Answer:
6 hours
Step-by-step explanation:
Make an equation
Each hour costs $3, and there is a $12 cost regardless of the hours. We know that Lucy spent $30.
3h+12=30
Subtract 12 from both side s
3h=18
Divide both sides by 3
h=6
So, she rented it for 6 hours
Chloe has 10 books on her bookshelf. 3 of these books have blue covers, and 7 have red covers.
2 of the blue books are mystery novels, and 1 is a fantasy novel.
5 of the red books are mystery novels, and 2 are fantasy novels.
Chloe closes her eyes and randomly selects a book from her bookshelf. Let A be the event that she selects a red
book and B be the event that the book is a mystery novel.
Which of the following statements are true?
Answer:
D
Step-by-step explanation:
The outcomes of events. A and B are dependent on each other.
The question relates to probability in Mathematics, specifically the probability of selecting a red (event A) or a mystery novel (event B) from Chloe's bookshelf. Both probabilities are 7/10 as 7 out of 10 books are red or mysteries. The probability of both A and B occurring simultaneously is 5/10, as 5 out of 10 of the books are red mysteries.
Explanation:The subject of this question is the calculation of probabilities in Mathematics. Here we have two events: event A, defined as selecting a red book, and event B, defined as selecting a mystery novel. Considering Chloe's bookshelf, she has 7 red books out of a total of 10, meaning that the probability of event A is 7/10. In addition, she has 7 mystery novels out of a total of 10 books, meaning that the probability of event B is 7/10 also.
It can be said that both events A and B are independent, because the colour of the book does not affect what genre it is. Also, it's worth mentioning that the likelihood of both A and B occurring, meaning the selection of a red mystery novel is (5/10) as 5 out of 10 books are red and mysteries.
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Explain how you could use 25% of a number to find the number
Answer:
you know 25% is one fourth of 100%, aka the whole number, so just multiply the 25% of the number times 4 to get the whole number
Solve the system by the substitution method.
7x + 8y = -22
3x - y = 26
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution set is { } (Type an ordered pair.)
O B. There are infinitely many solutions.
O C. There is no solution.
Answer:
A) The solution set is (6,-8).
Step-by-step explanation:
3x - y = 26
-3x - 3x Subtract 3x from both sides
-y = -3x + 26 Divide both sides by -1
y = 3x - 26
Now plug this into 7x + 8y = -22 to solve for x
7x + 8(3x - 26) = -22 Distribute
7x + 24x - 208 = -22 Combine like terms
31x - 208 = -22
+ 208 + 208 Add 208 to both sides
31x = 186 Divide both sides by 31
x = 6
Plug this into y = 3x - 26 to solve for y
y = 3(6) - 26 Multiply
y = 18 - 26 Subtract
y = -8
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Final answer:
The system of equations is solved using the substitution method, resulting in x = 6 and y = -8. Hence, the correct choice is the ordered pair (6, -8).
Explanation:
To solve the system of equations by the substitution method, let's start by solving the second equation for y:
3x - y = 26
=> y = 3x - 26.
Now, substitute this expression for y into the first equation:
7x + 8(3x - 26) = -22
=> 7x + 24x - 208 = -22
=> 31x = 186
=> x = 6.
Now, substitute x back into the expression we found for y:
y = 3(6) - 26
=> y = 18 - 26
=> y = -8.
The solution to the system is the ordered pair (6, -8), which means the correct choice is:
O A. The solution set is { (6, -8) } (Type an ordered pair.)
(20 points)
Which number can be multiplied with a rational number to illustrate that the product of
two rational numbers is rational
Answer:
The answer would be B) -2 1/8
Step-by-step explanation: i just took the test and i got that right
Answer:
B) -2⅛
Step-by-step explanation:
All other options are irrational
An equilateral triangle is similar to a scalene triangle. True or False
Answer:
False.
Step-by-step explanation:
All the sides of an equilateral triangle are equal.
None of the sides of a scalene triangle are equal to each other.
Therefore, an equilateral triangle is not similar to a scalene triangle.
The distance from a ship to two lighthouses on the shore are 4 miles and 7 miles respectively. If the angle between the two lines of sight is 45, find the distance between the lighthouses
Answer:
5 miles
Step-by-step explanation:
In the diagram, the distance between the lighthouse is |AB|=c.
Using Cosine Rule,
c²=a²+b²-2abCos C
=7²+4²-2(4)(7)Cos 45°
=49+16-56cos45°
=25.40
c=√25.40=5.04 miles
The distance between the lighthouses is approximately 5 miles.
Answer:
The distance between the two lighthouse is 5miles
Step-by-step explanation:
Since the shape of the sketch is a right angled triangle we use SOHCAHTOA to solve. An image showing the step by step working is attached.
A Broadway theater has 400 seats, divided into orchestra main, and balcony seating. Orchestra seats sell for $70, main seats for $45, and balcony seats for $35. If all the seats are sold, the gross revenue to the theatre is $18,800. If all the main and balcony seats are sold , but only half the orchestra seats are sold, the gross revenue is $16,000. How many are there of each kind of seat.
Answer:
-80 orchestra seats
-200 main seats
- 120 balcony seats
Step-by-step explanation:
Let x b number of orchestra seats
Let y be number of main seats
Let z be number of balcony seats.
Thus, we have the following equations;
For all seats sold;
70x + 45y + 35y = 18,800 - - - - eq1
For half of orchestra sold;
70•½•x + 45y + 35y = 16,000 - - eq2
For total seats;
x + y + z = 400 - - - - eq3
Solving eq1, eq2 and eq3 simultaneously, we have;
x = 80
y = 200
z = 120
Thus, we have;
-80 orchestra seats
-200 main seats
- 120 balcony seats
Water drains very slowly from the nearly level ground in the Gulf Prairies and Marshes ecoregion of Texas. How does the slow movement of water impact the ecoregion?
A. Sediment carried in the water causes significant physical weathering.
B. The water increases the amount of sediment eroded by wind.
C. Sediment carried in the slowly moving water is deposited.
D. The slowly moving water erodes sediment.
Answer:
The correct option is;
C. Sediment carried in the slowly moving water is deposited.
Step-by-step explanation:
Here we note that the drainage rate of the water is slow and the plane of the drainage is given as level ground.
Therefore, there would less mass transport of sedimentary materials from the region and the level planes with slow drainage would favor the deposition of sediments along the level plane
From the above, the correct option is C.
Answer:
C
Step-by-step explanation:
of 100 students, 32 are taking Calculus, 29 are taking French, and 13 are taking both Calculus and French, if a student is picked at random
what is the probability that the student is taking Calculus or French?
(Reduce fraction to lowest form)
Step-by-step explanation:
The total number of students = 100
Let A represents calculus and B represents French
The no of students taking calculus = 32
The no of students taking French = 29
The no of students taking calculus and french = 13
the probability that the student is taking Calculus or French = ?
P (AUB) = P(A) + P(B) - P(A∩B)
= [tex]\frac{32}{100}[/tex] + [tex]\frac{29}{100}[/tex] - [tex]\frac{13}{100}[/tex]
= [tex]\frac{48}{100}[/tex]
Reducing to lowest fraction, it becomes [tex]\frac{12}{25}[/tex]
The probability that the student is taking Calculus or French = [tex]\frac{12}{25}[/tex]
The probability that a randomly selected student is taking Calculus or French is 12/25.
To find the probability that a randomly picked student is taking either Calculus or French, we use the principles of set theory, specifically the formula for the union of two sets:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Here,
A = Students taking Calculus = 32
B = Students taking French = 29
A ∩ B = Students taking both Calculus and French = 13
Total students = 100
The formulas for the probabilities are:
P(A) = 32/100
P(B) = 29/100
P(A ∩ B) = 13/100
Now substitute these values into the union formula:
P(Calculus or French) = 32/100 + 29/100 - 13/100 = 48/100 = 12/25
Therefore, the probability that a randomly picked student is taking either Calculus or French is 12/25.
Suppose that a coin is tossed three times and the side showing face up on each toss is noted. Suppose also that on each toss heads and tails are equally likely. Let HHT indicate the outcome heads on the first two tosses and tails on the third, THT the outcome tails on the first and third tosses and heads on the second, and so forth. (a) Using set-roster notation, list the eight elements in the sample space whose outcomes are all the possible head-tail sequences obtained in the three tosses.
Answer:
S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
Step-by-step explanation:
As can be seen in the Sample Tree attached, the eight elements in the sample space whose outcomes are all the possible head-tail sequences obtained in the three tosses are:
S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
When tossing a coin three times, there are 8 possible outcomes listed as HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. These elements represent all possible head-tail sequences for three coin tosses.
When a coin is tossed three times, each outcome is a sequence of heads (H) and tails (T). Since there are two possible outcomes for each toss, the total number of possible sequences is 23 = 8. Let's list these sequences using set-roster notation.
The sample space is:
HHHHHTHTHHTTTHHTHTTTHTTTThese elements cover all possible outcomes where each toss can either result in heads or tails.
How does the mean absolute deviation (MAD) of the data in set 1 compare to the mean absolute deviation of the data in set 2?
Set 1: 82, 80, 90
Set 2: 82, 80, 60, 90
1 The MAD of set 1 is 6 less than the MAD of set 2.
2 The MAD of set 1 is 5 less than the MAD of set 2.
3 The MAD of set 1 is 5 more than the MAD of set 2.
4 The MAD of set 1 is 6 more than the MAD of set 2.
Answer:
The MAD of set 1 is 5 less than the MAD of set 2.
Step-by-step explanation:
Which mathematical terms originated from the Arabic mathematician, al-Khwarizmi
Answer:
algorithm
Step-by-step explanation:
It sounds like algorithm.
The mathematical terms that originated from the Arabic mathematician, al-Khwarizmi, are ""algorithm"" and ""algebra.""
Al-Khwarizmi was a Persian mathematician and astronomer who lived in the 8th and 9th centuries. His works were instrumental in the development of algebra and the use of Hindu-Arabic numerals. The term ""algorithm"" is derived from a Latinization of his name, Algoritmi, and originally referred to the numerical methods he described in his treatise on arithmetic.
The word ""algebra"" comes from the Arabic word ""al-jabr,"" which appears in the title of his book ""Kitab al-Jabr wa-l-Muqabala"" (The Compendious Book on Calculation by Completion and Balancing). This book laid the foundations for algebra as a branch of mathematics, and the terms he introduced are still in use today to describe mathematical procedures and the study of equations and algebraic structures.
A television station shows commercials for 13/12 minutes each hour. How many 45-second commercials can it show?
The television station can show 1 full 45-second commercial during the 13/12 minutes of advertising time allocated each hour.
The question involves calculating how many 45-second commercials can be shown during the 13/12 minutes of advertising time allocated by a television station each hour. To solve this, we first need to convert the minutes to seconds and then divide by the length of one commercial.
13/12 minutes is equal to 13/12 × 60 seconds, which gives us 65 seconds of advertising time per hour. One commercial is 45 seconds long. Therefore, the number of 45-second commercials that can be shown is 65 divided by 45.
Divide the total advertising seconds by the duration of one commercial: 65 / 45 = approximately 1.44.
Since we cannot show a fraction of a commercial, the television station can show 1 full 45-second commercial per hour.
Cathy is asked to find the length of AC. She could use the Pythagorean Theorem and AC2 = 32 + 22. What other formula could she use? A) (0 + 3)2 - (1 + 3)2 B) (0 + 1)2 - (3 + 3)2 C) (0 - 3)2 + (1 - 3)2 D) (0 - 1)2 + (3 - 3)2
Answer:
Cathy is asked to find the length of AC. She could use the Pythagorean Theorem and AC^2 = 3^2 + 2^2. What other formula could she use?
A) (0 + 3)^2 - (1 + 3)^2
B) (0 + 1)^2 - (3 + 3)^2
C) (0 - 3)^2 + (1 - 3)^2
D) (0 - 1)^2 + (3 - 3)^2
Option C is the right choice.
Step-by-step explanation:
Given:
Cathy have used Pythagoras formula to find the hypotenuse.
Hypotenuse of the right angled triangle = AC
We know that:
In right angled triangle:
Hypotenuse square (h)^2 = Square of one side (p)^ + Square of another sides (b)^
⇒ [tex]h^2=p^2+b^2[/tex]
In Cathy's calculation:
⇒ [tex]AC^2=3^2+2^2[/tex]
⇒ [tex]AC^2=9+4[/tex]
⇒ [tex]AC^2=13[/tex]
We have to look for another equation.
Lets see the options individually.
A. [tex]AC^2=(0 + 3)^2 - (1 + 3)^2= 9-16 = 7[/tex]
B. [tex]AC^2=(0 + 1)^2 - (3 + 3)^2=1-0 =1[/tex]
C. [tex]AC^2=(0 - 3)^2 + (1 - 3)^2 =9+4=13[/tex]
D. [tex]AC^2=(0 - 1)^2 + (3 - 3)^2=1+0 =1[/tex]
So,
The other formula Cathy can use is, C i.e. (0 - 3)^2 + (1 - 3)^2 .
Option C is the right choice.
The correct answer is option C) (0 - 3) + (1 - 3)
If AC is the hypotenuse, and the lengths of the other two sides are 3 and 2, then AC = 3 + 2.
However, Cathy can also use the distance formula, which is derived from the Pythagorean Theorem. The distance formula calculates the distance between two points in a coordinate plane. If we have two points (x1, y1) and (x2, y2), the distance d between these points is given by:
d = (x2 - x1) + (y2 - y1)
Given that one endpoint of AC, let's call it A, is at (0, 3) and the other endpoint, let's call it C, is at (1, -3), we can apply the distance formula to find AC:
AC = (1 - 0) + (-3 - 3)
AC = (1) + (-6)
AC = 1 + 36
AC = 37
Therefore, the length of AC is the square root of 37, which is 37.
Let's evaluate the other options to see why they are incorrect:
A) (0 + 3) - (1 + 3): This formula would calculate the difference between the squares of the distances from the origin to two points, which does not correspond to the distance between two points.
B) (0 + 1) - (3 + 3): Similar to option A, this formula calculates the difference between the squares of the distances from the origin to two points, which is not the correct application of the Pythagorean Theorem for finding the distance between two points.
D) (0 - 1) + (3 - 3): This formula incorrectly calculates the distance by subtracting the y-coordinates instead of the x-coordinates and does not account for the difference in x-coordinates properly.
Thus, the correct formula to use, other than the direct application of the Pythagorean Theorem, is the distance formula, which in this case is option C) (0 - 3) + (1 - 3).
The diameter of a circle is 4 cm. Which equation can be used to find its circumference
A: C = pi x 44
B: C = pi x 2
C: C = 16 x pi
D: C = pi x 4
Answer:
D: C = 4π
Step-by-step explanation:
The formula for circumference is C = 2πr
The diameter is 4 which means the radius is 2.
Plug the value of r into the formula.
C = 2π2
C = 4π
D: C = 4π
after graphing 4x-2y=5 and y=x, in how many points do they intersect
Answer:
1 at (2.5, 2.5)
Step-by-step explanation:
you can try graphing it on desmo
0.53 x 0.67 =
Pls pls pls pls pls pls
A can of cat food has a diameter of 8 cm. Which measurement is the best estimate for the circumference of the cat food inside the can?
Answer:
ok The circumference of a circle is 2πr or πD if diameter is given.
The answer is 25.13 cm
Step-by-step explanation:
Now method 1:
C=2πr
So finding for radius in this equation=diameter/2
8/2=4 cm
So now 2 × 22/7 × 4
176/7=25.13 cm
OR
C=πD
22/7 × 8
176/7=25.13 cm
x = 2, y = 8
The variables x and y vary directly. Use the given values to write an equation that relates x and y
Which statement is true about the graphs of the two lines y =-4/5x+
2 and y=-5/4x-1/2?
The slopes are the only thing we care about when it comes to determining if the lines are parallel or perpendicular. The y intercepts do not affect the answer, so we can ignore them entirely.
The slopes of the two given equations are -4/5 and -5/4. Note how they are both negative. This means that we do not have perpendicular lines. One slope must be positive and the other negative, for perpendicular lines to form.
Another way to see it: the two slopes must multiply to -1 to have perpendicular lines form. We see that (-4/5)*(-5/4) = 1 instead.
Yet another way to see it: The term "opposite reciprocals" means we flip the fraction and we flip the sign (from positive to negative). The reciprocal part happens, but the sign change does not happen.
The lines are not parallel because the slopes would have to be equal for that to happen.
An initial population of 7 chipmunks in Mary's yard increases by 6% each year. If the function f(x) = abx models this situation, what is the population of the chipmunks in 5 years? (to the nearest whole number)
Answer: there would be 9 chipmunks after 5 years.
Step-by-step explanation:
An initial population of 7 chipmunks in Mary's yard increases by 6% each year. It means that the population is increasing in an exponential rate.
The function that models the situation is expressed as
f(x) = ab^x
Where
a represents the initial population of chipmunks
b represent the rate of growth
x represent the number of years
From the information given,
a = 7
b = 1 + 6% = 1 + 6/100 = 1.06
x = 5 years
After 5 years,
f(5) = 7 × 1.06^5
f(5) = 9
Andy invests $500 into an account with 4.8% interest, compounded continuously. How much will be in the account in 10 years?
Answer:
The Correct answer:
$799.06
Final answer:
To find out how much Andy will have in his account after 10 years with a 4.8% interest compounded continuously, we use the formula A = Pe^{rt}. Substituting the values, we find that the amount will be approximately $808.85.
Explanation:
To calculate how much Andy will have in his account in 10 years with an initial investment of $500 at a 4.8% interest rate compounded continuously, we use the formula for continuous compounding, which is A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), and t is the time in years.
Using the given values:
P = $500
r = 4.8% or 0.048
t = 10 years
Let's compute the final amount:
A = 500 * e^0.048 * 10
Now we calculate the exponent:
e^0.48 (approximately 1.6177)
And then the final amount:
A = 500 * 1.6177 ≈ $808.85
After 10 years, the amount in Andy's account, compounded continuously at a rate of 4.8%, will be approximately $808.85.
A large online video game tournament begins with 65,53665,536 teams. The number of teams, t,t, remaining after each round, r,r, can be expressed as t=65,536(12)r.t=65,536(12)r. Eight teams will advance to the quarterfinals. The number of rounds necessary for there to be 88 teams left can be modeled as r=log(1k)log(12).r=log(1k)log(12). What is the value of k?k?
Answer:
k=8192
Step-by-step explanation:
The number of teams,t remaining after each round, r, can be expressed as:
[tex]t=65,536(\frac{1}{2})^r[/tex]
8 Teams will advance to the quarterfinals.First, we determine the round,r at which there will be 8 teams left.
[tex]t=65,536(\frac{1}{2})^r\\8=65536*0.5^r\\0.5^r=8 \div 65536\\2^{-1r}=2^{-13}\\-r=-13\\r=13[/tex]
Using this value of r
[tex]If \: r=\frac{Log\frac{1}{k}}{Log\frac{1}{2}} \\Since\: r=13\\13=\frac{Log\frac{1}{k}}{Log\frac{1}{2}}\\$Cross Multiply$\\Log\frac{1}{k}=13 X Log 0.5\\ $Using a Log b=Log $b^{a}\\Log\frac{1}{k}= Log 0.5^{13}\\\frac{1}{k}=0.5^{13}\\\frac{1}{k}=\frac{1}{8192}\\k=8192[/tex]
A biologist is studying the effects that applying insecticide to a fruit farm has on the local bat population. She collects 23 bats and finds the mean weight of this sample to be 503.4 grams. Assuming the selected bats are a random sample, she concludes that because the sample mean is an unbiased estimator of the population mean, the mean weight of bats in the population is also 503.4 grams. Explain why this is an incorrect interpretation of an unbiased estimator.
Answer:
The insufficient or relatively small size of the random sample does not guarantee the unbiasedness of the sample mean in any statistical study.Step-by-step explanation:
In Statistics,if the sample mean is an unbiased estimator of population mean,then the expected value of the sample mean is equal or identical to the actual population mean.As the researcher increases the size of the random sample in any statistical study or research, the sample mean increasingly approaches the actual population mean and hence, with increasing sample size with relation to the actual population of the study,the sample mean will become an unbiased estimator of the population mean.In this instance, the biologist has selected only 23 bats for the concerned study which might not be enough considering the entire or actual local bat population. Therefore, even a random sampling of 23 bats will not necessarily ensure that the sample mean will be an unbiased estimator of the population mean, in this case. Hence, the biologist would have to increase the size of the random sample to establish the unbiasedness of the sample estimate or the mean.Which of the following shows the extraneous solution to the logarithmic equation below? log Subscript 3 Baseline (18 x cubed) minus log Subscript 3 Baseline (2 x) = log Subscript 3 Baseline 144
The extraneous solution of the logarithmic problem log₃( 18x³) -log(2x) = log₃144 is -4.
What is Logarithm?A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c = b[/tex] can be written as,
log[tex]_a[/tex]b = c
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
Solving the function using the basic logarithmic value, we get,
log₃( 18x³) -log(2x) = log₃144
log₃ (18x³/2x) = log₃144
log(9x²) = log₃144
Take antilog.
9x² = 144
x = ±4
If we solve further we will get that the value of x can be either -4 or 4, if take the value of x as -4, in the beginning then you will get log₃(18(-4)³) as the log of negative value which is impossible.
Hence, x=-4 is an extraneous solution for the given expression log₃( 18x³) -log(2x) = log₃144.
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Find the slope and y-intercept of the line that is parallel to y = 3x - 3 and passes through the point (-2,-7)
Answer:
y = 3x - 1
Step-by-step explanation:
The slope of this line is 3x and the y-intercept is -1.
I graphed the equation and the point along with the new equation below.
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Frans filing cabinet is 6 feet tall, 1 3/3 feet wide, and 3 feet deep. She plans to paint all the sides except the got on of the cabinet. Find the area of all the sides.
Answer:
52 square feet
Step-by-step explanation:
We are given that
Length,l=6 feet
Width,b=[tex]1\frac{1}{3}=\frac{4}{3}[/tex] feet
Depth,h=3 feet
Area of all painted sides except bottom=[tex]lb+2(bh+hl)[/tex]
Using the formula
Area of all painted sides except bottom=[tex]6\times \frac{4}{3}+2(\frac{4}{3}\times 3+3\times 6)[/tex]
Area of all painted sides except bottom=[tex]8+2(4+18)[/tex]
Area of all painted sides except bottom=[tex]8+44[/tex]
Area of all painted sides except bottom=52 square feet
A 13 ft ladder leaning against a building touches the building exactly 12 feet above the ground. How far is the building is the base of the ladder round to the nearest hundredth foot
............................
Kala earns 41 dollars each week working part-time at a bookstore. She earns one additional dollar for each book that she sells.
Let A be the amount (in dollars) that Kala earns in a week if she sells B books.
Write an equation relating A to B. Then use this equation to find the amount of money Kala earns if she sells 14 books.
Equation:
Amount Kala earns if she sells 14 books: dollars
Answer:
A = 41+B
A = 55
Step-by-step explanation:
A be the amount (in dollars) that Kala earns in a week
B = books sold
Kala earns 41 dollars each week working part-time at a bookstore. This does not depend on selling any books
She earns 1 dollar for each book sold
A = 41+B*1
A = 41+B
Let B = 14
A = 41+14
A = 55
Answer:
Equation: A = 41 + B
Amount Kala earns if she sells 14 books: 55 dollars
Step-by-step explanation:
A = 41 + B
B = 14
A = 41 + 14
A = 55
How would you do this question?
2/3 a = 8