6.) Write another expression that is equivalent to 6.4 ÷ 0.08.
Test scores for a class of 7 students are: 89, 72, 96, 87, 64, 93, 80 What is the mean test score? What is the median test score? What is the mode of this data set? Find the standard deviation of this data set using the table method that is in the Course Notes, please show your work. You can think of the class of 7 students as a population.
For the given set of data, the value of mean is 83, median is 87 and standard deviation is 11.03
What is standard deviation?Standard deviation is a measurement of how evenly distributed a set of numbers is. Since the variance is the average of the squared deviations from the mean, it is the square root of the variance.
The mean score is - Sum of all scores / total number of scores
= 89 + 72 + 96 + 87 + 64 + 93 + 80 / 7
= 83
So the mean of given scores is 83
Median = central term
= 64, 72, 80, 87, 89, 93, 96
Median = 87
Mode of the data is - no mode as there are no recurring terms given
Standard deviation -
variance = (89 - 83)² +(72 - 83)² + (96 - 83)² + (87 - 83)² + (64 - 83)² + (93 - 83)² + (80 - 83)² / 7
= 121.71
standard deviation = √variance
⇒ standard deviation = 11.03
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Solve for x.
4x^2 - 10 = 90
Working alone, Rob can mop a warehouse
in six hours. Molly can mop the same
warehouse in nine hours. How long would
it take them if they worked together?l
It will take Molly and Rob 54/15 hours to mop the warehouse.
What is defined as the concept of work and time?Work is described as anything that has an impact or has an outcome. When it is stated somebody has done a certain work, it means that he or she has completed all of the work. As a result, if Manu accomplishes his work in 5 days, he will complete 100% of the work in 5 days.As a result, we could indeed say that he completes 20% of a work in one day. Similarly, he completes 40% of a work in two days and 60% of a work in three days.For the given question;
Rob takes 6 hours for cleaning the ware house.
Let 'R' be the work done by rob.
Then, work done by Rob in 6 hours is 1/R = 1/6.
Similarly;
Let work by Molly is 'R'.
The, work done by Molly in 1 hour is 1/M = 1/9.
The total work done by both is 1 hour is;
1/R + 1/M = 1/6 + 1/9
Om simplification;
1/R + 1/M = 15/54.
Thus, the total time taken by doing the work is; 54/15 hours.
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First make a substitution, and then use integration by parts to evaluate the integral.
Answer: 1/2 ([tex]\pi[/tex]) sin [tex]\pi[/tex] + ∫ x cos [tex]\pi ^{2}[/tex] dx + c
1/2 ([tex]\frac{\pi }{2}[/tex]) sin [tex]\frac{\pi }{2}[/tex] + ∫ x cos [tex]\frac{\pi }{2} ^{2}[/tex] dx + c
Step-by-step explanation:
We can't just integrate straight away, so we try substitution.
While trying substitution, we observe that we could integrate cos([tex]x^{2}[/tex]) x dx
by substitution.
So, let's split the integrand and use integration by parts.
we can represent θ = x,
so, we can write,
= ∫[tex]x^{3} cos x^{2} dx[/tex]
= ∫ [tex]x^{2} cos (x^{2} )xdx[/tex]
We notice that we could rewrite this as ∫ u cos(u) 1/2 du, but we don't see how to integrate that, so we'll continue with parts for now.)
= ∫ [tex]x^{2} cos (x^{2} )xdx[/tex]
Let u=[tex]x^{2}[/tex] and dv = [tex]cos(x^{2} )xdx[/tex]
Clearly du= 2x dx, and
we can integrate dv by substitution to get.
= 1/2 sin [tex]x^{2}[/tex]
uv - ∫ vdu = 1/2 [tex]x^{2}[/tex] sin([tex]x^{2}[/tex]) - ∫ x sin ([tex]x^{2}[/tex]) dx
Integrate by substitution again to finish.
∫ [tex]x^{3} cos (x^{2}) dx[/tex] = 1/2 [tex]x^{2} sin x^{2}[/tex] + ∫ x cos [tex]x^{2}[/tex] dx + c
Then,
x = √[tex]\pi[/tex] and √[tex]\frac{\pi }{2}[/tex]
∫ [tex]x^{3}[/tex] cos [tex]x^{2}[/tex] dx = 1/2 (√[tex]\pi ^{2}[/tex]) sin √[tex]\pi ^{2}[/tex] + ∫ x cos [tex]\pi ^{2}[/tex] dx + c
= 1/2 ([tex]\pi[/tex]) sin [tex]\pi[/tex] + ∫ x cos [tex]\pi ^{2}[/tex] dx + c
∫ [tex]x^{3}[/tex] cos [tex]x^{2}[/tex] dx = 1/2 ([tex]\frac{\pi }{2}[/tex]) sin [tex]\frac{\pi }{2}[/tex] + ∫ x cos [tex]\frac{\pi }{2} ^{2}[/tex] dx + c
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Given the function f(x) = 4x − 1 and the linear function g(x), which function has a greater slope?
f(x) has a greater slope.
g(x) has a greater slope.
The slopes of f(x) and g(x) are the same.
The slope of g(x) is undefined.
After the solution, we can conclude that (A) the slope of f(x) is higher.
What is the slope?A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x). The letter M stands for the slope of a function of the form y=Mx+C, so the slope of the function F(x) =4.Now that you have a function but can only evaluate it using a table, you can determine the slope using the following formula:
[tex]m=\frac{y^2-y^1}{x^2-x^1}[/tex]
Simply choose two points from the table to enter into the formula; in this example, we'll use points (4, 7) as our points 1 and our second point is (6,9).
This implies:
x¹ = 4y¹ = 7x² = 6y² = 9You just need to enter it into the formula:
m = 9-7/6-4m = 2/2m = 1Now that we know both slopes, you can see that g(x) has a slope of 1, while f(x) has a slope of 4, indicating that f(x) has a steeper slope than g(x).
Therefore, (A) f(x) has a greater slope.
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The complete question is given below:
Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?
x g(x)
2 5
4 7
6 9
f(x) has a greater slope.
g(x) has a greater slope.
The slopes of f(x) and g(x) are the same.
The slope of g(x) is undefined.
Answer:
After the solution, we can conclude that (A) the slope of f(x) is higher.
Step-by-step explanation:
What is the slope?
A line's steepness can be determined by looking at its slope.
The slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The letter M stands for the slope of a function of the form y=Mx+C, so the slope of the function F(x) =4.
Now that you have a function but can only evaluate it using a table, you can determine the slope using the following formula:
Simply choose two points from the table to enter into the formula; in this example, we'll use points (4, 7) as our points 1 and our second point is (6,9).
This implies:
x¹ = 4y¹ = 7
x² = 6y² = 9
You just need to enter it into the formula:
m = 9-7/6-4
m = 2/2
m = 1
Now that we know both slopes, you can see that g(x) has a slope of 1, while f(x) has a slope of 4, indicating that f(x) has a steeper slope than g(x).
Therefore, (A) f(x) has a greater slope.
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The complete question is given below:
Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?
x g(x)
2 5
4 7
6 9
f(x) has a greater slope.
g(x) has a greater slope.
The slopes of f(x) and g(x) are the same.
The slope of g(x) is undefined.
Which library has more volumes, Baton Rouge or El Paso? What number sentence shows the comparison? A. Baton Rouge; 1,232,185 < 1,277,003 B. El Paso; 1,232,185 > 1,277,003 C. Baton Rouge; 1,232,185 > 1,277,003 D. El Paso; 1,232,185 < 1,277,003
The library has more volumes in El Paso.
The number sentence that shows the comparison is 1,232,185 < 1,277,003
Hence, El Paso; 1,232,185 < 1,277,003. Option D
This is further explained below.
What is a library?Generally, A library is a collection of resources, such as books or other forms of media, that are made available for use rather than being kept only for the purpose of the show.
A library is a facility that makes resources available for physical or digital access, and it may exist either as a real place or as a virtual area, or both.
In conclusion, The library has more volumes in El Paso.
The number sentence that shows the comparison is 1,232,185 < 1,277,003
Hence, El Paso; 1,232,185 < 1,277,003.
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In two or more complete sentences, explain how to use ordered pairs of points in f(x)=2x+5 and g(x)= x-5/2 to determine if f(x) and g(x) are inverses of each other.
The ordered pair given are not inverse to each other because:
Substituting a value say 5/2 into f(x)=2x+5 gives 10Substituting 10 into g(x)= x-5/2 does not return 5/2How to know inverse functionsWhen two functions are inverse to each other substituting a value A in function say AA will give answer say X, substituting the answer X to the the other function say BB returns the value A.
Instance
say function AA, plug in A gives X
the inverse will be:
say function BB plug in X gives A
So, we have f(x)=2x+5 and g(x)= x-5/2
plugging in say 5/2 in f(x) will give
f(x) = 2 * 5/2 + 5
f(x) = 5 + 5
f(x) = 10
We plug in 10 to g(x)= x-5/2
g(x) = 10 - 5/2
g(x)= 7/2
since 7/2 ≠ 5/2 the pair of functions are not inverse to each other
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The lengths of pregnancies in a small rural village are normally distributed with a mean of 260 days and a standard deviation of 17 days. What percentage of pregnancies last beyond 221 days?
Answer:
9882 hzjsjs en kIskoaisjdjksjssjjdjsjsjjzjsjsjzjNNKsk
Two trains leave the same station at the same time but are headed in opposite directions. One train travels at 80 mph and the other train travels at 65 mph. How much time passes until the trains are 580 miles apart?
__Hours.
38.7 hours would have passed until the trains are 580 miles apart
How much time passes until the trains are 580 miles apart?The given parameters are
Train 1 = 80 mph
Train 2 = 65 mph
The difference in the speeds of the trains is
d = 80mph - 65mph
Evaluate
d = 15mph
The distance moved is
Distance = 15 * t
At 580 miles apart, we have
15 * t = 580
Divide by 15
t = 38.7 hours
Hence, 38.7 hours would have passed until the trains are 580 miles apart
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I need help!
Estimate the instantaneous rate of change of the function f(x)=−4x2−3x+1 at x=−3 using the average rate of change over successively smaller intervals.
The instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
What is the instantaneous rate of change of the function at the given point?The instantaneous rate of change is simply the change in the derivative value at a specific point.
Given the data in the question;
f(x) = −4x² − 3x + 1Point x = -3To determine the instantaneous rate of change of the function, first find the derivative of the function.
f(x) = −4x² − 3x + 1
Applying sum rule, with respect to x
d/dx[ -4x² ] + d/dx[ -3x ] + d/dx[ 1 ]
[ 2 × -4x¹ ] + [ 1 × -3x⁰ ] + d/dx[ 1 ]
[ -8x ] + [ -3 ] + d/dx[ 1 ]
-8x - 3 + d/dx[ 1 ]
Differentiate using constant rule
-8x - 3 + [ 0 ]
-8x - 3
f'(x) = -8x - 3
Next, plug x = -3 into the derivative and simplify.
f'(x) = -8x - 3
f'(-3) = -8(-3) - 3
f'(-3) = 24 - 3
f'(-3) = 21
Therefore, the instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.
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A city has 27 fewer wooden park benches
than metal park benches. There are 24 wooden benches.
How many metal benches are there?
There are 51 metal benches in the park
According to the question we have been given that
Number of wooden benches = 24
We have to calculate number of metal benches.
Let the number metal benches be x.
The according to the question
W = x - 27 where, W = wooden benches
Here , W = 24
Putting the required in the above equation for x we get
24 = x - 27
x = 24 + 27
x = 51
Hence the number of metal benches = 51 and we can see that 27 less of metal benches is 24 which is the number of wooden benches.
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PLEASE HELP WITH THIS QUESTION! ILL GIVE BRAINLYEST
Jill won 55 pieces of gum playing the bean
bag toss at her school's game night. Later,
she gave one to each of her friends. She
only has 40 remaining. How many did
she give away
Answer:
15 gum
Step-by-step explanation:
55-40 = 15
Is y=10•0.93^x exponential decay, exponential growth or neither
Answer: Exponential decay
Explanation: The base of the actual exponential function, [tex]0.93^{x}[/tex], is less than 1, which means that the output will become smaller.
Compare -2.3 and -8/3 using symbols <, >, or =.
₋2.3 < ₋8/3 is the correct answer.
Given, we need to compare the terms.
₋8/3 = ₋2.67
therefore, 2.3 is less than 2.667
hence we form it as ₋2.3 < ₋2.67
we form: ₋2.3 < ₋8/3
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Francisco earns seven dollars an hour at his part-time job last week he worked 16 hours what was his gross pay for the week what was his salary for the year if he works 16 hours a week all year
Answer:
he works 7 dollars an hour so 16 x 7 = 112 that's for a whole week a year would be 356 x 7 = 2,555 that's 1 whole year
Step-by-step explanation:
sorry if i got this wrong
Among fatal plane crashes that occurred during the past 65 years, 260 were due to pilot error, 62 were due to other human error, 315
were due to weather, 682 were due to mechanical problems, and 313 were due to sabotage.
Fill in the relative frequency for each category. Write answers in percentage form and round to one decimal place as needed. Do not include the percent symbol.
Answer: Pilot Error: 15.9%
Human Error: 3.8%
Weather: 19.3%
Mechanical Problems: 41.8%
Sabotage: 19.2%
Step-by-step explanation:
260+62+315+682+313=
322+997+313=
1319+313=1632 total crashes
Pilot error: 260/1632=
0.159=
0.159*1=
0.159*100%=15.9%
Human error: 62/1632=
0.03799=
0.038=
0.038*100%=3.8%
Weather: 315/1632=
0.193=
0.193*100%=19.3%
Mechanical Problems: 682/1632=
0.41789=
0.418=41.8%
Sabotage: 313/1632=
0.191789=
0.192=19.2%
51 is 33 1/3 of what number
Step-by-step explanation:
33 1/3 = (3×33 + 1)/3 = 100/3
51 = 100/3 × x
153 = 100x
x = 153/100 = 1.53
1.53 × 33 1/3 = 51
so, "that" number is 1.53.
CAN YOU PLEASE HELP ME ON #18 PLEASE!!
Answer:
x=90, y= 130
Step-by-step explanation:
Suppose in a class, 27 students got an A on the first exam and 15 students got an A on the third exam. Twelve students got an A on both the first and third exams. What is the conditional probabilty of getting an A on the third exam given that they got an A on the first exam, P(A third | A first)?
Given that:
In a class, 27 students got an A on the first exam.15 students got an A on the third exam.12 students got an A on both the first and third exams.To find:
What is the conditional probability of getting an A on the third exam given that they got an A on the first exam, P(A third | A first)?So, according the question,
Let's assume, total no. of students in class is x.
So, we know that
Conditional probability P( A IIIrd | A Ist ) = [tex]\frac{P(III^{rd} \cap I^{st}) }{P(I^{st})}[/tex]
From question,
P( A IIIrd ∩ A Ist) = 12/x. and
P(A Ist) = 27/12.
Now, putting the values
So, we will get
P( IIIrd | Ist ) = [tex]\frac{P(III^{rd} \cap I^{st}) }{P(I^{st})}[/tex]
P( IIIrd | Ist ) = [tex]{(\frac{12}{x})}\div {(\frac{27}{x} )}[/tex]
= [tex]\frac{12}{x} \times \frac{x}{27}[/tex]
= 12/27
= 4/9
Answer:
So, 4/9 is the Conditional probability of getting an A on the third exam given that they got an A on the first exam,To learn more about Conditional probability, please click on the link:
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PLS PLS PLS PLS PLS PLS PLS PLS LAST QUESTION JUST HELP ME PLS I BEG U describe a real-world situation where you can apply finding the unit rate
the growth of a plant or the amount of money you'll have off a banks interest overtime
Alex is thinking of a number that is multiplied by 7 and the added with 27. The result is
equal to 111.
44) What is the equation that you can write to solve for the number if the unknown
number is x.c
The equation that can be used to solve for the unknown number that Alex is thinking is 7x + 27 = 111
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the unknown number. The number is multiplied by 7 and the added with 27. The result is equal to 111. Hence:
7x + 27 = 111
The equation that can be used to solve for the unknown number that Alex is thinking is 7x + 27 = 111
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May I get help with my math?
Answer:
I don't know and your read in which class
which equation show the relationship between x,the number of minutes ,and y ,the price
Answer:
ummm idek
Step-by-step explanation:
What company has the absolute advantage when it comes to producing phones?
a. Gonzalez and Bros. Inc
b. The G company Inc
c. they both do
d. neither
(Option a) Gonzalez and Bros . Inc has the absolute advantage when it comes to producing phones.
Absolute advantage theory
In his book The Wealth of Nations, the 18th-century economist Adam Smith proposed the concept of absolute advantage to describe how countries could benefit from trade by specializing in producing and exporting the goods that they can make more successfully than other countries.
On the other hand, China, Thailand, and Vietnam create and export low-cost manufactured goods. These three countries benefit greatly from their much lower unit labor costs.
Here, option a Gonzales and Bros. Inc has the absolute advantage when it comes to producing phones.
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12 divided by 3 - 6(2) -8 divided by 4
Enter the sentence as an equation or inequality. Use x to represent any unknown number The sum of 2 and a number is 23.
The sentence can be written as:
x + 2 = 23
And the solution is x = 21.
How to write the sentence as an equation?Here we have the sentence:
" The sum of 2 and a number is 23."
Let's define x as the number, then we can write the equation:
x + 2 = 23
This is a simple linear equation, to solve this we need to subtract 2 in both sides of the equation, we will get:
x + 2 - 2 = 23 - 2
x = 21
We conclude that the number is 21.
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-4(2w+7) simply with distributive property
Answer:
[tex]{ \tt{ - 4(2w + 7)}} \\ = { \tt{( - 4 \times 2w) + ( - 4 \times 7)}} \\ = { \tt{ - 8w - 28}}[/tex]
Brett works for the local farmer, delivering feed and produce to the local community. He uses his own truck for the deliveries. He
gets paid a travel allowance of 64 cents per kilometer travelled. How much car travel allowance would Brett get paid for
travelling a total of 87km?
Select one:
O $55.68
O $67.24
O $54.86
O $45.90
If there is currently $139.50 petty cash in the tin how much do I need to withdraw from the bank to make $200.00 in the tin?
Brett will get paid $55.68 for travelling a total of 87 kilometers at an allowance of 54 cents per kilometer.
According to the International System of Units (SI), one kilometer is equal to 1,000 meters in American English. The United States and the United Kingdom are significant outliers, where the statute mile is the unit of measurement used to express distances between geographical locations on land.
One Kilometer is roughly equivalent to 0.621 miles.
Brett delivers produce for the farmer using his truck.
He gets paid a travel allowance of 64 cents per kilometer.
So to calculate his total allowance we multiply the allowance with the distance travelled.
Brett gets paid: $0.64×87=$55.68
Hence Brett gets paid $55.68. So the first option is correct.
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