Mike and alice recycled 147 bottles altogether. Mike recycled 6 times as many bottles as Alice. How many bottles did alive recycle

Answer:

The rule for finding a reflection of a point across the y-axis is that the y-coordinate will stay the same but the x-coordinate will become its opposite. Thus, in the context of the problem, point (3,6) would become (-3,6) if reflected across the y-axis.

Step-by-step explanation: If you were going to reflect a point across the x-axis, the x-coordinate would stay the same. You're not moving it and it shouldn't change signs. The y-coordinate, however, would become its opposite because it'd be joining a new quadrant. Think of it like this:

Y-AXIS = Y remains the same and gains a neighbor; X changes because it isn't the center of attention.

X-AXIS = X remains the same and gains a neighbor; Y changes because it isn't the center of attention.

Basically, the letter of the axis is the number that doesn't change.

I hope I helped!

Answer:  C) (x + 5i)(x - 5i)

Step-by-step explanation:

x² + 25 can be rewritten as x² - (-25)

Now use the difference of squares to factor: a² - b² = (a + b)(a - b)

√x² = x      √-25 = 5i

--> x² + 25 = (x + 5i)(x - 5i)

The remainder is non-zero, so [tex]x-3[/tex] is not a factor of [tex]2x^3-4x^2-8[/tex] (or whatever the given polynomial is supposed to be)

The Remainder Theorem suggests that if you substitute '3' into the polynomial equation [tex]2x^3 - 4x^2 - 8x + 1[/tex], the result is -5, which is the same as the remainder of that polynomial equation divided by x - 3.

Eric used the Remainder Theorem in his calculation, which is a mathematical principle in algebra. It states that the remainder of a polynomial f(x), when divided by a linear divisor x - a, is equal to f(a). In this scenario, when he plugged '3' (the value of 'a') into the equation [tex]2x^3 - 4x^2 - 8x + 1[/tex], he obtained a resultant value of -5.

This indicates that when the polynomial [tex]2x^3 - 4x^2 - 8x + 1[/tex] is divided by x - 3, the remainder is -5. This remainder would also be the result if 3 substituted for x in the original polynomial equation, as per the Remainder Theorem.

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ANSWER

See explanation

EXPLANATION

The standard form of a quadratic equation is:

[tex]y = a {x}^{2} + bx + c[/tex]

To convert this function to standard form, you follow the steps below:

For example:

Given the standard form:

[tex]y = 2 {x}^{2} + 12x + 10[/tex]

Factor 2 from the variable terms

[tex]y = 2 {(x}^{2} + 6x) + 10[/tex]

Add and subtract the square of 3.

[tex]y = 2 {(x}^{2} + 6x + 9 - 9) + 10[/tex]

[tex]y = 2 {(x}^{2} + 6x + 9) + 2( - 9) + 10[/tex]

Factor the perfect square an simplify

[tex]y = 2 ({x + 3)}^{2} - 8[/tex]

This is the vertex form

yes, one can rewrite an equation in standard form to vertex form.

Below are the steps to convert the equation in standard form to vertex form.

What do the mathematical term standard form mean?

There are various ways to represent a parabola's equation, including standard form, vertex form, and intercept form.

A parabola's typical form is standard form i.e  y = ax2 + bx + c.

Here, variables x and y represent points on the parabola, and real numbers (constants) a, b, and c are real numbers (constants) where a 0.

By completing the square, change y = a (x - h)2 + k from standard form to vertex form (y = a (x - h)2 + k).  

The vertex form is y = a (x - h)2 + k in this case.

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Answer:

10mn

Step-by-step explanation:

[tex]5mn - 8mn + 13mn = 10mn[/tex]

If Willie ends up with only 20CDs that would be half of what he had at first and 20 plus 20 which would be the other half would be 40. 6 minus 40 would be 34 which he started with.

Answer:34

Step-by-step explanation:

Answer: $3.20

Step-by-step explanation:

$3.50 reduced by 20%= $3.30

$3.30-10%= $3.20.

Answer:

the mode

the mean

Step-by-step explanation:

Measures of central tendency are measures of center or location of a distribution or a data set. The most commonly used measures of center of a distribution are the;

mean

median

mode.

Answer:

  A

Step-by-step explanation:

Repeated values in the domain of a function are not allowed.

B: -6 is repeated in the domain

C: a list of numbers, not a relation

D; 7 is repeated in the domain

__

A is a relation with no repeated domain values. It matches the requirement.

Answer:

(13.8,1.42) (18,3.7)(16.7,3.21) and so on REMEMBER ITS (X,Y)

Step-by-step explanation:

The mathematical expectation is a weighted sum:

[tex]E(X) = \displaystyle \sum_{i=1}^n x_ip(x_i)[/tex]

i.e. we multiply each outcome with its probability, and sum all these terms.

There are 16 possible outcomes for the spin, and here's table with wins/losses:

[tex]\begin{array}{c|cccc}&1&4&4&5\\1&L&L&L&L\\4&L&W&W&W\\4&L&W&W&W\\5&L&W&W&W\end{array}[/tex]

So, there are 9 winning spins and 7 losing spins. Since all the spins have the same probability, the probablity of winning $8 is 9/16, and the probability of losing $2 is 7/16. This leads to a mathematical expectation of

[tex]E(A) = 8\cdot \dfrac{9}{16}-2\dfrac{7}{16} = \dfrac{29}{8}[/tex]

In the case of the three coin flips, all triplets have the same probability of 1/8, and the eight triplets are

TTT, TTH, THT, HTT, THH, HTH, HHT, TTT

So, Danielle wins with 3 triplets, and loses with 5 triplets. The mathematical expectation is

[tex]E(B) = 6\cdot \dfrac{3}{8}-1\dfrac{5}{8} = \dfrac{13}{8}[/tex]

So, the first method is better, and the difference is 29/8-13/8 = 2.

After calculating the expected values, Danielle expects to make $0.875 more by choosing Option B over Option A, as it has a higher mathematical expectation.

To calculate which option has a greater mathematical expectation (expected value), we must consider the possible outcomes of each option and their probabilities. We then multiply each outcome by its probability and sum the results.

We have 3 possible sums that would result in Danielle winning $8: 5+4, 4+5, and 4+4. Any other sum results in losing $2. The probability of spinning a 5 on the first spin is 1/4, and so is the probability of spinning a 4. Therefore, the probability of getting a sum greater than 6 is:

P(sum > 6) = P(5+4) + P(4+5) + P(4+4) = (1/4)*(1/4) + (1/4)*(1/4) + (1/4)*(1/4) = 3/16.

The probability of getting a sum of 6 or less is 1 - 3/16 = 13/16. The expected value for Option A is:

E(A) = (3/16)*$8 + (13/16)*(-$2) = $0.25.

Danielle wins $6 if she gets exactly one head. The probability of getting exactly one head in three flips (HHT, HTH, THH) is:

P(exactly one head) = [tex](1/2)^3 + (1/2)^3 + (1/2)^3 = 3/8[/tex].

The probability of not getting exactly one head is 1 - 3/8 = 5/8. The expected value for Option B is:

E(B) = (3/8)*$6 + (5/8)*(-$1) = $1.125.

Comparing the expected values, Option B has a higher expected value than Option A. Therefore, the amount Danielle expects to make by choosing Option B over Option A is:

E(B) - E(A) = $1.125 - $0.25 = $0.875.

Danielle expects to make $0.875 more by choosing Option B.

To find the value of x in the given equation sin(2x+14)=cos(46), we can start by simplifying the equation and setting the angles inside the sin function equal to each other. Solving the resulting equation will yield the value of x, which is 15.

To find the value of x in the given equation sin(2x+14)=cos(46), we can start by simplifying the equation. Since sin and cos are complementary functions, we can rewrite cos(46) as sin(90-46). This gives us sin(2x+14)=sin(90-46).

Next, we can set the angles inside the sin function equal to each other: 2x+14 = 90-46. Solving this equation will give us the value of x.

Subtracting 14 from both sides, we have 2x = 90-46-14. Simplifying further, 2x = 30. Finally, dividing both sides by 2, we find x = 15.

Answer:

c

Step-by-step explanation:

Answer:

f(t) = 5(4)^t

f(3) = 5(4^3) = 5 * 64 = 320

Answer:

y < -2/3x +4

Step-by-step explanation:

The line intersects the y-axis at y=4, so that is the y-intercept.

The line drops 2 units for each 3 units to the right, so the slope is ...

(change in y)/(change in x) = -2/3

The slope-intercept form of the equation for a line is a form you have memorized:

y = mx + b . . . . . . for slope m and y-intercept b

Using the values we read from the graph, the equation of the line is ...

y = -2/3x + 4

The line is dashed, so the inequality does not include points on the line. The solution just includes y-values less than (below) those on the line. Hence the inequality is ...

y < (-2/3)x +4

Answer:

B. √{x} + √{x - 1}

Step-by-step explanation:

As hinted in the question, we have to simplify the denominator.

To understand it easier, let's imagine we have x - y in the denominator.  If we multiply it with x + y we'll get x² - y², right?  Check the next line:

(x - y) (x + y) = x² + xy -xy - y² = x² - y²

If we have the square of those nasty square roots, it will be much simpler to deal with.  So, let's multiply the initial fraction using x+y, but with the real values:

[tex]\frac{1}{\sqrt{x} - \sqrt{x - 1} } * \frac{\sqrt{x} + \sqrt{x - 1}}{\sqrt{x} - \sqrt{x - 1}} = \frac{\sqrt{x} + \sqrt{x - 1}}{(\sqrt{x} )^{2} - (\sqrt{x - 1} )^{2} }[/tex]

Then we simplify:

[tex]\frac{\sqrt{x} + \sqrt{x - 1}}{(\sqrt{x} )^{2} - (\sqrt{x - 1} )^{2} } = \frac{\sqrt{x} + \sqrt{x - 1}}{(x) - (x - 1) } = \frac{\sqrt{x} + \sqrt{x - 1}}{ 1 }[/tex]

So, the answer is B. √{x} + √{x - 1}

Answer: B

Step-by-step explanation:

Answer:

slope= 2  y-intercept= -3

Step-by-step explanation:

the equation y=2x-3 is in slope-intercept form (y=mx+b), and m is the slope and b is the y-int. m=2 and b=-3

Answer:

The conic section that represents the equation 3x + 4y = 12 is a line.

3x + 4y = 12 represents the equation of the line from the given options of the conic section  circle ,ellipse,  parabola,  hyperbola,  line.

" Conic section defined as the curve which is obtained when the plane is cut out from the cone."

According to the question,

Circle : Equation of the circle given by [tex](x-h)^{2} + (y-k)^{2} =r^{2}[/tex]

Conic section circle is not the correct answer.

Ellipse :  Equation of the ellipse given by [tex]\frac{x^{2} }{a^{2}} + \frac{y^{2} }{b^{2}}=1[/tex]

Conic section ellipse is not the correct answer.

Parabola : Equation of the Parabola given by [tex]y^{2} = 4ax[/tex]

Conic section parabola is not the correct answer.

Hyperbola: Equation of the Hyperbola given by [tex]\frac{x^{2} }{a^{2}} - \frac{y^{2} }{b^{2}}=1[/tex]

Conic section hyperbola is not the correct answer.

Line : Equation of the line given by [tex]Ax + By + C =0[/tex]

3x + 4y = 12 represents [tex]Ax + By + C =0[/tex] .

Hence, 3x + 4y = 12 represents the equation of the line.

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[tex]\textbf{Answer}[/tex]

65 degrees

[tex]\textbf{Explanation}[/tex]

Determine which trigonomic function is required

The opposite leg is 13 and the adjacent leg is 6

We will be using tangent function

tan^-1 (13/6)

tan^-1 (13/6) = 65

for this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle. Then, according to the figure we have:

[tex]tg (x) = \frac {13} {6}\\x = arctg (\frac {13} {6})\\x = 65.22485943[/tex]

Round,

[tex]x = 65[/tex] degrees

Answer:

65

Answer:

4.782608696  x  10^10

Step-by-step explanation:

47.83.

To find the result of 330 billion divided by 6.9 billion, we can simplify the question by dividing both numbers by a billion, which gives us 330 divided by 6.9. Now, we perform the division: 330 \/ 6.9 = 47.8260869565. However, since we're dealing with significant figures usually present in population data, we might want to round the answer to a reasonable number of significant digits. So the result would be approximately 47.83.

Answer:

16 x 32

Step-by-step explanation:

If you enlarge by 8 times, you are multiplying each dimension by 8.  2*8=16 and 4*8=32

By multiplying each dimension of the original photograph (2" x 4") by the scale factor (8), we get the dimensions of the enlarged photograph as 16" (length) and 32" (width)

The problem you presented is a simple application of scale factors in math. You need to determine the new dimensions of the enlarged photograph. For a rectangular photograph with original dimensions of 2" x 4", if the photograph is enlarged by a scale factor of eight, we multiply each dimension by the factor 8.

So, for the length: 2" x 8 = 16"

And, for the width: 4" x 8 = 32"

Therefore, the dimensions of the new photograph after enlargement would be 16" by 32".

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Answer:

1/4 ft vertically per 1 ft horizontally, or 3inches per foot

Step-by-step explanation:

Translate these words into symbols:  One point is at (4 ft, 12 in) and the other is at (6 ft, 18 in).  Now find the slope of the line connecting these two points:

As we move from (4 ft, 12 in) to (6 ft, 18 in), x increases by 2 ft and y increases by (1/2) ft.

Thus, the slope of this line is m = rise / run = (1/2 ft) / (2 ft) = (1/4) ft per ft

Answer:

D) 3 inches up per foot across

Step-by-step explanation:

Pretty sure its right

Answer:d

Step-by-step explanation:

d

Follow below steps:

The student asked which statement is true about the value of the expression (6^-n)(6^n). To find the value of this expression, we can use the laws of exponents. These laws state that when we multiply powers with the same base, we add the exponents. Since one exponent is negative and the other is positive but both absolute values of the exponents are equal, their sum will be zero. So, (6^-n)(6^n) simplifies to 6^(n-n), which simplifies further to 6^0. According to the rules of exponents, any number raised to the power of zero is equal to 1. Therefore, the value of the expression is 1 for all values of n.

Answer:

f-1(x)=x-7/3

Step-by-step explanation:

The inverse of f(x) is, [tex]f^{-1}(x)=\frac{x-7}{3}[/tex]

Given function is, [tex]y=f(x)=3x+7[/tex]

Solve for x.

                 [tex]y=3x+7\\\\3x=y-7\\\\x=\frac{y-7}{3}[/tex]

Therefore, inverse function of f(x) is,

                     [tex]f^{-1}(x)=\frac{x-7}{3}[/tex]

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Answer:

36 dream catcherss

Step-by-step explanation:

Jane's production rate:  

1 dream catcher

6 days

Zena's production rate:  

1 dream catcher

4 days

Production rate when working together:  

1

6

+  

1

4

=  

5

12

. This ratio means it will take 12 days to make 5 dream catchers.

Set up a ratio for 15 dream catchers.  

dream catcher

days

=  

5

12

=  

15

d

→ 5d = (12)(15) → 5d = 180 → d = 36

Answer: 36 days

Step-by-step explanation:

Hi, to answer this we have to calculate the production rate of each one, by dividing the number of catchers by the time spent.

Jane: 1/6 dream catcher per day

Zena: 1/4 dream Catcher per day

Adding both results:

1/6 +1/4 =5/12 dream catcher per day (both)

Finally we have to divide the 15 dream catchers needed by the rate (5/12 per day) to obtain the number of days that will take to make 15 dream catchers

x = 15 / (5/12) =36 days.

Feel free to ask for more if needed or if you did not understand something.

Rectangle RECT has a twice larger area than Triangle TRI. The area of Triangle TRI is mn/2 square centimeters, while the area of Rectangle RECT is mn square centimeters.

Comparing the Areas of Triangle TRI and Rectangle RECT:

Step 1: Calculate the Area of Triangle TRI:

The formula for the area of a triangle is (1/2) * base * height.

In this case, the base is m centimeters and the height is n centimeters.

Therefore, the area of Triangle TRI = (1/2) * m * n = mn/2 square centimeters.

Step 2: Calculate the Area of Rectangle RECT:

The formula for the area of a rectangle is length * width.

In this case, the length is n centimeters and the width is m centimeters.

Therefore, the area of Rectangle RECT = n * m square centimeters.

Step 3: Compare the Areas:

Now we have the areas of both shapes:

Triangle TRI: mn/2 square centimeters

Rectangle RECT: mn square centimeters

Observe that the area of Rectangle RECT is exactly twice the area of Triangle TRI.

There are [tex]2^{10}[/tex] possible outcomes when flipping 10 coins.  Of those  [tex] {10 \choose 8} [/tex]  have exactly 8 heads.   So the probability is

[tex]p = \dfrac{ {10 \choose 8} }{ 2^{10} } = \dfrac{10(9)/2}{2^{10}}=\dfrac{45}{1024}[/tex]

Answer: 45/1024

well, let's say we know "r" and also "y", can we get the angle and the rectangular "x"?

[tex]\bf \begin{cases} y=rsin(\theta )\\ x=rcos(\theta ) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y=rsin(\theta )\implies \cfrac{y}{r}=sin(\theta )\implies sin^{-1}\left( \cfrac{y}{r} \right)=\theta[/tex]

and once we know what angle θ is, since x = rcos(θ), we know "r" already, and we know θ as well, so we know "x" as well.

Knowing the radius 'r' and the y-coordinate 'y', we can calculate both, Cartesian and polar coordinates. We calculate 'x' using the Pythagorean Theorem. The angle in polar coordinates is then obtained using this 'x' and 'r' through the arccos function.

In the context of polar coordinates and rectangular coordinates, if we know the radius 'r' and the y-coordinate 'y', we can potentially locate the specific point in the Cartesian plane. However, it's important to note that the conversion between polar and rectangular coordinates typically relies on both r and the angle Ф in polar coordinates and x, y in rectangular coordinates.

The answer to the posed question would be (d), it is possible to get Cartesian coordinates and polar coordinates.

We can get 'x' by using Pythagorean Theorem as x = sqrt(r^2 - y^2).

Similarly, the angle Ф in polar coordinates can be obtained if we know 'r' and 'x' (which we've now calculated) using the formula Ф = arccos(x / r)

Therefore, we can indeed calculate both, Cartesian and polar coordinates using the only 'r' and 'y'.

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Answer:

r = 1/2

Step-by-step explanation:

Each entry is diminished by a factor of 1/2 times the previous entry.

so r = 1/2

The next number in the series is 1 and then the one after that is 1/2 and then 1/4 ...

Answer:

140

Step-by-step explanation:

The arithmetic series is 5, 7, 9, 11, ........., 23.

First u have to determine the no. of terms that can be done by using

Tₙ = [a + (n - 1)d]

Tₙ-------nth term

a---------first term

n---------no.of terms in the series

d---------common difference

here a = 5,d = 2.

let it contain n terms Tₙ= [a + (n-1)d]

Substitute Tₙ, a, and d in the equation

23 = 5 + (n - 1)2

Subtract 5 from each side.

18 = (n-1)2

Divide each side by 2

(n - 1) = 9

Add 1 to each side

n = 9 + 1 = 10

The sum of the arithmetic sequence formula: Sₙ= (n/2)[2a+(n-1)d]

Substitute Sₙ, a, n and d in the equation

Sₙ= (10/2)[2(5) + (10-1)2]

Sₙ= (5)[10 + (9)2]

Sₙ= 5[10 + 18]

Sₙ= 5[28] = 140

Therefore the sum of the arithmetic sequence is 140.

The sum of the arithmetic sequence 5, 7, 9, 11,...,23 is calculated by first finding the number of terms (10 in this case), then applying the formula for the sum of an arithmetic sequence. The sum is 140.

The question is asking to find the sum of an arithmetic sequence consisting of the numbers between 5 and 23, increasing by 2 each time. An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. This is the common difference. In this case, the common difference is 2.

Instead of adding each individual term, we use the formula for the sum of an arithmetic sequence. The formula is S_n = n/2 ( a + l ) where n is the number of terms, a is the first term, and l is the last term.

First, we need to find the number of terms (n). This can be found with the formula n = ( l - a ) / d + 1 where d is the common difference, a is the first term, and l is the last term. In this case, n = (23 - 5) / 2 + 1 = 10.

Therefore, the sum of this sequence is S_10 = 10/2 * (5 + 23) = 140.

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