The true statements are Numbers with same absolute value are opposites because they are same distance from each other and from 0 on the number line. The |7.1| = 7.1. So, correct options are B, C and E.
b) Numbers with the same absolute value are opposites because they are the same distance from each other. This is true because absolute value is the distance from a number to zero on the number line, and if two numbers have the same distance from zero, then they must be equidistant from zero and therefore, they are opposite in sign.
c) The |7.1| = 7.1 because the distance from 7.1 to 0 on the number line is 7.1 units. This is true because the absolute value of a number is always positive, and it represents the distance of that number from zero on the number line.
d) The |-8.4| = 8.4 because the distance from -8.4 to 8.4 on the number line is 0 units. This is false, as the distance between -8.4 and 8.4 on the number line is 16.8 units. The correct value of the absolute value of -8.4 is 8.4.
e) Numbers with the same absolute value are opposites because they are the same distance from 0 on the number line. This is true because 0 is the midpoint of the number line, and if two numbers have the same distance from 0, then they must be equidistant from zero and therefore, they are opposite in sign.
Therefore, the correct statements are b, c, and e.
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Mae lee is going to but a new car. The car she wants costs $24. 599. She has $5. 000 to use as a down payment and will take a loan out for the rest. The interest rate on the loan is 4. 25% for 5 years how much interest will mae lee pay in all? round your answer to the nearest cent show all your work and explain each step
The interest that has to be paid for the car is $ 4534.2.
What is compound interest?Compound interest is a type of interest calculation in which the interest earned is added to the principal amount.
The principal is the sum that is left to be paid after the down payment hence;
Principal = $24, 599 - $5, 000
= $19599
A = P(1 + r/n)^nt
A = amount
P =principal
r = rate
n = Number of times compounded
t = time
Then we have that;
A = 19599( 1 + 0.0425)^5
A = $24133.2
Then ;
Interest = Amount - Principal
Interest = $24133.2 - $19599
=$ 4534.2
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help meee 5774 + 252 - 2586 ×35
Answer:
The answer is -84,484
Step-by-step explanation:
using Bodmas
multiplication first
5774+252-(2586×35)
5774+252-90510
6026-90510
-84,484
A recipe for snack mix has a ratio of 2 cups nuts, 4 cups pretzels, and 3 cups raisins. How many cups of nuts are there for each cup of raisins?
Answer: 1 cups of nuts : 1 1/2 cups of raisins
Step-by-step explanation:
The dot plot shows the number of magazines bought in a month by 21 people in a office:
Dot plot labeled Number of Magazines Bought shows 10 dots over 0, 7 dots over 1, 2 dots over 2, 1 dot over 3, and 1 dot over 9
Is the median or the mean a better center for this data and why?
Median; because the data is not normally distributed and clusters on the left
Mean; because the data is not normally distributed and clusters on the left
Median; because the data is symmetric with an outlier
Mean; because the data is symmetric with an outlier
The median is a better center for this data because the data is not normally distributed and clusters on the left.
Median; because the data is not normally distributed and clusters on the left. The dot plot shows that the data is skewed to the left with most people buying fewer magazines. The median is less sensitive to outliers and gives a better representation of the center of this skewed distribution. The mean would be affected by the outlier (1 person bought 9 magazines), which would pull the mean to the right and give a misleading representation of the center of the data.
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Please help me with this page I’m so confused
Answer:
f(0) = 1
g(-2) = 3
f(-7)= und
g(4) x f(3) = -2 x 0 = 0
g(-4) = 2
g(x) = 0 --> x = 6, 0.5
f(x) = -1 --> x = -3, 5
f(g(3)) = f(-3) = -1
g(f(-2) = g(0) = -3
f(g(1)) = f(-3) = -1
f(g(5)) = f(-1) = 1
g(f(-4)) = g(-2) = 2
g(g(-6)) = g(4) = -2
g(f(0)) = g(1) = -3
g(f(-6)) = und
Step-by-step explanation:
In order to find the first group, such as f(0), you want to look at the f graph and find 0 on the x-axis. Wherever the y coordinate is will be the correct answer.
To find one such as f(g(3)), you want to dissect it like it is 2 problems. First, we want to find g(3) which is -3. Then we will find -3 on the f graph and find the answer with that y-coordinate.
select all expressions equivalent to (3^3*3^-4)^-3
The expressions that are equivalent to (3^3*3^-4)^-3 are (3^-1)^-3, 3^3 and 27
Selecting all expressions that are equivalent to (3^3*3^-4)^-3From the question, we have the following parameters that can be used in our computation:
(3^3*3^-4)^-3
Evaluating the expression in the brackets using the law of indices, we have
(3^3*3^-4)^-3 = (3^-1)^-3
Next, we open the brackets
This gives
(3^3*3^-4)^-3 = 3^(-1 *-3)
When evaluated, we have
(3^3*3^-4)^-3 = 3^3
Evaluate the exponents
This gives
(3^3*3^-4)^-3 = 27
Hence, the expressions that are equivalent to (3^3*3^-4)^-3 are (3^-1)^-3, 3^3 and 27
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Find the mass of the thin bar with the given density function p(x) = 2 + x^2; for 0 ≤ x ≤ 1 О 0 O 7/3
O-2 O 2
The mass of the thin bar with the given density function is 7/3.
To find the mass of the thin bar with the given density function p(x) = 2 + x^2 for 0 ≤ x ≤ 1:
You need to integrate the density function over the given interval.
Here are the steps to do that:
STEP 1: Set up the integral for mass:
Mass = ∫(density function) dx from x = 0 to x = 1
STEP 2:Plug in the given density function:
Mass = ∫(2 + x^2) dx from x = 0 to x = 1
STEP 3:Integrate the function with respect to x:
Mass = [2x + (x^3)/3] evaluated from x = 0 to x = 1
STEP 4: Evaluate the integral at the limits:
Mass = (2(1) + (1^3)/3) - (2(0) + (0^3)/3)
STEP 5: Simplify the expression:
Mass = (2 + 1/3) - 0
STEP 6: Calculate the final mass:
Mass = 2 + 1/3 = 7/3
So, the mass of the thin bar with the given density function is 7/3.\
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The radius of a circle is 18 in. Find its area in terms of pi
Answer:
324π
Step-by-step explanation:
Area of circle = r² · π
r = 18 in
Find its area in terms of pi.
We Take
18² · π = 324π
So, the area of the circle is 324π.
Answer:
A = 324π
Step-by-step explanation:
A = πr²
A = π(18)²
A = π(324)
A = 324π
help i need this done pls 50 points
The length of the diagonal is 12. 7in
How to determine the lengthTo determine the length of the diagonal, we need to know the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides of a triangle.
The other two sides are the opposite and the adjacent sides.
From the information given in the diagram, we have that;
The opposite side = 12in
The adjacent side = 4in
Substitute the values
x² = 12² + 4²
find the squares
x² = 160
find the square root
x = 12. 7 in
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(20. 60 S-AQ) To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the cockroaches and measured the amount of sugar in various tissues. Five roaches fed the sugar D-glucose and dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts: Amounts of D-glucose 55. 95 68. 24 52. 73 21. 5 23. 78
The mean amount of D-glucose in cockroach hindguts is 44.24 micrograms, with a standard deviation of 26.16 micrograms. The 96% confidence interval for the mean is (20.19, 68.29) micrograms.
We will first calculate the mean, standard deviation, and then the 96% confidence interval for the given data on D-glucose amounts in cockroach hindguts.
Data: 55.95, 68.24, 52.73, 21.5, 23.78
1. The mean is calculated as follows.
Mean = (55.95 + 68.24 + 52.73 + 21.5 + 23.78) / 5 = 221.2 / 5 = 44.24
The mean amount of D-glucose in cockroach hindguts is approximately 44.24 micrograms.
2. To find the standard deviation, we calculate the variance first:
Variance = [(55.95 - 44.24)^2 + (68.24 - 44.24)^2 + (52.73 - 44.24)^2 + (21.5 - 44.24)^2 + (23.78 - 44.24)^2] / (5 - 1) = 2739.736 / 4 = 684.934
Standard Deviation = √684.934 = 26.16 (rounded to two decimal places)
The standard deviation of D-glucose in cockroach hindguts is approximately 26.16 micrograms.
3. To calculate the 96% confidence interval, we need to find the margin of error:
Margin of Error = (Critical value * Standard Deviation) / √sample size
For a 96% confidence interval, the critical value (z-score) is approximately 2.05.
Margin of Error = (2.05 * 26.16) / √5 ≈ 24.05
Now, we can find the confidence interval:
Lower limit: Mean - Margin of Error = 44.24 - 24.05 = 20.19
Upper limit: Mean + Margin of Error = 44.24 + 24.05 = 68.29
The 96% confidence interval for the mean amount of D-glucose in cockroach hindguts approximately is (20.19, 68.29) micrograms.
Note: The question is incomplete. The complete question probably is: To study the metabolism of insects, researchers fed cockroaches measured amounts of a sugar solution. After 2, 5, and 10 hours, they dissected some of the cockroaches and measured the amount of sugar in various tissues. Five roaches fed the sugar D-glucose and dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts: Amounts of D-glucose 55. 95, 68. 24, 52. 73, 21. 5, 23. 78. The researchers gave a 96% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions. The insects are a random sample from a uniform population grown in the laboratory. We therefore expect responses to be Normal. What is the mean, standard deviation, and confidence interval?
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4 (2) This question is about the series n2 + 4n +3 n=1 (a) Show that this series converges, using the integral test. (Hint: Partial fraction decomposition.) (b) Notice this is not a geometric series, so we shouldn't expect to know what it converges to. But use the decomposition 4 into the difference n2 4n of two sums. (c) Use index shifts to make these sums looks similar enough to rewrite this expression without Σ. 4 (d) Take the limit as B+ 0 to find n2 + 4n +3 B from part (a) to break m2 + An + 3 n=1 n=1 (2) 10
(a) Given: f(x) = x^2 + 4x + 3.
The partial fraction decomposition of f(x) is:
f(x) = (x+1)(x+3)
Now, we need to find the integral of this function from 1 to infinity:
∫[1,∞] (x+1)(x+3) dx
Since the integral converges, we can conclude that the series also converges.
(b) This series is not geometric, so we don't know what it converges to. However, we can decompose the given series as the difference of two sums:
Σ(n^2 + 4n + 3) = Σ(n^2) - Σ(4n)
(c) We can use index shifts to make these sums look similar enough to rewrite the expression without Σ:
Σ(n^2) - Σ(4n) = Σ(n^2 - 4n)
(d) To find the limit as B approaches 0, we can evaluate the limit of the expression n^2 + 4n + 3:
lim(B→0) (n^2 + 4n + 3) = n^2 + 4n + 3
So, the limit of the series is n^2 + 4n + 3.
A segment with endpoints A (2, 6) and C (5, 9) is partitioned by a point B such that AB and BC form a 3:1 ratio. Find B.
A. (2. 33, 6. 33)
B. (3. 5, 10. 5)
C. (3. 66, 7. 66)
D. (4. 25, 8. 25)
To find the coordinates of point B, we can use the section formula which states that the coordinates of the point that divides a segment with endpoints (x1, y1) and (x2, y2) in the ratio of m:n are given by:
((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))
The coordinates of point B are (4.25, 8.25), and the answer is (D).
Here, A (2, 6) and C (5, 9) are the endpoints of the segment, and we want to partition the segment in the ratio of 3:1. So, we have:
m:n = 3:1
m+n = 4
Solving for m and n, we get:
m = 3, n = 1
Now, substituting values in the section formula, we get:
((35 + 12)/(3+1), (39 + 16)/(3+1)) = (4.25, 8.25)
Therefore, the coordinates of point B are (4.25, 8.25), and the answer is (D).
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Answer:
(4.25, 8.25)
Step-by-step explanation:
i took the quiz
The circumstances of the base the cone is 60π cm. If the volume of the cone is 21,600π cm cubed, what is the height?
Answer:
h = 24 cm
Step-by-step explanation:
Given:
C (base) = 60π cm
V (volume) = 21,600π cm^3
Find: h (height) - ?
[tex]c = 2\pi \times r[/tex]
[tex]2\pi \times r = 60\pi[/tex]
[tex]2r = 60[/tex]
[tex]r = 30[/tex]
We found the length of the radius
v = 1/3 × πr^2 × h
1/3 × π × 900 × h = 21600π
Multiply both sides by 3:
2700π × h = 64800π / : 2700π
h = 24 cm
The talk-time battery life of a group of cell
phones is normally disributed with a mean of 5
hours and a standard deviation of 15 minutes.
a)what percent of the phones have a battery life of at least 4 hours and 45 minutes? b)what percent of the phones have a battery life between 4. 5 hours and 5. 25 hours? c)what percent of the phones have a battery life less than 5 hours of greater than 5. 5 hours?
a) Approximately 79.38% of the phones have a battery life of at least 4 hours and 45 minutes.
b) Approximately 34.13% of the phones have a battery life between 4.5 hours and 5.25 hours.
c) Approximately 50% of the phones have a battery life less than 5 hours or greater than 5.5 hours.
a) What percentage battery life of 4 hours and 45 minutes?
a) For phones with a mean battery life of 5 hours and a standard deviation of 15 minutes, we can calculate the percentage of phones with a battery life of at least 4 hours and 45 minutes. By converting 4 hours and 45 minutes to minutes (4*60 + 45 = 285 minutes) and using the z-score formula, we find that the z-score is (285 - 300) / 15 = -1. Hence, the percentage is approximately 1 - 0.8359 = 0.1641, which is about 16.41%.
b) What percentage battery life between 4.5 hours and 5.25 hours?
b) To determine the percentage of phones with a battery life between 4.5 hours and 5.25 hours, we need to calculate the z-scores for both values. Converting the hours to minutes, we have 4.5 hours = 270 minutes and 5.25 hours = 315 minutes. The z-scores are (270 - 300) / 15 = -2 and (315 - 300) / 15 = 1. By referring to the standard normal distribution table, we find that the area between -2 and 1 is approximately 0.6141. Thus, the percentage is 0.6141 * 100 = 61.41%.
c) What percentage battery life less than 5 hours?c) For the percentage of phones with a battery life less than 5 hours or greater than 5.5 hours, we need to calculate the z-score for both cases. The z-score for 5 hours is (300 - 300) / 15 = 0, and the z-score for 5.5 hours is (330 - 300) / 15 = 2. By referring to the standard normal distribution table, we find that the area to the left of 0 is 0.5 and the area to the right of 2 is 1 - 0.9772 = 0.0228. Adding these percentages, we get 0.5 + 0.0228 = 0.5228, which is approximately 52.28%.
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18. A singer sells a single as a music download and CD, making a total profit of £246. 64.
She sells 456 CD singles, earning 35p for every single sold.
She earns 17p for each music download of the single.
How many music downloads did she sell?
The singer sold approximately 512 music downloads for 17p and 456 CDs for 35p and earned a total profit of £246. 64.
Given data:
Total profit = £246. 64
The price for each music download is = 17p
Number of CDs sold = 456 CD
Price for each CD = 35p
Assume that the singer sold x music downloads. when she earns 17p for each music download then her total earnings from music downloads will be 0.17x. The total earnings from selling the CD are,
= 0.35 × 456
= 159.6.
From the above data, we can write the equation to find the value of x by,
0.17x + 159.6 = 246.64
0.17x = 246.64 - 159.6
0.17x = 87.04
x = 87.04/0.17
x = 512
Therefore, the singer sold approximately 512 music downloads.
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The volume of a cone is 2700π cm^3. The diameter of the circular base is 30. What is the height of the cone.
Answer: 36
Step-by-step explanation:
[tex]\frac{1}{3} \pi 15^{2} h=2700\pi \\75h=2700\\h=36[/tex]
A regular pentagonal prism has an edge length 9 m, and height 13 m. Identify the volume of the prism to the nearest tenth
The volume of the regular pentagonal prism with an edge length of 9 m and a height of 13 m is approximately 1811.6 m³ to the nearest tenth.
To find the volume of a regular pentagonal prism with an edge length of 9 m and a height of 13 m, follow these steps:
Step 1: Find the apothem (a) of the base pentagon. Use the formula a = s / (2 * tan(180/n)), where s is the edge length and n is the number of sides (5 for a pentagon).
a = 9 / (2 * tan(180/5))
a ≈ 6.1803 m
Step 2: Calculate the area (A) of the base pentagon. Use the formula A = (1/2) * n * s * a.
A = (1/2) * 5 * 9 * 6.1803
A ≈ 139.3541 m²
Step 3: Determine the volume (V) of the pentagonal prism. Use the formula V = A * h, where h is the height.
V = 139.3541 * 13
V ≈ 1811.6033 m³
So, the volume of the regular pentagonal prism with an edge length of 9 m and a height of 13 m is approximately 1811.6 m³ to the nearest tenth.
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Marvin is paying off a $6,800 loan that he took out for his new business. The loan has a 5. 2% interest rate and Marvin will pay it off in 5 years by making monthly payments of $128. 95. Find the total cost of repayment and the interest Marvin will pay on his loan
The total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.
To find the total cost of repayment, we need to calculate the total amount that Marvin will pay over the course of 5 years. Since he is making monthly payments, we need to first find the total number of payments he will make:
Total number of payments = 5 years x 12 months/year = 60 payments
The total amount Marvin will pay is then:
Total amount = 60 payments x $128.95/payment = $7,737.00
To find the total interest Marvin will pay, we need to subtract the original amount of the loan from the total amount he will pay:
Total interest = Total amount - Loan amount
Total interest = $7,737.00 - $6,800.00
Total interest = $937.00
Therefore, the total cost of repayment will be $7,737.00, and Marvin will pay $937.00 in interest over the 5-year period.
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Tell whether the angles are adjacent or vertical. Then find the value of x. Please help with this question
Without using a protractor, estimate the measure of the angle below. Explain how you made your estimate.
The profit ( in hundreds of dollars) from selling units of a product is given by
the profit function P(x) = x^2/ 2x + 1 Find the marginal profit when 4 units are produced
and sold and interpret your answer using words, numbers and units. Be very specific.
(Round the number part of your answer to the nearest cent.)
the marginal profit when 4 units are produced and sold is approximately -$69.14. This means that when producing and selling the 4th unit, the profit will decrease by $69.14.
To find the marginal profit when 4 units are produced and sold, we first need to find the derivative of the profit function P(x) with respect to x. The given profit function is:
P(x) = (x^2) / (2x + 1)
Now, let's find its derivative, which represents the marginal profit function:
dP/dx = (d/dx(x^2))/(2x + 1) - (x^2)(d/dx(2x + 1))/((2x + 1)^2)
First, find the derivative of x^2 and 2x + 1:
d/dx(x^2) = 2x
d/dx(2x + 1) = 2
Now, substitute these values into the marginal profit function:
dP/dx = (2x)/(2x + 1) - (x^2)(2)/((2x + 1)^2)
Next, we'll find the marginal profit when 4 units are produced and sold. So, let's substitute x = 4 into the marginal profit function:
dP/dx(4) = (2 * 4)/(2 * 4 + 1) - (4^2)(2)/((2 * 4 + 1)^2)
dP/dx(4) = (8)/(9) - (32)(2)/(81)
dP/dx(4) = (8 - 64)/(81)
dP/dx(4) = -56/81
Since the profit is in hundreds of dollars, we need to multiply the marginal profit by 100 to get the value in dollars. Then, round to the nearest cent:
Marginal profit in dollars = (-56/81) * 100 ≈ -$69.14
So, the marginal profit when 4 units are produced and sold is approximately -$69.14. This means that when producing and selling the 4th unit, the profit will decrease by $69.14.
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Charles draws △PQR, with m∠QPR = 130°, m∠PQR = 30°, and m∠PRQ = 20°.
Which triangle represents Charles’s triangle??
Answer:
Please look at the picture provided to see the correct triangle because each figure has no a,b, or c. Thanks
True or false.
Solids with curves (such as cylinders) cannot be laid out as a net.
Answer:
Step-by-step explanation:
False.
Solids with curves can be laid out as a net. In fact, there are many solids with curves that can be represented by a net. For example, a cylinder can be represented by a net consisting of two circles for the top and bottom faces and a rectangle wrapping around the circumference of the circles for the side face. Similarly, a cone can be represented by a net consisting of a circle for the base and a sector of a circle for the lateral face, which can be unfolded and attached to the circular base.
While it may be more difficult to visualize and create a net for a solid with curves compared to a solid with flat faces, it is still possible to do so in many cases.
In 0, MCA = 100° and AB CD. Also, the center of the circle, point O, is the intersection of CB and AD. What is m<1
The required value of te angle ∠3 = 100 degree.
What is Circle?A circle is a shape that is made up of all of the points in a plane that are at a certain distance from the center. Alternatively, it is the plane-moving curve traced by a point at a constant distance from a given point.
According to question:From the figure of the circle, we can identify that AD and CD are two diameter of the circle.
and ∠COA = ∠3 is inscribed angle made by up by 2 radian of the circle
So, arcCA = ∠3 = 100 degree
Thus, required value of te angle ∠3 = 100 degree.
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solve the equation |4x +9|=|6-5x|
|4x +9|=|6-5x|
4x+5x=6-9
9x=-3
x=-3/9
x=-1/3
Answer:
x = 15
x = - ⅓
Step-by-step explanation:
|4x+9| = |6-5x|
4x+9=6-5x or 4x+9=-6+5x
Lets do the first one first
4x+9=6-5x
9x=-3
x= -3/9 = -1/3
4x+9=-6+5x
15=x
So the two solutions are x = 15 and x = -⅓
Amelie has 385 muffins that she must package into boxes. Each box must hold 9 muffins. Amelie divides 385 by 9 and gets an answer of 42 R 7. What is the correct interpretation of R 7 for this situation?
In Amelie's situation, the remainder of 7 indicates that she has 7 muffins left over that cannot be packed into a full box of 9.
When Amelie divides the total number of muffins (385) by the number of muffins per box (9), she obtains a quotient of 42 and a remainder of 7. The quotient represents the number of complete boxes that Amelie can fill with 9 muffins each, while the remainder represents the number of muffins that cannot be put into a full box.
In other words, the quotient tells us how many full boxes Amelie can pack, and the remainder tells us how many muffins are left over after packing all the full boxes. In this case, Amelie can pack 42 full boxes, each with 9 muffins, which totals to 378 muffins. The remaining 7 muffins cannot fill a full box, and they are left over after all the full boxes are packed.
The "R 7" notation is commonly used to indicate the remainder in long division problems. The letter "R" stands for "remainder," and the number following it (in this case, 7) represents the actual remainder. The remainder is important because it indicates how many items are left over after dividing them into equal-sized groups.
In Amelie's situation, the remainder of 7 indicates that she has 7 muffins left over that cannot be packed into a full box of 9.
Overall, interpreting the "R 7" in this problem helps us understand how many full boxes of muffins Amelie can pack and how many muffins are left over after packing the full boxes.
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Can someone help me with this question and show the steps please
The student council wants to determine the best date for the end-of-year dance for the 350 students. They survey every 5th student who gets off the bus one morning. Eighteen students voted for May 2, 39 students voted for May 9, and 13 students voted for May 16. Which date is it likely that 105 of the 350 students would choose for the dance?
There is a probability that 105 of the 350 students would select May 9 for the dance.
What is the sample about?To solve the above we need to find the proportion of students in the sample who voted for each date and this can be done by:
May 2: 18/70
= 0.257
May 9: 39/70
= 0.557
May 16: 13/70
= 0.186
if the whole population of 350 students voted, then
May 2: 0.257 x 350
= 90
May 9: 0.557 x 350
= 195
May 16: 0.186 x 350
= 65
From the above calculation, we can see that if 105 students out of 350) were to choose a date, the most likely date that they will select is May 9, since it is the one that has the highest proportion of votes in the sample.
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The sum of the series below is 10,900. how many numbers, n, are in the series? 19 20.5 22 23.5 ... 181 27 100 109 135
There are 109 terms in given series.
Here, we have,
According to the statement
we have given that the sum of series is AP series and
This is 19 20.5 22 23.5 ... 181
And the sum of series is 10,900
Now, we have to find the number of terms in the series.
Then we use the summation formula which is
S = n/2 (a + L)
Substitute the all given values in it like
L = 181
A = 19 and S= 10,900
then
10,900= n/2(19+181)
10,900= n/2(200)
After solve the equation for n
10,900= 100n
n = 10,900 / 100
n = 109
There are 109 terms in given series.
So, There are 109 terms in given series.
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Misty needs 216 square inches of metal
to make a yield sign. If the height of the sign is 18 inches,
how long is the top edge of the sign?
24 inches
12 inches
198 inches
22 inches
pls give explanation not just the awnser
The answer is 96 inches, which is equivalent to 8 feet.
Find out the length of the top edge of the yeild sign ?To find the length of the top edge of the yield sign, we need to use the formula for the area of a trapezoid:
A = (b1 + b2)h/2
where A is the area of the trapezoid, h is the height, b1, and b2 are the lengths of the two parallel bases of the trapezoid.
In this case, we are given the area of the sign (216 square inches) and the height (18 inches), but we don't know the length of either base. However, we do know that the shape of a yield sign is that of a regular octagon, which means it has eight equal sides and eight equal angles.
If we draw a line from the top of the sign to the midpoint of one of the sides, we will form a right triangle with the height of the sign as one leg, half the length of the top edge as the other leg, and the length of one of the sides as the hypotenuse. We can use the Pythagorean theorem to find the length of the side:
a^2 + b^2 = c^2
where a is the height of the sign (18 inches), b is half the length of the top edge (what we are trying to find), and c is the length of one of the sides.
Since the sign has eight sides, we can divide the total area by 8 to get the area of one of the eight triangles that make up the sign. We can then use this area to find the length of one of the sides:
A = (bh)/2
216 sq. in. = (bh)/2
432 sq. in. = bh
Since the sign is a regular octagon, each of the eight triangles has the same base (the side of the octagon) and height (half the length of the top edge), so we can use this equation to solve for b:
432 sq. in. = b(18 in.)/2
b = 48 in.
Now we know that half the length of the top edge is 48 inches, so the full length of the top edge is:
2(48 in.) = 96 in.
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