If y = 4 when x = -6, find y when x = 15.

The range of the function for this situation is the interval [398.25, 400] gallons.

To determine the range of the function f(x) = 400 - 0.35x for the given situation, we need to find the possible values of the amount of water remaining in the pool.

The function f(x) represents the amount of water remaining (in gallons) after x minutes, where x ranges from 0 to 5.

To find the range of the function, we evaluate f(x) for the extreme values of x in the given range (0 to 5).

For x = 0, the initial amount of water remaining:

f(0) = 400 - 0.35(0) = 400 gallons

For x = 5, the amount of water remaining after 5 minutes:

f(5) = 400 - 0.35(5) = 400 - 1.75 = 398.25 gallons

Therefore, the range of the function for this situation is the interval [398.25, 400] gallons.

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Answer:

To understand their poems better

Step-by-step explanation:

First you have a general knowledge on why the author made the poem

Second you now have more info to use in order to understand the poems

Third is the same reason why there are people in history books.

We see BC is in the middle of the lines AB and BD, therefore mABC + mCBD = mABD.

We're given mABD = 75, mABC = 40.

Therefore, mCBD = mABD - mABC = 75 - 40 = 35.

Answer:

∠CBD = 35°

Step-by-step explanation:

We are told in the question that m∠ABD = 75° and m∠ABC = 40°. We are then asked what the value of m∠CBD is.

As we can see from the diagram, ∠ABD is made up of the angles ABC and CBD. Therefore:

∠ABD = ∠ABC + ∠CBD

⇒ 75° = 40° + ∠CBD

⇒ 75° - 40° = 40° + ∠CBD - 40°       [

⇒ 35° = ∠CBD

∴ ∠CBD = 35°

Dyscalculia is a learning disorder that affects a person’s ability to do the math.

A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.

The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.

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To translate the phrase "increased by a number" into an expression using x to represent a number, we can use the addition operation. The expression would be -22 + x.

Here's a step-by-step breakdown Start with the number -22. The phrase "increased by a number" suggests that we need to add something to -2 Since x represents the number we want to add, we can simply write it as + x. Combine -22 and x using the addition operator to get the final expression: -22 + x.

For example, if x = 5, then the expression -22 + x would evaluate to -22 + 5 = -17. Remember, when translating phrases into algebraic expressions, it's important to carefully consider the meaning of the words and choose the appropriate operation. In this case, since we want to add a number to -22, we used the addition operation.

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The lower limit of the 99% confidence interval is approximately 14.8615 minutes.

To calculate the standard error of the mean, we use the formula:

Standard Error of the Mean = Standard Deviation / √(Sample Size)

Given that the standard deviation is 1.25 minutes and the sample size is 500, we can calculate the standard error of the mean as follows:

Standard Error of the Mean = 1.25 / √(500) = 0.0559 (rounded to four decimal places)

Next, to determine the lower limit of the 99% confidence interval, we need to use the formula:

Lower Limit = Mean - (Z * Standard Error of the Mean)

Since we want the lower limit of the 99% confidence interval, we need to find the corresponding Z-value for a 99% confidence level. The Z-value can be obtained from a standard normal distribution table or by using a statistical calculator.

For a 99% confidence level, the Z-value is approximately 2.576.

Substituting the values into the formula, we have:

Lower Limit = 15 - (2.576 * 0.0559) ≈ 14.8615 (rounded to four decimal places)

Therefore, the lower limit of the 99% confidence interval is approximately 14.8615 minutes.

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Answer:

Step-by-step explanation:

Since we are finding the x-intercepts, that implies that this is a parabola that opens either up or down as opposed to right or left. It would benefit us to know the equation of the parabola so we could factor it to find the roots (which are also known as the x-intercepts).

Here's what we know:

h = 1, k = 20, x = 0, and y = 20. Filling in the vertex form of a parabola is already halfway to factored, so we'll use that format as opposed to the standard form, which is

\(y=ax^2+bx+c\). The vertex form is

\(y=a(x-h)^2+k\) and filling in our values from above:

\(16=a(0-1)^2+20\) and

\(16=a(1)+20\) and

-4 = a. So the equation for the parabola is

\(y=-4(x-1)^2+20\). Now set it equal to 0 and factor.

\(-20=-4(x-1)^2\) and divide both sides by -4 to get:

\(5=(x-1)^2\) and take the square root of both sides to get

±\(\sqrt{5}=x-1\) and then add 1 to both sides to get the x-intercepts (or roots or solutions or zeros...they're all the same).

x = 1 ±√5 and you're done!

Answer:

u = vector (-6 , -6)

Step-by-step explanation:

u = vector(a , b)

Left (-) 6 units and down (-) 6 units

The translation vector for the image is (-6,-6).

A translation vector is a type of transformation that moves a figure in the coordinate plane from one location to another. Vectors are given in the form ( x y ) where x is the movement horizontally and y is the movement vertically.

For the given situation,

The image of a point (1, 2) under a translation is (-5, -4) .

The translation vector can be found by calculating the movement horizontally and vertically as

⇒ \((-5-1,-4-2)\)

⇒ \((-6,-6)\)

Hence we can conclude that the translation vector for the image is (-6,-6).

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To find g(x), the translation 3 units up of f(x) = | x |, we need to shift the graph of f(x) upward by 3 units.

The absolute value function f(x) = | x |  has a V-shaped graph with the vertex at the origin (0, 0). To shift it up by 3 units, we need to modify the equation as follows: g(x) = | x | + 3. The expression |x| represents the distance of x from 0, and adding 3 to it shifts the entire graph vertically by 3 units. Therefore, g(x) is given by: g(x) = | x |  + 3. This can be written in the desired form a| x - h | + k as: g(x) = 1 | x - 0 | + 3.

So, g(x) = |x - 0| + 3, is the translation 3 units up of f(x)=|x|. write your answer in the form a|x–h| k, where a, h, and k are integers.

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Data that are accurate, consistent, and available in a timely fashion are considered C) high-quality.

High-quality data is characterized as being reliable, consistent, and timely. High-quality data offers a strong foundation for analysis and decision-making because it is accurate, error-free, and consistent.

It is a valuable asset for organizations because it promotes accurate reporting and analysis, increases operational efficiency, and allows for informed decision-making. Although database management systems like Oracle and Microsoft SQL Server can assist with managing and storing data, the quality of the data is unrelated to the particular technology or program employed.

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Answer:

Step-by-step explanation:

slope=(6-2)/(1-4)=4/-3=-4/3

eq. of line is y-2=-4/3(x-4)

The double asterisk operator (**) is used to raise the radius to the power of 3, which represents r³ in the formula.

To compute the volume of a sphere, the given formula is used. It is: volume of a sphere = (4.0 / 3.0) πr³ where r is the radius of the sphere.

Therefore, to find the volume of the sphere given the sphere_radius and pi, the formula above is used, as shown below: sphere_volume = (4.0 / 3.0) * pi * sphere_radius**3

where sphere_radius is the given radius of the sphere and pi is the constant pi.

The double asterisk operator (**) is used to raise the radius to the power of 3, which represents r³ in the formula.

Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is an irrational number, which means it cannot be expressed as a simple fraction or as a finite decimal. The decimal representation of pi goes on infinitely without repeating.

The value of pi is approximately 3.14159, but it is typically rounded to 3.14 for simplicity in calculations. However, to maintain accuracy, mathematicians and scientists often use more decimal places, such as 3.14159265359, depending on the level of precision required for their calculations.

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Full question:

Given sphere_radius and pi, compute the volume of a sphere and assign to sphere_volume. Volume of sphere = (4.0 / 3.0) π r3

Answer:

1/7  

Step-by-step explanation:

Divide the top and bottom by 4 to get

1 / 7

Answer:

1/7

Step-by-step explanation:

4 and 28 are divisible by 4.

4/4 = 1

28/4 = 7

4/28 = 1/7

Answer: Hope this helps!

Step-by-step explanation:

the negative number is -1

the positive number is 13.5

Answer:

x= -7/4

Step-by-step explanation:

8x= -14

Divide both sides by 8

8x/8 = -14/8

Simplify

x= -7/4

Answer:

x=-7/4 is an improper fraction

Step-by-step explanation:

8x=-14

dividing 8 on both sides

x=-14/8

cancelling by 2

x=-7/4

i hope this will help you :)

The value of the expression:\(x^2 * x^{1*2} * x^1\), x=9 is 6561.

To evaluate the expression \(x^2 * x^{1*2} * x^1\), x=9  we simply substitute 9 for each x in the expression and simplify using the rules of exponents.

To convert the given expression into mathematical notation for x=9, we can write it as:

(9^2) * (9^(2*1)) * (9^1)

where ^ represents the exponentiation operator.

Simplifying the expression further, we get:

81 * 9² * 9

\(x^2 * x^1 * x^2 * x^1*x\), x=9  becomes:

Therefore, the value of the expression: \(x^2 * x^{1*2} * x^1\), x=9 is 6561.

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Complete Question:

Evaluate the expression  \(x^2 * x^{1*2} * x^1\), where x=9.

The mean number of people with the genetic mutation in these groups is 80 as this follows a Binomial Distribution.

It is given that 10% of the population has a genetic mutation. We have a sample of 800 here.

Let X be the random variable that defines the number of people with the mutation in the sample.

Since every person can or can't have the mutation, this is a Binomial distribution.

Here,

n = 800

p = 0.1

According to the formula for a Binomial Distribution,

the mean = np

Therefore, the mean for the above distribution will be

800 X 0.1

= 80.

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Answer:

12x + 50 =210

Step-by-step explanation:

Given the data on the world problem, we know that one of our terms will be 12x because it says "each month" in the problem. If his mom is going to give him 50 dollars, and the Jordans cost 210, then we can write  a simple equation.

x = number of months it will take him

\(12x+50=210\)

Answer: 5.8=x

Step-by-step explanation:

$210=Price

$12=Each Month

$50=From Mom

120-50=70

70/12=5.8 Months

The unit price of the red ribbon is $0.88 per meter.

What is rate ?

A rate is a measure of the speed of something in relation to another quantity or measurement. It is a ratio that expresses how much of one quantity occurs in a given amount of another quantity. In other words, it is a comparison of two different measurements.

To find the unit price of the red ribbon, we need to divide the total cost by the number of units (in this case, meters) in the roll:

Unit price =  cost / Number of units

In this case, the total cost is $7.92 and the number of units is 9 meters. So, we have:

Unit price = $7.92 / 9 meters

Using a calculator or by performing long division, we can simplify this expression to find the unit price:

Unit price = $0.88 per meter

Therefore, the unit price of the red ribbon is $0.88 per meter.

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The correct answer is Option C. A researcher might choose purposive sampling over systematic sampling for several reasons. One key reason is that purposive sampling allows the researcher to study a particular type of participant.

This means that the researcher can select individuals who possess specific characteristics or traits that are relevant to their study.

By handpicking participants, the researcher can ensure that the sample represents the specific population they are interested in studying, which is particularly useful when investigating rare or hard-to-reach populations.

On the other hand, systematic sampling involves selecting participants at regular intervals from a larger population.

This method may not provide the same level of control in selecting participants based on specific characteristics.

While systematic sampling can be more efficient in terms of time and cost, it may not be suitable for certain research objectives that require a targeted approach.

It is important to note that neither method is inherently cheaper or more expensive than the other, and the choice between them depends on the research objectives and the specific population under investigation.

Therefore, option A is incorrect.

Option B is also incorrect because external validity is still important in research regardless of the sampling method chosen.

Option D is also incorrect since researchers using purposive sampling must still specify their population of interest.

Thus, the correct answer is option C.

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Answer: -12ab^3

Step-by-step explanation: (-3ab^3) 4 -12ab^3

On solving the provided question, we can say that - the function value will be \(g(x) = -3 + 12x + 15\) and

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

Here,

\(y =a(x-x1)(x-x2),\) y equals a(x-5)(x+1)

g(x) = -3(x-5)(x+1)

\(g(x) = -3(x-5)(x+1)\)

g(x) = -3 + 12x + 15

y-intercept of g(x) is (0,15)

Therefore , the solution to the given problem of the equation comes out be  y-intercept of g(x) is (0,15).

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Answer:

x<=12

Step-by-step explanation:

3x+(-4)<=2x+8

3x-4<=2x+8

3x-2x-4<=8

x-4<=8

x<=8+4

x<=12

Answer:

12 ≤ x

Step-by-step explanation:

3x-4 ≥ 2x+8

3x-3x-4 ≥ 2x-3x+8

-4-8 ≥ -1x+8-8

-12 ≥ -1x

You divide -1 on both sides and get...

12 ≤ x

Because you have to switch the sign around. I hope this helps!!

The length of the third side of the triangle is approximately 158.3 units (rounded to one decimal place).

To find the length of the third side of the triangle, we can use the Law of Cosines, which states that for a triangle with sides a, b, and c, and angle C opposite side c:

c^2 = a^2 + b^2 - 2abcos(C)

Given the values a = 247, c = 204, and angle B = 52.4 degrees, we can rearrange the equation as:

c^2 - a^2 - b^2 = -2abcos(C)

Substituting the known values, we have:

204^2 - 247^2 - b^2 = -2 * 247 * b * cos(52.4)

Simplifying and solving for b, we find:

b ≈ 158.3

Therefore, the length of the third side of the triangle is approximately 158.3 units, rounded to one decimal place.

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To determine the Taylor's expansion of the function ln(4 + z^2) in the region |z| < 2, we first need to rewrite the function using the hint provided. We can rewrite ln(4 + z^2) as ln(4(1 + (z^2/4))) and use the properties of logarithms:

ln(4 + z^2) = ln(4) + ln(1 + z^2/4).

Now, we can apply the basic Taylor's expansion formula for ln(1 + x) around x = 0:

ln(1 + x) = Σ (-1)^(n+1) * x^n / n, for n = 1 to infinity.

In our case, x = z^2/4. So, the Taylor's expansion for ln(1 + z^2/4) is:

ln(1 + z^2/4) = Σ (-1)^(n+1) * (z^2/4)^n / n, for n = 1 to infinity.

Now, combine this with the constant term ln(4):

ln(4 + z^2) = ln(4) + Σ (-1)^(n+1) * (z^2/4)^n / n, for n = 1 to infinity.

This is the Taylor's expansion of the function ln(4 + z^2) in the region |z| < 2.

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One way to write the steps could be like this:

\(2\text{x}+3\text{y} = 6\\\\2\text{x} = 6-3\text{y}\\\\\text{x} = \frac{6-3\text{y}}{2}\\\\\text{x} = \frac{6}{2}-\frac{3\text{y}}{2}\\\\\text{x} = 3-\frac{3}{2}\text{y}\\\\\)

Other methods may be possible.

The unknown arc length of the appendix cone with slant length of 13cm is approximately 56.5cm, and this measurement is justified by using the formula for arc length and the given information about the cone's slant length and angle x.

To find the unknown arc length of the appendix cone with slant length of 13cm, we can use the formula:

arc length = (angle/360) x 2πr

where angle is in degrees, r is the radius of the base, and 2πr is the circumference of the base.

We know the slant length of this cone is 13cm, and we can use the Pythagorean theorem to find the radius of the base:

\(r = √(slant length^2 - height^2) = √(13^2 - 9^2) = √120 ≈ 10.95cm\)

Now, we can substitute the values into the formula:

arc length = (x/360) x 2π(10.95) = (x/360) x 68.91

To find x, we can use the information from the other cone:

arc length = (x/360) x 2π(9) = (x/360) x 56.55

We are given that the arc length of this cone is 42cm, so we can set up the equation:

(x/360) x 56.55 = 42

Solving for x, we get:

x ≈ 269.2 degrees

Now we can substitute this value into the formula for the arc length of the first cone:

arc length = (x/360) x 2π(18) = (269.2/360) x 113.1 ≈ 84.8cm

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Answer:

125,000

Step-by-step explanation: