Answer:
[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]
Step-by-step explanation:
Given that a regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.
we have to find the area of pentagon.
Apothem=a=3 cm
Perimeter=s=21.8 cm
[tex]\text{Area of regular pentagon=}\frac{1}{2}\times apothem\times perimeter[/tex]
[tex]\frac{1}{2}\times s \times a[/tex]
[tex]=\frac{1}{2}\times 21.8\times 3[/tex]
[tex]=\frac{65.4}{2}=32.7 cm^2[/tex]
[tex]\text{Hence, area of regular pentagon is }32.7 cm^2[/tex]
Option 3 is correct.
Jonathon's Yo-Yo has a string that is three and a half feet long. If Jonathon cuts six inches off of the string, how many feet will the string be
what’s the answer to
2(x+6) + 3x +4
Which of the following is a trinomial with constant term?
The answer is F) x+4y+7
Choose the equation of the vertical line passing through the point (-2, 3).
y = 3
x = 3
y = -2
x = -2
Question 10 (Multiple Choice Worth 5 points)
[4_05]Choose the equation of the horizontal line that passes through the point (-5, 1).
y = -5
x = 1
y = 1
x = -5,
A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, then its volume is:
A) 36
B) 12sqrt3
C)18sqrt3
D)24sqrt3
E)36sqrt3
The correct answer was E. Hoping someone could explain how that is.
Final answer:
The correct answer is E) 36sqrt(3), which is the volume of the described solid.
Explanation:
The student's question relates to finding the volume of a solid with unusual properties: it has a circular base and each plane cross-section perpendicular to the x-axis is an equilateral triangle. We will solve this problem using calculus, specifically by integrating the cross-sectional area along the x-axis.
The circular base of the solid defines the limits of integration, as it gives the diameter of the solid which, in turn, represents its height because the triangle is equilateral.
The radius given is 3, so the diameter (and hence the height of the solid) is 6.
The area of an equilateral triangle with side length s is (sqrt(3)/4) * s².
Since the side length of the triangles is equal to the diameter of the base, s is 6.
Therefore, the area of each cross-section is (sqrt(3)/4) * 6².
Now, to find the volume, we integrate the area of each cross-section along the height of the solid. Doing this gives us:
Volume = [tex]int_0^6 ((sqrt(3)/4) * 6^2) dx[/tex]Thus, the correct answer is E) 36sqrt(3), which is the volume of the described solid.
60 PTS, Will Mark Brainliest
Listed in the Item Bank are key terms and expressions, each of which is associated with one of the columns. Some terms may display additional information when you click on them. Drag and drop each item into the correct column. The order does not matter.
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box.
For the quadrilateral ABCD and the inscribed circle, the measure of angle c will be 62⁰.
We already know that the opposite angles of an inscribed quadrilateral are supplementary in nature.
Therefore, In this problem
m<D+m<B=180⁰
m<C+m<A=180⁰
First, we have to find the value of x
m<D+m<B=180⁰
then substitute the values to solve for x, we get
(x+20)⁰ + (3x)⁰ = 180⁰
4x = 180⁰ - 20⁰
x = 160/4
x = 40⁰
second, to find the measure of angle A
m<A = (2x+38)⁰
put the value of x from first step,
angle A = 2(40)⁰+38⁰=118⁰
third, to find the measure of angle C
m<C+118⁰=180⁰
m<C = 180⁰-118⁰
angle C = 62⁰
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Maria wants to solve the following system using the elimination method:
4x + 9y = 59
x + y = 17
What number should the equation x + y = 17 be multiplied by to eliminate y?
4
−4
9
−9
Answer:
d
Step-by-step explanation:
i took the test
Which unit would you use to measure the weight of a flea?
mg
g
ounces
kg
What is the value of tan D?
The value of tan D would be as follows:
[tex]\frac{12}{5}[/tex]Find the value of TanGiven that,
A right-angled triangle EFD,
As we know,
Tan = Opposite sides' length/adjacent sides' length
So,
it is given that,
The length of the opposite side = 12
Adjacent Side's length = 5
∵ The value of Tan D [tex]= 12/5[/tex]
Thus, the above-mentioned answer is correct.
Learn more about "Trigonometry" here:
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y=2x-7
3x-4y=8 can someone solve for x and y ? What method is used ? elimination or subtraction ?
use the graph for all 3 question
1) Henry, a 41-year-old male, bought a $100,000, 10-year life insurance policy through his employer. Henry is paid biweekly. what is his annual life insurance premium?
A)$455
B)$578
C)$1033
D)$1368
2) Karen, a 52-year-old female, bought a $75,000, 20-year life insurance policy though her employer. Karen is paid weekly. How much is deducted from her paycheck for life insurance?
A)$10.86
B)$25.33
C)$35.12
D)$50.65
3) Nikos, a 39-year-old male, bought a $300,000, 20-year life insurance policy.
What is the total amount he will pay for 20 year of coverage?
A)$13,650
B)$27,300
C)$30,990
D)$61,980
Answer:
1: B) $578
2: B) $25.33
3: D) $61,980
Step-by-step explanation:
1) Henry's premium = ($100,000 / $1,000) x $5.78 = $578
2) Karen's total premium = ($75,000 / $1,000) x $17.56 = $1,317
if she is paid weekly, then the premium must be divided by 52 weeks = $1,317 / 52 weeks = $25.33 deducted per week
3) Nikos's premium per year = ($300,000 / $1,000) x $10.33 = $3,099
times 20 years = $3,099 x 20 = $61,980
Batteries of each type have lifetimes before recharge that can be assumed independent and Normally distributed. The mean and standard deviation of the lifetimes of the Duxcell batteries are 10 and 2 minutes respectively, the mean and standard deviation for the Infinitycell batteries are 14 and 3 minutes respectively.
Part a) What is the probability that a Duxcell battery will last longer than an Infinitycell battery?,
Answer:
0.1562
Step-by-step explanation:
Step 1
In this tep we define the normal distributions in this problem. . The lifetime of the Duracell battery is a normal random variable X with parameters (10,4). The lifetime of the Infinitycell battery is a normal random variable with parameters (14.9).
Step 2
Define the new normal distribution formed by the combination of these two distributions. We define a random variable Z such that
,[tex]Z=X-Y.[/tex]
This will be a random variable with mean of [tex]\mu_x-\mu_y=10-14=-4[/tex]. This random variable will have a variance of [tex]\mu_z^2 =\mu_x^2+\mu_y^2=2^2+3^2=13[/tex]. The mean for this distribution is [tex]\mu_z=\sqrt{13}[/tex] . The random variable Z is normally distributed with parameters (-4,13)
Step 3
The next step is to calculate the probability that [tex]Z=X-Y>0[/tex]. For that we perform the calculation shown below. Along the way , we will use the method of transforming any normal distribution to the standard normal distribution.This transformation is [tex]z=\frac{x-u}{\sigma}[/tex].
[tex]P(Z>0)=P(X-Y>0)=P(Z>0)\\P(Z>0)=1-P(Z<0)\\P(Z>0)=1-P(\tfrac{0-(-4)}{\sqrt{13}})=1-P(\tfrac{4}{\sqrt{13}})\\P(Z>0)=1-0.8438\\P(Z>0)=0.1562[/tex]
Round to the nearest hundredth 42.052
Which is the most appropriate unit to measure the length of a slice of pizza?
Trey wants to plant grass in his backyard. His backyard is in the shape of a rectangle. Its length is 31
feet and its width is 24
feet. Suppose each pack of seed covers 12
square feet. How many packs of seed will he need to cover the backyard?
To find out how many packs of seeds Trey needs, we need to first determine the area of his backyard which is 744 square feet. Each pack of seed cover 12 square feet. Therefore, dividing the total area by the area a pack of seed covers, we find that he needs 62 packs of seeds.
Explanation:The subject of this question is Mathematics. Specifically, it involves the concept of area and multiplication, commonly taught in middle school. Trey's backyard is in the shape of a rectangle, and we know that the area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 31 feet and the width is 24 feet. Multiplying these numbers gives us a total area of 744 square feet.
Each pack of seed covers 12 square feet. So, to figure out how many packs Trey needs, we would divide the total area by the area each pack covers. Dividing 744 by 12 gives us 62, which means Trey will need to buy 62 packs of seeds.
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In the wrong hands, which of the following pieces of personal information would present the greatest risk for identity theft?
a.
address
b.
date of birth
c.
mother’s maiden name
d.
social security number
Answer:
D. social security number
Step-by-step explanation:
If a thief uses your your Social Security number for financial gain, you’re a victim of financial identity theft, criminal identity theft and also utility fraud.
Hope this will helpful.
Thank you.
Answer:
The correct option is D. social security number
Step-by-step explanation:
Address : Address cannot do much harm in the case of identity theft because other identity related information cannot be stolen by using the address.
So, this option is rejected.
Date of Birth : By using date of birth, no information about anyone's personal identity can be found. So this also cannot be related to identity theft.
So, this option is also rejected.
Mother's maiden name : This option is also not helpful in case of identity theft as this will not give any valuable information about someone's identity.
So, this option is also rejected.
Social security number : This number holds every personal information about a person so by using this complete identity of a person can be accessed and will present the greatest risk for identity theft.
Hence, The correct option is D. social security number
A regular hexagon has a perimeter of 120 m. Find its area. Leave your answer in simplest radical form.
In a billiards game, Pete hits a ball that is 20in. from a wall. The ball travels 34 in. until it hits the wall and bounces to a position that is 16 in. from the wall.
What proportion can be used to find the distance, x, the ball traveled after it bounced off the wall to get to the ending position? CHECK ALL THAT APPLY!
Contact your teacher if you cannot see the diagram.
Question 1 options:
34/x = 20/16
16/20 = x/34
20/16 = x/34
20/16 = 34/x
How do I solve #21???? Please don't just give me the answer.... tell me how u got it... thanks!
Alexandra paid \$7$7dollar sign, 7 to park her car for 333 hours at the parking garage. The garage charges an hourly parking rate. Write an equation that shows the relationship between the number of hours parked (p)(p)left parenthesis, p, right parenthesis and the cost in dollars (
c.(
c.left parenthesis, c, right parenthesis.
Answer:
c=7/3p
Step-by-step explanation:
Let's find the constant of proportionality.
in the proportional relationship between p, the number of hours parked, and c, the cost in dollars, one constant of proportionality is the cost per hour. It is the number we multiply by the number of hours to get the total cost.
p×?=c
px?=c
?= [tex]c/p[/tex]
= 7/3
the constant of proportionality is 7/3 this means we can multiply 7/3 by the numbers of hours to get the total cost
Now, let's write the equation: total cost
total cost=cost per hour×number of hours
[tex]c=7/3p[/tex]
John has opened 8 gifts and 6 of them have been toys. What is the probability that the next Gift ?he opens will be a toy
Part 1.] Does the graph have even symmetry, odd symmetry, or neither?
Part 2.] Does the graph of y = sin x have even symmetry, odd symmetry, or neither?
Part 3.] Identify the transformations that describe the graph of an even function. Select all that apply.
reflection over the x-axis; reflection over the y-axis; reflection over the line y=x; 90° rotation around the origin; 180° rotation around the originA number cube is rolled 450 times. The number 3 comes up 67 times.
What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
Ok so I did this if I am right?
67/3 = 22.3
450/3 = 150
22.3/150 = ?
or
22/150 =
This where I get lost. I need a fraction. @whpalmer4 or @Taz_kapadia or @tcarroll010
There are 250 degrees in the sum of the interior angles of a polygon. Always, sometimes, never
Wich fraction is equivalent to negative 7 over 8
The measure of an angle is 45°. what is the measure of a supplementary angle?
a rabbit traveled 60 meters in 4 seconds. what is the unit rate? enter your answer into the box.
Use the table to determine the location with the greatest amount of rainfall and the location with the least amount of rainfall.
a.Using complete sentences, identify the location with the greatest amount of rainfall and the location with the least amount of rainfall, and express the ratio of their respective rainfalls as a whole number.
b. Describe what this ratio tells you.
Needles, California 0.1173 m
Mt. Waialeale, Hawai'i 11.4 m
Puako, Hawai’i 25.6 cm
Death Valley, California 57 mm
Mojave, California 160 mm
Hilo, Hawai'i 480 cm,
The other person answered Part A, so I'll answer Part B (at least I'll try my best to)
"With every 200 millimeters of rain in Waialeale, there will be 1 millimeter of rain in Death Valley." <- This is what I put for B
Sorry I'm late and if I'm wrong, good luck to everyone who sees this
Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is given by the series 3 + 10 + 17 + 24 + ...
a. If you were to write this series in summation notation, give
i.the lower limit of the sum
ii.the upper limit of the sum
iii.the explicit formula of the sum
b. Find the total number of beads in the necklace. Explain your method for finding the total number of beads.
Show all your work.
Answer:
a)
i.the lower limit of the sum
: n=1
ii.the upper limit of the sum
: n=18
iii.the explicit formula of the sum
: [tex]a_n=7n-4[/tex]
b) 1,125 beads
Step-by-step explanation:
a) The number of beads per row of Dante's necklace is given by the series:
3 + 10 + 17 + 24 + ...
The first term of this series is [tex]a_1=3[/tex].
There is a constant difference of [tex]d=10-3=7[/tex].
To write this series in summation notation, we need to determine the explicit formula which is given by:
[tex]a_n=a_1+d(n-1)[/tex]
We plug in the values to get:
[tex]a_n=3+7(n-1)[/tex]
[tex]\implies a_n=3+7n-7[/tex]
[tex]\implies a_n=7n-4[/tex]
The summation notation is given by:
[tex]\sum^{18}_{n=1}(7n-4)[/tex]
b) The total number of beads in the necklace is given by the sum of the first 18 terms of the sequence.
This is given by [tex]S_n=\frac{n}{2}(2a_1+d(n-1))[/tex]
We substitute the values to obtain:
[tex]S_{18}=\frac{18}{2}(2\cdot3+7(18-1))[/tex]
[tex]S_{18}=9(6+119)[/tex]
[tex]S_{18}=9(125)[/tex]
[tex]S_{18}=1125[/tex]
Therefore the total number of beads is 1125
The arithmetic series 3, 10, 17, 24,... in which each term increases by 7 can be described in summation notation with a lower limit of 1, an upper limit of 18, and an explicit formula of 7n - 4. The total number of beads in Dante's 18-row necklace, computed using the arithmetic series sum formula, is 1125 beads.
Explanation:The series described here is an arithmetic series, where each term increases by the same amount, 7 in this case.
a. To express this series in summation notation, you must know:
The lower limit of the sum: In the series, the first term is 3, so the lower limit, often denoted as n, is 1.The upper limit of the sum: As there are 18 rows, n, or the number of terms in our sum, will be 18.The explicit formula for the sum: For an arithmetic series, the sum is given by the formula S = n/2 * (a + l) where n is the number of terms, a is the first term and l is the last term. However, we need the general term to express the series in summation notation, which is given by a + (n-1)d in an arithmetic progression. Here, a=3 and d, the difference is 7. So the general term is 3 + (n-1)*7 = 7n - 4.b. To find the total number of beads in the necklace, you use the formula for the sum of an arithmetic series. For the last term, l, we use the formula a+(n-1)d = 3+(18-1)*7 = 122. Hence, the total number of beads is S = 18/2 * (3 + 122) = 1125.
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