The track below has two straight lengths and two curved ends. What is the area of the field inside the track? Round your answer to the nearest meter.

The graph that represents the linear inequality y < 2x - 3 include the following: A. graph A.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have following the linear inequality:

y = mx + b

y < 2x - 3 (it means the dashed boundary line would be shaded below).

Since the y-intercept is equal to -3, we can reasonably infer and logically deduce that only graph A represents the linear inequality y < 2x - 3 while the y-intercept of graph B is equal to 1.

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[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3[/tex]

Answer:

236 ft^3

Step-by-step explanation:

Base radius = 5 ft

Height = 3 ft

Volume =   πr^2h

              =  π × 5^2 × 3

              =  75π

               =  235.61944901923 feet^3

Nearest Cubic Foot = 236 ft^3

Nearest Cubic Foot:

Hence Answer is:

236 ft^3

Hope this helps!

Hello!

∠AED and ∠BEC are opposite angles

so ∠AED = ∠BEC = 36°.

The patient needs to be given 0.04 mL of solution.

Given data:

Mass of dextrose = 500mg;

Volume of solution = 250mL;

Percentage by mass = 5%;

Density of solution = 1.0 g/mL

We need to calculate how many mL of solution should be given to the patient. We can start the calculation by finding the mass of the solution.

We know that 5% by mass solution contains 5g dextrose in 100g solution.

Therefore, in 250mL (or 250g) solution,

the mass of dextrose = 5/100 × 250 = 12.5g

Now, we have the mass of dextrose in the solution as 12.5g and we need to give 500mg to the patient.

So, the volume of solution required to get 500mg dextrose = (500/1000)/12.5 = 0.04 mL

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The following table shows the number of hours 45 hospital patients slept for one night. Use the table to answer the questions:Hours of Sleep | Patients0-2 | 53-5 | 96-8 | 179-11 | 2212-14 | 10a) How many patients slept between 6 and 11 hours?A total of 22 patients slept between 6 and 11 hours.

To find out, we need to add the number of patients who slept for 6-8 hours (17) and those who slept for 9-11 hours (5). Therefore, 17+5=22.b)

The mode is the value that occurs most frequently in the data set. In this case, the mode is the number of hours that the highest number of patients slept.

From the table, we can see that 9-11 hours is the mode because 22 patients slept for that number of hours, which is more than any other number of hours.c)

The median is the middle value in the data set when the data are arranged in numerical order. In this case, we have 45 patients, so we need to find the middle value between the 22nd and 23rd patients. These patients slept for 9-11 hours, so the median is 9-11 hours.

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Answer:

[tex]\displaystyle \sin\theta=\frac{\sqrt{7}}{4}[/tex]

Step-by-step explanation:

[tex]\displaystyle \cos^2\theta+\sin^2\theta=1\\\\\biggr(\frac{3}{4}\biggr)^2+\sin^2\theta=1\\\\\frac{9}{16}+\sin^2\theta=1\\\\\sin^2\theta=\frac{7}{16}\\\\\sin\theta=\frac{\sqrt{7}}{4}[/tex]

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

Cos ∅ = 3/4

SOHCAHTOA

Sin∅ = opp/ hyp

Cos ∅ = adj/ hyp •°• adj = 3 hyp = 4

Using Pythagorean theorem

hyp² = adj² + opp²

4² = 3² + opp²

•°• opp = √ 7

sin ∅ = √7 /4

This means that approximately 51.57% of the students would have scores between 60 and 75.

The problem is asking for the percentage of students that would have scores between 60 and 75 in a normally distributed test with a mean score of 70 and a standard deviation of 15.

To solve the problem, first we need to standardize the scores by using the formula:

z = (x - μ) / σ where z = the standardized score x = the raw score μ = the mean score σ = the standard deviation Then,

we can find the area between the z-scores corresponding to 60 and 75 using a standard normal distribution table or calculator.

The area represents the percentage of students who scored between 60 and 75.

To find the z-score corresponding to 60:x = 60μ = 70σ = 15z = (60 - 70) / 15 = -0.67

To find the z-score corresponding to 75:x = 75μ = 70σ = 15z = (75 - 70) / 15 = 0.33

Now, we can find the area between -0.67 and 0.33 using a standard normal distribution table or calculator.Using a calculator, we can use the normalcdf function to find the area:normalcdf(-0.67, 0.33) = 0.5157

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The distance from the house that should place the base of the ladder is approximately 5.95 feet.

We can start by modeling the situation as a right triangle. Doing this will allow us to use basic trigonometric functions to determine how far the base of the ladder should be placed from the house. Imagine the house makes a 90 degree angle with the ground. The ladder gets propped against the house, making a 75 degree angle with the ground. We can use the fact that cos(75°) = base distance/length of ladder to figure out the length of the base. Multiplying both sides by length of ladder we get, length of ladder × cos(75°) = base distance. Now, by plugging in the length of the ladder we find that base distance = 5 2381/2500 or roughly 5.95 feet.

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Based on the information provided, if we convert 50° from Celcius to Fahrenheit the temperature is 122° Fahrenheit.

To convert the temperature from Celsius to Fahrenheit we will use the formula suggested. This can be expressed as the temperature in Celsius x 1.8 + 32. Now, let's calculate the new temperature:

t x 1.8 + 32

50 x 1.8 + 32

90 +32

122° Fahrenheit

Therefore, the temperature in Fahrenheit is 122° Fahrenheit, however, this formula can be applied to convert any temperature.

Note: This question is incomplete, here is the missing section.

Convert 50° from Celcius to Fahrenheit

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Answer:
[tex]3x-2+\frac{5}{x}[/tex]

Step-by-step explanation:

To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:

(9x^3 - 6x^2 + 15x) ÷ (3x^2)

To simplify the division, we divide each term of the polynomial by 3x^2:

(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)

To divide monomials with the same base, we subtract the exponents. So:

9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x

(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2

15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x

Putting it all together, we have:

(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x

Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.

The value of length of side AB is,

⇒ AB = 5 units

We have to given that;

The figure is shown a trapezoid.

Hence, By using Pythagoras theorem we get;

⇒ AB² = 4² + (5.25 - 2.25)²

⇒ AB² = 16 + 3²

⇒ AB² = 16 + 9

⇒ AB² = 25

⇒ AB = √25

⇒ AB = 5 units

Therefore, The value of length of AB is,

⇒ AB = 5 units

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Note that the   probability that the third largest   observation in the sample is less than 0.7 is 0.4864.

The probability that the   third largest observation in the sample is less than 0.7 is the probability that the first two   observations are greater than 0.7.

The probability that a single observation is greater than   0.7 is 0.3.

The probability that two observations are greater than   0.7 is  -

P(X1 > 0.7, X2   > 0.7)

= (0.7)²

P(X3 < 0.7)   = 1 - (0.7)³

= 0.4864

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The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.

In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.

In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.

This concept is essential to the development of computer programs that are efficient, reliable, and secure.

In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.

In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.

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The function [4x⁻⁴ - 3x ³ + 6x -10]/ x +1 is described accordingly.

The graph of the function [4x⁻⁴ - 3x³ + 6x - 10]/(x + 1) represents a rational function.

It may exhibit vertical asymptotes at x = -1, where the function approaches infinity or negative infinity.

The graph can also have x-intercepts and may show different behavior based on the values of x.

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Full question

Describe the [4x⁻⁴ - 3x ³ + 6x -10]/ x +1

The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

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a) Brand X median = 13 hours

Brand Y median = 16 hours

b) It is found that Brand Y consists of batteries with better battery life compared to Brand X

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Median represents the middle value of the given data when arranged in a particular order.

a) We need to get the median value of each of the two data sets, each dataset consists of 5 distinct points. The median value is the mid-value of each of the plots as;

The third value counting from either end of the plots

For Brand X, the median value = 13 hours

For Brand Y, the median value = 16 hours

b) Secondly, to compare the median values of the data sets, the median value of the second brand (Brand Y) is bigger than the inner value of the first brand (Brand X)

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Answer:

A sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

Step-by-step explanation:

The diameter of a sunflower pollen grain is [tex]3.0 * 10^{-5}[/tex] meters.

The diameter of a ginger pollen grain is [tex]1.5 * 10^{-4}[/tex] meters.

We can divide the diameter of the sunflower pollen grain by the diameter of the ginger pollen grain to compare the sizes of these grains.

This gives us:

[tex]\frac{3.0 * 10^{-5} }{1.5 * 10^{-4 }}= 0.2[/tex]

This means that a sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

So the answer is A sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

Answer: Your answer is B. A sunflower pollen grain is 0.2 times as large as a ginger pollen grain.

Step-by-Step Explanation: Take them both and divide them (3.0*10^(-5))/(1.5*10^(-4)) Solving the equations first and that makes:

Scientific Notation 2⋅10^−1

Or expanded form 0.2

Hope it helped :D

The difference in earnings between the highest- and lowest-paid rock climbers reflects:

Compensating differentials.

Given,

Earnings differences among the rock climbers in the US .

While most earn less than $10,000 per year, the best generally those who've accomplished the most dangerous climbs-can earn as much as $300,000 per year through sponsorships, public speaking engagements, books, and movies.

Now,

The basis of earning differentiation is that how much risky rock climbing can a person do successfully. If a person is having average rock climbing skills than he will earn $10000 per year approximately and if a person is having extra ordinary rock climbing skills than he will earn $30000 per year approximately .

So,

It totally depends on the skill set of the rock climber .

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Answer:

I'm sorry, but you haven't provided any information about the function F(x). In order to determine the value of x when F(x) equals 7, I need to know the specific form or equation of the function. Could you please provide more details or the equation of F(x)?

Step-by-step explanation:

Step-by-step explanation:

multiple the given number and you can get the answer :)

The equation of the line in slope-intercept form is y = 3x - 6.To write the equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can use the given information.

To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the y-intercept (b). Given that the line passes through the point (3, 3) and has a slope of 3, we can substitute these values into the equation

Given that the line passes through the point (3, 3) and has a slope of 3, we can substitute these values into the equation.

The slope-intercept form equation becomes y = 3x + b.

To find the value of b, we substitute the coordinates (3, 3) into the equation:

3 = 3(3) + b

3 = 9 + b

b = -6

In this equation, the slope (m) is 3, indicating that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3. The y-intercept (b) is -6, indicating that the line crosses the y-axis at the point (0, -6).

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The  mean is 5.907, and the standard deviation is 0.677.

To construct a binomial probability distribution, we need the parameters n and p, where n is the number of trials and p is the probability of success in each trial.

From the provided data, it appears that we have the probability distribution for a binomial random variable X with n = 6 trials. The probabilities are as follows:

P(0) = 0.0156

P(1) = 0.0938

P(2) = 0.2344

P(3) = 0.3125

P(4) = 0.2344

P(5) = 0.0938

P(6) = 0.0156

The sum of these probabilities should be equal to 1.

Now, let's compute the mean (μ) and standard deviation (σ) using the formulas:

μ = np

σ = √(np(1 - p))

So, p = P(success)

= P(1) + P(2) + P(3) + P(4) + P(5) + P(6)

= 0.0938 + 0.2344 + 0.3125 + 0.2344 + 0.0938 + 0.0156

= 0.9845

Now, we can calculate the mean and standard deviation:

μ = np = 6 x 0.9845 ≈ 5.907

σ = √(np(1 - p))

= √(6 x 0.9845 x (1 - 0.9845))

= 0.677

Therefore, the mean is 5.907, and the standard deviation is 0.677.

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An equation of the line in slope-intercept form that is perpendicular to line g and passes through the point (1, −2) is y = 3x - 5.

Here, we have,

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

m represent the slope.

x and y represent the points.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 6)/(0 + 3)

Slope (m) = -1/3.

For the equation of line g, we have:

y - 6 = (x + 3)

y - 6 = -1/3(x + 3)

y = -x/3 + 1 + 6

y = -x/3 + 7

Therefore, the slope, m = -1/3.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1/3 × m₂ = -1

m₂ = 3

At data point (1, -2), an equation of this line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - (-2) = 3(x - 1)

y + 2 = 3x - 3

y = 3x - 5

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Answer:

Step-by-step explanation:

The relative change in average television sizes is 5.94%.

To calculate the absolute change in average television sizes, we subtract the initial average size from the final average size:

Absolute change = Final average size - Initial average size

Absolute change = 42.8 inches - 40.4 inches

Absolute change = 2.4 inches

Therefore, the absolute change in average television sizes from the time of Joseph's deployment to the time he returned is 2.4 inches.

To calculate the relative change in average television sizes, we divide the absolute change by the initial average size and then multiply by 100 to express it as a percentage:

Relative change = (Absolute change / Initial average size) × 100

Relative change = (2.4 inches / 40.4 inches) × 100

Relative change = 0.05940594× 100

Relative change = 5.94%

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The polynomial in standard form is - x⁶ -2x⁴ + 5x - 4 = 0.

The polynomial expression you provided is indeed valid, and we can write it in standard form by rearranging the terms:

f(x) = f(x) - 2x⁴ - x⁶ - 4 + 5x

f(x) - f(x) = -x⁶ - 2x⁴ + 5x - 4

The term "f(x)" appears on both sides of the equation, so we can subtract it from both sides:

0 = - x⁶ -2x⁴ + 5x - 4

Now, we have the polynomial equation in standard form:

- x⁶ -2x⁴ + 5x - 4 = 0

In this form, the polynomial is written with the terms arranged in descending order of the exponents (from highest to lowest), and the constant term is on the right side of the equation.

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The closest amount to $1,225.38 is $1,226.84. Therefore, the correct answer is $1,226.84.

To calculate the monthly payment for a 15-year term mortgage, we need to consider the purchase price, down payment, and the interest rate associated with the FICO score range.

Given information:

Purchase price: $181,700.00

Down payment (20%): $181,700.00 * 0.20 = $36,340.00

FICO score: 760

Loan amount: Purchase price - Down payment = $181,700.00 - $36,340.00 = $145,360.00

Looking at the Monthly Principal & Interest Factor chart, for a 15-year term and a FICO score of 750-769, the APR is 6.0. The corresponding factor for this APR is $8.44.

To calculate the monthly payment, we multiply the loan amount by the factor:

Monthly payment = Loan amount * Factor = $145,360.00 * $8.44 = $1,225.38 (rounded to the nearest cent)

Among the given options, the closest amount to $1,225.38 is $1,226.84. Therefore, the correct answer is:

$1,226.84.

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Answer:

To calculate the future value of an investment compounded annually, we can use the formula:

Future Value = Principal Amount * (1 + Interest Rate)^(Number of Periods)

In this case, the principal amount is $3200, the interest rate is 2.4% (or 0.024), and the investment is compounded annually for 4 years.

Plugging these values into the formula, we get:

Future Value = $3200 * (1 + 0.024)^4

Calculating the exponent first:

(1 + 0.024)^4 = 1.024^4 = 1.09985925696

Multiplying the principal amount by the exponent:

Future Value = $3200 * 1.09985925696

Future Value ≈ $3,519.47

Therefore, the investment will be worth approximately $3,519.47 after 4 years when compounded annually at a rate of 2.4%.

Step-by-step explanation:

The function is solved and the table of values of y = { 4 , 3 , 2 , 1 , 0 }

Given data ,

Let the function be represented as A

Now , the value of A is

y = ( -x / 3 ) + 2

Let the table of values of the input x be represented as table A , where

x = { -6 , -3 , 0 , 3 , 6 }

Let the table of values of the output y be represented as table B, where

when x = -3

y = ( -( -3 ) / 3 ) + 2

y = 1 + 2 = 3

when x = 0

y = ( 0/3 ) + 2

y = 2

when x = 3

y = ( -3/3 ) + 2

y = 1

when x = 6

y = ( -6/3 ) + 2

y = 0

Hence , the table of values of the function is y = { 4 , 3 , 2 , 1 , 0 }

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Answer:

Brenda will be able to afford the $20,000 car after 10 years.

Step-by-step explanation:

To determine whether Brenda will be able to afford a $20,000 car after 10 years, we need to calculate the future value of her investment with an interest rate of 4.5%.

The formula for calculating the future value of an investment is:

FV = PV * (1 + r)^n

Where:

FV = Future Value

PV = Present Value (initial investment)

r = Interest rate

n = Number of periods

In this case, Brenda's initial investment (PV) is $15,000, the interest rate (r) is 4.5% (or 0.045 as a decimal), and the number of periods (n) is 10 years.

Let's calculate the future value of Brenda's investment:

FV = $15,000 * (1 + 0.045)^10

FV = $15,000 * (1.045)^10

FV ≈ $22,292.26

After 10 years, Brenda's investment will grow to approximately $22,292.26.

Since the future value of her investment is greater than the cost of the car ($20,000), Brenda will be able to afford the $20,000 car after 10 years.