Answer:
The number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]
Step-by-step explanation:
Given the initially 30 bacteria present in the culture.
Also, the number of bacteria got doubled every hour.
So, using the equation
[tex]A=A_0r^{n-1}[/tex]
Where [tex]A[/tex] is number of bacteria after [tex]n[/tex] hours.
[tex]A_0[/tex] is bacteria present initially.
[tex]r[/tex] is the common ration, in our problem it is given that bacteria doubles every hour. So, [tex]r=2[/tex]
And [tex]n[/tex] is the number of hours. In our problem we need amount of bacteria at the end of [tex]8th[/tex] hours. So, [tex]n=8[/tex]
Plugging values in the formula we get,
[tex]A=30(2)^{8-1}\\A=30\times 2^7\\A=30\times 128\\A=3840[/tex]
So, number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]
Graph g(x)=3x2−12x−3 .
Answer:
See the image.Step-by-step explanation:
The function is given by [tex]g(x) = 3x^{2} - 12x - 3[/tex].
Differentiating the function, we get [tex]\frac{d g(x)}{dx} = 6x - 12[/tex].
Now, at x = 2, 6x - 12 will be 0.
Hence, at x = 2, either the function will have maximum or minimum value.
g(2) = 12 - 24 -3 = -15.
g(1) = 3 -12 -3 = -12.
g(0) = -3.
Hence, the given function passes through (2, -15), (1, -12) and (0, -3).
Please help ASAP!!
Find the variance and standard deviation of the given set of data to the nearest tenth. {530, 150, 320, 500, 200, 690, 770}
A. variance = 48,326.5, standard deviation = 219.8
B. variance = 56,381, standard deviation = 237.4
C. variance = 219.8, standard deviation = 48,326.5
D. variance = 48,326.5, standard deviation = 24,163.3
Answer:
Step-by-step explanation:
variance = 48,326.5, standard deviation = 219.8
Answer: variance = 48,326.5, standard deviation = 219.8
Step-by-step explanation: I completed the quiz, and option A. variance = 48,326.5, standard deviation = 219.8 was the correct answer!
Deep Blue, a deep sea fishing company, bought a boat for $250,000. After 9 years, Deep Blue plans to sell it for a scrap value of $95,000. Assume linear depreciation.
Answer:
Therefore, we use the linear depreciation and we get is 17222.22 .
Step-by-step explanation:
From Exercise we have that is boat $250,000.
The straight line depreciation for a boat would be calculated as follows:
Cost boat is $250,000.
For $95,000 Deep Blue plans to sell it after 9 years.
We use the formula and we calculate :
(250000-95000)/9=155000/9=17222.22
Therefore, we use the linear depreciation and we get is 17222.22 .
To calculate the annual depreciation expense for Deep Blue's boat using the straight-line method, subtract the salvage value from the purchase price and divide by the number of years of useful life, resulting in an annual depreciation expense of $17,222.22.
To determine the annual depreciation, subtract the salvage value from the purchase price and divide by the useful life of the asset in years:
Subtract the salvage value from the purchase price: $250,000 - $95,000 = $155,000.
Divide the result by the number of years of useful life: $155,000 / 9 years = $17,222.22.
Therefore, Deep Blue would record an annual depreciation expense of $17,222.22.
A flying squirrel's nest is 56 feet high in a tree. From its nest, the flying squirrel glides 70 feet to reach an acorn that is on the ground. How far is the acorn from the base of the tree?
Answer:
Step-by-step explanation:
The driver of a 810.0 kg car decides to double the speed from 23.6 m/s to 47.2 m/s. What effect would this have on the amount of work required to stop the car, that is, on the kinetic energy of the car? KEi= × 105 J KEf= × 105 J times as much work must be done to stop the car.
Answer:
KEi = 2.256×10^5 JKEf = 9.023×10^5 J4 times as much workStep-by-step explanation:
The kinetic energy for a given mass and velocity is ...
KE = (1/2)mv^2 . . . . . m is mass
At its initial speed, the kinetic energy of the car is ...
KEi = (1/2)(810 kg)(23.6 m/s)^2 ≈ 2.256×10^5 J . . . . . m is meters
At its final speed, the kinetic energy of the car is ...
KEf = (1/2)(810 kg)(47.2 m/s)^2 ≈ 9.023×10^5 J
The ratio of final to initial kinetic energy is ...
(9.023×10^5)/(2.256×10^5) = 4
4 times as much work must be done to stop the car.
_____
You know this without computing the kinetic energy. KE is proportional to the square of speed, so when the speed doubles, the KE is multiplied by 2^2 = 4.
The formula for the surface area of a sphere is A=4pi r*2, where r is the length of the radius. Find the surface area of the sphere with a radius of 14. Use 22/7 as pi
Answer:
Step-by-step explanation:
area=4×22/7×14²=4×22×28=2464 units²
The surface area of a sphere with a radius of 14 is 2464 square units. When considering significant figures, this is rounded to 2500 square units to match the two significant digits of the given radius.
To find the surface area of a sphere with a radius of 14, using the given value of 22/7 for , the formula A = 4*pi*r2 is used. Plugging in the numbers:
A = 4 * (22/7) * (14)²
A = 4 * (22/7) * 196
A = 4 * 22 * 28
A = 88 * 28
A = 2464
Thus, the surface area of the sphere is 2464 square units.
A one year membership to metro gym costs $460. There is a fee of $40 when you join, and the rest is paid monthly. Write an equation to represent the situation that can help members find how much they pay per month
Answer: The equation that would help members to find how much they would pay per month is
40 + 12x = 460
Step-by-step explanation:
Let x represent the amount of money that members would pay per month.
Let y represent the number of months for which a member uses the gym.
There is a fee of $40 when you join, and the rest is paid monthly. This means that the cost of using the gym for x months would be
40 + xy
A one year membership to metro gym costs $460. Therefore are 12 months in a year. Therefore,
40 + 12x = 460
12x = 460 - 40 = 420
x = 420/12 = 35
The equation that would help members to find how much they would pay per month is
In a sheet metal operation, three identical notches and four identical bends are required. If the operations can be done in any order, how many different possible sequences are there to complete the manufacturing?
The problem can be solved using combinatorics, specifically the permutation of a multiset. Using the formula P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is total number of operations and n1, n2,... are the number of each identical operation, the number of different possible sequences to complete the manufacturing operation are 35.
Explanation:The number of sequences of the operations can be found by using the formula for permutations of multiset - a concept in combinatorics part of mathematics. Permutations of a multiset are the number of ways in which we can arrange all the elements of the multiset considering the repetition of elements. We have 7 operations in total: three identical notches (type A) and four identical bends (type B). The formula is:
P(n; n1, n2, ..., nk) = n! / (n1! * n2! *...* nk!), where n is the total number of items(7 in this case), n1,n2,...,nk are the number of each type of item.
Therefore, the number of different possible sequences to complete the manufacturing is: P(7 ; 3, 4) = 7! / (3! * 4!). This evaluates to 35.
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⇒How many solutions does the equation 10-3x +10x-7=5x-5+2x+8 have? a. One solution b. Two solutions c. No solutions d. Infinitely many solutions
Answer: d. Infinitely many solutions
Step-by-step explanation:
The given equation is expressed as
10-3x +10x-7 = 5x-5+2x+8
The first step is to make all the terms containing the variable to be on the left hand side of the equation and the constants to be on the right hand side of the equation.
10-3x +10x-7=5x-5+2x+8
10 - 7 + 10x - 3x = 5x + 2x - 5 + 8
7x + 3 = 7x + 3
Subtracting 7x and 3 from the left hand side and the right hand side of the equation, it becomes.
7x - 7x + 3 - 3 = 7x - 7x + 3 - 3
0 = 0
It has infinitely many solutions because as any value of x would satisfy both sides of the equation.
The area of a rectangle is 32a^3b^4 square units. The length is 4a^2b. Find the width. show your work
Answer:
The answer to your question is width = 8ab³
Step-by-step explanation:
Data
Area = 32a³b⁴ u²
length = 4a²b u
Formula
Area of a rectangle = width x length
Solve for width
width = [tex]\frac{Area}{length}[/tex]
Substitution
width = [tex]\frac{32a^{3}b^{4}}{4a^{2}b}[/tex]
Simplify using rules of exponents, just remember that in a division we subtract the exponents and divide the coefficients normally.
width = 8 a²b³
Answer:
Step-by-step explanation: 32a^3 is -8 < a < - 8 axis interceptions 32a^3 vertical asymphotes None Extreme points of a32a^3 0,0
Sean reads on Monday Tuesday and Wednesday. He reads 3 times as many minutes on Tuesday as he does on Monday. He reads 4 times as many minutes on Wednesday as he does on Monday. Sean reads 45 minutes on Tuesday. How many minutes does Sean read on Wednesday?
Sean reads 60 minutes on wednesday
Solution:
Given that,
Let "x" be the number of minutes read on monday
Let "y" be the number of minutes read on tuesday
Let "z" be the number of minutes read on wednesday
He reads 3 times as many minutes on Tuesday as he does on Monday
Number of minutes read on tuesday = 3 times the number of minutes read on monday
y = 3x --------- eqn 1
He reads 4 times as many minutes on Wednesday as he does on Monday
Number of minutes read on wednesday = 4 times the number of minutes read on monday
z = 4x ------- eqn 2
Sean reads 45 minutes on Tuesday
y = 45
Substitute y = 45 in eqn 1
45 = 3x
x = 15
Substitute x = 15 in eqn 2
z = 4(15)
z = 60
Thus he reads 60 minutes on wednesday
Final answer:
Sean reads for 60 minutes on Wednesday, calculated by knowing he reads four times as many minutes on Wednesday as on Monday, and he reads 45 minutes on Tuesday which is three times his Monday reading time.
Explanation:
Since Sean reads 3 times as many minutes on Tuesday as he does on Monday, and he reads 45 minutes on Tuesday, we can determine that he reads 45 minutes ÷ 3 = 15 minutes on Monday. Sean then reads 4 times as many minutes on Wednesday as he does on Monday. So, he must read 15 minutes × 4 = 60 minutes on Wednesday.
William cycles at a sped of 15 miles per hour. He cycles 12 miles from home to school. If he increases his cycling speed ny 5 miles per hour how much faster will he arrive his school
Answer:he would arrive 0.2 miles faster.
Step-by-step explanation:
Distance = speed × time
Time = distance/speed
William cycles at a sped of 15 miles per hour. He cycles 12 miles from home to school. This means that the time it takes William to get to school from home would be
12/15 = 0.8 hours
If he increases his cycling speed by 5 miles per hour, his new speed becomes
15 + 5 = 20 miles per hour
Therefore, the new time it takes William to get to school from home would be
12/20 = 0.6 hours
The difference in both times is
0.8 - 0.6 = 0.2 hours
Therefore, he would arrive 0.2 miles faster.
Pam is taking a train from the town of Rome to the town of Florence. Rome is located 40 miles due west of the town of Paris. Florence is 35 miles east, and 55 miles north of Rome. On her trip, how close does Pam get to Paris?
Answer:
Pan is closest to Paris when she gets to Florence when she is 35 miles away
Step-by-step explanation:
With Paris at (0,0), Rome is 40miles west which is on the negative x axis.
Florence is 35 miles closer (east to Paris) so we have -45 + 35 = -10
and 55 mikes north of Rome which is on the positive y-axis. So Florence is at point (-10,55)
The distance between the two points Florence and Paris is √(x2 - x1)^2 + (y2 - y1)^2
x1 = 0, y1 = 0
x2 = -10, y2 = 55
So we have
√(-10-0)^2 + (55-0)^2
= √(-10)^2 + (55)^2
= √ 100 + 3025
= √3125
= 55.9 mikes from Paris
Pam is closest to Paris when she gets to Florence when she is 35 miles away
Pam gets closest to Paris when she is 5 miles away, which occurs when she travels directly east from Rome before heading north to Florence.
Explanation:Pam is taking a train from Rome to Florence, and we need to find out how close she gets to Paris along the way. Rome is 40 miles due west of Paris, and Florence is 35 miles east and 55 miles north of Rome. While traveling from Rome to Florence, Pam would initially get closer to Paris as she travels east, but as she moves north, the closest point to Paris would be directly east from Rome before moving north.
Step-by-Step ExplanationDetermine the initial distance of Rome to Paris, which is 40 miles to the east.Since Florence is 35 miles east of Rome, Pam would at least come within 5 miles of Paris (40 miles - 35 miles).However, when traveling north to reach Florence, Pam's distance to Paris increases. Thus, the closest Pam gets to Paris on her trip is 5 miles, when she is directly east of Rome, before heading north.A prison administration wants to know whether the prisoners think the guards treat them fairly. Explain how each of the following components could be used to produce biased results, versus how each could be used to produce unbiased results.A) Component 2: The researcher who had contact with the parcipants. B) Component 4: The exact nature of the measurements made or question asked.
Answer:
A prison administration wants to know whether the prisoners think the guards treat them fairly. The explanation, of each component could be used to produce biased and unbiased results, is as follow
A) Component 2:
If the prison guards ask the questions from the prisoners directly by themselves then it is highly like to get the biased results. If the person are hired outside from the staff then it will minimize the probability of biased results rather it will allow to get the best results.B) Component 4:
The question asked from prisoner would be biased if it is like "You don't have any complaints about how you are treated, do you?" The same question can be unbiased if asked in such a way "We are interested in your opinion about your treatment by the guards. Do you think you are fairly or unfairly treated by them?"Bias in research on prisoner-guard dynamics can result from the involvement of researchers and the phrasing of questions. To ensure unbiased results, neutral interactions and carefully worded questions are vital.
Biased Research Components in Prisoner-Guard Dynamics
In research, it is crucial to mitigate factors that can lead to bias. Two such components in the study of prisoner-guard dynamics are researcher involvement and the phrasing of measurements and questions. If the researcher has direct contact with participants, they can unknowingly influence responses based on their body language, tone, or preconceived notions.
To produce unbiased results, researchers should maintain a neutral demeanor and minimize unnecessary interaction. The exact nature of measurements and questions can also introduce bias. Leading or emotional language in survey questions can skew results towards a specific answer. To avoid this, questions must be neutrally worded and designed to reflect the respondent's true perspective without influence.
The Derby Dragons have a mean height of 72.0 inches and a standard deviation of 1.2. The Aviston Aces have a mean height of 70.8 inches and a standard deviation of 0.7. The Ballwin Bears have a mean height of 73 inches and a standard deviation of 1.0. On average, which team is a taller? Which team has players whose heights are more consistent?
Answer: Ballwin Bears
Step-by-step explanation:
Answer:
The Ballwin Bears are taller on average, and the Aviation Aces have players whose are more consistent.
Step-by-step explanation:
(This is the correct answer on Knewton-alta)
Use the distributive property to remove the parentheses.
(8x-10)1/2=
Answer:
The answer to your question is 4x - 5
Step-by-step explanation:
[tex](8x -10)\frac{1}{2}[/tex]
Distributive property, this property allows us to multiply two terms separately. That means that in this problem [tex]\frac{1}{2}[/tex] will multiply the first term, and after that the second term. One half multiply 8x and also - 10.
[tex]\frac{8x}{2} - \frac{10}{2}[/tex]
Simplify and result
[tex]4x - 5[/tex]
Using the distributive property on [tex](8x - 10) \times \frac{1}{2}[/tex], we get [tex]4x-5[/tex]
Given: [tex](8x - 10) \times \frac{1}{2}[/tex]
To find: simplify using distributive property
Distributive property can be depicted by [tex]x(a+b) = xa + xb[/tex]
We can use this property and solve as follows:
[tex](8x - 10) \times \frac{1}{2} = [\frac{1}{2} \times 8x] - [10 \times \frac{1}{2}] = 4x -5[/tex]
We get the expression without parentheses [tex]4x-5[/tex]
Practice simplifying rational expressions with negative exponents.
Answer:
Part 1:- option first is correct
[tex]-\frac{1}{2}ab^{12}[/tex]
Part 1:- option third is correct
[tex]\frac{w^{10}}{3y^{4}}[/tex]
Step-by-step explanation:
Given:
The given ration expressions are.
1. [tex]\frac{-2a^{2}b^{4}}{4ab^{-8}}[/tex]
2. [tex]\frac{-5w^{4}y^{-2}}{-15w^{-6}y^{2}}[/tex]
We need to simplify the given expressions.
Solution:
Part 1:-
Given expression is
[tex]=\frac{-2a^{2}b^{4}}{4ab^{-8}}[/tex]
Using law of exponents [tex]\frac{x^{m} }{x^{n} } = x^{(m-n)}[/tex]
[tex]=-\frac{a^{2-1}b^{4-(-8)}}{2}[/tex]
[tex]=-\frac{a^{1}b^{4+8}}{2}[/tex]
[tex]=-\frac{ab^{12}}{2}[/tex]
[tex]=-\frac{1}{2}ab^{12}[/tex]
Therefore, option first [tex]-\frac{1}{2}ab^{12}[/tex] is correct.
Part 2:-
Given expression is.
[tex]=\frac{-5w^{4}y^{-2}}{-15w^{-6}y^{2}}[/tex]
Using law of exponents [tex]\frac{x^{m} }{x^{n} } = x^{(m-n)}[/tex]
[tex]=\frac{w^{4-(-6)}y^{-2-2}}{3}[/tex]
[tex]=\frac{w^{4+6}y^{-4}}{3}[/tex]
[tex]=\frac{w^{10}y^{-4}}{3}[/tex]
[tex]=\frac{w^{10}}{3y^{4}}[/tex]
Therefore, third option [tex]\frac{w^{10}}{3y^{4}}[/tex] is correct.
Tessa is cooking steak for her family. She wants to be sure the steak has an internal temperature of at least 160 degrees Fahrenheit. She uses a thermometer to measure the internal temperature at two randomly chosen places. The minimum reading in the sample is 165 degrees Fahrenheit. Identify the population, the parameter, the sample, and the statistic______________.
Answer:
Population : all the steaks Tessa can cook
Parameter : minimum internal temperature of 160 degrees Fahrenheit
Sample : two random thermometer readings
Statistic : minimum sample reading of 165 degrees Fahrenheit
Step-by-step explanation:
Let's recall the definitions of these statistical concepts and match it with the information that were provided to us:
Populations can be the complete set of all similar items that exist, in our case, all the steaks that Tessa can cook.Parameter is is a value that describes a characteristic of an entire population, such as the minimum temperature of the steaks Tessa is cooking in Fahrenheit degrees.Sample is a subset of the population, in our case, the two random readings of the thermometer Tessa did.Statistic is a characteristic of a sample, for our problem, it's the minimum reading of 165 degrees Fahrenheit.What is a good science fair projects for 5th graders
I'm not sure of whether or not you're aware of this, but you asked this question in the math section. Nevertheless, I remember in 5th grade I did a project on whether or not it is possible to use solar energy to heat up different colored bags filled with water, and to determine which one would heat up the quickest. If that one doesn't pique your interest, you can go to sciencebuddies.com and search through a variety of project ideas if you'd like. That's where I found mine.
Final answer:
A good science fair project for 5th graders could be the 'Race of the Cans' experiment. Students can collect cans with different types of food and predict which can will win a race down an inclined plane.
Explanation:
A good science fair project for 5th graders could be the 'Race of the Cans' experiment. In this experiment, students can collect several cans containing different types of food and predict which can will win the race down an inclined plane. They can then explain their prediction and see if it is correct. Another option is to collect empty cylindrical containers of the same size and fill them with different materials like wet or dry sand to see how it affects the race.
A certain shop repairs both audio and video components. Let A denote the event that the next component brought in for repair is an audio component, and let B be the event that the next component is a compact disc player (so the event B is contained in A). Suppose that P(A) = .625 and P(B) = .05. What is P(B/A)?
Answer:P(A/B)=0.08
Step-by-step explanation:
The probability formula to find p(A/B) is :
P(A/B) = p(A n B) / p(A)
Which means that B is contain in A and p(A n B) is p(B)
p(A n B)=p(B)=0.05
p(A)=0.625
Therefore
P(A/B) = p(A n B) / p(A)=p(B) / p(A)
P(A/B)=0.05 / 0.625
P(A/B)=0.08
The expression $x^2 15x 54$ can be written as $(x a)(x b),$ and the expression $x^2 - 17x 72$ written as $(x - b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a b c$?
Answer: a=6 b=9 c=8
Step-by-step explanation:
The problem consists of finding the roots of the quadratic equations:
[tex]x^2+15x+54=0\\[/tex]
[tex]x^2-17x+72=0\\[/tex]
The roots can be found with the following equation for solving quadratic equations:
[tex]x_{12}=\frac{-B\pm\sqrt{B^2-4AC}}{2A}[/tex] for equation: [tex]Ax^2+Bx+C=0[/tex]
After solving the equations you can write the result as:
[tex]x^2+15x+54=(x+6)(x+9)\\[/tex]
[tex]x^2-17x+72=(x-9)(x-8)[/tex]
Answer:
b = 9
a = 6
c= 8
Therefore, a,b,c = 6,9,8
Question:
The expression $x^2 - 15x - 54$ can be written as $(x-a)(x-b),$ and the expression $x^2 - 17x + 72$ written as $(x - b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a b c$?
Step-by-step explanation:
To determine the values of a,b and c.
We need factorize the two equations.
i) x^2 -15x +54
x^2 -6x -9x +54
x(x-6) -9(x-6)
=(x-6)(x-9)
ii) x^2 -17x +72
x^2 -9x -8x +72
x(x-9) -8(x-9)
=(x-9)(x-8)
From the question:
Comparing
(x-a)(x-b) to (x-6)(x-9)
And
(x-b)(x-c) to (x-9)(x-8)
We can see that b is common in the two cases and also 9 is common in the two factorised equations.
So,
b = 9
a = 6
c= 8
Therefore, a,b,c = 6,9,8
You deposited $10,000 into a savings account at 6%. After a certain amount of time, you earned $4,800. How long did you have your money in the savings account?
Answer:
800 months
Step-by-step explanation:
The formula for interest is:
(Capital * saving account * time) / 100
So:
(10000 * 0.06 * x) / (100) = 4800
We clear x:
(10000 * 0.06 * x) = (100) * 4800
x = 480,000 / (10000 * 0.06)
x = 800 months (66.67 years)
To determine the duration for which the deposited $10,000 at 6% interest grew to a total of $14,800 ($10,000 principal + $4,800 interest), the formula for compound interest can be re-arranged to solve for the time variable. You'll use the amount of money accumulated, the principal amount, the annual interest rate, and the assumption that the interest is compounded annually. Plug these values into the formula to calculate the number of years.
Explanation:You deposited $10,000 into a savings account at 6% interest. To determine how long it took for you to earn $4,800 in interest, we can use the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of times that interest is compounded per year.t is the time the money is invested for, in years.In this case, we can rearrange the formula to solve for t, because you want to find out how many years it took for your investment to turn into A = $10,000 + $4,800 = $14,800. Assuming the interest is compounded annually (n = 1), the formula becomes:
t = ln(A/P) / n * ln(1 + r/n)
Plugging in the numbers gives us:
t = ln($14,800 / $10,000) / ln(1 + 0.06)
By calculating this, you can get the number of years you had the money in the savings account.
Imogene's car travels 294 mi averaging a certain speed. If the car had gone 7 mph faster, the trip would have taken 1 hour less. Find the average speed
Answer:
42 mph
Step-by-step explanation:
If you start with the assumption that the answer is an integer, you can solve a problem like this by looking at the factors of 294.
294 = 2·3·7² = 6·49 = 7·42
At 42 mph, the 294-mile trip took ...
time = distance/speed = 294 mi/(42 mi/h) = 7 h
At a speed 7 mph faster, the 294-mile trip took ...
(294 mi)/(49 mi/h) = 6 h . . . . . 1 hour less
The average speed of Imogene's car for the 294-mile trip was 42 miles per hour.
_____
Alternative solution
If you let s represent Imogene's speed, you can use the above time and distance relationship to write an equation relating the trip times:
294/s = 294/(s+7) +1
Multiplying by s(s+7), we get ...
294(s+7) = 294s +s(s+7)
2058 = s^2 +7s . . . . . . . . . . . subtract 294s
We can complete the square by adding (7/2)^2 = 12.25 to both sides
2070.25 = s^2 +7s +12.25 = (s +3.5)^2
±45.5 = s +3.5 . . . . . take the square root; next subtract 3.5
-3.5 +45.5 = s = 42 . . . . use the positive solution
Imogene's average speed was 42 mph.
Imogene's average speed was 294 mph. We solve this by using the relationship between distance, speed, and time, and applying it to the specific constraints of the problem. By setting s = speed, we use two equations representing each scenario and solve for s.
Explanation:Let's assign 's' to Imogene's average speed for the trip. The time taken at this speed is the distance traveled (294 mi) divided by 's' (speed = distance/time), making the time = 294/s. If the car was faster by 7 mph, the speed would be s+7 mph, and the time taken would then be 294/(s+7). The problem states that the second scenario would take 1 hour less, so 294/s = 294/(s+7) + 1.
Cross-multiplication and simplification of this equation result in (294s + 2058) = 294(s +7) or 294s + 2058 = 294s + 2058, which simplifies to 2058 = 7s, or s = 294 mph. Therefore, Imogene's average speed was 294 mph.
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The French club sold rose bouquets and chocolate hearts for Valentine's Day. The roses sold for $5 and the hearts sold for $3. The number of bouquets sold was 15 more than the number of hearts sold. If the club collected a total of $339, how many of each gift was sold?
Answer:
33 hearts sold, 48 roses sold
Step-by-step explanation:
x- number of roses sold
y- number of hearts sold
x=15+y <- " The number of bouquets sold was 15 more than the number of hearts sold"
5x+3y=339
5(15+y)+3y=339
75+5y+3y=339
8y=339-75
8y=264
y=33
x=15+33=48
The number of chocolate hearts sold was 33, and the number of bouquets sold was 48 for a total revenue of $339.
Explanation:Let's assume the number of chocolate hearts sold was 'x'. Since the number of bouquets sold was 15 more than the number of hearts sold, the number of bouquets sold would be 'x + 15'.
The price of each rose bouquet is $5, so the total revenue from selling bouquets would be '5(x + 15)'.
Similarly, the price of each chocolate heart is $3, so the total revenue from selling hearts would be '3x'.
Since the total revenue collected was $339, we can set up an equation: '5(x + 15) + 3x = 339'.
Simplifying the equation, we get '8x + 75 = 339'.
Subtracting 75 from both sides of the equation, we get '8x = 264'.
Dividing both sides of the equation by 8, we get 'x = 33'.
Therefore, 33 chocolate hearts were sold, and the number of bouquets sold would be '33 + 15 = 48'.
The endpoints of a diameter of a circle are (3, -2) and (-5, 8). What is the equation of the circle in standard form?
Answer:
(x + 1)² + (y − 3)² = 41
Step-by-step explanation:
The center of the circle is the midpoint of the diameter.
(h, k) = ((x₂ + x₁)/2, (y₂ + y₁)/2)
(h, k) = ((3 + -5)/2, (-2 + 8)/2)
(h, k) = (-1, 3)
The radius is half the length of the diameter.
r = ½ √((x₂ − x₁)² + (y₂ − y₁)²)
r = ½ √((3 − -5)² + (-2 − 8)²)
r = ½ √(8² + 10²)
r = √41
Therefore, the equation of the circle is:
(x − h)² + (y − k)² = r²
(x + 1)² + (y − 3)² = 41
The standard form of equation of the circle is (x + 1) + (y - 3) = (6.40)².
What is distance between two points?The length of the line segment bridging two points on a plane is known as the distance between the points.
The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}
Given is that the endpoints of a diameter of a circle are (3, -2) and (-5, 8).
The center: (3-5/2, -2+8/2) = (-1, 3)
The diameter d = √{(x₂-x₁)² + (y₂-y₁)²}
d = √{(-5-3)² + (8 + 2)²}
d = √{64 + 100}
d = √164
d = 12.81
The radius r = 6.40
The standard form of equation of the circle is,
(x + 1) + (y - 3) = (6.40)²
Therefore, the standard form of equation of the circle is,
(x + 1) + (y - 3) = (6.40)²
To learn more about the distance between two points;
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A sample of 40 employees from the local Honda plant was obtained and the length of time (in months) worked was recorded for each employee. A stemplot of these data follows. In the stemplot, 5|2 represents 52 months.What would be a better way to represent this data set?
A. Display the data in a time plot.
B. Split the stems.
C. Use a pie chart.
D. Use a histogram with class width equal to 10.
Answer:
Option D = Use a histogram with class width equal to 10
Step-by-step explanation:
A histogram will be better to represent the data. A histogram is a graphical representation of a frequency distribution, where you have rectangular bars placed side by side. the vertical axis represent the frequency while the horizontal axis represent the variable being represented which is the length of time worked by the employees.
One of the advantages of the histogram is that it has no gaps between the bars and it is mostly used for grouped data. This explains why the best representation ad the best option is to use the HISTOGRAM.
Final answer:
Option D, a histogram with class width equal to 10, would likely be the best representation for the data set of the length of time worked by employees, as it would facilitate easy viewing of data distribution and patterns.
Explanation:
The question asks for a better way to represent a data set of the length of time worked by employees at a local Honda plant. The provided options include a time plot, split stems, a pie chart, and a histogram with a class width of 10. Looking at the options:
A time plot is more suitable when the data involves changes over time and when you're looking for trends.Splitting the stems in a stemplot can provide a finer breakdown of the data, which might be helpful if the data is quite detailed or clustered. However, it may not necessarily be a better representation.A pie chart is not ideal for this type of numerical, continuous data as pie charts are best for categorical data and showing proportions/parts of a whole.A histogram with class width equal to 10 would be beneficial because it groups the data into intervals, making it easier to see the distribution and identify patterns such as the range of months employees have worked, any concentrations of data points, and outliers.In conclusion, option D, which suggests using a histogram with a class width equal to 10, would likely be the best graphical representation for this data set.
Find the height of a right square pyramid that has a rectangular base area of 70 square units and a volume of 140 cubic units. A. 2 units B. 6 units C. 1 units D. 18 units
Answer:
B) 6 units
Step-by-step explanation:
The formula of the volume of the Pyramid is 1/3×area of the base×height
1/3×70×height=140
Dividing both sides by 70
1/3×height=2
Multiplying both sides by 3
Height = 6
Final answer:
The height of a right square pyramid with a rectangular base area of 70 square units and a volume of 140 cubic units is 6 units, by using the volume formula of the pyramid.
Explanation:
The question asks us to find the height of a right square pyramid with a given base area and volume. To find the height, we need to use the formula for the volume of a pyramid, which is given by the formula: Volume = (Base Area * Height) / 3. We are given the base area as 70 square units and the volume as 140 cubic units.
Using the formula to solve for the height we get:
Height = (Volume * 3) / Base Area = (140 * 3) / 70 = 6 units. Therefore, the height of the pyramid is 6 units.
What is the Translation Postulate?
Answer: to suggest or accept that a theory or idea is true as a starting point for reasoning or discussion.
Step-by-step explanation:
Here's an example: Astronomers postulate that the comet will reappear in 4000 years.
The process of using sample statistics to draw conclusions about the population parameters is referred to as
A. inferential statistics
B. sampling
C. the scientific method
D. descriptive statistics
Answer:
Option A) inferential statistics
Step-by-step explanation:
We describe inferential statistic as:
Inferential Statistic:
It s the process of estimating population parameter with the help of a sample from the population.A random sample from the population is used to describe the population with the help of sample statistic.A smaller subset is used to inference about the larger set.Thus, the correct answer is
Option A) inferential statistics.
Answer:
Step-by-step explanation:
2.) Fill in the blank.
csc^2 0 = cot ^2 0 + ___
A.) sec ^2 0
B.) -cos ^2 0
C.) -tan ^2 0
D.) 0
E.) 1
Answer:
E.) 1
Step-by-step explanation:
Firstly we will solve for L.H.S.
L.H.S. =[tex]Csc^2\theta[/tex]
Since we know that [tex]Csc^2\theta[/tex] is the inverse of [tex]Sin^2\theta[/tex].
So we can say that;
[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex]
Now For R.H.S.
[tex]Cot^2\theta+1[/tex]
Since we can rewrite [tex]cot^2\theta[/tex] as [tex]\frac{cos^2\theta}{sin^2\theta}[/tex].
Now we can say that the R.H.S. is;
[tex]\frac{cos^2\theta}{sin^2\theta}+1[/tex]
Now we add the fraction and get;
[tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}[/tex]
Now according to trigonometric identity;
[tex]cos^2\theta+sin^2\theta=1[/tex]
So, [tex]\frac{cos^2\theta+sin^2\theta}{sin^2\theta}=\frac{1}{sin^2\theta}[/tex]
Here,
[tex]csc^2\theta=\frac{1}{sin^2\theta}[/tex] and [tex]Cot^2\theta+1[/tex] = [tex]\frac{1}{sin^2\theta}[/tex]
L.H.S. = R.H.S.
Hence [tex]csc^2\theta=cot^2\theta+1[/tex]