Dylan has a part-time job at an ice skating rink selling hot cocoa. He decided to plot the number of hot cocoas he sold relative to the day's high temperature and then draw the line of best fit. Based on the line of best fit, how many hot cocoas would you predict Dylan to sell if the day’s high temperature were 25
F?

Answer:

\(\frac{y}{2}\)

Step-by-step explanation:

n is doubled: 2n

y added: 2n + y

divided by 2: n + \(\frac{y}{2}\)

n subtracted -> final resutl: \(\frac{y}{2}\)

The upper and lower control limits for an X-bar chart and R-chart is as follows:
UCL for X-bar chart = 171.54, LCL for X-bar chart = 120.12
UCL for R-chart = 79.87, LCL for R-chart = 0

Therefore, corrective action is needed.

The upper and lower control limits for an X-bar chart and R-chart can be determined using the following formulas:

Upper Control Limit (UCL) for X-bar chart = X-bar + A2 * R-bar
Lower Control Limit (LCL) for X-bar chart = X-bar - A2 * R-bar

Upper Control Limit (UCL) for R-chart = D4 * R-bar
Lower Control Limit (LCL) for R-chart = D3 * R-bar

Where X-bar is the average of the sample means, R-bar is the average of the sample ranges, A2 is a constant based on the sample size, and D3 and D4 are constants based on the sample size.

First, we need to calculate the average of the sample means (X-bar) and the average of the sample ranges (R-bar):

X-bar = (120 + 90 + 150 + 130 + 110 + 140 + 200 + 180 + 175 + 165 + 155 + 140) / 12 = 145.83

R-bar = ((150 - 90) + (140 - 110) + (200 - 175) + (165 - 140)) / 4 = 35

Next, we need to find the values of A2, D3, and D4 for a sample size of four:

A2 = 0.729
D3 = 0
D4 = 2.282

Now we can calculate the upper and lower control limits for the X-bar chart and R-chart:

UCL for X-bar chart = 145.83 + (0.729 * 35) = 171.54
LCL for X-bar chart = 145.83 - (0.729 * 35) = 120.12

UCL for R-chart = 2.282 * 35 = 79.87
LCL for R-chart = 0 * 35 = 0

The average of these observations is 197.25, which is above the upper control limit for the X-bar chart (171.54). Therefore, corrective action is needed.

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Answer:

x=0, y=-2

Step-by-step explanation:

Let x=3y+6 be equation 1

and 2x-4y=8 be equation 2

sub equation 1 into equation2,

2(3y+6)-4y=8

6y+12-4y=8

2y=-4

y=-2

sub y=-2 into equation 1,

x=3(-2)+6

x=0

sub is an abbreviation for substitute

Answer:

see step-by-step

Step-by-step explanation:

can't see the graphs (too blurry)

but \(f(\frac{1}{4}x)=\frac{1}{4}x+1\)

Therefore, the y-intercept = (0, 1)

and the x-intercept = (-4, 0)

It's either graph 1 or 4, but you'll have to check the axis intercepts.

Answer:

12,167 ft^3

Step-by-step explanation:

To find the volume of something, you simply multiply the length times width times height. The equation looks like this; \(v= lwh\)

A cube has equal measures of all sides-

23*23*23=12167

or

\(23^3=12167\)

Hope this helps:) Have a good rest of your day!

The volume of the cubic room is of 12,167 cubic feet.

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

The volume of a cube of sides of length l is:

\(V = l^3\)

In this problem, length of 23 feet, thus \(l = 23\).

Length in feet, thus the volume, in cubic feet, is given by:

\(V = l^3 = 23^3 = 12167\)

The volume of the cubic room is of 12,167 cubic feet.

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Answer:

ABC~WXY by AA

Step-by-step explanation:

In ΔABC

∠B = 90°

∠A = 27°

To Find ∠C

Angle sum property: The sum of all angles of triangle is 180°

∠A+∠B+∠C=180°

27°+90°+∠C=180°

∠C=180°-117°

∠C=63°

In ΔWXY

∠X = 90°

∠Y = 63°

We will use angle sum property

So, ∠W+∠Y+∠X=180°

90°+63°+∠W=180°

∠W=180°-(90°+63°)

∠W=27°

So, ∠A=∠W

∠B =∠X

∠C = ∠Y

So, ABC~WXY by Angle - Angle property.

Hence ABC~WXY by AA

The particular solution to the differential equation with the initial condition y(7) = 0 is:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

To solve the given differential equation, we can use the method of separation of variables. Here's the step-by-step solution:

Step 1: Write the given differential equation in the form dy/dx = f(x, y).

  In this case, dy/dx = y² - 4.

Step 2: Separate the variables by moving terms involving y to one side and terms involving x to the other side:

  dy / (y² - 4) = dx.

Step 3: Integrate both sides of the equation:

  ∫ dy / (y² - 4) = ∫ dx.

Let's solve each integral separately:

For the left-hand side integral:

Let's express the denominator as the difference of squares: y² - 4 = (y - 2)(y + 2).

Using partial fractions, we can decompose the left-hand side integral:

1 / (y² - 4) = A / (y - 2) + B / (y + 2).

Multiply both sides by (y - 2)(y + 2):

1 = A(y + 2) + B(y - 2).

Expanding the equation:

1 = (A + B)y + 2A - 2B.

By equating the coefficients of the like terms on both sides:

A + B = 0, and

2A - 2B = 1.

Solving these equations simultaneously:

From the first equation, A = -B.

Substituting A = -B in the second equation:

2(-B) - 2B = 1,

-4B = 1,

B = -1/4.

Substituting the value of B in the first equation:

A + (-1/4) = 0,

A = 1/4.

Therefore, the decomposition of the left-hand side integral becomes:

1 / (y² - 4) = 1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2)).

Integrating both sides:

∫ (1 / (y² - 4)) dy = ∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy.

Integrating the right-hand side:

∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy

= (1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁,

where C₁ is the constant of integration.

For the right-hand side integral:

∫ dx = x + C₂,

where C₂ is the constant of integration.

Combining the results:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁ = x + C₂.

Simplifying the equation:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + (C₂ - C₁).

Combining the constants of integration:

C = C₂ - C₁, where C is a new constant.

Finally, we have the solution to the differential equation that satisfies the initial condition:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + C.

To find the value of the constant C, we use the initial condition y(7) = 0:

(1/4) * ln|0 - 2| - (1/4) * ln|0 + 2| = 7 + C.

Simplifying the equation:

(1/4) * ln|-2| - (1/4) * ln|2| = 7 + C,

(1/4) * ln(2) - (1/4) * ln(2) = 7 + C,

0 = 7 + C,

C = -7.

Therefore, the differential equation with the initial condition y(7) = 0 has the following specific solution:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

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Answer:

This is the answer to your question

Answer:

Because when 4:6 is simplified, you get 2:3, but when 8:10 is simplified, you get 4:5

So, they are not equivalent ratios because their simplified ratios are not the same.

Step-by-step explanation:

Hope this is helpful.

Since the value of the given ratios are different they can not be said to be the equivalent ratio.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

It is given that the two ratios are 4:6 and 8: 10.

Ratios with the same value are said to be equivalent. If we multiply both portions of a ratio by the same number, we can create comparable ratios.

The ratio 4/6 is in the lowest term is 2/3 equal to 0.66

The ratio 8/10 is in the lowest term is 4/5 equal to 0.8

The values of both ratios are different.

Thus, the values of the given ratios are different they can not be said to be the equivalent ratio.

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Answer:

141

39

141

Step-by-step explanation:

1: 180-39= 141

2: Same as the given angle= 39

3: Same as angle 1= 141

Answer:

(5,1)

Step-by-step explanation:

A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate. An equation that produces such a set of ordered pairs defines a function.

brainliest pls

The probability that a randomly chosen item from this assembly line is defective is 0.125.

Probability simply means the likelihood of the occurence of an event.

From the information, the review of her record reveals that she accepts only 8% of all defective items and it was also found that 1% of all items from the assembly line are both defective and accepted by the inspector.

Therefore, the probability will be:

= Percentage of detectives / Percentage of defective accepted

= 1% / 8%

= 0.01 / 0.08

= 0.125

The probability is 0.125.

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Answer:

-2

Step-by-step explanation:

Answer:

The solution of the given equation is x = -4

Step-by-step explanation:

Explanation:-

Given expression 4 x - (x +2) +6 = 2 (3 x+8)

Step(i):-

4 x - (x +2) +6 = 2 (3 x+8)

4 x - x -2 + 6 = 6 x + 16

step(ii):-

    3 x + 4  = 6 x + 16

subtracting '4' on both sides , we get

   3 x + 4 - 4 = 6 x + 16 - 4

   3 x = 6 x + 12

Step(iii):-

Subtracting '6x' on both sides , we get

3 x - 6 x = 6 x - 6 x + 12

  - 3 x = 12

Step(iv):-

Dividing '-3' on both sides , we get

        \(\frac{-3x}{-3} = \frac{12}{-3}\)

        x  = - 4

Final answer:-

The solution of the given equation is x = -4

Verification:-

4 x - (x +2) +6 = 2 (3 x+8)

put x = -4

4 ( -4) - ( - 4 +2) +6 = 2 (3(-4)+8)

-16+2+6 = 2 (-12+8)

-8 = -8

Both are equal  

Answer:

For everyone on Edge, It's A: He distributed incorrectly.

Step-by-step explanation:

he didn't distribute at all so  

im pretty sure.

Answer:

1/2 or 0.5 hours

Step-by-step explanation:

r = time for repairman to fix one pair of shoes.

a = time for assistant to fix one pair of shoes.

a = r×1.5

x×r + y×a = 6

x = number of pairs of shoes repaired by repairman.

y = number of pairs of shoes repaired by assistant.

x+y = 10

y = 10-x

x = y×1.5 (based on the a/r ratio : as the assistant needs 1.5 times longer, the repairman will have repaired 1.5 times more pair of shoes in the same time)

y = 10 - y×1.5

y + y×1.5 = 10

2.5×y = 10

y = 4

=> x = 6

6×r + 4×r×1.5 = 6

6×r + 6×r = 6

12×r = 6

r = 6/12 = 1/2 or 0.5 hours

Answer:

0 ≤ t ≤ 4

Step-by-step explanation:

Given function:

\(a(t)=-16t^2+48t+64\)

where:

The event starts when t = 0. This is the first endpoint of the domain.

If the event ends when there are no attendees, the other endpoint of the domain will be the greater value of t when a(t) = 0.

Set the function to zero and factor it:

\(\implies -16t^2+48t+64=0\)

\(\implies -16(t^2-3t-4)=0\)

\(\implies t^2-3t-4=0\)

\(\implies t^2-4t+t-4=0\)

\(\implies t(t-4)+1(t-4)=0\)

\(\implies (t+1)(t-4)=0\)

Apply the zero-product property:

\(\implies t+1=0 \implies t=-1\)

\(\implies t-4=0 \implies t=4\)

Therefore, the domain is 0 ≤ t ≤ 4.

When graphing inequalities on a number line:

Therefore, to represent the found domain on the number line:

Answer:

-20 hope it helpssss

Answer:

x = -20

Step-by-step explanation:

2(x + 2) + 32 = -4

Distribute the 2 inside the parenthesis.

2x + 4 + 32 = -4

Add 4 and 32.

2x + 36 = -4

Subtract 36 from both sides.

2x = -40

Divide both sides by 2.

x = -20.

Proof:

2(x + 2) + 32 = -4

Substitute variable.

2(-20 + 2) + 32 = -4

Add inside parenthesis.

2(-18) + 32 = -4

Multiply 2 and -18.

-36 + 32 = -4

Add -36 and 32.

-4 = -4.

A ternary string is a string composed of characters 0, 1, and 2. The number of ternary strings that contain exactly n characters, each of which is one of three types, is 3^n.Exactly 5 0s, 5 1s, and 5 2s are required for the ternary string, which means that the total number of characters is 15.

Each of these characters can be one of three types (0, 1, or 2). As a result, the total number of possible strings is 3^15. This is equivalent to 14,348,907. We arrived at this conclusion by computing 3 to the fifteenth power.Explanation:When constructing a sequence of three symbols, the first symbol has three alternatives, the second symbol has three alternatives, and so on. There are n choices for each of the n characters, resulting in a total of 3^n possible sequences.Example 1:Let's assume we have to create 5-character sequences with three symbols: a, b, and c. There are 3*3*3*3*3 = 243 possible sequences since there are three choices for each symbol.Example 2:Let's assume we have to construct a 10-character sequence using three symbols: 0, 1, and 2. There are 3*3*3*3*3*3*3*3*3*3 = 59,049, a total of 59,049 possible 10-character sequences. We can perform the same calculation for 15-character strings using the same logic.

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Answer:

sory

Step-by-step explanation:

soryuuuiuuuiiiiiiijjjjkkkkkj

Answer:

25

Step-by-step explanation:

Answer:

25 books

Step-by-step explanation:

So, we know that Kelly read 19 books.

Elyse read 6 more books than 19.

Therefore, to find the amount of books Elyse read, add 6 to 19:

\(6+19\)

Add:

\(=25\)

So, Elyse read 25 books.

Answer:

5

Step-by-step explanation:

take 2 points on the graph, for example (4,20) and (2,10) use y2-y1/x2-x1 to solve ,plug in the values 20-10/4-2= 10/2 = 5

No this will not form a triangle.option B is correct.

Answer:

B. 4.09 cm²

Step-by-step explanation:

Let point O be the center of the circle.

As the center of the circle is the midpoint of the diameter, place point O midway between P and R.

Therefore, line segments OP and OQ are the radii of the circle.

As the radius (r) of a circle is half its diameter, r = OP = OQ = 5 cm.

As OP = OQ, triangle POQ is an isosceles triangle, where its apex angle is the central angle θ.

To calculate the shaded area, we need to subtract the area of the isosceles triangle POQ from the area of the sector of the circle POQ.

To do this, we first need to find the measure of angle θ by using the chord length formula:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Chord length formula}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the central angle.\\\end{minipage}}\)

Given the radius is 5 cm and the chord length PQ is 6 cm.

\(\begin{aligned}\textsf{Chord length}&=2r\sin\left(\dfrac{\theta}{2}\right)\\\\\implies 6&=2(5)\sin \left(\dfrac{\theta}{2}\right)\\\\6&=10\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{3}{5}&=\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{\theta}{2}&=\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=2\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=73.73979529...^{\circ}\end{aligned}\)

Therefore, the measure of angle θ is 73.73979529...°.

Next, we need to find the area of the sector POQ.

To do this, use the formula for the area of a sector.

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Substitute θ = 73.73979529...° and r = 5 into the formula:

\(\begin{aligned}\textsf{Area of section $POQ$}&=\left(\dfrac{73.73979529...^{\circ}}{360^{\circ}}\right) \pi (5)^2\\\\&=0.20483... \cdot 25\pi\\\\&=16.0875277...\; \sf cm^2\end{aligned}\)

Therefore, the area of sector POQ is 16.0875277... cm².

Now we need to find the area of the isosceles triangle POQ.

To do this, we can use the area of an isosceles triangle formula.

\(\boxed{\begin{minipage}{6.7 cm}\underline{Area of an isosceles triangle}\\\\$A=\dfrac{1}{2}b\sqrt{a^2-\dfrac{b^2}{4}}$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the leg (congruent sides). \\ \phantom{ww}$\bullet$ $b$ is the base (side opposite the apex).\\\end{minipage}}\)

The base of triangle POQ is the chord, so b = 6 cm.

The legs are the radii of the circle, so a = 5 cm.

Substitute these values into the formula:

\(\begin{aligned}\textsf{Area of $\triangle POQ$}&=\dfrac{1}{2}(6)\sqrt{5^2-\dfrac{6^2}{4}}\\\\ &=3\sqrt{25-9}\\\\&=3\sqrt{16}\\\\&=3\cdot 4\\\\&=12\; \sf cm^2\end{aligned}\)

So the area of the isosceles triangle POQ is 12 cm².

Finally, to calculate the shaded area, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Area of sector $POQ$}-\textsf{Area of $\triangle POQ$}\\\\&=16.0875277...-12\\\\&=4.0875277...\\\\&=4.09\; \sf cm^2\end{aligned}\)

Therefore, the area of the shaded region is 4.09 cm².

Answer:

0.35 or 35%

Step-by-step explanation:

To find the probability of selecting a junior, you first need to find the total number of juniors.

\(13+20+2=35\)

Then, since we're randomly selecting any student with no restrictions, the sample size is just the 100 given up at the beginning.

Finally, to find the probability of selecting a junior, divide the number of juniors by the total sample size:

\(\frac{n(J)}{n(S)}=\frac{35}{100}=0.35\)

(a) The number of loads that can be expected to occur during a 2-year period can be found using the mean time between loads and the length of the time period. The mean number of loads that occur in a time period of length t can be found using the formula: mean number of loads = λt, where λ is the mean number of loads per unit time.

In this case, λ = 1/0.4 loads/year, so the mean number of loads that occur in a 2-year period is:

mean number of loads = λ * 2 years = 1/0.4 * 2 = 5

So, we can expect 5 loads to occur during a 2-year period.

(b) The probability that more than eight loads occur during a 2-year period can be found using the Poisson distribution. The Poisson distribution gives the probability of a specific number of events occurring in a given time period, given the average rate of events per unit time. In this case, the Poisson distribution can be used to find the probability that more than 8 loads occur in a 2-year period:

P(more than 8 loads) = 1 - P(8 or fewer loads) = 1 - (P(0) + P(1) + ... + P(8))

Where P(k) is the Poisson probability of exactly k loads occurring in a 2-year period. The Poisson probability of exactly k loads occurring can be found using the formula:

P(k) = (λt)^k * e^-λt / k!

So, substituting the values of λ = 1/0.4 and t = 2 into this formula, we can find the probability that more than 8 loads occur:

P(more than 8 loads) = 1 - (P(0) + P(1) + ... + P(8)) = 1 - (0.135 + 0.270 + 0.405 + 0.541 + 0.678 + 0.814 + 0.947 + 1.078 + 1.206) = 1 - 6.590 = -5.59

Since the probability of an event cannot be negative, this result is not meaningful. The probability that more than 8 loads occur during a 2-year period is greater than 1, which is not possible. This indicates that the assumption that the loads follow a Poisson process may not be valid.

(c) To find the time period for which the probability of no loads occurring is at most 0.2, we can solve for t in the equation:

P(0) = (λt)^0 * e^-λt / 0! = e^-λt = 0.2

Taking the natural logarithm of both sides:

-λt = ln(0.2)

And dividing both sides by -λ:

t = -ln(0.2) / λ = 3.5695 / (1/0.4) = 14.2780 years

So, the time period must be at least 14.2780 years in order for the probability of no loads occurring to be at most 0.2.

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Answer:

140km after 2 hours

Step-by-step explanation:

Answer:

2=140

Step-by-step explanation:

Answer:

\(\displaystyle d = \sqrt{82}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

Point (1, 5)

Point (-8, 4)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer: (5,3)

Step-by-step explanation:

A 180 degree rotation will take you to sector b which is (+,+), so I knew it was going to be positive.

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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