Emma buys packets of coloured beads.
Purple beads are sold in packets of 8
Red beads are sold in packets of 5
Blue beads are sold in packets of 10
Emma wants to buy an equal number of purple, red and blue beads.
What is the smallest number of each colour Emma could buy?

A higher percentage of people who did not wear wrist guards (41.67%) experienced wrist injuries compared to those who did wear wrist guards (11.32%).

Based on the information provided, we can analyze the data on injuries to in-line skaters. Let's break down the given numbers:

Total number of people interviewed: 161

Number of people wearing wrist guards: 53

Number of people wearing wrist guards with wrist injuries: 6

Number of people not wearing wrist guards: 108

Number of people not wearing wrist guards with wrist injuries: 45

From this information, we can calculate the following:

Percentage of people wearing wrist guards with wrist injuries:

(Number of people wearing wrist guards with wrist injuries / Number of people wearing wrist guards) × 100

= (6 / 53)× 100 ≈ 11.32%

Percentage of people not wearing wrist guards with wrist injuries:

(Number of people not wearing wrist guards with wrist injuries / Number of people not wearing wrist guards)×100

= (45 / 108) ×100 ≈ 41.67%

These calculations provide insights into the likelihood of wrist injuries in relation to wearing wrist guards while inline skating. The data suggests that the percentage of wrist injuries among those wearing wrist guards is lower (11.32%) compared to those not wearing wrist guards (41.67%). This indicates that wearing wrist guards may offer some protection against wrist injuries while inline skating.

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After calculating using hypothesis the test static ( Z ) is 1.84. As total sample  of the computer chips is 900 and revealed 63%.

An explanation for a phenomenon is put up as a hypothesis. According to the scientific method, a hypothesis must be testable in order to qualify as a scientific hypothesis. Typically, scientists base their hypotheses on prior observations that leave room for doubt on the validity of the existing body of knowledge.

Null Hypothesis H0 p=0.60

Alternative Hypothesis H1: p 0.60

Below H O , the test statistic is,

Z =  \(\frac{P - p}{\sqrt{pq/n} }\)  = \(\frac{0.63 - 0.60}{0.60 * 0.40/900}\) = 1.8371  ≈ 1.84

Hence , Z = 1.84

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Monthly payment before deferral: $345.09. Balance after deferral: $67,901.53. Monthly payment after deferral: $380.57. Monthly payment to pay off debt within 25 years from graduation: $421.63.

To calculate the monthly payment for a student loan, we can use the loan amortization formula.

Monthly payment calculation:

We can use the formula for calculating the monthly payment on an amortizing loan:

PMT = (P * r) / (1 - (1 + r)^(-n))

where PMT is the monthly payment, P is the loan amount, r is the monthly interest rate, and n is the total number of payments.

Given:

P = $62,100 (loan amount)

r = 4.6% per year / 12 months = 0.046/12 (monthly interest rate)

n = 25 years * 12 months = 300 (total number of payments)

Substituting these values into the formula, we can calculate the monthly payment:

PMT = (62,100 * (0.046/12)) / (1 - (1 + (0.046/12))^(-300))

Balance after deferral period:

To calculate the balance after the deferral period of 2 years, we need to calculate the interest accrued during that period and add it to the original loan amount:

Interest accrued during deferral = P * r * deferral period (in years)

New balance = P + Interest accrued during deferral

New monthly payment after deferral period:

To calculate the new monthly payment after the deferral period, we can use the same formula as before, but with the new balance and the remaining number of payments:

New PMT = (New balance * r) / (1 - (1 + r)^(-n))

Monthly payment to pay off the debt within 25 years from graduation:

To calculate the monthly payment to pay off the debt within 25 years from graduation, we need to adjust the remaining number of payments:

Remaining number of payments = 25 years * 12 months - deferral period

Then we can use the same formula as before to calculate the monthly payment.

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Answer:

$75

[It is easy to say $60, but don't forget to add Samuel to the total]

Step-by-step explanation:

There are 5 people in total:

1  Samuel

4 friends

5 people who can spend up to $15 each.

(5 people)*($15/person) = $75 total spent on supplies

On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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Answer:

2.9 or 2.90

Step-by-step explanation:

The fraction is 10 so it's pretty easy as decimals run through tens

Answer:

Below

Step-by-step explanation:

12 C 2  = 12! / ( 10! 2!) = 66 ways

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

Answer:

B.

Step-by-step explanation:

1) The parabola 1 unit up, so it should be +1. A or B.

2) The parabola is opening up, so it will have positive coefficient. 0.2. This is B.

Answer:

x≈5

Step-by-step explanation:

x^2-5x6=0

x^2-30=0

x^2-30+30=30+0

x^2=30

x≈5

Answer:

q = 6r + 16

r = q/6 - 8/3

Step-by-step explanation:

Make q independent:

q - 10 = 6r + 6

q = 6r + 16

Make r independent:

q - 16 = 6r

(q - 16) / 6 = r

r = q/6 - 8/3

Answer:

105°

Step-by-step explanation:

Bya angle sum property of triangle

40+35+x=180

x= 180-75

x= 105°

Hope it helps you

1) The property P that we need to prove by induction is as P(p) = length p = length (rem R p) + numR p. 2) For the base case, we need to prove P([]) = length [] = length (rem R []) + numR []. 3) Inductive hypothesis is P(p) = length p = length (rem R p) + numR p. 4) For the step case, we need to prove P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p).

1) The property P that we need to prove by induction is as follows:

For all lists of directions p, the property P(p) is defined as:

P(p) = length p = length (rem R p) + numR p

If we can prove this property P by induction, it implies the goal of the exercise, which is to show that length p = length (rem R p) + numR p.

2) Base case goal:

For the base case, we need to prove the following goal:

For an empty list of directions p = [], the property P(p) holds:

P([]) = length [] = length (rem R []) + numR []

Proof:

P([]) simplifies to:

length [] = length (rem R []) + numR []

Using the definition of the length function and rem function, we have:

0 = length [] + numR []

Since the length of an empty list is 0, and there are no occurrences of R in an empty list, numR [] is also 0. Therefore, the base case goal holds.

3) Inductive hypothesis:

Assuming that the property P holds for a list p, we assume the following inductive hypothesis:

P(p) = length p = length (rem R p) + numR p

4) Step case goal:

For the step case, we need to prove the following goal:

Assuming P(p), we need to show that P(L:p) holds:

P(p) → P(L:p) : length (L:p) = length (rem R (L:p)) + numR (L:p)

Proof:

Using the definition of the length function and rem function, we have:

length (L:p) = length (L:(rem R p)) + numR (L:p)

Expanding the length and rem functions, we get:

1 + length p = 1 + length (rem R p) + numR (L:p)

Since L is not equal to R, numR (L:p) remains unchanged:

1 + length p = 1 + length (rem R p) + numR p

By canceling out the common terms on both sides, we get:

length p = length (rem R p) + numR p

This matches the property P(p), so the step case goal holds.

By proving the base case and the step case, we have proven the property P(p) by induction, which implies that length p = length (rem R p) + numR p for all lists of directions p.

Correct Question :

length []=0

length (x:xs)=1+ length xs

​−L1

−L2

Consider the following data types and functions: data Direction =L∣R numR : [Direction] -> Int

numR []=0

numR (L:p)= numR p

numR (R:p)=1+ numR p

Answer the following questions:

1. What precisely should we prove by induction? Specifically, state a property P, including possible quantifiers, so that proving this property by induction implies the (above) goal of this exercise.

2. State (including possible quantifiers) and prove the base case goal.

3. State (including possible quantifiers) the inc्acuctive hypothesis of the proof.

4. State (including possible quantifiers) and prove the step case goal.

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Answer:

b

Step-by-step explanation:

Answer:

399/1000

three hundred and ninety-nine divided by one thousand

Step-by-step explanation:

Answer:

3 books on each shelf

5 books on each shelf

Step-by-step explanation:

Answer:

Can someone please help me with this question?

Step-by-step explanation:

Answers:

Hope you could get an idea from here.

Doubt clarification - use comment section.

The absolute maximum value is 8 at x=3, and the absolute minimum value is -16 at x=-1.

To find the absolute maximum and minimum values of the function F(x) = x^2 - 4x - 9, we need to calculate the function's critical points and calculate the function at these points.

The critical points can be found by setting the first derivative of the function equal to zero and solving for x:
F'(x) = 2x - 4 = 0
2x = 4
x = 2

We now need to calculate the function at x=-1, x=2, and x=3 to find the absolute maximum and minimum values:
F(-1) = (-1)^2 - 4(-1) - 9 = -16
F(2) = 2^2 - 4(2) - 9 = -3
F(3) = 3^2 - 4(3) - 9 = 8

Therefore, the absolute maximum value is 8 at x=3, and the absolute minimum value is -16 at x=-1.

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Answer:

(x-1)^2+(y-2)^2=6.25

Step-by-step explanation:

Origin: (1, 2)

Radius: 2 1/2

(x-1)^2+(y-2)^2=2.5^2

(x-1)^2+(y-2)^2=6.25

Answer: ( x - 1 )^2 + ( y - 2 )^2 = 6.25

Step-by-step explanation:

This means that most 10-year-olds will have heights close to the mean, and the majority of heights will fall within 6 inches of the mean.

The heights of 10-year-olds, regardless of gender, closely follow a normal distribution. This means that the majority of 10-year-olds will have heights close to the average, or mean, height of 55 inches.

The standard deviation of 6 inches tells us that most heights will fall within 6 inches of the mean. In a normal distribution, the majority of data points are concentrated around the mean.

In this case, the mean height of 10-year-olds is 55 inches. However, there will be some variation in heights, and this is indicated by the standard deviation of 6 inches.

The standard deviation tells us how much the heights vary from the mean. In this case, most heights will fall within 6 inches above or below the mean of 55 inches.

For example, if we consider one standard deviation above the mean (55 + 6 = 61 inches) and one standard deviation below the mean (55 - 6 = 49 inches), we can say that approximately 68% of 10-year-olds will have heights between 49 and 61 inches.

This is because, in a normal distribution, about 68% of the data falls within one standard deviation of the mean.

The heights of 10-year-olds, regardless of gender, closely follow a normal distribution with a mean of 55 inches and a standard deviation of 6 inches.

This means that most 10-year-olds will have heights close to the mean, and the majority of heights will fall within 6 inches of the mean.

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Answer:

2

Step-by-step explanation:

The distance d from y to the line through u and the origin is 13.74. This is calculated by finding the projection of y onto the line, and then taking the length of the projection.

The line through u and the origin has direction vector u, which is (3, 6, -5). The projection of y onto this line is given by the following formula:

projection = (y · u) / ||u|| * u

where · is the dot product and ||u|| is the length of u.

Plugging in the values for y and u, we get the following:

projection = ((10)(3) + (-9)(6) + (5)(-5)) / ||(3, 6, -5)|| * (3, 6, -5)

= -42 / 14.14 * (3, 6, -5)

= (-3, -6, 3)

The length of the projection is then given by the following formula:

length = ||projection||

= sqrt((-3)^2 + (-6)^2 + (3)^2)

= 13.74

Therefore, the distance d from y to the line through u and the origin is 13.74.

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The distance d from y to the line through u and the origin is 13.74. This is calculated by finding the projection of y onto the line, and then taking the length of the projection.

The line through u and the origin has direction vector u, which is (3, 6, -5). The projection of y onto this line is given by the following formula:

projection = (y · u) / ||u|| * u

where · is the dot product and ||u|| is the length of u.

Plugging in the values for y and u, we get the following:

projection = ((10)(3) + (-9)(6) + (5)(-5)) / ||(3, 6, -5)|| * (3, 6, -5)

= -42 / 14.14 * (3, 6, -5)

= (-3, -6, 3)

The length of the projection is then given by the following formula:

length = ||projection||

= sqrt((-3)^2 + (-6)^2 + (3)^2)

= 13.74

Therefore, the distance d from y to the line through u and the origin is 13.74.

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Answer:D . No the translation did not preserve the segment length

Step-by-step explanation:

Dijkstra's Algorithm is the best search strategy to find the shortest distance between PER and CBR4 in the given tree.

Dijkstra's Algorithm:

Dijkstra's Algorithm is used to determine the shortest path between a starting node and a destination node. Dijkstra's algorithm maintains a set of unvisited nodes, and this algorithm is also known as the shortest path first algorithm. The process of Dijkstra's Algorithm is given below:

First, create a set that includes the starting node, and set the shortest distance to zero. Each of the neighbors of the starting node is visited, and the distance between the starting node and its neighbors is calculated. It's called the tentative distance. The tentative distance is compared to the current shortest distance for that particular neighbor. If the tentative distance is shorter than the current shortest distance, then the current shortest distance is updated. When all of the neighbors of the current node have been visited, mark the current node as visited and remove it from the set of unvisited nodes. The node with the lowest tentative distance is now considered the current node. Repeat steps 2 to 4 until the destination node is reached. To find the shortest distance between PER and CBR4, Dijkstra's Algorithm is the best search strategy because it considers all the neighbors of the starting node and calculates the shortest distance from it.

By implementing Dijkstra's Algorithm, the best strategy will be found along with the number of steps and visiting sequence.

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Answer:

a: 36

b: 32

Step-by-step explanation:

Lizard views: 4

Since Ferret has 9 times as much as Lizard views, you can multiply it by 9:

4 x 9 = 36 views

To find the difference, subtract Ferret views with Lizard views:

36 - 4 = 32 views

Therefore, Caleb paid approximately $14,067.90 for the shares.

Let's assume the amount Caleb paid for the shares is represented by the variable "x". According to the given information, his selling price was 130% of the amount he paid.

Selling price = 130% of the amount paid

$18,189.27 = 1.3 * x

To find the amount he paid for the shares, we can solve the equation for "x" by dividing both sides by 1.3:

x = $18,189.27 / 1.3

Calculating this, we find:

x ≈ $14,067.90

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Answer:

Step-by-step explanation:

when adding a negative plus a positive, count forward the amount you're adding from the negative number. Like -5+2, -5--> -4--> -3