option C. [tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{3}{12}[/tex]

A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.

Given a number line, where it is divided into twelfths, with each twelfth labeled.

So the labeled numbers are [tex]\frac{1}{12}[/tex], [tex]\frac{2}{12}[/tex], ..............[tex]\frac{10}{12}[/tex], [tex]\frac{11}{12}[/tex], [tex]\frac{12}{12}[/tex].

A dashed arrow is shown starting at ten-twelfths and ending at, as well as pointing to, seven-twelfths.

Arrow starts at [tex]\frac{10}{12}[/tex] and ends at [tex]\frac{7}{12}[/tex].

There is a distance of [tex]\frac{10}{12}[/tex] - [tex]\frac{7}{12}[/tex] = [tex]\frac{3}{12}[/tex].

So the first form of expression is [tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] in order to get [tex]\frac{7}{12}[/tex].

Then the dashed arrow starts from [tex]\frac{7}{12}[/tex] and ends at [tex]\frac{3}{12}[/tex].

There is a distance of [tex]\frac{7}{12}[/tex] - [tex]\frac{3}{12}[/tex] = [tex]\frac{4}{12}[/tex].

So the second form is [tex]\frac{7}{12}[/tex] - [tex]\frac{4}{12}[/tex] in order to get [tex]\frac{3}{12}[/tex].  

So the complete description of the number line is,

[tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{3}{12}[/tex]

Hence the correct option is [tex]\frac{10}{12}[/tex] - [tex]\frac{3}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{3}{12}[/tex].

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Answer: also too tiny

Step-by-step explanation:

show a closer picture

The probability of exactly 90 defective washers is approximately 0.021, and the probability of at least 2 defective items is approximately 0.985.

A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. The probability of exactly 90 defective washers being chosen and the probability of at least 2 defective items being found can be calculated using the hypergeometric distribution formula.

A. The probability of exactly 90 defective washers being chosen can be calculated using the hypergeometric distribution. The probability mass function of the hypergeometric distribution is given by:

P(X = 90) = (400 choose 90) * (1100 choose 110) / (1500 choose 200)

Substituting the given values, we get:

P(X = 90) ≈ 0.021

B. The probability of at least 2 defective items can be calculated as 1 minus the probability of 0 or 1 defective item. The probability of 0 defective items is given by:

P(X = 0) = (1100 choose 200) / (1500 choose 200)

The probability of 1 defective item is given by:

P(X = 1) = (400 choose 1) * (1100 choose 199) / (1500 choose 200)

Substituting these values, we get:

P(X >= 2) = 1 - P(X = 0) - P(X = 1) ≈ 0.985.

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The complete question is:

A shipment of 1500 washers contains 400 defective and 1100 non-defective washers. Two hundred washers are chosen at random (without replacement) and classified as defective or non-defective_ a) What is the probability that exactly 90 defective washers are found? (Do NOT compute out:) b) What is the probability that at least 2 defective items are found?

Option A. segment EH and segment E prime H prime both pass through the centre of dilation is true.

Given triangle EFG:

  E(0, 5), F(1, 1), G(-2, 1)

  Center of dilation is H(0, 1)

  The scale factor is k = 3

The rule for this dilation is:

   (x, y) → (k(x - a) + a, k(y - b) + b)

   (x, y) → (3x, 3(y - 1) + 1) = (3x, 3y - 2)

The coordinates of E'F'G' are:

  E → E' = (0, 5) → (0, 13)

  F → F' = (1, 1) → (3, 1)

  G → G' = (-2, 1) → (-6, 1)

  Points H and H overlap as the centre of dilation at (0, 1)

a. Segment EH and segment E prime H prime both pass through the centre of dilation.

  True

b. The slope of segment EF is similar to the slope of segment E prime H prime.

   False

c. Segment EG will overlap Segment E prime G prime.

   False

d. The Segment EH ≅ to segment E prime H prime.

   False

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The correct question is:

Coordinate plane with triangle EFG with E at 0 commas 5, F at 1 comma 1, and G at negative 2 commas 1. Point H at 1 comma 1 is on segment GF, and points E and H are connected with a segment.

Triangle EFG is dilated by a scale factor of 3 centered at (0, 1) to create triangle E'F'G'. Which statement is true about the dilation?

a. segment EH and segment E prime H prime both pass through the center of dilation.

b. The slope of segment EF is the same as the slope of segment E prime H prime.

c. segment E prime G prime will overlap segment EG.

d. segment EH ≅ segment E prime H prime.

Answer:

37.7 mm

Step-by-step explanation:

The coordinates of R′ for the dilation centered at P with scale factor 0.5 is (2, 2.5).

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

Given:

Dilation of a figure or image is to enlarge or shorter it from the original length by a scale factor.

The coordinate of the R' after the dilation is (-1,-0.5)

Given:

The points of PQRS are Q(-3,2), R(1,2), P(-3,-3), S(1,-3).

The given points are dilated. This dilation can be measured by subtracting the point P from each point . Thus the point of Q is,

Q' = Q- P

Q' = (-3 -(-3), 2- (-3))

Q' = (0, 5)

Similarly for R' = R- P

R' = (1 -(-3), 2- (-3))

R' = (4, 5)

and, after dilation by scale factor 0.5 then

R" = 0.5 x (4, 5)

R" = (2, 2.5)

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The height of the plane to the nearest meter is, 1023. So option A  is correct

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

To find the height of the plane, we can use the following formula:

height = horizontal distance x tanα

Plugging in the given values, we have:

height = 4,812 × tan(12°)

          = 4,812 × 0.21213

          = 1,015.7 meters

Rounding to the nearest meter, the height of the plane is 1,016 meters.

So the answer is 1,016 meters

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The 100 percent of the asked number is 5x/4

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Given that, 80% of a number is x, we need to find 100% of the number,

Let the number be y,

Therefore,

80% of y = x

y = 5x/4

Therefore, the number is 5x/4

100% of 5x/4 = 5x/4

Hence, the 100 percent of the asked number is 5x/4

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The sampling distribution of the mean will be approximately normal, regardless of the underlying population distribution.

Population sampling is the process of selecting a representative sample from a larger population for the purpose of making statistical inferences about the population.

a. The sampling distribution for samples of 25 customer receipts for a supermarket for a year would likely be approximately normally distributed. This assumes that the receipts are randomly selected from the entire population of receipts and that the population distribution of receipts is roughly normal.

The central limit theorem suggests that for a sufficiently large sample size (usually at least 30), the sampling distribution of the mean will be approximately normal, regardless of the underlying population distribution.

b. The sampling distribution for samples of 25 insurance payouts in a particular geographical area in a year would likely be positively skewed, assuming that most payouts are relatively small and a few are very large. The central limit theorem may still apply, but the distribution of the sample means would not be exactly normal.

c. The sampling distribution for samples of 25 call centre logs of inbound calls tracking handling time for a credit card company during the year would likely be approximately normally distributed. This assumes that the call centre logs are randomly selected from the entire population of logs and that the population distribution of handling times is roughly normal.

The central limit theorem suggests that for a sufficiently large sample size (usually at least 30), the sampling distribution of the mean will be approximately normal, regardless of the underlying population distribution.

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There are 6, 8, 10 are yellow pencils.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single one.

Unitary method is a technique so that we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. This is the method that we use for most of the calculations in math.

We are given that if there are 5, 7, 9, 11, or 13 blue ones.

Then the rest could be the yellow pencils.

Which are as follows;

6, 8, 10

These could be the yellow pencils are there, if there are 5, 7, 9, 11, or 13 blue ones

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The complete question is;

There are total number of 8 pencils. How many yellow pencils are there if there are 5, 7, 9, 11, or 13 blue ones

Answer:

-tan(θ)

Step-by-step explanation:

We can use the following trigonometric identity to simplify tan(pi - theta):

tan(pi - theta) = -tan(theta)

Therefore, the simplified expression is:

tan(pi - theta) = -tan(theta)

Answer:

z = 4

Step-by-step explanation:

2z+2=10

To solve for z, subtract 2 from each side.

2z+2-2=10-2

2z=8

Divide each side by 2

2z/2 = 8/2

z = 4

The scientific notation of 5 x 10−7 is 5 x 10 to the power of negative 7.

Notation is a set of symbols and instructions used to represent numbers, equations, and other mathematical expressions. Notation is used to explain rules and procedures, as well as make complex mathematical concepts easier to read and understand. Notations can range from simple abbreviations to complex mathematical symbols. In mathematics, notation can help to simplify complex problems and provide a way for mathematicians to communicate their ideas.


This means that it is 5 times as small as 1. The scientific notation of 8.5 x 10^−4 is 8.5 x 10 to the power of negative 4. This means that it is 8.5 times as small as 1. Therefore, 5 x 10−7 is 8.5 times smaller than 8.5 x 10^−4. By dividing the two numbers, we get 8.5/5 = 1.7. This means that 5 x 10−7 is 1.7 times smaller than 8.5 x 10^−4.

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The subgroups of A4 and their orders are.

Subgroups of order 2 =  {(), (1 2), (1 3), (1 4), (2 3), (2 4), (3 4)}, each of order 2

Subgroups of order 3= {(), (1 2 3), (1 3 2)}, each of order 3

Subgroup of order 4=  {(), (1 2 4 3), (1 4)(2 3), (1 3)(2 4)}, of order 4

Full group A4: {all even permutations, order 12}

A subgroup is a subset of a group that is itself a group under the same group operation.

We have,

Group A4 is the group of even permutations of four elements.

It has order 12.

i.e

4! = 24 total permutations of four elements, but half of them are odd and thus not in A4.

To find all the subgroups of A4.

We can use the fact that the order of a subgroup must divide the order of the group.

Thus, the possible orders of subgroups are 1, 2, 3, 4, 6, and 12.

And,

We also know that there is a subgroup of order 1 (the trivial subgroup, consisting of just the identity permutation) and a subgroup of order 12 (the full group A4).

To find the other subgroups,

We can look for elements that generate subgroups of different orders.

One useful element to consider is the 3-cycle (1 2 3), which generates a subgroup of order 3.

This subgroup consists of the identity, the 3-cycle (1 2 3), and the 3-cycle (1 3 2).

There are two such subgroups in A4, corresponding to the three possible choices of which element to leave out of the 3-cycle.

Another useful element is the 2-cycle (1 2), which generates a subgroup of order 2.

This subgroup consists of the identity and the 2-cycle (1 2).

There are three such subgroups in A4, corresponding to the three possible pairs of elements to include in the 2-cycle.

Now,

We can consider the product of the 3-cycle (1 2 3) and the 2-cycle (1 2), which is the 4-cycle (1 2 4 3).

This generates a subgroup of order 4, consisting of the identity, the 4-cycle (1 2 4 3), and the two 2-cycles (1 4) and (2 3).

Thus,

The subgroups of A4 and their orders are.

Subgroups of order 2 =  {(), (1 2), (1 3), (1 4), (2 3), (2 4), (3 4)}, each of order 2

Subgroups of order 3= {(), (1 2 3), (1 3 2)}, each of order 3

Subgroup of order 4=  {(), (1 2 4 3), (1 4)(2 3), (1 3)(2 4)}, of order 4

Full group A4: {all even permutations, order 12}

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The complete question.

Find all of the subgroups in A4 that have order 12.

What is the order of each subgroup using 3-cycle and 2-cycle?

The alternative hypothesis for this problem is that the population variance is significantly more than 0.003, represented as [tex]H1: S2 > 0.003.[/tex]

To test this hypothesis, we can use a chi-square test of variance. This test is calculated as [tex]X2 = (n-1) * (s2/σ2)\\[/tex], where n is the sample size, s2 is the sample variance, and σ2 is the hypothesized population variance.

In this case, the sample size is 26, so n = 26. The sample variance is 0.06, so s2 = 0.06. The hypothesized population variance is 0.003, so σ2 = 0.003. Plugging these values into the formula above gives us [tex]X2 = (26-1) * (0.06/0.003) = 75.[/tex]

Since this value is greater than the critical value of the chi-square distribution at α = 0.05, the null hypothesis can be rejected and it can be concluded that the population variance is significantly more than 0.003.

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The given relationship is a function, as of the given condition it consists of 3 sub-functions,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,

Let's assume that, 3-time intervals

1 . 0 to 5

2. 5 to 7  

3. 7 to 10

So for intervals, we have 3 different equation of functions which represents the distance traveled by Camilla in time t.

Thus,  the given relationship is a function, as of the given condition it consists of 3 sub-functions.

When she increased her pace, she principally made up for lost time standing at the position. assuming that she made it in the same quantum of time if she did not stop, you can assume that she didn't waste presently time because she picked up the pace.

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In the diagram, the area of the square c is 2009

The area of the square is solved using the formula

length x length

The lenght is caluclalted using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required dimensions

x² = 35² + 28²

x² = 1225 + 784

x² =  2009

x = √2009

x = 44.82

Area of the square is x² =  2009

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Answer:

the number is 14.

Step-by-step explanation:

Let's start by using algebra to solve the problem.

We can translate the given information into an equation:

5x + 2 = 72

where x is the unknown number.

To solve for x, we need to isolate it on one side of the equation. We can do this by first subtracting 2 from both sides:

5x = 70

Then, we can divide both sides by 5:

x = 14

Therefore, the number is 14.

The measure (in degrees) of ∠4 would be 63 degree

If the total of the measurements of two angles equals 90 or 180 degrees, respectively, such angles are said to be complimentary and supplementary.

Complementary angles are the one whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.

A triangle's three angles add up to 180 degrees. The third angle is the result of 64 degrees being subtracted.

They have the same measurements, m 4 = 90.

A + 27 = 90

A = 63

Therefore, they are complimentary, their combined angles equal 90.

A = 63 degree

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The similar doll's quilt has a width of (1/4) yards.

Two or more than two shapes are said to be similar if they have equal corresponding measures of angles and the ratio of corresponding sides should be the same.

Given, The daughter's quilt has a length of 2 yards and a width of 1 yard

and the other similar quilt ahs a length of (1/2) yards.

Now, (1/2)/(2) = 1/4.

Therefore, The width of a similar quilt is (1/4)×1 = 1/4 yards.

Q. A woman sews similar quilts for her daughter's doll. If the daughter's quilt has a length of 2 yards and a width of 1 yard, and the doll's quilt has a length of 1/2 yard, what is the width of the doll's quilt?

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Answer: thanks for 14 points

Step-by-step explanation:lol

To calculate the interest charged for the month on a credit card with a balance of $1000 and an APR of 28% after making a $400 payment on the 11th day of a 31-day month, we need to first calculate the average daily balance for the month.

The average daily balance is calculated as follows:

(Previous balance × number of days in billing cycle) + (New charges × number of days since posting of new charges) - (Payments and credits × number of days since payment/credit) / Number of days in billing cycle

In this case, the previous balance is $1000, the number of days in the billing cycle is 31, the new charges are 0, the number of days since posting of new charges is 20 (since the payment posted on the 11th day of the month), the payment/credit is $400, and the number of days since payment/credit is 21. Plugging in these values, we get:

($1000 × 31) + (0 × 20) - ($400 × 21) / 31 = $727.10

Therefore, the average daily balance for the month is $727.10.

To calculate the interest charged for the month, we multiply the average daily balance by the daily periodic rate, which is the APR divided by 365 (since there are 365 days in a year):

$727.10 × (0.28 / 365) × 31 = $19.97

Therefore, the interest charged for the month is $19.97.

Answer:

Step-by-step explanation:

7/4