Graph the solution set of the following inequality. I 2x-1|>3

The volume of the composite figure is 6,330.24 in^3

We know that the volume of half a sphere of radius R is:

V = (2/3)*pi*R^3

Here we know that pi = 3.14 and R = 12 inches, then the volume is:

V = (2/3)*3.14*(12 in)^3 = 3,617.28 in^3

And the volume of a cone of height H and radius R is:

v = (1/3)*pi*R^2*H

So here the volume is:

v = (1/3)*3.14*(12in)^2*18in = 2,712.96 in^3

Then the total volume is:

3,617.28 in^3 +  2,712.96 in^3 = 6,330.24 in^3

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Answer d=t*v

Step-by-step explanation: the distance is the time spent times 60 miles per hour.

The starting price of a hotem room is $48.00.

After 1 year, this price increases by 5.1%, meaning it's increased by a factor of 1.051 or 1 + 0.051:

$48.00 (1 + 0.051) ≈ $50.45

After another year, this price increases by another 5.1%, so the previous amount is increased by a factor of 1.051, which is equivalent to 1.051² times the initial price:

$50.45 (1 + 0.051) = $48.00 (1 + 0.051)² ≈ $53.02

After another year, another increase:

$53.02 (1 + 0.051) = $48.00 (1 + 0.051)³ ≈ $55.72

And so on. You should start to see where the given formula comes from,

\(y = a(1+r)^t\)

where a = $48.00 is the starting price, r = 0.051 is the rate at which the price increases, and t is number of years.

Then in 32 years, the price of the room will be

$48.00 (1 + 0.051)³² ≈ $235.79

Answer:

96

Step-by-step explanation:

3x + 5x = 8x.

8 altogether -->  3 tulips and 5 daisies

16 altogether --> 6 tulips and 10 daisies

24 altogether ---> 9 tulips and 15 daisies

etc

etc

48 altogether --> 12 tulips and 20 daisies

96 altogether --> 15 tulips and 25 daisies

Answer:

55 : 56.6666666667

Step-by-step explanation:

3:5 ÷ 3 = 1 : 1.66666666667 + 55= 56.6666666667

Answer: about 14% of the 7 grade don't play sports

Step-by-step explanation: i think

Answers:

10.

B: Austin did not combine -3 and -9 correctly.

11.

x=8.5

12.

2r-4s

13.

10x+3y

14.

k=2

Answer: 52.5

Step-by-step explanation:

35 dollars 30% off is $24.5, 27 dollars 30% off is $18.90, and 13 dollars 30% off is $9.10 so all together it equals 52.5.

Answer:

a) C) The system has no solutions only when h=3 and k is any real number.

b) D) The system has a unique solution when \(h=(-\infty,3)U(3,\infty)\) and k is any real number.

c) The system has may solutions when h=3 and k=15

Step-by-step explanation:

a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:

\(x_{1}+hx_{2}=3\)

so

\(x_{1}=3-hx_{2}\)

Next we can substitute this into the second equation so we get:

\(5(3-hx_{2})+15x_{2}=k\)

We distribute the 5 into the first parenthesis so we get:

\(15-5hx_{2}+15x_{2}=k\)

and group like terms:

\(-5hx_{2}+15x_{2}=k-15\)

we factor x2 so we get:

\(x_{2}(-5h+15)=k-15\)

and solve for x2:

\(x_{2}=\frac{k-15}{-5h+15}\)

this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:

\(-5h+15= 0\)

and solve for h:

\(-5h= -15\)

\(h=\frac{-15}{-5}\)

\(h= 3\)

so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.

b)

For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.

So we take the second equation and factor it:

\(5x_{1}+15x_{2}=k\)

we start by factoring a 5 from the left side of the equation so we get:

\(5(x_{1}+3x_{2})=k\)

Next, we divide both sides of the equation into 5 so we get:

\(x_{1}+3x_{2}=\frac{k}{5}\)

we now compare it to the first equation:

\(x_{1}+hx_{2}=3\)

\(x_{1}+3x_{2}=\frac{k}{5}\)

In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and \(\frac{k}{5}=3\)

when taking the second condition and solving for k we get that:

\(k=3(5)\)

so

k=15

Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:

D) The system has a unique solution when and k is any real number.

c)

We have already solved part c on the previous part of the problem, so the answer is:

The system has many solutions when h=3 and k=15

Answer:

Below are the steps to divide fractions.

Step-by-step explanation:

We have 2 set of fractions here as an example.

\(\frac{1}{2} / \frac{3}{5}\)

The method to do this is: KCF

or

Keep, Change, Flip

Keep the first fraction as the same number.

Change the divide sign to a multiply sign.

Flip 3 and 5.

Now you have a multiplication problem.

\(\frac{1}{2}\) x \(\frac{5}{3}\)

To solve this multiplcation problem, multiply top and bottom (numerator and denominator) individually.

\(\frac{5}{6}\)

Answer:

r = 8

Step-by-step explanation:

Given that M is directly proportional to r² then the equation relating them is

M = kr² ← k is the constant of proportionality

To find k use the condition when r = 2 , M = 14

k = \(\frac{m}{r^{2} }\) =\(\frac{14}{4}\)  = \(\frac{7}{2}\)

M = r² ← equation of proportion

When M = 224, then

224 =\(\frac{7}{2}\)r² ← multiply both sides by 2

7r² = 448 ( divide both sides by 7 )

r² = 64 ( take the square root of both sides )

r = \(\sqrt{64}\) = 8

have wonderful day

Answer:

Looks right, b is right

Step-by-step explanation:

The rest are false

Answer:

yes you are right

Step-by-step explanation:

B is correct

Answer:

Bigger size   / smaller size = 40

Step-by-step explanation:

Notice that we      

36 / (9/10)    =    30 / (3/4)   = 40

Therefore the proportion model would be

Bigger size   / smaller size = 40

Answer:

300

Step-by-step explanation:

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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The measure of angle ADC in the geometric system is equal to 55°.

In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:

m ∠ CDE + m ∠ EDF = 180°

(2 · x + 1) + (x - 7) = 180°

3 · x - 6 = 180°

3 · x = 186°

x = 62

m ∠ CDE = 2 · x + 1

m ∠ CDE = 2 · 62 + 1

m ∠ CDE = 125°

m ∠ ADC = 180° - 125°

m ∠ ADC = 55°

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Answer:

75,600 m/h (21 m/s, 0.02 km/h)

Step-by-step explanation:

Hey there!

The answer to your question is \(21 mps\)

To find the rate of speed, we have to find the meters per second, or mps. The formula for this is  \(\frac{distance}{time} = speed\). So:

\(\frac{63}{3} = s\)

\(21 = s\)

This means that the speed is 21 meters per second, or 21 mps.

Hope it helps and have an amazing day!

Answer:

Step-by-step explanation:

If y = 2, we can substitute y in the expression for 2

8y - 2 = (8 * 2) - 2

8*2 = 16

16-2 = 14

Explanation:

Replace y with 2. Then use the order of operations PEMDAS to simplify until getting a single number.

8y-2

8*2-2

16 - 2

14

Therefore, 8y-2 = 14 when y = 2

Phrased another way: The solution to 8y-2 = 14 is y = 2

Answer:

A square pyramid has 5 faces: 1 square base and 4 triangular faces.

The area of the base is:

A = s^2

where s is the length of the base edge.

In this case, s = 1 m, so:

A = 1^2 = 1 m^2

The area of each triangular face is:

A = 1/2 * b * h

where b is the base of the triangle (which is equal to the length of one side of the square base) and h is the height of the triangle (which is given as 1 m).

In this case, b = 1 m and h = 1 m, so:

A = 1/2 * 1 * 1 = 0.5 m^2

The total surface area of the pyramid is the sum of the area of the base and the area of the four triangular faces:

SA = A_base + 4 * A_triangles

SA = 1 + 4(0.5)

SA = 1 + 2

SA = 3 m^2

Therefore, the surface area of the pyramid is 3 square meters.

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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Answer: -2

I hope this helps and may God bless you! Have a nice day, bye! :)

Answer:

i think you put the 7.3X2+9.1 then divided it by 8.7 -6.1

Step-by-step explanation:

let me see if i can help you

Answer:

18.1

Step-by-step explanation:

(7.3)2+9.1 / (8.7-6.1)

PEMDAS

Paranthesis first so: 7.3 x 2 = 14.6 , 8.7 - 6.1 = 2.6

So the equation becomes 14.6 + 9.1 / 2.6

Division next since there are no exponents or multiplication: 9.1 / 2.6 = 3.5

Equation becomes 14.6 + 3.5

Addition next: 14.6 + 3.5 = 18.1

Answer:

x=22/7

Step-by-step explanation:

4x-12+x=-2x+10

5x-12=-2x+10

5x=-2x+10+12

5x=-2x+22

5x+2x=22

7x=22

x=22/7

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

Answer:

Step-by-step explanation:

-2x+3x=-21+6

or x=-15

Answer:

x=3

Step-by-step explanation:

-2x-6=3x-21

Add 21 to both sides of the equation

Add 2x to both sides of the equation

Divide each side by 5 to isolate x

Answer:

\(6 \pm 2.861(0.3354)\)

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 20 - 1 = 19

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 19 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.99}{2} = 0.995\). So we have T = 2.861.

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 2.861\frac{1.5}{\sqrt{20}} = 2.861(0.3354)\)

In which s is the standard deviation of the sample and n is the size of the sample.

The format of the confidence interval is:

\(S_{M} \pm M\)

In which \(S_{M}\) is the sample mean

So

\(6 \pm 2.861(0.3354)\)

Given for the cone:

given for the spheres:

Find volume of cone:

\(\sf \hookrightarrow \dfrac{1}{3} \pi r^2h\)

\(\sf \hookrightarrow \dfrac{1}{3} \pi (3a)^2(4a)\)

\(\sf \hookrightarrow 12\pi a^3\)

Find volume of sphere:

\(\sf \hookrightarrow \dfrac{4}{3} \pi r^3\)

\(\sf \hookrightarrow \dfrac{4}{3} \pi a^3\)

Divide volume of cone by volume of sphere:

\(\sf \hookrightarrow \dfrac{12\pi a^3}{ \dfrac{4}{3} \pi a^3}\)

\(\rightarrow 9\)

Therefore proved 9 such spheres can be made using the metal cone.

We know that volume of cone is \(12\pi a^3\)

\(\sf \rightarrow 12\pi a^3 = 12936\)

\(\sf \rightarrow a^3 = \dfrac{12936}{12\pi}\)

\(\sf \rightarrow a = \sqrt[3]{\dfrac{12936}{12\pi}}\)

\(\sf \rightarrow a =7\)

Therefore the radius of sphere is 7 cm

Given dimensions of the room:

Length: \(\displaystyle\sf 12.5 \,m\)

Width: \(\displaystyle\sf 9 \,m\)

Height: \(\displaystyle\sf 7 \,m\)

Area of each wall:

\(\displaystyle\sf Area_1 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_2 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_3 = 9 \times 7 = 63 \,m^2\)

\(\displaystyle\sf Area_4 = 9 \times 7 = 63 \,m^2\)

Area of each door:

\(\displaystyle\sf Area_{\text{door}} = 2.5 \times 1.2 = 3 \,m^2\)

Area of each window:

\(\displaystyle\sf Area_{\text{window}} = 1.5 \times 1 = 1.5 \,m^2\)

Total area occupied by doors:

\(\displaystyle\sf Total_{\text{doors}} = 2 \times Area_{\text{door}} = 2 \times 3 = 6 \,m^2\)

Total area occupied by windows:

\(\displaystyle\sf Total_{\text{windows}} = 4 \times Area_{\text{window}} = 4 \times 1.5 = 6 \,m^2\)

Total wall area excluding doors and windows:

\(\displaystyle\sf Total_{\text{wall\,area}} = (Area_1 + Area_2 + Area_3 + Area_4) - Total_{\text{doors}} - Total_{\text{windows}}\)

\(\displaystyle\sf = (87.5 + 87.5 + 63 + 63) - 6 - 6\)

\(\displaystyle\sf = 275 - 6 - 6\)

\(\displaystyle\sf = 263 \,m^2\)

Cost of painting the walls:

\(\displaystyle\sf Cost_{\text{painting}} = Total_{\text{wall\,area}} \times 3.50\)

\(\displaystyle\sf = 263 \times 3.50\)

\(\displaystyle\sf = 920.50 \,Rs\)

Therefore, the cost of painting the walls of the room at Rs. 3.50 per square meter is Rs. 920.50.

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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The simplified form of expression \(\frac{(5m^3n^3)^2}{n}\) is \(25m^6n^5\)

Consider the expression \(\frac{(5m^3n^3)^2}{n}\)

We know that the exponent rule that \((a\times b)^m=a^m \times b^m\)

and \((a^m)^n=a^{m\times n}\)

where a, b, m and n real numbers.

Consider the numerator of above expression.

\((5m^3n^3)^2\)

Using the rule  \((a\times b)^m=a^m \times b^m\) ,

\((5\times m^3\times n^3)^2\\\\= 5^2\times (m^3)^2\times (n^3)^2\\\)

We know that the square of 5 is 25

so, 5² = 25

Now we use the rule \((a^m)^n=a^{m\times n}\)

so, above expression becomes,

\(5^2\times (m^3)^2\times (n^3)^2\\\\=25\times m^{3\times 2}\times n^{3\times 2}\\\\=25\times m^6 \times n^6\)

Also, we know that inverse of any value can be written as \(\frac{1}{a} =a^{-1}\)

So, using this rule of exponent the value of 1/n would be \(n^{-1}\)

So, the expression \(\frac{(5m^3n^3)^2}{n}\) becomes,

\(\frac{(5m^3n^3)^2}{n}\\\\=\frac{25\times m^6 \times n^6}{n}\\\\=(25\times m^6 \times n^6)\times n^{-1}\\\\=25\times m^6 \times n^6\times n^{-1}\)

We know that if the base of exponents are same then we add the powers of exponents.

So, our expression becomes,

\(=25\times m^6\times n^{6-1}\\\\=25\times m^6\times n^5\)

This is the required expression.

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