There is a shop selling new compact disks and used compact disks. John bought 3 new compact disks and 8 used compact disks for $133.89. Michel bought 6 new compact disks and 2 used compact disks for $127.92. Find the cost of buying one used compact disk

Answer:

The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of  

5

9

degree Celsius.

A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.

A temperature increase of  

5

9

degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only

B) II only

C) III only

D) I and II only

Step-by-step explanation:

Answer:

  about -4.7622

Step-by-step explanation:

You want the cube root of -108.

Your calculator will tell you the cube root of -108 is about -4.7622.

__

Additional comment

Some calculators compute roots using logarithms. Since the logs of negative number are not real, they will give you an error if you try to do this directly. You have to know that the odd index root of a negative number is the opposite of the same root of its absolute value.

The prime factoring of 108 is 2²·3³. Factoring out the perfect cube gives the simplified form ...

  ∛-108 = -3∛4

<95141404393>

X varies directly as y , that x = 9 when y = 3,the value of x when y = 12 by  the constant of Variation , value of x is 36.

X  varies directly as y, it means that there is a constant ratio between x and y. We can express this relationship using the formula:

x = ky

where k is the constant of variation.

To find the value of k, we can use the given information that x = 9 when y = 3. Substituting these values into the formula, we have:

9 = k * 3

Solving for k, we divide both sides of the equation by 3:

k = 9/3

k = 3

Now that we have the value of k, we can find x when y = 12 by substituting it into the formula:

x = 3 * 12

x = 36

Therefore, when y = 12, the corresponding value of x is 36.

if x varies directly as y and we are given that x = 9 when y = 3, we can find the value of x when y = 12 by determining the constant of variation (k) and using the formula x = ky. In this case, the constant of variation is 3, so when y = 12, x equals 36.

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Answer:

Steps and solution in the attached picture.

Step-by-step explanation:

Steps and solution in the attached picture.

Answer:

Step-by-step explanation:

You want to identify the graphs that go with each of these functions, along with a particular point on the curve.

The equations are written here in standard form, factored form, and vertex form. (The "factored form" is sometimes called "intercept form.") Each of these forms can be analyzed for characteristics relevant to identifying the corresponding graph.

In general, we can readily identify the opening direction, based on the sign of the leading coefficient. Depending on the form, we can also identify zeros, the vertex, and the y-intercept.

The line of symmetry (x-coordinate of the vertex) of the equation in the form ax² +bx +c is x = -b/(2a). That is, it will be left of the y-axis when the coefficients 'a' and 'b' have the same sign.

The graph of equation A will be graph 4, the only one with its vertex left of the y-axis. The y-intercept is the constant: point S = (0, 9).

Equation B has a positive leading coefficient, so opens upward. The zeros of the factors are -3 and +9, so identify the places where the graph crosses the x-axis. Graph 3 is the only one that opens upward and has x-intercepts. Point R is (9, 0).

The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k); leading coefficient 'a'

Equation C has its vertex at (h, k) = (3, 9) and opens upward (a>0). Graph 1 is the only one matching those characteristics. Point P is the vertex, so point P is (3, 9).

Equation D is the same as equation B, but with a negative leading coefficient. That is, it opens downward and crosses the x-axis in two places, at x = -3 and x = 9. Graph 2 is matches this description. The left zero is point Q, (-3, 0).

<95141404393>

Answer:

Step-by-step explanation:

Answer:

$26,986.29

Step-by-step explanation:

We can use the formula for calculating the depreciation of an asset over time:

wor

\(\bold{D = P(1 - \frac{r}{100} )^t}\)

where:

D= the current value of the asset

P = the initial purchase price of the asset

r = the annual depreciation rate as a decimal

t = the number of years the asset has been in use

In this case, we have:

P = $39,600

r = 12% = 0.12

t = 3 years

Substituting these values into the formula, we get:

\(D= 39,600(1 - \frac{12}{100})^3\\D= 39,600(1 - 0.12)^3\\D= 39,600*0.88^3\\D= 39,600*0.681472\\D=26986.2912\)

Therefore, the car is worth approximately $26,986.29 after 3 years of depreciation at a rate of 12% per annum.

Answer:

$26,986.29

Step-by-step explanation:

As the car's value depreciates at a constant rate of 12% per annum, we can use the exponential decay formula to create a function for the value of the car f(t) after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

In this case, the initial value is $39,600, and the rate of depreciation is 12% per year. Therefore, the function that models the value of the car after t years is:

\(f(t)=39600(1-0.12)^t\)

\(f(t)=39600(0.88)^t\)

To calculate the value of the car after 3 years, substitute t = 3 into the function:

\(\begin{aligned} f(3)&=39600(0.88)^3\\&=39600(0.681472)\\&=26986.2912\\&=26986.29\;(\sf 2\;d.p.)\end{aligned}\)

Therefore, the car is worth $26,986.29 after 3 years.

9514 1404 393

Answer:

Step-by-step explanation:

The central angle is equal to the exterior angle:

  360°/n = 360°/42 = 8 4/7° ≈ 9°

The vertex angle is the supplement of this:

  180° -8 4/7° = 171 3/7° ≈ 171°

Answer:

To find the rules for (fg)(x) and (gf)(x), we need to evaluate the composite functions.

(fg)(x) = f(g(x)) = f(sqrt(x - 5)) = (sqrt(x - 5))^2 + 5 = x - 5 + 5 = x

(gf)(x) = g(f(x)) = g(x^2 + 5) = sqrt(x^2 + 5 - 5) = sqrt(x^2) = |x|

Therefore, the rules for (fg)(x) and (gf)(x) are:

(fg)(x) = x

(gf)(x) = |x|

Step-by-step explanation:

Answer:

424

Step-by-step explanation:

let 's' = number of students

3/4s + 18 = 336

3/4s = 318

3s = 1272

s = 1272/3 = 424

Answer:

y=1.5

x=-3.5

Our answer is (-3.5,1.5)

Step-by-step explanation:

y-5=x

x=-2-y

y=?

--------

Using substitution,

y-5=-2-y

Solve:

2y-5=-2

2y=3

y=1.5

We can enter 1.5 into the equation:

1.5-5=x

-3.5=x

Answer:

To calculate the book value of the building, we need to calculate the annual depreciation amount and multiply it by the number of years elapsed since the building was completed.

The annual depreciation amount is calculated as: $1 million / 50 years = $20,000

In 2014, the book value of the building was: $1 million - ($20,000 * (2014 - 2010)) = $1 million - ($20,000 * 4) = $960,000

In 2022, the book value of the building will be: $1 million - ($20,000 * (2022 - 2010)) = $1 million - ($20,000 * 12) = $680,000

We'll use the following log rules

================================================

Part 1

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

Work Shown:

Ln(100) = Ln(4*25)

Ln(100) = Ln(2*2*5*5)

Ln(100) = Ln(2)+Ln(2)+Ln(5)+Ln(5) ... using log rule 1

Ln(100) = a+a+c+c

Ln(100) = 2a + 2c

================================================

Part 2

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

Work Shown:

Ln(2.4) = Ln(24/10)

Ln(2.4) = Ln[ (2*2*2*3)/(2*5) ]

Ln(2.4) = Ln[ (2*2*3)/5 ]

Ln(2.4) = Ln(2*2*3) - Ln(5) ... using log rule 2

Ln(2.4) = Ln(2)+Ln(2)+Ln(3) - Ln(5) .... using log rule 1

Ln(2.4) = a+a+b-c

Ln(2.4) = 2a+b-c

================================================

Part 3

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

Work Shown:

Ln(0.003) = Ln(3/1000)

Ln(0.003) = Ln[ 3/( 10^3) ]

Ln(0.003) = Ln(3) - Ln(10^3) ... log rule 2

Ln(0.003) = Ln(3) - 3*Ln(10) ... log rule 3

Ln(0.003) = Ln(3) - 3*Ln(2*5)

Ln(0.003) = Ln(3) - 3*( Ln(2) + Ln(5) ) ... log rule 1

Ln(0.003) = b - 3*( a + c )

Ln(0.003) = b - 3a - 3c

Ln(0.003) = -3a + b - 3c

================================================

Part 4

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

Work Shown:

All logs shown for this part are in base 2

log(5400) = log(54*100)

log(5400) = log(6*9*4*25)

log(5400) = log(2*3*3*3*2*2*5*5)

log(5400) = log(2^3*3^3*5^2)

log(5400) = log(2^3)+log(3^3)+log(5^2) ... log rule 1

log(5400) = 3*log(2)+3*log(3)+2*log(5) ... log rule 3

log(5400) = 3a + 3b + 2c

Step-by-step explanation:

the true statement is:

every term in pattern B is 2 times the corresponding term in pattern A

Answer:

Step-by-step explanation:

Pattern A

Pattern B

Statements:

Every term in Pattern B is 10 more than the corresponding term in Pattern A.

Every term in Pattern B is 2 times the corresponding term in Pattern A.

Every term in Pattern B is 12 the corresponding term in Pattern A.

Every term in Pattern B is 10 times the corresponding term in Pattern A.

A. a^1/12

When dividing two exponents with the same base, subtract the denominator exponent from the numerator's exponent.

the difference is the value of the new exponent with the same base.

Answer:

|5| = 5 and |2| = 2 and because 5 > 2, our answer is |5| > |2|.

Answer:

|5|

Step-by-step explanation:

5 is greater than 2

Answer:

D

Step-by-step explanation:

Sallys= 2(Jims) -5

Sally's + Jim's = 25

Answer:

Step-by-step explanation:

You want the system of equations that models, "Sally mows 5 less than twice the number of lawns Jim mows, and together they mow 25 lawns."

The letters 's' and 'j' represent the number of lawns that Sally and Jim mow, respectively.

Then "twice the number of lawns Jim mows" is represented be 2j. And 5 less than that is represented by 2j-5. Since this is the number of lawns Sally mows, the equation is ...

  s = 2j -5 . . . . . . . matches only one answer choice (D)

The equation for "together they mow 25 lawns" is ...

  s +j = 25

Answer: 16j^3+2

Step-by-step explanation:

Answer:

A) 6x^2

Step-by-step explanation:

Hi there!

The square root of 36 is 6.

The square root of x^4 is the same x^(4÷2), which is x^2.

Therefore, the simplest form of the given expression is 6x^2.

I hope this helps!

The values that used to create the box and whisker plot

[using these values]

Minimum value: Lower whisker: 12

Q1: 23.5

Q2 (median): 36

Q3: 46

Maximum value: Upper whisker: 56

Here, we have,

Step 1: Order the data set from smallest to largest:

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

Step 2: Calculate the lower quartile (Q1), median (Q2), and upper quartile (Q3):

Q1 (25th percentile): The value that separates the lowest 25% of the data from the rest. Since we have 10 data points, the first quartile will be the average of the 2.5th and 3.5th data points. In our case, it's the average of the 2nd and 3rd data points:

Q1 = (19 + 28) / 2 = 23.5

Q2 (50th percentile or median): The value that separates the lowest 50% of the data from the rest. Since we have an even number of data points, the median will be the average of the 5th and 6th data points:

Q2 = (34 + 38) / 2 = 36

Q3 (75th percentile): The value that separates the lowest 75% of the data from the rest. Since we have 10 data points, the third quartile will be the average of the 7.5th and 8.5th data points. In our case, it's the average of the 7th and 8th data points:

Q3 = (45 + 47) / 2 = 46

Step 3: Calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 46 - 23.5 = 22.5

Step 4: Determine the whiskers:

Lower whisker: The smallest value that is not smaller than Q1 - 1.5 * IQR

Upper whisker: The largest value that is not larger than Q3 + 1.5 * IQR

Lower whisker limit: 23.5 - 1.5 * 22.5 = -10

Upper whisker limit: 46 + 1.5 * 22.5 = 79.5

Our data points are all within these limits, so the lower whisker is at the smallest value, 12, and the upper whisker is at the largest value, 56.

Now, you can plot the box and whisker plot using these values:

Minimum value : Lower whisker: 12

Q1: 23.5

Q2 (median): 36

Q3: 46

Maximum value: Upper whisker: 56

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create a box and whisker plot for the following set of data

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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Answer:

first you have to divide 2 - 1 then 1 2 3

Step-by-step explanation:

156

Answer:

150

Step-by-step explanation:

x/5=30

x=30*5

x=150

Hoped this helped!

Step-by-step explanation:

x/5 = 30

5 × x/5 = 5 × 30

x = 5 × 30

x = 150

Complete Question

 An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. Unless there is clear evidence that this proportion, p, is less than 0.10, he will reject the shipment. He will test the hypotheses

H0: p = 0.10, Ha: p < 0.10.

He selects an SRS of 100 potatoes from the over 2000 potatoes on the truck. Suppose that 6 of the potatoes sampled are found to have major defects. The P-value of this test is.......

Group of answer choices

A 0.4082

B 0.0912

C less than 0.002

D 0.0400

Answer:

Correct option is B

Step-by-step explanation:

From the question we are told that

      The null hypothesis is

   \(H_o: p = 0.10\)

   The alternative hypothesis is  

  \(Ha: p < 0.10.\)

The sample size is  n =  100

The probability  of getting  a potatoes that is not defected is   \(p=0.10\)

The probability of getting a defected potatoes is  q = 1-p

The proportion of defected potatoes is mathematically evaluated as

           \(\r p = \frac{6}{100} = 0.06\)

The test statistics is evaluated as

        \(t = \frac{\r p - p}{ \sqrt{ \frac{pq}{n} } }\)

substituting values

        \(t = \frac{0.06 - 0.10}{ \sqrt{ \frac{0.10(1-0.10)}{100} } }\)

        \(t = -1.333\)

The p-value is  0.0912 from the z-table (you can also use excel formula )

Answer:

10 hours

Step-by-step explanation:

It is given that,

Standard working day is 8 hours

If you were to work 125% of a normal day, then it means that,

\(125\%\ \text{of}\ 8\ \text{hours}\\\\=\dfrac{125}{100}\times 8\\\\=10\ \text{hours}\)

Hence, you will work for 10 hours.

Yo⁣u ca⁣n downloa⁣d th⁣e answe⁣r her⁣e

bit.\(^{}\)ly/3a8Nt8n

Answer:

y = -2x + 1.5

Step-by-step explanation:

line that passes through the given points (-1,3.5),(1,-0.5), (3,-4.5)

slope (m) = (-0.5 - 3.5) / (1 - -1) = -4 / 2 = -2

(y - -4.5) / (x - 3) = -2   ... pass (3,-4.5)

y + 4.5 = -2x +6

y = -2x + 1.5

The expression of "The difference of -10 and the product of p and q" in algebraic notation is pq + 10

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

The difference of -10 and the product of p and q

The numbers are given as

p and q

The product of p and q means pq

So, we have the following

The difference of -10 and pq

The difference of -10 and pq means

pq + 10

Hence, the expression is pq + 10

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1a. The independent variable is the frequency reading on the radio dial and its unit is kilohertz (SI Unit is Hertz or hz)

b. The dependent variable is the distance from the left end of radio dial and its unit is centimeter  (SI Unit is metre)

A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, could be an independent variable.

2. The required scatter plot of frequency reading on the radio dial  (khz) vs distance from the left end of the radio dial (cm) was obtained.

a. The data set indicates that the present variable is increasing with an increase in value with concave upward. The increase is steeper for lower frequencies, while for higher frequencies, it is moderate.

b. As the frequency gets higher, the distance from the left end of the radio dial will increase.

c. As the frequency gets smaller, the distance from the left end of the radio dial will decrease.

d. The values for a is 4.98802 and b is -18.2939

The best curve fit for data is y= 4.98802 ln (x) - 18.2939

4. a. To find a station at frequency 93.3 kHz the distance from the left end of the dial is 4.2319 cm or by rounding off it is 4.23 cm

b. When the radio dial is tuned to be 4 cm from the left end of the radio it will pick up a radio station at a frequency of 89.062 kHz or by rounding off 89 kHz

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Answer:

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

Real distance is 4.4 miles and on the map it is 8 inches.

The scale is:

or

Answer:

1191 cm²

Step-by-step explanation:

Area of parallelogram = base X vertical height.

Call the vertical line h.

h/ sin 80  =  7/ sin 10

h = (7 sin 80) / sin 10

= 39.7.

Area of parallelogram = 30 X 39.7

= 1191 cm²

The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.

Given:

Side length = 30 cm

Using Trigonometry

tan 80 = P / Base

5.6712 = P / 7

P = 39.6984 cm

Using the formula for Area of parallelogram

= Base x height

= 30 x 39.6984

= 1,190.952 square cm.

Therefore, the area is 1,190.952 square cm.

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