Answer:
Volume of regular pentagonal prism = 1.72 cm³ (Approx.)
Step-by-step explanation:
Given:
Side of regular pentagonal prism = 1 cm
Height of regular pentagonal prism = 1 cm
Find:
Volume of regular pentagonal prism
Computtaion:
Volume of regular pentagonal prism = (1/4)[√5(5+2√5)]a²h
Volume of regular pentagonal prism = (1/4)[√5(5+2√5)](1)²(1)
Volume of regular pentagonal prism = (1/4)[√5(5+2√5)]
Volume of regular pentagonal prism = (0.25)[√5{5+4.472}]
Volume of regular pentagonal prism = (0.25)[√5{9.472}]
Volume of regular pentagonal prism = (0.25)[√47.36]
Volume of regular pentagonal prism = (0.25)[6.8818]
Volume of regular pentagonal prism = 1.72045
Volume of regular pentagonal prism = 1.72 cm³ (Approx.)
Answer:
217.96 or 218.0 in Big Ideas Math
Thanks Harlan for helping me understand this problemStep-by-step explanation:
volume of the whole prism - smaller inner prism
Bigger Prism (apothem = 4, height = 6)
360/5 = 72 72/2 = 36
4 · tan (36) = 2.906
2.906 · 4 = 11.6247
11.6247 · 5 = 58.1234 ← The area of the Pentagon
58 · 6 = 348.740 ← The Bigger Prism Volume
Smaller Prism (apothem = 3, height = 4)
Keep in mind that the bottom, sides, and top of the box is one centemeters thick ⇒ smaller pentagon ⇒ (apothem = 4-1, height = 6 - 2)
3 · tan (36) = 2.1796
2.1796 · 3 = 6.5389
6.5389 · 5 = 32.6944 ← small Pentagon Area
32.6944 · 4 = 130.7777 ← Small Pentagon Prism Volume
Final Step
Area of big prism - small prism
348.74041 - 130.7777 = 217.9627
Round to the nearest tenth ⇒ 218.0
the concavity of a function is described by its
expression
1st derivative
2nd derivative
3rd derivative
The concavity of a function is described by its second derivative.
-The expression will not directly tell us whether the function is concave up or concave down and where it changes, though graphing the function may give us some sort of idea.
-The first derivative tells us the critical/important values (where there could be asymptotes), as well as where the function is increasing/decreasing.
-The second derivative tells us again the critical/important values, but also where the function is concave up/down. We find concavity in the same way we find increasing/decreasing using the first derivative.
-The third derivative, at least in my experience, has only been used to find acceleration of a function.
Hope this helps!! :)
The concavity of a function is described by its 2nd derivative
The concavity of a function is dependent on the rate of change of a function's derivative
Assume the derivative of a function is f'(x), so the second derivative would be represented as: f"(x)
When f"(x) > 0, then the function is concave downward.
However, if f"(x) < 0, then the function is concave upward.
Hence, the concavity of a function is described by its 2nd derivative
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A class of 36 students is going on a field trip. They will take 4 buses. Each bus will have the same number of students. How many students will be on each bus?
Answer:
144
I hope that helped!
Jim wants to buy an electric saw marked $98.00. If the salesperson offers him a discount of 15%, how much will he have to pay for the saw?
Answer:
$83.30
Step-by-step explanation:
Find how much he will have to pay by multiplying the price by 0.85, since this will calculate what 85% of the price is (with the 15% discount):
98(0.85)
= 83.3
So, he will have to pay $83.30 for the saw
y’all pls i’m in pain here
Answer:
it's the first one
Step-by-step explanation:
sorry if im wrong but i think it's right
Answer:
its the first
Step-by-step explanation:
first see how much it increases (1/2x)
and then where on the y line its crossing (+4)
sorry for bad english
PLEASE TELL ME THE VALUE
Answer:
Hello! answer: there are 7 quarters which are worth 25 cents each 6 dimes which are worth 10 cents each
there are 5 nickels which are worth 5 cents each and there are 8 pennies which are worth 1 cent each
the total value off all of these together is $2.68
Harry purchased 5 liter of blackberries. His younger brother ate 1/6 liter of the
blackberries on the way home. How many liters does he have left?
liter
Math
Answer:
f
Step-by-step explanation:
sro;y :-(
Answer:
Since his bro ate 1/6litre...
The remaining is simply
5 - 1/6 = 29/6litres
The area of a triangle is 14 square inches, and the triangle's height is 7 inches. Use the formula A = bh, where A is area, b is
base, and h is height, to find the length of the base of the triangle.
•49 inches
•1 inch
•2 inches
•4 inches
length of base is2 inches:
Answer:
Solution given:
According to the questionArea of triangle=14 square inches
bh=14
7*b=14
b=14/7
b=2
length of base is2 inches:
if
A=½bh
then
Area of triangle=14 square inches
½bh=14
½*7*b=14
b=14*2/7
b=4 inches
the length of the base of the triangle is 4inches.
The length of the base of the triangle will be;
⇒ b = 2 inches.
Option 3 is true.
What is mean by Triangle?
A triangle is a three sided polygon , which has three vertices and three angles with sum 180 degree.
Given that;
The area of a triangle = 14 square inches
Height of a triangle = 7 inches
Now,
The given formula for a triangle is;
⇒ A = bh
Where, A is the area, b is base and h is the height of the triangle.
Substitute all the values in above equation, we get;
⇒ A = bh
⇒ 14 = b x 7
Divide by 7, we get;
⇒ 14/7 = b
⇒ b = 2 inches.
Therefore,
The length of the base of the triangle will be;
⇒ b = 2 inches.
Option 3 is true.
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Can somebody tell me the answer for this one
What’s the answer to this one?
Sum of the interior angles of any triangle equal 180 degrees , Thus :
A + B + C = 180
48 + B + 67 = 180
B + 115 = 180
B = 180 - 115
B = 65 degrees
Answer:
B = 65°
Step-by-step explanation:
Area of triangle,
→ 180° = A + B + C
→ 180° = 48° + B + 67°
→ 180° = 115° + B
→ B = 180° - 115°
→ B = 65°
Can someone please help answer?
At a student art fair, 100 projects were on display. Of all the
3
art projects, were paintings and were photographs.
4.
5
How many of the projects were photographs or paintings?
Answer: 90 projects in all 1/5 were photographs 1/5 of 90=90/5=18
Step-by-step explanation: done :)
Answer:
i cannot see the numbers, can you type them out??
Step-by-step explanation:
i can add answer once you tell me
What is the slope of the line that passes through the points (-1, 0) and (3, 8)?
If you reject a joint null hypothesis using the F-test in a multiple hypothesis setting, then: A) a series of t-tests may or may not give you the same conclusion. B) the regression is always significant. C) all of the hypotheses are always simultaneously rejected. D) the F-statistic must be negative. Answer: A
Answer:
A) a series of t-tests may or may not give you the same conclusion
Step-by-step explanation:
F test is a statistical test, used for testing overall significance in a regression model. It denotes, how well - multiple explanatory (or independent) variables in a regression model effect the variation in dependent variable.
Rejecting a f test implies that - the set of multiple explanatory (or independent) variables 'jointly' effect the dependent variable significantly. However the individual independent variables might or might not effect dependent variable (independently) significantly.
So, the individual t tests might or might not give same conclusion.
ASAP A student population in a school was 972. Next year they are projected to have a 25% increase in student population. How many students will they have next year?
Answer:
3888
Step-by-step explanation:
Answer:
25% of 972= 243
243+972=1215 students
An investment of $8500 increases in value by 4.5% every year. How long until the investment
reaches about $17,323. Round to the nearest whole year
Answer:
16 years
Step-by-step explanation:
Given data
Principal= $8500
Rate= 4.5%
Final amount= $17,323
The expression to find time in compound interest is given as
t= ln(A/P)/r
substitute
t= ln(17323/8500)/0.045
t= ln(2.038)/0.045
t=0.711/0.045
t= 15.8 years
Hence the total time is about 16 years
PLEASE SOLVE QUICK IM UNDER A LOT OF STRESSSSSSS
In 15–20, write the number positioned at each point.
Answer:
See below.
Step-by-step explanation:
15.) -3.25
16.) -4.5
17.) 1.25
18.) -5.75
19.) 0.5
20.) -2.5
A number line is a horizontal line that has equally spread number increments. The points at A, B, C, D, E and F are -3.25, -4.5, 1.25, -5.75, 0.5 and -2.5
What is Number system?A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
A number line is a horizontal line that has equally spread number increments. The points at A, B, C, D, E and F are
15.) -3.25
16.) -4.5
17.) 1.25
18.) -5.75
19.) 0.5
20.) -2.5
Therefore the points at A, B, C, D, E and F are -3.25, -4.5, 1.25, -5.75, 0.5 and -2.5.
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Round off 54951 to the nearest 10,000.
Answer 50,000
Step-by-step explanation:
The area of the base of a cylinder is equivalent to the base of a circle? A) True. B) False
Answer:
Yes
Step-by-step explanation:
The base of both the cylinder and Circle are both circles.
Question 8
1 pts
Jerome went apple picking with his family. In his bag he had four Granny Smith
apples, two Honeycrisp apples, three Gala apples, and one Fuji apple. What is
the probability that he will pick a Honeycrisp apple out of his bag, eat it, and
then choose another Honeycrisp apple? Write your answer as a simplified
fraction.
Answer:
Total apples=10
no.of honeycrisp Apple=2
1). Probability-2/10. =1/5
now total apples left=9
tolyal honey crisp apples left=1
2) probability=1/9
The Probability that Jerome pick a Honeycrisp apple out of his bag is 1/5.
The Probability the Jerome pick to choose another Honeycrisp apple out of his bag is 1/9.
What is probability?Probability is "possibility that deals with occurrence random events".
According to the question,
Total number of apples = 10 apples
Total number of Honeycrisp apples = 2 apples
Formula for probability = [tex]\frac{Number of favorable events}{Total number of events}[/tex]
Probability that Jerome pick a Honeycrisp apple out of his bag = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex].
After taking one honey crisp apple remaining one left so subtracting one from total number of apples.
10 - 1 = 9
Probability that Jerome pick to choose another Honeycrisp apple out of his bag = 1/9.
Hence, the Probability that Jerome pick a Honeycrisp apple out of his bag is 1/5.
The Probability the Jerome pick to choose another Honeycrisp apple out of his bag is 1/9.
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1.Show that the points (5,5),(6,4),(-2,4) and (7,1) are concyclic .Also find the equation ,centre and radius of the circle on which they lie.
Answer:
See belowStep-by-step explanation:
This is how I solved it.
Plotted the given points. See the attached.
Identified two pairs to connect, the two chords.
(5. 5) with (7, 1) and (6,4) with (-2, 4).Determined the equation of both lines:
y -5 = [( 1 - 5)/(7-5)](x - 5) ⇒ y - 5 = -2(x - 5)y = -2x + 15and
y = 4 (horizontal line)Identified perpendicular bisectors of those two chords, they both pass through the center of circle.
Midpoints of the chords:
[(5 + 7)/2, (5 + 1)/2] = (6, 3)and
(6 - 2)/ 2 = 2The equations:
y - 3 = 1/2(x - 6) ⇒ y = 1/2x x = 2 (perpendicular to y = 4 and passing through x = 2)Solving the system found the intersecting of those, the center.
Found the center:
(2, 1)Found the distance from the center to one of the points (7, 1):
7 - 2 = 5, this is the radiusThe equation of circle:
(x - 2)² + (y - 1)² = 25Verified all the other points are on same circle, confirmed.
Find the height of the tower using the information given in the illustration. A right triangle has a a vertical side as the height of the Eiffel Tower, a horizontal side of length 130 feet across the ground, and an unlabeled hypotenuse. The angle formed by the hypotenuse and the horizontal side measures 85.691 degrees. 130 ft The height of the tower is nothing feet.
Answer:
1725.1 feet
Step-by-step explanation:
It is given that there is a right angled triangle having a base of length of 130 feet. The angle between the hypotenuse and the base is given as 85.691 degrees.
Therefore, to find the height, we know :
[tex]$\tan \theta = \frac{\text{height}}{\text{base}}$[/tex]
[tex]$\tan 85.691 = \frac{\text{h}}{\text{130}}$[/tex]
[tex]$13.27 = \frac{\text{h}}{\text{130}}$[/tex]
h = 13.27 x 130
= 1725.1 feet
Therefore, the height of the Eiffel tower = 1725.1 feet
Help pls this is 5th grade math
Answer:
1.35
2.54
3.32
4.64
5.121
6.70
Answer:
1: 35
2: 54
3: 32
5: 64
6: 121
7: 70
Step-by-step explanation:
1: 180-(110+35)
2: 180-(74+52)
3: 180-(58+90)
5: 180-(52+64)
6: 180-(36+23)
7: 180-(56+54)
Drag the tiles to the boxes to form correct pairs.
Match the values associated with this data set to their correct descriptions.
{6, 47, 49, 15, 43, 41, 7, 36}
First quartile, 11
Median, 45
Third quartile, 38.5
Difference of largest value and median, 10.5
Answer:
Step-by-step explanation:
Help me PLEASEEEEEEEEEEEEE
Answer:
Option A:[tex] \frac{4}{5} \: gallon \: per \: week[/tex]Step-by-step explanation:
Given,
Gallon of juice drank in 5 weeks = 4
Therefore,
Gallon of juice drank in 1 week
[tex] = \frac{4}{5} (ans)[/tex]
Helpp plzz will mark brainleast
NO LINKS PLS HELP MMEEE
Answer:
4. 84.82 6. 7238.23 5. 1415.81 7. 1570.8
Step-by-step explanation:
Answer:
4. 254.47ft^3
5. 4247.43yd^3
6. 21714.69 in^3
7. 4712.39 ft^3
hope this helps
have a good day :)
Step-by-step explanation:
In April 1986, a flawed reactor design played a part in the Chernobyl nuclear meltdown. Approximately 14252 becqurels (Bas), units of radioactivity, were initially released into the environment. Only areas with less than 800 Bas are considered safe for human habitation. The function f) = 14252(0.5) describes the amount, (), in becqurels, of a radioactive element remaining in the area of years after 1986. Find f(220) to determine the amount of becqurels in 2206. Determine if the area is safe for human habitation in the year 2206.
A. Yes, because by 2206, the radioactive element remaining in the area is less than 800 Bqs.
B. No, because by 2206, the radioactive element remaining in the area is greater than 800 Bqs.
C. Yes, because by 2206, the radioactive element remaining in the area is greater than 800 Bqs.
D. No, because by 2206, the radioactive element remaining in the area is less than 800 Bqs.
Answer:
A. Yes, because by 2206, the radioactive element remaining in the area is less than 800 Bqs.
Step-by-step explanation:
Function for the amount of radioactivity:
The function for the amount of radioactivity, in t years after 1996, is given by:
[tex]f(t) = 14252(0.5)^{\frac{t}{32}}[/tex]
Find f(220) to determine the amount of becqurels in 2206.
[tex]f(220) = 14252(0.5)^{\frac{220}{32}} = 121.42[/tex]
121.42 < 600, so the area will be safe, and the correct answer is given by option A.
can a triangle consists of an acute angle a right angle and a obtuse angle
Answer:
No
Step-by-step explanation:
All triangles have to equal 180 degrees. The sum of those angles would be greater than 180
The number of Internet users in Latin America grew from 25.8 million in 2009 to 70.6 million in 2016. Use the geometric mean to find the annual growth rate. (Round your answer to 2 decimal places.)
Answer:
the annual growth rate is 15.47 %
Step-by-step explanation:
Given the data in the question;
Internet users grew from 25.8 million to 70.6 million,
from the year 2009 to the year 2016.
Using geometric mean, Annual growth rate = ?
To determine the average growth rate of a time series using geometric mean, we use the following formula;
[tex]r_{geo[/tex] = [ [tex]([/tex] Xₙ / X₀ [tex])^{\frac{1}{n}[/tex] ] - 1
where Xₙ is the data value of the last year { 70.6 million }
X₀ is the data value for the first year { 25.8 million }
n is the sample size or the time difference, ( 2016 - 2009 = 7 )
so we substitute;
[tex]r_{geo[/tex] = [ [tex]([/tex] 70.6 / 25.8 [tex])^{\frac{1}{7}[/tex] ] - 1
[tex]r_{geo[/tex] = [ [tex]([/tex] 2.736434 [tex])^{\frac{1}{7}[/tex] ] - 1
[tex]r_{geo[/tex] = [ 1.15466 ] - 1
[tex]r_{geo[/tex] = 0.15466
[tex]r_{geo[/tex] = ( 0.15466 × 100 )%
[tex]r_{geo[/tex] = 15.47 %
Therefore, the annual growth rate is 15.47 %