Select the sets that are not functions.

B = {(1, 2), (2, 1), (3, 0), (4, -1)}
D = {(1, 1), (1, 2), (1, 3), (1, 4)}
A = {(1, 2), (2, 3), (3, 4), (4, 5)}
C = {(-1, 3), (0, 3), (1, 3), (2, 3)}
E = {(6, 2), (7, 3), (6, -1), (5, 4)}

Answer:

Step-by-step explanation:

8 oz goes to 0.23/oz

10 oz goes to 0.29/oz

16 oz goes to 0.22/oz

Lastly, 12 oz goes to 0.26/oz

Hope this helps!

Answer:

40% of the balls were basketballs

Step-by-step explanation:

\(\frac{12}{30} = \frac{x}{100}\)

12*100 = 1200

1200/30 = 40

Answer:

These kind of questions are called simply.

According to simply, there's a rule of solving which is BODMAS.

BODMAS stand for bracket of Divide, Multiple, Add, Subtraction.

> (9)2-4

> 18-4

> 16

• (6+3)2-4 = 16

2. 23+(14-4)÷2

> 23+10÷2

> 23+5

> 28

• 23+(14-4)÷2 = 28

Step-by-step explanation:

Hope it helps you

The equation for plan (2) is y = 10x.

Two or more expressions with an equal sign are defined as an equation.

Given that, the second plan costs $10 for each bowling visit.

Therefore, the total cost, y, for x bowling visit is:

y = 10x

Hence, the equation for the plan (2) is y = 10x.

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Answer:

0.6778 to 4 dec. places.

Step-by-step explanation:

That is  387 / (184+387)

= 387 / 571

= 0.677758

Mike comes to a stop 105.3 feet above sea level while trekking on a mountain. The vertical separation between Mike and the mountain's base is 101.5 feet .

Given that,

Mike comes to a stop 105.3 feet above sea level while trekking on a mountain. There are 3.8 feet of sea level below the mountain's base.

We have to find what is the vertical separation between Mike and the mountain's base.

The Mike comes to a stop 105.3 feet above sea level while trekking on a mountain.

3.8 feet of sea level below the mountain's base.

We just have to do the difference of the above sea level feet and below sea level feet.

=105.3-3.8

=101.5

Therefore, the vertical separation between Mike and the mountain's base is 101.5 feet .

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The consecutive page no. are 126 and 127.

An example of a run of consecutive integers is 1, 2, 3, 4. Another illustration is 7, 8, and 9. An integer sequence is a set of numbers where each term is one more than the term before it.

Continually following one another, from smallest to greatest, are consecutive numerals. For instance, the sequence of the numerals 1, 2, 3, 4, 5, and so forth.

The next two numbers are (n + 1) and (n + 2) if n is an integer. Take 1 for n as an example. Its subsequent numbers can be read as (2 and 3), or as (1 + 1) and (1 + 2).

let the consecutive page numbers be x and x+1

according to question ,

          x + x + 1 = 253

          2x = 252

            x = 126

so the consecutive page numbers are 126 and 127.

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Answer:

13i, -13i

Step-by-step explanation:

To solve this equation, we need to take the square root of both sides. The square root of 169 can be either 13 or -13, but this time, they asked for -169. Whenever we take the square root of a negative number, we put the letter i, which stands for imaginary. It is never capitalized, so we remove the negative sign from -169, and take the square root of that. We get -13 and 13 as our answers, and we multiply both numbers by i to get -13i and 13i. Any solutions with i in it are considered complex solutions

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3600\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}\)

\(A = 3600\left(1+\frac{0.02}{12}\right)^{12\cdot 18}\implies A=3600(\frac{601}{600})^{216} \implies A \approx 5158.44\)

The smallest positive integer y is the product of these additional factors y = 2¹⁴ * 3⁴ * 7².

To find the smallest positive integer y such that the product xy is a perfect cube, we first need to find the prime factorization of x. Given that x = 7 * 24 * 48, we can break down the factors further:

x = 7 * (2³ * 3) * (2⁴ * 3)
x = 2⁷ * 3² * 7

Now, for xy to be a perfect cube, the exponents of all prime factors must be divisible by 3. Currently, the prime factorization of x has exponents 7, 2, and 1 for 2, 3, and 7, respectively.

To make each exponent divisible by 3, we must multiply x by additional factors:

For 2: (2⁷)³ = 2²¹, so we need 2⁽²¹⁻⁷⁾ = 2¹⁴
For 3: (3²)³ = 3⁶, so we need 3⁽⁶⁻²⁾ = 3⁴
For 7: (7¹)³ = 7³, so we need 7⁽³⁻¹⁾ = 7²

Hence, the smallest positive integer y is the product of these additional factors:

y = 2¹⁴ * 3⁴ * 7²

So, y is the smallest positive integer such that xy is a perfect cube.

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Somebody better answer thing

Answer:

1.) 38.2

2.) -62.8

4.) -38.2

Answer:

-75 meters

Step-by-step explanation:

First, subtract 15 from 50, since it is going up:

50 - 15

= 35

Then, add 40, since it is going back down:

35 + 40

= 75

So, the new position is -75 meters relative to sea level

First condition of submarine=50 m below the sea=-50 m

It goes up 15 m, that means we must add up 15 m.

-50 m+15 m=

15 m-50 m=-35 m (35 m below the sea)

And, then goes down 40 m, so we subtract it with 40 m.

-35 m-40 m=-75 m (75 m below the sea)

So, the right answer is 2. (-75 meters)

Thank you.

Answer:

(-6,9)

Step-by-step explanation:

x + y = 3

0 + y = 9

We can subtract the two equations.

(x-0) + (y-y) = (3-9)

x=-6

y=9

(-6,9)

Answer:

here are the answers! :)

Step-by-step explanation:

The value represents the amplitude of the function. Therefore, the amplitude of the cosine curve function of the graph is 2.

The amplitude of a function is simply the maximum point or value of the given function.

From the question, we have:

Maximum = 2

The value represents the amplitude of the function.

Therefore, the amplitude of the cosine curve function of the graph is 2.

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If the beakers were not perfectly insulated, the sum of their temperatures would likely change over time because some of the thermal energy (heat) from the beakers would be transferred to the outside environment. This would cause the temperature of the beakers to decrease.

As the temperature of the beakers decreases, the sum of their temperatures would also decreases. This is because the sum of the temperatures is simply the total amount of thermal energy contained in the beakers. If some of this thermal energy is transferred to the outside environment, the sum of the temperatures will decrease.

The rate at which the sum of the temperatures decreases will depend on the rate at which heat is transferred from the beakers to the outside environment. Factors that can affect this rate include the temperature difference between the beakers and the outside environment, the surface area of the beakers that are in contact with the outside environment, and the insulation properties of the beakers (such as the thickness of any insulation material).

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To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first plot the curve on a polar graph.

From the graph, we can see that the curve has two loops - one larger loop and one smaller loop. The larger loop encloses the smaller loop.

To find the area inside the larger loop and outside the smaller loop, we can use the formula:

Area = 1/2 ∫[a,b] (r2 - r1)2 dθ

where r2 is the equation of the outer curve (larger loop) and r1 is the equation of the inner curve (smaller loop).

The limits of integration a and b can be found by setting the angle θ such that the curve intersects itself at the x-axis. From the graph, we can see that this occurs at θ = π/2 and θ = 3π/2.

Plugging in the equations for r1 and r2, we get:

r1 = 1/2 + cos(θ)
r2 = 1/2 - cos(θ)

So the area inside the larger loop and outside the smaller loop is:

Area = 1/2 ∫[π/2, 3π/2] ((1/2 - cos(θ))2 - (1/2 + cos(θ))2) dθ

Simplifying and evaluating the integral, we get:

Area = 3π/2 - 3/2 ≈ 1.07

Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is approximately 1.07. Note that this area is smaller than the total area enclosed by the curve, since it excludes the area inside the smaller loop.
To find the area inside the larger loop and outside the smaller loop of the limaçon given by the polar equation r = 1 + 2cos(θ), follow these steps:

1. Find the points where the loops intersect by setting r = 0:
1 + 2cos(θ) = 0
2cos(θ) = -1
cos(θ) = -1/2
θ = 2π/3, 4π/3

2. Integrate the area inside the larger loop:
Larger loop area = 1/2 * ∫[r^2 dθ] from 0 to 2π
Larger loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 0 to 2π

3. Integrate the area inside the smaller loop:
Smaller loop area = 1/2 * ∫[r^2 dθ] from 2π/3 to 4π/3
Smaller loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 2π/3 to 4π/3

4. Subtract the smaller loop area from the larger loop area:
Desired area = Larger loop area - Smaller loop area

After evaluating the integrals and performing the subtraction, you will find the area inside the larger loop and outside the smaller loop of the given limaçon.

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Answer: 54.861

Step-by-step explanation:

Answer:

its 3.3 x 10 with 8 squared

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

180-(60+40)=180-60-40=180-100=80

Answer:

Angle CAB= 80 Degrees

Step-by-step explanation:

The angle A can be found by taking the sum of angles in the 2 separate triangles and adding them together.

We know that a straight line is 180 degrees. The angle ADC is given to be 90 degrees, therefore angle BDA is also 90 degrees because 180-90=90 degree (congruent angle). (both the small triangles are right angle triangles) This gives us 2 angle measurements in each triangle. This means for both triangkes we can add the 2 angle measurements to find the sum of both andlges and subtract that number from 180 because 180 is the sum of all angles in a triangle.

For Triangle BDA we add angle B (40 degrees) and angle D (90 degrees)

Angle= 180- (40+90)

Angle= 180-130

Angle= 50 degrees

For triangle DAC we add angle D(90 degrees) and angle C(60 degrees)

Angle= 180- (90+60)

Angle = 180-150

Angle= 30 degrees

To find the angle measurement for angle CAB we add the answer from both the calculations as shown above (add 50 and 30)

Angle CAB= 50+30

Angle CAB= 80 degrees

Therefore angle CAB= 80 degrees

9514 1404 393

Answer:

  y = 20·2^x

Step-by-step explanation:

Use the given points to write two equations, then solve for 'a' and 'b'.

  20 = a·b^0 = a

  5120 = a·b^8 = 20·b^8   ⇒   256 = b^8

  b = 256^(1/8) = 2

Your function is ...

  y = 20·2^x

The best estimate for the percent equivalent of 7 15 is Approximate 46%.

What is a percentage in math?

Given : 7/15

To convert a number in to percentage we multiply it by 100.

\(\frac{7}{15} = \frac{7}{15} * 100\)

\(\frac{7}{15} = \frac{700}{15}\)

\(\frac{7}{15} =\)   46 %

Therefore, Approximate 46%.

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To estimate\(e^{0.1}\) within an error of 0.00001 using Taylor's inequality, we should use the first 8 terms of the Maclaurin series for \(e^{x}\).

Taylor's inequality provides a bound on the error between an approximation and the actual value of a function using its Taylor series expansion. The inequality states that for a function f(x) and its nth degree Taylor polynomial P_n(x), the error |f(x) - P_n(x)| is bounded by M * |x - a|^(n+1) / (n+1)!, where M is an upper bound for the absolute value of the (n+1)th derivative of f(x) in the interval of interest.

In the case of estimating e^0.1 using the Maclaurin series for e^x, we know that the Maclaurin series expansion of e^x is given by\(e^x = 1 + x + (x^2)/2! + (x^3)/3! + ... + (x^n)/n! + ...\)

To determine the number of terms needed, we need to find the smallest value of n that satisfies the inequality |x^(n+1) / (n+1)!| ≤ 0.00001, where x = 0.1.

By substituting the values of x and M into the inequality, we can solve for n. However, since the calculation involves a recursive process, it is more efficient to use software or a calculator that supports symbolic computation. Using such tools, we find that n = 7 is sufficient to estimate e^0.1 within an error of 0.00001.

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Answer:

6.6/100 or 3.3/5

Step-by-step explanation:

6.6% or 6 3/5% now since those are all out of 100 (since percentages) you just put #/100 and get your fraction

The final answers of the matrices are:

cb-a = [[-11, 14, -8], [-5, 0, -3], [11, -14, 20]]

ca = [[-1], [0], [3]]

To find the product of two matrices, we need to multiply the elements of each row in the first matrix with the corresponding elements of each column in the second matrix and then add them together.

If the number of columns in the first matrix is not equal to the number of rows in the second matrix, the product is not defined and the answer is "dne" (does not exist).

First, let's compute cb:

cb = [[2,5],[−4,−2],[−1,−5]] * [[3,−1,2],[−3,3,−4]] = [[(2*3)+(5*-3), (2*-1)+(5*3), (2*2)+(5*-4)], [(-4*3)+(-2*-3), (-4*-1)+(-2*3), (-4*2)+(-2*-4)], [(-1*3)+(-5*-3), (-1*-1)+(-5*3), (-1*2)+(-5*-4)]]

cb = [[-9, 13, -12], [-6, 2, 0], [12, -14, 18]]

Now, let's compute cb-a:

cb-a = [[-9, 13, -12], [-6, 2, 0], [12, -14, 18]] - [[2, -1, -4], [-1, 2, 3], [1, 0, -2]] = [[-9-2, 13-(-1), -12-(-4)], [-6-(-1), 2-2, 0-3], [12-1, -14-0, 18-(-2)]] cb-a = [[-11, 14, -8], [-5, 0, -3], [11, -14, 20]]

Finally, let's compute ca:

ca = [[2,5],[−4,−2],[−1,−5]] * [[2],[-1],[-4]] = [[(2*2)+(5*-1)+(0*-4)], [(-4*2)+(-2*-1)+(0*-4)], [(-1*2)+(-5*-1)+(0*-4)]] ca = [[-1], [0], [3]]

So, the final answers are:

cb-a = [[-11, 14, -8], [-5, 0, -3], [11, -14, 20]]

ca = [[-1], [0], [3]]

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The probability that the coin will land heads up on the first flip, tails up on the second flip, and tails up on the third flip is (1/8).

If we toss a coin, we have two possible outcomes: head or tail. Now:

P(E) = Favourable outcomes / Total outcomes

      = 1/2

As per the question, we need heads on the first throw and tails on the next two throws. We know that for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

Let A be the event of getting head on the first throw and B and C be events of getting tails on the second and third throws of dice respectively.

P(A) = P(B) = P(C) = 1/2

So, P(A∩B∩C) = (1/2)*(1/2)*(1/2) = 1/8

So, the Required probability is (1/8)

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The correct form of the partial fraction decomposition for the expression \($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2}$\) is:

\(\frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{Cx+D}{x^2+7} + \frac{Ex+F}{(x^2+7)^2}\) (Option 1).

The given expression can be written in the form \($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2}$\). To decompose this into partial fractions, we need to find the values of constants A, B, C, D, E, and F such that the expression can be written in the form of the options given.

Using partial fraction decomposition method, we can write the expression as:

\($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2} = \frac{A}{x+1} + \frac{B}{(x+1)^2} + \frac{Cx+D}{x^2+7} + \frac{Ex+F}{(x^2+7)^2}$\)

Then we multiply both sides by the denominator of the expression on the left and simplify to get:

\($4x^3+3x^2 = A(x+1)(x^2+7)^2 + B(x^2+7)^2 + (Cx+D)(x+1)^2(x^2+7) + (Ex+F)(x+1)^2$\)

Next, we can solve for the unknown constants by equating the coefficients of the same powers of x on both sides of the equation. We will end up with a system of linear equations, which can be solved using various methods.

After solving, we get the coefficients as:

\(A = -\frac{1}{2}$, $B = \frac{5}{4}$, $C = 0$, $D = -\frac{1}{4}$, $E = 0$, and $F = \frac{3}{28}$.\)

Therefore, the correct form of the partial fraction decomposition for the given expression is:

\($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2} = -\frac{1}{2(x+1)} + \frac{5}{4(x+1)^2} - \frac{1}{4(x^2+7)} + \frac{3}{28(x^2+7)^2}$\)

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Complete Question:

Which is the correct form of the partial fraction decomposition for the expression \($\frac{4x^3+3x^2}{(x+1)^2(x^2+7)^2}$\)?

A statement that is true for the functions f(x) and g(x) include the following: B. they share a common x-intercept.

In Mathematics and Geometry, the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or the value of "f(x)" or "g(x)" is equal to zero (0).

When g(x) = 0, the x-intercept of g(x) can be calculated as follows;

g(x) = -2x² + 2

0 = -2x² + 2

0 = -2(x² - 1)

x² - 1 = 0

x² = 1

x = ±√1

x = 1 or x = -1

Therefore, the x-intercept of g(x) are (-1, 0) and (1, 0).

By critically observing the graph representing the function f(x) shown above, we can logically deduce that the x-intercept of f(x) are (-1, 0) and (3, 0).

In conclusion, (-1, 0) is a common x-intercept to both f(x) and g(x).

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The greatest monomial factor of 15x³y² + 45x²y² + 30x²y³ is  15x²y².

What is a monomial factor?

Each term of a given polynomial contains a monomial factor, which can be either a number, a variable, or a mix of both. A polynomial with only one term is called a monomial. An algebraic expression known as a "monomial" has a single term but can also have multiple variables and a higher degree.

Here, we have

Given: 15x³y² + 45x²y² + 30x²y³

We have to determine the greatest monomial factor.

= 15x³y² + 45x²y² + 30x²y³

We factor out a 15 and divide each term by 15 as well.

= 15x²y²(x + 3 + 2y)

The greatest common factor is 15x²y² because, according to our factored equation, it is most commonly factored out for all the terms in the original polynomial equation.

Hence, the greatest monomial factor of 15x³y² + 45x²y² + 30x²y³ is  15x²y².

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