Gary works at a bicycle store in Vancouver. For the start of spring, the manager of the store has ordered 50 mountain bikes and 10 racing bikes.
Which conjecture is Gary most likely to make from this evidence?

Hence, 75 is the result of adding the six consecutive integers starting at 10.

Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a 1 difference.

We can find the sum of these numbers by adding them up if there are six consecutive numbers and 10 is the smallest one.

The six numbers in order are x, x+1, x+2, x+3, x+4, and x+5. We are aware that x equals 10 because 10 is the smallest number.

The six numbers are therefore 10, 11, 12, 13, 14, and 15.

We simply put them together to determine their sum:

10 + 11 + 12 + 13 + 14 + 15 = 75

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Answer:

To ensure that you have grabbed 250 balls of one color, you need to use the Pigeonhole Principle. The worst-case scenario is that you grab 249 balls of each color, totaling 996 balls. Therefore, the smallest amount of balls you need to grab is 997, which guarantees that you have grabbed 250 balls of one color.

To explain further, let's consider the worst-case scenario where you grab 249 red balls, 249 green balls, 249 blue balls, and 249 yellow balls. This totals to 996 balls. However, if you grab just one more ball, you will have a total of 997 balls, and since there are only four colors, at least one color will have 250 balls or more. Therefore, by grabbing 997 balls, you can be sure that you have grabbed at least 250 balls of one color.

Answer:

997

Step-by-step explanation:

I multiplied 249 by 4 first. This is because I wanted to find how many balls the person could grab in total without having 250 of the same color.

249*4= 996

However, the question wants to guarantee that one color has 250.

So I did 996+1=997. (which means there could be: 249 red, 249 yellow, 249 green, and 250 blue)

This means that every other color could be at 249, but one would guarantee to be at 250 with 997 pulls

After addressing the issue at hand, we can state that Keep in mind that any probability model must have these probabilities sum up to 1, as is the case here.

Calculating the probability that an event will occur or that a statement is true is the subject of probability theory in mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and an approximate probability of 0 denotes how likely an event appears to be to occur. A mathematical representation of the likelihood that an event will take place is called probability. You can also express probabilities as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible options that actually occur when compared to all possible outcomes, leading to a certain event.

A probability model for selecting a bead can be defined as follows:

Let the actions of choosing a glass, wood, or brass bead be represented by G, W, and B, respectively. We can suppose that the likelihood of choosing a particular type of bead is inversely correlated with the quantity of that type of bead in the box. As a result, we have:

P(W) = 96/300 = 8/25 P(B) = 144/300 = 12/25 with P(G) = 60/300 = 1/5

Keep in mind that any probability model must have these probabilities sum up to 1, as is the case here.

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The correct question is -

Write a probability model for choosing a bead.

Choosing Beads

Glass 60

Wood 96

Brass 144

Answer:

The dimensions of the rectangle are 5 by 24.

Step-by-step explanation:

Sometimes it's easy to finish solving the system and think that the x and y coordinates are your answer. Remember what the question is asking for - the dimensions of the rectangle.

Answer:

-4+3n     (if first value corresponds to n=0)

or

-7+3n     (if first value corresponds to n=1)

Step-by-step explanation:

Notice form each term you just need to add 3
For example, the first term is -4, then the second is -4+3=-1

then the third is -4+3+3=2

So you can start from -4 and 3 for each value.

If n=0 is the start value the sequence will be -4+3n

if the first term is n=1  the sequence will be  -4+3(n-1)=-7+3n

So depends if your sequence starts from n=1 or n=0 (which is usually just a convention)

a. The first term of the sequence is 16.

b. the common difference is d = 32

c. the explicit formula is f(n) = 16 + (n - 1)32

d. the stone falls a distance of 144 feet during the 5th second.

a. The first term of the arithmetic sequence is given to be 16.

b. To find the common difference, we can subtract the second term from the first term, then the third term from the second term:

48 - 16 = 32

80 - 48 = 32

Therefore, the common difference is d = 32.

c. Using f(n) = f(1) + (n - 1)d,

where

f(1) = 16 and d = 32,

we can write the explicit formula for the distance traveled during the nth second as:

f(n) = 16 + (n - 1)32

d. To find the distance traveled during the 5th second, we plug in n = 5 into the explicit formula:

f(5) = 16 + (5 - 1)32

f(5) = 16 + 4*32

f(5) = 16 + 128

f(5) = 144

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ANSWER IS ON VERY BOTTOM.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. We are given the diameter of the cylinder, which is 4 inches, so the radius is half of that, or 2 inches. We are also given the volume of the cylinder, which is V = cubic inches.

Substituting these values into the formula, we get:

cubic inches = π(2 inches)^2h

Simplifying, we have:

cubic inches = 4πh

To solve for h, we can divide both sides by 4π:

h = cubic inches / 4π

Using a calculator to evaluate this expression, we get:

h = 5.027 inches (rounded to three decimal places)

Therefore, the height of the poster storage tube is approximately 5.027 inches.

The height of the poster storage tube in inches is 40 inches.

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

A poster storage tube in the shape of a cylinder.

Volume = 122.5π inches³

Diameter = 3.5 inches

Radius = Diameter / 2 = 1.75 inches

Volume of the cylinder = π r² h

where r is the radius of the base and h is the height of the cylinder.

Substituting,

π (1.75)² h = 122.5π

(1.75)² h = 122.5

h = 122.5 / (1.75)²

h = 40 inches

Hence the height of the cylinder is 40 inches.

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The complete question is as follows :

A poster storage tube in the shape of a cylinder has a diameter of 3.5 inches and a volume of 122.5 (pi) cubic inches. What is the height of the poster storage tube in inches?

A triangular bandana has an area of 86 square inches. The height of the triangle is 5 3/8 inches. An equation to find the length of the base of the triangle is 86 = 1/2 * b * 43/8

The length of the triangle's base is 32 inches.

We know that the formula for calculating the area of a triangle is:

1/2 * base * height = area

We also know that the triangle's height is 5 3/8 inches, which may be expressed as a mixed number:

Height = 5 + 3/8 inch = 43/8 inch

Let b be the base of the triangle.

Substituting these numbers into the area formula yields:

86 = 1/2 * b * 43/8

To find b, multiply both sides of the equation by 2/43:

86 * 2/43 = 2/43 * 1/2 * b * 43/8

4 = b/8

b = 32

As a result, the length of the triangle's base is 32 inches.

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Therefore , the solution of the given problem of volume comes out to be the cylinder's height is roughly 5.353 inches, which is the nearest to 119/22 inches.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Cubic measurements are denoted by the characters cm3 and in3. To determine an item's size, you could use its bulk, though. The object's weight is typically transformed into mass units like grammes and kilos.

Here,

The formula for a cylinder's capacity can be used to calculate the height:

=> V = πr^2h

where the volume is V, the radius is r, and the height is h.

Inputting the numbers provided yields:

=> 1 1/16 = π(1/4)^2h

Simplifying:

=> 1.0625 = π(1/16)h

=> 1.0625 = (π/16)h

Adding 16/ to both sides:

=> h = (16/π) x 1.0625

=> h = 16.8125/π

=> h ≈ 5.3529

=> H = 5.353 inches is the result of rounding to the closest thousandth.

As a result, the cylinder's height is roughly 5.353 inches, which is the nearest to 119/22 inches.

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On solving the question we have that As a result, the coordinates of coordinates  point S after dilation with the origin as the Centre and a scale factor of 12 are (24, 12). Option (D) (16,-8), however, is incorrect.

In geometry, a coordinate system is a method that uses one or more numbers or coordinates to determine the precise location of points or other physical objects on a basis, such as Reference frame. Pairs of figures called coordinates are employed in order to locate a point or item on a double plane. The x and y parameters of a location on a 2D plane are two integers that describe its position. a set of digits which represent precise positions. In most cases, the figure has two numbers. The first number represents the front-to-back distance, while the second column represents the top-to-bottom distance. As in (12.5), there are 12 divisions below and 5 units above.

To determine the image of point S after dilation with the origin as the centre and a scale factor of 12, multiply S's coordinates by the scale factor of 12.

As a result, the coordinates of point S after dilation are as follows:

S' = (12 × 2, 12 × −1)

S' = (24, −12)

As a result, the coordinates of point S after dilation with the origin as the centre and a scale factor of 12 are (24, 12).

Option (D) (16,-8), however, is incorrect.

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The value of tan α is  [tex]\frac{3}{4}[/tex] . This value has been obtained by using the concept of trigonometry.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the study of right-angle triangles, which even includes their sides, angles, and relationships.

We know that the value of tan α is the ratio of a triangle's base to the triangle's perpendicular.

In the question, we are given that the base is 15 and the perpendicular is 20.

So, from the above information, we get the value as

⇒tan α = [tex]\frac{15}{20}[/tex]

⇒tan α = [tex]\frac{3}{4}[/tex]

Hence, the value of tan α is  [tex]\frac{3}{4}[/tex] .

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The polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has a degree of 2, a leading coefficient of 49, and a constant coefficient of 60.

The polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has the following degree, leading coefficient, and constant coefficient:

Degree: The degree of a polynomial is the maximum degree of any term in it.

Here, the term of highest degree is (7x + 3)2 which has a degree of 2.

Therefore, the degree of the polynomial is 2. Leading coefficient: The leading coefficient of a polynomial is the coefficient of the term of highest degree.

Here, the term of highest degree is (7x + 3)2 and it has a coefficient of 49.

Therefore, the leading coefficient of the polynomial is 49. Constant coefficient: The constant coefficient of a polynomial is the coefficient of the term of degree 0.

Here, there is only one such term, which is the constant term 60 (obtained by multiplying the constant terms of each factor: 5 × 4 × 9).

Therefore, the constant coefficient of the polynomial is 60.

Therefore, the polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has a degree of 2, a leading coefficient of 49, and a constant coefficient of 60.

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The value of  tan(A - B)  will be 15/8.

As mentioned,  cscA= -17/15 and A is in Quadrant III and sinB=12/13 where B is in Quadrant I To find tan(A - B), we need to have the values of sin (A - B) and cos (A - B).We know that, sin(A - B) = sinAcosB - cosAsinB and cos(A - B) = cosAcosB + sinAsinB.Since we have the values of sinA, cosA, and sinB, let's find the values of cosA and cosB.First, let's find cosA. We know that cscA = 1/sinA. Therefore, sinA = -15/17.Since A is in Quadrant III, sinA < 0, cosA < 0, and tanA > 0.

By using the Pythagorean identity sin^2A + cos^2A = 1, we get cosA = -8/17.Next, let's find cosB. We know that sin^2B + cos^2B = 1.

Therefore, cosB = sqrt(1 - sin^2B) = 5/13.

Since B is in Quadrant I, sinB > 0, cosB > 0, and tanB > 0.

Now, we have sinA, cosA, sinB, and cosB.

Using the values of sinA, cosA, sinB, and cosB, let's find sin(A - B) and cos(A - B).

sin(A - B) = sinAcosB - cosAsinB= (-15/17)(12/13) - (-8/17)(5/13)= -180/221

cos(A - B) = cosAcosB + sinAsinB= (-8/17)(12/13) + (-15/17)(5/13)= -96/221

Finally, tan(A - B) = sin(A - B) / cos(A - B)= (-180/221) / (-96/221)= 15/8. Therefore, tan(A - B) = 15/8.

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The side opposite to angle B is AC. The side adjacent to angle B is BC. The hypotenuse is segment AB.

A pair of sides are referred to as neighboring if they have a shared angle. The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, lies opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles.

From the figure we observe that the side opposite to angle B is AC.

The angle adjacent to angle B is BC.

The hypotenuse is segment AB.

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Answer:

Q1: no idea

Q2: 2 kids get 2 pieces of taffy and 1 piece of licorice and the other three get 2 pieces of licorice and 1 piece of taffy.

Step-by-step explanation:

question 2 is quite obvious but no one can get the same amount of everything so the answer that i gave makes the most sense.

It will take 55 days to finish the renovation with 25 men.

If 34 men can finish the renovation in 40 days, we can say that the number of men is inversely proportional to the number of days needed to finish the work. Therefore, we can write:

Number of men × Number of days = Constant

We can find the value of the constant by using the given information:

34 men × 40 days = 1360

This means that the constant is equal to 1360.

If 9 men withdraw before the work started, then the number of men who will work on the renovation is 34 - 9 = 25.

We can now use the constant to find the number of days needed to finish the renovation with 25 men:

25 men × Number of days = 1360

Number of days = 1360 ÷ 25

Number of days = 54.4

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Answer: 2 hours

Step-by-step explanation: (10 min) / (25 square feet)   =  (X minutes) / (300 square feet)

Cross-multiply to solve, as we always do with proportions:

10 * 300  = 25 * x

3000       = 25X

3000/25  = 25X /25

    120     = X

120 minutes * (1 hour / 60 minutes) = 2 hours

Answer: 1, 3, 5 and 15

Step-by-step explanation:

trust me bro

When "down" is positive and air friction is disregarded, the time it takes for the rock to touch the ground may be calculated using the formula [tex]h(t)=16t2-100[/tex] to be roughly 6.25 seconds.

the formula[tex]h(t)=16t2 - 100[/tex]when a rock is dropped from a height of 100 feet, and assuming that "down" is positive and air friction is neglected, represents the height of the rock at time t in seconds.

As the rock will land at the value of t when h(t) = 0, we must determine that value in order to determine how long it takes for the rock to land.

When we set h(t) to 0 we obtain 0 = 16t2 - 100.

[tex]16t^2 = 100 \st^2 = 100/16 \st^2 = 6.25 \st = ±√6.25[/tex]

The only viable answer in this case is[tex]t = 6.25 = 2.5[/tex] seconds since time cannot be negative. As a result, there was a 2.5 second delay between when the rock was dropped and when it landed.

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About 16 people among the 1,000 insured people can file a claim for a surgical procedure.

Profit is the financial gain earned by a business or an individual after deducting all the expenses and costs associated with generating that revenue. It represents the difference between the total revenue earned and the total expenses incurred.

The total amount collected in premiums over 3 years for Bracken is:

$100 x 1,000 x 3 = $300,000

Assuming x people among the 1,000 insured people file a claim for a surgical procedure, the total amount paid out in claims by Bracken would be:

$25,000 x x = $25,000x

The total deductible paid by the claimants would be:

$3,500 x x = $3,500x

So, the total amount paid out by Bracken would be:

$25,000x + $3,500x = $28,500x

For Bracken to break even, the total amount collected in premiums should be equal to the total amount paid out in claims plus the deductible for 3 years.

$300,000 = $28,500x + $3,500(1,000 - x)

Simplifying and solving for x, we get:

x = 16

Therefore, about 16 people among the 1,000 insured people can file a claim for a surgical procedure for Bracken to break even over the passage of 3 years.

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The complete question is:

Atrap and Bracken are two rival insurance companies. Atrap and Bracken have premiums of $150 and $100 and deductibles of $2,500 and $3,500 respectively. The average expense of surgery is $25,000. For Bracken to break even (suffer no loss and earn no profit) over the passage of 3 years, about how many people among the 1,000 insured people can file a claim for a surgical procedure?

a -10

b- 14

c- 16

d- 17

e- 20

From the given information provided, the probability of P(X ≤ 6), P(X˃ 4) and P(|X- 5| ˃ 1) is 0.6915, 0.6915 and 0.3829 respectively.

(i) To find P(X ≤ 6), we need to standardize the value of 6 using the formula:

Z = (X - μ) / σ

where μ = 5 and σ = 2 (since the standard deviation is the square root of the variance, which is 4).

So, we have:

Z = (6 - 5) / 2

Z = 0.5

We can then look up the probability of Z ≤ 0.5 in a standard normal distribution table, or use a calculator to find:

P(X ≤ 6) = P(Z ≤ 0.5) = 0.6915

(ii) To find P(X > 4), we again need to standardize the value of 4:

Z = (4 - 5) / 2

Z = -0.5

Then, we can use the fact that the total area under a normal distribution curve is 1 to find the probability of X being greater than 4:

P(X > 4) = 1 - P(X ≤ 4) = 1 - P(Z ≤ -0.5)

Using a standard normal distribution table:

P(X > 4) = 0.6915

(iii) To find P(|X - 5| > 1), we first need to transform this inequality into a standard normal distribution by standardizing both sides:

|X - 5| > 1

implies:

X - 5 > 1 or

X - 5 < -1

which gives:

X > 6 or X < 4

We can then standardize each inequality separately. For X > 6, we have:

Z = (6 - 5) / 2

Z = 0.5

and for X < 4, we have:

Z = (4 - 5) / 2 = -0.5

Then, using the fact that the total area under a normal distribution curve is 1, we can find the probability of both events occurring:

P(|X - 5| > 1) = P(X > 6 or X < 4) = P(Z > 0.5 or Z < -0.5)

Since the standard normal distribution is symmetric around 0:

P(Z > 0.5 or Z < -0.5) = 2 × P(Z < -0.5)

Using a standard normal distribution table:

P(|X - 5| > 1) = 0.3829

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The multiplicative rate of change of a function is calculated by taking the ratio of the change in the output to the change in the input, which in this case would be 2.

The multiplicative rate of change of a function is the rate at which the output of the function changes in relation to the input. It is calculated by taking the ratio of the change in the output to the change in the input. The formula for this is:

Multiplicative Rate of Change = (Change in Output)/(Change in Input)

For example, if a function f(x) has an input of 3 and an output of 9, then the multiplicative rate of change of the function would be 2. This can be calculated by taking the difference between the output and the input, which is 9 - 3 = 6, and dividing it by the difference between the input and the output, which is 3 - 0 = 3. Thus, the multiplicative rate of change of the function is 6/3 = 2.

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complete question:

What is the multiplicative rate of change of the function f(x) = 3x?

A graph of each inequality is shown in the grid below.

A shape which the solution region represent is a rectangle.

In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

0.4r ≤ 120     .....equation 1.

r ≥ 4(360/5)    .....equation 2.

By evaluating the given system of inequalities, we have;

r ≤ 120/0.4

r ≤ 300

r ≥ 4(360/5)

r ≥ 4(72)

r ≥ 288

By combining the system of inequalities, we have:

288 ≤ r ≤ 300

Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region between the solid line, and the point of intersection of the lines on the graph representing each.

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The value of the expression x² + 2y ÷ 2w + 3z for w = 2, x = 5, y = 8, and z = 3 will be; ⇒ 3.15

Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is;

⇒ x² + 2y ÷ 2w + 3z

And, The values are w = 2, x = 5, y = 8, and z = 3.

Now,

The expression is;

⇒ x² + 2y ÷ 2w + 3z

Substitute all the values of w = 2, x = 5, y = 8, and z = 3 in above equation, we get;

⇒ x² + 2y ÷ 2w + 3z

⇒ 5² + 2 × 8 ÷ 2 × 2 + 3 × 3

⇒ 25 + 16 ÷ 4 + 9

⇒ 41 ÷ 13

⇒ 3.15

Thus, The value of the expression x² + 2y ÷ 2w + 3z for w = 2, x = 5, y = 8, and z = 3 will be;

⇒ 3.15

The complete question is-

What is the value of x2 + 2y ÷ 2w + 3z for w = 2, x = 5, y = 8, and z = 3?

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The figure similar to figure E after dilation is figure F.

The transformation, or f: X X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the picture X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

We know that when a figure is dilated the ratio of their sides are same, that is they are proportional.

From the graph we observe that the line passes through the point F and E. Thus, the sides of the figure are proportional or in linear relation with each other.

Hence, the figure similar to figure E after dilation is figure F.

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Answer:

5

Step-by-step explanation:

3^2+4^2

9+16=25

sqrt25

The equation of the line that is perpendicular to the equation is y = -1/5x

The given line has a slope of 5, which means that any line perpendicular to it will have a slope that is the negative reciprocal of 5. The negative reciprocal of 5 is -1/5.

Let m be the slope of the line perpendicular to y = 5x - 2. Then, the equation of this line can be written in point-slope form as:

y - y1 = m(x - x1)

where (x1, y1) is the point where the line passes through, which is the origin in this case. So, we have:

y - 0 = (-1/5)(x - 0)

Simplifying this equation, we get:

y = (-1/5)x

Therefore, the line perpendicular to y = 5x - 2 and passing through the origin has a slope of -1/5 and a y-intercept of 0. Its equation is y = (-1/5)x.

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