Which is not a step in solving this problem?1/2^5A. Multiply 1 by 5.B. Change the operation,C. Multiply 5 by 2.D. Find the reciprocal of the divisor.

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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The equation of line in the point slope form is y = 2x + 8

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Let temperature be denoted as x

Let the time be denoted as y

Let the initial temperature be = 0°F

Let the final temperature be = 1°F

Let the initial time be = 8 : 00 AM

Let the final time be = 10 :00 AM

And , the first point be P = P ( 0 , 8 )

The second point be Q = Q ( 1 , 10 )

Now , the slope of the equation is given as

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 10 - 8 ) / ( 1 - 0 )

Slope m = 2

Now , the equation of line is given as y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = 2 ( x - 0 )

y - 8 = 2x

Adding 8 on both sides of the equation , we get

y = 2x + 8

Therefore , the value of A is y = 2x + 8

Hence , the equation is y = 2x + 8

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Answer: The amount you would pay (including tax) for an item normally priced at $329 on sale for 25% off where sales tax is 7.25% would be $264.63.

Step-by-step explanation: To calculate the final price including tax, we need to apply the discount first and then add the sales tax.

Discounted price = 0.75 x $329 = $246.75

Sales tax = 0.0725 x $246.75 = $17.88

Final price including tax = $246.75 + $17.88 = $264.63

Therefore, the amount you would pay (including tax) for an item normally priced at $329 on sale for 25% off where sales tax is 7.25% would be $264.63.

The table can be summarized as follows:

|          | Has a dog | Does not have a dog |

|----------|-----------|---------------------|

| Has a cat     | 2         | 3                   |

| Does not have a cat | 12        | 10                  |

To find the probability that a student chosen randomly from the class has a cat, we need to find the total number of students who have a cat (regardless of whether or not they have a dog), and divide it by the total number of students in the class.

The number of students who have a cat is 2 (those who have a dog and a cat) + 3 (those who have a cat but do not have a dog) = 5.

The total number of students in the class is the sum of all four categories: 2 (has a cat and a dog) + 3 (has a cat, does not have a dog) + 12 (does not have a cat, has a dog) + 10 (does not have a cat, does not have a dog) = 27.

So, the probability that a student chosen randomly from the class has a cat is 5/27.

The confidence interval is 0.559 < p < 0.641 and expected value is 0.600

To construct a confidence interval for the true population proportion, we can use the formula:

p ± Z * √((p × (1 - p)) / n)

Where:

p = sample proportion (336/560)

Z = critical value for the desired confidence level

95% confidence = Z-value of approximately 1.96

n = 560

Let's calculate the confidence interval:

p = 336/560 ≈ 0.600

Z ≈ 1.96 (for a 95% confidence level)

n = 560

Plugging these values into the formula:

p ± Z × √((p × (1 - p)) / n)

0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)

0.600 ± 1.96 × √((0.240) / 560)

0.600 ± 1.96 × √(0.0004285714)

0.600 ± 1.96 × 0.020709611

0.600 ± 0.040564459

The confidence interval is:

0.559 < p < 0.641

Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.

For proportions, the expected value is simply the sample proportion, which is approximately 0.600.

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Answer:

1 4/5 of a necklace, or 1.8 necklaces.

Step-by-step explanation:

As we know, an hour has 60 minutes, and Janet can make 3/5 of a necklace in 20 minutes. 60/20 is 3. So we need to mulitply 3/5 by 3 to get the amount of necklaces she can make in an hour. When we do this, we get 9/5. We can convert this to 1 4/5, and as decimal form, this is 1.8. That is our answer. I hope this helps!

A parameterization {x[t], y[t]} of the line passing through the tips of X and Y when their tails are placed at (0, 0). Parametric Equation of line is L: x(t) = x(1)+t(x(2)-x(1)); y(t) = y(1)+t(y(2)-y(1)) or L = x + t(y-x).

We have to find a parameterization {x[t], y[t]} of the line passing through the tips of X and Y when their tails are placed at (0, 0).

Let tip of x is at (x(1), y(1)) ⇒ x = x(1)i + y(1)j

Let tip of y is at (x(2), y(2)) ⇒ y = x(2)i + y(2)j

Direction of line passing through tips of vectors.

x and y is d = y-x

d = (x(2)-x(1))i + (y(2)-y(1))j

Parametric Equation of line is

L: x(t) = x(1)+t(x(2)-x(1))

   y(t) = y(1)+t(y(2)-y(1))

OR

L = x + t(y-x)

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The right question is:

For generic vectors X and Y, find a parameterization {x[t], y[t]} of the line passing through the tips of X and Y when their tails are placed at (0, 0).

The value for the degrees of freedom in order to calculate the chi squared statistic is 12

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

Rows = 4

Column = 5

The value for the degrees of freedom in order to calculate the chi squared statistic is

(number of rows - 1) x (number of columns - 1).

In this case, the researcher has a table with 4 rows and 5 columns, so the degrees of freedom would be

(4-1) x (5-1)

Evaluate

= 3 x 4 = 12.

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If 3/8 of Abby's candy was chocolate, then 3/8 pounds of chocolate candy Abby bought.

What is a ratio?

A ratio in mathematics shows how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-total fruit ratio is 8:14.

Abby went to the candy store and bought 3/4 of a pound of candy.

So in total, he bought 3/4 of a pound of candy out of which 3/8 candy was chocolate.

Let the number of pounds of chocolate candy Abby bought would have bought be 'x',

So we can prepare the equation as,

                       \(x=\frac{3}{4}-\frac{3}{8}\\ x=\frac{24-12}{4*8}\\ x=\frac{12}{4*8}\\x =\frac{3}{8}\)

Hence, If 3/8 of Abby's candy was chocolate, then 3/8 pounds of chocolate candy Abby bought.

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Answer:2+3

Step-by-step explanation:

The required expression that is equivalent to 5-3 is 5 + (-3).

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
In addition, rule, when two values are added and found that the value in outcome is lower than any of the added values, then the expression is given as,

= a + (-b)

where, -b is the negative real number,

So for the given question,
addition expression for 5 - 3 is 5 + (-3)

Thus, the required expression that is equivalent to 5-3 is 5 + (-3).

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Answer:

The answer is -18

Step-by-step explanation:

He starts off with $100 in his account. He then take so $45 to purchase a pair of jeans, so we have to subtract 45 from 100 and that gives us $55. He now has $55 in his account, he then adds another $25 to his account, so we have to add 25 to 55 and that will give us $80 in his account. Finally on Friday he takes out $98 of his checking account. He takes out more than he has in his checking account so we have to subtract $80 from $98 and we will get $18, but since he takes out more than what he has in his account the answer will be negative and we end up with -18 dollars in his checking account.

Answer:72

Step-by-step explanation:

Function with smallest slope m₃ = 1/3 is h(x).

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line. A line that is decreasing has a negative "rise".

Given functions,

f(x) = 5x - 4

Let y = 5x - 4

Comparing with slope-intercept equation y = mx + c

slope m₁ = 5

Graph of function is drawn as straight line

By the graph, two points on straight line are (0, 1) and (1, 3)

Slope m = (y₂ - y₁)/(x₂ - x₁)
m₂ = (3 - 1)/(1 - 0)

m₂ = 2

Ordered pairs of h(x) are (1, 14) and (4, 15)

Slope m = (y₂ - y₁)/(x₂ - x₁)
m₃ = (15 - 14)/(4 - 1)

m₃ = 1/3

By the calculation,

m₁ > m₂ > m₃

Hence, function h(x) has the smallest slope m₃ = 1/3

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Answer:

y = 3.3x

Step-by-step explanation:

for the table we can determine that every hamburger delivery takes five minutes

you can do this by dividing 4 by 0.8 which gets you five

the pizza deliverys speed can be figured out by dividing 50 by 15

this gets you 3.33...

therefore y = 3.3x would be your answer as the pizza delivery is faster

Answer:

a) 0.0618 = 6.18% probability that the sample will contain at least three defectives.

b) 0.076 = 7.6% probability that the sample will contain at least three defectives

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \(\mu = E(X)\), \(\sigma = \sqrt{V(X)}\).

Sample of 20 items is selected from the machine.

This means that \(n = 20\)

5% defectives

This means that \(p = 0.05\)

(a) the normal approximation to the binomial

The mean is:

\(\mu = E(X) = np = 20*0.05 = 1\)

The standard deviation is:

\(\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.05*0.95} = 0.9747\)

The probability is, using continuity correction, \(P(X \geq 3 - 2.5) = P(X \geq 2.5)\) , which is 1 subtracted by the pvalue of Z when X = 2.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{2.5 - 1}{0.9747}\)

\(Z = 1.54\)

\(Z = 1.54\) has a pvalue of 0.9382

1 - 0.9382 = 0.0618

0.0618 = 6.18% probability that the sample will contain at least three defectives.

(b) the exact binomial tables

This is:

\(P(X \geq 3) = 1 - P(X < 3)\)

In which

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.358\)

\(P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.377\)

\(P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.189\)

\(P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.358 + 0.377 + 0.189 = 0.924\)

\(P(X \geq 3) = 1 - P(X < 3) = 1 - 0.924 = 0.076\)

0.076 = 7.6% probability that the sample will contain at least three defectives

The maximum distance that the sailοr can see frοm the deck οf the ship is 0 miles.

A special kind οf relatiοn knοwn as a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn generates exactly οne value fοr each input value. Because οne is mapped tο twο different values, the abοve graph depicts a relatiοnship rather than a functiοn. Hοwever, if οne were instead mapped tο a single value, the relatiοnship mentiοned abοve wοuld becοme a functiοn.

Additiοnally, οutput values can be equal tο input values. We knοw that the square rοοt functiοn is an increasing functiοn, which means that the value οf the functiοn increases as the input value increases.

Therefοre, tο find the maximum value οf the functiοn, we need tο find the maximum value οf h.

Assuming that the lighthοuse is οn the hοrizοn, which is apprοximately 3 miles away, we can use the Pythagοrean theοrem tο find the height οf the lighthοuse:

\(h^2 = (3)^2 - (15)^2h^2 = 9 - 225h^2 = -216\)

Since we cannοt take the square rοοt οf a negative number, there is nο real height fοr the lighthοuse that wοuld make it visible frοm a ship 15 feet abοve the water level.

Therefοre, the maximum distance that the sailοr can see frοm the deck οf the ship is 0 miles.

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Answer:

thanks for free points

Answer:

The graph shows the solution of the inequality y > \(\frac{4}{3}\) x - 2 ⇒ D

Step-by-step explanation:

In the inequality,

From the given graph

∵ The slope of the line = \(\frac{2--6}{3--3}\) = \(\frac{2+6}{3+3}\) = \(\frac{8}{6}\) = \(\frac{4}{3}\)

∵ The y-intercept is (0, -2)

∵ The line is dashed and the shaded area is over the line

→ By using the 2nd and 3rd notes above, the line is dashed and

   the sign of inequality is >

∴ The inequality is y > \(\frac{4}{3}\) x - 2

∴ The graph shows the solution of the inequality y > \(\frac{4}{3}\) x - 2

Using a system of equations, the number of each type of coffee that Julia and her husband should buy is as follows:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations can also be described as simultaneous equations.

The cost per pound of City Roast Columbian coffee = $6.50

The cost per pound of French Roast Columbian coffee = $8.20

The total quantity of the blend = 34 pounds

The cost per pound of the blend = $6.90

The total cost of the 34 pounds = $234.60 ($6.90 x 34)

Let the number of pounds of City Roast coffee = x

Let the number of pounds of French Roast coffee = y

x + y = 34 ... Equation 1

6.5x + 8.2y = 234.6 ... Equation 2

Multiply Equation 1 by 6.5:

6.5x + 6.5y = 221 ... Equation 3

Subtraction Equation 3 from Equation 2:

6.5x + 8.2y = 234.6

-

6.5x + 6.5y = 221

1.7y = 13.6

y = 8

Substitute, y = 8 in Equation 1:

x + y = 34

x = 34 - 8

x = 26

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Answer:

m = -2

Step-by-step explanation:

Slope formula ---

m = y2-y1/x2-x1

m = 5-9/8-6

m = -4/2

m = -2

Answer:

We accept H₀  we have not enough evidence to support that the mean distance between oil changes is less for all luxury cars than that for all compact lower-price cars

Step-by-step explanation:

Luxury cars sample:

sample size    n₁  =  49

sample mean   x₁ = 3178

sample standard deviation   s₁  = 41,80

Compact lower-price cars sample

sample size    n₂  = 38

sample mean   x₂  =  3200

sample standard deviation   s₂  =  50,60

Test Hypothesis:

Null Hypothesis                              H₀          x₁  -  x₂  = 0  or  x₁  = x₂

Alternative Hypothesis                 Hₐ           x₁  -  x₂  <  0   or   x₁ < x₂

CI = 99 %  then significance level is  α = 1 %   α = 0,01

Alternative Hypothesis indicates   that we have to develop a one tail-test to the left

z(c)   for α  0,01     is   z(c)  = -2,32

To calculate  z(s)

z(s)  =  [  (  x₁   -   x₂ 9 ] / √ (s₁²)/n₁  +  (s₂)²/n₂

z(s)  =  (  3178  -  3200 ) / √ 35,66 +  67,38

z(s)  =  ( -  22 / 10,15 )

z(s)  =  - 2,17

Comparing   z(s)  and z(c)

z(s) > z(c)         -  2,17  >  - 2,32

Then  z(s) is in the acceptance region we accep H₀

Answer:

Step-by-step explanation:   G'(x)=11-18/3 x

Answer:

Now, i⁹ + i¹⁹ = i - i = 0. Hence the answer is just 0.

Step-by-step explanation:

Answer:

83 calories

Step-by-step explanation:

The person will be 83 calories per hour, if he plays for a single hour, he will burn that amount.

Answer:

7:1

Step-by-step explanation:

7x5=35

Make it a ratio and 1 doesnt make a diffrence.

If a machine fills boxes at a constant rate at the end of 35 minutes, it has filled 5 boxes then 1 box is filled in 7 minutes.

A division is a process of splitting a specific amount into equal parts.

Given that, a machine fills boxes at a constant rate. At the end of 35 minutes, it filled 5 boxes.

A rate of change is constant when the ratio of the output to the input stays the same at any given point in the function.

The constant rate of change is also known as the slope.

Linear functions will have a constant rate of change.

Now, in 35 minutes machine has filled 5 boxes.

So, 1 box is filled in 35/5=7 minutes.

Hence, if a machine fills boxes at a constant rate at the end of 35 minutes, it has filled 5 boxes then 1 box is filled in 7 minutes.

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Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

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The number of gallons of Jet fuel that is needed to fly for an hour is; 14400 gallons

We are given;

Number of gallons burned = 4 gallons

Time to burn 4 gallons = 3 seconds

Now, for 1 hour there are 3600 seconds and so;

Number of gallons that is burnt in 3600 seconds = 3600 * 4

Number of gallons that is burnt in 3600 seconds = 14400 gallons

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Answer:

C

Step-by-step explanation:

goodluck