Please help me out with my math!

Answer:

Step-by-step explanation:

a) The function to represent the scenario is f(x) = 56 - 8x, where x is the number of sips Anna takes.

b) Anna can take 7 sips before she needs to refill.

c)

The graph of the function is given below:

\begin{center}

\begin{tikzpicture}

\begin{axis}[

   axis lines = left,

   xlabel = $x$,

   ylabel = {$f(x)$},

   ymin = 0,

   ymax = 56,

   xtick = {0,1,2,3,4,5,6,7},

   ytick = {0,8,16,24,32,40,48,56}

]

\addplot[

   domain=0:7,

   samples=2,

   color=black,

]

{56 - 8*x};

\end{axis}

\end{tikzpicture}

\end{center}

d) The domain of the function in set notation is {0,1,2,3,4,5,6,7}.

Answer:

Not a function because an output has two different inputs

Step-by-step explanation:

Answer:

blip

Step-by-step explanation:

blipgg

Answer:

Step-by-step explanation:

2x + 20° = 3x - 10° ( being corresponding angles )

3x - 2x = 20° + 10°

x = 30°

mineral física cuántica que es la luz que me sirve para apagar bu j

Answers:

\((f \circ g)(x) = \sqrt{\frac{5x-3}{x-1}}\\\\\\(g \circ f)(x) = \frac{1}{2\sqrt{4x+5}-2}\\\\\)

=========================================================

Work Shown for part 1

\((f \circ g)(x) = f(g(x))\\\\f(x) = \sqrt{4x+5}\\\\f(g(x)) = \sqrt{4*g(x)+5}\\\\f(g(x)) = \sqrt{4*\frac{1}{2x-2}+5}\\\\f(g(x)) = \sqrt{\frac{4}{2x-2}+5}\\\\f(g(x)) = \sqrt{\frac{4}{2x-2}+5*\frac{2x-2}{2x-2}}\\\\f(g(x)) = \sqrt{\frac{4}{2x-2}+\frac{5(2x-2)}{2x-2}}\\\\f(g(x)) = \sqrt{\frac{4+5(2x-2)}{2x-2}}\\\\f(g(x)) = \sqrt{\frac{4+10x-10}{2x-2}}\\\\f(g(x)) = \sqrt{\frac{10x-6}{2x-2}}\\\\f(g(x)) = \sqrt{\frac{2(5x-3)}{2(x-1)}}\\\\f(g(x)) = \sqrt{\frac{5x-3}{x-1}}\\\\\)

----------------------------------

Work Shown for part 2

\((g \circ f)(x) = g(f(x))\\\\g(x) = \frac{1}{2x-2}\\\\g(f(x)) = \frac{1}{2*f(x)-2}\\\\g(f(x)) = \frac{1}{2\sqrt{4x+5}-2}\\\\\)

We could optionally rationalize the denominator, but I think that is just extra busy work in my opinion.

The value of x for which (f - g)(x) = 0 is x = 12.

To find the value of x for which (f - g)(x) = 0, we need to subtract g(x) from f(x) and set the resulting expression equal to zero. Let's perform the subtraction:

(f - g)(x) = f(x) - g(x)

= (16x - 30) - (14x - 6)

= 16x - 30 - 14x + 6

= 2x - 24

Now, we can set the expression equal to zero and solve for x:

2x - 24 = 0

Adding 24 to both sides:

2x = 24

Dividing both sides by 2:

x = 12

Therefore, the value of x for which (f - g)(x) = 0 is x = 12.

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Answer:

2y=3x=-4

Step-by-step explanation:

grouping like terms

y+ly =4x-x=-4

2y=3x=-4

If tan(x) = -3/2 and x terminates in quadrant II, then sin(x) = -3/√13, cos(x) = -2/√13. Using double angle formulas, we can find that sin(2x) = -24/13, cos(2x) = 5/13, and tan(2x) = -24/5.

We can start by drawing a right triangle in quadrant II with a reference angle α, such that tan(α) = 3/2. Then, since x terminates in quadrant II, we have x = π - α. Using the Pythagorean theorem, we find that the adjacent side of the triangle is -2 and the hypotenuse is √13. Therefore, sin(x) = -3/√13 and cos(x) = -2/√13.

Next, we can use double angle formulas to find sin(2x), cos(2x), and tan(2x). Specifically, we have:

sin(2x) = 2sin(x)cos(x) = 2(-3/√13)(-2/√13) = -24/13

cos(2x) = cos²(x) - sin²(x) = (-2/√13)² - (-3/√13)² = 5/13

tan(2x) = (2tan(x))/(1 - tan²(x)) = (2(-3/2))/(1 - (-3/2)²) = -24/5

Therefore, we have found that sin(2x) = -24/13, cos(2x) = 5/13, and tan(2x) = -24/5.

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Yes, you can find the standard error now by taking the standard deviation divided by the square root of the sample size.

The standard deviation in a data set is the mean deviation of the data from their mean.

For sample size n for a data set with data points X1, X2, X3……..Xn for exact standard deviation:

1. Calculates the arithmetic mean M of the set data by adding them all and dividing by n.

M = ( X1+X2+ X3+…..+Xn) / n

2. Calculate the deviation (D) for each data point from the mean M

D = (Xi-M) for all

3. Squaring and sum of all deviations, sum of squares (SS)

4. Divide SS by n.This quantity is the sample variance V

5. Take the square root of V.

6. This quantity is the sample standard deviation, SD.

There are some specific terms and issues to consider. If you are estimating the standard deviation of a population from a sample and the population mean $ is not known, M serves as an unbiased estimate of $. Again, SS is divided by (n-1), not n.

The resulting standard deviation is an unbiased estimate of the population standard deviation based on the sample size, n. If the population mean is known, use that mean instead of the sample mean. , and the SD of the sample is only calculated for n through SS dives.

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The unknown measures of the congruence figure are

In polygon PQRS

angle Q = 94 degrees

In polygon WXYZ

WX = 15 cm

RS = 8 cm

A congruence polygon is a polygon that can be divided into congruent triangles. In other words, a congruence polygon is a polygon that can be divided into smaller triangles that are all the same size and shape.

To form a congruence polygon, the polygon must be decomposed into triangles that have the same side lengths and angle measures.

In polygon PQRS

angle Q = angle x = 94 degrees

In polygon WXYZ

WX = PQ = 15 cm

RS = YZ = 8 cm

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When a rectangle is rotated about the y-axis, it creates a solid shape known as a cylindrical shell or a hollow cylinder.

When a rectangle is rotated about the y-axis, each point on the rectangle traces a circular path.  

The resulting shape is a solid formed by the collection of these circular paths, creating a cylindrical shell or a hollow cylinder.

The height of the cylinder corresponds to the length of the rectangle, while the circumference of the cylinder corresponds to the width of the rectangle. The rotation about the y-axis gives the shape a cylindrical appearance, with the y-axis running through the center.

This shape is often used in calculus and geometry to calculate volumes and solve related problems. It is important to note that the rotation about the y-axis assumes that the longer side of the rectangle is aligned parallel to the y-axis.

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When a rectangle is rotated about the y-axis, it creates a solid shape known as a cylindrical shell or a hollow cylinder.

When a rectangle is rotated about the y-axis, each point on the rectangle traces a circular path.  

The resulting shape is a solid formed by the collection of these circular paths, creating a cylindrical shell or a hollow cylinder.

The height of the cylinder corresponds to the length of the rectangle, while the circumference of the cylinder corresponds to the width of the rectangle. The rotation about the y-axis gives the shape a cylindrical appearance, with the y-axis running through the center.

This shape is often used in calculus and geometry to calculate volumes and solve related problems. It is important to note that the rotation about the y-axis assumes that the longer side of the rectangle is aligned parallel to the y-axis.

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Answer:

56????

Step-by-step explanation:

Yes, monotone is a sequence.

We say that a sequence (xn) is increasing if xn ≤ xn+1 for all n and strictly increasing if xn < xn+1 for all n.

Similarly, we define decreasing and strictly decreasing sequences. Sequences which are either increasing or decreasing are called monotone.

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Answer:

a

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

m= 2,5 / 0-(4) simplify (-3,-4) and then divide two negative values to make it positive 3/4

Answer: You want to know how many hours he was reading per week. 5/6 * 3 = 15/6 Hours = 5/2 Hours = 2 Hours 30 minutes.

150 minutes

Step-by-step explanation:

5/6 = 50/60. 60 min in an hour. so 5/6 would mean 50 min of 60. he spent 50 minutes each day reading. now since it says 3 days, youd multiply that by 3. ultimately, youd get 150 min in total.

Answer:

After the third bounce the ball reaches a height of less than 50cm.

Step-by-step explanation:

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, and it's called common ratio. The nth term of a geometric sequence is given by:

\(A_n = A_0(r)^{n}\)

In which \(A_0\) is the first term and r is the common ratio.

A ball is dropped from a height of 5m.

This means that \(A_0 = 5\)

After each bounce it rises to 35% of its previous height.

This means that \(r = 0.35\)

Thus

\(A_n = A_0(r)^{n}\)

\(A_n = 5(0.35)^{n}\)

After how many bounces does the ball reach a Height of less than 50cm?

50cm = 0.5m. This is n for which \(A_n = 0.5\). Thus

\(A_n = 5(0.35)^{n}\)

\(0.5 = 5(0.35)^{n}\)

\((0.35)^n = \frac{0.5}{5}\)

\((0.35)^n = 0.1\)

\(\log{(0.35)^n} = \log{0.1}\)

\(n\log{0.35} = \log{0.1}\)

\(n = \frac{\log{0.1}}{\log{0.35}}\)

\(n = 2.19\)

Rounding up:

After the third bounce the ball reaches a height of less than 50cm.

Yes , the integer k is divisible by 4 and statement (1) alone is sufficient to determine that k is divisible by 4.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

To determine if the integer k is divisible by 4, let's analyze the given statements:

Statement (1): 8k is divisible by 16.

This means that 8k is a multiple of 16. Since 16 is divisible by 4, we can conclude that k must be divisible by 4 as well. Therefore, statement (1) alone is sufficient to determine that k is divisible by 4.

8k = 16

k = 2

b)

This statement does not provide direct information about the divisibility of k by 4. While 12 is divisible by 4, the fact that 9k is divisible by 12 does not guarantee that k itself is divisible by 4.

9k = 12

k = 12/9

k = 4/3

So , it is not an integer

In conclusion, statement (1) alone is sufficient to determine that k is divisible by 4. Statement (2) is not sufficient on its own.

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If the probability of rolling three 7s in a row with a pair of dice is 0.0046, then this a independent event probability here

The probability of rolling three 7s in a row with a pair of dice is an example of an "independent event" probability, because each roll of the dice is independent of the previous rolls.

To calculate this probability, we can use the formula for the probability of independent events:

P(A and B and C) = P(A) x P(B) x P(C)

where P(A) is the probability of event A, P(B) is the probability of event B, and P(C) is the probability of event C.

In this case, the probability of rolling a 7 on a single roll of a pair of dice is 1/6, since there are 6 possible outcomes (1, 2, 3, 4, 5, or 6) on each die, and only one of those outcomes (rolling a 6) will not result in a sum of 7.

Therefore, the probability of rolling three 7s in a row is:

P(7 and 7 and 7) = (1/6) x (1/6) x (1/6) = 1/216

This is equivalent to approximately 0.0046, or 0.46%, as stated in the question.

Therefore, the type of probability in this case is an "independent event" probability.

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The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true so, here The probability of the type I error.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true so, here The probability of the type I error.

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The equation of the vertical line passing through the point (3,0) is x = 3. This means that all the points on the line have an x-coordinate equal to 3, and can have any y-coordinate.

"x = constant," where "constant" is the x-coordinate of any position on the line, is how a vertical line is expressed. All locations on the Cartesian plane with x-coordinates equal to the constant value and any y-coordinate are represented by the equation x = constant.

For instance, x = 3 is the equation for the vertical line going through the coordinates (3, 0). As a result, any y-coordinate is possible at any place along the line, and every point's x-coordinate is equal to 3.

A vertical line is a line that runs perpendicular to the Y-axis in a coordinate field. It runs in a straight path from top to bottom and vice versa. The x-coordinate at every location along this line will be equal.

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Jonathan made $228 in these two days of working on Monday and Tuesday.

Fractions indicate pieces of a whole or group of objects. A fraction is divided into two pieces. The numerator is the number at the top of the line. It specifies how many equal pieces of the total or collection are taken. The number below the line is referred to as the denominator. It displays the total number of equal portions into which the whole is divided or the total number of the same objects in a collection.

Given that he makes $16 per hour

On Monday he made =  5 1/2 × 16

                                    = $88

On Tuesday he made = 8 3/4  × 16

                                     = $140

Total money he made = 140 + 88

                                     = $228

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Answer:

42√3

Step-by-step explanation:

4√27 = 4√(9)(3) = 12√3

6√75 = 6√(25)(3) = 30√3

12√3 + 30√3 = 42√3

Answer:

If I did my math right your answer would be $2376

I really hope you get this right. I apologize if I'm wrong

Answer:

Step-by-step explanation:

8.5

Using Cosine law,

the angle between two shortest sides of triangle is 85.1°..

We have provided that,

A garden has triangular shape.

let "AB" , "BC" , "CA" be sides of triangular shape garden and

we have the sides of triangle are 475 feet , 595 feet and 401 feet i.e AB = 475 , AC = 595 ,

BC= 401

we have to measure of angle between two shortest sides i.e angle between side AB and BC

let x degree be an angle between two shortest sides of triangle .

Using cosine rule ,

(AC)² = (BC)² + (AB )² - 2 AB×BC Cosx

=> (595)² = (401)² + ( 475)² - 2× 475 ×401 Cosx

=> 2(475×401) Cosx = (401)² + (475)² - (595 )²

=> 2 ( 475×401) Cosx = 32401

=> Cosx = 0.085

=> x = cos⁻¹(0.085) = 85.1°

Hence, the angle between two shortest sides of triangle is 85.1°

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