s(3)=4(3)-7+(3+1)^2
s(3)=12-7+16
s(3)=21
Answer:
21
Step-by-step explanation:
We find that s(x) = 4x - 7 + (x + 1)^2. Expanding, we get s(x) = x^2 + 6x - 6. Plugging in x = 3, we have s(3) = 3^2 + 6 x 3 - 6 = 21.
Alternatively, we can compute that f(3) = 5 and g(3) = 16, so s(3) = f(3) + g(3) = 21.
4. A rectangular strip of aluminum, 30 cm long and 10 cm wide, is rolled into the form of a cylinder.
Which would have the greater volume, a cylinder 10 cm high with circumference of 30 cîn or a cylinder
30 cm high with circumference of 10 cm?
Answer:
A cylinder 10 cm high with a circumference of 30 cm would have a greater volume
Step-by-step explanation:
Volume of a Cylinder
Given a cylinder of radius r and height h, the volume is calculated as:
[tex]V=\pi r^2h[/tex]
It's given a rectangular strip of aluminum 30 cm long and 10 cm wide. If we roll it to form a cylinder we can do it in two ways.
Rolling it across its length will make the cylinder have a height of h=10 cm and the circumference of the base equal to 30 cm.
The circumference of a circle of radius r is:
[tex]C=2\pi r[/tex]
Thus the radius is:
[tex]\displaystyle r=\frac{C}{2\pi}[/tex]
[tex]\displaystyle r=\frac{30}{2\pi}=\frac{15}{\pi}[/tex]
Thus the volume of the cylinder is:
[tex]V=\pi ( \frac{15}{\pi})^2*10[/tex]
[tex]V=\pi ( \frac{225}{\pi^2})*10[/tex]
[tex]V= \frac{2250}{\pi}[/tex]
If we rolled the strip across its width, then the height will be h=30 cm and the circumference C=10 cm, thus the radius is:
[tex]\displaystyle r=\frac{10}{2\pi}=\frac{5}{\pi}[/tex]
And the volume is:
[tex]V'=\pi ( \frac{5}{\pi})^2*30[/tex]
[tex]V'=\pi ( \frac{25}{\pi^2})*30[/tex]
[tex]V'= \frac{750}{\pi}[/tex]
Dividing V/V' = 3. The first volume it 3 times as much as the second volume.
A cylinder 10 cm high with a circumference of 30 cm would have a greater volume
Find the difference 0.2−0.05. Show your reasoning.
The difference 0.2−0.05 is equal to 0.15.
To find the difference between 0.2 and 0.05.
The larger number is 0.2.
The smaller number is 0.05.
When you subtract 0.05 from 0.2, you align the decimal points and subtract each digit accordingly:
[tex]0.2 - 0.05[/tex]
[tex]= 0.15[/tex]
So, the difference between 0.2 and 0.05 is 0.15.
To learn more on Equation:
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Can you guys help me with these unit rates
Answer:
2. 38
3. 12
5. 7
9. 13
Which student solved the equation 107 d = 1,733.4 correctly?
Gianna's work: 107 d = 1,733.4. 1,733.4 times 107 = 185,473.8.
Teddy's work: 107 d = 1,733.4. 1,733.4 minus 107 = 1,626.4.
Sid's work: 107 d = 1,733.4. 1,733.4 + 107 = 1,880.4.
Sammi's work: 107 d = 1,733.4. 1,733.4 divided by 107 = 16.2.
Answer:
It's D, Sammi's work. Hope it helps! Remember your perfect, your awesome, your worth it, just the way you are, you deserve this world! Have an amazing day!
Step-by-step explanation:
Answer:
The person above me is correct.
the equations are
A. y=5/3 x -5
B. y=3/5 x -5
C. y=5/3 x +5
D. y=3/5 x +5
Answer:
A
Step-by-step explanation:
Ralph Chase plans to sell a piece of property for $150000. He wants the money to be paid off in two ways a - short-term note at 11% interest and a long-term note at 8% interest. Find the amount of each note if the total annual interest paid is $15200
.
Answer:
Amount on 11% note = $106,666.67
Amount on 8% note = $43,333.33
Step-by-step explanation:
Let the amount for the short-term note at 11% interest be x.
Thus, the amount for the short-term note at 8% interest will be (150000 - x)
Now we are told that the total interest paid is $15,200.
Thus;
0.11x + 0.08(150000 - x) = 15200
0.11x + 12000 - 0.08x = 15200
Rearranging gives;
0.03x = 15200 - 12000
0.03x = 3200
x = 3200/0.03
x = $106666.67
Thus, amount for 8% note = $150000 - $106666.67 = $43,333.33
A line with a slope of 8 and includes the points (8,-10) and (10,w).What is the value of k?
Answer:
w = 6
Step-by-step explanation:
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]\frac{w-[-10]}{10-8}=8\\\\\frac{w+10}{2}=8\\\\w+10= 8*2\\[/tex]
w +10 = 16
w = 16 - 10
w = 6
The measure of an angle is 166º. What is the measure of its supplementary angle?
HELP PLZZ
Answer:
14
Step-by-step explanation:
To make 166 a supplementary angle you should add 14 because supplementary angles equal 180.
Answer:
14
Step-by-step explanation:
Supplementary angles add to 180 degrees.
Let x be the unknown supplement
x+166 = 180
x+166-166 = 180-166
x =14
The unknown supplement is 14
The length of the base of an isosceles triangle is x. The length of a leg is 4x - 2. The perimeter of the triangle is 95. Find x.
Answer:
x = 11
Step-by-step explanation:
sides of triangle measure: 'x', '4x-2' and '4x-2' since isosceles means both legs are equal
perimeter is the sum of all sides, so set up equation:
95 = 4x - 2 + 4x - 2 + x
95 = 8x - 4 + x
95 = 9x - 4
99 = 9x
x = 11
what is the difference of 4.042 and 3.155
Answer: 0.887
Step-by-step explanation:
PLEASE HELP!! I HAVE 30 MINS
#1) 9a+2-6a
#2) -p^6
#3) 5n^2
#4) -10n^4+9-7n^5+n^6
it is 9a+2-6a is 3a+2
it is -p^6 is -531441
5n^2 is 25n2
-10n^4+9-7n^5n^6 i di not know
How are these three numbers related. 50 1/2, 1/4, 202
Answer: If you divide 202/4=50.5 or 50 1/2
Step-by-step explanation:
An experiment was conducted that recorded the weight of a new bar of soap after each use. The line of best fit for the data collected is
y = -5.6x + 123, where y is the weight of the bar of soap, in grams, and x is the number of times that the bar was used.
Which statement describes the meaning of the y-intercept for the line of best fit equation?
Answer:
The initial weight of the bar soap is 123g
Step-by-step explanation:
No options but the question can still be solved.
Given
[tex]y = -5.6x + 123[/tex]
Required
What does the y intercept mean
Start by calculating the y intercept (i.e. when x = 0)
The equation becomes
[tex]y = -5.6*0 + 123[/tex]
[tex]y = 0 + 123[/tex]
[tex]y = 123[/tex]
This means that the initial weight of the bar soap is 123g
Ten 4th grade girls and ten 7th grade girls were randomly selected. Their heights, in inches, are recorded below:
4th Grade
44, 48, 48, 51, 52, 52, 54, 54, 57, 60
7th Grade
52, 55, 57, 57, 58, 60, 60, 62, 64, 65
On average, 7th grade girls tend to be about (these are your answer options for your answer put one of these numbers and tell me which grade) 6,7,5,8 inches taller than 4th grade girls, and ( Answer choices ) there is more variability in the height of 4th grade girls or there is more variability in the height of 7th grade girls.
Answer:
7
Step-by-step explanation:
average of 7th grade - average of 8th grade = 7
average of 7th = (52+55+57+57+58+60+60+62+64+65)/10
= 590/10
= 59
average of 4th = 44+48+48+51+52+52+54+54+57+60
= 520/10
= 52
59 - 52 = 7
please give me brainliest if it is helpful for you
Answer: Hoped I help
7 and there is more variability in the height of 7th grade girls
Step-by-step explanation:
4th grade
44+48+48+51+52+52+54+54+57+60
found the median which is 52 and 52 but you add them and divide them by 2 to get the median which is 104/2= 52
7th grade
52+55+57+57+58+60+60+62+64+65
median is 60 + 58=118/2= 59
59-52= 7
and
there is more variabilty in the hieght f 7th grade girls. because 4th grade has a lot of modes already while 7th grade has only like two so 7th grade will have more variability.
Please help and how do you know this answer
Answer:
21
Step-by-step explanation:
Answer:
1.67
Step-by-step explanation:
25/15 = 1.67
The mean is estimated by dividing the total of the values by the range of values.
14. Which shows how to find 5 x 72 mentally by using the Distributive
Property?
A. 5(7) + 5(2) B. 5(70) + 5(2) C. 205 + 70) D. 5(70)+2
Answer:
B
Step-by-step explanation:
5(70)= 350
5(2)= 10
350+10=360
72(5)= 360
i hope this helps!
Due to expected droughts, the farmer will only be planting crops on 3/ 4 of this area. How would you correctly calculate the size of this new area? A. the total area multiplied by 4 divided by 3 B. the total area divided by 3 C. the total area divided by 4 D. the total area multiplied by 3 divided by 4 math
Answer:your answer is D.
Step-by-step explanation:
When dividing fractions you must flip the numerator and denominator so that would leave you with 6/1 divided by 3/4, solve this and then you have an improper fraction so after you multiply by 3 you must divide because of the improper fraction and you will divide by 4.
Answer:
d .the total area multiplied by 3 divided by 4
Step-by-step explanation:
.
the total area multiplied by 3 divided by 4
Move values to the lines to complete each equation.
|8| =
|-8| =
-|8| =
-|-8| =
Answer:
I think this is what you meant not sure tho
Step-by-step explanation:
|8| = correct as it is
|-8| = correct as it is
-|8| = |-8|
-|-8| = |8|
Look at the following number sequence.
6, 9, 12, 15, . . .
Based on the pattern, what are the next two terms?
Answer:
18, 21
Step-by-step explanation:
By finding the difference between each term, you can find the pattern. 9-6=3, 12-9=3, 15-12=3, so we know that each term is 3 more than the last.
Therefore, by following the pattern of +3, the next term is 15+3=18 and the one after that is 18+3 = 21
Answer:
the next two terms would be 18 and 21
Among fatal plane crashes that occurred during the past 55 years, 347 were due to pilot error, 83 were due to other human error, 596 were due to weather, 374 were due mechanical problems, and 114 were due to sabotage. Construct the relative frequency distribution.
Required:
What is the most serious threat to aviation safety, and can anything be done about it?
Answer:
Pilot error = 347 / 1487 = 0.233 = 23.3%
Other human error = 83 / 1514 = 0.055 = 5.6%
Weather = 596 / 1487 = 0.401 = 40.1%
Mechanical problem = 374 / 1487 = 0.233 = 23.3%
Sabotage = 114 / 1487 = 0.077 = 7.7%
Step-by-step explanation:
Given the data :
Pilot error = 347
Other human error = 83
Weather = 596
Mechanical problem = 374
Sabotage = 114
Cummlative sum = (347 + 83 + 596 + 374 + 114) = 1487
Relative frequency :
Pilot error = 347 / 1487 = 0.233 = 23.3%
Other human error = 83 / 1514 = 0.055 = 5.6%
Weather = 596 / 1487 = 0.401 = 40.1%
Mechanical problem = 374 / 1487 = 0.233 = 23.3%
Sabotage = 114 / 1487 = 0.077 = 7.7%
Based on the relative frequency estimate, Weather is the most serious threat to aviation safety.
Deployment of more weather monitoring technologies
The map of a town is placed on a coordinate grid. Use the map to find
the distance between the post office and the lake.
What is the sum of the interior
angle measures of a polygon
that has 7 sides?
Sum = [?]
Hint: Sum = (n-2)180
Answer:
Sum = 900 degrees.
Step-by-step explanation:
Sum = (n-2)180
=(7-2)180
=(5)180
=900
Answer:
900 degrees
Step-by-step explanation:
The formula for calculating the sum of the interior angles of a regular polygon is : ( n - 2) × 180°. when n is number of sides.
Sum of angles = ( n-2) × 180
Sum of angles = (7-2) × 180
Sum of angles = 5 × 180
Sum of angles = 900 degrees
Help me write an explanation
Answer:
9.375 grams
Step-by-step explanation:
30 days = 3(10 days)
m = 75·0.5³ = 9.375 grams
Tell whether the ordered pair is a solution to the system of linear equations. 1 point
63 + 3y = 12
(5.-6):
4x + y = 14
Yes
No
Maybe
Next
Page 1 of 3
Forms
Tell whether the ordered pair is a solution to the system of linear equations
Yes
No
Maybe
Answer:
(5,-6) is a solution
Step-by-step explanation:
Given
[tex]6x + 3y = 12[/tex]
[tex]4x + y = 14[/tex]
Required
Tell whether (5,-6) is a solution
In (5,-6): x = 5 and y = -6.
Substitute these values in the given equations
[tex]6x + 3y = 12[/tex] becomes
[tex]6 * 5 + 3 * -6 = 12[/tex]
[tex]30-18 = 12[/tex]
[tex]12 = 12[/tex]
[tex]4x + y = 14[/tex] becomes
[tex]4 * 5 - 6 = 14[/tex]
[tex]20 - 6 = 14[/tex]
[tex]14 = 14[/tex]
Because both solutions are true, then (5,-6) is a solution
how de you find standard deviation
Answer:
Work out the Mean (the simple average of the numbers)
Then for each number: subtract the Mean and square the result.
Then work out the mean of those squared differences.
Take the square root of that and we are done!
Are the hypontuse and the height of this triangle the same?
Answer:th hypotenuse and the height can’t possibly be the same size because the Pythagorean theorem is a^2 +b^2=c^2
Step-by-step explanation:
Answer:
hypotenuse is equal to side of this square.
but hypotenuse is never be equal to hieght of the triangle.
Which is the logarithmic equation log8 64 = a, written in exponential form?
Step-by-step explanation:
log8 64 = a
cut log and base^a
64 = 8^a
8^a = 64
or a = 2
Answer:
[tex]8^a = 64[/tex], which gives [tex]a=2[/tex].
Step-by-step explanation:
When you see [tex]\log_8(64)=a[/tex], think: [tex]a[/tex] is the number such that [tex]8^a = 64[/tex]. Mathematical intuition gives us that [tex]a=2[/tex] immediately, but we can also work this out more methodologically:
[tex]8^a = 64\\(2^3)^a = 2^6\\2^{3a} = 2^6\\3a = 6\\a = 2[/tex]
And this solution suffices.
please i really need to know the answer
Answer:
y = 10x + 30
Slope is 10
Y intercept is 30
Clint pays $80
Step-by-step explanation:
Let me know if you need any explanations
Here are some statistics about the masses of a group of 50 students
Mean = 12 Median = 14 Range = 17
a) If the mass of every student increase by 4 Kg , What are the new statistics?
b) If the mass of every student doubles , What are the new statistics
Step-by-step explanation:
A.
po sana makatulong po
3.X + 20 = 120
Hey I need this done by 9pm tonight, I know that we have to switch the expression to multiplication but then after that one step I don’t get it can someone pls help me
3x+20=100
Now you would need to move the constant to the right side and change within it’s sign
3x=100-20
Now you would subtract the numbers so for 100-20 would give you 80
So now you then do 3x=80
But if you want to divide the equation, divide it by both sides by 3
Which would give you x=80/3, x=26.6 or x=26 2/3