Stanley is making trail mix out of 10 bags of nuts and 20 bags of dried fruits. He want each new portion of trail mix to be identical, containing the same combination of dried fruits with no bags left over. What is the greatest number of portions of trail mix Stanley can make?​

If the expression 1/2x was placed in the form ax^b where a and b are real numbers, then a + b equal to option (4) -1/2

The given expression is 1/(2x), which can be rewritten as:

1/(2x) = 1/2 × (1/x)

Here, we can see that the expression can be written in the form of ax^b, where a = 1/2 and b = -1.

To see why a = 1/2, notice that 1/2 is the coefficient of (1/x). And to see why b = -1, note that x^(-1) is the exponent on the variable x

So, we have:

1/(2x) = (1/2) × x^(-1)

And, a + b = (1/2) + (-1)

Add the numbers

= -1/2.

Therefore, the correct option is (4) -1/2.

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1. An acute angle is οne that is less than 90 degrees.

An angle smaller than the right angle is called an acute angle. In οther wοrds, the angle which is less than 90 degrees fοrms an acute angle. The pοlygοns such as triangle, parallelοgram, trapezοid, etc. cοnsist οf at least οne acute angle

2. Obtuse angle: A measurement οf an angle that is greater than 90 degrees but less than 180 degrees.

3. A right angle is οne that is exactly 90 degrees.

4. A straight angle is οne that is exactly 180 degrees in length.

5. Adjacent angles are twο angles that share a cοmmοn vertex and a cοmmοn side.

6. A pair οf nοn-adjacent angles fοrmed by the intersectiοn οf twο lines are knοwn as vertical angles. They are οf equal size.

7. Cοmplementary angles are defined as twο angles that add up tο 90 degrees.

8. Twο angles that add up tο 180 degrees are referred tο as supplementary angles.

9. Angles with the same measure are said tο be cοngruent.

10. A linear pair is twο adjacent angles that fοrm a straight line and add up tο 180 degrees.

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The answer is d please

At the end of the year, the expression that shows the total number of students is [tex]22+s[/tex]

An expression is a mathematical phrase that can contain numbers, variables, and operators. It doesn't contain an equal sign (=) or a value.

Mrs. Jeffers started the school year with 22 students. During the school year, another s student joined her class.

The expression that shows the number of students at the end of the year is.[tex]22+s[/tex]

The symbol "+" is an operator that stands for addition, and "s" is a variable that represents the number of students who joined the class.

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The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.

Since we know that,

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

The formula for a 30-60-90 triangle is this:

1) Side opposite to 30 will be value a.

2) Side opposite to 60 will be value a√3

3) Hypotenuse will be 2a.

AB is opposite of the angle with 30 degree measurement.

BC is opposite of the angle with 60 degree measurement.

The sides of an isosceles right triangle are in the ratio,

1:1:√2

where √2 is the hypotenuse.

For the example, BC = 2√2, then AC = 2√2  x √2 = 4.

Therefore, the three pairs are;

1. (AB = 6, BC = 6)

5. (AB = 4, AC = 4√2)

6.(BC = 2√2, AC = 4).

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The complete question is attached below:

The width of the rectangular field is 51 meters

To find the width of the rectangular field, we need to use the formula for the perimeter of a rectangle, which is:

Perimeter = 2 × (length + width)

We are given that the perimeter of the rectangular field is 292 m and the length is 95 m. So, we can plug in these values into the formula and solve for the width:

292 = 2 × (95 + width)

First, we can simplify the right side of the equation:

292 = 190 + 2 × width

Next, we can isolate the variable (width) on one side of the equation by subtracting 190 from both sides:

292 - 190 = 2 × width

102 = 2 × width

Finally, we can solve for the width by dividing both sides by 2:

width = 51 m

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The probability that the first ball is yellow if the second ball is black is 1/14. The correct option is D.

The given question is a classic example of dependent events in probability. As the balls are drawn without replacement, the second event's outcome will depend on the outcome of the first event.

Probability = Number of favorable events/ Total number of events

The probability of the first ball being yellow is [tex](5/15)[/tex], while the probability of the second ball being black is [tex](3/14)[/tex].

Mathematically represented as P(Yellow ball on the first draw) = P(Yellow ball) = [tex]5/15[/tex]

P(Blackball on second draw given Yellow ball on the first draw) = P(Blackball | Yellow ball) = [tex]3/14[/tex]

As both the events are dependent, we need to find the joint probability of both the events, which can be calculated as P(Yellow ball on the first draw and Blackball on the second draw) = P(Yellow ball) × P(Blackball | Yellow ball)

P (Yellow ball on the first draw and blackball on second draw) = [tex](5/15) × (3/14) = 3/42 = 1/14.[/tex]

Therefore, the correct option is D.

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U is a binomial random variable with n trials and probability of success given by 1 - p.

As Y is a binomial random variable with n trials and probability of success given by p. Using the moment-generating functions method, it can be shown that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The binomial distribution is described by two parameters: n, which is the number of trials, and p, which is the probability of success in any given trial. If a binomial random variable is denoted by Y, then:[tex]P(Y = k) = \binom{n}{k}p^{k}(1 - p)^{n-k}[/tex]

The method of generating moments can be used to show that U = n - Y is a binomial random variable with n trials and probability of success given by 1 - p. The moment-generating function of a binomial random variable is given by: [tex]M_{y}(t) = [1 - p + pe^{t}]^{n}[/tex]

The moment-generating function for U is: [tex]M_{u}(t) = E(e^{tu}) = E(e^{t(n-y)})[/tex]

Using the definition of moment-generating functions, we can write: [tex]M_{u}(t) = E(e^{t(n-y)})$$$$= \sum_{y=0}^{n} e^{t(n-y)} \binom{n}{y} p^{y} (1-p)^{n-y}[/tex]

Taking the summation of the above expression: [tex]= \sum_{y=0}^{n} e^{tn} e^{-ty} \binom{n}{y} p^{y} (1-p)^{n-y}$$$$= e^{tn} \sum_{y=0}^{n} \binom{n}{y} (pe^{-t})^{y} [(1-p)^{n-y}]^{1}$$$$= e^{tn} (pe^{-t} + 1 - p)^{n}[/tex]

Comparing this expression with the moment-generating function for a binomial random variable, we can say that U is a binomial random variable with n trials and probability of success given by 1 - p.

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Answer:

$0.02

Step-by-step explanation:

0.60/30

The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.

A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).

The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.

A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:

The formula for the area of a trapezoid is as follows:

Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height

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If e = 12 and the equation is true, then the answer to the equation is 12.

You can solve the equation as before if it has the form axe + b = c, where x is the variable. Addition and subtraction should be "undone" first, followed by multiplication and division.

We insert e = 12 into the equation and check to see if the equation is true to see if the given value of the variable is a solution of the equation 9 = (3/4)e, where e = 12.

9 = (3/4)e

9 = (3/4)(12)

9 = 9

If e = 12 and the equation is true, then the answer to the equation is 12.

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The number of ways of doing both things is N = m × n

Since there are m ways of doing one thing and n ways of doing another, to find how many ways are there to do both, we proceed as follows.

Since there are m ways of doing one thing and n ways of doing another, to find the number of many ways to do both things,we multiply both numbers together.

So, then number of ways of doing both things is N = m × n

So, there are m × n ways of doing both things

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Answer:

x = 10

y = -9

Step-by-step explanation:

x = -3y - 17

2x + 3y = -7

Plug in x

2 (-3y - 17) + 3y = -7

-6y - 34 + 3y = -7

-3y = 27

y = -9

Plug in the value you got for y back into the equation to find the x value

x = -3(-9) - 17

x = 10

Therefore, on average, each cow produced 169.41 ml of milk today.

The average, also known as the arithmetic mean, is a statistical measure that is calculated by adding together a set of numbers and then dividing the sum by the total number of values in the set. The result is a single value that represents the central tendency of the data set.

Given by the question.

To find the average amount of milk produced by each cow, we need to divide the total amount of milk by the number of cows.

Average milk produced by each cow = (Total milk produced)/ (Number of cows)

Total milk produced = 2090 ml + 780 ml = 2870 ml

Number of cows = 17

Therefore,

Average milk produced by each cow = 2870 ml/17

= 169.41 ml

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To calculate the product of two random variables that follows the normal distribution with mean 0 and variance 1 by using the covariance formula

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Given that two random variables follow a normal distribution with mean 0 and variance 1.

Let X and Y be two independent normal random variables such that X ~ N(0,1) and Y ~ N(0,1)

Now, The expected value of the product of two random variables is given by;

E[XY] = E[X]E[Y] + Cov(X,Y)

Where E[X] and E[Y] are the means of the two random variables X and Y respectively.

Cov(X, Y) is the covariance between the two random variables, which can be calculated using the formula;

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

Now, E[X] = E[Y] = 0 as both have a mean of 0.

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

⇒ E[XY] = the expected value of the product of X and Y.

As X and Y are independent, their covariance will be zero, which implies;

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Thus, we can calculate the product of two random variables that follow a normal distribution with mean 0 and variance 1 using the above formula for covariance.

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Answer: This statement is known as the Law of Sines and can be proven using trigonometry and the properties of similar triangles.

Consider a triangle ABC with sides of lengths a, b, and c opposite to the angles A, B, and C respectively. Let's draw an altitude from vertex A to side BC, splitting side BC into two segments: BD of length x and CD of length c-x.

Using the Pythagorean theorem, we can write:

a^2 = x^2 + h^2 (1)

b^2 = (c-x)^2 + h^2 (2)

where h is the length of the altitude from A to BC.

Dividing equation (1) by sin^2(A) and equation (2) by sin^2(B), we get:

a^2 / sin^2(A) = x^2 / sin^2(A) + h^2 / sin^2(A)

b^2 / sin^2(B) = (c-x)^2 / sin^2(B) + h^2 / sin^2(B)

Since angles A and B are complementary (i.e. A + B = 90 degrees), we have sin(A) = cos(B) and sin(B) = cos(A). Substituting these identities and rearranging the equations, we get:

a^2 / sin(A) = x / cos(B) + h / sin(B)

b^2 / sin(B) = (c-x) / cos(A) + h / sin(A)

Multiplying both equations by sin(A)sin(B), we obtain:

a^2 sin(B) = x sin(A) cos(B) + h sin(A)

b^2 sin(A) = (c-x) sin(B) cos(A) + h sin(B)

Now, we use the fact that h = a sin(B) = b sin(A), which follows from the definition of sine as opposite/hypotenuse. Substituting this into the above equations and simplifying, we get:

a / sin(A) = 2R

b / sin(B) = 2R

c / sin(C) = 2R

where R = a/(2sin(A)) = b/(2sin(B)) = c/(2sin(C)) is the radius of the circumcircle of triangle ABC. This is the Law of Sines in its usual form.

From this, we can see that the ratio of the sines of any two angles in a triangle equals the ratio of the lengths of their opposite sides, as required.

Step-by-step explanation:

Answer:

[tex]\frac{m}{11}[/tex]

Step-by-step explanation:

To write the given expression as a fraction, put m in the numerator and 11 in the denominator as shown: [tex]\frac{m}{11}[/tex]

This would be the quotient of m and 11 expressed as a fraction!

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Answer: x=1

Step-by-step explanation:

Vertical angles mean they are equal to each other. So first you would set the two equations equal to each other.

7x+26=4x+29

Then subtract 4x from both sides.

7x+26−4x=29

combine 7x and −4x to get 3x.

3x+26=29

Then subtract 26 from both sides.

3x=29−26

subtract 26 from 29 to get 3.

3x=3

Lastly divide both sides by 3.

3/3x=3/3

Divide 3 by 3 to get 1.

x=1

The value of ML in the given quadrilateral which is a trapezoid is 58 units.

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

Trapezoids are defined differently by different people. A trapezoid can have one and only one pair of parallel sides, according to one school of mathematics, whereas another contends that a trapezoid can have several pairs of parallel sides. If we take into account the second definition, then a parallelogram is also a trapezoid under that definition.

We know that, A median on a trapezoid will be parallel to the bases, with a length equal to the sum of the bases divide by 2.

Thus,

45 = 3x + 11 + 10x - 12 / 2

45 = 13x - 1/ 2

90 = 13x - 1

91 = 13x

x = 7

Substitute the value of x in ML:

ML = 10x - 12

ML = 10(7) - 12

ML = 70 - 12

ML = 58

Hence, the value of ML in the given quadrilateral which is a trapezoid is 58 units.

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The total number of students which attend the art class is 52 which is 89.75 of the total enrolled students that is 58.

A Latin word with the meaning "out of one hundred" is percentage.

Working with parts of 100 is much easier than working with thirds, twelfths, and other fractions, especially since many fractions lack a consistent (non-recurring) decimal equivalent.

Significantly, this also makes comparing percentages more simpler than comparing fractions with various denominators. This contributes to the widespread usage of the metric measuring system and decimal currencies.

Total students enrolled for art class = 58

Percentage of cancelled students = 10.3%

Then, Percentage of non-cancelled students = 100 - 10.3 = 89.7%

So,

Attended students = 89.7% of 58.

= 89.7*58 / 100

= 52.06

= 52 (approx)

Thus, the total number of students which attend the art class is 52 which is 89.75 of the total enrolled students that is 58.

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The exponential equation that fits the data points (0,35), (1,50), (2,100), (3,200), and (4,400) is y = 35 * (10/7)^x.

To find an exponential equation that fits the given data points, we can use the general form of an exponential equation:

y = a * b^x

where y is the dependent variable (in this case, the second coordinate of each data point), x is the independent variable (the first coordinate of each data point), a is the initial value of y when x is 0, and b is the growth factor.

Using the given data points, we can create a system of equations:

35 = a * b^0

50 = a * b^1

100 = a * b^2

200 = a * b^3

400 = a * b^4

The first equation tells us that a = 35, since any number raised to the power of 0 is 1. We can then divide the second equation by the first equation to get:

50/35 = b^1

Simplifying, we get:

10/7 = b

We can now substitute a = 35 and b = 10/7 into the remaining equations and solve for y:

y = 35 * (10/7)^x

This is the exponential equation that fits the given data points. We can use it to find the value of y for any value of x. This equation gives us a way to predict the value of y for any value of x.

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Answer: $318/mo

Step-by-step explanation:

First, we get the remainder, which is the difference between $9, 632 and $2,000. That gives us $7, 632.

Then, since we know she will pay in 24 months, we assume she pays the same amount each month and divide $7, 632 by 24 = $318/mo

these are the whole statements: Cosine function has a 24-period period. The cosine function's midline has the equation y = 19.25. The cosine function has a 15.25 amplitude.

A mathematical equation, such as 6 x 4 = 12 x 2, states that two amounts and values are equal. two. Countable noun. A scenario known as an equation means that two or more components must be taken into account in order to comprehend or understand the overall situation.

Midline = (34.5 Plus 4) / 2 (34.5 + 4) = 19.25 Maximum value plus Minimum value

As a result, the following equation represents the data's model for the midline of a cosine function:

y = 19.25

The biggest deviation from the function's midline is its amplitude in the cosine function. The maximum amount of v(x) was 34.5 cm/s, and the minimum is 4 cm/s, according to the data provided. The cosine function used to model the data has the following amplitude:

Amplitude is calculated as (highest value – minimum values) / 2 (or 34.5 - 4) / 2 (or 15.25).

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Answer:

f(x) = (5/6)x - (1/4)

f(-8) = (5/6)(-8) - (1/4)

f(-8) = (5/3)(-4) - (1/4)

f(-8) = (-20/3) - (1/4)

f(-8) = (-80-3)/12

f(-8) = -83/12

Answer:

So 3 blue buckets and 4 white buckets were purchased

Step-by-step explanation:

We can solve this by algebra

Let B = number of blue buckets bought

Let W = number of white buckets bought

Total buckets bought:
B + W = 7    (1)

Each blue bucket can hold 2 gallons of water
So B blue buckets can hold 2B gallons of water

Each white bucket can hold 5 gallons of water
So W white buckets can hold 5W gallons of water

Totally they can hold
2B + 5W gallons

We are given that they both can hold  26 gallons of water

So our second equation is
2B + 5W = 26   (2)

By eliminating one of the variable terms we can solve for the other variable term

Let's eliminate the term for variable B

Multiply equation (1) by 2

(1) x 2 ==> 2(B + W) = 2(7)

2B + 2W = 14    (3)

Subtract (3) from (2); B terms are same so they cancel out

(2) - (3):
2B + 5W = 26    [tex]\bold{-}[/tex]
2B + 2W = 14
---------------------
0    +  3W = 12
------------------------

3W = 12
W = 12/3

W = 4

Substitute W= 4 in equation 1
B + W = 7
=> B + 4 = 7

B = 3

So 3 blue buckets and 4 white buckets were purchased

The parabolic trajectory of the falling prey can be described by the equation y = 228 – x2/57, where y is the height above the ground and x is the horizontal distance traveled in meters. In this case, the prey was dropped at a height of 228 m and flying at 19 m/s. To calculate the total distance traveled by the prey, we can use the equation for the parabola to solve for x.

We can rearrange the equation y = 228 – x2/57 to solve for x, which gives us[tex]x = √(57*(228 – y))[/tex]. When the prey hits the ground, the height (y) is 0. Plugging this into the equation for x, we can calculate that the total distance traveled by the prey is[tex]x = √(57*(228 - 0)) = √(57*228) = 84.9 m.\\[/tex] Expressing this answer to the nearest tenth of a meter gives us the final answer of 84.9 m.

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The time in hours which it will take them for working together for terri is about 1.71 hours.

Inverse Proportion: When two quantities are related in such a way that the product of one quantity with the reciprocal of the other quantity remains constant, it is said to be in inverse proportion.

Let's calculate their working rate:

Terri takes 3 hours to complete the painting of her living room, so she can paint her living room in [tex]\frac{1}{3} hours[/tex]

Angela takes 4 hours to complete the painting of the living room, so she can paint her living room in [tex]\frac{1}{4} hours[/tex]

If both work together, then the time taken to complete the work will be less than the time taken by each of them individually.

To find the time taken by both working together, we will add their rates.

Terri's work rate = [tex]\frac{1}{3} hours[/tex]

Angela's work rate = [tex]\frac{1}{4} hours[/tex]

Work rate when working together = Terri's rate + Angela's rate= [tex]\frac{1}{3} + \frac{1}{4} = \frac{7}{12}[/tex]

Thus, both will take [tex]\frac{12}{7} = 1.71 hours[/tex] approximately to complete the painting of the living room when they work together.

Therefore, the time in hours is about 1.71 hours.

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Answer:

8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

When n = 1:

n² + 7 = 1² + 7 = 8

When n = 2:

n² + 7 = 2² + 7 = 11

When n = 3:

n² + 7 = 3² + 7 = 16

When n = 4:

n² + 7 = 4² + 7 = 23

When n = 5:

n² + 7 = 5² + 7 = 32

When n = 6:

n² + 7 = 6² + 7 = 43

Therefore, the first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Answer:

When n = 1, n² + 7 = 1² + 7 = 8

When n = 2, n² + 7 = 2² + 7 = 11

When n = 3, n² + 7 = 3² + 7 = 16

When n = 4, n² + 7 = 4² + 7 = 23

When n = 5, n² + 7 = 5² + 7 = 32

When n = 6, n² + 7 = 6² + 7 = 43

The first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

ᓚᘏᗢ

hope u have a good day man

The calculation shows that 9,000 scientists have seen the deep ocean through Alvin's windows; and

a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

1) If on each of the 4,500 dives Alvin carried a new pilot and two new scientists, then the total number of scientists who have seen the deep ocean through Alvin's windows is:

4,500 dives x 2 scientists per dive = 9,000 scientists

Therefore, 9,000 scientists have seen the deep ocean through Alvin's windows.

2) To calculate the total number of people who traveled in Alvin, we can add the number of pilots and scientists on each dive and multiply by the number of dives:

4,500 dives x (1 pilot + 2 scientists)

= 4,500 x 3

= 13,500 people

Therefore, a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

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