Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A librarian is expanding some sections of the city library. He buys books at a special price from a dealer who charges one price for any hardback book and another price for any paperback book. For the children's section, Mr. Howard purchased 100 new hardcover books and 72 new paperback books, which cost a total of $1,760. He also purchased 97 new hardcover books and 72 new paperback books for the adult fiction section, spending a total of $1,718. What is the special price for each type of book?The special price is $ for hardcover books and $ for paperback books.

Since we are looking for the speed you ran back home, which is r - 3, we can discard the solution of 1.8 (which would give a negative speed) and conclude that you ran back home at a speed of 2.8 miles per hour slower than your speed on the way to the park.

Speed is a measure of how fast an object is moving. It is defined as the distance traveled by the object per unit of time. The most common unit of speed is meters per second (m/s), but other units like kilometers per hour (km/h) and miles per hour (mph) are also used.

Speed is a scalar quantity, which means it only has a magnitude (i.e., the numerical value) and no direction. For example, if a car is traveling at a speed of 60 km/h, we only know how fast it is moving, but we don't know in which direction it is traveling.

Average speed is calculated by dividing the total distance traveled by the time taken to travel that distance. Instantaneous speed is the speed at a particular instant in time and can be found by calculating the rate of change of position with respect to time.

Speed can be influenced by several factors, such as the distance traveled, the time taken to travel that distance, and the presence of obstacles or resistance.

a. The total time you ran can be calculated by adding the time it took you to run to the park and the time it took you to run back home. Let's assume that you ran at a constant speed of "r" miles per hour. Then:

Time to run to the park = Distance / Speed = 18 / r

Time to run back home = Distance / Speed = 15 / (r - 3)

Total time = 18 / r + 15 / (r - 3)

b. To find how fast you ran back home, we can set up an equation using the information given:

Distance = 15 miles

Speed = r - 3 miles per hour (since you were 3 miles per hour slower on the way back)

Time = Distance / Speed

15 / (r - 3) = Time it took to run back home

We don't have enough information to solve for r directly, but we can simplify the equation by multiplying both sides by (r - 3):

15 = Time x (r - 3)

Now we can substitute the expression for the total time we found in part a:

[tex]15 = (18 / r + 15 / (r - 3)) x (r - 3)[/tex]

Expanding and simplifying:

[tex]15r(r - 3) = 18(r - 3) + 15r15r^2 - 45r = 18r - 54 + 15r15r^2 - 48r + 54 = 0[/tex]

Dividing both sides by 3:

5r^2 - 16r + 18 = 0

Using the quadratic formula:

[tex]r = [16 \± \sqrt{(16^2 - 4 \times 5 \times 18)] / 10}r = [16 \± 2] / 10r = 1.8 or 2.8[/tex]

Since we are looking for the speed you ran back home, which is r - 3, we can discard the solution of 1.8 (which would give a negative speed) and conclude that you ran back home at a speed of 2.8 miles per hour slower than your speed on the way to the park.

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The atomic number of an element always indicates the following: B. the number of protons in an atom.

In Chemistry, a chemical element can be defined as a pure substance that comprises atoms having the same atomic number (number of protons) in its nuclei and as such, it is the primary constituent of matter.

Mathematically, mass number is represented by this mathematical expression:

A = Z + N  or [tex]^A_ZC[/tex]

Where:

In conclusion, the number of protons is also referred to as an atomic number.

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Answer:

19.72

Step-by-step explanation:

Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, the value of the account will reach $153,400 after 9 years.

To calculate this, we can use the formula for the future value of a single sum invested with an inverted interest rate compounded continuously.

Future Value = Present Value × (1 + r)n

Where:

We can solve for n to find out how many years it will take to reach $153,400.

153,400 = 96,000 × (1 + 0.035)n

153,400/96,000 = (1 + 0.035)n

Taking the natural log of both sides and simplifying:

ln(153,400/96,000) = n × ln(1.035)

n = ln(153,400/96,000)/ln(1.035)

n ≈ 8.99

To the nearest year, it will take 9 years for the value of the account to reach $153,400.

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The coordinates of C are (-6, -3)

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

A = (-9, -5)

B = (6, 5)

m : n = 1 : 4 i.e. 1/5

The coordinate is then calculated as

C = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

C = 1/5 * (1 * 6 + 4 * -9, 1 * 5 + 4 * -5)

Evaluate

C = (-6, -3)

Hence, the coordinate is (-6, -3)

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Answer:

exponential decay

Step-by-step explanation:

because the value that is being multiplied 0.85 is less then 1 then the value decreases.

Ex. when x=0, y=2770, then when x=1, y=2770(0.85) = 2354.5...

The variable V represents Victoria's age and the variable D represents her dad's age.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.

The equation that relates Victoria's age (V) to her dad's age (D) when Victoria is 18 years old is:

D = V + 18

The variable V represents Victoria's age and the variable D represents her dad's age.

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The IQR measures the spread of the middle 50% of the data.

Without knowing the actual values of the fuel economy ratings or the summary statistics, we cannot provide an exact answer. However, we can make some general observations about the effects of removing an extreme outlier on the standard deviation and the interquartile range (IQR).

First, the standard deviation measures the spread of the data around the mean. Removing an extreme outlier that is far from the mean could potentially decrease the standard deviation, as the remaining values may be more tightly clustered around the mean. However, the effect on the standard deviation will depend on the exact values of the data points and how much they vary from the mean.

Second, the IQR measures the spread of the middle 50% of the data. Removing an extreme outlier that is far from the bulk of the data may not have a significant effect on the IQR, as the remaining.

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The probability of at least one appearance in a 21-alternate period is 0.969803

(a) The appearance  rate is 10 passengers nanosecond , so the anticipated number of advents  in nanosecond is also 10. The probability of no advents  in one minute is given by the Poisson distribution with parameter lambda = 10:

P(X = 0) = [tex]e^{(-lambda)}[/tex] [tex]lambda^{0}[/tex] / 0! =  [tex]e^{(-10)}[/tex]* [tex]10^{0}[/tex] / 1! = 0.000045 (rounded to 6 decimal places)

Therefore, the probability of no arrivals in one-minute period is 0.000045.

(b) To compute the probability that three or fewer passengers arrive in one-minute period, we can use the cumulative distribution function (CDF) of the Poisson distribution:

P(X <= 3) = sum from i=0 to 3 of P(X = i)

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

= [tex]e^{-10}[/tex] *[tex]10^{0}[/tex] / 0! + [tex]e^{(-10)}[/tex] * [tex]10^{1}[/tex]/ 1! + [tex]e^{(-10)}[/tex] * [tex]10^{2}[/tex] / 2! + [tex]e^{(-10) }[/tex]* [tex]10^{3}[/tex]/ 3!

= 0.010336 (rounded to 6 decimal places)

Therefore, the probability that three or fewer passengers arrive in one-minute period is 0.010336.

(c) The arrival rate is 10 passengers per minute, which is equivalent to 10/60 = 1/6 passengers per second. Therefore, the expected number of arrivals in a 21-second period is (1/6) * 21 = 3.5 passengers. The probability of no arrivals in a 21-second period is given by the Poisson distribution with parameter lambda = 3.5:

P(X = 0) = [tex]e^{(-lambda)}[/tex] * l[tex]lambda^{0}[/tex] / 0! = [tex]e^{(-3.5)}[/tex] * [tex]3.5^{0}[/tex]/ 1! = 0.030197 (rounded to 6 decimal places)

Therefore, the probability of no arrivals in a 21-second period is 0.030197.

(d) The probability of at least one arrival in a 21-second period is equal to 1 minus the probability of no arrivals:

P(at least one arrival) = 1 - P(no arrivals)

= 1 - 0.030197

= 0.969803 (rounded to 6 decimal places)

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Step-by-step explanation:

The prime factor of the 144 is 24 x 32. The exponents in the prime factorisation are 4 and 2. Add the number 1 with the exponents and multiply it. (4+1)(2+1) = 5 x 3 = 15.

Answer:

25 / 2

Step-by-step explanation:

12.5% = 125 / 10 ( simplify the fraction with 5 )

= 25 / 2

I am to believe the answer is Yes because you add the exponents

The conversion of 65 kilos in pounds is equivalent to approximately 143.3 pounds.

Its name derives from the Latin word "poundus" meaning "weight". The £ symbol comes from an ornate L in Libra. The pound was a unit of currency as early as 775AD in Anglo-Saxon England, equivalent to 1 pound weight of silver.The approximation we use for kilograms (kg) to pounds (lb) is 1 kg = 2.2 lb. To convert from kilogram to pound, we multiply by 2.2. To convert from pound to kilogram, we divide by 2.2.

To convert 65 kilograms to pounds, you can use the conversion factor of 1 kilogram = 2.20462 pounds.

Therefore,65 kilograms = 65 x 2.20462 pounds= 143.3003 pounds (rounded to 4 decimal places)

So, 65 kilograms is equivalent to approximately 143.3 pounds.

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The characteristics of a data set are enumerated by descriptive statistics. You can test a hypothesis or determine whether your data can be applied to a larger population by using inferential statistics.

To summarize a given data set, which may be a sample of a population or a representation of the entire population, brief informational coefficients known as descriptive statistics are used.

The two primary subcategories of descriptive statistics are measures of central tendency and measures of variability (spread). Descriptive statistics are thus used to summarize the data. Descriptive statistics can only ever make claims about the data set from which they were derived, using only the data that you have.

Statistical inference is the process of determining characteristics of an underlying probability distribution through the use of data analysis. Inferential statistical analysis, for instance, infers characteristics of a population by testing hypotheses and producing estimates.

Inferential statistics looks to identify some characteristic or overarching pattern about a large group through the study of a smaller sample size in the hopes that the results will apply to the larger group.

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Answer:

28 daisies

Step-by-step explanation:

4:2 = daisies:carnations

4:6 = daisies:total flowers

4/6 = x/42    x=number of daisies

6x = 4(42) = 168

x = 168/6 = 28

y = number of carnations = 42 - 28 = 14

Double check the answer:

28/14 = 4/2    ratio is correct!

Answer: 50 meters

Perimeter = 2W x 2L OR W+W+L+L (the measurement of all sides of a shape)

Width = 9 meters

Length = 16 meters

9(2) + 16(2) = 50 meters

the value of a is 7/6 and the value of b is 0.

The tangent is an immediate line that simply touches the curve at a given point. The regular is an immediate line this is perpendicular to the tangent. the slope of any line perpendicular to a line with slope m is the terrible reciprocal −1/m.

Given a curve y = ax + b/√x.

with the constant value of a and b.

First, we need to find the derivative of the curve y = ax + b/√x in order to find the gradient of the tangent to the curve at any given point. We can use the quotient rule to differentiate the equation:

dy/dx = a - (b/2)x^(-3/2)

Now we can find the gradient of the tangent to the curve at the point (4, 12) by substituting x = 4 into this equation:

dy/dx = a - (b/2)4^(-3/2) = a - b/16

The gradient of the normal to the curve at this point is the negative reciprocal of the gradient of the tangent, so:

-1/m = -(a - b/16)

We know that the equation of the normal is given by:

3y + 2x = 44

We can use this to substitute in y in terms of x:

y = (44 - 2x)/3

Now we can substitute this into the expression for -1/m:

-1/m = -(a - b/16) = -(dy/dx) = -(a - b/2x^(3/2)) = -(a - b/2(4)^(3/2))

-1/m = -(a - b/8)

Simplifying this equation, we get:

1/m = a - b/8

Substituting the value of m = -3 into this equation (because the gradient of the normal is -3), we get:

-1/3 = a - b/8

Multiplying through by 8, we get:

-8/3 = 8a - b

We also know that the curve passes through the point (4, 12), so we can substitute this into the equation for the curve:

12 = 4a + b/2

Multiplying through by 2, we get:

24 = 8a + b

Now we have two equations in two variables:

-8/3 = 8a - b

24 = 8a + b

Adding the two equations together, we get:

56/3 = 16a

Dividing through by 16, we get:

a = 7/6

Substituting this into one of the equations, we get:

24 = 8(7/6) + b

b = 0

Therefore, the value of a is 7/6 and the value of b is 0.

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Answer:

Step-by-step explanation:

first step you want round that into decimal

Answer:

34/5

Step-by-step explanation:

The coordinates of Room 1314 are given as follows:

(2, 13).

We are going to label the rooms are follows:

Then the coordinates of Room 1314 are obtained applying the proportions in the context of the problem.

Room 1314 is located five-sevenths of the distance from Room 1305 to Room 1324, hence the equation is given as follows:

Z - X = 5/7(Y - X).

Then the x-coordinate is obtained as follows:

x + 8 = 5/7(6 + 8)

x = 10 - 8

x = 2.

The y-coordinate is obtained as follows:

y + 2 = 5/7(19 + 2)

y + 2 = 15

y = 13.

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The value of x is given as follows:

59º.

To obtain the value of x, we must consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angles for the triangle in this problem are given as follows:

Hence the value of x is obtained as follows:

35 + 96 + x = 180

x = 180 - 131

x = 59º.

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The height of the silo, to the nearest meter is, 84.9 m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A surveyor needs to determine the height of a large grain silo.

And,  He positions his transit 65 m from the silo and records an angle of elevation of 52º.

Now, By the given condition we can formulate;

tan 52° = x / 65

x = 83.2 m

Here, the height of the transit is 1.7 m,

Thus, The height of the silo, to the nearest meter is,

83.2 + 1.7 m

84.9 m

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Answer:

Step-by-step explanation:

f(x)=2(3^x)+1

f(2)=2(3^2)+1

f(2)=2(9)+1

f(2)=18+1

f(2)=19

The required number of dollars in a year per 37 dollars in an hour equals 324,120 dollars.

Number of dollars in one hour is equal to 37 dollars.

Relation between year and hour .

1 year = 12 months

1 month = 31, 30 or 28 days

Total number of days in a year = 365 days

Number of hours in 1 day = 24 hours

Number of hours in 365 days = ( 365 × 24 ) hours

                                                 = 8760 hours

In 1 hour = 37 dollars

⇒ 8760 hours = ( 37 × 8760 ) dollars

⇒ 8760 hours = ( 324,120 ) dollars

⇒ 1year = (  324,120  ) dollars

Therefore, the number of dollars in a year is equal to  324,120 dollars.

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The probability of selecting the integer 318 is 0

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

Sample space = 1 to 50

The integer 318 is not in the range of integers that the random number generator can select from (1 to 50).

Hence, the required probability of selecting the integer 318 is 0.

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Quadrilateral MNOP is similar to quadrilateral QRST. The measure of side RS is approximately 39.2 units.

If two quadrilaterals are similar, their corresponding sides are in proportion. Therefore, we can set up a proportion between the corresponding sides of quadrilaterals MNOP and QRST as follows:

MN / QR = NO / ST = OP / RS

We are given the lengths of MN, NO, and OP, but we need to find the length of RS. We can solve for RS by rearranging the proportion as follows:

OP / RS = MN / QR

RS = OP / (MN / QR)

We can substitute the given values to get:

RS = 58 / (19 / 13)

Simplifying this expression gives:

RS = 58 * (13 / 19) = 39.241 ≈ 39.2

Therefore, the measure of side RS is approximately 39.2 units.

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____The given question is incomplete, the complete question is given below:

Quadrilateral MNOP is similar to quadrilateral QRST. Find the measure of side RS. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale. QT =58, PM= 19 ON=13.

Answer:1. a+b/a-b

2. 8/x-y

3. 2q+p/pq^2

Don’t know how to do the last two sorry

Step-by-step explanation:

The value of minutes can be converted to hours by dividing the value of minute by 60 so 115000 minutes means 1916.66 hours.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

With the help of our conversion tools, you can convert 115000 Minutes to Days (min to d). Use the direct conversion formula below to convert 115000 min to d.

115000 min = 79.861111111111 d.

Also, you can change 115000 Minutes into other Time (common) units.

We will create an equation to convert 115000 minutes to hours, then utilise the equation to perform the conversion. Since there are 60 minutes in an hour, we can construct our equation as follows:

Hours = Minutes / 60

In the equation above, we may convert 115000 minutes to hours by substituting 115000 minutes, giving the following result:

115000 / 60 = Hours

1916 2/3 hours divided by 115000 minutes is 1916.66667 hours.

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