Answer:
C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.
Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
Step-by-step explanation:
The sample mean obtained was :
[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}= 144.3[/tex]
A. The given value is a parameter parameter for the year year because the data collected represent a population population.
False. The data colected represent a sample of the population of interest, so for this case is not a parameter because we don't have the information about all the population of interest.
B. The given value is a parameter parameter for the year year because the data collected represent a sample sample.
False. First the sample average is not a parameter, and second the population mean is not equal to the sample mean most of the times.
C. The given value is a statistic statistic for the year year because the data collected represent a sample sample.
Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
D. The given value is a statistic statistic for the year year because the data collected represent a population.
False. If is an statistic can't represent the population, since the parameter represent the population not the statistic.
In this exercise we have to use the knowledge of statistics to be able to identify the correct statement, so I can say that it is:
The letter C
So knowing the statistics topics we can recognize the true alternative:
A. False. The information in visible form colected show a sample of the inhabitants of a place of interest, so for this case exist not a limit cause we forbiddance bear the facts about all the inhabitants of a place of interest.
B. False. First the sample average exist not a limit, and second the inhabitants of a place mean happen inadequate the average value most of the opportunity.
C. Correct. The value reported is an statistic since represent a SAMPLE of the population of interest.
D. False. If exist an detail of action can't represent the inhabitants of a place, because the limit represent the inhabitants of a place not the detail of action.
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Consider the numbers 0, 10, 20, 30, and 40. Multiply each by 4 and compare the result to 60 to determine into which of the following intervals? What number can you multiply by 4 and then add 8 to the product to get?
a. 0 to 10.b. 10 to 20.c. 20 to 30.d. 30 to 40.
Answer:
Option (b) 10 to 20
Step-by-step explanation:
Let the number obtained between the interval be 'x'
Therefore,
according to the question:
multiplying the number with 4 and then adding 8 to it to get 60
thus,
mathematically, we get
4x + 8 = 60
or
4x = 60 - 8
or
4x = 52
or
x = 13
Hence,
The 13 lies between the interval 10 to 20
Option (b) 10 to 20
Write and solve an equation that represents the following: A number decreased by 12 is 24.
x - 24 = 12; x = 36
x - 12 = 24; x = 36
24 - 12 = x; x = 12
x + 12 = 24; x = 12
Answer:
x - 24 = 12; x = 36
or
x - 12 = 24; x = 36
Step-by-step explanation:
Find an equation of the line that
a. has the same y-intercept as the line y+7x+3=0 and
b. Is parallel to the line -11x-12y=-7
Write your answer in the form y=mx+b
Answer:
y = (-11/12)x - 3
Step-by-step explanation:
Recall that for a linear equation in the form y = mx + b,
m = slope and b = y-intercept.
hence to satisfy parts (a) and (b) of the questions, we need to extract the y-intercept from the equation in part (a) and the slope from part (b)
For part (a)
given: y+7x+3=0 (rearrange this to get slope-intercept form)
y+7x+3=0 (subtract 3 from both sides)
y + 7x = -3 (subtract 7x from both sides)
y = -7x - 3
we can see that the y-intercept is -3.
For part (b)
given: -11x -12y=-7 (rearrange this to get slope-intercept form)
-11x -12y=-7 (add 11x toboth sides)
-12y = 11x - 7 (divide both sides by -12)
y = (-11/12) - (7/12)
we can see that the slope is (-11/12).
combining the y-intercept from part (a) and the slope from part (b) into the general equation given in the first line above,
y = (-11/12)x - 3 (answer)
The population of Hawaii is growing by about 5% per year. If that rate were to continue, how long would it take for the population of Hawaii to double?
Answer:
14.2 years
Step-by-step explanation:
The multiplier of the population each year is 1 +5% = 1.05, so after n years the population has been multiplied by 1.05^n. You want to find the value of n that makes this expression equal to 2:
2 = 1.05^n
log(2) = n·log(1.05) . . . . . take logarithms
log(2)/log(1.05) = n ≈ 14.2
Growing at a rate of 5% per year, it will take about 14.2 years for the population to double.
For any nonempty set $T$ whose elements are positive integers, define $f(T)$ to be the square of the product of the elements of $T$. For example, if $T=\{1,3,6\}$, then $f(T)=(1\cdot 3\cdot 6)^2 = 18^2 = 324$. Consider the nonempty subsets $T$ of $\{1,2,3,4,5,6,7\}$ that do not contain two consecutive integers. If we compute $f(T)$ for each such set, then add up the resulting values, what do we get?
Answer:
We get
$225+324+441+576+784+1125+2304+3136+4900+11025=24840$
Step-by-step explanation:
$(1\cdot 3\cdot 5)^2 = 15^2 = 225$
$(1\cdot 3\cdot 6)^2 = 18^2 = 324$
$(1\cdot 3\cdot 7)^2 = 21^2 = 441$
$(1\cdot 4\cdot 6)^2 = 24^2 = 576$
$(1\cdot 4\cdot 7)^2 = 28^2 = 784$
$(1\cdot 5\cdot 7)^2 = 35^2 = 1125$
$(2\cdot 4\cdot 6)^2 = 48^2 = 2304$
$(2\cdot 7\cdot 7)^2 = 56^2 = 3136$
$(2\cdot 5\cdot 7)^2 = 70^2 = 4900$
$(3\cdot 5\cdot 7)^2 = 105^2 = 11025$
We get
$225+324+441+576+784+1125+2304+3136+4900+11025=24840$
A nonzero polynomial with rational coefficients has all of the numbers [1 sqrt{2}, ; 2 sqrt{3}, ;3 sqrt{4},; dots, ;1000 sqrt{1001}]as roots. What is the smallest possible degree of such a polynomial?
Answer:
Its degree can be at least 1970
Step-by-step explanation:
for each root of the form √q, where q is not a square, we have a root -√q. Therefore, we need to find, among the numbers below to 1000, how many sqaures there are.
Since √1000 = 31.6, we have a total of 30 squares:
2², 3², 4², ...., 30², 31²
Each square gives one root and the non squares (there are 1000-30 = 970 of them) gives 2 roots (one for them and one for the opposite). Hence the smallest degree a rational polynomial can have is
970*2 + 30 = 1970
Rocky finished a 200-meter race in 5/12 of a minute.The winner finished 21/25 of Rocks time to finish the race.How much time did the winner use to finish the race
Answer the winner finished the race in 1.75 minutes
Step-by-step explanation:
Rocky finished a 200-meter race in 5/12 of a minute.
The winner finished 21/25 of Rocks time to finish the race. This means that the time that the winner took in finishing the race would be
5/12 × 21/5 = 21/12 of a minute.
Converting to decimal, it becomes
1.75 minutes
Step-by-step explanation:
5/12 x 21/25=105/300
105/300 divided by 5=21/60
21/60 divided by 3 =7/20
the winner use 7/20 of a minute or time to finish the race
hope it help you
Sam tested every 50th candy bar from the assembly line to make sure there were enough peanuts in each bar. He found 15% did not have enough peanuts. Which type of sampling did he use?
Answer: Sam used systematic random sampling .
Step-by-step explanation:
A systematic random sampling is a kind of random sampling technique in which a sample is drawn from a large population such that their participants selected according to a random initial point but a fixed periodic interval.Here , Sam tested every 50th candy bar from the assembly line to make sure there were enough peanuts in each bar.
i.e. the period of selecting candy bars is fixed as 50.
By definition of systematic random sampling , we can cay that Sam used systematic random sampling .
Sam is using systematic sampling in his testing, which is where elements from an ordered dataset are selected at regular intervals. This method is popular in quality checking in manufacturing due to its simplicity and efficiency.
Explanation:In the situation described, Sam is using a type of sampling known as systematic sampling. Systematic sampling is a method in which elements from an ordered dataset are selected at regular intervals. In this case, Sam checks on every 50th candy bar, which is consistent with this type of sampling approach.
It's important to note that while he is taking samples at regular intervals, there's an element of randomness because we don't know the order in which the candy bars with fewer or more peanuts come onto the assembly line. Systematic sampling is often useful when there's no reason to expect a pattern that might affect the sample, like in this case with the peanuts in the candy bars.
Manufacturers, like in this case Sam, often use this type of sampling when testing product quality due to its simplicity and efficiency. However, the key is to ensure that the interval at which you're sampling doesn't align with any potential pattern in the population to avoid bias.
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How to construct an equilateral triangle inscribed in a circle
Answer:
Step-by-step explanation:
Set your compass to length say AB and draw a circle centre A, without adjusting the compass, draw another circle with centre B. Name their intersectin C and D, erase the other part of the circle and leave just the intersect C and D. Draw a circle with centre A that passes through the intersection C and D, also draw a straight line that passes through centre C and D. Make an intersection say E on the circle by puting your comass on C and D. Join C and D to this intersection E.
What is the difference? StartFraction x Over x squared minus 16 EndFraction minus StartFraction 3 Over x minus 4 EndFraction StartFraction 2 (x + 6) Over (x + 4) (x minus 4) EndFraction StartFraction negative 2 (x + 6) Over (x + 4) (x minus 4) EndFraction StartFraction x minus 3 Over (x + 5) (x minus 4) EndFraction StartFraction negative 2 (x minus 6) Over (x + 4) (x minus 4) EndFraction
Answer:
D
Step-by-step explanation:
[-2(x-6)] / [(x+4)(x-4)]
To simplify the given expression, we can break it down into fractions and multiply them together step by step.
Explanation:The given expression is quite complex, but we can simplify it step by step. Let's break it down:
Simplify the first fraction: StartFraction \frac{x}{x^2 - 16} \EndFractionSimplify the second fraction: StartFraction \frac{3}{x - 4} \EndFractionMultiply the two fractions together: StartFraction \frac{2(x + 6)}{(x + 4)(x - 4)} \EndFractionMultiply the result by the third fraction: StartFraction \frac{-2(x + 6)}{(x + 4)(x - 4)} \EndFractionMultiply the result by the fourth fraction: StartFraction \frac{x - 3}{(x + 5)(x - 4)} \EndFractionMultiply the result by the fifth fraction: StartFraction \frac{-2(x - 6)}{(x + 4)(x - 4)} \EndFractionBy following these steps, we have simplified the given expression.
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Jose is standing next to a mailbox when he begins walking north from the mailbox at a constant speed of 4 feet per second. How far is Jose north of the mailbox 7 seconds after he started walking?
Answer:
28feet
Step-by-step explanation: To calculate how far Jose walked after 7seconds, we use the formular: Distance travelled/ Time = Speed
Mathematically, v=d/t
Where v=4ft/sec , t= 7seconds
Substituting these values in
4 =d/ 7
Cross multiplying
4×7=d
28=d
Distance Jose walked =28ft
In a study of weight gains by college students in their freshman year, researchers record the amounts of weight gained by randomly selected students (as in Data Set 6 "Freshman 15" in Appendix B). Is the data from a discrete or continuous data set?
Answer:
For this particular case they are interested on the amount of weight gained by randomly selecting some students, we need to remember that the weight can't be a discrete random variable since this random variable can take values on a specified interval and with decimals, so for this case the best conclusion is that we have a continuous data set.
Step-by-step explanation:
Previous concepts
We need to remember that continuous random variable mans that the values are specified over an interval in the domain, so is possible to have decimal values for the possible outcomes of the random variable.
By the other hand a discrete random variable only can take integers for the possible outcomes of the random variable over the specified domain.
Solution to the problem
For this particular case they are interested on the amount of weight gained by randomly selecting some students, we need to remember that the weight can't be a discrete random variable since this random variable can take values on a specified interval and with decimals, so for this case the best conclusion is that we have a continuous data set.
The data from a study on weight gains by college students in their first year is a continuous data set. This is because the data (weight gain) can take on any value including decimal values within a certain range.
Explanation:The data collected from a study on weight gains by college students in their freshman year is considered to be a "continuous data set." This is because the weight gain, which is typically measured in pounds or kilograms, can take on any value within a certain range, including decimal values, reflecting the continuous nature of the data. For example, one student might gain 1.5 pounds, another might gain 2.3 pounds, and so on. It doesn't have to be in whole numbers, unlike in a discrete data set.
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I = prt
I = simple interest, p = principal, r = rate, t = time.
You want to study at the Hogwarts School of Witchcraft and Wizardry after five years. You need 800 pieces of muggle-money to study there. You decide to deposit some pieces in the bank at an annual interest rate of %12.
Answer:
The amount we need to invest is 500 muggle money.
Step-by-step explanation:
Amount needle to study at Hogwarts = A = 800 muggle money
Principle amount that we need to invest = P
Duration of investment = T = 5 years
Rate if simple interest = R = 12%
Simple interest = S.I
A = S.I + P
[tex]800=\frac{P\times 12\times 5}{100}+P[/tex]
[tex]800=0.6P+P[/tex]
[tex]800=1.6P[/tex]
P = [tex]\frac{800}{1.6}=500[/tex]
The amount we need to invest is 500 muggle money.
Suppose the following are given to you: D ( q ) = − 0.00029 q 2 − 0.0716 q + 557 C ( q ) = 81 q + 18300 Find the profit function.
Profit function= 81q +18300+0.00029q2+0.0716q-557
Step-by-step explanation:A profit function shows the relationship between a company's total profit and output.
The profit function is equal to the company's total rebenue(TR) minus total cost of the company(TC).
Mahemathically,Profit = TR-TC.
Let D(q)= TC=-0.00039q2-0.0716q+557C(q)
Let TR= 81q +18300.
Profit=TR-TC
Profit =81q+18300-(-0.00029q2-0.0716q+557)
Profit=81q+18300+0.00029q2+0.0716q-557.
A football player punts the ball at a 45.0º angle. When the ball returns to the ground, it will have a horizontal displacement of 60.6 m. What is the initial speed of the ball?
The initial speed of the ball is approximately [tex]\( 24.38 \ m/s \)[/tex].
To find the initial speed of the ball, we can use the projectile motion equations. The horizontal displacement (range) can be expressed as:
[tex]\[ R = \frac{V_0^2 \sin 2\theta}{g} \][/tex]
where:
- [tex]\( R \)[/tex] is the horizontal displacement (60.6 m),
- [tex]\( V_0 \)[/tex] is the initial speed,
- [tex]\( \theta \)[/tex] is the launch angle (45.0º),
- [tex]\( g \)[/tex] is the acceleration due to gravity (9.8 m/s²).
First, convert the launch angle to radians: [tex]\( \theta = 45.0º \times \frac{\pi}{180} \approx 0.785 \ rad \)[/tex].
Now, substitute the values into the range equation and solve for [tex]\( V_0 \)[/tex]:
[tex]\[ 60.6 = \frac{V_0^2 \sin 2 \times 0.785}{9.8} \][/tex]
[tex]\[ V_0^2 = \frac{60.6 \times 9.8}{\sin 1.57} \][/tex]
[tex]\[ V_0^2 \approx \frac{60.6 \times 9.8}{1} \][/tex]
[tex]\[ V_0^2 \approx 594.48 \][/tex]
[tex]\[ V_0 \approx \sqrt{594.48} \][/tex]
[tex]\[ V_0 \approx 24.38 \ m/s \][/tex]
So, the initial speed of the ball is approximately [tex]\( 24.38 \ m/s \)[/tex].
Assigned Media Question Help What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? Choose the correct answer below.
A. The mean and standard deviation have the values of 0 and 1
B. The mean and standard deviation have the values of 0 and g 0.
C. The mean and standard deviation have the values of p = 1 and 0.
D. The mean and standard deviation have the values of - 1 and 0 -1.
Answer:
A
Step-by-step explanation:
The normal probability has two parameters mean and standard deviation. Every normal probability distribution can become a standard normal probability distribution when mean is zero and standard deviation is 1. This means that standard normal probability distribution centers at 0 and the spread about the mean is 1.
The volleyball team and the wrestling team at Weston High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $9 from past fundraisers. The wrestling team has raised $101 in the past, and they are making $3 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. How many cars will that take? What will that total be?
The volleyball and wrestling teams need to wash 23 cars each for their total funds raised to be equal. After washing this number of cars, each team will have raised a total of $92.
Explanation:In this scenario, the money each team has already raised and the amount they make per car equals the total they will have raised. We can express this as two equations and solve for the number of cars (let's call this 'x').
For the volleyball team:$4x + $9
For the wrestling team:$3x + $101
Setting these two equations equal to each other because they will have raised the same total gives us:
$4x + $9 = $3x + $101
The solution of this equation is x=23 cars. From this equation, we can also find the total raised by each team, which is $4*23 + $9 = $92 for each team.
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The hypothesis was that all three segments of the regulatory region are required for highest expression of the Hoxd13 gene. Is this hypothesis supported by the results?
Answer:
Yes, it is.
Step-by-step explanation:
The hypothesis made on the Hoxd13 gene expression justified the results obtained. This is because if one of the three segments is removed, the value of the expression level will be reduced to approximately below 100% of the control. Therefore, it can be inferred that the theoretical analysis justified the results obtained.
The Sahara Desert has an area of approximately 9 400 000 km^2. While estimates of its average depth vary, they center around 150 m. One cm^3 holds approximately 8 000 grains of sand. a. Approximately how many grains of sand are in the Sahara Desert? b. What fraction of the Sahara is made by 1 grain of sand? c. A small dump truck can carry approximately 20.5 m^3 of sand. Suppose a long line of dump trucks were to dump a load of sand every 30 seconds. How many years would it take to re-create the Sahara Desert?
Answer:
a). [tex]1.128\times 10^{25}[/tex] grains
b). [tex]\frac{1}{8000}[/tex]
c). [tex]6.54305\times 10^{7}[/tex] years
Step-by-step explanation:
a). Given Sahara desert has an area of approximately = 9400000 km²
= 9400000×(10000000000) cm²
= [tex]9.4\times 10^{16}[/tex] cm²
Depth of the desert = 150 m
= 15000 cm
Volume of desert = Area × Depth
= [tex]9.4\times 10^{16}\times 15000[/tex]
= [tex]1.41\times 10^{21}[/tex] cm³
Since 1 cm³ holds sand grains = 8000
Therefore, Grains in Sahara Desert = [tex]1.41\times 10^{21}\times 8000[/tex]
= [tex]1.128\times 10^{25}[/tex]
b). Since 1 cm³ = 8000 grains
1 grain = [tex]\frac{1}{8000}[/tex] cm³
c). A truck can carry sand = 20.5 m³ Or [tex]20.5\times (10^{2})^{3} cm^{3}[/tex]
= [tex]2.05\times 10^{7}[/tex] cm³
Now time taken to recreate Sahara Desert = [tex]\frac{\text{Total amount of sand}}{\text{Sand in one truck}}\times 30[/tex] seconds
= [tex]\frac{1.41\times 10^{21}}{2.05\times 10^{7}}\times 30[/tex]
= [tex]20.6341463\times 10^{14}[/tex] seconds
= [tex]\frac{20.6341463\times 10^{14} }{365\times \times 24\times 3600}[/tex] years
= [tex]6.54305\times 10^{7}[/tex] years
The Sahara Desert contains approximately 1.13 x 10^25 grains of sand. One grain of sand makes up a fraction of 8.85 x 10^-26 of the Sahara's total. It would take approximately 5.83 x 10^8 years for a line of small dump trucks, unloading every 30 seconds, to recreate the Sahara Desert.
Explanation:First, let's convert everything to the same units. The area of the Sahara Desert is 9,400,000 km^2 which is equal to 9.4 x 10^12 m^2. The average depth is approximately 150m, so the total volume of the Sahara is 9.4 x 10^12 m^2 * 150 m = 1.41 x 10^15 m^3. Since 1 m^3 = 1 x 10^6 cm^3, we have a total of 1.41 x 10^21 cm^3.
a. Each cm^3 contains 8,000 grains of sand, so the total number of grains in the Sahara is 8,000 * 1.41 x 10^21 = 1.13 x 10^25.
b. The fraction made by one grain is simply 1 divided by the total number of grains in the Sahara, which is 1/(1.13 x 10^25) = 8.85 x 10^-26. This fraction is incredibly small because the number of grains of sand in Sahara is incredibly large.
c. A small dump truck carries approximately 20.5 m^3 of sand. If a truck dumps its load every 30 seconds, this amounts to 2,419,200 m^3 of sand per year. To transport the equivalent of the Sahara would take 1.41 x 10^15 m^3 /2,419,200 m^3 per year = approximately 5.83 x 10^8 years.
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Classify each number below as a rational number or an irrational number. −17.6 , 81 , 15π , (square root −29), 13/14
Answer:
Rational Numbers
−17.6 (-176/10)
81
13/14
Rational Numbers
15π
square root −29
Step-by-step explanation:
Rational Numbers are those numbers which can be written as Ratio of two numbers.
Irrationational Numbers are those which cannot be written as ratio of two numbers. such as recurring numbers.
e.g 0.26262626.........
A bike shop rents mountain bikes for a $4.004.00 insurance charge plus $2.502.50 for each hour. For how many hours can a person rent a bike with $17.75?
Answer: the person can rent the bike for 5.5 hours.
Step-by-step explanation:
Let x represent the number of hours that a person rents the bike.
Let y represent the total cost of renting the bike for x hours.
A bike shop rents mountain bikes for a $4.00 insurance charge plus $2.50 for each hour. This means that the expression for the total cost of renting the bike for x hours would be
y = 2.5x + 4
Therefore, if a person has $17.75, the number of hours for which he can rent the bike would be
17.75 = 2.5x + 4
2.5x + 4 = 17.75
2.5x = 17.75 - 4
2.5x = 13.75
x = 13.75/2.5
x = 5.5 hours
Assume that the following statements are true.
A. If Trisha is drinking water, then it is dinnertime.
B. If it is lunchtime, then Rob is drinking milk and nothing else.
C. If it is dinnertime, then Anna is drinking iced tea and nothing else.
D. If it is breakfast time, then Sarah is drinking milk and nothing else.
E. Trisha is drinking water.
Using only the information given above, determine if "Anna is drinking iced tea" must be true, may be true, or is not true. Explain your reasoning. Assume that the following statements are true.
A. If Trisha is drinking water, then it is dinnertime.
B. If it is lunchtime, then Rob is drinking milk and nothing else.
C. If it is dinnertime, then Anna is drinking iced tea and nothing else.
D. If it is breakfast time, then Sarah is drinking milk and nothing else.
E. Trisha is drinking water.
Based on the provided conditional statements, if Trisha is drinking water, then it's dinnertime. Additionally, if it's dinnertime, then Anna is drinking iced tea. Given that Trisha is drinking water, we can conclude that Anna is drinking iced tea.
Explanation:The question here is dealing with conditional statements in logic. It's important to understand that if a conditional statement is true, and the first part (the condition) is true, then the second part must be true as well. In this case, Statement A states that if Trisha is drinking water, then it is dinnertime. So, if Trisha is drinking water (which is confirmed by Statement E), then it is dinnertime.
Statement C further adds to our understanding by stating that if it is dinnertime, then Anna is drinking iced tea and nothing else. Since based on Statements A and E, we know it is dinnertime, then following the logic from Statement C, we can conclude that Anna is drinking iced tea.
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This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 11 vans and 9 buses with 624 students. High School B rented and filled 5 vans and 1 bus with 126 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.
Answer:
There were 15 students in van and 51 students in the bus.
Step-by-step explanation:
Let the number of students in each van be 'x'.
Let the number of students in each bus be 'y'.
Given:
For High School A
number of vans = 11
Number of buses =9
Number of students = 624
now we can say that;
Total Number of students is equal to sum of the number of vans multiplied by the number of students in each van and Number of buses multiplied by the number of students in each bus.
framing in equation form we get;
[tex]11x+9y = 624 \ \ \ \ equation\ 1[/tex]
For High School B
number of vans = 5
Number of buses = 1
Number of students = 126
now we can say that;
Total Number of students is equal to sum of the number of vans multiplied by the number of students in each van and Number of buses multiplied by the number of students in each bus.
framing in equation form we get;
[tex]5x+y = 126 \ \ \ \ equation\ 2[/tex]
On solving both equation we will get the number of students in vans and buses.
First we will multiply equation 2 by 9 we get;
[tex]9(5x+y)=126\times 9\\\\45x+9y = 1134 \ \ \ \ equation\ 3[/tex]
Now Subtracting equation 2 from equation 1 we get;
[tex]45x+9y-(11x+9y)=1134-624\\\\45x+9y-11x-9y = 510\\\\34x=510[/tex]
Now dividing both side by 34 we get;
[tex]\frac{34x}{34}=\frac{510}{34}\\\\x= 15[/tex]
Now we will substitute the value of 'x' in equation 2 we get;
[tex]5x+y=126\\\\5\times15+y=126\\\\75+y =126\\\\y=126-75 = 51[/tex]
Hence There were 15 students in van and 51 students in the bus.
40 points!! What is the limit of the infinite series?
As n goes onto infinity, the expression [tex]\frac{3n^5}{4n^5+1}[/tex] will approach [tex]\frac{3}{4}[/tex]. Note the 3 and 4 come from the leading coefficients of the numerator and denominator respectively. This only works because the degrees for the numerator and denominator are both the same (both are 5).
Since [tex]\frac{3n^5}{4n^5+1}[/tex] is not approaching 0 when n gets really large, adding on successive terms of these values will have the infinite sum diverge. After some very large n, we are effectively adding on 3/4 each time and that just makes the overall sum keep growing forever.
Answer: The sum divergesFinal answer:
The limit of an infinite series depends on whether it converges or diverges. If it converges, the limit is the value the series approaches as the number of terms approaches infinity. If it diverges, it does not have a finite limit.
Explanation:
The limit of the infinite series depends on the specific series being referred to. To find the limit of an infinite series, you need to determine if it converges or diverges. If the series converges, then the limit is the value that the series approaches as the number of terms goes to infinity. If the series diverges, then it does not have a finite limit.
For example, consider the series 1/2 + 1/4 + 1/8 + ... This is a geometric series with a common ratio of 1/2. It converges to the value of 1, so the limit of this series is 1.
Some various tests and properties can be used to determine if a series converges or diverges. Some common ones include the ratio test, the root test, and the comparison test.
In Canada, $1 and $2 bills have been replaced by coins. When Marissa returned home to San Fran from a trip to Canada, she found that she had acquired 37 of these coins, with a total value of 51 canadian dollars. How many coins of each denomination did she have?
Answer:
$1 coin is 23
$2 coin is 14
Step-by-step explanation:
We need to form mathematical equations that we can solve from this Long citation.
Firstly, let the numbers of $1 coins be a and that of $2 be b.
We know that there are 37 coins. Hence
a + b = 37
Now, total is 51 Canadian dollars.
a + 2b = 51
Let’s now solve this simultaneously
From 2 , a + b + b = 51
Let’s say this is 3. Now substitute 1 into 3.
37 + b = 51, b = 51 - 37 = 14
Since a + b = 37
a = 37 - 14 = 23
PLEASE HELP!!!
Complete the following proof.
Given: LE=16,LN=40,FM=27,LM=45
Prove: ∆NLM~∆ELF
Answer:
Below.
Step-by-step explanation:
3. LF + 27 = 45
5. 18/45 = 16/40
6. 2/5 = 2/5
8.
Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course. 30% of the SAT prep students were admitted to their first choice college, as were 20% of the other students. You overhear a high school student say he got into the college he wanted. What is the probability he didn't take an SAT prep course?
Answer:
The required probability is 0.927
Step-by-step explanation:
Consider the provided information.
Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course.
That means 95% of students didn't enrolled in SAT prep course.
Let P(SAT) represents the enrolled in SAT prep course.
P(SAT)=0.05 and P(not SAT) = 0.95
30% of the SAT prep students were admitted to their first choice college, as were 20% of the other students.
P(F) represents the first choice college.
The probability he didn't take an SAT prep course is:
[tex]P[\text{not SAT} |P(F)]=\dfrac{P(\text{not SAT})\cap P(F) }{P(F)}[/tex]
Substitute the respective values.
[tex]P[\text{not SAT} |P(F)]=\dfrac{0.95\times0.20 }{0.05\times0.30+0.95\times0.20}[/tex]
[tex]P[\text{not SAT} |P(F)]\approx0.927[/tex]
Hence, the required probability is 0.927
To find the probability that the student didn't take an SAT prep course, we use conditional probability. The probability is approximately 0.6842 or 68.42%.
Explanation:To find the probability that the student didn't take an SAT prep course, we need to use conditional probability. Let's denote the events as follows:
A: The student got into the college they wantedB: The student took an SAT prep courseThe probability that the student didn't take an SAT prep course can be calculated using the formula:
P(A' | B') = (P(B') - P(A ∩ B')) / P(B')
We are given that 5% of the students took an SAT prep course, so P(B') = 1 - 0.05 = 0.95. We are also given that 30% of the SAT prep students were admitted to their first choice college, so P(A ∩ B') = 0.3. Finally, we are given that 20% of the other students were admitted to their first choice college, so P(A' ∩ B') = 0.2. Plugging these values into the formula:
P(A' | B') = (0.95 - 0.3) / 0.95 = 0.6842
Therefore, the probability that the student didn't take an SAT prep course is approximately 0.6842 or 68.42%.
Learn more about Conditional probability here:https://brainly.com/question/32171649
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Superman needs to save Lois from the clutches of Lex Luther. After flying for 15 seconds, he is 2100 meters from her. Then at 18 seconds he is 1980 meters from her.
A) Write an equation in slope-intercept form to model this situation where m is the distance in meters and s is the time in seconds.
B) How far is Superman away from Lois after flying for 6 seconds?
Part A
x = time in seconds that have gone by
y = distance in meters Superman is away from Lois
"After flying for 15 seconds, he is 2100 meters from her" means we have the point (x,y) = (15, 2100)
"at 18 seconds he is 1980 meters from her" tells us we have a second point (x,y) = (18,1980)
--------
Find the slope of the line through these two points
m = (y2-y1)/(x2-x1)
m = (1980-2100)/(18-15)
m = (-120)/(3)
m = -40
The slope is -40 which means Superman is getting 40 meters closer each second. I.e, the distance is dropping 40 meters per second
--------
Use one of the points and the slope to find the y intercept b
y = mx+b
2100 = (-40)*15 + b
2100 = -600 + b
2100+600 = b
b = 2700
This is the starting distance Superman is away from Lois
--------
Since m = -40 and b = 2700, we know the y = mx+b equation becomes y = -40x+2700.
Replace x with s, replace y with m. We now have m = -40s+2700
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Final Answer: m = -40s+2700============================================
Part B
Plug s = 6 into the equation we found for part A. Then simplify.
m = -40s+2700
m = -40*6+2700
m = -240+2700
m = 2460
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Final Answer: 2460 metersThe quantity b squared minus 4 ac is called the ______ of a quadratic equation. If it is ______, the equation has no real solution.
The quantity b squared minus 4 ac is called the Discriminate of a quadratic equation.
If it is negative the equation has no real solution.
Given thatThe quantity b squared minus 4 ac is called the ______ of a quadratic equation.
If it is ______, the equation has no real solution.
According to the questionQuadratic equation;Quadratic equations are equations that are often called a second degree.
It means that it consists of at least one term which is squared. Because of this reason, it is called “quad” meaning square.
The general form of a quadratic equation is [tex]\rm ax^2+bc+c=0[/tex] where a, b, and c are numerical coefficients or constants, and the value of x is unknown.
One fundamental rule is that the value of the first constant never can be zero.
Here, [tex]\rm ax^2+bc+c=0[/tex] is the equation.
Then,
Discriminate = [tex]\rm b^2-4ac[/tex]Therefore, The quantity b squared minus 4 ac is called the Discriminate of a quadratic equation.
If it is negative the equation has no real solution.
To know more about Quadratic Equation click the link given below.
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Sally is reading a book that has 590 pages. She already read some of it last week. She plans to read 50 pages tomorrow. By then, she will be 1/5 of the way through the book. How many pages did Sally read last week?
Answer:Sally read 68 pages last week.
Step-by-step explanation:
Let x represent the number of pages that Sally read last week. The book has a total of 590 pages. She already read some of it last week.
She plans to read 50 pages tomorrow and by then, she will be 1/5 of the way through the book. This means that the total number of pages that she would have read by tomorrow would be
1/5 × 590 = 118
It means that the sum of the number of pages that she read last week and the 50 pages that she planned to read tomorrow is 118. Therefore
50 + x = 118
x = 118 - 50 = 68
Answer: Sally read 68 pages last week.
Step-by-step explanation:
x =Sally read last week. The book has a total of 590 pages. She already read some of it last week.
She plans to read 50 pages tomorrow and by then, she will be 1/5 of the way through the book. This means that the total number of pages that she would have read by tomorrow would be
1/5 × 590 = 118
It means that the sum of the number of pages that she read last week and the 50 pages that she planned to read tomorrow is 118. Therefore
50 + x = 118
x = 118 - 50 = 68