9 books cost $47.25. What is the unit rate?

The number of cards left to be signed is 32 cards.

To determine the number of cards left to be signed, we need to calculate the number of cards signed by each person and subtract it from the total number of cards.First, Emily signed 2/5 of the cards, which is equal to (2/5) * 75 = 30 cards.

Next, we need to find the number of cards remaining after Emily signed. To do this, we subtract the cards Emily signed from the total number of cards:

75 - 30 = 45 cards.

Now, Josh signs 1/9 of the remaining cards, which is equal to (1/9) * 45 = 5 cards.

After Josh signs his portion, we need to find the number of cards still remaining. We subtract the cards Josh signed from the previous remaining cards:

45 - 5 = 40 cards.

Finally, Tatiana signs 20% of what Josh had left, which is equal to 20/100 * 40 = 8 cards.

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Due to length restrictions, we kindly invite to read the explanation for further details on how to go across the maze with linear functions.

In this problem we find a maze formed by representations of linear functions on Cartesian plane, of which we must determine the slope of each line until finish is reached. This can be done by understanding the following instructions based on results from secant line formula:

The procedure to go across the maze is shown below:

FAIL

SUCCESS

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The expression, (6x - 2) - (-x + 5), is simplified as 7x - 7. The student's error was wrong calculation in the final steps where he subtracted 2 from 5.

A simplified expression is an expression that is evaluated to its simplest form, that is, it cannot be simplified further.

Given:

(6x - 2) - (-x + 5)

Open the bracket by multiplying each of the terms in (-x + 5) by the negative sign (-):

6x - 2 + x - 5

Combine like terms

7x - 7

Thus, the expression, (6x - 2) - (-x + 5), is simplified as 7x - 7. The student's error was wrong calculation in the final steps where he subtracted 2 from 5.

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Answer:

(3x + 2)(-x^3 - 3) =

3x(-x^3 - 3) + 2(-x^3 - 3) =

-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)

now multiply that by (3+x)...

(3+x)(-3x^4 - 2x^3 - 9x - 6) =

3(-3x^4 - 2x^3 - 9x - 6) + x(-3x^4 - 2x^3 - 9x - 6) =

-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =

-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)

the coefficient of x^4 = -11 <==

Step-by-step explanation:

Answer:

(3x + 2)(-x^3 - 3) =

3x(-x^3 - 3) + 2(-x^3 - 3) =

-3x^4 - 2x^3 - 9x - 6 <== result of multiplying (3x+2)(-x^3-3)

now multiply that by (3+x)...

(3+x)(-3x^4 - 2x^3 - 9x - 6) =

3(-3x^4 - 2x^3 - 9x - 6) + x(-3x^4 - 2x^3 - 9x - 6) =

-9x^4 -6x^3 - 27x - 18 - 3x^5 - 2x^4 - 9x^2 - 6x =

-3x^5 - 11x^4 - 6x^3 - 9x^2 - 33x - 18 <== result of multiplying by (3 + x)

the coefficient of x^4 = -11 <==

Step-by-step explanation:

Measure of angle ABC = (3x)°

Measure of angle CBD = (15x+18)°

Since angle ABC and angle CBD are a linear pair their sum will be equal to 180°¿

Which means :

\( =\tt 3x + 15x + 18 = 180\)

\( =\tt 18x + 18 = 180\)

\( = \tt18x = 162\)

\( =\tt x = \frac{162}{18} \)

\(\color{plum} \tt= x = 9\)

Thus, the value of x = 9.

From that equation, we know that the value of x = 9.

Which means :

Measure of angle ABC :

\( =\tt 3x\)

\( =\tt 3 \times 9\)

\(\tt\color{plum} \: angle \: ABC = \tt27°\)

Measure of angle ABC = 27°

Therefore, the measure of angle ABC = 27°

We know that x = 9

Which means :

Measure of angle CBD :

\( =\tt 15x + 18\)

\( = \tt15 \times 9 + 18\)

\( = \tt135 + 18\)

\(\color{plum} \tt \: angle \: CBD = 153°\)

Thus, angle CBD = 153°

Since the measure of angle ABC and angle CBD equals 180°[27+153=180°], we can conclude that we have found out the correct value of each angle.

Therefore, the measure of angle CBD = 153°

Answer:

Blue Star

a.                                   The Ford TriVan   The Honda CityVan

Total life-cycle costs          $94,368                $90,936

Based on life cycle cost, the Honda CityVan is the best choice.

b. Blue Star needs to put on the Ford TriVan 9,032 miles more for the cost to be equal with the Honda CityVan's.

c. The crossover point in years = 5 months

Step-by-step explanation:

a) Data and Calculations:

                                        The Ford TriVan   The Honda CityVan

Purchase costs                  $28,000                 $32,000

Fuel efficiency per gallon   24 miles                 37 miles

Operating cost per mile     $0.20                     $0.22

Total operating costs         $4,400                   $4,840

Estimated annual distance 22,000 miles        22,000 miles

Gallons of fuel consumed  916.7 (22,000/24) 594.6 (22,000/37)

Total cost of fuel                 $3,896                  $2,527

Fuel cost per mile              $0.18                      $0.115

Total cost per mile             $0.38                     $0.335

Expected life of truck         8 years                   8 years

Average gas price = $4.25 per gallon

Total costs:

                                        The Ford TriVan   The Honda CityVan

Annual costs:

Total operating costs         $4,400                   $4,840

Total cost of fuel                $3,896                   $2,527

Annual costs                      $8,296                   $7,367

Life cycle costs:

Annual costs for 8 years   $66,368                $58,936

Purchase costs                  $28,000                $32,000

Total life-cycle costs          $94,368                $90,936

Difference in costs between Ford TriVan and Honda CityVan = $3,432 ($94,368 - $90,936)

Miles to put on the Ford TriVan for the life cycle cost to be equal to the life cycle cost of the Honda CityVan

= Difference in costs divided by total cost per mile of the Ford TriVan

= 9,032 miles ($3,432/$0.38)

Annual distance = 22,000 miles

Monthly distance = 1,833 miles

9,032/1,833 = 4.93 months or 5 months approximately

Answer:

x > -11/10

Step-by-step explanation:

-2/6(4-x) < 4(x+1/2)

-1/3(4-x) < 4x + 2

-4/3 + 1/3x < 4x + 2

-4 +x < 12x + 6

x - 12 x < 6 + 4

-11x < 10

x > -11/10

200.60 interest does andy’s account earn.

Let x be the amount of interest earned by Andy's account.

According to the problem, Andy's account earns 0.3% more interest than Marty's account, which means that Andy's account earns the same amount plus an additional 0.3% of that amount. Mathematically, we can express this as:

x = 200 + 0.3% of 200

Simplifying the right-hand side of the equation, we get:

x = 200 + 0.003 × 200

x = 200.60

Therefore, the answer is option 1: 200.60.

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Therefore, the equation of the line passing through (0, 2) and (6, 6) in y=mx+b form is y = (2/3)x + 2.

We must ascertain the slope (m) and the y-intercept in order to compute the equation of a line with the formula y=mx+b. (b).

The following formula determines the slope of a line via the points (x1, y1) and (x2, y2):

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

Using (0, 2) and (6, 6), we can calculate:

m = (6 - 2)/(6 - 0) = 4/6 = 2/3

As a result, the line has a 2/3 slope.

We may use the point-slope form of the equation to determine the y-intercept:

y - y1 = m(x - x1)

Using the slope we just discovered and the location (0, 2), we have:

y - 2 = (2/3)x

When we simplify this equation, we obtain:

y = (2/3)x + 2

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Answer:

\(x=3\text{ or } x=-15\)

Step-by-step explanation:

So we have the equation:

\(|2x+12|=18\)

Definition of Absolute Value:

\(2x+12=18\text{ or } 2x+12=-18\)

Subtract 12 from both sides for both equations:

\(2x=6\text{ or } 2x=-30\)

Divide both sides by 2 for both equations:

\(x=3\text{ or } x=-15\)

And we're done!

Answer:

Step-by-step explanation:

4). Domain: ( - ∞ , ∞ )

Range: [ - 4 , ∞ )

5). Domain: ( - ∞ , ∞ )

Range: ( - ∞ , ∞ )

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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Answer:

I'm gonna head with B forgive me I'd I'm wrong

Answer:

Below

Step-by-step explanation:

32/2 x 100% = 1600 %

Answer:

415 miles

Step-by-step explanation:

Start with the speed equation:

speed = distance/time

Now solve the speed equation for distance:

distance = speed × time

Apply the speed equation solved for distance to the two parts of the trip.

4 hours at 55 mph:

distance = 55 mph × 4 hours = 220 miles

3 hours at 65 mph:

distance = 65 mph × 3 hours = 195 miles

Add the two distances to find the total distance:

total distance = 220 miles + 195 miles = 415 miles

Answer: 415 miles

Answer:

415 miles

Step-by-step explanation:

Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.

How far did he drive?

d=rt

For the first part of the trip:

d = 55 * 4 = 220 miles

For the second part of the trip:

d = 65*3 =195 miles

Add the miles together

220+195 = 415 miles

The main answer is that without specific values or elements for sets A and B, we cannot determine the result of A - B and B - A.

To find A - B, we need to subtract the elements in set B from set A. Similarly, to find B - A, we need to subtract the elements in set A from set B.

However, I need the specific values or elements of sets A and B to perform the calculations. Could you please provide the values or elements of the sets?In order to perform set subtraction, we need the specific elements or values of sets A and B. Set subtraction involves removing the common elements between the sets.

Let's say set A is {1, 2, 3} and set B is {2, 3, 4}. To find A - B, we remove the elements in set B from set A. Thus, A - B would be {1}.

To find B - A, we remove the elements in set A from set B. Therefore, B - A would be {4}.

Please provide the values or elements of sets A and B, and I will be able to calculate A - B and B - A accordingly.

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The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.

The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.

The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.

An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.

In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

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Answer:

125 minutes

Step-by-step explanation:

got it right on edge

Answer:

B. 125 minutes

Step-by-step explanation:

edge 2020

Answer:

d

Step-by-step explanation:

The length of the arc is 20π/3 cm or approximately 20.94 cm.

To find the length of the arc, we need to know the angle of the sector that the arc belongs to, as well as the radius of the circle.

The sector angle is shown in the diagram to be 150 degrees, and the radius is shown to be 8 cm.

The following formula can be used to determine the length of an arc:

(Angle of Sector / 360) x 2r Equals length of arc

Inputting the values provided yields:

Arc length equals (150 / 360) x 2. (8)

Arc length = (5/12) x 16

Arc length = 20/3

As a result, the arc measures 20/3 cm, or roughly 20.94 cm.

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The length of the segment shown in the graph is 10 units

The endpoints on the line segment are : (2, - 1) and (-4,7)

The Length of a line segment can obtained using the relation :

Length = √(x2 - x1)² + (y2 - y1)²

Here,

x2 = - 4, x1 = 2, y2 = 7, y1 = - 1

Length of segment = √((-4) - 2)² + (7 - (-1))²

Length of segment = √(-6)² + (8)²

Length of segment = √36 + 64

Length of segment = √100 = 10 units

Therefore, the length of the segment on the graph shown is 10 units.

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A random number table can be used by first assigning a number to each subject and then randomly selecting the subjects for each group.

This is table that contains random numbers and it is used to select random samples.

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If one of the rows in the matrix of a system of linear equations is a multiple of another row, the row-reduced form of the matrix will have a row of zeros.

One of the steps in the row reduction process is the elimination of a variable by subtracting a multiple of one row from another row. This operation will produce a row of zeros if one row is a multiple of another.

Hence, when one of the rows in the matrix of a system of linear equations is a multiple of another row, the row-reduced form of the matrix will have a row of zeros.

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Answer:

It has equal numbers of neutrons and protons.

Since the graph never crosses the x-axis, the function has no real zeros

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

The graph (see attachment)

From the graph, we can see that the graph does not cross the x-axis at any point

This means that the graph has no real zero

Hence, the relationship between the zero and x-intercept is (b)

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Given:

Two cards are drawn from a standard deck of 52 cards without replacement.

To find:

The probability that both cards selected for black.

Solution:

We know that,

Total number of cards = 52

Total number of red cards = 26

Total number of black cards = 26

\(\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\)

Probability of selecting first black card is

\(\text{Probability}=\dfrac{26}{52}\)

\(\text{Probability}=\dfrac{1}{2}\)

Number of remaining total cards = 52-1 = 51

Number of remaining black cards = 26-1 = 25

Probability of selecting second black card is

\(\text{Probability}=\dfrac{25}{51}\)

So, the probability that both cards selected for black is

\(\text{Probability}=\dfrac{1}{2}\times \dfrac{25}{51}\)

\(\text{Probability}=\dfrac{25}{102}\)

Therefore, the required probability is \(\dfrac{25}{102}\).

The probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 8/25 or 0.32 (rounded to the nearest millionth).

1. Calculate the total number of students on the Student Government Board by summing up the numbers in the table:

  Total Students = 2 + 2 + 2 + 4 + 0 + 3 + 4 + 2 = 19

2. Calculate the total number of graduate students on the Student Government Board:

  Total Graduate Students = 2 + 0 = 2

3. Calculate the total number of students living in on-campus housing:

  Total On-Campus Housing = 2 + 2 + 0 + 4 + 2 = 10

4. Calculate the probability of selecting a graduate student from the Student Government Board by dividing the total number of graduate students by the total number of students:

  Probability of Graduate Student = Total Graduate Students / Total Students = 2 / 19

5. Calculate the probability of selecting a student living in on-campus housing by dividing the total number of students in on-campus housing by the total number of students:

  Probability of On-Campus Housing = Total On-Campus Housing / Total Students = 10 / 19

6. Calculate the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing by summing up the probabilities from steps 4 and 5:

  Probability = Probability of Graduate Student + Probability of On-Campus Housing = 2 / 19 + 10 / 19

7. Simplify the fraction if necessary. In this case, the fraction cannot be simplified further, so the final probability is 2 / 19 + 10 / 19 = 12 / 19.

8. Convert the fraction to a decimal by dividing the numerator by the denominator: 12 / 19 ≈ 0.631578947, which rounds to 0.632 (rounded to the nearest thousandth).

9. Finally, express the probability as a fraction in lowest terms: 12 / 19 is already in lowest terms.

Therefore, the probability that a randomly chosen member of the Student Government Board is a graduate student or lives in on-campus housing is 12/19 or approximately 0.632 (rounded to the nearest thousandth).

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Answer:

Step-by-step explanation:

From the given information:

Let X be the random variable;

The mean survival time is E(X):

E(X) = μ

E(X) = ∝β

E(X) = 5 × 10

E(X) = 50

To find the standard deviation, we must first determine the variance:

\(V(X) = \sigma ^2\)

\(V(X) = \alpha \beta ^2\)

\(V(X) = 5 \times (10)^2\)

\(V(X) = 5 \times 100\)

\(V(X) = 500\)

The standard deviation is:

\(\sigma =\sqrt{V(X)}\)

\(\sigma =\sqrt{500}\)

\(\sigma =22.361\)

The standard deviation of survival time = 22.361

(c)

P(X>30) = 1 - P(X ≤ 30)

\(= 1 - \int \limits ^{30}_{0} \ f(x) \ dx\)

\(= 1 - \int \limits ^{30}_{0} \dfrac{1}{\beta^{\alpha} \Gamma \alpha }x^{a-1} e ^{-x/\beta } \ dx\)

\(= 1 - \int \limits ^{30}_{0} \dfrac{1}{\beta^{\alpha} \Gamma (5)}x^{5-1} e ^{-x/10 } \ dx --- (1)\)

So, if:

\(y = \dfrac{x}{10}\)

\(dy = \dfrac{dx}{10}\)

10dy = dx

and limits of y are 0 and 3.

because;

for x = 0

\(y = \dfrac{0}{\beta}\)

y = 0

For x = 30

\(y = \dfrac{30}{10}\)

y = 10

From (1);

\(P(X> 30) = 1 - \int \limits ^{30}_{0} \dfrac{1}{\beta^{\alpha} \Gamma (5)}x^{5-1} e ^{-x/10 } \ dx\)

\(P(X> 30) = 1 - \int \limits ^{3}_{0} \dfrac{(10y)^4}{10^{5} \Gamma (5)}e ^{-y } \ dy\)   since y = x/β

\(P(X> 30) = 1 - \int \limits ^{3}_{0} \dfrac{10^4 y^4 \ e^{-y} }{10^{4} \Gamma (5)} \ dy\)

\(P(X> 30) = 1 - \int \limits ^{3}_{0} \dfrac{y^4 \ e^{-y} }{ \Gamma (5)} \ dy\)

Since;

\(F(a, \alpha )= \int \limits ^a_0 \dfrac{y^{a-1}e^{-y}}{\Gamma (\alpha )} dy\)

Then;

P(X> 30) = 1 - F(3,5)

From the table of incomplete gamma function;

P(X > 30) = 1 - 0.185

P(X > 30) = 0.815

Thus, the probability that an animal survives more than 30 weeks is 0.815

a)The mean survival time of a randomly selected animal of the type used in the experiment is 50.

b)Standard deviation of survival time is 22.36

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

Suppose x is the random variable.

It is given that α= 5 and β=10.

So, the mean survival E(x)=α β

The mean survival E(x) =5*10

The mean survival E(x) =50

We know that Variance =α β²

So, Variance = 5*10²

Variance =500

We know that standard deviation σ = √Variance

σ = √500

σ = 22.36

Therefore, a)the mean survival time of a randomly selected animal of the type used in the experiment is 50.

b)Standard deviation of survival time is 22.36

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The standard deviation is:

The standard deviation of survival time = 22.361