Digital genius manufactures a cell phone charging pad that can fully charge any cell phone that is placed on it in 15 minutes. the analytics department determined that at a price of $103.00 each, the demand would be 6 thousand pads, and at $53.00 each, the demand would be 16 thousand pads. based on the assumption that a linear relationship exists between price and demand, the price-demand equation is given by where x is the number of thousands of pads in demand. at what price point should they sell the pads to have a demand of 14 thousand pads?

x questions are the leaves and 4 of the following words in sentence of your own experience are the plants that are the plants that are the plants that are the plants that are

Answer:

Step-by-step explanation:

The formula for calculating the time it will take for an investment to reach a certain amount given a rate of return and regular withdrawals is:

Time = (ln(Final Balance/Initial Balance))/(ln(1 + Rate of Return))

In this case, the Initial Balance is $100,000, the Final Balance is $0, and the Rate of Return is 2.66%.

Time = (ln(0/100000))/(ln(1 + 0.0266))

Time = (-11.51)/(0.026101)

Time = -440.17

Since the time is given in years, we need to round the answer to the nearest year.

Answer: It will take 440 years for the account to have a balance of $0.

The expression 2x cos 6x can be rewritten using product to sum identities as 1/2(cos(8x) + cos(-4x))

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

The product to sum identities we are going to need in this case is given by the formula:

cos(a) cos(b) = 1/2 (cos(a+b) + cos(a-b))

Since we have cos 2x cos 6x. Thus:

cos 2x cos 6x = 1/2 (cos(2x+6x) + cos(2x-6x))

                       = 1/2 (cos(8x) + cos(-4x))

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Ella has 5.7 pounds of flour, and needs 0.6 of a pound of flour for each cake. This mean that she can bake a total of 9 cakes.

Step 1: Ella has 5.7 pounds of flour

Step 2: Each cake requires 0.6 of a pound of flour

Step 3: 5.7/0.6 = 9.5 (rounded down to 9)

Step 4: Ella can bake 9 cakes

Ella has 5.7 pounds of flour which she wants to use for baking cakes. Each cake requires 0.6 of a pound of flour, so to figure out how many cakes she can make, we need to divide the amount of flour she has by the amount of flour needed for one cake. 5.7/0.6 = 9.5 (rounded down to 9), so Ella can bake 9 cakes. This is because the 0.5 of a pound of flour leftover is not enough to make an entire cake, so it is discarded. This means that Ella can make 9 cakes with the 5.7 pounds of flour she has.

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For two numbers to be proportional, they need to be directly increasing or decreasing in a constant ratio.

If this drawing is proportional, we can see that 12 was divided by 2 to get 6. We can do the same to 8.

8 ÷ 2 = 4

The width of the new drawing is 4.

It can be concluded that -

A table drawn up to show the distribution of the frequency of occurrence of a given characteristic according to some specified set of class intervals.

Given is that each day for three weeks, Kenisha records the number of eggs her chickens lay. The frequency table attached at the end shows her data.

[1] -

Number of days for which layed eggs are 5 or more -

5 + 5 + 2 = 12

[2] -

The greatest number of eggs laid down are equivalent to 7.

Therefore, it can be concluded that -

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The total balance in John's account after depositing his paycheck is, 800.47.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The balance in John's account before depositing his paycheck = 249.50

And, He deposit 550.97 in his account.

Here, The balance in John's account before depositing his paycheck = 249.50

Hence, The total balance in John's account after depositing his paycheck is,

⇒ 249.50 + 550.97

⇒ 800.47

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In the right triangle the value of x is solved to be  4

The figure attached is a right triangle and the value of x can be worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The problem is described in a right angle triangle as below

hypotenuse = x

adjacent = 10 miles

The value of x is calculated using cos, CAH

cos 60 = Adjacent / hypotenuse

cos 60 = 2 / x

x = 2 / cos 60

x = 4

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The number of times an analog wave is measured each second during an analog-to-digital conversion is known as the sampling rate. Generally, the sampling rate should be at least twice the highest frequency present in the signal, in order to accurately capture the signal in the digital domain.

An analog-to-digital conversion is the process of converting an analog signal (such as a sound wave or radio wave) into a digital signal. The number of times an analog wave is measured each second during the conversion process is known as the sampling rate. In order to accurately capture the signal in the digital domain, the sampling rate should generally be at least twice the highest frequency present in the signal. The higher the sampling rate, the more accurately the signal will be recorded. For example, CD quality audio has a sampling rate of 44.1 kHz, meaning that 44,100 samples are taken of the analog signal each second.

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The inverse function of tangent (tan^-1) is also known as arctangent. The domain of arctangent function is all real numbers and its range is (-π/2, π/2).

The tangent function, tan(x), is defined for all real numbers x, but it's not defined when x = (nπ + π/2), where n is an integer. So the domain of the tangent function is all real numbers except (nπ + π/2), where n is an integer.

When we take the inverse of a function, we switch the roles of the domain and range, so the domain of the tangent function becomes the range of the inverse function and the range of the tangent function becomes the domain of the inverse function. The range of the tangent function is all real numbers, but it is not defined for (nπ + π/2), where n is an integer. So the domain of the arctangent function is all real numbers except (nπ + π/2), where n is an integer.

The range of arctangent function is (-π/2, π/2) because the range of arctangent function is the set of all possible values of the input of tangent function for which it is defined.

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a. The sample mean for U is 21.55 and the sample mean for F is 8.39.

b. sample median for U is 17 and the sample median for F is 8.

c. trimmed mean for U is 17 and the trimmed mean for F is 7.95.

d. trimmed percentage for U is 18.18% and the trimmed percentage for F is 13.33%.

a) Sample mean can be calculated by adding values and dividing the sum by the number of the values.

< Strong > Mean(U) < / Strong > =

[tex]\frac{6.0 +5.0 + 11.0 + 33.0 + 4.0+5.0+80.0+18.0 + 35.0+17.0+23.0}{11}[/tex] = 21.55

< Strong > Mean(F) < / Strong > =  [tex]\frac{2.0 + 15.0 + 12.0 + 8.0 + 8.0 + 7.0 + 6.0 + 19.0 + 3.0+9.8+22.0+9.6+2.0+2.0+0.5}{15}[/tex] = 8.39

b) Sample median is the middle value of a sorted sample:

Sorted(U)= [ 4.,  5.,  5.,  6., 11., 17., 18., 23., 33., 35., 80.]

Sorted(F)=[ 0.5,  2. ,  2. ,  2. ,  3. ,  6. ,  7. ,  8. ,  8. ,  9.6,  9.8, 12. , 15. , 19. , 22.]

Median(U)=17, which is the 6th (middle) value

Median(F)=8, which is the 8th (middle) value

c) If we delete the smallest and largest observation, we have:

U= [  5.,  5.,  6., 11., 17., 18., 23., 33., 35., ]

F= [ 2. ,  2. ,  2. ,  3. ,  6. ,  7. ,  8. ,  8. ,  9.6,  9.8, 12. , 15. , 19. ]

Using the above equation for the new samples, we have:

TrimmedMean(U)= 17

TrimmedMean(F)=7.95

d) Trimming percentages can be found by dividing the number of removed values by the old sample size

That is, for U: [tex]\frac{2}{11} = 0.18[/tex] 18.18%

for F: [tex]\frac{2}{15} = 0.13[/tex] ,13.33%

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Answer:

He was driving at 66 2/3 miles per hour

Step-by-step explanation:

200/3 = 66 2/3

The ratio of the number of fallen dominoes to the number of dominoes still standing is 34 : 15

Ratio refers to a number representing a comparison between two or more quantities.

Number of Austen's dominoes that are standing = 15

Number of Austen's dominoes that have fallen over= 34

The ratio of the number of fallen dominoes to the number of dominoes still standing = 34 : 15

Therefore, 34 : 15 is the ratio of fallen dominoes to standing dominoes.

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The domain of f(x) = -√x² - 4 is x ≥ 2 or x ≤ -2

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. The chosen x-value is referred to as being in the domain of f if a function f successfully produces a single value y using a value for x.

In the given question,

the domain of f(x) = -√x² - 4.

x ≥ 2 or x ≤ -2

all real numbers

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Answer:

B

Step-by-step explanation:

-3x + 2y =  ?  You forgot to put what this equals, but it does not matter.

3x + 6y = 9

       9y = ?

When we add -3x and 3x the x's drop out.

The distance that is covered is directly proportional to the time. This is true

The relationship between two quantities where their ratio equals a constant value is known as a direct proportion or direct variation. When the ratio x:y is constant, two values, x and y, are said to be directly proportional to one another.

It should be noted that there are two main types of proportionality with are direct proportion and inverse proportion. In this case, two variables x and y are said to be in direct proportion when y ∝ x (or x ∝ y). This implies, y = kx, for a constant k. While two variables x and y are said to be in inverse proportion if y ∝ 1/x (or x ∝ 1/y).

Regarding the question There's a first proportion. This will be:

2/1 = 4/2

= 2

The constant of proportionality is 2.

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Answer:

1

Step-by-step explanation:

PEMDAS?  omg

Parenthesis, Exponents, Multiplication, Division ,Addition ,Subtraction

so we gon solve the parenthesis first. Basically, we will subtract 1 from 2.

(2-1)= 1

after dis we do dah exponents. we put 1 to the power of 6. 1*1*1*1*1*1= 1

1 to the 6th power is 1 :o

The two solutions for x are x = -4 + 4i and x = -4 - 4i. These solutions are in standard form, as required.

The given equation is a quadratic equation in x, of the form ax2 + bx + c = 0, where a = 1, b = 8 and c = 20.

To solve this equation, we use the quadratic formula, which states that the two roots of the equation are:

x = [-b ± √(b2 - 4ac)] / 2a

Since a = 1, the formula simplifies to:

x = [-8 ± √(82 - 4(1)(20))] / 2

Substituting the values for a, b and c, we get:

x = [-8 ± √(-64)] / 2

Taking the positive and negative square roots of -64, we get:

x = [-8 ± 8i] / 2

Simplifying, we get:

x = -4 ± 4i

Therefore, the two solutions for x are x = -4 + 4i and x = -4 - 4i. These solutions are in standard form, as required.

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The probability that both lights showed red is given as follows:

3/5.

A probability is obtained by the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have to find the correct nodes in the tree that result in both crossings red, and their probabilities.

For the first crossing, the probability of red is given as follows:

4/5.

For the second crossing, the probability of red is given as follows:

3/4.

Hence the probability of red in both lights is given as follows:

4/5 x 3/4 = 3/5.

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Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of plotting data.

The most typical method of utilizing a chart to convey data is to graph the correlation of two additional variables. Diagrams created by hand or using a computer are also acceptable. From the origin, go three up, then 2 pieces to the right. On the reference system, it is important to display the digits for positions 2, 3, and 4. Be really explicit with your points. The pinkish squiggle with the letter P represents the value of 2.3. You must first generate a number line for each number in a collection of data to be able to create a chart.

Here,

Given :

Data gathered from hospitals is frequently used by institutions like the US Center of Disease Control (cdc).

In order to determine what data they use,

From the information provided, it is clear that they are using second-party data.

Therefore ,the data they employ includes Second Party Data as a result, which is the solution to the given challenge of charting the data.

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The equation for the line of best fit that predicts how much money travelers will spend in 2008 is y = 20x + 320.

What is the equation of the line?

The equation y = mx + c is the general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y-intercept (the point at which the line crosses the y -axis).

This is a linear function,

let's say the equation is y =ax + b,

the points (1.5, 350) and (4, 400)

a = (400-350) /(4 - 1.5)

= 50/2.5

= 20

y = 20x + b,

350 = 20(1.5) + b

350 = 30 + b

350 -30 = b

b = 320

y = 20x + 320

so, in 2008,

x =15,

y = 20(15) + 320 = 300 + 320 = 620

Hence, the equation for the line of best fit that predicts how much money travelers will spend in 2008 is y = 20x + 320.

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For: The basis step to prove P(k) is that at k = 1, _____ is true. for series .

What is series and sequence?

The foundational concepts in arithmetic are sequence and series. A sequence is an ordered collection of components where repetitions of any kind are permitted, but a series is the accumulation of all elements.    

                          One of the many illustrations of a sequence or series is a mathematical progression.

Let P(k) be a statement that 1/1*2+1/2*3+ ... + 1/k*(k+1)=

 The basis step to prove P(k) is that at k = 1, _____ is true.

Basic step - P(1) is true,

     to show that 1/1.2 = 1/1+1

      the left hand side of the equation is  1/1.2 = 1/2 right hand side

  1/1 + 1 = 1/2

   1/2  = 1/2

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Answer:

To find the greatest number of tickets Jessica can buy, we can solve the inequality for t.

First, we divide both sides of the inequality by 5:

32/5 ≥ t

Then, we can simplify by dividing 32 by 5:

6.4 ≥ t

The result tells us that t, the number of tickets, must be less than or equal to 6.4

Since t represents the number of tickets, it must be a whole number, so the greatest number of tickets Jessica can buy is 6.

Answer:

6 tickets (t)

Step-by-step explanation:

32/$5=6 2/5 so 6 tickets (t)

The probability of picking all 6 numbers correctly are 1 in 1,947,792.

1 in 32 x 1 in 31 x 1 in 30 x 1 in 29 x 1 in 28 x 1 in 20

= 1 in 1,947,792

Hannah's chances of picking all 6 numbers correctly are 1 in 1,947,792. This is calculated by taking the odds of correctly picking each number and multiplying them together. The odds of correctly picking the first number is 1 in 32, the second number is 1 in 31 (as one of the numbers has already been selected), the third 1 in 30, fourth 1 in 29, fifth 1 in 28, and finally the bonus number is 1 in 20. When all of these odds are multiplied together, the total odds of correctly picking all 6 numbers is 1 in 1,947,792. This means that there is a very small chance of Hannah picking all of the numbers correctly, but it is still possible.

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[tex]\hspace{13em} \begin{array}{cll} term&value\\ \cline{1-2} a_5&16\\ a_6&16r\\ a_7&16rr\\ a_8&16rrr\\ a_9&16rrrr\\ a_{10}&16rrrrr=\frac{1}{2}\\ a_{11}&\frac{1}{2}r\\ a_{12}&\frac{1}{2}rr \end{array}~\hfill \\\\\\ 16r^5=\cfrac{1}{2}\implies r^5=\cfrac{1}{32}\implies r=\sqrt[5]{\cfrac{1}{32}}\implies r=\cfrac{1}{2} \\\\[-0.35em] ~\dotfill\\\\ a_{12}=\cfrac{1}{2}rr\implies a_{12}=\cfrac{1}{2}r^2\implies a_{12}=\cfrac{1}{2}\left( \cfrac{1}{2} \right)^2\implies a_{12}=\cfrac{1}{8}[/tex]

Answer: A

Step-by-step explanation:

Answer:

29/14

Explanataion:

The measure of angle ∠LMN = 105°

What is a parallelogram?

A parallelogram is a quadrilateral, which is a four-sided polygon, with opposite sides that are parallel. Additionally, opposite angles in a parallelogram are congruent (equal in measure). So, if a figure has parallel opposite sides and congruent opposite angles, then it is called a parallelogram.

In the given figure, quadrilateral LMNO is a parallelogram in which ∠L = 25x° and ∠MNO = (22x + 9)°

We have get the measurement of ∠LMN

Since in a parallelogram opposite angles are equal.

Therefore 25x = 22x + 9

25x - 22x = 9

3x = 9

x = 3

From another property of a parallelogram, we know that consecutive angles are supplementary.

∠LMN + ∠ONM = 180°

∠LMN = 180 - ∠OLM = 180 - (25x) = 180 - (25×3)

∠LMN = 180 - 75 = 105°

Hence, the measure of angle ∠LMN = 105°

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Probability that the person randomly chosen from the town's population is under 18 or employed part time is the probability of a randomly chosen person is under 18 plus the probability of a randomly chosen person is  employed part-time subtracting the probability that they are both under 18 and employed part-time.

In order to find the probability that a person is under 18 or employed part-time, you would need to know the proportion of the population that is under 18 and the proportion of the population that is employed part-time. Then you can use the following formula:

P(under 18 or part-time) = P(under 18) + P(part-time) - P(under 18 and part-time)

Where P(under 18 and part-time) is the probability that a person is under 18 and employed part-time at the same time.

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Given that it regularly overstated the population minimum, sample minimum looks to be a biased estimator.

a measurement made using sample data that consistently underestimates or overestimates the real quantity in the target population. A biassed estimator, then, is one whose average value deviates from the value of the parameter it claims to represent. referred to as a skewed statistic.

When the anticipated value of the estimator equals the parameter value, the estimator is considered to be unbiased if its bias is equal to zero for all values of the parameter.

An estimate is considered biassed when it deviates from the genuine population value. When an estimator stays faithful to the population parameter, it is said to be unbiased.

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The complete question is as follows: