3) You have a giant, giant hot tub. The hot tub just so happens to be a perfect cylinder. You cannot fill it
all the way to the top, or the water would splash out when you get in. The hot tub is 12 feet wide and 4
feet tall. The instructions say to leave 6 inches at the top of the hot tub. How many cubic feet of water
will you need?

Answer:

100 + 50m = 250

50m = 250 - 100

50m/50 = 150/50

m = 3

Alyson will have to save for 3 months to have a total of $250.

Answer:

Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy) log b ( x ) - log b ( y ) = log b ( x y ) . log3(4010) log 3 ( 40 10 ). Step 2.

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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Answer:

Step 2

Step-by-step explanation:

Distributive Property: \(a(b+c)=ab+ac\)

Isaac's Steps are outlined below:

\(\text{Step 1:} (4.2)(-5.4) = (-5.4)(4.2) \\\\\text{Step 2:} = (-5.4)(4) + (-5.4)(0.2) \\\\\text{Step 3:} = (-21.6) + (-1.08) \\\\\text{Step 4:} = -22.68\)

We observe that in Step 2:

\((-5.4)(4.2)=(-5.4)(4+0.2)=(-5.4)(4) + (-5.4)(0.2)\)

Therefore, Isaac applied the distributive property in Step 2.

Answer:

step 2

Step-by-step explanation:

I took the test

Answer:

i think that it is 30 i'm not so sure

Step-by-step explanation:

The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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Answer:

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Step-by-step explanation:

A. Yes. She solved the problem correctly.

B. No. She multiplied the dividend by the divisor instead of finding the reciprocal.

C. No. She multiplied the denominators instead of finding a common denominator.

D. No. She multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.

Her workings

7 ÷ 2/ 5

=1/ 7 × 2/ 5

= 2/35

Dividend=7

Divisor=2/5

The correct working

7 ÷ 2/ 5

=7 × 5/2

=35/2

Answer:

D

Step-by-step explanation:

I got an 100% on the quiz I took with this question :)

Hope I could help good luck on passing!!

Answer:

It's 64 !!

Step-by-step explanation:

Answer:

If you multiply 6 by an even number, it will end in the same digit. For example, 6 x 4 = 24, so 4 and the 4 in 24 are the same. The number in the tens place will be half the number in the ones place, so the 2 in 24 is half of 4

Answer:

2x-6=0

2x=6

x=6/2

x=3

..

The Taylor series formula in summation notation f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n } where f^n(a) denotes the nth derivative of f(t) evaluated at t = a.

Since the functions f(t) and g(t) have not been given in the question, I cannot provide a specific answer to this question. However, I can provide a general approach to finding the power series expansion of a function about a point.

To find the power series expansion of a function f(t) about a point t = a, we can use the Taylor series formula:

f(t) = f(a) + f'(a)(t-a) + (1/2!)f''(a)(t-a)^2 + (1/3!)f'''(a)(t-a)^3 + ...

where f'(a), f''(a), f'''(a), ... are the first, second, third, and higher-order derivatives of f(t) evaluated at t = a.

To find the first four nonzero terms of the power series expansion, we can calculate the values of f(a), f'(a), f''(a), and f'''(a) at t = a, substitute them into the Taylor series formula, and simplify the resulting expression. The first four nonzero terms will be the constant term, the linear term, the quadratic term, and the cubic term.

To find the general term of the power series expansion, we can write the Taylor series formula in summation notation:

f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n }

where f^n(a) denotes the nth derivative of f(t) evaluated at t = a. The general term of the power series expansion is given by the expression in the curly braces. We can use this expression to find any term in the series by plugging in the appropriate values of n and f^n(a).

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The x-intercept of the graph is at (-2, 0)

A line is defined as the shortest distance between two points. The equation of a line in slope-intercept form is expressed as;

y = mx + b

where

m is the slope

b is the y-intercept

The x - intercept of a  line is the point where the y-coordinates is 0

Given the coordinate points (0, 1) and (2,2)

Find the slope

Slope = 2-1/2-0
Slope = 1/2

The y-intercept is 1 and the required equation will be y = 1/2x + 1

If the value of y is 0, then;

0 = 1/2x + 1

1/2x = -1

x = -2

Hence the x-intercept of the graph is at (-2, 0)

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Complete question

What is the x-intercept of the graph?

graph of a linear function going through points 0 comma 1 and 2 comma 2

a

(−2, 0)

b

(0, −2)

c

(0, 1)

d

(1, 0)

Step-by-step explanation:

I really don't know sorry

Answer: 20

Step-by-step explanation: the equation would be 15 / 3/4, or 15/1 / 3/4 (the / meaning divide). You would divide it by multiplying the reciprocal of 3/4 (4/3) and 15(/1) , which you would get 20.

Answer:

q = 40 degrees

r = 60 degrees

p = 100 degrees

Step-by-step explanation:

before we start we need to know that angles on a straight line equal 180 and angles in a triangle add up to 180.

by knowing this we can workout

q= 180 - 140 = 40 therefor q = 40 degrees

r= 180-120=60 therefor r = 60 degrees

p = 180 - q - r

180 - 40 - 60 = 100 therefor p = 100 degrees

A. In the alternate universe, the p subshell would have 5 orbitals.

B. In the alternate universe, the d subshell would have 10 orbitals.

In the alternate universe where the possible values of mℓ range from -l-1 to l+1, the number of orbitals in each subshell can be determined.

A. For the p subshell, the value of l is 1. Therefore, the range of mℓ would be -1, 0, and 1. Including the additional values of -2 and 2 from the alternate universe, the total number of orbitals in the p subshell would be 5 (mℓ = -2, -1, 0, 1, 2).

B. For the d subshell, the value of l is 2. In the conventional universe, the range of mℓ would be -2, -1, 0, 1, and 2, resulting in 5 orbitals. However, in the alternate universe, the range would extend to -3 and 3. Including these additional values, the total number of orbitals in the d subshell would be 10 (mℓ = -3, -2, -1, 0, 1, 2, 3).

Therefore, in the alternate universe, the p subshell would have 5 orbitals, and the d subshell would have 10 orbitals.

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Answer:

x = 9

∠B = 40°

Explanation:

because the lines are parallel, a and b are alternate angles. this means that they are equal. thus, we know that:

5x - 5 = 3x + 13

(add 5 to each side) 5x = 3x + 18

thus, 2x = 18 and x = 9.

we can now find ∠B by substituting 9 for x into the equation:

3x + 13

= 3 × 9 + 13

= 27 + 13

= 40°

i hope this helps! :D

Answer:

x = 9

<B = 40 degrees

Step-by-step explanation:

Hi,

5x - 5 = 3x + 13

Subtract 3x...

2x - 5 = 13

Add 5...

2x = 18

Divide by 2...

x = 9

Now find <B

3(9) + 13

27 + 13

<B = 40 degrees

hope this helps :)

Answer:

B

Step-by-step explanation:

Circle Y has a greater area than Circle X by approximately \($159.25\pi cm^2.\)

To determine which circle has a greater area and by how much, we will be using the formula which is given as, \($A = \pi r^2, where A\) is the area and \($r$\) is the radius.

As the first step we will calculate the radius of each circle:

For Circle X, the diameter is given as 18 cm. The radius, \($r_X$\), is half the diameter, so \($r_X = \frac{18}{2} = 9 cm.\)

For Circle Y, the diameter is given as 31 cm and the radius, \($r_Y$\), is half the diameter, so \($r_Y = \frac{31}{2} = 15.5 cm.\)

Now, for the next step, we can calculate the area of each circle:

The area of Circle X, \($A_X$\), is given by \($A_X = \pi (r_X)^2 = \pi (9)^2 = 81\pi cm^2.\)

The area of Circle Y, \($A_Y$\), is given by \($A_Y = \pi (r_Y)^2 = \pi (15.5)^2 = 240.25\pi cm^2\)

Comparing the two areas, we can see that \($A_Y > A_X$\). The difference in their areas is \($A_Y - A_X = 240.25\pi - 81\pi = 159.25\pi cm^2$\). Therefore, Circle Y has a greater area than Circle X by approximately \($159.25\pi cm^2$\).

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The addition property and division properties are used to solve the expression.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 3x - 4 = 1

Now, We can solve as;

⇒ 3x - 4 = 1

Add 4 both side,

⇒ 3x - 4 + 4 = 1 + 4

⇒ 3x = 5

Divide by 3;

⇒ x = 5/3

Thus, The addition property and division properties are used to solve the expression.

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The random variation that occurs in any time series is called the irregular component.

The irregular component refers to the random fluctuations or unpredictable patterns that are observed in a time series. It represents the unexplained variability in the data that cannot be attributed to any identifiable pattern, such as seasonal patterns, cyclical effects, or trends. It is often characterized by short-term fluctuations that occur randomly and do not follow a specific pattern or trend.

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There are a total of 12 choices for a small cup and 12 choices for the flavor, resulting in 12 possible selections. For the large cup, there are 12 choices for the first scoop and 11 choices for the second scoop (excluding the flavor already chosen), resulting in 132 possible selections.

The number of possible selections, we consider the choices for each cup size separately.

For a small cup, there are 12 flavors to choose from, so there are 12 possible selections.

For the large cup, we need to choose two different flavors. We have 12 choices for the first scoop, and once we have chosen a flavor, there are 11 remaining flavors for the second scoop (since it must be different from the first). This gives us a total of 12 * 11 = 132 possible selections.

Therefore, combining the possibilities from the small cup (12) and the large cup (132), there are a total of 12 + 132 = 144 possible selections at Cold Cup o' Cream.

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Answer:

since the decay rate constant of0.0 250 min.

hence the time required for the sample to decay to one forth of it's initial value is

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 1/5 to the power of 15

Answer: -6x + 21y = -42Now we can solve for y:21y = -42 + 42

y = 0Substitute y = 0 back into one of the original equations:-3x + 14(0) = -28

-3x = -28

x = 9/1So the solution to the system of equations is (x, y) = (9, 0).

Step-by-step explanation:

The growth constant is 0.69 and the population will increase to 12900 after approximately 3.7 years.

We have, Sunset Lake is stocked with 2500 rainbow trout and after 1 year the population has grown to 7050. Assuming logistic growth with a carrying capacity of 25000,

The logistic growth model is given by the equation

dN/dt=rN[(K-N)/K]

where, dN/dt = rate of change of population with respect to time,

N = population size at time t,

r = intrinsic rate of natural increase (growth constant),

K = carrying capacity.

The population size, "N" after 1 year = 7050

The initial population, "N₀" = 2500

The carrying capacity, K = 25000

We can use the following formula to find the value of the growth constant,

r = 2.303/t{ln(N_t/N₀) }........... (1)

Where, t = time taken for the population to increase from N_0 to N_t= 1 year (given)

Substituting the given values in equation (1), we get

r = 2.303/1 ln(7050/2500) ⇒ 0.688 ≈ 0.69

The value of the growth constant is 0.69.

Now, we can use the logistic growth equation to find the time required for the population to reach 12900.

dN/dt=rN[(K-N)/K]

Given, N₀ = 2500 and K = 25000

Differentiating both sides with respect to t,

dN/dt = rN[(K-N)/K] + Ndr/dt

Substituting the values of N, r, and K in the above equation, we get,

dN/dt= 0.69N[(25000-N)/25000] + N{dN/dt}

Let the population N become 12900 at time t = t₁

Therefore, at time t = 0, the population N₀ = 2500

Also, at time t = 1, the population N₁ = 7050

Substituting these values in the above equation, we get,

dN/dt= 0.69N[(25000-N)/25000] + N₁

dN/dt= 0.69(2500)[(25000-2500)/25000] + N₁

Solving for N₁, we get, N₁ = 7825

Substituting N₁ = 7825 in the above equation,

dN/dt= 0.69(7825)[(25000-7825)/25000] + N₁

dN/dt= 3263.25/1.69 ⇒ 1930.4

Now, to find t1, we can use the following formula;

ln[(K-N₁)/(K-N₀)] = rt₁

Substituting the given values, we get,

ln[(25000-12900)/(25000-2500)] = 0.69t₁

On solving for t₁, we get;

t₁ = ln[(1575/22500)]/0.69 ≈ 3.7 years

Hence, the population will increase to 12900 after approximately 3.7 years.

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The margin of error when the confidence level of 74% is 0.26. Then the correct option is B.

The probability or the chances of error while choosing or calculating a sample in a survey is called the margin of error.

The mean of a normally distributed population from a sample.

The confidence level of 74%.

Then the margin of error is given as

Margin of error = 1 – α

Margin of error = 1 – 0.74

Margin of error = 0.26

The margin of error when the confidence level of 74% is 0.26. Then the correct option is B.

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Answer:

0.26 or B

Step-by-step explanation:

Mercury has the greater density than that of Venus .

Answer:

mercury has higher density than venus