A pool charges $4 each visit or you can buy a membership for $100. Write and solve an inequality to find how many times a person should use the pool so that a membership is less expensive than paying each time. Write an inequality and solve. PLEASE HELP ME!!

Using coordinate geometry,

The problem provides two pieces of information about Hannah's jogging routine: she started with 3 41 miles and added 1/21 miles every week. We can use this information to create a linear equation that represents the number of miles Hannah jogged as a function of the number of weeks she has been jogging.

To create this equation, we first identify the starting value, which is 3 41 miles. This is also the y-intercept of the line. Next, we determine the slope of the line, which is the rate at which the number of miles increases each week. The slope is equal to the change in y (miles) divided by the change in x (weeks), which in this case is (1/21 - 3/41)/1 = -2/1 = -2. Therefore, the slope of the line is -2.

Putting these two pieces of information together, we get the equation y = -2x + 3 41, where y is the number of miles jogging and x is the number of weeks of jogging. This is a linear equation in slope-intercept form, where the slope is -2 and the y-intercept is 3 41.

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Yes, it is possible to have a c2 strictly convex function on a compact domain that is not also strongly convex.

Let's have a look at the following details of it.

A strictly convex function is a function whose Hessian matrix is positive-definite for all arguments. As a result, if f is differentiable and convex, it is strictly convex if and only if its Hessian matrix is positive-definite for all arguments.

The Definition of Strong Convexity: A function is said to be strongly convex if it meets the following criteria:
Let C be a convex subset of a Hilbert space H, and let f:C→ℝ be a continuously differentiable function. There is a positive constant μ such that, for all x,y∈C: f(y)≥f(x)+⟨∇f(x),y−x⟩+μ/2‖y−x‖2

Thus, it is clear from the above-mentioned definitions that it is possible to have a c2 strictly convex function on a compact domain that is not also strongly convex.

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Giovanna deposited $1600 into two accounts, half in First Oak and half in West United.

Interest earned in First Oak account after 5 years at 6% simple interest:

= 0.06 x $800 x 5

= $240

Interest earned in West United account after 5 years at 5% compounded annually:

= $800 x (1 + 0.05)^5 - $800

= $800 x 1.27628 - $800

= $221.02

Total interest earned in both accounts:

= $240 + $221.02

= $461.02

Therefore, Giovanna will have earned $461.02 in interest from both accounts at the end of 5 years.

The quotient of 3.013 × [tex]10^{8}[/tex] and 6.55 × [tex]10^{5}[/tex] expressed in scientific notation is equal to 0.46 × [tex]10^{3}[/tex].

In Mathematics, a quotient is a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

Generally speaking, any numerical data (number) can be written in scientific notation as shown below:

a × [tex]b^n[/tex]

Where

Next, we would rewrite the given numerical data (number) in scientific notation by dividing by 6.55 × [tex]10^{5}[/tex] as follows:

Scientific notation = 3.013 × [tex]10^{8}[/tex]/(6.55 × [tex]10^{5}[/tex])

Scientific notation = 0.46 × [tex]10^{8-5}[/tex]

Scientific notation = 0.46 × [tex]10^{3}[/tex].

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Answer:

432

Step-by-step explanation:

go 16x27 and that is your answer

Answer:

The area of the figureo will be 432

BECAUSE :-

You have to multiply 16 × 27 = 432

Hope Its Help You !!

a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.

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Total longer distance is [tex]3\frac{2}{21} miles[/tex], that kiki run during the second week of track practice than the first week of track practice.

We have, a runner Kiki and she runs on track for practice. In first week,

Distance runs by Kiki on track practic = [tex]4 \frac{3}{7} miles[/tex]

which is a mixed fraction so, simplify it into simple fraction that is 25/7 miles. In second week,

Distance runs by Kiki on track practice = [tex]6 \frac{2}{3} miles[/tex]

After simplification, it is equals to 20/3 miles. We have to calculate the longer distance that kiki run during the second week of track practice than the first week of track practice. Let the distance run during second week be longer by 'x miles' from distance run during first week. The required distance can be calculated by difference between the distance that kiki run during the second week of track practice and the first week of track practice. So, [tex]x = \frac{20}{3} - \frac{25}{7 }[/tex].

taking least common multiple of (3,7)= 21

=> [tex] x = \frac{20× 7 - 3× 25}{21} [/tex]

[tex] =>x = \frac{ 140 - 75}{21} = \frac{65}{21 }[/tex].

Hence, required distance value is

[tex]3\frac{2}{21} [/tex].

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Real GDP increase in 2019 was $16 trillion, representing a 6.67% increase from 2012. The price level rose by 5% from 2012 to 2019, with a GDP price index of 105 in 2019.

To calculate the percentage increase in production from 2012 to 2019, we need to use the following formula:

Percentage increase in production = ((Real GDP in 2019 - Real GDP in 2012) / Real GDP in 2012) x 100

Substituting the given values, we get:

Percentage increase in production = ((16 trillion - 15 trillion) / 15 trillion) x 100

Percentage increase in production = (1 trillion / 15 trillion) x 100

Percentage increase in production = 6.67%

Therefore, there was a 6.67% increase in production from 2012 to 2019.

To calculate the percentage increase in price level from 2012 to 2019, we can use the following formula:

Percentage increase in price level = ((GDP price index in 2019 - GDP price index in 2012) / GDP price index in 2012) x 100

Substituting the given values, we get:

Percentage increase in price level = ((105 - 100) / 100) x 100

Percentage increase in price level = (5 / 100) x 100

Percentage increase in price level = 5%

Therefore, the price level rose by 5% from 2012 to 2019.

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Answer:

Step-by-step explanation:

One potential drawback of using a histogram is that it can be sensitive to the choice of bin width or bin size. If the bin size is too small, the histogram may appear too noisy or have too many empty bins, which can obscure patterns in the data. If the bin size is too large, important features of the distribution may be lost or smoothed out. Additionally, histograms do not always show the actual values of the data points, but rather a summary of the data. This means that some details about the data may be lost, such as the exact values of outliers or individual data points.

Answer: V≈339.29 in

Step-by-step explanation:

As a result, the circumference of the circular walkway is approximately 367.06 square feet.

A circle is a geometric shape made up of all points that are equally spaced apart from the center. It is a flat, two-dimensional object whose radius or diameter serves as its sole defining characteristic. A circle's circumference is the distance around it, while the area of the circle is the amount of space inside it.

given

We must deduct the area of the smaller circle from the size of the larger circle in order to determine the area inside the circular path. Let's use the abbreviations "r" for the smaller circle's radius and "R" for the larger circle's radius. We are aware that the circumference of the smaller circle, which is 132 feet, is equal to the distance around the circular path.

The wider circle's circumference is 132 feet.

2πR = 132

R = 21

The breadth of the circular path, which is equal to the difference between the radii of the two circles, can now be used to calculate the radius of the smaller circle:

R - r = diameter of the circle

21 - r = diameter of the circle

r = 18

The smaller circle therefore has a radius of 18 feet.

Inside the arc of the path, there is:

R2 - r2 equals (21 - 18) = (44 - 324) = (117) 367.06 square feet.

As a result, the circumference of the circular walkway is approximately 367.06 square feet.

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The empirical rule states that approximately 95% of the population lies within 2 standard deviations of the mean for a normal distribution, but you found that the z-scores that mark off the middle 95% of the standard normal distribution are -1.96 and 1.96. This does not represent a contradiction, and I will explain why is it so ?

The empirical rule, also known as the 68-95-99.7 rule, is a useful guideline to help us understand the proportions of data in a normal distribution. According to this rule, about 68% of the data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. However, it is essential to note that the empirical rule is a simplified approximation.

On the other hand, the z-scores that you calculated, -1.96 and 1.96, are more precise values based on the actual standard normal distribution. These values come from a more accurate calculation using the cumulative distribution function (CDF) of the normal distribution, which gives the exact probability for any given range of z-scores.

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The decision that most clearly reflects a lack of understanding of the concept of sunk costs is "You study eight hours for a final exam even though there is no way now that you can pass the course".

Sunk costs refer to any costs that have already been incurred and cannot be recovered. Sunk costs are irrelevant in decision-making because they are already gone and cannot be recovered. Decision-makers must only consider future costs and benefits when making decisions.

A lack of understanding of sunk costs may result in individuals making decisions based on past costs rather than future costs and benefits. Decision-making that is influenced by sunk costs may result in inefficient resource allocation and lost opportunities.

Individuals must ignore sunk costs and instead focus on future costs and benefits to make effective decisions.

In the given options, "You study eight hours for a final exam even though there is no way now that you can pass the course" is the decision that most clearly reflects a lack of understanding of the concept of sunk costs.

Even though the student has already spent 8 hours studying, the sunk costs are irrelevant because the student cannot pass the course now. The student should focus on future costs and benefits and use the remaining time to study for other courses.

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Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.

In mathematics, an angle is a figure made up of two rays that share a shared endpoint and are referred to as the sides of the angle and the vertex of the angle, respectively. Angles are typically measured in degrees, radians, or other angle measurement units. Angles can be categorized based on how wide they are. An acute angle is one that is less than 90 degrees, an obtuse angle is one that is higher than 90 degrees but less than 180 degrees, and a right angle is one that is 90 degrees. A reflex angle is greater than 180 degrees but less than 360 degrees, and a straight angle is precisely 180 degrees.

given

Since a polygon with that many sides would have sides that are extremely tiny in relation to the radius, if a regular polygon has 360 sides, it is a circle. Since every group of points in a regular polygon has an equal exterior angle and the sum of all exterior angles in a circle is 360 degrees, each exterior angle in a regular polygon would be measured as follows:

360 edges / 360 degrees = one degree.

Each interior angle of a regular polygon with n sides can be determined using the following formula:

Inner angle is equal to (n-2) x 180 / n.

When we enter n = 360 into this algorithm, we obtain:

(360-2) x 180 degrees / 360 = 178 degrees is the interior angle.

Therefore, each internal angle would be 178 degrees in a regular polygon with 360 sides.

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The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).

For option 1: intersection point (1,1)

substitute the values of x & y in the given equation.

1 = 3 (1) - 2

1 = 1

LHS = RHS

For option 2: point (1,1)

substitute the values of x & y in the given equation.

1 = 2 (1) + 3

1 = 5

LHS ≠ RHS

For option 3: point (1,1)

substitute the values of x & y in the given equation.

1 = -2 (1) + 3

1 = 1

LHS = RHS

For option 4: point (1,1)

substitute the values of x & y in the given equation.

1 = - [tex]\frac{1}{2}[/tex] (1) + 3

1 = [tex]\frac{5}{2}[/tex]

LHS ≠ RHS

For option 5: point (1,1)

substitute the values of x & y in the given equation.

1 = - [tex]\frac{1}{3}[/tex] (1) + 3

1 = [tex]\frac{8}{9}[/tex]

LHS ≠ RHS

Therefore, correct option for the given graph is option 1 and option 3.

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Ten chairs are arranged in a circle. The number of subsets of this set of chairs that contain at least three adjacent chairs is 310.

The given that 10 chairs arranged in a circle.

            Now we have to find the number of subsets of this set of chairs that contain at least three adjacent chairs.

           To solve this, we can use the concept of permutations and combinations. The first step is to consider the number of ways in which three chairs can be selected and arranged in a subset that is adjacent to each other.

           This can be done in 10 different ways, as there are 10 chairs in total and we can select any one of them as the starting point.

           The next step is to consider the number of ways in which we can add additional chairs to this subset. For example, we can add a fourth chair to the subset in two different ways: either to the left of the first chair or to the right of the third chair.

            Similarly, we can add a fifth chair to the subset in four different ways, a sixth chair in six different ways, and so on. Using this logic, we can create the following table:

                    Length of subset number of ways to select the subset number of ways to add chairs

           Total number of subsets31 (adjacent)

                                = 10  ---43 (adjacent) 10*2

                                =20---55 (adjacent)10*4

                                =40---67 (adjacent)10*6

                                =60---79 (adjacent)10*8

                               =80---810 (adjacent)10*10

                               =100---

              As we can see from the table, the total number of subsets that contain at least three adjacent chairs is given by:

           Total number of subsets = 10 + 20 + 40 + 60 + 80 + 100

                                                     = 310

       Therefore, the number of subsets of this set of chairs that contain at least three adjacent chairs is 310.

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Step-by-step explanation:

A is not proportional

Use the graph to record the value of y axis when x is 1, 2, 3, 4, 5, 6

And record the values of x when y is 1, 2, 3, 4, 5, 6 till the end

Using the graph Value of y

(1, 0.9) (2,1.5) (3,2.2) (4,2.5) (5, 3) (6,4) (7, 5) (10,6)

Using the graph, find the value of x when y is 1 - 10)

1.2, 2.5, 5,.....

The slope of the graph also shows that it is not proportional

B is proportional

X is 0 and y is 0

When x is 5, y is 10

Ratio x: y = 5:10 = 1:2

When x is 10, y is 20

Ratio x:y is 10: 20 = 1:2 same as above

C is not proportional

When Moyra is 32, daughter is 8

When her daughter is 22, Moyra will also be 4years older, which is 36

32: 8 = 4:1

36: 12 =3:1

This means that the cube will have less surface area than the rectangular prism.

Surface area is a measure of the total exposed area of an object, or the total area of its two-dimensional surface. It is a measurement of the total exposed area of a three-dimensional object and is used to calculate the amount of material needed to cover a given area. Surface area is commonly used in physics, chemistry, engineering, and mathematics.

The prism with the least surface area of the same volume is the cube. This is because a cube has equal length, width, and height, allowing for all of the sides to be equal in size. This means that the area of each side is the same and all six sides of the cube are congruent. This creates the least amount of surface area for a given volume, as compared to any other prism. To illustrate this, take a cube and a rectangular prism with the same volume. The cube will have 6 smaller sides, while the rectangular prism will have 5 larger sides and 1 smaller side. This means that the cube will have less surface area than the rectangular prism.

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The percentage of the student body that is at least 20 years old is 50%.

The ages of students at a university are normally distributed with a mean of 20. To find the percentage of the student body that is at least 20 years old solution to the is as follows: As the Mean of ages of students at a university, μ = 20. Age is normally distributed so it will be divided into two groups  Therefore, the mean age is equal to the median age. As the age is normally distributed, 50% of the population will have an age greater than or equal to 20 years old. Thus, the percentage of the student body that is at least 20 years old is 50%. Hence, the required percentage of the student body that is at least 20 years old is 50%.

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Answer:

Sam made 21 shots, and Wil made 27 shots.

The probability of drawing the first yellow ball on the eighth draw is 1/2772.

The probability of drawing a yellow ball on the eighth draw is the probability of drawing 7 non-yellow balls followed by a yellow ball.

The probability of drawing a non-yellow ball on the first draw is 7/12 since there are 7 non-yellow balls out of a total of 12 balls in the bag. After the first non-yellow ball is drawn, there will be 6 non-yellow balls left out of a total of 11 balls. So the probability of drawing a non-yellow ball on the second draw is 6/11. Continuing in this manner, the probability of drawing 7 non-yellow balls in a row is

(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6)

Now, there are 5 yellow balls left out of a total of 5 + 7 + 3 = 15 balls. So the probability of drawing a yellow ball on the eighth draw is 5/15.

Therefore, the probability of drawing the first yellow ball on the eighth draw is

(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6) × (5/15)

Simplifying this expression, we get

(7 × 6 × 5 × 4 × 3 × 2 × 1 × 5) / (12 × 11 × 10 × 9 × 8 × 7 × 6 × 15)

which simplifies to:

1/2772

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The given question is incomplete, the complete question is:

A bag contains 3 red balls, 4 green balls, and 5 yellow balls. If balls are drawn one at a time without replacement, what is the probability that the first yellow ball is drawn on the eighth draw?

Answer:

226.865 square inches.

Step-by-step explanation:

The equation for the area of a circle is [tex]\pi r^2[/tex]. Let's use 3.14 for pi. The radius can be found by dividing 17/2 = 8.5. 8.5 squared is 72.25. Finally, multiply by pi to get 226.865.

Answer:

let angle GJK be x

GJK=GHK (Base angle of isosceles triangle)

Step-by-step explanation:

x=5x+8

5x-x=8

4x=8

x=8/4

x=2 ans.

Hence,

5x+8

5*2+8

10+8

18.ans

From the given information provided, there were 311 children who swam at the pool that day.

Let's use C to represent the number of children who swam at the pool and A to represent the number of adults who swam at the pool.

From the problem, we know that:

C + A = 402 (Equation 1) (The total number of people who used the pool was 402)

1.50C + 2.00A = 648.50 (Equation 2) (The total receipts from admission were $648.50)

To solve for C and A, we need to eliminate one of the variables. We can do this by multiplying Equation 1 by 1.50, which will give us:

1.50C + 1.50A = 603 (Equation 3)

Now we can subtract Equation 3 from Equation 2 to eliminate C:

2.00A - 1.50A = 648.50 - 603

0.50A = 45.50

A = 91

So there were 91 adults who swam at the pool that day. To find the number of children, we can substitute A = 91 into Equation 1:

C + 91 = 402

C = 311

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ARMY DISBANDED MEANS SOLDIERS WERE RELEASED FROM SERVICE

When George Washington became president in 1789, the army he had

commanded in the American Revolution had disbanded. This means that

the soldiers were released from service and the military units were

dissolved after the end of the war.He pursued two intertwined interests:

military arts and western expansion. At 16 he helped survey Shenandoah

lands for Thomas, Lord Fairfax. Commissioned a lieutenant colonel in 1754,

he fought the first skirmishes of what grew into the French and Indian War.

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The constant angular acceleration of the centrifuge is approximately [tex]-331283[/tex] rad/min² in the negative direction.

To find the constant angular acceleration of the centrifuge, we can use the following kinematic equation:

ω² = ω₀² + 2αθ

Here, ω is the final angular velocity (0 rad/min, since it comes to rest), ω₀ is the initial angular velocity (3450 rev/min), α is the constant angular acceleration we want to find, and θ is the angular displacement (45.8 revolutions).

First, we need to convert the given angular values to radians. We know that 1 revolution equals 2π radians.

Initial angular velocity, ω₀ = 3450 rev/min × 2π rad/rev = 6900π rad/min

Angular displacement, θ = 45.8 rev × 2π rad/rev = 91.6π rad

Now, substitute the values into the kinematic equation:

[tex]0 = (6900π)² + 2α(91.6π)[/tex]

[tex]α = - (6900π)² / (2 × 91.6π)[/tex]

[tex]α ≈ -331283 rad/min²[/tex]

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Answer:

the area ot the triangle is half the area of the rectangle, so the area of the triangle is what sqauare units

Answer: It's  much easier to form a rectangle and multiply the width and the length and then divide it by 2  

Answer:

10

Step-by-step explanation:

7 rounds to 10

9 rounds to 10

19 rounds to 20

so Vicki has 40 birds

9 rounds to 10

12 rounds to 10

29 rounds to 30

so johnny has 50 birds

now subtract 50-40=10

The new perimeter is 127.2 inches if it is multiplied by 19.

What do you mean by the are and perimeter of the square ?

The area of a square is calculated by squaring the length of one of its sides. If the area of a square is multiplied by a factor, the length of the sides will be multiplied by the square root of that factor. One way to express the concept of perimeter for a square is to state that it is the total distance around the outer boundary of the shape, which is equal to the sum of the lengths of all four sides.

Determining the the value of perimeter :

The area of the square is [tex]7.3 \times 7.3 = 53.29[/tex] square inches.

If this area is multiplied by 19, the new area will be 1012.51 square inches.

To find the new side length of the square, we take the square root of the new area:

[tex]\sqrt{1012.51} = 31.8[/tex] (rounded to one decimal place)

Therefore, the new side length of the square is 31.8 inches.

To find the new perimeter, we multiply the new side length by 4:

[tex]31.8 \times 4 = 127.2[/tex]inches

So the new perimeter is 127.2 inches.

To summarize, when the area of the square with side length 7.3 inches is multiplied by 19, the perimeter is multiplied by the square root of 19, which is approximately 4.36. The new perimeter is 127.2 inches.

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