A 20-gallon bathtub is to be filled with water that is exactly 100°F. The hot water supply is 175°F and the cold water supply is 20°F. When mixed, the temperature will be a weighted average based on the amount of each water source in the mix. How much of each should be used to fill the tub as specified?

The rule for g(x) = f(x-1)-3 is g(x) = (x-1)⁶-3(x-1)³ - 1

A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable. Based on the information given, we can see that the variables that are illustrated in the question are f and g.

In order to write the rule for g(x) = f(x-1)-3 when f(x) = x⁶ - 3x³ + 2, replace x with x-1 in f(x) and subtract 3. That is:

g(x) =  f(x - 1) - 3

g(x) = (x-1)⁶ - 3(x - 1)³ + 2 - 3

g(x) = (x-1)⁶ - 3(x - 1)³- 1

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In a given study that the null hypothesis asserts the expected value of a phenomenon is 100 resulting in a 95% confidence interval reported as [98.76, 105.24], then we fail to reject the null hypothesis.

Therefore the answer is d) Fail to reject the null hypothesis.

A 95% confidence interval is a range of values that there is a 95% chance that the true value of a population parameter falls within. In this case, the 95% confidence interval is [98.76, 105.24], which includes the expected value of 100 that is stated in the null hypothesis.

Therefore, we fail to reject the null hypothesis because the data does not provide sufficient evidence to suggest that the true value of the population parameter is different from what is stated in the null hypothesis.

It's worth to mention that, Failing to reject the null hypothesis doesn't mean accepting it, it means that we don't have enough evidence to say that the parameter is different from the null hypothesis, it could be due the sample size, or other factors.

--The question is incomplete, complete question is as follows--

"Assume for a given study that the null hypothesis asserts the expected value of a phenomenon is 100. A research study results in a 95% confidence interval reported as [98.76, 105.24]. What decision would you make based on this confidence interval?

a) A decision cannot be made on a confidence interval; a hypothesis test is required.

b) Retain the null hypothesis.

c) Reject the null hypothesis.

d) Fail to reject the null hypothesis."

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The Geometric Mean (GM) is the average value or mean that, in mathematics, represents the centre tendency of a group of numbers by calculating the product of their values.

The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.

The geometric mean can be calculated in two steps: To obtain their product, multiply all values collectively. Calculate the product's nth root (n is the number of values).

The geometric mean of 14 and 20 must be determined. Let's see the numbers:

a = 14 and b = 20

For two numbers, the geometric mean is calculated as follows:

[tex]$M=\sqrt{a b}$[/tex]

Filling in the values as shown in the formula above:

[tex]$M=\sqrt{14 \times 20}$$M=\sqrt{7 \times 2 \times 5 \times 4}$$M=16.73$[/tex]

Therefore, the answer is 16.73.

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The required geometric mean of 14 and 20 is 16.73.

The Geometric Mean (GM) in mathematics is the average value or mean that represents the centre tendency of the group of numbers by calculating the product of their values. Basically, n is the entire amount of data values, and we multiply the numbers collectively before taking their nth root.

The geometric mean can be calculated in two steps: To obtain their product, multiply all values collectively. Calculate the product's nth root (n is the number of values).

The geometric mean of 14 and 20 must be determined. Let's see the numbers:

a = 14 and b = 20

For two numbers, the geometric mean is calculated as follows:

G.M = [tex]\sqrt{ab}[/tex]

Filling in the values as shown in the formula above:

G.M = [tex]\sqrt{14(20)}[/tex]

G.M = [tex]\sqrt{280}[/tex]

Therefore, the answer is 16.73.

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P(even) is  50%

It is simple to calculate the likelihood of one die roll.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

First, keep in mind that a prime number is an integer that has exactly two factors: 1 and the number itself (which is why 1 does not qualify: it has only one factor). The appropriate numbers from 6 onward are 2,3,5. Your response, given that there are six sides, is: P(prime) = 3/6 = 1/2 = 50%

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The Distance that Ellie ran each evening is 16.5 miles for a entirety week.

We can use the following equation to find how many miles, x, Ellie ran each afternoon:

x + 2.5(3) = 24

Here, x represents the number of miles Ellie ran each afternoon, 2.5 represents the number of miles she ran each morning, and 3 represents the number of days she trained. The total number of miles she ran, 24, is on the right side of the equation.

To solve for x, we can start by simplifying the left side of the equation:

x + 7.5 = 24

Then, we can subtract 7.5 from both sides:

x = 16.5

So, Ellie ran 16.5 miles each afternoon.

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The Osborne 1 was the first laptop ever released, and it weighed 11 kg in 1981. Since then, the average rate of weight decrease has been 4.7% per year. This means that in 2019, a laptop would have weighed around 2.3 kg.

1981: 11 kg

1982: 10.5 kg (11 kg - 0.55 kg = 10.5 kg)

1983: 10.02 kg (10.5 kg - 0.48 kg = 10.02 kg)

1984: 9.55 kg (10.02 kg - 0.47 kg = 9.55 kg)

2019: 2.3 kg (3.44 kg - 1.14 kg = 2.3 kg)

The Osborne 1 was the first laptop ever released in 1981, and it weighed 11 kg. Since then, the average rate of weight decrease has been 4.7% per year. This means that the mass of a laptop decreases by 0.47 kg every year on average. So, in 1982 it would have weighed 10.5 kg, in 1983 it would have weighed 10.02 kg, and so on. By 2019, the weight of a laptop would have decreased to 2.3 kg as a result of this 4.7% average rate of weight decrease.

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[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=1\\ y=27 \end{cases}\implies 27=ab^1\implies 27=ab \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} x=2\\ y=243 \end{cases}\implies 243=ab^2\implies 243=abb\implies \cfrac{243}{ab}=b \\\\\\ \stackrel{\textit{substituting from the 1st equation}}{\cfrac{243}{27}=b\implies \boxed{9=b}} \\\\\\ 27=ab\implies \cfrac{27}{b}=a\implies \cfrac{27}{9}=a\implies \boxed{3=a}~\hfill {\Large \begin{array}{llll} y=3(9)^x \end{array}}[/tex]

The percentage statement is 9.5 is 19% of 50

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

9.5 is what % of 50

Complete the blank with x

So, we have the following representation

9.5 = x% of 50

So, we have

9.5 = x% * 50

Divide both sides by 50

0.19 = x%

Multiply both sides by 100

So, we have

x = 19

Hence, the solution is 19

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Answer:

The intersection of the two intervals = 4, 5, 6,.......∞ = (4, ∞)

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-3, ∞)

Step-by-step explanation:

The given intervals are;

First interval  = (-3, ∞)

Second interval  = (4, ∞)

Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,∞

The second interval includes 4, 5,.....,∞

Which gives the intersection as 4, 5, 6,.......∞

The union is the interval that combines the two sets of intervals which is given as follows;

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,∞

[tex]( x - 4 ) + ( 2x - 7 )[/tex]

Combine Like Terms:

[tex](x+2x)+(-4+-7)[/tex]

[tex](3x)+(-11)[/tex]

[tex]\fbox{3x - 11}[/tex]

Answer:3x-11

Step-by-step explanation:

(x-4)+( 2x-7)

x-4+2x-7

3x-11

Gary, Mary, and Rory have 96 candies altogether.

Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".

After Gary gives Mary half of all his candies, he would have x/2 candies.

Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.

And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.

Now, we know that Gary would have 12 more candies than he had originally, which means:

x/2 + x/8 = x/2 + x/4 - 12

We can combine like terms and simplify the equation:

x/2 + x/8 = x/4 + x/4 - 12

x/8 = 12

x = 8 * 12

x = 96

Thus, Gary, Mary, and Rory have 96 candies altogether.

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Answer: 5.6

Step-by-step explanation:

the opposite of an negative number...

So your answer would be....

        =5.6

Answer:

[tex]5.6[/tex] or [tex]\dfrac{1}{-5.6}[/tex]

Step-by-step explanation:

The additive inverse of [tex]-5.6[/tex] is [tex]-1 \cdot -5.6 = \boxed{5.6}[/tex]

or...

If you mean the multiplicative inverse of  [tex]-5.6[/tex], then the answer would be [tex]\dfrac{1}{-5.6}[/tex]

The coefficient of XY in 7xy is 7

Any integer or symbol that multiplies the variable of a single term or the terms of a polynomial to represent a constant value is known as a coefficient in mathematics. In some phrases, a letter might be substituted for the usual number. For example, x is the variable and a and b are the coefficients in the formula: ax2 + bx + c.

What is a coefficient?

A coefficient is a quantity or number that is coupled with a variable. Frequently, an integer is multiplied by the variable and written next to it. The variables that don't have a corresponding number are presumed to have a coefficient of 1.

Seven is the coefficient of XY in 7xy.

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Using combination, 5184 nine-digit numbers can be made using each of the digits 1 through 9 exactly once with the digits alternating between odd and even.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to arrange the components of set A, as you can see.

If the first letter is even, there are 4 first digit possibilities (not 5 because it can't start with 0), 4 third digit possibilities, 3 fifth digit possibilities, etc., making the total 4!

If an odd number is the first letter, there will be 5!*4! different ones.

Add the two together now.

4*4!*4! + 5!*4!=5184

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The slope intercept form of the equation is

y = -1/4x -11/4

One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.

Any location that is not on the line will not fulfill the coordinates.

This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.

The line passes through (1,-3)

slope = -1/4

The equation of the line

y = mx + c

here m is the slope and c is the intercept.

putting the point and slope in the equation

-3 = -1/4 *1 + c

⇒ c = -11/4

So the slope intercept form of the equation is

y = -1/4x -11/4

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Answer:

The inverse property definition states when added together with its additive inverse, the sum of the two numbers will be zero. When a number is multiplied by its multiplicative inverse, the product will be one

Step-by-step explanation:

The final value of a_5 is 27a.
The equation a_n=a_{n-1}+5a is a recursive formula that gives the value of a_n in terms of the value of a_{n-1}. To find the value of a_5, we need to apply this formula repeatedly, starting with the given initial value of a_1=7a.

Using the recursive formula:

a_2 = a_1 + 5a = 7a + 5a = 12a

a_3 = a_2 + 5a = 12a + 5a = 17a

a_4 = a_3 + 5a = 17a + 5a = 22a

a_5 = a_4 + 5a = 22a + 5a = 27a

so a_5 = 27a

This is the final result and no need to calculate more.

Thus the final value of a_5 is 27a.

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Yes, A triangle has sides of lengths 10, 24, and 26 is a right triangle.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.

The formula states that in a right triangle:

The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

(Hypotenuse)² = (Base)² + (Altitude)²

c²=a²+b²

The three numbers which satisfy the above formula are the Pythagorean triplets

Properties of right angle:

consider c=26 a=10, b=24 substitute in above formula:

26²=10²+24²

⇒676=100+576

⇒676=676

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Answer: get yio colors straightv

Step-by-step explanation:

The option that is not true about cluster sampling is option  A: Cluster sampling has the advantage of reducing sampling variability.

Cluster sampling often leads to larger sampling variability than other types of sampling methods, such as simple random sampling or stratified sampling, because clusters may not be a representative sample of the population and the individuals within a cluster may be more similar to each other than to individuals in other clusters.

Therefore, This increases the chance that the sample will not be representative of the population, which can result in a higher level of sampling error.

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Answer:

25x^6y^2

Step-by-step explanation:

Since it is a square all sides are the same. So you multiply 5x^3y and 5x^3y together to get the area. That would get you 25x^6y^2.

Answer:    It is not possible for me to determine which line LR is not a transversal to without more context. A transversal is a line that intersects two or more other lines at different points. In order to determine which line LR is not a transversal to, I would need to know the other lines that are involved and the points at which they intersect.

Step-by-step explanation:

The total cost is £2033.

The field is in the shape of a semicircle, so the radius of the field is half the diameter or 50 m / 2 = 25 m.

The circumference of a circle is given by 2 * pi * r, where r is the radius of the circle.

So the circumference of the semicircle is 2 * pi * 25 = 50 * pi m.

The cost of the fence is £29.86 per meter. So the cost of the fence is 50 * pi * £29.86 = £1493.

Jim takes three days to build the fence and charges £180 per day.

So the cost for the labour is 3 * £180 = £540.

Adding the cost of the labour to the cost of the fence: £1493 + £540 = £2033

So the total cost is £2033.

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Answer:

d

Step-by-step explanation:

The sine , cosine and tangent of an acute angle can be find by using:

Acute Angle:

Acute angles are defined as angles less than 90 degrees, i.e. angles between 0° and 90°. Examples include 60°, 30°, 45°. A triangle with all interior angles less than 90° is called an acute triangle. For example, an equilateral triangle is an acute triangle because its interior angles are 60°.

Sine of an Acute Angle :

The sine of an angle in a right triangle is the ratio of the opposite side of the angle to the hypotenuse. The sine function is the important periodic function in trigonometry, with period 2π. To understand the derivation of sin x, consider the unit circle centered at the origin of the coordinate plane. On the boundary (perimeter) of this circle the variable point P moves. Note that P is in the first quadrant and OP makes an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis.

Cosine:

Cosine or cos x is the trigonometric periodic function. Imagine a unit circle centered at the origin of the coordinate plane. The variable point P moves on the circumference of this circle. From the figure, we can see that P is in the first quadrant and OP forms an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis. A triangle is therefore formed by connecting the points O, P, and Q as shown. where OQ is the base and PQ is the height of the triangle.

Tangent:

The tangent function is one of the six most important trigonometric functions, commonly written as tan x. It is the ratio of the opposite side to the adjacent side of the angle considered in a right triangle. There are various trigonometric identities and formulas related to the tangent function that can be derived using various formulas. The period expression for the tangent function f(x) = a tan (bx) is given by Period = π/|b|. The tangent function tan x is periodic, with period π/1 = π (because b = 1 for tan x).

So the formula for tan x is:

tan x = sin x/cos x

tan x = opposite side/adjacent side

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Answer:i need to know what youre trying to find first

Step-by-step explanation:

For given right triangle, the length of hypotenuse x = 4/√3

Here we have been given a 30° - 60°- 90° right triangle.

A side opposie to angle 60 degrees measures 2 units.

And x is the hypotenuse of right tirnagle.

To find the value of x, consider sine of angle 60 degrees.

sin(60°) = (opposite side of angle 60°) / hypotenuse

From tirgonometric table, sin(60°) = √3 / 2

So, above equation becomes,

√3/ 2 = 2/x

x = 2 × (2/√3)

x = 4/√3

We can see that the value of x is in in simplest radical form with a rational denominator.

Therefore, x = 4/√3

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Answer:

Step-by-step explanation:

we konw the speed of burn is 1.25 inchs per hour. so, the left candle is

15-1.25t. the answer is L=15-1.25t

Answer:

A. 6x - 4

Step-by-step explanation:

[tex]\sf 8-3(4-2x)[/tex]

Distribute:-

[tex]\sf 8+(-3)(4)+(-3)(-2x)[/tex]

[tex]\sf 8+-12+6x[/tex]

Combine Like Terms:-

[tex]\sf (6x)+(8+-12)[/tex]

[tex]\sf 6x+-4[/tex]

** + * - = -**

[tex]\sf 6x-4[/tex]

Therefore, option A. 6x - 4 is your answer!

_____________________

Hope this helps!

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