There are 25 pupils in a class who take part in a drinking milk initiative. Pupils have a 210
millilitre glass each. During the break each pupil drinks a full glass of milk. Milk comes in 1000
millilitre bottles. How many bottles of milk are needed?

Answer:

(a - 1)(3p - 2)

Step-by-step explanation:

3p(a - 1) - 2(a - 1) ← factor out (a - 1) from each term

= (a - 1)(3p - 2)

From the given graph, CE is longer than CD.

The length of the line segment bridging two locations in a plane is known as the distance between the points. d=√((x₂ - x₁)²+ (y₂ - y₁)²) is a common formula to calculate the distance between two points. This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

Coordinates of E(8,6)

Coordinates of C(6,1)

Coordinates of D(3,-3)

x=8, y=6

x=6, y=1

x=3, y=-3

Distance CE=√{(8-6)² +(6-1)²} = √29

Distance CD=√{(6-3)² +(1+3)²}= √25=5

Therefore, CE is longer than CD.

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Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.

In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.

The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:

[tex]nCk = n! / (k! *(n-k)!)[/tex]

where n! denotes the factorial of n, i.e., the product of all positive integers up to n.

by the question.

Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:

[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]

Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]

Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).

Since a_i >= 4 for i=1, we have:

[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]

Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:

[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]

This gives us:

[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]

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Answer:

Below

Step-by-step explanation:

Mass of bouncies + box = 17342     subtract mass of box from both sides

   mass of bouncies  =  17342 - 429 = 16913 g

Unit mass per bouncy = 505 g / 45 bouncy  

Number of Bouncies =  16913 gm / ( 505 g / 45 bouncy )  = 1507.1 bouncies

  With the given info, I am afraid it IS 1507 bouncies in the box

      maybe since the question asks for APPROXIMATE number, the answer is     1510 bouncies    ( rounded answer) ....or 1500

Answer:

Step-by-step explanation:

You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.

The contrapositive of the given statement is "If it is not a cat, then it is a lion."

The contrapositive of the statement "If it is not a lion, then it is a cat" can be obtained by negating the original statement and switching the positions of the antecedent (the "if" part) and the consequent (the "then" part).

The contrapositive takes the form:

"If it is not a cat, then it is a lion."

So, the contrapositive of the given statement is "If it is not a cat, then it is a lion."

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False, the probability that A or B will occur is P(A or B) = P(A) + P(B) - P(A and B).

Probability refers to the measure of the likelihood or chance of a particular event occurring. It is expressed as a number between 0 and 1, where 0 indicates an impossible event, and 1 indicates a certain event.

This formula is known as the Addition Rule for Probability and states that to calculate the probability of either event A or event B occurring (or both), we add the probability of A happening to the probability of B happening, but then we need to subtract the probability of both A and B happening at the same time to avoid double counting.

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The vertices of the resulting image, quadrilateral H’ I’ J’ K’ include the following:

H' (4, -1).

I' (2, -3).

J' (-4, 1).

K' (-2, 3).

In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

In Geometry, rotating a point 270° about the origin would produce a point that has the coordinates (y, -x).

By applying a rotation of 270° about the origin to quadrilateral HIJK, the location of its vertices is given by:

(x, y)                                   →         (y, -x)

Ordered pair H (1, 4)        →    Ordered pair H' (4, -(1)) =  (4, -1).

Ordered pair I (3, 2)        →    Ordered pair I' (2, -(3)) =  (2, -3).

Ordered pair J (-1, -4)        →    Ordered pair J' (-4, -(-1)) =  (-4, 1).

Ordered pair K (-3, -2)        →    Ordered pair K' (-2, -(-3)) =  (-2, 3).

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Answer:

The second figure.

Step-by-step explanation:

The first figure's perimeter is:

70 in + 42 in + 56 in = 168 inches.

And the second figure's perimeter is:

42 in + 33 in + 33 in + 64 in = 172 inches.

Therefore, Figure 1 < Figure 2.

(a)  n = 10, p = 1/4, and x = 5. Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)

(b) P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)

Here n = 10, p = 1/4, and x = 5.Using the formula of binomial probability function,P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)

Find P(More than 3)For this, we need to calculate P(4), P(5), P(6),...,P(10) and add them.Using the formula of binomial probability function,P(4) = 10C4 * (1/4)^4 * (3/4)^6 = 0.2503 (rounded to three decimal places)P(5) = 10C5 * (1/4)^5 * (3/4)^5≈ 0.0267 (rounded to three decimal places)P(6) = 10C6 * (1/4)^6 * (3/4)^4≈ 0.0014 (rounded to three decimal places)P(7) = 10C7 * (1/4)^7 * (3/4)^3≈ 0.0001 (rounded to three decimal places)P(8) = 10C8 * (1/4)^8 * (3/4)^2≈ 0.0000 (rounded to three decimal places)P(9) = 10C9 * (1/4)^9 * (3/4)^1≈ 0.0000 (rounded to three decimal places)P(10) = 10C10 * (1/4)^10 * (3/4)^0≈ 0.0000 (rounded to three decimal places)P(More than 3) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10)≈ 0.2784 (rounded to three decimal places)

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The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)

Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:

(x-2)² = (x-2) * (x-2)

= x * x - 2 * x - 2 * x + 2 * 2

= x² - 4x + 4

So, the expression (x-2)² is equivalent to x² - 4x + 4.

However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:

(x-2)² = (x-2) * (x-2)

= (x-2)²

So, (x-2)² is equivalent to itself.

Hence the correct option is (B).

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Complete Question:

Which expressions are equivalent to (x−2)²?

Select the correct choice.

A. (x + 2) (x - 2)

B. x² - 4x + 4

C. x² - 2x + 5

D. x² + x - 2x

The average time gap between the first cyclist's time and each of the remaining cyclists' times (second through fifth) in the 1995 Volta a Catalunya cycle race is approximately 6 minutes and 7 seconds.

To calculate this, we need to subtract the time of the first cyclist from each of the remaining cyclists' times (second through fifth).The time for the first cyclist was 41:38:33.

The times for the remaining cyclists were as follows:

We can calculate the difference for each cyclist by subtracting the first cyclist's time from their own time:

Adding up all of the times and dividing by four, we get an average of 00:06:07.

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Answer:

  138°

Step-by-step explanation:

You want the measure of the angle at two tangents when they intercept an arc of 42°.

The short answer is that the exterior angle x is the supplement of the measure of the arc:

  x = 180° -42°

  x = 138°

An exterior angle where secants meet is half the difference of the arcs of the circle they intercept. Here, the secants have been located so the corresponding chord length between the near and far circle intercept points have degenerated to zero. That is, they are tangents.

The angle relation still holds:

  x = (long arc - short arc)/2 = ((360° -42°) -42°)/2 = (360° -2·42°)/2

  x = 180° -42° = 138°

The tangents, together with their associated radii form a quadrilateral. The angles at the tangents are 90°, and the total of all angles is 360°. This gives us the relation ...

  x + 90° +42° +90° = 360°

  x +42° = 180° . . . . . . . . . . . . . subtract 180°

  x = 180° -42° = 138°

(We solved this with an extra step, so you could see the same "supplementary angles" relationship between x and 42°.)

In this particular question, we are being asked to find the number of normal subgroups of order 7 in a group of order 14. Before we begin, let's try to understand the different types of subgroups.Subgroups can be of two types: Proper Subgroups and Improper SubgroupsProper Subgroups are defined as subgroups which have more than one element and not equal to the entire group. Improper Subgroups are the subgroups which contain every element of the group.To determine the number of normal subgroups of order 7 in a group of order 14,

we need to use the following formula: `n_p = n/H`, where `n` represents the total number of subgroups of the group, `p` is the order of the subgroup we are looking for, and `H` is the normalizer of the subgroup in question.Using this formula, we can find that the order of the group is 14, and since 7 is a prime number, any subgroup of order 7 will be cyclic. Now, let's look at the different subgroups of the group of order 14:As 7 is a prime number and 7 divides 14, there will be one unique subgroup of order 7, and it will be cyclic.Since the group of order 14 is not a cyclic group, there are no other subgroups of order 7 besides the cyclic subgroup. Thus, the number of normal subgroups of order 7 in a group of order 14 is 1.

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Total seats in plane: 186

108+64+14

5/7 of 14 is: 10

14÷7= 2

2x5= 10

5/16 of 64 is: 20

64÷16=4

5×4= 20

5/9 of 108 is: 60

108÷9= 12

12x5= 60

60+20+10=90

90/186 of seats are being used

simplified: 15/31

No

Answer:

[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]

Step-by-step explanation:

[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]

Each side has length of a?

[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]

a. In the sample:i. The average value of birth weight for all mothers is 7.17 pounds.

ii. For mothers who smoke is 6.82 pounds.

iii. For mothers who do not smoke is 7.28 pounds.b. i. The difference in average birth weight for smoking and nonsmoking mothers can be estimated using the sample data. The difference is given by the formula:

Difference = X1 – X2, where X1 is the average birth weight of mothers who smoke and X2 is the average birth weight of mothers who do not smoke.Using the sample data, the estimated difference in average birth weight for smoking and nonsmoking mothers is: 7.28 – 6.82 = 0.46 pounds.ii. The standard error for the estimated difference can be calculated using the formula:SE(Difference) = sqrt[(SE1)^2 + (SE2)^2]where SE1 and SE2 are the standard errors of the two sample means.Using the sample data, the standard error for the estimated difference is:SE(Difference) = sqrt[(0.23)^2 + (0.12)^2] = 0.26 pounds.iii. The 95% confidence interval for the difference in average birth weight for smoking and nonsmoking mothers can be calculated using the formula:CI(Difference) = Difference ± (t-value) × (SE(Difference))where (t-value) is the value from the t-distribution table for a 95% confidence level with n1 + n2 – 2 degrees of freedom (where n1 and n2 are the sample sizes for smoking and nonsmoking mothers).Using the sample data, the 95% confidence interval for the difference in average birth weight is:CI(Difference) = 0.46 ± (2.048) × (0.26) = (0.04, 0.88) pounds.

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If x is a positive integer , 4x^1/2 is equivalent to product of 2 and square root of x, wherein it would surely be a positive value greater than 2.

Positive integers are the numbers on the number line which are greater then zero and extend on the right hand side of the number line till infinity. These numbers are also whole numbers in itself such as 1, 2, 3...,∞. When 4x^1/2 is calculated, it is assumed that 4x is raised to power half, which will provide the answer as 2√x.

It is because square root of 4 will be 2 and that of x will be √x. Square roots are the numbers obtained by multiplying a specific number by the number itself. For example: 3×3 = 9 or square root of 9 is 3.

If some positive integer is fixed in the equation, the desired outcome would be obtained as follows:

If x=4, (4×4)^1/2 = 4

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The value of the unknown lengths in these similar triangles is FH is 6.67 units and EG is 27 units.

A triangle is a polygon with three sides and three angles. It is a two-dimensional shape that is commonly studied in mathematics, geometry, and other fields. The sum of the angles in a triangle is always 180 degrees, and the lengths of the sides can vary. Triangles can be classified based on the lengths of their sides and the measures of their angles. Common types of triangles include equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have many important properties and are used in various applications, including construction, engineering, and physics.

Here,

1. Let x be the length of FH. We have:

AB/EF = BD/FH

12/8 = 10/x

Cross-multiplying, we get:

12x = 80

x = 80/12

x ≈ 6.67

Therefore, FH ≈ 6.67.

2. Let y be the length of EG. We have:

AC/BD = FH/EG

15/9 = 5/y

Cross-multiplying, we get:

5y = 135

y = 135/5

y ≈ 27

Therefore, EG ≈ 27.

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In Rosettenville, a suburb of Johannesburg, South Africa, Robert Brozin and Fernando Duarte acquired the Chicken Land restaurant in 1987, launching Nando's.

The eatery was renamed Nando's in honor of Fernando. The restaurant incorporated influences from former Mozambican Portuguese colonists, many of whom had relocated to Johannesburg's southeast after their country gained independence in 1975. Expansion was an essential component of their vision from the beginning. Nando's had already grown from one restaurant in 1987 to four by 1990. It became increasingly difficult to implement a common strategy and decision-making became inefficient as new outlets were maintained as separate businesses.

In 1995, Nando's International Holdings (NIH) was established as a new international holding because managing this growingly complex global structure had become extremely challenging. The South African branch of Nando's Group Holdings (NGH) was successfully listed on the Johannesburg Stock Exchange on April 27, 1997. NGH was 54% owned by NIH, with the remaining 26% available to the general public and former joint venture partners. The main goals of the share offer and listing were to broaden the group's capital base and enable group restructuring.

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[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ r=2.8 \end{cases}\implies s=\cfrac{(42)\pi (2.8)}{180}\implies s=\cfrac{49\pi }{75}\implies s\approx 2.05 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Perimeter of the sector} }{2.8~~ + ~~2.8~~ + ~~2.05} ~~ \approx ~~ \text{\LARGE 7.65}[/tex]

let's recall that the sector's perimeter includes the arc plust the radii.

The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.

The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.

z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.

z = {x-μ}/{σ}  = {-20-0}/{8}  = −2.5

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.

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The point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

What is Segment?

In geometry, a segment is a part of a line that has two endpoints. It can be thought of as a portion of a straight line that is bounded by two distinct points, called endpoints. A segment has a length, which is the distance between its endpoints. It is usually denoted by a line segment between its two endpoints, such as AB, where A and B are the endpoints. A segment is different from a line, which extends infinitely in both directions, while a segment has a finite length between its two endpoints.

To find the point that partitions segment AB in a 1:4 ratio, we need to use the midpoint formula to find the coordinates of the point that is one-fourth of the distance from point A to point B. The midpoint formula is:

((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment.

So, let's first find the coordinates of the midpoint of segment AB:

Midpoint = ((-3 + 7)/2, (2 - 10)/2)

= (2, -4)

Now, to find the point that partitions segment AB in a 1:4 ratio, we need to find the coordinates of a point that is one-fourth of the distance from point A to the midpoint. We can use the midpoint formula again, this time using point A and the midpoint:

((x1 + x2)/2, (y1 + y2)/2) = ((-3 + 2)/2, (2 - 4)/2)

= (-1/2, -1)

So, the point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

Step-by-step explanation:

348.55

Probability of D2 being sunny = 0.78.

On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.

Therefore, we need to find the chances that D2 is sunny.

There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.

Now, Let us find the probability of D2 being sunny.

We have the following possible cases for D2.

D1 = Sunny; D2 = Sunny

D1 = Sunny; D2 = Rainy

D1 = Rainy; D2 = Sunny

D1 = Rainy; D2 = Rainy

The probability of D1 being sunny is 0.9.

When a sunny day follows a sunny day, the probability is 0.8.

When a sunny day follows a rainy day, the probability is 0.6.

Therefore, the probability of D2 being sunny is given by the formula:

Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.

Therefore, the probability that D2 is sunny are 0.78 or 78%.

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If there are 500 students in total, the number of students who made the honor roll is 10 students, given that the ratio of students who made the honor roll to the total number of students is 1:50.

The number of students who made the honor roll can be found using proportions. Here's how to do it:

Let X be the number of students who made the honor roll.

The proportion can be set up using the given ratio as follows:

1:50 = X:500

Cross-multiplying this equation and solving for X gives:

50X = 500

X = 10

Therefore, 10 students made the honor roll.

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Ramona's economic profit last year was $92,000 - $55,000 = $37,000. Therefore, the correct option is b. $37,000.

Ramona owns a small coffee shop, where she works full-time. Her total revenue last year was $200,000, and her rent was $5,000 per month. She pays her one employee $3,000 per month, and the cost of ingredients averages $1,000 per month. Ramona could earn $55,000 per year as the manager of a competing coffee shop nearby. Her economic profit last year was $37,000.An economic profit can be calculated by subtracting total costs from total revenue. Given that Ramona's total revenue is $200,000, her total cost is $5,000 + $3,000 + $1,000 = $9,000 per month. Multiplying this by 12 gives us her total cost for the year: $9,000 x 12 = $108,000. Ramona's economic profit last year was therefore $200,000 - $108,000 = $92,000. However, this figure doesn't take into account the opportunity cost of Ramona earning $55,000 as the manager of a competing coffee shop nearby. This needs to be subtracted from Ramona's economic profit.

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