Semicircles of diameter 2'' are lined up as shown. What is the area, in square inches, of the shaded region in a 1-foot length of this pattern?

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is  52!/(47! * 5!).

The expression that you can use to find the number of ways to choose 5 cards from a 52-card deck is 52 choose 5, which is equal to 52!/(47! * 5!), where the exclamation point indicates the factorial function. This is known as the binomial coefficient, and it represents the number of ways to choose a certain number of items from a larger set. In this case, the binomial coefficient is used to find the number of ways to choose 5 cards from a deck of 52 cards.

The order of the cards is irrelevant in card games like poker. A five-card draw of 1,2,7,9, K is equivalent to a draw of K,7,9,1,2. What counts is the fundamental overall group.

Order is irrelevant, therefore we utilize a combination (instead of a permutation)

We will substitute n = 52 and r = 5 into the nCr combination formula, which is n C r = (n!)/(r!*(n-r)!)

so we obtain:

n C r = r!*(n-r)!/(n!)

52 C 5 = (52!)/(5!*(52-5)!)

52 C 5 = (52!)/((52-5)!*5!)

The complete question is:-

Which expression can you use to find the number of ways to choose 5 cards from a 52-card deck?

a) (52-5)! / 52!5!

b) 52! / (52-5)!

c) 52! / (52-5)!5!

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The given quadratic equation 4x^2 - 4x + 1 = 0 has one real solution

by its discriminant.

The discriminant of a quadratic equation ax^2 + bx +c = 0 is given by

            D = b^2- 4ac

Now from the equation that we have 4x^2 - 4x +1 = 0

             a = 4

             b = -4   and

             c = 1

Hence the discriminant (D) is given by :

             D = b^2- 4ac

                 = (-4)^2- 4(4)(1)

                 = 0

Now check for discriminant D, (D=0)

Therefore the discriminant of a given equation is 0.

So the roots of given equation are real and equivalent.

Hence the equation given 4x^2 - 4x + 1 =0 has only one real solution.

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The probability that Onex will have an EBIT that is below $0 is 0.38%. The correct answer is C.

The first step in solving this problem is to calculate the z-score, which is a measure of how many standard deviations a value is from the mean. In this case, the mean EBIT is $240,000, and the standard deviation is $90,000.

To find the z-score for an EBIT of $0, we subtract the mean from the value and divide by the standard deviation as follows:

This gives us a z-score of -2.67. Next, we use Table V, which is a table of standard normal distribution values, to find the probability that a value with a z-score of -2.67 will fall below 0. The probability is 0.38%, which means there is a very low chance that Onex's EBIT will be below $0.

This question should be provided with answer choices, which are:

The correct answer is C.

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Answer:

y-1=3(x-2)

Step-by-step explanation:

This is the equation you have to fill in y-y1=m(x-x1) to fill in this you have to lable the points (2,1)

x,y

Among the five friends Eric, Mark, Tom, Danny, and Cliff the fourth in line is Danny.

Given the information, we can make the following deductions:

Eric is the first one in line.

Cliff is standing directly behind Danny, so he is the fifth one in line.

Mark is somewhere behind Eric and Tom, but there are two people between Cliff and Mark, so it's Tom is the third one in line.

As we know that Mark is somewhere behind Eric and somewhere in front of Tom, Mark is the second one in line.

The five friends standing sequence will be - Eric, Mark, Tom, Danny, and Cliff.

Hence, the Fourth one in line is Danny.

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Answer:

----------------------------

Parallel lines divide transversals proportionally.

Set proportions and solve for x:

The probability that a randomly selected student plays basketball, given that they run track is 0.38.

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability.

Assume that events A and B are two independent occurrences with probabilities P(A) and P(B), respectively, such that the probability that event B will occur given that event A is given by: P(B|A) = P(A∩B)/P (A)

Given:

Percentage of the students who play basketball, P(A) = 31%

Percentage of the students who run track, P(B)= 29%

Percentage of the students who participate in both sports, P(A∩B) = 11%

The probability that a randomly selected student plays basketball, given that they run track is:

P(A|B) = P(A∩B)/P(B)

          = 11/29

          = 0.38

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This fraction can be simplified to P(woman) = 21/49 or approximately 0.428.

What is probability ?

Probability is a measure of the likelihood of an event occurring, represented as a number between 0 and 1. 0 indicates that an event is impossible, and 1 indicates that an event is certain to happen. It is the ratio of number of favorable outcomes to the total number of possible outcomes.

In this case, the number of favorable outcomes is the number of women in the class, which is 63. The total number of possible outcomes is the total number of students in the class, which is 63 women + 86 men = 149 students. Therefore, the probability of selecting a woman is,

P(woman) = 63/149

So , This fraction can be simplified to P(woman) = 21/49 or approximately 0.428.

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Therefore , the solution of the given problem of ratio comes out to be

there are 32 fauvists .

Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.

Here,

Given :

the ratio is 13:4

and there were 104 impressionists

Let x be the fauvisits

=> 13:4 = 104/x

=>  13 /4  = 104/x

=> x = 104 *4 /13

= >x  = 32

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At $63 price point should they sell the pads to have a demand of 14 thousand pads.

p(x) = -5x + 133

Substitute x with 14,

p(14) = -5(14) + 133

       = -70 + 133

       = 63.

The chance of an event happening given that another event has already occurred (via assumption, supposition, statement, or evidence) is known as conditional probability in the field of probability theory. [1] This particular approach depends on event B happening in some way connected to another event A. In this case, a conditional probability analysis with respect to event B is possible.

The probability of A under the condition B is typically expressed as P(A|B)[2] or PB if the event of interest is A and the event B is known to have occurred or is assumed to have done so (A). This can alternatively be thought of as the percentage of possibility that B and A will collide.

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Answer:

2.45%

Step-by-step explanation:

(2.86 - 2.79) / 2.86 = 0.0245

0.0245 x 100 = 2.45%

Answer: Based on the histogram, it is not possible to determine the exact number of people who travel more than 30 miles to work. However, we can estimate the number of people by using the histogram.

Step-by-step explanation: The histogram shows the frequency density of people traveling different distances to work.

The Y-axis shows the frequency density, and the X-axis shows the distance in miles.

The histogram is divided into bars, each representing a range of distances.

We can see that the majority of people travel less than 30 miles to work, with the highest frequency density being around 20 miles.

However, the histogram does not provide the exact number of people for each bar. Therefore, we cannot determine the exact number of people who travel more than 30 miles to work.

b) Sam travels around 20 miles to work.

Explanation:

205 people out of 550 people is approximately 37% of the total number of people surveyed.

The closest bar on the histogram to 37% is the one around 20 miles.

Therefore, it can be estimated that the distance that Sam travels is around 20 miles.

The estimate of the average pulse rate in beats per minute of an animal that weighs 640 kilograms is given as follows:

29.6 beats per minute.

The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.

(this is because there are multiple types of regression, such as logistic, exponential and quadratic regression).

The points for this problem are given as follows:

(3, 130), (28,75), (56, 75), (192, 95), (362,48), (465, 66), (521, 34).

Inserting these points into a calculator, the regression equation is given as follows:

y = -0.11x + 100.

Hence, for a weight of x = 640 kg, the estimate of the average heart rate is given as follows:

y = -0.11(640) + 100

y = 29.6 beats per minute.

The table is given by the image presented at the end of the answer.

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Answer:

Step-by-step explanation: Applying BODMAS rule,

[tex](8a-6a^2 +9)+(-10a-8+8a^2)-(-3)\\=8a-6a^2+9-10a-8+8a^2+3\\=2a^2-2a+12[/tex]

Answer: The answer to part a is the same if you eat 5 cookies from each batch as you are baking because the number of cookies you have is the product of the number of batches times the number of cookies per batch minus the number of cookies you eat.

In the expression 14(5) + 2 = 3(24)

14(5) represents the total number of cookies you put in 14 bags. (14 x 5) = 70

2 represents the number of cookies left after you have put 5 cookies in each of the 14 bags.

3(24) represents the total number of cookies you made from the 3 batches of cookies. (3 x 24) = 72

So the equation can be read as:

The total number of cookies you put in bags (70) plus the number of cookies left (2) is equal to the total number of cookies made from the 3 batches (72).

Step-by-step explanation:

The function that fits the points (-1, 21) (3, 45) (4, 81) is 6x²-6x+9.

Quadratic Regression is a method according to which we can make an equation of a quadratic curve from given no. of x and y data points

Quadratic Regression Equation(y) = a + b x + c x^2

The formula for its coefficients is,

c = { [ Σ x2 y * Σ xx ] - [Σ xy * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }

b = { [ Σ xy * Σ x2x2 ] - [Σ x2y * Σ xx2 ] } / { [ Σ xx * Σ x2x 2] - [Σ xx2 ]2 }

a = [ Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x 2 / n ] }

Where,

Σ x x = [ Σ x 2 ] - [ ( Σ x )2 / n ]

Σ x y = [ Σ x y ] - [ ( Σ x * Σ y ) / n ]

Σ x x2 = [ Σ x 3 ] - [ ( Σ x 2 * Σ x ) / n ]

Σ x2 y = [ Σ x 2 y] - [ ( Σ x 2 * Σ y ) / n ]

Σ x2 x2 = [ Σ x 4 ] - [ ( Σ x 2 )2 / n ]

x and y are the Variables.

a, b, and c is the Coefficients of the Quadratic Equation

n = Number of Values or Elements

Σ x= Sum of First Scores

Σ y = Sum of Second Scores

Σ x2 = Sum of the square of the First Scores

Σ x 3 = Sum of Cube of First Scores

Σ x 4 = Sum of Power Four of First Scores

Σ xy= Sum of the Product of First and Second Scores

Σ x2y = Sum of Square of First Scores and Second Scores

when we input the points (-1,21),(3,45),(4,81)

we get the equation 6x²-6x+9

which looks like this (The image has been attached),

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The second post is 30 feet tall because the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall.

1. ratio of shadows is 2:1, so for every 2 feet of shadow, the post is 1 foot tall

2. 60 feet of shadow divided by 2 is 30 feet tall

3. 24 feet of shadow divided by 2 is 12 feet tall

4. 30 feet tall is the second post

The goal post that casts a 60-foot shadow is 20 feet tall, and the ratio of the shadows is 2:1, meaning that for every 2 feet of shadow, the post is 1 foot tall. To find the height of the second post, we divide the length of the shadow by 2. The second post casts a 24-foot shadow, so when we divide it by 2, the post is 12 feet tall. Therefore, the second post is 30 feet tall. This is because for every 2 feet of shadow, the post is 1 foot tall, so for the 60-foot shadow, the post was 20 feet tall, and for the 24-foot shadow, the post is 12 feet tall. Therefore, the second post is 30 feet tall.

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There are 26 rows and 34 seats per row in the movie theater.

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Let x represent the number of seats per row and y represent the number of rows.

The number of seats in a row is 8 greater than the number of rows, hence:

x = y + 8    (1)

The total number of seats in the theater is 884, hence:

xy = 884

but x = y + 8. Substituting:

(y + 8)(y) = 884

y² + 8y - 884 = 0

y = 26

x = y + 8 = 26 + 8 = 34

There are 26 rows

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Simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2%.

1.To calculate simple interest, multiply the principal (initial amount) by the number of years, the interest rate, and the interest rate.

Contrarily, compound interest is computed by first adding the interest from earlier periods to the principal, and then computing the interest for the subsequent period on the updated sum.

Consider Mr. Henry investing P150,000 in ABC Bank at an annual simple interest rate of 2%:

Year 1: Interest earned is P3,000 (P150,000 x 2%).

Year 2: Interest earned is P3,000 ($150,000 x 2%).

Year 3: Interest earned is P3,000 ($150,000 x 2%).

Year 4: Interest earned is P3,000 ($150,000 x 2%).

Year 5: Interest earned is P3,000 ($150,000 x 2%).

Interest earned overall: P15,000

After five years, the total will be P150,000 plus P15,000, or P165,000.

Let's imagine Mr. Henry makes a P150,000 investment in Union Bank at a 2% yearly compound rate:

Year 1: P150,000 multiplied by 2% yielded P3,000 in interest, for a total of P153,000.

Year 2: P153,000 multiplied by 2% to be P3,060 in interest, for a total of P156,060.

Year 3: P156,060 multiplied by 2% to equal P3,121.20 in interest, for a total of P159,181.20.

Year 4: P159,181.20 multiplied by 2% yielded P3,183.624 in interest, for a total of P162,364.824.

Year 5: P162,364.824 multiplied by 2% yields P3,247.29696 in interest, for a total of P165,612.12096.

Interest earned in whole was P15,612.12096.

2 .If I were Mr. Henry, I would pick the 2% compounded annual offer from Union Bank. This is so that after five years, the total sum will be larger due to compound interest. Compound interest increases the amount on which interest is computed in the following period by adding the interest from prior periods to the principal. Due to this, the interest earned during the subsequent period will increase, and so on. As a result, after a certain amount of time, interest accrues more quickly and the overall amount is higher.

  Therefore , simple interest is p15612.12 and compound interest is p16500.If I was were Mr. henry ,I will choose offer of 2% .

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The angle through which the plane turns is B; 90 degrees clockwise

When determining the angle of turn, it is important to consider the direction of rotation (in this case, clockwise) and the starting and ending points (in this case, South East to North).

We are given that  plane is heading in a direction of 045° and changes course in a clockwise direction to 135°.

To Subtract the angles to get the answer

135 - 45 = 90

In terms of compass, 45 degrees is directly pointed at northeast while 135 degrees is pointed directly at southeast. We have zero degrees pointed straight north.

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Answer: It is not possible to determine whether rectangle EFGH is the result of a dilation of rectangle ABCD with a center of dilation at the origin just by looking at the statement provided.

A dilation is a transformation that changes the size of a shape but not its shape or orientation. In a dilation, the center of dilation is a fixed point and all other points move away from or towards it by a scale factor.

The statement provided does not include any information about the scale factor, the coordinates or measurements of the rectangle's vertices or any other information that would allow to determine if EFGH is the result of a dilation of ABCD. The statement only indicates that the center of dilation is at the origin.

In order to determine if rectangle EFGH is the result of a dilation of rectangle ABCD with a center of dilation at the origin, we would need additional information such as the scale factor, the coordinates or measurements of the rectangle's vertices, and the direction of dilation (enlargement or reduction)

It's worth noting that a dilation with center of dilation at origin can be performed only if the shape is symmetric.

Step-by-step explanation:

Note that the very first step in verifying a statement about a product is represented by the acronym C.L.A.I.M. The first letter "C" stands for Claim.  

L - Logic: Examining the logic of the claim to see if it is reasonable and if the evidence offered supports the assertion.

A - Attribution: Identifying the source of the assertion and assessing its reliability.

I - Investigation: Research and evidence collecting to support or reject the allegation.

M - Measurement: Evaluating the quality and quantity of evidence obtained and assessing whether or not it supports the claim being made.

Following the CLAIM technique allows one to assess the correctness and validity of a claim and make an educated judgment about the product or service in issue.

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The circumference of a circle is the distance encircling its edge. The length measured through the centre of a circle is its diameter. The radius of a circle is the distance from the centre to any point on the edge. The diameter and radius are identical in size, or 2r=d2 r=d.

Circumference =2×227×21=132 cm. Q.

Another way to think about the circle's circumference curve is to look at its 360-degree arc. As a result, a circle's diameter is equal to its 360-degree arc's length.

(a) Circumference of the circle = 2πr

= 2 × 22/7 × 14 cm

= 2 × 22 × 2 cm

= 88 cm

(b) Circumference of the circle = 2πr

= 2 × 22/7 × 28 mm

= 2 × 22 × 4 mm

= 176 mm

© Circumference of the circle = 2πr

= 2 × 22/7 × 21 cm

= 2 × 22 × 3 cm

= 132 cm

Therefore, 176 mm and 132 cm is the circumference of a circle.

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One possible solution of the inequality x + y ≤ 18 and 0.1x + 0.05y ≥ 1.20 is 12 dimes and 4 nickels

An equation is a expression that shows the relationship between numbers and variables.

Let y represent the nickels and x represent the dimes

1 nickel = $0.05, 1 dime = $0.1

She has a maximum of 18 coins worth at least $1.20 combined. Hence:

x + y ≤ 18    (1)

Also;

0.1x + 0.05y ≥ 1.20    (2)

One possible solution is 12 dimes and 4 nickels

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The expression for the t1 with the tension in cable 1 that does not depend on t2 is T1sinθ1 + T2sinθ2 = mg

While we looking into the given diagram we have identified that the angle made by strings 1 and 2 are 01 and 02 respectively.

Here we also know that the tension made by strings 1 and 2 are T1 and T2 respectively.

Here let us considering that the diagram shown is the following tension components are available

And the weight of the block mg acting on the body directing the force downwards then the components are written as,

Here the Vertical component of T1 is T1 sinθ1 which acts upwards and the horizontal component of T1 is T1cosθ1 which acts to the left

Where as the another vertical component of T2 is T2sinθ2 which acts upwards then the horizontal component of T2 is T2cosθ2 acting towards right

Here we have to maintain a state of equilibrium, then the upward forces and downwards forces must be equal even as the forces on the right and left hand side must balance

According to this details the balancing the vertical components we obtain

=> T1sinθ1 + T2sinθ2 = mg

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53 dollar t is the cost of goods if manufacturing costs equal $50 each ,packaging equals $1.00 each, delivery equals $2.00 each, and advertising equals $1,000

what is cost ?

Definition: A cost function is a mathematical formula used to used to chart how production expenses will change at different output levels. In other words, it estimates the total cost of production given a specific quantity produced.

50$ + 1$ + 2$ = 53$

50 for the production

1$ for packaging

2$ for delivery

Hence 53 dollar t is the cost of goods if manufacturing costs equal $50 each ,packaging equals $1.00 each, delivery equals $2.00 each, and advertising equals $1,000

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Answer:

Step-by-step explanation:

The area of a rectangle can be found by multiplying its length and breadth. In this case, the length is 11/5 cm and the breadth is 13/5 cm. Therefore, the area of the rectangle is (11/5 cm)*(13/5 cm) = 143/25 sq. cm = 5.72 sq. cm.

10, 24, 26 are the Pythagorean triples. Therefore, option (i), (iii) and (iv) are the correct answers.

Pythagorean triples are a²+b² =c² where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.

i) 10, 24, 26

Here, 26²=10²+24²

676=100+576

676=676

So, the given set of numbers are Pythagorean triples

ii) 2, 3, 5

Here, 5²=2²+3²

25≠13

So, the given set of numbers are not Pythagorean triples

iii) 3a, 4a, 5a; where a is any whole number

Here, (5a)²=(3a)²+(4a)²

25a²=9a²+16a²

25a²=25a²

So, the given set of numbers are Pythagorean triples

iv) 7, 24, 25

Here, 25²=24²+7²

625=576+49

625=625

So, the given set of numbers are Pythagorean triples

v) 12, 13, 15

Here, 15²=12²+13²

225=144+169

225≠313

So, the given set of numbers are not Pythagorean triples

Therefore, option (i), (iii) and (iv) are the correct answers.

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x 2, and the second side is expressed by  2x-25 , The value of x is 5.

What is isosceles triangles ?

An isosceles triangle is a triangle with two sides of equal length. These two sides are called the legs and they are congruent. The third side is called the base and it is not necessarily congruent to the legs. The angle opposite to the base is called the vertex angle.

To solve for x, we can start by isolating x on one side of the equation.

We can do this by subtracting x^2 from both sides ,

x^2 - x^2 = 2x-25 - x^2

we get 0 = 2x - 25 - x^2

Now we can add x^2 to both sides ,

x^2 = 2x - 25

Now we can move the -25 to the other side of the equation ,

x^2 - 2x + 25 = 0

Now we can factor the left side of the equation ,

(x-5)(x-5) = 0

Now we can solve for x by setting each factor equal to zero ,

x-5 = 0 , x = 5

x 2, and the second side is expressed by  2x-25 , The value of x is 5.

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The value of adjacent side x in radical form is obtained as 7/√2.

What is radical form?

Instead of employing exponents to describe the same item, a radical form of an expression uses radical signs like the square root, cube root, etc.

The given triangle is a right-angled triangle with other two angles measuring 45° as given in the diagram.

The value of hypotenuse is 7.

The adjacent side is taken to be x.

Apply the cosine formula -

cos θ = adjacent / hypotenuse

cos 45° = x/7

1/√2 = x/7

x = 7/√2

Therefore, the value of x in radical form is 7/√2.

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