The values of x that make the inequality x > 1/2 true are Choice A (2 1/3) and Choice D (1).
Explanation:The inequality x > 1/2 means that we are looking for any values of x that are greater than 1/2. Looking at our choices, Choice A (2 1/3) and Choice D (1) are correct since these values are greater than 1/2. Choices B (0), C (-1 1/2) and E (-3/4) are all less than 1/2, so they do not make the inequality true.
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A rectangular prism 5 feet long by 5 feet high by 6 feet deep and wide 15 tons what was the volume of the average stone how much did it one cubic foot of the stone weigh
Answer:
One cubic foot of the stone weigh 10 tons.
Step-by-step explanation:
There is a mistake in the question, thus it is corrected:
A typical stone on the lowest level of the great pyramid in Egypt was a rectangular prism 5 feet long by 5 feet high by 6 feet deep and weighed 15 tons. What was the volume of the average stone and how much did it one cubic foot of the stone weigh?
Now, to find the volume of average stone and how much one cubic foot of stone weigh.
Dimension of rectangular prism:
Length = 5 feet.
Height = 5 feet.
Width = 6 feet.
Now, to get the volume of stone which was a rectangular prism we put formula:
[tex]Volume=length\times width\times height[/tex]
[tex]Volume=5\times 6\times 5[/tex]
[tex]Volume=150\ cubic\ feet.[/tex]
The volume of the average stone was = 150 cubic feet.
Weight of stone = 15 tons.
Now, to get one cubic foot of the stone weigh we divide the volume of the average stone by weight of stone:
The volume of the average stone ÷ weight of stone
[tex]150\div 15[/tex]
[tex]=10\ tons.[/tex]
Therefore, one cubic foot of the stone weigh 10 tons.
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 42 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 48 births.
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
c. Is the result of 42 girls a result that is significantly high? What does it suggest about the effectiveness of the method?
Answer:
a) [tex]\mu = 24,\sigma = 3.46[/tex]
b) Significantly low:
[tex]x < 17.08[/tex]
Significantly high:
[tex]x > 30.92[/tex]
c) 42 girls are significantly high.
Step-by-step explanation:
We are given the following in the question:
[tex]p = 0.5[/tex]
a) mean and the standard deviation for the numbers of girls in groups of 48 births
[tex]\mu = np = 48(0.5) = 24\\\sigma = \sqrt{np(1-p)} = \sqrt{48(0.5)(1-0.5)} = 3.46[/tex]
b) Range rule of thumb
Significantly low: According to this rule the observations lying below two standard deviation of mean is considered significantly low.
[tex]x = \mu - 2\sigma\\x = 24 - 2(3.46) = 17.08[/tex]
Significantly high: According to this rule the observations lying above two standard deviation of mean is considered significantly high.
[tex]x = \mu + 2\sigma\\x = 24 + 2(3.46) = 30.92[/tex]
c) Significance of 42 girls
[tex]42 > \mu + 2\sigma[/tex]
Since 42 is greater than 30.92, 42 girls are significantly high. Thus, the method is not significant.
A ball slides up a frictionless ramp. It is then rolled without slipping and with the same initial velocity up another frictionless ramp (with the same slope angle). In which case does it reach a greater height, and why
Answer:
Rolling case achieves greater height than sliding case
Step-by-step explanation:
For sliding ball:
- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.
- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.
- The ball slides it only has translational kinetic energy as follows:
ΔK.E = ΔP.E
0.5*m*v^2 = m*g*h
h = 0.5v^2 / g
For rolling ball:
- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:
ΔK.E = ΔP.E
0.5*m*v^2 + 0.5*I*w^2 = m*g*h
- Where I: moment of inertia of spherical ball = 2/5 *m*r^2
w: Angular speed = v / r
0.5*m*v^2 + 0.2*m*v^2 = m*g*h
0.7v^2 = g*h
h = 0.7v^2 / g
- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.
A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle.
Explanation:A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle. This is because, when the ball slides up, it gains potential energy which is then converted to kinetic energy as it rolls up the second ramp. The ball will reach a greater height because it retains some of the initial energy it gained from sliding up the first ramp.
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In a lilac paint mixture, 40% of the mixture is white paint, 20% is blue, and the rest is he rest is red. There are 4 cups of blue paint used in a batchof lilac paint. How many cups of white paint are used
Answer:
8
Step-by-step explanation:
The ratio of white paint to blue paint in the mix is ...
40% : 20% = 2 : 1
We can multiply this ratio by 4 cups to find ...
white : blue = 8 cups : 4 cups
There are 8 cups of white paint in the mixture.
Answer: the number of cups of white paint are used is 8
Step-by-step explanation:
Let x represent the total number of cups of paint used in the mixture.
40% of the mixture is white paint, this means that the number of cups of white paint used is 0.4x
20% of the mixture is blue paint, this means that the number of cups of blue paint used is 0.2x
If the rest is red, it means that the number of red cups used is
x - (0.2x + 0.4x) = 0.4x
There are 4 cups of blue paint used in a batch of lilac paint. This means that
0.2x = 4
x = 4/0.2 = 20
Therefore, the number of cups of white paint are used is
0.4 × 20 = 8
An 18-slice pizza was made with only pepperoni and mushroom toppings, and every slice has at least one topping. Exactly ten slices have pepperoni, and exactly ten slices have mushrooms. How many slices have both pepperoni and mushrooms
Answer:
2
Step-by-step explanation:do it on a piese of parer them it will make more sence
solve the following problems using 5-D process part 2
(Describe/Draw, Define, Do, Decide, and Declare)
a. The number of girls in the Spanish Club is four more than twice the number of boys. There are 61 students in the Spanish Club. Find the number of boys and the number of girls in the Spanish Club.
b. Carrie and John went bowling together. They each bowled one game. Carrie knocked down 12 more pins than John did. The sum of their bowling games was 230. What was Carrie's and John's bowling scores?
The two problems are almost identical: you have to set up a system, and then solve it.
In the first case, let [tex]g[/tex] and [tex]b[/tex] be, respectively, the number of girls and boys.
We know that [tex]g=2b+4[/tex] (the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that [tex]g+b=61[/tex] (there are 61 students in total).
So, we have the system
[tex]\begin{cases}g=2b+4\\g+b=61\end{cases}[/tex]
We can use the first equation to substitute in the second
[tex]g+b=61 \iff (2b+4)+b=61 \iff 3b+4=61 \iff 3b=57 \iff b=19[/tex]
And then solve for [tex]g[/tex]:
[tex]g=2b+4=2\cdot 19+4=38+4=42[/tex]
For the second problem, let [tex]c[/tex] and [tex]j[/tex] be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system
[tex]\begin{cases}c=j+12\\c+j=230\end{cases}[/tex]
And you can solve it in the very same way we solved the previous one.
In a network of 40 computers, 5 hold a copy of a particular file. Suppose that 7 computers at random fail. Let F denote the number of computers that fail and have a copy of the file. A) What is E[F]?B) What is the range of F? C) What is the probability that F = 2?
Answer:
a. E(F)=0.875
b. 99.9976%
c. P(X=2)=0.1683
Step-by-step explanation:
a. We notice that this is a binomial distribution with the probability of success;
[tex]p=\frac{5}{40}=0.125[/tex]
#We are given the sample size, n=7. The Expected value is calculated as:
[tex]E(X)=np\\\\E(F)=np , n=7, p=0.125\\\\E(F)=7\times 0.125\\\\=0.875[/tex]
Hence the expectation, E(F)=0.875
b. To calculate the probability of the range of F, we need to calculate all possible outcomes of F in the given sample;
[tex]P(X\leq 5)=1-P(X=6)-P(X=7)\\\\=1-{7\choose 6}(0.125)^6(1-0.125)^1-{7\choose 7}(0.125)^7(1-0.125)^0\\\\=1-0.000023365-0.000000476\\\\=0.999976158\\\\=99.9976\%[/tex]
Hence, the range of F is 99.9976%
c. The probability that F=2 is calculated using the binomial distribution function as:
[tex]P(X=2)={7\choose 2}(0.125)^2(1-0.125)^5\\\\=0.1683[/tex]
Hence, the probability of F=2 is 0.1683
Using the hypergeometric distribution, it is found that:
a) E(F) = 0.875
b) The range is {0, 1, 2, 3, 4, 5}
c) 0.1741 = 17.41% probability that F = 2.
The computers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There are 40 computers, hence [tex]N = 40[/tex].Of those computers, 7 fail, hence [tex]n = 7[/tex].5 of the computers hold a copy, hence [tex]k = 5[/tex].Item a:
The expected value of the hypergeometric distribution is:
[tex]E(F) = \frac{nk}{N}[/tex]
Hence:
[tex]E(F) = \frac{35}{40} = 0.875[/tex]
Item b:
The range is the possible values that F can assume, which is from 0 to k, hence 0 to 5.
Item c:
The probability is P(X = 2), applying the hypergeometric distribution.
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,40,7,5) = \frac{C_{5,2}C_{35, 5}}{C_{40,7}} = 0.1741[/tex]
0.1741 = 17.41% probability that F = 2.
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The amount of time it takes for a student to complete a statistics quiz is uniformly distributed (or, given by a random variable that is uniformly distributed) between 32 and 64 minutes. One student is selected at random. Find the probability of the following events.
A. The student requires more than 59 minutes to complete the quiz.
Probability =
B. The student completes the quiz in a time between 37 and 43 minutes.
Probability =
C. The student completes the quiz in exactly 44.74 minutes.
Probability =
Answer:
(A) 0.15625
(B) 0.1875
(C) Can't be computed
Step-by-step explanation:
We are given that the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 32 and 64 minutes.
Let X = Amount of time taken by student to complete a statistics quiz
So, X ~ U(32 , 64)
The PDF of uniform distribution is given by;
f(X) = [tex]\frac{1}{b-a}[/tex] , a < X < b where a = 32 and b = 64
The CDF of Uniform distribution is P(X <= x) = [tex]\frac{x-a}{b-a}[/tex]
(A) Probability that student requires more than 59 minutes to complete the quiz = P(X > 59)
P(X > 59) = 1 - P(X <= 59) = 1 - [tex]\frac{x-a}{b-a}[/tex] = 1 - [tex]\frac{59-32}{64-32}[/tex] = [tex]1-\frac{27}{32}[/tex] = 0.15625
(B) Probability that student completes the quiz in a time between 37 and 43 minutes = P(37 <= X <= 43) = P(X <= 43) - P(X < 37)
P(X <= 43) = [tex]\frac{43-32}{64-32}[/tex] = [tex]\frac{11}{32}[/tex] = 0.34375
P(X < 37) = [tex]\frac{37-32}{64-32}[/tex] = [tex]\frac{5}{32}[/tex] = 0.15625
P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875
(C) Probability that student complete the quiz in exactly 44.74 minutes
= P(X = 44.74)
The above probability can't be computed because this is a continuous distribution and it can't give point wise probability.
Constructing arithmetic sequences Learn Recursive formulas for arithmetic sequences(Opens a modal)Recursive formulas for arithmetic sequences(Opens a modal)Explicit formulas for arithmetic sequences(Opens a modal)Explicit formulas for arithmetic sequences(Opens a modal)Arithmetic sequence problem(Opens a modal)Converting recursive
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is an = a1 + (n-1)d, and the explicit formula is an = a1 + (n-1)d.
Explanation:An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is given by: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. The explicit formula for an arithmetic sequence is given by: an = a1 + (n-1)d. The explicit formula allows you to directly find any term in the sequence without having to find the previous terms.
Very urgent... I need it right now.. please help me with explanation!
Answer:
a) Water height, H(g) = 8g^2 + 3g -4 - [9g^2 -2g -5] = 8g^2 + 3g -4 -9g^2 + 2g +5 = -g^2 +5g +1
b) g = 1
H(g) = -(1)^2 + 5(1) + 1 = -1 + 5 + 1 = 5
g=2
H(g) = -(2)^2 + 5(2) + 1 = -4 + 10 + 1 = 7
g=3
H(g) = -(3)^2 + 5(3) + 1 = -9 +15 +1 = 5
c) Greatest height
Find the vertex of the parabole
The vertex is at the mid point between the two roots.
To find the roots you can use the quadratic equation
The result is g = 5/2 + [√29]/2 and g = 5/2 - [√29]/2
The middle poin is 5/2 = 2.5
Now find H(2.5) = -(2.5)^2 + 5(2.5) + 1 = 7.5 ≈ 7.3
hope this helps
PLEASE HELP ME IDK HOW TO DO THIS
The table shows the highest daily temperature in degrees Fahrenheit averaged over the month for Cosine City, where m is the number of months since January 2001. (m = 0 represents January 2001.) *see attached table*
A sine function is written to represent the data.
What is the amplitude, period, and vertical shift of this equation?
Answer:
Amplitude is 17
Period = 12
Vertical shift of 50
Step-by-step explanation:
One complete cycle in 12 months
Mean line is at y = 50, so vertical shift of 50
Amplitude = 67-50 = 17
Or , 50 - 33 = 17
The vertical shift, amplitude, and period of the given equation would be as follows:
Amplitude [tex]= 17[/tex]
Period [tex]= 12[/tex]
Vertical Shift [tex]= 50[/tex]
What is Temperature?Given that,
Duration of the cycle [tex]= 12[/tex] months
∵ Period [tex]= 12 months[/tex]
The Mean line lies at [tex]y = 50[/tex]
So,
The vertical shift [tex]= 50[/tex]
Now,
Amplitude [tex]= 67-50[/tex]
[tex]or[/tex]
[tex]50 - 33[/tex]
[tex]= 17[/tex]
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A bookcase has 4 shelves. The bottom shelf has 10 books. Each of the other shelves has 5 more books than the shelf below it. How many books are in the bookcase.
Answer:
70
Step-by-step explanation:
identify the type of function shown in the graph.
The type of Function shown in the graph
Step-by-step explanation:
1.The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value.
2.Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each has a unique graph that is easy to visually differentiate from the rest.
3.we can represent a function using a graph. Graphs display many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis.
Answer:
y= 1/2 csc (x)
Step-by-step explanation:
probably
I need helpp please help me!!!
Answer:
SAS
Step-by-step explanation:
The workers in a factory are organized into five-person teams. When conducting a work-environment survey, a researcher randomly selected 10 teams to obtain a total sample of 50 workers. The researcher used ____ sampling.
Answer:
cluster sampling
Step-by-step explanation:
ideal groups of objects are naturally chaos arranged in groups, and randomly selected. Unlike class sampling, with homogeneously arranged groups and only a few randomly selected objects from each group, in cluster sampling, each group is allocated in a chaotic and all objects in the group become part of the sample.
Define a function called isSenior that takes a parameter containing an integer value and returns True if the parameter is greater than or equal to 65, and False otherwise.
Answer:
So if the parameter 's value is 7 or 803 or 141 the function returns true . But if the parameter 's value is -22 or -57, or 0, the function returns false .
My Code:
bool is Positive ( int x ) {
if ( x > 0 )
{
return true;
}
else {
return false ;
}
}
For every positive 2-digit number, x, with tens digit t and units digit u, let y be the 2-digit number formed by reversing the digits of x. Which of the followingexpressions is equivalent to x − y ?a) 9(t − u) b) 9(u − t) c) 9t − u d) 9u − t e) 0
Answer:
a) 9(t - u)
Step-by-step explanation:
x = 10t + u
y = 10u + t
x - y = 10t + u - 10u - t
= 9t - 9u
= 9(t - u)
A TRAFFIC LIGHT IS RED FOR 38 SECONDS YELLOW FOR 10 SECONDS AND GREEN FOR ONE MINUTE AND TWELVE SEONDS. IN A CONSTANTLY REPEATING CYCLE, WHAT IS THE PROBABILITY THAT AT THE MOMENT A PASSING PEDESTRIAN GLANCES AT IT, THE LIGHT WILL BE GREEN
PLEASE HELP
A student says that the function f(x)=3x4+5x2+1 is an even function. Is the student's statement true or not true, and why?
1) The student's claim is not true, because for any input of x, f(x)=−f(x).
2) The student's claim is not true, because for any input of x, f(x)=f(−x).
3) The student's claim is true, because for any input of x, .f(x)=−f(x).
4) The student's claim is true, because for any input of x, f(x)=f(−x).
Answer:
It's D.
Step-by-step explanation:
Final answer:
The function f(x) = 3x⁴+5x²+1 is an even function because f(-x) equals f(x) for any value of x, confirming the student's statement as true.
Explanation:
The function f(x) = 3x4+5x2+1 is indeed an even function. This can be determined by checking if f(-x) = f(x) for any value of x. An even function is symmetrical about the y-axis and does not change when x is replaced with -x. Applying this to the given function:
f(-x) = 3(-x)4+5(-x)2+1 = 3x4+5x2+1
f(x) = 3x4+5x2+1
Since f(-x) and f(x) are indeed equal, the function is even. Therefore, the correct answer to the student's statement that the function is even is: 4) The student's claim is true, because for any input of x, f(x) = f(-x).
The measure of the seven angles in a nonagon measure 138, 154, 145, 132, 128, 147, and 130. If the two remaning angles are equal in measure, what is the measure of each angle
Answer:
The measure of each angle is 143 degrees.
Step-by-step explanation:
We are given the following in the question:
A nonagon in which measure of seven angles are:
138, 154, 145, 132, 128, 147, 130.
Angle sum property of a nonagon:
The sum of interior angles if a nonagon are 1260 degrees.Let the two equal angle of nonagon be x degrees. Thus, we can write:
[tex]138+154+ 145+132+ 128+ 147+ 130+2x = 1260\\\Rightarrow 974 + 2x = 1260\\\Rightarrow 2x = 1260 - 974\\\Rightarrow 2x = 286\\\Rightarrow x = 143[/tex]
Thus, the measure of two equal angles is 143 degrees.
Final answer:
Using the formula for the sum of interior angles of a polygon and subtracting the sum of the seven given angles from the total, we find that the remaining two equal angles in a nonagon each measure 111 degrees.
Explanation:
The measure of the seven angles in a nonagon are given as 138, 154, 145, 132, 128, 147, and 130 degrees. To find the measure of each of the remaining two equal angles, we first need to calculate the sum of the angles in a nonagon. Using the formula for the sum of interior angles (S = (n-2) × 180 degrees, where n is the number of sides), we find that a nonagon has interior angles that add up to 1260 degrees. We then sum the seven given angles and subtract this total from 1260 to find the total measure of the remaining two angles. Finally, we divide this result by 2 to get the measure of each of the two equal angles. This allows us to determine that the measure of each of the two equal angles in the nonagon is 111 degrees.
a. Money market accounts
b. Single stocks
c. Bonds
d. Mutual funds
e. Fixed annuities
f. Real estate
For this assignment:
1. Put the investments in order by least risk to greatest risk. You can list by letter only (for example: a, b, c, d, e, f).
2. On a second line, order the investments by least return to greatest return. Again, you can list by letter only.
3. Review the sorted lists, and determine the one investment type you would select to start your investment portfolio. Provide a one-paragraph explanation of why you selected the investment along with your expected returns.
Answer:
Investments in order by least risk to greatest risk: A, C, E, D, F, B.
Step-by-step explanation:
In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?
A) 5
B) 4
C) 3
D) 2
E) 0
Step-by-step explanation:
Below is an attachment containing the solution.
A ship departs from Port miami with 5678 tons of cargo the ship docks at the Bahamas and the uploads some cargo the crew also loads three times the quantity of cargo that was unloaded of the ship holds 8588 tons now how many tons of cargo did the ship unload at the bahamas
Answer: the ship unloaded 1455 tons of cargo at the bahamas.
Step-by-step explanation:
Let x represent number of tons of cargo that the ship unloaded at the bahamas.
The initial number of tons of cargo in the ship is 5678 tons. If it unloads x tons of cargo, the number of tons of cargo left would be
5678 - x
The crew also loads three times the quantity of cargo that was unloaded. This means that the number of tons of cargo that it loaded is 3x. The total number of tons of cargo in the ship would be
5678 - x + 3x
= 5678 + 2x
If the ship holds 8588 tons now, it means that
5678 + 2x = 8588
2x = 8588 - 5678
2x = 2910
x = 2910/2
x = 1455 tons of cargo
- Two consecutive integers are 5 and 6. Write a quadratic equation that
could be used to determine these two integers.
Answer:
x^2 -11x +30 = 0
Step-by-step explanation:
If these two integers are solutions of the quadratic, then its factors are ...
(x -5)(x -6) = 0
Multiplying this out, we get ...
x^2 -11x +30 = 0
Nolini says that if the denominator is more than twice the numerator, the fraction can always be replaced with a 0. Is she correct? Give an example in your explanation.
Answer:
yes
Step-by-step explanation:
It depends on how accurate you want your answer to be, but basically yes, imagine we set our numerator to be x, and our denominator to be 2x, if we built our fraction we will get that:
[tex]\frac{x}{2x}=\frac{1}{2}[/tex]
If the denominator of a fraction is exactly twice the numerator, then the fraction will be simplified to 1/2 or 0.5.
Now, the greater the denominator is, the closer the fraction will get to zero.
Take for example I had an fraction like this:
[tex]\frac{3}{6}=0.5[/tex]
which approximates to 0. If we made the denominator bigger, let's say 7, we would get:
[tex]\frac{3}{7}=0.43[/tex]
notice the answer is closer to 0 this time, so it's valid to round it to zero. If we made the denominator greater, let's say 25, we would get:
[tex]\frac{3}{25}=0.12[/tex]
and so on. So it is true that if the denominator of a fraction is greater than twice the numerator, we can always replace the fraction with a 0 (depending on how accurate you want your answer to be).
If the denominator is more than twice the numerator, the number is therefore less than halve, 1/2 but cannot always be replaced with a 0.
An example;
Suppose we have a numerator, 2.
Then, we have a denominator which is more than twice the numerator; say 5
The resulting fraction is therefore;
2/5.The fraction 2/5 is definitely less than 1/2 but cannot always be replaced with a 0.
Read more on fractions:
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By selling a laptop at $1,000 for which consumers are willing to pay up to $1,200, a consumer electronics firm makes a profit of $400 per unit. In this scenario, the amount $600, that is ($1200 – $1000) + $400, is the
Answer:
600
Step-by-step explanation:
A 24.6 g marble sliding to the right at 62.0 cm/s overtakes and collides elastically with a 12.3 g marble moving in the same direction at 15.5 cm/s. After the collision, the 12.3 g marble moves to the right at 77.5 cm/s. Find the velocity of the 24.6 g marble after the collision. cm/s
Answer:
Velocity of the 24.6 g marble is 31 cm/s.
Step-by-step explanation:
Given:
Marble 1:
Mass of the marble [tex](m_1)[/tex] = 12.3 gm
Velocity of [tex]m_1[/tex] before collision [tex]v_1_i[/tex] = 15.5 cm/s
Velocity of [tex]m_1[/tex] after collision [tex]v_1_f[/tex] = 77.5 cm/s
Marble 2:
Mass of the marble [tex](m_2)[/tex] = 24.6 gm
Velocity of [tex]m_2[/tex] before collision [tex]v_2_i[/tex] = 62 cm/s
Velocity of [tex]m_2[/tex] after collision [tex]v_2_f[/tex] = ?
From the law of conservation of momentum, we know that momentum before equals the momentum after :
So,
⇒ [tex]P(i)=P(f)[/tex]
⇒ [tex](m_1\times v_1_i )+(m_2\times v_2_i) =(m_1\times v_1_f)+(m_2\times v_2_f)[/tex]
⇒ Plugging the values.
⇒ [tex](12.3\times 15.5) +(24.6\times 62)=(12.3\times 77.5)+(24.6\times v_2_f)[/tex]
⇒ [tex]190.65+1525.2=953.25+24.6\times v_2_f[/tex]
⇒ [tex]1715.85=953.25+24.6\times v_2_f[/tex]
⇒ [tex]1715.85-953.25=24.6\times v_2_f[/tex] ...subtracting both sides 953.25
⇒ [tex]762.6=24.6\times v_2_f[/tex]
⇒ [tex]\frac{762.6}{24.6}\ =v_2_f[/tex] ...dividing both sides with 24.6
⇒ [tex]31=v_2_f[/tex]
⇒ [tex]v_2_f =31[/tex] cm/s
The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.
A company's revenue can be modeled by r=2t^2-23t+77, where r is the revenue (in millions of dollars) for the year that is t years since 2005. Predict when the revenue was or will be at 14 million
Answer:
t=2652
Step-by-step explanation:
In which of the following scenarios would the distribution of the sample mean x-bar be normally distributed? Check all that apply.
a. We take repeated random samples of size 10 from a population of unknown shape.
b. We take repeated random samples of size 15 from a population that is normally distributed.
c. We take repeated random samples of size 50 from a population of unknown shape.
d. We take repeated random samples of size 25 from a population that of unknown shape.
Answer:
is d
Step-by-step explanation:
Two welders worked a total of 46 h on a project. One welder made $34/h, while the other made $39/h. If the gross earnings of the two welders was $1,669 for the job, how many hours did each welder work?
Answer:
x = 25 Total worked hours by welder winning 34 $ /h
y = 21 Total worked hours by welder winning 39 $ /h
Step-by-step explanation:
Let call
"x" numbers of hours worked by welder winning 34 $/h
"y" numbers of hours worked by welder winning 39 $/h
Then according to problem statement
x + y = 46 ⇒ y = 46 - x
1669 = 34*x + 39*y ⇒
We got a two equation system, solving
1669 = 34*x + 39* ( 46 - x ) ⇒ 1669 = 34*x + 1794 - 39*x
1669 - 1794 = - 5*x ⇒ -125 = - 5*x
x = 125/5 ⇒ x = 25
And as y = 46 - x y = 46 - 25 ⇒ y = 21