Billy Bob is filling his bathtub with water. At one minute, there are 5
gallons, at two minutes there are 8 gallons, and at 3 minutes there are
11 gallons of water in the tub.
If this pattern continues, how many gallons of water will be in the tub
at 7 minutes?

The Z-score associated with the upper 5 percent is 1.645. The credit score that defines the upper 5 percent is approximately 748.05.

To find the credit score that defines the upper 5 percent, we can use the Z-score formula. The Z-score is calculated by subtracting the mean from the given value and dividing the result by the standard deviation.
In this case, we want to find the Z-score that corresponds to the upper 5 percent. The Z-score associated with the upper 5 percent is 1.645 (approximately).
To find the credit score that corresponds to this Z-score, we can use the formula:
Credit Score = (Z-score * Standard Deviation) + Mean
Substituting the values, we get:
Credit Score = (1.645 * 90) + 600
Credit Score = 148.05 + 600
Credit Score = 748.05
Therefore, the credit score that defines the upper 5 percent is approximately 748.05.

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The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

A hypothesis is a put forth explanation for a phenomenon (plural: hypotheses).

A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.

Despite the frequent confusion between the terms "hypothesis" and "theory," a scientific hypothesis differs from a scientific theory.

A working hypothesis is a theory that has been tentatively accepted and is proposed for future study[1], starting with an informed guess or thinking.

Hence, The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

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The amount paid back when the loan is paid in full at the end of that period will be $77,546.3.

Given that:

Principal, P = $35,000

Rate, r = 7.5% or 0.075

Time, n = 11 years

The amount (A) is calculated as,

A = P(1 + r)ⁿ

If the loan is paid in full at the end of that period, then the amount paid back is calculated as,

A = $35,000 x (1 + 0.075)¹¹

A = $35,000 x (1.075)¹¹

A = $35,000 x 2.2156

A = $77,546.3

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Answer:

Step-by-step explanation:

The correct option is B. The statement "The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A." is true. The statement is the definition of the algebraic multiplicity of an eigenvalue of A.

A matrix is diagonalizable if and only if each eigenvalue of the matrix has an algebraic multiplicity that is equal to its geometric multiplicity. To get the characteristic equation of a matrix, the determinant of the matrix A   I is set to zero. The characteristic equation of an nn matrix A is given by AI = 0. The characteristic equation's roots are the matrix's eigenvalues.

The algebraic multiplicity of an eigenvalue is the number of times it appears as the root of the characteristic equation. The geometric multiplicity of an eigenvalue is the number of linearly independent eigenvectors corresponding to that eigenvalue. So, the correct option is B.

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Answer:

the two-digit number is 65.

Step-by-step explanation:

Let's assume that the tens and units digits of the two-digit number are x and y, respectively.

According to the given condition,

10x + y < 6(x + y) - 1 (less than 6 times the sum of its digits by 1)

Simplifying the above equation, we get:

4x - 5y < -1 (dividing both sides by 2)

Also, it is given that the difference between the digits is 1, so we can write:

x - y = 1 (difference between the digits is 1)

Now, we need to solve these two equations to find the values of x and y.

Multiplying the second equation by 4, we get:

4x - 4y = 4

Adding this equation to the first equation, we get:

4x - 5y + 4x - 4y = 3

Simplifying the above equation, we get:

8x - 9y = 3

Now, we can solve these two equations simultaneously to find the values of x and y.

Multiplying the second equation by 8, we get:

8x - 8y = 8

Subtracting this equation from the previous equation, we get:

y = 5

Substituting this value of y in the equation x - y = 1, we get:

x - 5 = 1

x = 6

Therefore, the two-digit number is 65.

Answer:

the answer I got is 14.0

hope it helps

Answer: I believe it is 5,720

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The triangles are the same. Congruent is when all three sides are equal to each other on both triangles

Line segment is a a measurable part of a line that consists of two points, called endpoints.

a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given that measurable part of a line that consists of two points, called endpoints is a line segment.

A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.

Hence, line segment is a a measurable part of a line that consists of two points, called endpoints.

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Answer:

Step-by-step explanation:

Answer:

x = 12.1243557....

Step-by-step explanation:

14² = 7² + x²

Isolate x.

x² = 14² - 7²

x² = 196 - 49 = 147

√x² = √147

x = √147 = 12.1243557....

Answer:

12.1 rounded to the nearest tenth.

Step-by-step explanation:

\(7^{2} +x^{2} = 14^{2}\)       \(7^{2}\) means 7x7 = 49; \(14^{2}\) means 14x14 = 196

49 + \(x^{2}\) = 196       Subtract 49 from both sides of the equation

\(x^{2}\) = 147

\(\sqrt{x^{2} }\) =\(\sqrt{147}\)

x = \(\sqrt{147}\)      This would be the exact answer.

12.1   is your answer rounded to the nearest tenth

The numbers in order from least to greatest will be;

⇒ 0.002, 0.02, 0.05, 0.2

The numbers arrange in order to least to greatest number is called Ascending order.

Given that;

The numbers are,

⇒ 0.02, 0.002, 0.2, 1/20

Now,

Since, The numbers are,

⇒ 0.02, 0.002, 0.2, 1/20

⇒ 0.02, 0.002, 0.2, 0.05

Hence, The numbers in order from least to greatest is written as,

⇒ 0.002, 0.02, 0.05, 0.2

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Answer:

[15, ∞).

Step-by-step explanation:

–3(6 – 2x) ≥ 4x + 12

-18 + 6x ≥ 4x + 12

6x - 4x ≥ 12 + 18

2x ≥ 30

x ≥ 15

This means that the minimum of x is 15, and the most is infinity, which is the same thing as [15, ∞).

Hope this helps!

The function f(x) = 5 - 2x equals its average value at x = 1. To find the point(s) at which the function f(x) = 5 - 2x equals its average value on the interval [0,2], we first need to determine the average value of the function on that interval.

The average value of a function f(x) on the interval [a, b] is given by:

Avg = (1 / (b - a)) * ∫[a, b] f(x) dx

In this case, the interval is [0, 2]. So, the average value of f(x) on this interval is:

Avg = (1 / (2 - 0)) * ∫[0, 2] (5 - 2x) dx

Simplifying:

Avg = (1 / 2) * ∫[0, 2] (5 - 2x) dx

Avg = (1 / 2) * [5x - x^2] evaluated from 0 to 2

Avg = (1 / 2) * [(5 * 2 - 2^2) - (5 * 0 - 0^2)]

Avg = (1 / 2) * [10 - 4 - 0]

Avg = (1 / 2) * 6

Avg = 3

The average value of the function f(x) = 5 - 2x on the interval [0, 2] is 3.

To find the point(s) at which the function equals its average value, we set f(x) equal to the average value and solve for x:

5 - 2x = 3

Subtracting 3 from both sides:

2 - 2x = 0

Adding 2x to both sides:

2 = 2x

Dividing both sides by 2:

1 = x

Therefore, the function f(x) = 5 - 2x equals its average value at x = 1.

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Answer:

90 times

Step-by-step explanation:

I don't rly know how to explain it but it's 90 and I hope this helps you at least know the answer if not then sorry for wasting your time and may God bless you:)

Answer:

\(\huge\boxed{f^{-1}(x) = \frac{7x-5}{3}}\)

Step-by-step explanation:

Given the function:

\(f(x) = \frac{3x+5}{7}\)

Put f(x) = y

\(y = \frac{3x+5}{7}\)

Interchange x and y

\(x = \frac{3y+5}{7}\)

Solve for y

\(x = \frac{3y+5}{7}\)

Multiplying both sides by 7

\(7x = 3y+5\)

Subtracting y to both sides

\(7x-5 = 3y\)

Dividing both sides by 3

\(\frac{7x-5}{3} = y\)

OR

\(y = \frac{7x-5}{3}\)

Put y = \(f^{-1}(x)\)

So,

\(f^{-1}(x) = \frac{7x-5}{3}\)

Hope this helped!

Answer:

10^5

Step-by-step explanation:

An easy way is to count the number of zeroes. 100,000 has 5 zeroes and so it is 10^5, or 10*10*10*10*10.

Answer: 10^5

Step-by-step explanation:

There’s 5 zeroes so the exponent is 5

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

Answer: 440-25h = m

Step-by-step explanation:

She makes 25 dollars per hour (25h=m)

If u subtract the amount that the console costs the equation becomes

440-25=m

Im assuming u are in 7th grade math which is what i was in last year so i hope this helps! :)

Answer:

Approximately \(50\; \rm m \cdot s^{-2}\), assuming that air resistance is negligible and that the rock was released with zero initial velocity.

Step-by-step explanation:

Let \(g\) denote the gravitational acceleration on this planet.

Let \(x\) denote the displacement of this rock during this fall. Let \(t\) denote the duration of this fall. Assume that the rock was released with an initial velocity \(v_{0} = 0\; \rm m \cdot s^{-1}\).

Assume that the air resistance is negligible (such that gravity is the only force on this rock). The acceleration \(a\) of the rock during the fall would be constantly equal to the gravitational acceleration \(g\).  

Since the acceleration of the rock during the fall was constantly \(a = g\), the following SUVAT equation would apply:

\(\displaystyle x = \frac{1}{2}\, a \, t^{2} + v_{0}\, t\).

Rearrange this equation to find an expression for acceleration \(a\):

\(\begin{aligned}a &= \frac{x - v_{0}\, t}{t^{2} / 2}\end{aligned}\).

Convert the height and duration of this fall to standard units:

\(\begin{aligned}h &= 89\; \rm km \times \frac{10^{3}\; \rm m}{1\; \rm km} \\ &= 8.9\times 10^{4}\; \rm m\end{aligned}\).

\(\begin{aligned}t &= 0.99\; \rm min \times \frac{60\; \rm s}{1\; \rm min} \\ &= 59.4\; \rm s\end{aligned}\).

Substitute in the values to find the value of acceleration \(a\):

\(\begin{aligned}a &= \frac{x - v_{0}\, t}{t^{2} / 2} \\ &= \frac{89000\; \rm m}{(59.4\; \rm s)^{2} / 2} && (\text{Note that $v_{0} = 0\; \rm m\cdot s^{-1}$.}) \\ &\approx 50\; \rm m\cdot s^{-2} \end{aligned}\).

By the assumptions above, the acceleration of this rock during this fall would be equal to the gravitational acceleration on this planet. Thus, \(g \approx 50\; \rm m\cdot s^{-2}\) on this planet.

\(\large\underline{\sf{Solution-}}\)

Given:

\( \rm \longmapsto x = a \sin \alpha \cos \beta \)

\( \rm \longmapsto y = b \sin \alpha \sin \beta \)

\( \rm \longmapsto z = c\cos \alpha\)

Therefore:

\( \rm \longmapsto \dfrac{x}{a} = \sin \alpha \cos \beta \)

\( \rm \longmapsto \dfrac{y}{b} = \sin \alpha \sin \beta \)

\( \rm \longmapsto \dfrac{z}{c} = \cos \alpha\)

Now:

\( \rm = \dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } \)

\( \rm = { \sin}^{2} \alpha \cos^{2} \beta + { \sin}^{2} \alpha \sin^{2} \beta + { \cos}^{2} \alpha \)

\( \rm = { \sin}^{2} \alpha (\cos^{2} \beta + \sin^{2} \beta )+ { \cos}^{2} \alpha \)

\( \rm = { \sin}^{2} \alpha \cdot1+ { \cos}^{2} \alpha \)

\( \rm = { \sin}^{2} \alpha + { \cos}^{2} \alpha \)

\( \rm = 1\)

Therefore:

\( \rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } = 1\)

Answer:

A. 3 bags of popcorn

F. $12.25

G. 6 bags of popcorn

Heya, I hope this helped you! If you divide 3.5 by 2, it is $1.75 for each bag of popcorn. I hope this helped! <3

Answer: A. Murderer bought three bags

F. $21.00

G. 6 bags

Step-by-step explanation:

divide 3.50 by 2 gives you 1.75 and 1.75+3.50= 5.25 which is the total spent.

1.75 x 6 is equal to 10.50 and 12.82-2.32= 10.50

Explanation:

The initial expression is:

To know the value of m, we need to solve the equation for m, so adding 7 to both sides of the equation, we get:

Then, we can multiply both sides by 4, so:

Your answer will be -1 2/10, or -1 1/5 if you're looking for a simplified answer. My method is called KCF, or Keep Change Flip. First, you don't have to do anything with the -4/5. Next, you would want to change the division to multiplication. It is possible to just divide across, but changing it to multiplication is way easier and will save time. After that, you would switch -2/3 to -3/2. FLIPPING THE SECOND FRACTION DOES NOT MEAN THE NEGATIVE TURNS INTO A POSITIVE. Your answer would be 12/10, but we aren't done just yet. 10 goes into 12 once, now we have 1 2/10 left over. If you simplify you will get 1 1/5. So there you have it! I answered you question as best as I could and I hope this was helpful.

34.422

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