Question
The points in the table lie on a line. Find the slope of the line.

The margin of error that corresponds to a 95 % confidence interval for the proportion of residents that are opposed to the use of photo - cops for issuing traffic tickets is 0.04.

Given:

in a survey of 500 residents, 300 were opposed to the use of photo-cops for issuing traffic tickets.

Sample size n = 500

Number of success X = 300

Sample proportion p = X/n

= 300/500

= 30/50

= 3/5

= 0.6

z score at 95% = 1.96

Margin of error = z * [tex]\sqrt{p(1-p)/n}[/tex]

= 1.96 * [tex]\sqrt{0.6(1-0.6)/500}[/tex]

= 0.04

Therefore the margin of error that corresponds to a 95 % confidence interval is 0.04.

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Answer:

The 4th scatter plot indicates a linear relationship

Step-by-step explanation:

The first and third scatter plot graphs are too noisy to indicate a proper trend. The second scatter plot is quadratic and the fourth one is linear.

Answer:

15:19 15/19

Step-by-step explanation:

The relation between the total cost y and the number of units made x is

y = 3x.      

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Given:

The cost (the price) of each single item is $3 and the cost of 10 units is $30.

So, the relation between the total cost y and the number of units made x is

y = 3x.      

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Answer:

m > -20

Step-by-step explanation:

Multiply the 5 on both sides. Now you have 3m > -60. Divide both sides by 3. Now you have m > -20.

Voila

Population of Wisconsin is 9.3 × 10⁰ times greater than the population of Vermont.

As given in the question,

Population of Wisconsin is equal to  5.82 × 10⁶

Population of Vermont is equal to  6.24 × 10⁵

Let 'x' represents the number of times population of Wisconsin is greater than the Vermont

⇒ x = ( population of Wisconsin ) / (Population of Vermont)

⇒ x = ( 5.82 × 10⁶ ) / ( 6.24 × 10⁵ )

⇒ x = 0.933 × 10⁶⁻⁵

⇒ x = 0.933 × 10¹

⇒ x = 9.3 × 10⁰ ( Standard notation , rounding to nearest tenth)

Therefore, population of Wisconsin is 9.3 × 10⁰ times greater than the population of Vermont as per given data.

The complete question is:

The approximate populations of Wisconsin and Vermont (as of 2019) are listed below: Wisconsin: 5.82 × 10⁶ Vermont: 6.24 × 10⁵. How many times greater was the population of Wisconsin than the population of Vermont? Write your answer in standard notation, rounding to the nearest tenth.

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Answer:$156

Step-by-step explanation:

SI=principal x rate x time/100

=150 x 4 x 1/100

=$6

amount = principal+SI

=150+6

=$156

Answer:

For the first one
Part a:
115x + 685y >= 2300

Part b:
See explanation below

Second one:

1.5x + 1.0y >= 2000

Rest of explanation below

Step-by-step explanation:

First one.
Let x be the number of skimboards sold and y be the number of longboards sold.

Then revenue from sales of x units at $115 and y units at $685 would be

115x + 685y

This must be at lest the overhead to make zero loss

So the inequality is
115x + 685y ≥ 2300   (Answer a)

Part b

Any combination of x and y which satisfies this inequality will provide a profit. I have provided a graph of this inequality using an online graphing calculator. I am not sure what your teacher wants you to use.

Any point in the shaded region represents a combination of x and y which satisfies that inequality. However since you cannot sell a fraction of a surfboard, only points which represent whole numbers can be valid. Also only values of x and y >=0 can be chosen.  So any point in the shaded region which has x and y non-negative and x and y whole numbers will generate a profit

Again I am not sure whether this question is asking for a specific value or possible values.

A specific value can be (x=5, y = 10) which is well within the shaded region. This represents 5 skimboards and 10 longboards with a revenue of 5 x 115 + 10 x 685 = $ 7425

Or you could sell 0 skimboards and 4 longboards giving you a revenue of
4 x 685 = $2,740

Or 20 skimboards and zero long boards which is a revenue of $2300 which breaks even with the overhead

Second Question: Modeling

Using x for number of hot dogs sold and y for number of sodas, the inequality is

(a) 1.0x + 1.25y >= 2000

(b) Graph attached

(c)  5 solution points plotted

Here are 5 values that fill fit the inequality

Hope that helps. Sorry, best I could do

Answer:

0.49

Step-by-step explanation:

Answer:

0.49

Step-by-step explanation:

0.4 < x < 0.5

Answer:

22.5

Step-by-step explanation

22.5 is the correct answer because 4.50 times 5 is 22.5 :))))

Answer:

22.5

if one baseball cost $ 4.50 , we multiply it by 5 , or add 4.50+4.50+4

.50+4.50+4.50 same thing.

The value of 103.019 rounded to the nearest tenth is 103.0.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For whole numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The significant figures are preserved when numbers are rounded off.

Round the number up if 5, 6, 7, 8, or 9 follow the number you are rounding. For instance, 40 when rounded to the nearest ten is 38. Round the number down if the rounded number is followed by a 0, 1, 2, 3, or 4.

Therefore, the number is 103.0.

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Answer:

103.0

Step-by-step explanation:

The odds against selecting a history are 31/16.

Probability is the concept that describes the likelihood of an event occurring. In many situations, it is necessary to foresee how something will turn out in the actual world. We may be aware of the result of an event or not. When this occurs, we state that there is a possibility that the event will occur.

Probability is the ratio of the most likely outcomes to all other possible outcomes of an event. The number of successful outcomes for an experiment with 'n' outcomes may be expressed using the symbol x. The following formula can be used to determine the likelihood of an event.

Probability(Event) = favorable outcome/Total outcome = x/n

Number of playwrights = 47

Number of histories = 16

Therefore, the odds against selecting a history are

(47 - 16) / 16

= 31/16

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Linear equation of attendance in terms of the price is A = -225p + 4925

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Attendance as a function of ticket price.

A(p) = mp + b

We have two points (p, A):  (15, 1550), (9, 2900)

Slope:  m = (2900-1550)/(9-15) = 1350/-6 = -225

A = -225p + b

Using (15, 1550) as (p, A) find b

1550 = -225(15) + b

1550 = -3375 + b

4925 = b

A = -225p + 4925

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3+4=7 is the total of all possible integer values of n.

Integers include zero, a positive natural number, and a negative integer represented by a minus sign.

The negative numbers are the inverse additions of the comparable positive numbers.

In mathematical notation, the letter Z is widely used to denote a set of numbers.

An integer is a whole number that can be positive, negative, or zero and is not a fraction.

Integer examples include -5, 1, 5, 8, 97, and 3,043.

So, the two inequalities are resolved independently. We add 3n to both sides of the first inequality, -3n7n-20, to find the solution:

Then, we add 20 to both sides to get 010n-20:

20<10n.

Lastly, multiplying both sides by 10 yields 2n, indicating that n must be bigger than 2.

We deduct 3n from both sides of the second inequality, 7n-203n:

Add 20 on both sides of 4n-200 to obtain:

4n<20.

Lastly, n must be less than 5 since the result of dividing both sides by 4 is n5.

Only the numbers 3 and 4 are greater than 2 and less than 5.

Therefore, 3+4=7 is the total of all possible integer values of n.

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Answer:

c) 4/3

Step-by-step explanation:

The minimum value within a 1 sd range of the average as calculated from the given data is  1.84 ml.

standard deviation range = [average - SD, average + SD]

Here ,

the maximum value =

average - SD = 2.5 - 0.66 = 1.84  ml

and the maximum value =

average + SD = 2.5+ 0.66 = 3.16 ml

Both the standard deviation and range are indicators of how widely distributed a set of data is. Given that they are both measures of variance, each number conveys to us in its own particular way how dispersed the data are.

Although the range and standard deviation do not directly correlate, there is a general method that can be used to connect these two statistics. The range rule for standard deviation is another name for this connection.

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The distance from Lakewood than to Bluepoint is 17.98 miles.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Distance between Bluepoint to Arcadia = 5.38 miles.

Distance between Arcadia to Lakewood= 12.6 miles.

Distance between Lakewood to Dayton = 12.88 miles.

So, the distance from Lakewood than to Bluepoint

= 12.6 +5 .38

= 17.98 miles

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Answer:

y = 5/6x+11/12

Step-by-step explanation:

divide by -1 on both sides to get 10x+11=12y

divide by 12 on both sides

Caleb pays £80 when he orders the bed

From the question, we have the following parameters that can be used in our computation:

Total cost of the bed = £400

Proportion paid when ordering the bed = 1/5

Using the above as a guide, we have the following:

Amount paid when ordering the bed = Proportion paid when ordering the bed * Total cost of the bed

Substitute the known values in the above equation, so, we have the following representation

Amount paid when ordering the bed = 1/5 * £400

Evaluate the products

So, we have the following representation

Amount paid when ordering the bed = £80

Hence, the amount is £80

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Complete question

Caleb is buying a new bed costing £400 He pays 1/5 of the total cost when he orders the bed and the rest on delivery. How much does he pay when he orders the bed?

The speed of the bill's motor boat is found as 20 mph.

Here, we're trying to determine the motorboat's speed.

The speed on the skis would be (x + 10) mph if his motorboat speed is x mph.

There are four hours in all;

Speed = distance/time mathematically.

Skiing time is 27/x+10.

The motorboat time is 62/x.

The result of adding both is 4.

Thus;

27/(x + 10) + 62/x = 4

27(x) + 62(x + 10) = 4(x)(x + 10)

27x + 62x + 620 = 4(x² + 10x)

89x + 620 = 4x² + 40x

4x² -49x-620 = 0

By the quadratic formula;

{-b ± √(b²-4ac)}/2a

In which  a = 4, b = -49 and c = -620

= 49 ± √(-49)² -4(4)(-620)/8

Thus,

49+ 111/8 or 49-111/8

As, speed is not negative.

= (49 + 111)/8

= 20 mph

Thus, the speed of the bill's motor boat is found as 20 mph.

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The nth partial sum of an infinite sequence is the sum of first n terms starting from the first one. The partial sum of the sequence is given as 280.

An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.

This difference is known as the common difference of the sequence.

Given that,

The sequence is  13,22,31,40....

The first term of the sequence is a₁ = -13.

The  difference between consecutive terms is,

22 - 13 = 9

31 - 22 = 9

And, 40 - 31 = 9

Since, the difference between two consecutive terms are same, the given sequence is arithmetic.

The sum of first n terms of an arithmetic sequence is given as,

Sₙ = n/2(2a₁ + (n - 1)d)

Substitute n = 7 to obtain,

S₇ = 7/2(2 × 13 + (7 - 1) × 9)

    = 7/2 × 80

    = 280

Hence, the seventh partial sum of the given sequence is 280.

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Answer:

0 , All real numbers are solutions.

Step-by-step explanation:

Let's solve your equation step-by-step.

−4(v+1)+6v=2(v+2)−8

Step 1: Simplify both sides of the equation.

−4(v+1)+6v=2(v+2)−8

(−4)(v)+(−4)(1)+6v=(2)(v)+(2)(2)+−8(Distribute)

−4v+−4+6v=2v+4+−8

(−4v+6v)+(−4)=(2v)+(4+−8)(Combine Like Terms)

2v+−4=2v+−4

2v−4=2v−4

Step 2: Subtract 2v from both sides.

2v−4−2v=2v−4−2v

−4=−4

Step 3: Add 4 to both sides.

−4+4=−4+4

0=0

Answer:

no solution

Step-by-step explanation:

-4(v + 1) + 6v = 2(v + 2) - 8

-4v - 4 + 6v = 2v + 4 - 8

2v - 4 = 2v - 4

0 = 0

no solution

The average speed during her drive that morning would be 43.5 miles/hr.

What is Average Speed?

Calculating average speed involves dividing the whole distance traveled by the total time it took to cover that distance.

Explanation:

Time = 24 min = 0.4 hr

Entire way = 0.6 + 15.4 + 1.4

                  = 17.4 miles

[tex]Average \ speed = \frac{Distance}{Time}\\\\Average \ speed = \frac{17.4}{0.4} \\\\Average \ speed = 43.5 miles/hr[/tex]

Hence, The average speed during her drive that morning would be 43.5 miles/hr.

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Answer:

4860 bacteria

Step-by-step explanation:

The given scenario can be modelled using an exponential function with base e.

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$y=Ae^{kx}$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $k$ is some constant.\\\end{minipage}}[/tex]

Define the variables:

Given the initial number of bacteria is 20, then A = 20.

[tex]\implies y=20e^{kx}[/tex]

If the bacteria triples its number in 16 hours, then when x = 16:

[tex]\implies y=3 \times 20= 60[/tex]

Substitute x = 16 and y = 60 into the equation and solve for k:

[tex]\begin{aligned}y&=20e^{kx}\\\implies 60&=20e^{16k}\\\dfrac{60}{20}&=e^{16k}\\3&=e^{16k}\\\ln 3&=\ln e^{16k}\\ \ln3&=16k \ln e\\\ln3&=16k\\k&=\dfrac{1}{16} \ln 3\end{aligned}[/tex]

Therefore, the equation that models the given scenario is:

[tex]\large\boxed{y=20e^{\left(\frac{1}{16}x \ln 3\right)}}[/tex]

To find how many bacteria there are after 80 hours, substitute x = 80 into the equation and solve for y:

[tex]\implies y=20e^{\left(\frac{1}{16}(80) \ln 3\right)}[/tex]

[tex]\implies y=20e^{\left(5 \ln 3\right)}[/tex]

[tex]\implies y=20e^{\left(\ln 3^5\right)}[/tex]

[tex]\implies y=20e^{\left(\ln 243\right)}[/tex]

[tex]\implies y=20 \cdot 243[/tex]

[tex]\implies y=4860[/tex]

Therefore, there are 4860 bacteria after 80 hours.

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

Please note that I have solved this question so that you can calculate the number of bacteria for any number of hours, part hours, etc.

However, there is a much simpler way of solving this particular question.

If the number of bacteria triples every 16 hours, then it will triple 5 times within 80 hours since 80 ÷ 16 = 5.

Therefore:

As you can see, the result is the same as the previous method.

Answer:

11x +98 just assume it to be an arithmetic progression

The required number of cups of sugar for 1 dozen of cookies is 3 cups.

Given that,
A recipe calls for 2 1/4 cups of sugar for 1 1/2 dozen cookies. What amount of sugar is needed for one dozen cookies? is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
For
2 1/4 cups   = 9 / 2 cups
number of cookies = 3/2 dozen
For.
1 dozen cookies = 9 / 2 / [ 3 / 2] = 3 cups of sugar

Thus, the required number of cups of sugar for 1 dozen of cookies is 3 cups.

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The margin of error would be higher at a 99% confidence level.

Confidence level is the probability, or degree of certainty, that the confidence interval would include the real population parameter when a random sample is drawn numerous times.

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The height of the triangle is 32 mm

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The area of a triangle can be represented as follows:

area of a triangle = 1 / 2 bh

where

Therefore, the triangle has an area of 32 mm² and base of 8 mm. Let's find the height of the triangle as follows:

area of a triangle = 1 / 2 bh

32 = 1 / 2 × 8 × h

4h = 32

divide both sides by 4

h = 32 / 4

h = 8 mm

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the 95% confidence interval for the proportion of all dies that pass the probe is [0.513,0.616].

Sampling is frequently used to estimate the percentage of population that possesses a particular attribute, such as the percentage of all faulty goods which come off an assembly line or the percentage among all buyers that enter a store and make a purchase before leaving. The population proportion is indicated p, while the sample proportion is written p. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.

The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance. When seen as a random variable, it will be represented by the letter P.

How to solve?

An article reported that in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 169 of these passed the probe.

So,p'=201/356=0.56460

The 95% confidence interval for the proportion of all dies that passed the probe will be,

p∈[p'±zα/2√p'(1−p')/n]

p∈[0.56460±1.96×√0.56460(1−0.56460)356]

p∈[0.513,0.616]

So the 95% confidence interval is [0.513,0.616].

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