Solve for x in the diagram below.

One water tank can be rented for 160 dollars, according to the provided statement.

The radius of a circular is the separation between its centre and perimeter. Always, the circumference is twice the radius.

The volume of the cylinder-shaped water tank is given by the formula

V = πr²h, where

r is the radius

h is the height.

Substituting the given values, we get:

V = π(4 feet)²(2 feet) = 32π cubic feet

The cost of renting the water tank is given by the product of the volume and the cost per cubic foot:

Cost = 5 dollars/cubic foot × 32π cubic feet

Multiplying these values, we get:

Cost = 160π dollars

Therefore, it costs 160π dollars to rent one water tank.

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238.20 cubic inches of cotton is needed if the remaining space is to be filled with cotton for padding. The volume of cotton needed is obtained by subtracting the volume of four glass balls from the volume of the box.

The radius of a glass ball = 2.5 inches.

The volume of a ball = \(\frac{4}{3}\pi r^3\)

                                   = \(\frac{4}{3}\times 3.14\times (2.5)^3\)

                                   = 65.42 cubic inches.

The volume of 4 balls = 4 × 65.42 cubic inches

                                    = 261.67 cubic inches.

Length of the box = 4 × 2.5 × 2 = 20 inches,

Width of the box = 2.5 × 2 = 5 inches,

Height of the box = 2.5 × 2 = 5 inches.

So,

the volume of the box = Length × Width × Height

                                     = 20 × 5 × 5

                                     = 500 cubic inches.

Now,

The volume of cotton needed = the volume of the box - the volume of 4 balls.

= 500 - 261.67

= 238.20 cubic inches.

Thus, if the remaining space is to be filled with cotton for padding, 238.20 cubic inches of cotton is needed.

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The average of the sample ranges for the weight of packages of Skittles is 0.11. So, the correct answer is (e) 0.11.

To find the average of the sample ranges for the weight of packages of Skittles, we first calculate the range for each sample. The range is the difference between the maximum and minimum values in each sample.

Sample 1: Range\(= 3.62 - 3.58 = 0.04\)

Sample 2: Range\(= 3.65 - 3.49 = 0.16\)

Sample 3: Range \(= 3.65 - 3.45 = 0.20\)

Sample 4: Range \(= 3.64 - 3.54 = 0.10\)

Sample 5: Range\(= 3.62 - 3.49 = 0.13\)

Next, we calculate the average of these sample ranges:

A\(verage = (0.04 + 0.16 + 0.20 + 0.10 + 0.13) / 5 = 0.11\)

Therefore, the average of the sample ranges for the weight of packages of Skittles is \(0.11\). So, the correct answer is (e) \(0.11.\)

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Note: The function is not an equation. I will form and solve an equation to answer the question.

Answer:

C. Two real solutions

Step-by-step explanation:

We have the following function:

f(x)=2(x-1)^2+4

It does not form an equation to solve, and therefore, there are no 'solutions'. We must equate the function to something to set a condition and solve it. We'll complete the equation.

Solve for x when:

f(x)=12

Substituting the function:

2(x-1)^2+4=12

Subtracting 4:

2(x-1)^2=8

Dividing by 2:

(x-1)^2=4

Taking square root:

x-1=\pm\sqrt{4}

Solving:

x=1\pm2

We have two real solutions x=3 and x=-1

Note if we had equated to 4, then the equation would have had only one real solution, and if we had equated to 0, we would have two complex solutions.

The solution of equation f(x) = 2x² - 4x + 6 is two complex solutions. Then the correct option is B.

The discriminant of a quadratic is a number that depends on the components and allows some characteristics of the roots to be deduced without calculating them.

The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,

D = b² - 4ac

The equation is given below.

f(x) = 2(x - 1)² + 4

f(x) = 2x² - 4x + 2 + 4

f(x) = 2x² - 4x + 6

The discriminant is given as,

D = (-4)² - 4×2×6

D = 16 - 48

D = - 32

D < 0

The roots are complex root.

The solution of equation f(x) = 2x² - 4x + 6 is two complex solutions. Then the correct option is B.

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The simplest form of fraction of the given terms is 43/40.

According to the statement

we have to find that the simplest form of the fraction by evaluating.

So, For this purpose, we know that the

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.

The given expression is

7/8+ 1/5

Now, to solve it take a LCM of it then

35+8/40

Now solve the term then the equation become

43/40.

Now, The simple form of the fraction become the 43/40.

So, The simplest form of fraction of the given terms is 43/40.

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Answer:

Don't worry, I gotcha.

Step-by-step explanation:

3       -6      -3

----  + ----  = ----

4         5       9

Answer:

the answer is 2

Step-by-step explanation:

The area expressions are 2x^2 + 4x + 2 and 2(x + 1)_^2

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

The figure

From the figure, we have

Rows = x^2 + x^2 = 2x^2

Columns = 4 * x + 1/2 * 4 = 4x + 2

Using the above as a guide, we have the following:

Area = 2x^2 + 4x + 2

When expressed as a binomial square, we have

Area = 2(x + 1)^2

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Answer:

sorry

Step-by-step explanation: im am no good at math

Option (c) expresses 1−2 4−8 16 in sigma notation.

To see why, let's expand the terms:

1 - 2 + 4 - 8 + 16 = (1 - 2) + (4 - 8) + 16
= -1 - 4 + 16
= 11

Notice that each term is multiplied by (-1)^(k+1) and (2)^k, where k is the index of summation. We can express this in sigma notation as:

∑k=-2^2 (-1)^(k+1) (2)^k

This means we start the summation with k=-2 and end with k=2, and each term is given by (-1)^(k+1) (2)^k. Evaluating this summation gives:

(-1)^1 (2)^-2 + (-1)^2 (2)^-1 + (-1)^3 (2)^0 + (-1)^4 (2)^1 + (-1)^5 (2)^2
= (1/4) - 2 + 1 - 2 + 4
= 1 - 2 + 4 - 8 + 16
= 11

Therefore, option (c) expresses 1−2 4−8 16 in sigma notation.

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The end of the long hand of the clock travels about 78.54 inches (25π) in 2 1/2 hours.

Clock can be defined as a machine in which a device that performs regular movements in equal intervals of time is linked to a counting mechanism that records the number of movements

The long hand of the clock completes one full revolution in 12 hours. Therefore, in one hour, it travels a distance equal to the circumference of a circle with a radius of 5 inches, which is given by 2πr = 2π(5) = 10π inches.

In 2 1/2 hours, the long hand of the clock travels a distance equal to (2 1/2) x 10π = 25π inches.

So, the end of the long hand of the clock travels about 78.54 inches (25π) in 2 1/2 hours.

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Answer:

105 = (5x-70)

Step-by-step explanation:

You are trying to find x so you would have to place that in to finally get to the end where x = 5

Answer:

the statement is not reversible

Step-by-step explanation:

Hi there!

We are given the statement "if x=3, then x²=9"

In this case, the hypothesis (p) is x=3, while the conclusion (q) is x²=9

Reversing the statement would make it so that q is first, then p is after.

In other words, if the statement was originally "if p, then q", then the reverse of that statement would be "if q, then p"

This is known as the CONVERSE of the statement. Sometimes, the converse is true, but not always. If both the statement and the converse are true, then it's known as a BICONDITIONAL, where it works both ways

So we'll need to test if the following statement "if x²=9, then x=3" is true

If you subtract 9 from both sides, x²=9 becomes this equation:

x²-9=0

Using the square of differences formula, where x is a and 3 (square root of 9) is b:

(x-3)(x+3)=0

Now using zero product property:

x-3=0

Add 3 to both sides

x=3

AND:

x+3=0

Subtract 3 from both sides

x=-3

We see that the answers from this equation are x=3 and x=-3.

*if you plug 3 and -3 back in the equation, we can see they both work. Remember that x² is equal to x*x, or (x)²:

If x=3:

(3)²=9

(3)(3)=9

9=9

If x=-3:

(-3)²=9

(-3)(-3)=9

9=9

Hence, the statement doesn't work in the converse

The option "the statement is not reversible" is not the answer.

Hope this helps!

Answer: B. SPHERE

Step-by-step explanation:

The geometric solid that is the best model for the head of a human being is sphere.

The volume of sphere is given by -

V = 4/3πr³

Given is to find the geometric solid is the best model for the head of a human being.

A human face can be considered somewhat as a sphere. It is almost round as sphere. The radius of an average human is approximately 28 cm. So, we can write the average volume of the given spherical head as-

Volume = 4/3πr³

Volume = 4/3π x 28 x 28 x 28

Volume = 29,269.3π cubic centimeters

Therefore, the geometric solid that is the best model for the head of a human being is sphere.

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Answer:

Step-by-step explanation:

Let the speed of the car is x, then the speed of motorcycle is x + 20

The distance = 120 km

Time:

Speed of the car is 40 km/h

Speed of the motorcycle is 60 km/h

Answer:

Speed of the car is 40 km/h

Speed of the motorcycle is 60 km/h

Answer:

7.8 x 10^-6 or 7.8E-6

Step-by-step explanation:

Answer: = 7.8 × 10-6

Step-by-step explanation: Hope this helps

In a taste test comparing a generic soda to a brand name soda, the count of correct guesses among 20 tasters follows a binomial distribution with parameters n = 20 (number of trials) and p = 0.25 (probability of guessing correctly). The taste tests are conducted independently, with tasters in separate locations to avoid interaction between them during the test.

Binomial distribution: The binomial distribution is a discrete probability distribution of the number of successes in a fixed number of independent trials. P(X=k)= nCk * pk * (1-p)n-k, Where P(X=k) is the probability of getting k successes in n trials, nCk is the number of ways to get k successes in n trials, p is the probability of success, and 1 - p is the probability of failure.

So, the formula for the mean and variance of the binomial distribution is as follows: μ = npσ2 = np (1 - p).

Now, we have to find n and p. Probability of success, p is 0.25 and the number of trials, n is 20.

Thus,p = 0.25, n = 20.

So, n and p are 20 and 0.25 respectively.

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The miles walked on Tuesday and Wednesday given the total miles walked is 5 miles and 15 miles respectively.

24 = 4 + 1/3w + w

24 - 4 = 1/3w + w

20 = 1 1/3w

20 = 4/3w

w = 20 ÷ 4/3

w = 20 × 3/4

= 60 /4

w = 15 miles

Miles walked on Tuesday = 1/3w

= 1/3 × 15

= 15/3

= 5 miles

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Answer:

\(12c⁹+27c⁷\)

Step-by-step explanation:

3c⁶(9c+4c³)

=(3c⁶)(9c+4c³)

=(3c⁶)(9c)+(3c⁶)(4c³)

=27c⁷+12c⁹

=12c⁹+27c⁷

The value of phone B is \(\omega = 840\).

Any equation with a maximum degree of 1 is said to be linear. In a linear equation, no variable has an exponent bigger than 1, thus. There is always a straight line on the graph of a linear equation.

Given that each term in a linear equation has an exponent of 1, graphing an algebraic equation always yields a straight line.  For this reason, it is referred to as a "linear equation." There are both one-variable and two-variable linear equations.

\(v= 1000\)

\((\frac{4}{5})^d\) is the value of phone A and

\(\omega = 840\) is the value of phone B.

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Complete Question;

For each cell phone, write an equation that relates the value of the phone in dollars to the years since release, t. Use v for the value of Phone A and w for the value of Phone B.

Step-by-step explanation:

try this option, all the details are in the attachment.

Note, the nine numbers. used in the solution are: 1, 2, 3, 4, 5, 6, 7, 8 and 9.

1. →v1 = (5, -3, 2, 7) is in the span of {→a, →b, →c} with coefficients x = -6, y = -1, and z = 2.

2. →v2 = (2, 7, 6, -7) is not in the span of {→a, →b, →c}.

3. →v3 = (30, -7, 10, 17) is not in the span of {→a, →b, →c}.

To determine whether each vector is in the span of {→a, →b, →c}, we need to check if it can be expressed as a linear combination of →a, →b, and →c. If it can, we can find the coefficients that give the linear combination. Let's go through each vector:

1. →v1 = (5, -3, 2, 7)

To express →v1 as a linear combination of →a, →b, and →c, we need to find coefficients x, y, and z such that →v1 = x→a + y→b + z→c.

Solving the equation, we get:

5→a - 3→b + 2→c = (5, -3, 2, 7)

(5, -1, 3, 3) - 3(5, 0, 1, 0) + 2(-10, 3, -3, -7) = (5, -3, 2, 7)

(5, -1, 3, 3) - (15, 0, 3, 0) + (-20, 6, -6, -14) = (5, -3, 2, 7)

(5 - 15 - 20, -1 + 0 + 6, 3 + 3 - 6, 3 + 0 - 14) = (5, -3, 2, 7)

(-30, 5, 0, -8) = (5, -3, 2, 7)

Since (-30, 5, 0, -8) is equal to (5, -3, 2, 7), →v1 is indeed in the span of {→a, →b, →c}.

2. →v2 = (2, 7, 6, -7)

Following the same process as above, we solve for the coefficients:

2→a + 7→b + 6→c = (2, 7, 6, -7)

(2, -7, 6, 6) + 7(5, 0, 1, 0) + 6(-10, 3, -3, -7) = (2, 7, 6, -7)

(2, -7, 6, 6) + (35, 0, 7, 0) + (-60, 18, -18, -42) = (2, 7, 6, -7)

(2 + 35 - 60, -7 + 0 + 18, 6 + 7 - 18, 6 + 0 - 42) = (2, 7, 6, -7)

(-23, 11, -5, -36) ≠ (2, 7, 6, -7)

Since (-23, 11, -5, -36) is not equal to (2, 7, 6, -7), →v2 is not in the span of {→a, →b, →c}.

3. →v3 = (30, -7, 10, 17)

Using the same approach, we solve for the coefficients:

30→a - 7→b + 10→c = (30, -7, 10, 17)

(30, -7, 10, 17) - 7(5, 0, 1, 0) + 10(-

10, 3, -3, -7) = (30, -7, 10, 17)

(30, -7, 10, 17) - (35, 0, 7, 0) + (-100, 30, -30, -70) = (30, -7, 10, 17)

(30 - 35 - 100, -7 + 0 + 30, 10 + 7 - 30, 17 + 0 - 70) = (30, -7, 10, 17)

(-105, 23, -10, -53) ≠ (30, -7, 10, 17)

Since (-105, 23, -10, -53) is not equal to (30, -7, 10, 17), →v3 is not in the span of {→a, →b, →c}.

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the advantages of being paid salary is u get it even if u work 1 hour and the disadvantage of getting paid hourly is u have to work for along time

Answer:

V = 30 in³

Step-by-step explanation:

the volume (V) of a pyramid is calculated as

V = \(\frac{1}{3}\) × B × h ( B is the area of the base and h the height ) , then

V = \(\frac{1}{3}\) × 6 × 15 = 2 × 15 = 30 in³

Answer:

The volume of the pyramid is 30 inches cube.

The base of the pyramid is an equilateral triangle with an area of 6 inches².  The height of the pyramid is 15 inches.

Therefore, the volume of the pyramid can be calculated as follows:

volume of the pyramid = 1 / 3 BH

where

B = base area

H = height of the pyramid

Therefore,

B = 6 inches²

H = 15 inches

Hence,

volume of the pyramid = 1 / 3 × 6 × 15

volume of the pyramid = 1 / 3 × 90

Therefore,

volume of the pyramid = 30 inches³

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Step-by-step explanation:

The approximate noon Sun angle at 41°N latitude (on Long Island) on February 14th is 61°. None of the provided answer choices match the correct answer.

To calculate the approximate noon Sun angle at 41°N latitude (on Long Island) on February 14th, we can use the analemma.

The analemma is a figure-8 shaped curve that represents the position of the Sun in the sky at the same time each day over the course of a year. It accounts for the Earth's axial tilt and elliptical orbit around the Sun.

To find the approximate noon Sun angle, we need to consider the declination of the Sun on February 14th and the latitude of Long Island.

On February 14th, the Sun's declination is approximately -12°.

The Sun angle at noon can be calculated using the following formula:

Sun angle = 90° - (latitude - declination)

Substituting the values, we have:

Sun angle = 90° - (41° - (-12°))

Simplifying this equation, we get:

Sun angle = 90° - 41° + 12°

Sun angle = 61°

Therefore, the approximate noon Sun angle at 41°N latitude (on Long Island) on February 14th is 61°.

None of the provided answer choices match the correct answer.

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When "down" is positive and air friction is disregarded, the time it takes for the rock to touch the ground may be calculated using the formula \(h(t)=16t2-100\) to be roughly 6.25 seconds.

the formula\(h(t)=16t2 - 100\)when a rock is dropped from a height of 100 feet, and assuming that "down" is positive and air friction is neglected, represents the height of the rock at time t in seconds.

As the rock will land at the value of t when h(t) = 0, we must determine that value in order to determine how long it takes for the rock to land.

When we set h(t) to 0 we obtain 0 = 16t2 - 100.

\(16t^2 = 100 \st^2 = 100/16 \st^2 = 6.25 \st = ±√6.25\)

The only viable answer in this case is\(t = 6.25 = 2.5\) seconds since time cannot be negative. As a result, there was a 2.5 second delay between when the rock was dropped and when it landed.

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Answer:

I think -1,14

Step-by-step explanation:

Because you add 5

Hi Plato/Edmentum Users!

The other person is correct!

Answer:

Step-by-step explanation:

5 * 1/8=  5/8

1/7*6=  6/7

Place the whole number over 1 and multiply.

The fraction which represent the number of sweaters Maggie knits in 8 days is 2/1 sweaters

Total number of sweaters Maggie knits = Sweaters Maggie knits per day × Number of days

= 1/4 × 8

= (1 × 8) / 4

= 8/4

= 2/1 sweaters

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