Solye for x.

5(x+1)

Answer:

Step-by-step explanation:

$92.43 / 0.74 = $124.91

The total bill is equal to $124.9

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here, the given bill as 74% of the total bill as $92.43

Thus the total bill must be = 92.43×100/74

                                            = $124.9

Hence, The total bill is equal to $124.9

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Answer:

The approximate number of gallons consumed by a person in 2010 will be 4.9 gallons

Step-by-step explanation:

Recall that the formula for exponential decrease is given by a function of the form:

\(f(x)=A\.(1-r)^x\)

where A is the initial value, r is the rate of decrease, and x is the time elapsed.

In our case, the initial value of gallons of juice per person (at the starting time = 1981) is 16.5 gallons. So A = 16.5 gallons.

the rate of decrease "r" is the decimal form of: 4.1%, that is r = 0.041

So we have:

\(f(x)=16.5\.(1-0.041)^x\)

Now we can calculate what the average number of gallons would be in the year 2010, knowing that between 1981 and 2010 there is an elapsed time in years of: 2010-1981 = 29 years. Then:

\(f(29)=16.5\,(1-0.041)^{29}=4.9 \,\, gallons\)

The approximate amount consumed per person in 2010 is  4.9 gallons.

The formula that would used to determine the average gallon of juice consumed in 2010 is:  

FV = P (1 - r)^n

FV = Future value  

P = Present value = 16.5 gallons  

R = rate of decrease = 4.1%  

N = number of years = 2010 - 1981 = 29

16.5 x (1 - 0.041)^29  = 4.9 gallons

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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:

1300 ppl

Step-by-step explanation:

35%  = .35 in decimal

.35 x =455

x = 455/.35 = 1300 ppl

Kristen have 8 cups more than Chris.

We will use unitary method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that Kristen has 8 gallons of water. Chris has 28 quarts of water.

We need to convert gallons and quarts to cups and subtract the values

1 gallon = 16 cups

7 gallons = 7 x 16 = 112 cups

1 quart = 4 cups

Therefore,

26 quarts = 26 x 4 = 104 cups

112 - 104 = 8 cups

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The matrix representation of the problem can be written as: ε = [ε1 ε2 ε3]'

The matrix representation of the linear regression problem can be expressed as Y = Xβ + ε, where Y is the n x 1 vector of the dependent variable (Yi),

X is the n x k matrix of the independent variables (xi),

β is the k x 1 vector of coefficients, and

ε is the n x 1 vector of errors.

In this case, n = 3 (number of observations), k = 2 (number of independent variables) and the matrix representation of the problem can be written as:

Y = Xβ + ε

Y = [0.3 0.8 -0.3]

X = [1 1 1; 1 2 0.1]

β = [β0 β1]'

ε = [ε1 ε2 ε3]'

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Answer:

4 inches by 3 inches. It should actually be 10 inches by 6 but its not on there.

The value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

The quadratic equation is given as:

–3 = –x^2 + 2x

Rewrite the equation as:

x^2 - 2x - 3 = 0

A quadratic equation is represented as;

ax^2 + bx + c = 0

So, we have

a = 1

b = -2

c = -3

The discriminant is

d = b^2 - 4ac

So, we have

d = (-2)^2 - 4 * 1 * -3

Evaluate

d = 16

Hence, the value of the discriminant for the quadratic equation –3 = –x2 + 2x is  16

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Answer:

16

Step-by-step explanation:

Answer:

The first value of a relation is an input value and the second value is the output value. A function is a specific type of relation in which each input value has one and only one output value.

An input is an independent value, and the output value is the dependent value, as it depends on the value of the input.

The freighter is approximately 164.33 miles from the city.

We can use the Law of Cosines to solve this problem. Let's label the distances as follows:

d: distance between the city and the freighter

x: distance between the city and the island

y: distance between the island and the freighter

First, we need to find x using the given coordinates:

N23°38'W is equivalent to S23°38'E, so we have:

cos(23°38') = x/48

x = 48cos(23°38') ≈ 42.67 miles

Next, we can use the coordinates of the freighter to find y:

N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:

23°38' + 11°26' + 12°16' = 47°20'

cos(47°20') = y/d

We can rearrange this equation to solve for y:

y = dcos(47°20')

Now we can use the Law of Cosines to solve for d:

d² = x² + y² - 2xy cos(90° - 47°20')

d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')

d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')

d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')

d ≈ 164.33 miles

Therefore, the freighter is approximately 164.33 miles from the city.

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Step-by-step explanation:

Here we will simplify the ratio 8:25 for you and show you how we did it.

To simplify the ratio 8:25, we find the greatest common divisor of 8 and 25, and then we divide 8 and 25 by the greatest common divisor.

The greatest common divisor that you can use to simplify 8:25 is 1. Which means the answer to ratio 8:25 simplified is: 8:25

Here is the math to illustrate better:

8/1 = 8 and 25/1 = 25

Thus, 8: 25 ratio simplified is 8:25

Link to understand better - https://thepercentagecalculator.net/SimplifyRatios/Simplify-Ratio-8-25.html

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

b = -17

Step-by-step explanation:

-2b - 12 = 22

     +12     +12

-2b = 34

-2b/-2    34/-2

b = -17

Answer:

-17

Step-by-step explanation:

-2B-12=22

-2B-2 (+12)=22+12 (add 12 to both sides to isolate the variable

-2B=24

-2B/-2=24/-2 (divide by -2 to isolate the variable)

B=-17

Answer:

A is 3 B is 4 and C is 2

Step-by-step explanation:

this is most likely right unless your usong a diffrent formula

The circumference of a circle with one-third the curvature of a circle of radius 1 is 18.85 units

What is circumference ?

The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.

If a circle has a radius of 1,

the curvature is inversely proportional to this

So, the curvature= 1

A circle with a curvature of 1/3 :

radius=3

Thus, the circumference of the circle  =  2 *π * radius

                                                               =  2*π * 3

                                                               =  6π

                                                               ≈ 18.85 units

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The path described by the limit of the radar is the circle 50 km circle, and

the path of the ship is the 60 km dashed straight line.

The shortest distance between the ship and Point O, \(\overline {OP}\) is (C) 40 km

Reasons:

The tracking distance of the radar, r = 50 km

Distance the ship moves while within the reach of the radar = 60 km.

Required:

The shortest distance between the ship and the Point O

Solution:

The closest distance between the path of the ship and the Point O is given

by the perpendicular distance from the Point O to the path of the ship

which is given by Pythagoras's theorem and that the perpendicular line

from O to the path of the ship bisects the length of the ship's path.

Let A and B represent the points where the path of the ship intersects with

the circumference of the radar, and let P represent the point the

perpendicular from O intersects AB, we have;

\(\overline {AO}\) = The radius of the radar = 50 km

\(\overline {AB}\) = \(\overline {AP}\) + \(\overline {PB}\)  (segment addition postulate)

\(\overline {AB}\)  = 60 (given)

\(\overline {AP}\) + \(\overline {PB}\) = 60 (transitive property)

\(\overline {AP}\) = \(\overline {PB}\) (definition of \(\overline {AB}\) bisected by \(\overline {OP}\))

∴ \(\overline {AP}\) + \(\overline {PB}\) = \(\overline {AP}\) + \(\overline {AP}\)  = 2× \(\overline {AP}\) = 60

\(\overline {AP}\) = 30

\(\overline {AO}\)² = \(\overline {OP}\)² + \(\overline {AP}\)² (Pythagoras's theorem)

\(\overline {OP}\)² = \(\overline {AO}\)² - \(\overline {AP}\)²

∴  \(\overline {OP}\)² = 50² - 30² = 1600

\(\overline {OP}\) = √(1600) = 40

\(\overline {OP}\) = 40

The shortest distance between the ship and Point O, \(\overline {OP}\) is (C) 40 km

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The shortest distance between the ship and point O is 40 kilometers. (Option C)

The shortest distance between the ship and point O is the distance perpendicular to the line segment AB. We calculate the angle B by the law of cosine:

\(B = \cos^{-1}\left[\frac{50^{2}-60^{2}-50^{2}}{-2\cdot (50)\cdot (60)} \right]\)

\(B \approx 53.130^{\circ}\)

Now we calculate the shortest distance by trigonometric functions:

\(d = OB\cdot \sin B\)

\(d = 50\cdot \sin 53.130^{\circ}\)

\(d = 40\,km\)

The shortest distance between the ship and point O is 40 kilometers. (Option C)

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Answer:

The psychologist finds that the estimated Cohen's d is 0.583.

Step-by-step explanation:

The Cohen's d is used to calculate the effect size, appied when a null hypothesis is rejected.

It can be calculated for this case of population mean as:

\(d=\dfrac{M-\mu}{\sigma}=\dfrac{6.5-5.8}{1.2}=\dfrac{0.7}{1.2}=0.583\)

The psychologist finds that the estimated Cohen's d is 0.583.

Answer:

The probability is 0.28157

Step-by-step explanation:

The number of answers are 40 answers ( 10 questions and 4 answer each)

The number of correct answers is only 10

So the probability that he answers 2 exactly out of 10 means he correctly selected 2 answers

The probability will be;

10 C 2/ 40 C 10

This mean out of the total 10 correct, he selects 2 and out of the total 40 , he selects 10

The probability of selecting a correct answer is;

1/4 while the probability of selecting a wrong one is 3/4

So probability of selecting 2 correct out of a total 10 will be

10 C 2 (1/4)^2 (3/4)^8

= 0.28157

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Sorted data :

388, 389, 389, 390, 391, 393, 393, 393, 396, 398, 399, 400, 400, 400, 401, 402, 402, 403, 403, 403, 404, 404, 404, 405, 405, 405, 406, 406, 406, 407, 407, 408, 408, 408, 409, 409, 411, 412, 412, 413, 414, 416, 416, 416, 419, 420, 420, 424, 424, 1650

n = number of observations = 50

1) first quartile of the data (Q1) : 1/4(n+1)th term

1/4(51)th term= 12.75th term = 400

2)3rd quartile :

3/4(51)th term = 38.25th term = 412

3)median of data (Q2) :

1/2(51)th term = 25.5 th term = 405

4) mean of data

Σx / n = 21501 / 50 = 430.02

5)Outlier : Values that are greater than Q3 + 1.5 IQR or less than Q1 - 1.5 IQR

IQR = Q3 - Q1 = 412 - 400 = 12

> Q3 + 1.5 IQR

> 412 + 1.5(12) = > 430

< Q1 - 1.5 IQR = < 400 - 1.5(12) = 382

Outlier = 1650

Median after outlier is deleted :

1/2(50) th term = 25 th term = 405

Mean after outlier is deleted :

Σx / n = 19851 / 49 = 405.122

Answer:

Step-by-step explanation:

Answer:

B,

Step-by-step explanation:

y - 7 = 3(x - 5)

y - 7 = 3x - 15

y = 3x - 8

answer is B

Answer:

y = 4x -13

y = 4x -13Step-by-step explanation:

y= mx + b

y= mx + b m is the Slope

y= mx + b m is the Slopem = 4

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = bThe line in slope intercept form is

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = bThe line in slope intercept form isy = 4x -13

The slope of the line on the graph will be a negative one. Then the correct option is A.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

From the graph, the two points are (-2, 2) and (2, -2). Then the slope is given as,

m = (- 2 - 2) / (2 + 2)

m = - 4 / 4

m = - 1

The slope of the line on the graph will be a negative one. Then the correct option is A.

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The complete question is attached below.

The mean absolute deviation is $106.6.

Given the table shows the amount Bill spent on 5 days last week.

DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.

Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,

the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:

Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406

The sum of all absolute deviations is:

10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.

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Answer:

Poisson distribution.

Step-by-step explanation:

We have the mean number of missing pulses per disk, which means that the distribution for X, the number of missing pulses, will be the Poisson distribution.

It is not the binomial distribution because we are not given the probability of a missing pulse on a disk, but the mean number of missing pulses.

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).

The expression "log 2 - log 4" can be simplified using                   logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."

The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:

A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.

B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.

C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.

D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.

Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.

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Answer:

Ali has 1528. She has 1146 more cards than Max. In total, there are 1910 cards.

Step-by-step explanation:

382 x 4 = 1528

1528 - 382 = 1146

1528 + 382 = 1910

Answer: