For exercises 5 and 6, find the measures and length of each arc. Express the answer in terms of pi

Scott does 35 sit-ups altogether every night.

A ratio is a comparison of two quantities, expressed as the quotient of one quantity divided by the other. Ratios can be written in different forms, such as using a colon (:) or a fraction (/).

For every 2 straight-leg sit-ups, Scott does 3 bent-leg sit-ups. Therefore, the ratio of straight-leg sit-ups to bent-leg sit-ups is 2:3.

If Scott does 10 straight-leg sit-ups every night, we can use this ratio to find out how many bent-leg sit-ups he does.

First, we can write the ratio as a fraction:

2/5 = 10/x

where x is the number of bent-leg sit-ups Scott does.

To solve for x, we can cross-multiply:

2x = 50

x = 25

Therefore, Scott does 25 bent-leg sit-ups every night.

To find the total number of sit-ups Scott does every night, we can add the number of straight-leg sit-ups to the number of bent-leg sit-ups:

10 + 25 = 35

Therefore, Scott does 35 sit-ups altogether every night.

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Answer:

[tex]( x + 2 )^{2} +(y-15)^{2} =9[/tex]

Hope this helps!

Step-by-step explanation:

Answer: 0.098 is the answer

Step-by-step explanation:

The tiles to the correct boxes to complete the pairs-

A: [tex](-3^{-2} )^{0}[/tex] = 1; B: [tex]3^{3}.3^{1}. 3^{2} .3^{-12}[/tex] [tex]= 1/729[/tex]  C: [tex]-3^{5} / -3^{8}[/tex] = -1/27 ; D: [tex]-3^{-3}. 3^{-3}[/tex] = - 1/729.

We can determine how many times a phrase has been multiplied by itself using an index, which is a tiny number.

Indexes is the plural of index.

Remember that a power is the result of a particular number of identical factors? For instance, the number [tex]3^{7}[/tex] is a power, where the base is the number 3, and the index or exponent is the number 7.

Given number with exponents :

A: [tex](-3^{-2} )^{0}[/tex]

[tex]= (-3^{0} )\\= 1[/tex]

B: [tex]3^{3}.3^{1}. 3^{2} .3^{-12}[/tex]

[tex]= 3^{3 + 1 + 2 -12}[/tex]

[tex]= 3^{-6}\\= 1/729[/tex]

C: [tex]-3^{5} / -3^{8}[/tex]

[tex]= -3^{5-8}\\= - 3^{-3}\\\= -1/27[/tex]

D: [tex]-3^{-3}. 3^{-3}[/tex]

[tex]= -3^{-3 - 3}\\= -3^{-6}\\\\= -1/729[/tex]

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The  probability that the person selects 2 coffees with artificial sweetener is 33/95.

Let A be the event that the first cup of coffee has artificial sweetener, and B be the event that the second cup of coffee also has artificial sweetener.

We want to find the probability of the intersection of A and B, i.e., the probability that both cups have artificial sweetener. We can use the formula for conditional probability:

P(A and B) = P(B|A) * P(A)

where P(B|A) is the probability of B given that A has occurred, and P(A) is the probability of A.

The probability of selecting a cup of coffee with artificial sweetener on the first draw is:

P(A) = 12/20

After the first cup has been drawn, there are now 11 cups with artificial sweetener left in the order, out of a total of 19 cups (since one cup has already been drawn). Therefore, the probability of selecting another cup with artificial sweetener on the second draw, given that the first cup had artificial sweetener, is:

P(B|A) = 11/19

So the probability of selecting two cups with artificial sweetener is:

P(A and B) = P(B|A) * P(A) = (11/19) * (12/20) = 33/95

Therefore, the probability that the person selects 2 coffees with artificial sweetener is 33/95.

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Answer:

formula for area of a circle = πr²

πr² = 92cm² first circle

πr² = 62cm² second circle

now to find the radius of a circle having the sum of the other circle.

πr² = 92 + 62

3.142 × r² = 154

r² = 154/3.142

r² = 49.013

take square root of both sides

r = √49.013

r = 7.000cm ≈ 7cm

Answer:

AD = 9

Step-by-step explanation:

B is the midpoint of AC and BC = 2 so AC = 4.

BD is given as 7 so all we need to do is add up the given values:

AC + BD - BC = AD

4 + 7 - 2 = 9

The measure of the angle ∠4 in the parallell lines and transversal is 59 degrees

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

The parallell lines and transversal

By the sum of angles on a straight line, we have the following equation

Angle 4 + 60 + 61 = 180

Evaluate

Angle 4 = 180 - 121

So, we have

Angle 4 = 59

Hence, the measure of the angle is 59 degrees

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Answer:

To find the vertex form of the quadratic equation, we need to first find the equation in standard form, which is:

f(x) = a(x - r)(x - s)

where r and s are the roots of the quadratic equation and a is a constant.

From the problem statement, we know that the roots of the quadratic equation are -2 and 6. Thus, we can write:

f(x) = a(x + 2)(x - 6)

To find the value of a, we can use the point (1, 15) that the function passes through. We substitute x = 1 and f(x) = 15 into the equation:

15 = a(1 + 2)(1 - 6)

15 = -15a

Thus, a = -1.

Substituting this value of a into the equation, we get:

f(x) = -(x + 2)(x - 6)

To convert this equation into vertex form, we need to complete the square. We can do this by adding and subtracting (2/2)² = 1 from the equation:

f(x) = -(x + 2)(x - 6) + 1 - 1

= -(x + 2)² + 16

Therefore, the vertex form of the equation of f(x) is f(x) = -(x + 2)² + 16.

Step-by-step explanation:

Hi if u have more questions , feel free to ask me on my pa d let or sn ap or disco r d

According to the given question the correct option  is (D) which is 84 and 6/7 square inches.

Surface area is indeed a measurement of how much overall space an object occupies. A three-dimensional shape's surface area is the sum of the area surrounding it. The term "surface area" refers to a three-dimensional shape's overall surface area. The surface area of a cuboid with six rectangular faces can be calculated by adding the areas from every face. As an alternative, you can name the dimensions of this box using the formula below: 2lh, 2lw, with 2hw make up the surface area (SA). Surface area is a unit used to describe how much space a three-dimensional form's surface takes up overall.

Given,

The formula: can be used to determine a cylinder's surface area.

surface area = 2πr^2 + 2πrh

where r is the cylinder's radius and h seems to be the cylinder's height.

In this case, the diameter of the mini muffins is 2 inches, so the radius is 1 inch. The height is 1 and 1/4 inches. When these values are added toward the formula, we obtain:

surface area = 2π(1^2) + 2π(1)(5/4) = 2π + 5π/2 = 9π/2

To find the amount of paper needed to wrap 6 mini muffins, we multiply the surface area of one mini muffin by 6:

6 × (9π/2) = 27π

Approximating π as 22/7, we get:

27π ≈ 27 × 22/7 = 84 and 6/7

Therefore, the answer is (D) 84 and 6/7 square inches.

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Step-by-step explanation:

192080 because we multiply its 980×196 =182080

Using the bar graph we can conclude that it rained 0.5 inches more in the summer of 2010 than in 2009.

Using rectangular bars that are proportional to the values they represent; a bar graph displays all the data. The graph's bars can be displayed either vertically or horizontally. Bar graphs, commonly referred to as bar charts, are a visual depiction of groups of data. It is one method of processing data. A bar graph is a great tool for representing data that are unrelated to one another and do not need to be displayed in any particular sequence. The bars provide a visual representation for comparing amounts in several categories. Together with the title, labels, and scale range, bar graphs have two axes that are horizontal and vertical and are also known as the x and y axes.

Here in the question,

We can see that in the summer of 2009 the rain was for 1.5 inches.

In the summer of 2010, the rain was for 2 inches.

Hence, the difference between the number of inches it rained=

2 - 1.5

= 0.5 inches.

Therefore, using the bar graph we can conclude that it rained 0.5 inches more in the summer of 2010 than in 2009.

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The commute times are shorter for City A but more predictable for City B. Thus, option c is correct.

In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. An interval can be written using interval notation, which uses parentheses, square brackets, or a combination of both to indicate whether the endpoints of the interval are included or excluded.

The interval [1, 5] represents a set of real numbers that includes all the numbers between 1 and 5, including 1 and 5 themselves. The square brackets indicate that the endpoints of the interval are included in the set. The left bracket "[" indicates that the interval includes the number 1, and the right bracket "]" indicates that the interval includes the number 5.

In interval notation, we can write this interval as:

[1, 5] = {x | 1 ≤ x ≤ 5}

This means that the set of all real numbers x, such that x is greater than or equal to 1 and less than or equal to 5, is equal to the interval [1, 5].

Graphically, we can represent this interval on a number line as follows:

 |-----|-----|-----|-----|-----|

 0     1     2     3     4     5

The interval [1, 5] is the closed interval between 1 and 5, including both endpoints, so we use closed circles to indicate that the endpoints are included in the interval:

 |-----|-----|-----|-----|-----|

 0     1     2     3     4     5

       [     ○-----○     ]

            1         5

The interval includes all the numbers on the number line between 1 and 5, including 1 and 5 themselves, but no other numbers outside of that range.

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Answer:

What is a mean?

A mean is the average of all the numbers in a data set.

How can I find mean?

to find mean you add up all the numbers in the data set; and divide them by the amount of numbers there are.

103+3+41+7=154

154÷4=38.5

The mean is 38.5

The pet will need 3 tablets of Albon for the treatment. This can be answered by the concept of Simple mathematics.

To calculate the required dosage, we need to convert the pet's weight from pounds to kilograms, which gives us 11.36 kg. On day 1, the pet requires 5 mg/kg of Albon, which amounts to 56.8 mg. Since each tablet contains 125 mg, we need to give the pet 0.454 tablets (56.8/125) which we will round up to 1 tablet. For the next 5 days, the pet requires 2.5 mg/kg of Albon, which amounts to 28.4 mg.

Therefore, we will give the pet 0.227 tablets (28.4/125) which we will round up to 1/4 of a tablet (0.25 tablets) each day. So, over the course of 6 days, the total number of tablets needed will be 1 + (0.25 x 5) = 2.25, which we will round up to 3 tablets.

Therefore, the owner will need to be dispensed with 3 tablets of Albon for the pet's treatment.

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Shama needs to buy 10 plants for her garden.

From the graph, we have

Area = 8 * 5 = 40

To determine how many plants Shama needs to buy, we need to use the given rule that she buys 1 plant for every 4 square feet of the garden.

Therefore, we can divide the total area of the garden by 4 to find how many plants she needs to buy:

Number of plants = Area of garden ÷ 4

Substituting the given values, we get:

Number of plants = 40 ÷ 4

Number of plants = 10

Therefore, Shama needs to buy 10 plants for her garden.

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Answer:

Step-by-step explanation:

a.

3:  Area = 3² = 9

100:  Area = 100² = 10,000

25:  Area = 25² = 625

s:  Area = s²

b.

Yes, the relationship is proportional.  The area of the square is the length of a side squared.  Area = (length)²

Answer:

the value of what you lose when you choose from two or more alternatives

Step-by-step explanation:

The final expression is 9c + 2.

What is an equation?

In mathematics, an equation asserts the equality of two expressions, usually separated by an equal sign (=). An equation is formed when two expressions are set equal to each other. The expressions can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

To simplify the expressions:

5c + 4c + 2 = 9c + 2

In this expression, we can add the coefficients of the like terms 5c and 4c to get 9c. Then we simply combine the constant term 2.

5c + 2[2c + 1] = 5c + 4c + 2

In this expression, we can distribute the 2 outside the brackets to get:

5c + 2(2c) + 2(1) = 5c + 4c + 2

Then, as in the previous expression, we can combine the like terms 5c and 4c to get 9c and simplify to get:

9c + 2

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Answer:

m∠2 = 130°

m∠3 = 25°

m∠4 = 25°

Step-by-step explanation:

Opposite angles of rhombi are congruent. Therefore,

m∠1 = m∠2 = 130°

The measures of the interior angles of a triangle add to 180°. Using this information, along with the isosceles triangle theorem, we can solve for m∠3 (which is also congruent to m∠4):

m∠2 + 2(m∠3) = 180°

↓ substituting in m∠2

130° + 2(m∠3) = 180°

↓ subtracting 130° from both sides

2(m∠3) = 50°

↓ dividing both sides by 2

m∠3 = 25°

m∠3 = m∠4 = 25°

Answer:

No, a non-complex equation cannot have 2 horizontal asymptotes. By definition, a horizontal asymptote is a horizontal line that the function approaches as x goes to positive or negative infinity. If there were two horizontal asymptotes, the function would have to approach two different horizontal lines as x goes to infinity, which is not possible for a single-valued function.

Similarly, a non-complex equation cannot have 2 vertical asymptotes. A vertical asymptote is a vertical line where the function approaches infinity or negative infinity as x approaches the line from either side. If there were two vertical asymptotes, the function would have to approach infinity or negative infinity as x approaches each line, which is not possible for a single-valued function.

Using a complex number as x does not change the behavior of asymptotes. If a function has a vertical asymptote at a real number, it will still have a vertical asymptote at that number when x is a complex number. Similarly, if a function has a horizontal asymptote, it will still have a horizontal asymptote when x is a complex number.

However, if a function has a vertical asymptote at a complex number, it may behave differently depending on the direction in which x approaches the asymptote. If the function approaches different values as x approaches the asymptote from different directions, then the function may not have a limit at the complex number and may not have a vertical asymptote. Similarly, if a function has a horizontal asymptote and is not defined for complex values of x, then it may not have a limit at infinity and may not have a horizontal asymptote.

Step-by-step explanation:

Answer:  24:1

Step-by-step explanation:

In the first step, you have to acknowledge how many of each tree there are in the question asked.

There is one cherry tree and 24 orange trees.

So the ratio of orange trees to cherry trees would be 24:1

Ike ran 12 miles and Gus ran 36 miles based on equation solving.

Assume that x is a representation of Ike's running distance. Gus ran three times as far as Ike, so his distance was three times Ike's.

Gus and Ike travelled a total of 48 miles, as far as we know. Thus, we can create the following equation:

x + 3x = 48

When we simplify this equation, we obtain:

4x = 48

When we multiply both sides by 4, we get:

x = 12

Ike afterwards ran 12 kilometres.

To confirm, we may calculate Gus's running distance by dividing Ike's distance by three:

3x = 3(12) = 36

And we can confirm that the total of their separations is 48:

12 + 36 = 48

Gus ran 36 miles while Ike ran 12 miles.

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Answer:

Step-by-step explanation:

Answer:

155 Units

Step-by-step explanation:

Rate of Bug (given) = 11 units PER MINUTE

It never changed direction, so it was going in positive direction (assume).

In 7:15 pm (evening), it was at Point 100,

We want the point at which it was at 7:20 pm.

7:20pm - 7:15pm = 5 minutes

So, time passed 5 minutes. It's rate is 11 units PER MINUTE, so in 5 mins:

11 * 5 = 55 units

Assuming he is going in positive direction, the bug will be at:

100 + 55 = 155 Units

Using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.

A triangle is a polygon with three edges and three vertices.

It belongs to the basic geometric shapes.

A triangle having vertices A, B, and C is known as triangle ABC.

Any three locations in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.

The closed, two-dimensional shape known as a triangle has three sides, three angles, and three vertices.

A triangle is part of a polygon.

So, we know that:

We must ascertain the value of x in order to determine the triangle's perimeter, IJK.

Using the ratio of comparable triangles and the triangles above, we have:

HF/KI = FG/IJ

Where,

HF = 35, KI = 77, FG = 27 and IJ = x

By changing the values, we obtain:

35/77 = 27/x

Take the cross product of the aforementioned equation, and we have:

35x = 27*77

x = 27*77/35 = 27 * 11/5 = 59.4

The triangle's perimeter is thus equal to the sum of its sides:

△IJK = 44 + 77 + 59.4 = 180.4

Therefore, using the equation and cross-multiplication method, we know that the perimeter of the triangle IJK is 180.4 units.

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Correct question:

Watch the help video on the perimeter of AIJK. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

The two true statements about the axis of symmetry are the first and second ones, so the correct option is the second one (counting from the top)

The axis of symmetry is a of a quadratic equation is a line that cuts the parabola in two equal halves.

For a quadratic of the form:

y = ax² + bx + c

Where the vertex is (h, k)

The axis of symmetry is the line of the form:

x = h

Then the two true statements are i and ii, the third and fourth statements are false because the vertex can be either a maximum or minimum, so we can't apply these restrictions.

Then the correct option is the second one.

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For the given circle the circumference is 34.54.

What is circumference?

Circumference is the distance around the edge of a circle or any curved, circular object. It can be thought of as the perimeter of a circle.

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle.

Substituting the given value of the diameter, we get:

C = π(11)

Using π = 3.14, we can evaluate the expression:

C = 3.14(11)

C = 34.54

Therefore, the circumference of the circle is 34.54 (rounded to two decimal places).

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At μ = 10.0932 level should the mean be set if it is required that only 1% of the bags weigh less than 9.5 kg.

Given Data:

σ = 0.04 kg

x = 9.5 kg

We want to determine μ such that: P(X ≤ 9.5)= 1% = 0.01

Thus, we know here probability of x is 0.1 which is  less than 9.5

so here Z is -2.326 by the standard table

Determine the z-score in the normal probability table in the appendix that has a probability closest to 0.01:

Then, we have here 1% to left when Z is - 2.326

Now,

The value corresponding to the z-score is then the mean increased by the product of the z-score and the standard deviation:

x = μ+ zσ

= μ− 2.33(0.04) = μ - 0.0932

Since , P(X ≤ 9.5) = 0.95% = 0.095, we know that x also has to be equal to 9.5:

   μ− 0.0932 = 9.5

Add 0.0932 to each side of the previous equation:

μ = 10+ 0.0932

= 10.0932

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Answer: 1017.36 km²

Step-by-step explanation:

Area of Circle = πr² = 3.14×18×18 = 1017.36 km²

The design is a randomized controlled trial (RCT), where participants are randomly assigned to treatment groups and tested on the dependent variable once to control for confounding variables and ensure that differences observed between groups are due to the treatment.

The type of design you are referring to is a randomized between-subjects design, also known as a randomized controlled trial (RCT). In this type of experiment, participants are randomly assigned to one of two or more treatment groups, each receiving a different level or type of the independent variable. Then, the dependent variable is measured only once after the treatment is administered. The purpose of this design is to control for potential confounding variables and to ensure that any differences observed between groups are due to the treatment and not to other factors.

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