1. A pool company is trying out several new drains. Drain A empties a pool at a rate of 2 gal/min. Drain B empties a pool at a rate of 5 gal/min. One pool has 108 gal of water in it. Write an equation for each drain that shows the amount of time it takes to empty the pool. Then solve each equation showing your work.

The curvature of a parabola y = ax^2 at the origin is given by 2a. If the curvature is 8 at the origin, a = 8/2 = 4. Therefore, the equation of a parabola that has a curvature of 8 at the origin is y = 4x^2.

The question involves finding an equation of a parabola that has a given curvature at a specific point, the origin, in this case. This falls into the field of calculus. The curvature, also known as concavity, of a parabola y = ax^2 at the origin is given by 2a. Therefore, if the curvature is 8 at the origin, a = curvature/2 = 8/2 = 4. Hence, the equation of the parabola would be y = 4x^2 .

As an example, if we needed to find the curvature of this parabola at any other point, we can use the second derivative, which in this case is constant and equal to 8, meaning the curvature is the same at every point on the parabola. So our quadratic equation meets the given condition of having a curvature of 8 at the origin.

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Answer:

Option B is correct .i.e., 12 × ( 2 + 3 )

Step-by-step explanation:

we are Given  an Expression = 24 + 36

we have to find an Expresion after factoring out  GCF

Full form of GCF is Greatest Common Factor.

First we find factors of 24 and 36 then their GCF

factors of 24 - 1, 2, 3, 4, 6, 8, 12, 24

factors of 36 - 1, 2, 3, 4, 6, 9, 12, 13, 36

⇒ GCF = 12

W have,

   24 + 36

⇒ 12 × 2 + 12 × 3

⇒ 12 × ( 2 + 3 )

Therefore, Option B is correct .i.e., 12 × ( 2 + 3 )

The temperature at noon was 2.4 degrees Fahrenheit.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

To determine the temperature at noon, we need to first calculate the temperature decrease between midnight and 7:00 a.m. and then add the temperature increase from 7:00 a.m. to noon.

The temperature decreased at a rate of 1.1 degrees Fahrenheit per hour, and it took 7 hours from midnight to 7:00 a.m., so the temperature decreased by a total of 7 hours x 1.1 degrees per hour = 7.7 degrees.

The temperature at 7:00 a.m. would therefore be 5.2 degrees - 7.7 degrees = -2.5 degrees Fahrenheit.

At noon, the temperature increased by a total of 4.9 degrees, so the temperature at noon would be -2.5 degrees + 4.9 degrees = 2.4 degrees Fahrenheit.

Thus, the temperature at noon was 2.4 degrees Fahrenheit.

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7x^3 +9x^2 +4x +7

The total velocity is represented by the sum of the two polynomials:

(2x^3-10x^2+7) + (5x^3+19x^2+4x) = x^3·(2+5) +x^2·(-10+19) +4x +7

... = 7x^3 +9x^2 +4x +7

The answer is

x =‌ −3/17

The probability that a randomly chosen battery will last between 6.8 as well as 9.2 hrs will be "0.68".

According to the question,

The probability that data values lies within standard deviation i.e.,

→ [tex](\mu -6) (\mu +6)[/tex] will be [tex]0.68[/tex]

The probability that data values lies within two standard deviation i.e.,

→ [tex](\mu -26)(\mu +26)[/tex] will be [tex]0.95[/tex]

The probability that data values lies within three standard deviation i.e.,

→ [tex](\mu -36) (\mu +36)[/tex] will be [tex]0.997[/tex]

Throughout the above examples,

→ [tex]\mu-6 = 8-1.2[/tex]

           [tex]= 6.8[/tex]

→ [tex]\mu +6 = 8+ 1.2[/tex]

            [tex]= 9.2[/tex]

Thus the above answer is correct.

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The probability that a randomly chosen battery will last between 6.8 and 9.2 hours, given a normal distribution with a mean of 8 hours and a standard deviation of 1.2 hours, is approximately 68.2% according to the empirical rule.

Calculating the Probability Using the Standard Deviation Rule

To calculate the probability of a battery lasting within this range, we find the z-scores for both limits and look up the corresponding areas under the normal distribution curve.

The standard deviation rule (or the 68-95-99.7 rule) tells us that for a normally distributed variable with mean (μ) and standard deviation (σ), approximately:

68% of the data falls within 1 standard deviation of the mean (μ ± σ).

95% of the data falls within 2 standard deviations of the mean (μ ± 2σ).

99.7% of the data falls within 3 standard deviations of the mean (μ ± 3σ).

Z-scores:

For 6.8 hours: (6.8 - μ) / σ =α- 1 hours)

For 6.8 hours: (6.8 - 8) / 1.2 = -1

For 9.2 hours: (9.2 - 8) / 1.2 = 1

The z-score corresponds to the number of standard deviations a value is from the mean. A z-score of -1 or 1 for a normal distribution typically encapsulates around 68.2% of the data (as part of the empirical rule).

Thus, we can say that the probability of a battery lasting between 6.8 and 9.2 hours is approximately 68.2%.

The correct answer is (-138).

Sure, let's break down the calculation step by step:

1. Follow the Order of Operations (PEMDAS/BODMAS):

  Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)

2. Calculate Exponents:

[tex]\(14^2 = 14 \times 14 = 196\)[/tex]

3. Substitute the Exponent Result Back into the Equation:

  (58 - 196 = -138)

So, [tex]\(58 - (14)^2 = -138\).[/tex]

The expression you provided is [tex]\(58 - (14)^2\).[/tex] According to the order of operations (PEMDAS/BODMAS), you first need to perform the operation inside the parentheses, which is squaring 14.

[tex]\[14^2 = 14 \times 14 = 196\][/tex]

After finding that \(14^2 = 196\), you substitute this value back into the original expression:

[58 - 196]

Finally, subtract 196 from 58:

[58 - 196 = -138]

Therefore, the correct answer is (-138).

Complete question

Evaluate. 58−(14)2=58-142= ________

Answer:

take 2 peices of bread

apply jelly

apply penut butter

Put the two peices of bread together

Step-by-step explanation:

edmentem

The sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree is approximately 0.7059.

To find the sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree, we can use the properties of similar triangles. Let's label the height of the tree as 'a' and the length of the shadow as 'b'. We have a right triangle with the height as the opposite side and the shadow as the adjacent side. The sine of the angle can be found using the formula sine(angle) = opposite/hypotenuse, which in this case is a/b. So, the sine of the angle is a/b = 60/85 = 0.7059 (rounded to four decimal places).

[tex]\boxed{{\text{Option b}}}[/tex] is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.

[tex]\boxed{{\text{Option c}}}[/tex] for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers.

Further Explanation:

For sample sizes greater than [tex]40[/tex].

a) the results of hypothesis tests and confidence intervals using the t distribution are highly sensitive to non-normality of the population from which samples are taken is not correct as the sample size is large the data is normally distributed.

b) the use of the t distribution assumes that the population from which the sample is drawn is normally distributed is correct as the condition to apply t-distribution is that the data is normally distributed.

c) for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers is correct as the sample size is small the data set is less normally distributed.

d) since the t distribution procedure is robust, it can be used even for small sample with strong skewness and extreme outliers is not correct as it is the contradiction of option (c).

[tex]\boxed{{\text{Option b}}}[/tex] is correct as the the use of the t distribution assumes that the population from which the sample is drawn is normally distributed.

[tex]\boxed{{\text{Option c}}}[/tex] for small sample sizes, the t distribution should not be used for data that is highly skewed and/or contains extreme outliers.

Learn more:

1. Learn more about normal distribution https://brainly.com/question/12698949

2. Learn more about standard normal distribution https://brainly.com/question/13006989

Answer details:

Grade: College

Subject: Statistics

Chapter: Normal distribution

Keywords: Z-score, Z-value, standard normal distribution, standard deviation, criminologist, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion.

Final answer:

Euclidean geometry and spherical geometry have distinct characteristics. The Parallel Postulate, triangle properties, geodesics, and applications differ between the two. Euclidean geometry relies on parallel lines, triangles with interior angles summing to 180 degrees, and straight geodesics, while spherical geometry lacks parallel lines, features triangles with angles >180 degrees, and utilizes great circles as geodesics. Spherical geometry finds applications in astronomy, navigation, Earth sciences, and cartography.

Explanation:

Euclidean Geometry vs Spherical Geometry

Euclidean geometry and spherical geometry are two different branches of geometry that have distinct characteristics and applications. Let's compare and contrast them:

1. Role of the Parallel Postulate

In Euclidean geometry: The Parallel Postulate states that given a line and a point not on that line, there is exactly one line that passes through the point and is parallel to the given line.

In spherical geometry: The Parallel Postulate is not true. In fact, there are no parallel lines in spherical geometry. On a sphere, any two lines will eventually intersect.

2. Triangles in Euclidean Geometry vs Spherical Geometry

In Euclidean geometry: Triangles have interior angles that sum up to 180 degrees. The angles of a triangle are classified as acute, obtuse, or right.

In spherical geometry: Triangles have interior angles that add up to more than 180 degrees. In fact, the sum can be greater than 540 degrees. Spherical triangles on a sphere are classified as acute-angled, right-angled, or obtuse-angled based on their angles.

3. Geodesics

In Euclidean geometry: Geodesics are straight lines and shortest paths between two points.

In spherical geometry: Geodesics are great circles or the arcs of circles on the surface of the sphere. They represent the shortest path between two points on a sphere.

4. Applications of Spherical Geometry

Spherical geometry has practical applications in various fields, including:

Astronomy: Spherical coordinates are used to locate celestial objects.

Navigation: Spherical trigonometry helps navigate across the Earth's curved surface.

Earth sciences: Spherical harmonics are used to represent the Earth's gravitational field.

Cartography: Representing the Earth's surface on a map or globe.

Answer: 265 calories

Step-by-step explanation:

The discretionary calorie allowance is the balance of a person can take after achieving the number of calories need to get essential nutrients.

Given : Every day Energy allowance for Ray =  2,000 calories

Energy level required to get essential nutrients =1,735 calories

Then Ray's discretionary calorie allowance =

Energy allowance - Calories required to get essential nutrients

=2000-1735=265 calories

Hence, Ray's discretionary calorie allowance will be 265 calories.

Final answer:

To maximize the area with 160 feet of fencing and one side provided by a barn, the fencing should create a rectangle with equal width for the two sides perpendicular to the barn. By expressing length in terms of width and using calculus to find the maximum area, we find a width of 40 feet and a length of 80 feet maximizes the area.

Explanation:

The farmer is using the barn wall as one side of the rectangular area he wants to fence. The remaining three sides require 160 feet of fencing. To maximize the area of the rectangle with a given perimeter, the shape should be a square; however, since one side is already provided by the barn, the best we can achieve is to have the two sides perpendicular to the barn be equal in length.

Let's use width w to denote the length of the two sides that are perpendicular to the barn and length l to denote the side parallel to the barn but not including the barn's wall itself. The total amount of fencing the farmer has is 160 feet, which we can express using the equation:

2w + l = 160

Since we're optimizing for area A, and A = w x l, we want to find the values of w and l that give us the maximum A. We can express l in terms of w using the perimeter equation:

l = 160 - 2w

Substituting this into the area equation gives us:

A = w x (160 - 2w) = 160w - 2w²

To find the maximum area, we take the derivative of A with respect to w and set it to zero to find critical points.

dA/dw = 160 - 4w = 0

Solving for w gives us w = 40 feet. Therefore, the dimensions that give the maximum area when one side of a rectangle is fixed are a width of 40 feet and a length of 80 feet.