find the slope
(8, 10), (-7, 14)

The amount of coffee worth $7 a pound that should be added is given by A = 45 pounds

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the amount of coffee worth $7 a pound that should be added be A

And , the amount of coffee worth $ 2 is = 30 pounds

Let the cost per pound for the mixture is = $ 5

The total amount of mixture = 5 ( 30 + A )

On simplifying the equation , we get

2 ( 30 ) + 7 ( A ) = 5 ( 30 + A )

60 + 7A = 150 + 5A

Subtracting 5A on both sides , we get

60 + 2A = 150

Subtracting 60 on both sides , we get

2A = 90

Divide by 2 on both sides , we get

A = 45 pounds

Hence , the amount of coffee is 45 pounds

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Answer:

x = -3

Topics are listed below.

Step-by-step explanation:

Topics of this question include:

Solve:

-Chetan K

Answer:

The value of x is 6.

Step-by-step explanation:

Concept :

Here, we will use the below following steps to find a solution using the transposition method:

\(\begin{gathered}\end{gathered}\)

Finding the value of x.

\(\begin{gathered}\quad\implies{\tt{9 - 4(5 - x)=3(x - 1) - 2 }}\\\\\quad\implies{\tt{9 - (4 \times 5 - 4\times x)=(3 \times x - 3 \times 1) - 2}}\\\\\quad\implies{\tt{9 - (20 - 4x)=(3x - 3) - 2}}\\\\\quad\implies{\tt{9 - 20- 4x=3x - 3- 2}} \\\\\quad\implies{\tt{- 11 - 4x=3x - 5}}\\\\\implies{\tt{- 4x + 3x = - 11 + 5}} \\ \\\implies{\tt{-x = - 6}}\\\\ \implies{\tt{ \cancel{-}\: x = \cancel{-} 6}}\\\\\quad\implies{\tt{x = 6}}\end{gathered}\)

Hence, The value of x is 6.

\(\rule{300}{2.5}\)

To find an explicit solution of the given differential equation, we can use separation of variables.

The explicit solution of the differential equation (x^2)dy/dx = (y^2) can be found by rearranging the equation and separating the variables:

\[ \frac{dy}{y^2} = \frac{dx}{x^2} \]

Integrating both sides, we get:

\[ \int \frac{1}{y^2} \, dy = \int \frac{1}{x^2} \, dx \]

This simplifies to:

\[ -\frac{1}{y} = -\frac{1}{x} + C \]

where C is the constant of integration.

To solve the given differential equation (x^2)dy/dx = (y^2), we use the technique of separation of variables. This involves rearranging the equation to separate the variables y and x on different sides of the equation.

We start by dividing both sides of the equation by (y^2):

\[ \frac{dy}{y^2} = \frac{dx}{x^2} \]

Next, we integrate both sides of the equation with respect to their respective variables. The integral of 1/y^2 with respect to y gives us -1/y, and the integral of 1/x^2 with respect to x gives us -1/x. Adding the constant of integration C to account for the antiderivative, we have:

\[ -\frac{1}{y} = -\frac{1}{x} + C \]

This equation represents the general solution to the given differential equation. The constant of integration C can be determined by applying initial conditions if they are given.

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Answer:

1/36

Step-by-step explanation:

\((-6)^{-2}\) can be written as:

\(\frac{1}{(-6)^{2} }\) (this is done by the law of indices \(a^{-m}=\frac{1}{a^{m} }\) )

then by simplifying the above expression, we get:

\(\frac{1}{(-6 * -6)} =\frac{1}{36}\)

So the final answer is 1/36 ( \(\frac{1}{36}\) )

we have y = [-1, -1, -1] + [-10, 5, 5], where [-1, -1, -1] is in W and [-10, 5, 5] is orthogonal to W.

To write vector y as the sum of a vector in W and a vector orthogonal to W, we need to find the projection of y onto W and then subtract it from y to obtain the orthogonal component.

Let's first find the projection of y onto W. The projection of a vector onto a subspace is given by the formula:

proj_W(y) = (y⋅u / ||u||^2) * u

where ⋅ represents the dot product and ||u|| represents the norm (magnitude) of vector u.

Given the information, we have:

y = [-11, 4, 4]

u = [1, 1, 1]

First, calculate the dot product of y and u:

y⋅u = (-11)(1) + (4)(1) + (4)(1) = -11 + 4 + 4 = -3

Next, calculate the norm squared of u:

||u||^2 = (1^2) + (1^2) + (1^2) = 1 + 1 + 1 = 3

Now, substitute these values into the projection formula:

proj_W(y) = (-3 / 3) * [1, 1, 1]

= [-1, -1, -1]

The projection of y onto W is [-1, -1, -1].

To obtain the orthogonal component z, we subtract the projection from y:

z = y - proj_W(y)

= [-11, 4, 4] - [-1, -1, -1]

= [-11 + 1, 4 + 1, 4 + 1]

= [-10, 5, 5]

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Here's a Scheme function that checks whether a matrix is symmetric or not:

```scheme

(define (is-symmetric-matrix matrix)

 (define (get-element matrix i j)

   (if (null? matrix)

       #f

       (if (= i 0)

           (if (null? (car matrix))

               #f

               (if (= j 0)

                   (car (car matrix))

                   (get-element (cdr matrix) i (- j 1))))

           (get-element (cdr matrix) (- i 1) j))))

 (define (is-matrix-symmetric-helper matrix i j)

   (if (null? matrix)

       #t

       (if (equal? (get-element matrix i j)

                   (get-element matrix j i))

           (is-matrix-symmetric-helper matrix i (+ j 1))

           #f)))

 (if (null? matrix)

     #t

     (is-matrix-symmetric-helper matrix 0 0)))

```

The function `is-symmetric-matrix` takes a matrix as an input, which is represented as a list of lists. It uses a helper function called `is-matrix-symmetric-helper` to compare each element of the matrix with its corresponding element in the transposed position. The `get-element` function is used to retrieve the element at position `(i, j)` in the matrix.

The `is-matrix-symmetric-helper` function recursively iterates over the matrix, comparing each element with its transposed element. If any pair of corresponding elements is found to be different, it immediately returns `#f` (False), indicating that the matrix is not symmetric. If it reaches the end of the matrix without finding any differences, it returns `#t` (True), indicating that the matrix is symmetric.

Finally, the main `is-symmetric-matrix` function first checks if the matrix is empty. If it is, it immediately returns `#t` since an empty matrix is considered symmetric. Otherwise, it calls the helper function with the initial indices `(0, 0)` and returns its result.

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Answer:

0.4

Step-by-step explanation:

1-0.6=0.4???????????????

Answer: no clue

Step-by-step explanation:

Speed = distance / time

Speed = 200 meters / 20 seconds

Speed = 10 meters / second

1 meter per second = 3.6 km per hour

10 meters per second x 3.6 = 36 km per hour

Answer: 36 kilometers per hour

Step-by-step explanation: Average speed = total distance / total time.

The resulting polynomial will have a degree of is \($g(h(x))$\)a polynomial that results from substituting \($h(x)$ into $g(x)$.\)\($(\text{degree of } h(x)) \times 6$.\)

To determine the degree of the polynomial $h(x)$, we need to analyze the degree of the composite polynomial \($f(g(x))g(h(x))h(f(x))$.\)

Let's break down the composite polynomial:

$f(g(x))$ is a polynomial that results from substituting $g(x)$ into $f(x)$. Since $g(x)$ is a polynomial of degree $3$ when substituted into $f(x)$ of degree $6$, the resulting polynomial will have a degree of \($6 \times 3 = 18$.\)

$g(h(x))$ is a polynomial that results from substituting $h(x)$ into $g(x)$. Since $h(x)$ is a polynomial of unknown degree when substituted into $g(x)$ of degree $3$, the resulting polynomial will have a degree of \($3 \times (\text{degree of } h(x))$.\)

$h(f(x))$ is a polynomial that results from substituting $f(x)$ into $h(x)$. Since $f(x)$ is a polynomial of degree $6$ when substituted into $h(x)$ of unknown degree, The resulting polynomial will have a degree of

\($(\text{degree of } h(x)) \times 6$.\)

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Answer:

6°

Step-by-step explanation:

It started at -2°f and increased b 8° so 2 of those degrees get you back to 0°f and the remains is 6 so 6°

Answer:

Rs 1,437.5

Step-by-step explanation:

VAT = 15% = 15/100 × Rs 1250 = Rs 187.5

the price inclusive of VAT = Rs 1,250 + Rs 187.5

= Rs 1,437.5

Answer:

Shortest distance of first mantel should be 3 ft from left end and shortest distance of second mantel should be 3 ft from right end

Step-by-step explanation:

Length of the mantel = 12 ft

Since first vase is 1/4 of the distance from one end of the mantel, then let's choose left end;.

Distance of first vase from left end = 1/4 × 12 = 3 ft

Also, distance of second vase from left end = 3/4 × 12 = 9 ft

This second vase is 9 ft from left end. Which means it is 3 ft from right end since the mantel is 12 ft in length.

Thus,shortest distance of first mantel should be 3 ft from left end and shortest distance of second mantel should be 3 ft from right end.

The velocity required to escape the gravitational attraction of Mars is 5.03 km/s.

To calculate the velocity required to escape the gravitational attraction of Mars, we need to find the escape velocity at the given altitude. The formula for escape velocity is:

ve = sqrt((2 * G * M) / r)

where ve is the escape velocity, G is the gravitational constant (approximately 6.674 × 10^-20 km³/kg·s²), M is the mass of Mars (approximately 6.417 × 10^23 kg), and r is the distance from the center of Mars to the spacecraft.

Given that the spacecraft is at an altitude of 384 km, we first need to add this to the radius of Mars (approximately 3,390 km) to get the distance r:

r = 3,390 km + 384 km = 3,774 km

Now we can plug these values into the escape velocity formula:

ve = sqrt((2 * 6.674 × 10^-20 km³/kg·s² * 6.417 × 10^23 kg) / 3,774 km)

ve ≈ 5.03 km/s

So, the velocity required to escape the gravitational attraction of Mars at an altitude of 384 km is approximately 5.03 km/s. Keep in mind that the velocity direction and magnitude required to actually return to Earth may be different.

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The data appears to follow a quadratic curve, and a quadratic model would best describe the data. The quadratic function that models the data is y = 2x^2 - x - 1.

To graph the given data set, we can plot the points on a coordinate plane as follows:

  |

8 |  

7 |    ●

6 |        

5 |        

4 |        

3 |        

2 |  ●  

1 |    ●  

0 |  ●  

-1 |    ●

-2 |  ●  

  |_____________

    -2 -1  0  1  2

From the graph, we can see that the data appears to follow a quadratic curve. Therefore, a quadratic model would best describe the data.

To write a quadratic function that models the data, we can use the standard form of a quadratic equation:

y = ax^2 + bx + c

where a, b, and c are constants to be determined.

To find the values of a, b, and c, we can use the data points and solve the resulting system of equations

-1 = 4a - 2b + c

-2 = a - 2b + c

-1 = c

2 = 4a + 2b + c

7 = 4a + 8b + c

Solving the system of equations, we get:

a = 2

b = -1

c = -1

Therefore, the function that models the data is:

y = 2x^2 - x - 1

So the corresponding answers to these questions are:

\(A) a= 7.33657 \\ b= 1.10757\\B)f(t)^{-1} = log (7.33657)+ t*log(1.10757)\\C)728.10886\\D) 2.86219\)

For the letter a, it will be necessary to calculate the values ​​of a and b, therefore:

\(f(t)=a*b^{t} \\f(7)=15 \\ a*b^{7}=15\\a=\frac{15}{b^{7}} \\f(12)=25\\a= \frac{25}{b^{12}}\\\frac{15}{b^{7}} =\frac{25}{b^{12}}=> b^{5}= 1.66667=> b= 1.10757\\a=\frac{15}{b^{7}}=> a=7.33657\)

So for the letter B we will do the logarithm so we will have:

\(P=f(t)=ab^{t}=(7.33657)(1.10757)^{t} \\f(t)^{-1} = log (7.33657)+ t*log(1.10757)\)

For the letter C we will use the formula given in the statement just substituting the value of t=45:

\(f(t)=ab^{t} \\f(45)=(7.33657)(1.10757)^{45} = 728.10886\)

The formula calculated on the letter B will be useful for the letter D only having to substitute t=45, therefore:

\(f(45)^{-1} = log (7.33657)+ 45*log(1.10757)\\f(45)^{-1} = 2.86219\)

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Therefore, the correct statement is that the t distribution is Symmetrical (option c).

The correct statement is:

c. The t distribution is symmetrical.

The t distribution, also known as the Student's t distribution, is a probability distribution that is used in statistical inference when the sample size is small or when the population standard deviation is unknown. It is similar to the normal distribution but has slightly thicker tails.

The t distribution is symmetrical, meaning it has a bell-shaped curve that is centered around its mean. The symmetry of the t distribution is a fundamental property that allows for the calculation of confidence intervals and hypothesis tests in statistical analysis.

Unlike the normal distribution, the t distribution has more probability in the tails, which means it has fatter tails. This indicates that extreme values are more likely to occur in the t distribution compared to the normal distribution when dealing with small sample sizes. As the sample size increases, the t distribution approaches the shape of the normal distribution.

Regarding options a, b, and d:

a. The t distribution is not positively skewed. Skewness refers to the asymmetry of a distribution, and the t distribution is symmetric.

b. The t distribution is not negatively skewed. Again, skewness does not apply to the t distribution as it is symmetric.

d. All the values of the t distribution are not positive. The t distribution takes both positive and negative values since it represents the distribution of t-statistics, which can be positive or negative depending on the sample data and the hypothesis being tested.

Therefore, the correct statement is that the t distribution is symmetrical (option c).

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Answer:

3x+2 is not less than 2x-5

Step-by-step explanation:

3(8)+2<2(8)-5; 24+2 < 16-5; 26 < 9

Answer:

that is alot  I  would help you but I don't know how to do it

Step-by-step explanation:

1/3

it is going to be smaller since its a dilation so its obviously neither of the whole numbers, and its not half of the originial one, its a little bit larger than half, its 1/3

option a is correct

The probability that the coin lands on heads if one of them is flipped and lands on heads with probability 0.6 is 0.6 × 1/2 + 0.3 × 1/2 = 0.45. Therefore, the probability that the coin lands on heads is 0.45.  

a) Let A be the event that the chosen coin is the one that lands on heads with probability 0.6 and B be the event that the coin lands on heads. Then, the required probability is P(A | B) = P(A and B) / P(B) .

Here, P(A and B) = probability that the chosen coin is the one that lands on heads with probability 0.6 and it actually lands on heads.

Since the probability that the coin lands on heads are 0.45 and the probability that the chosen coin is the one that lands on heads with a probability of 0.6 is 1/2, we have P(A and B) = 0.6 × 1/2 = 0.3. The probability that the coin lands on heads is 0.45.

So, P(B) = probability that the coin lands on heads = 0.45.P(A | B) = P(A and B) / P(B) = 0.3 / 0.45 = 2/3.

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Answer:

The answer is D.5(9a-2b)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

5x9a -5x2b= 45a - 10b

so that is the answer

Answer:

I would say B

Margin of error for 99% confidence interval is 0.0021

What is confidence interval?

he range of values that, should you repeat your experiment or resample the population in the same manner, you would anticipate your estimate to fall within a particular percentage of the time.

Main Body:

Given :

99% Confidence Interval for p

p = 0.24,n = 276000

Significance level = α = 1− confidence = 1 − 0.99 = 0.01

Critical z-value = zα/2 = z0.01/2 = z0.005 = 2.58 (closest value From z table)

Standard e

or of p : SE =

√p× (1 − p)n=√0.24 × 0.76276000

≈ 0.0008129

E = zα/2 ×√p× (1 − p)n

= 2.58 × 0.0008129 ≈ 0.002097

Hence ,Margin of Error or, E = 0.00210

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The volume of the solid is (1/24)\(\pi a^{3}\)

To find the volume of the solid, we can consider the cross sections perpendicular to the base. Since these cross sections are semicircles, we can use integration to calculate the volume.

Let's denote the variable for the perpendicular side of the triangle as y, which ranges from 0 to (1/2)a. For each y, the corresponding cross section is a semicircle with radius y. The area of each cross section is (1/2)πy^2.

To find the volume, we integrate the area of the cross sections over the range of y:

V = ∫[(1/2)\(\pi y^{2}\)]dy from 0 to (1/2)a

Evaluating the integral, we get:

V = (1/24)\(\pi a^{3}\)

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Answer:

Below.

Step-by-step explanation:

–10m4n3 + 8m2n6 + 3m4n3  – 2m2n6 – 6m2n6

= 8m2n6 – 2m2n6 – 6m2n6 – 10m4n3 + 3m4n3

= 8m2n6 - 8m2n6 – 7m4n3

= –7m4n3.

It is a mononomial.

Answer: B

Step-by-step explanation: because

Answer:

20

Step-by-step explanation:

\(\frac{-8*10^7}{-4*10^6}\\=2*10\\=20\)

Answer:

16.5f

Step-by-step explanation:

just know that’s right

Answer:

Question relates to a Arithmetic Sequence {30,32,34...} where d = 2

and the terms are the enumber of seats in each row.

S%5Bn%5D=%28n%2F2%29%282%2Aa%5B1%5D%2B+%28n-1%29d%29  |Sum of the seats in the 26 rows.

S%5B26%5D=%2826%2F2%29%282%2A30%2B+%2825%292%29 = 1430 seats in the ALL 26 rows

Step-by-step explanation: