Patrickhas$600inasavingsaccountthatearns10%interestperyear.Theinterestisnotcompounded.Howmuchwillhehaveintotalin1year?

Answer:

c) 5, -5

Step-by-step explanation:

5 + (-5)

= 5 - 5

= 0

The area and the circumference of the circle would be 4π square kilometers and 4π kilometers respectively.

The area of a circle with a radius r is given by:

The circumference of a circle with a radius r is given by:

Given that the radius of the circle is 2km, we can substitute r = 2 into these formulas to find the area and circumference:

In other words, the area and the circumference of the circle are 4π square kilometers and 4π kilometers respectively.

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The answer will be \(a^{-20-12a}\) that can be find out using exponential function.

What are exponential function ?

Exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change.

Like, f(x) = \(x^{a}\)

x is base and a is power.

Basic rules to solve this function :

1. If we take the product of two exponentials with the same base, we simply add the exponents:

x^ a * x^ b = x^ a + b.

2. If we take the quotient of two exponentials with the same base, we simply subtract the exponents:

x^ a / x^ b =  x^ a-b

3. We can raise exponential to another power, or take a power of a power. The result is a single exponential where the power is the product of the original exponents:

x^ (a)^ b = x^ (ab).

In given equation, \({a^{2^{-2^5}}/{a^{4a^3}}\)

So the answer is a^(-20-12a).

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Answer:

3.75 tons djdhdjrjrhejejjwjwjsjs

Answer:

3.75 US tons

Step-by-step explanation:

1 ton =2000 pounds

so  7,500÷2000 =3.75

-12 will be the term for y

Let us suppose that x= 0

then we will get

3y + 4 = x

and then it will be

3y+ 4 = 0

Now, we will move 4 to the right hand side and it being positive this side will become negative on right hand side

3y= -4

now,

3y = 1/4

y = 1/[4*3]

y=1/12

y= - 12

Hence the answer will be y= -12

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Answer: Show the table

Step-by-step explanation:

SHow the table

\( \frac{1 - 1}{2} = \frac{0}{2} \)

the result is 0

Answer:

2(x² + 5)

Step-by-step explanation:

To factor 2x² + 10, we can first factor out the greatest common factor of the terms, which is 2:

2x² + 10 = 2(x² + 5)

We can't factor anymore, so the answer is:

2(x² + 5)

Answer:

2(x² + 5)

Step-by-step explanation:

To factorise this, do the distributive property backwards. In other words:

2x² + 10

2x² ÷ 2 + 10 ÷ 2

x² + 5

2(x² + 5)

∴ 2(x² + 5) is the answer

Answer:

the person above is right it's 4.5 units

give them the crown

Answer:

Y=X+3

Step-by-step explanation:

The expression 8x + 4y is not equivalent to 4(2x + 1). Therefore, 8x + 4y = 4(2x + y)

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Let's determine whether the expression 8x + 4y is equivalent to 4(2x + 1).

Let's factorise to know whether the expressions are equivalent.

Therefore, using the common factors,

8x + 4y = 4(2x + y)

Hence, the expression are not equivalent .

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Answer:

The numbers are 19 and 5

Step-by-step explanation:

Given

Let the numbers be \(x\ and\ y.\)

So:

\(x = 9 + 2y\) --- First statement

\(x*y = 95\) --- second statement

Required

Find x and y

Substitute \(x = 9 + 2y\) in \(x*y = 95\)

\((9 + 2y) * y = 95\)

\(9y + 2y^2 = 95\)

Rewrite as:

\(2y^2 + 9y - 95 = 0\)

Expand

\(2y^2 -10y +19y- 95 = 0\)

Factorize

\(2y(y -5) +19(y- 5) = 0\)

\((2y +19)(y- 5) = 0\)

Solve for y

\(2y + 19 =0\) or \(y - 5 = 0\)

\(2y = -19\) or \(y = 5\)

\(y = -\frac{19}{2}\) or \(y=5\)

Since the numbers are positive, we take only:

\(y=5\)

Substitute \(y=5\) in \(x = 9 + 2y\)

\(x = 9 + 2 * 5\)

\(x = 9 + 10\)

\(x = 19\)

The numbers are 19 and 5

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

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The x-coordinates where the graphs of the equations intersect are x = -1 and x = 3

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

y = 2x

y = x² - 3

The x-coordinates where the graphs of the equations intersect is when both equations are equal

So, we have

x² - 3 = 2x

Rewrite the equation as

x² - 2x - 3 = 0

When the equation is factored, we have

(x + 1)(x - 3) = 0

So, we have

x = -1 and x = 3

Hence, the x-coordinates are x = -1 and x = 3

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Question

From least to greatest, What are the x–coordinates of the three points where the graphs of the equations intersect? If approximate, enter values to the hundredths.

y = 2x

y = x² - 3

By using the substitution method, we will see that the value of y is 23.

Here we have a system of linear equations, the system is:

y - x = 11

x = 12

The second equation is trivial, it just gives the value of x. Then we can use the substitution method and replace it in the first equation, then we will get:

y - 12 = 11

Now we can solve this for y, we will get:

y = 11 + 12

y = 23

That is the value of y.

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Answer:

The midpoint is (3, 3).

Step-by-step explanation:

We are given the two points A(9, 11) and B(-3, -5).

The midpoint is given by:

\(\displaystyle M=\Big(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\Big)\)

So:

\(\displaystyle M = \Big( \frac{9+(-3) }{2}, \frac{ 11+(-5) }{2} \Big) = (3,3)\)

The midpoint is (3, 3).

We want to show that AM = MB.

We can use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

The distance between A(9, 11) and M(3, 3) will then be:

\(AM=\sqrt{(9-3)^2+(11-3)^2}=\sqrt{6^2+8^2}=\sqrt{100}=10\)

And the distance between B(-3, -5) and M(3, 3) will be:

\(MB = \sqrt{ (3-(-3))^2 + (3-(-5))^2 } = \sqrt{(6)^2+(8)^2} = \sqrt{ 100 } = 10\)

So, AM = MB = 10.

Since AM = MB = 10, AM + MB = 10 + 10 = 20.

So, we want to prove that AB = 20.

By the distance formula:

\(AB=\sqrt{(9-(-3))^2+(11-(-5))^2}=\sqrt{12^2+16^2}}=\sqrt{400}=20\stackrel{\checkmark}{=}20\)

Step-by-step explanation:

51x + 23y = 116 ……….. (i)

23x + 51y = 106 ………… (ii)

Subtracting (ii) from (i)

28x – 28y = 10

28(x – y) = 10

⇒ (x – y) = 10/28 = 5/14

The solution of the expression x- y is 5/14.

Given Equation:

Equation 1: 51x + 23y = 116

Equation 2: 23x + 51y = 106

Now, multiply 23 in equation 1 and 51 in equation 2 gives

Equation 3: 1173x + 529y = 2,668

Equation 4: 1173x + 2601 y = 5406

Solving the Equation 1 and (3) gives

2601y - 529y = 5406 - 2668

2072y= 2738

y = 37/28.

Substituting the value of y= 37/28 in Equation 1 gives

51x + 23(37/28)= 116

51 x= 2397/28

x= 47/28

So, the value of x-y

= 47/28 - 37/28

= 10/28

= 5/14

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Answer:

Unable to read entire question, but see explanation for answer

Step-by-step explanation:

First, you need to find the unit rate per dog. If it takes 3 dogs 10 days to finish 30 pounds of food, then it takes 1 dog 1 day to finish 1 pound of food. I cannot read the entirety of the question because of the cropping, but you can find how much food a single dog eats in that amount of days by just multiplying by the number of days (say, 1 pound in 1 day, or 3 pounds in 3 days). Hope this helps!

Answer:

1

Step-by-step explanation:

took test

Answer:

y = -7/4

Step-by-step explanation:

The required answers are:

lim f(x) = -1

1-2-

lim f(x) = -1

1+2+

lim f(x) = -3

r2

f(2) = -3

Given image has a graph of the function f(x)

To find \(\lim_{x\rightarrow 2^-}f(x), lim f(2) 12+, lim f(x) 12 and f(2)\)

We have from the image of the graph the function f(x) is a discontinuous function with x=2 is the point of discontinuity.

Now from the graph the value of f(x) at x=2 i.e. f(2) = -3 as the graph has a bold dot at y=-3.

Next \(\lim_{x\rightarrow 2^-}f(x)=\lim_{x\rightarrow 2^+}f(x)=-1\) as in the graph of f(x) it has a small circle at y = -1.

As f(2) = -3 so \(\lim_{x\rightarrow 2}f(x)=f(2)=-3\)

Thus the required answers are

lim f(x) = -1

1-2-

lim f(x) = -1

1+2+

lim f(x) = -3

r2

f(2) = -3

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Answer:

-5/4

Step-by-step explanation:

Let \((x_1,y_1)=(-4,4)\) and \((x_2,y_2)=(0,-1)\). The slope of the line would be:

\(\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}\)

Answer: -5/4

Step-by-step explanation:

To find the slope between two points, you can use the formula:

Slope = (y2 - y1)/(x2 - x1)

Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:

slope = (4 - (-1))/(-4 - 0)

slope = (4 + 1)/(-4)

slope = 5/-4

Therefore, the slope between the two points is -5/4.

Answer:

Step-by-step explanation:

Given that

X1, X2, X3....... X18 are the volume of beverages in 18 bottles. These volumes have the same distribution and are independent of each other.

E.X(i) = 2.013L, while the Standard Deviation is given as

S D = X(i) = 0.005L

The average volume per bottle = X bar

E.X bar = E.X(i) = 2.013L

S D X bar = [S D X(i)]/√n = 0.005 /√18 = 0.005 / 4.24 = 1.18*10^-3L

Answer:

147 minutes (2 hours, 27 minutes)

Step-by-step explanation:

Answer:

1. C

2. B

3. A

4. D

Step-by-step explanation:

Answer: x ≈ 9

Step-by-step explanation:

Near the end of the picture 8.553364=x

x ≈ 9

Answer:

x = -6

y = 4

Step-by-step explanation:

Rewriting the equations :

Now, solving the two equations using substitution method, we get :

x = -6

y = 4

Answer:

y = 4

x = -6

Step-by-step explanation:

1/2 x + 1/4 y= -2        first equation

-2/3 x + 1/2 y = 6      second equation

solution:

from the first equation:

8(1/2 x + 1/4 y) = -2*8

8x*1/2 + 8y*1/4 = -16

8x/2 + 8y/4 = -16

4x + 2y = -16        third equation

from the second equation

6(-2/3 x + 1/2 y) = 6*6

6x*-2/3 + 6y*1/2 = 36

-12x/3 + 6y/2 = 36

-4x + 3y = 36        fourth equation

from the third & fourth equation:

 4x + 2y  = -16

-4x + 3y  = 36

   0  + 5y = 20

5y = 20

y = 20/5

y = 4

from the fourth equation:

-4x + 3y = 36

-4x + 3*4 = 36

-4x + 12 = 36

-4x = 36 - 12

-4x = 24

x = 24/-4

x = -6

Check:

from the first equation:

1/2 x + 1/4 y = -2

1/2 *-6 + 1/4 * 4 = -2

-3 + 1 0 -2

from the second equation:

-2/3 x + 1/2 y = 6

-2/3 * -6  +  1/2 * 4 = 6

4 + 2 = 6

To find the equation of a line that passes through the points (5, -3) and (-2, -4) in standard form, we can use the point-slope form of a linear equation and then convert it to standard form.

Determine the slope (m) of the line using the formula:

   m = (y2 - y1) / (x2 - x1)

For the given points (5, -3) and (-2, -4), we have:

   m = (-4 - (-3)) / (-2 - 5) = (-4 + 3) / (-2 - 5) = -1 / (-7) = 1/7

Use the point-slope form of a linear equation:

   y - y1 = m(x - x1)

Using the point (5, -3), we have:

   y - (-3) = (1/7)(x - 5)

Simplifying:

   y + 3 = (1/7)(x - 5)

Convert the equation to standard form:

Multiply both sides of the equation by 7 to eliminate the fraction:

   7y + 21 = x - 5

Rearrange the equation to have the x and y terms on the same side:

   x - 7y = 26

The equation of the line in standard form that passes through the points (5, -3) and (-2, -4) is x - 7y = 26.

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The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.