The surface area of a rectangular prism can be found using the formula:
A = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
Substituting the given values, we get:
A = 2(5 cm)(6 cm) + 2(5 cm)(7 cm) + 2(6 cm)(7 cm)
A = 60 cm² + 70 cm² + 84 cm²
A = 214 cm²
Therefore, the surface area of the rectangular prism is 214 cm².
The volumes of both containers are 6,912 cubic inches.
What is the height of container 2?
Set up an equation using the width and height from con-
tainer 2 to find the missing height.
V = lwh
Container 1
32 in.
12 in.
18 in.
Container 2
24 in.
? in.
16 in.
Answer:
let the height of second container be x
Then volume=6912
we know that volume of cuboid= lbh
so ，
24.x.16=6912
384.x=6912
x =6912divide 384
therefore x =18 that is the height of the container
Ralph earns $72,000 annually as an architect and is paid semimonthly. Alice also earns $72,000 but she is paid biweekly. How many more checks does Alice receive in a year when compared to Ralph?
Alice receives 2 more paychecks in a year compared to Ralph.
How to calculate the difference in the number of paychecksSince Ralph is paid semimonthly, he receives 24 paychecks in a year (twice a month). Alice, on the other hand, is paid biweekly, which means she receives 26 paychecks in a year (once every two weeks).
To calculate the difference in the number of paychecks, we can subtract the number of paychecks Ralph receives from the number Alice receives:
Number of paychecks for Alice - Number of paychecks for Ralph = 26 - 24 = 2
Therefore, Alice receives 2 more paychecks in a year compared to Ralph.
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The diagram shows parallel lines cut by two transversal lines creating a triangle. Which statement can be made from the diagram?
mAngleB + mAngleC + 55° = 180°
mAngleA + 60° + 55° = 180°
mAngleC = 55°
mAngleA = 55°
Answer:
The answer to your problem is, B. mAngleA + 60° + 55° = 180°
Step-by-step explanation:
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Let the triangle be represented as ABC:
Now , the first measure of angle = 55
The second measure of angle = 60
The angle of the first ∠A = 180
Substituting the values in the equation , we getFor a triangle , ∠A + ∠B + ∠C = 180°So , sum of the angles of a triangle mAngleA + 60° + 55° = 180°Thus the answer to your problem is, B. mAngleA + 60° + 55° = 180°
Read this excerpt from "A Student's Guide to Global Climate Change."
Higher sea level will mean less space at the beach. A combination of stronger storms and sea level rise could increase the rate of erosion along the coast, and some beaches could disappear altogether.
What can people do about it?
People already add sand to certain beaches to replace sand that has washed away. In the future, people might have to replenish beach sand more often, but this will cost more money. In other places, people might choose to build sea walls or other structures to protect the shore from erosion. Ideally, these projects will be planned carefully to prevent them from damaging important habitats for plants and animals.
Based on the excerpt, what conclusion can be drawn about sea walls?
If they are well planned, they will most likely be too expensive.
If they are well planned, they can replace sand that has been washed away.
If they are not well planned, they can damage other structures.
If they are not well planned, they can damage places with sea life.
The conclusion that can be drawn from the excerpt is: "If they are well planned, they can protect the shore from erosion while minimizing damage to important habitats for plants and animals." Therefore, the option "If they are well planned, they can replace sand that has been washed away" is not accurate, and the options "If they are well planned, they will most likely be too expensive," and "If they are not well planned, they can damage other structures" are not supported by the information provided in the excerpt. The correct answer is: "If they are not well planned, they can damage places with sea life."
Given h(x) = 4x + 3, find h(5)
PLEASE HELP will give brainliest
Using the recursive rule we know that the explicit formula for f(11) would be a₁₁ = a₁₀ + 11.
What is the recursive rule?A formula that explains how to move from one word in a sequence to the next is known as a recursive rule for a sequence.
The variable is typically used to represent the term "number." In other words, takes on the values 1, 2, 3, etc.
For the first, second, third, etc. terms.
So, the recursive rule formula is:
aₙ = aₙ₋₁ + d
d = 72 - 61 = 11
Then, insert values and calculate as follows:
aₙ = aₙ₋₁ + d
a₁₁ = a₁₁₋₁ + d
a₁₁ = a₁₀ + d
a₁₁ = a₁₀ + 11
Therefore, using the recursive rule we know that the explicit formula for f(11) would be a₁₁ = a₁₀ + 11.
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what’s the answer???
Answers and explanation:
[tex]3x^{2} +12x+9=(3x+3)(x+3)[/tex]
Factored form:
[tex](3x+3)(x+3)=0[/tex]
First zero:
[tex]3x+3=0[/tex]
[tex]3x=-3[/tex]
[tex]x=\frac{-3}{3} =-1[/tex]
Second zero:
[tex]x+3=0[/tex]
[tex]x=-3[/tex]
Ordered pair:
[tex]x=-1, x= -3[/tex]
Hope this helps.
can't get this rule answer. I got it wrong...
Answer:
Asymptotes can be defined as lines that the curve approaches but never touches or crosses.
Jerome uses the formula, P = DB, to find his approximate six-month premium when his driver risk factor, D, is 1.02 and the basic six-month premium is $500.
What will his monthly premium be?
A. $85.00
B. $270.60
C. $300.50
D. $332.00
Answer:
A) $85.00
Step-by-step explanation:
To find Jerome's monthly premium, we need to divide his six-month premium by 6:
P = DB/6
P = (1.02)(500)/6
P = 85
Therefore, Jerome's monthly premium will be $85. Answer choice A is correct.
a small jet can carry up to passengers and crew members. there is a weight restriction of pounds on board. the combined weight of each passenger (or crew member) and his luggage has a mean of pounds, with a standard deviation of pounds. what is the probability that the weight limit will be exceeded when there are exactly passengers and crew members on board?
The probability that the weight limit will be exceeded when there are exactly 40 passengers and 3 crew members on board is 0.031.
Mean = 196 × 43
Mean = 8428
Std. Dev. = 63 × √(43)
Std. Dev. = 63 × 6.56
Std. Dev. = 413.28
Here, μ = 8428, σ = 413.1186 and x = 9200. We must calculate P(X ≥ 9200).
he central limit theorem states that, for a sufficiently large sample size, the sample mean of all observations will be approximately normally distributed, regardless of the distribution of the population from which it was sampled.
The Central Limit Theorem is used to get the associated z-value.
z = (x - μ)/σ
z = (9200 - 8428)/413.28
z = 772/413.28
z = 1.87
Therefore,
P(X ≥ 9200) = P(z ≤ (9200 - 8428)/413.1186)
P(X ≥ 9200) = P(z ≤ 772/413.1186)
P(X ≥ 9200) = P(z ≥ 1.87)
P(X ≥ 9200) = 1 - 0.9693
P(X ≥ 9200) = 0.031
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The complete question is:
A small jet can carry up to 40 passengers and 3 crew members. There is a weight restriction of 9200 pounds on board. The combined weight of each passenger (or crew member) and his luggage has a mean of 196 pounds, with a standard deviation of 63 pounds. What is the probability that the weight limit will be exceeded when there are exactly 40 passengers and 3 crew members on board? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.
Botanists conduct field research to develop recovery plans for endangered species.
They use linear and exponential models and graphs to interpret the resulting data.
Seth tracks the average number of a plant species found in a forest area.
He uses volunteers to help search for the species.
The number n of plants found increases by r percent for each volunteer added to the search. Seth found p plants
before adding any volunteers.
Write an exponential growth function that relates the number n of plants found to the number X of volunteers Seth has.
Exponential growth function that relates the number n of plants found to the number x of volunteers Seth has,
[tex]n = p\left(1+\frac{r}{100}\right)^x[/tex]
How to find an exponential function?
Exponential function is the function of growth or decay with the power of the independent variable.
As, n is the number of plants increased.
r is the percent increase
p is the initial plants
and x is the volunteers
Compound Interest/ Exponential equation is,
[tex]n = p\left(1+\frac{r}{100}\right)^x[/tex]
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The exponential growth function [tex]n = p(1 + r)^X[/tex]
How to express exponential growth function?The exponential growth function that relates the number n of plants found to the number X of volunteers Seth has can be expressed as:
[tex]n = p(1 + r)^X[/tex]
where:
n is the number of plants found
p is the initial number of plants found before adding any volunteers
X is the number of volunteers added to the search
r is the percentage increase in the number of plants found per volunteer
he growth factor is represented by the term (1 + r), which is multiplied by the initial number of plants discovered to determine the new number of plants discovered when each volunteer is added. The value of (1 + r)X increases exponentially as X increases, resulting in an exponential increase in the number of plants found.
It is essential to keep in mind that the growth rate r in the formula must be expressed as a decimal rather than a percentage. For instance, r = 0.05 if the number of plants discovered increases by 5% for each volunteer added.
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What is the completely factor simplified form of the rational expression below?
x²+6x/x+5 4x+15/x+5
A. x²+2x-15/x+5
B. x²+2x+15x/+5
C.x+5
D. x-3
Answer:A
Step-by-step explanation:
To simplify the rational expression (x²+6x)/(x+5) + (4x+15)/(x+5), we first factor the numerator of the first fraction as x(x+6). Then, we factor the numerator of the second fraction as 4(x+3). Now, we can combine the fractions by finding a common denominator of (x+5) and adding the numerators:
(x²+6x)/(x+5) + (4x+15)/(x+5) = (x(x+6) + 4(x+3))/(x+5)
Simplifying the numerator further, we get:
(x²+6x + 4x + 12)/(x+5) = (x²+10x+12)/(x+5)
Now we can factor the numerator by finding two numbers that multiply to 12 and add to 10. Those numbers are 2 and 6. So we can write:
(x²+10x+12)/(x+5) = (x+2)(x+6)/(x+5)
Therefore, the completely factored and simplified form of the given rational expression is (x+2)(x+6)/(x+5). So the answer is A.
true or false: if one assumes two or more groups are from separate populations then the different groups are considered related samples for conducting statistical tests.
False. If one assumes two or more groups are from separate populations, the different groups are considered unrelated or independent samples for conducting statistical tests.
In statistical analysis, there are two types of samples: related (also known as dependent or paired) and unrelated (also known as independent or unpaired). Related samples are taken from the same population, often involving before-and-after measurements, repeated measures, or matched pairs.
Unrelated samples are taken from separate populations, with no inherent connection between the samples.
When you want to compare two or more groups, the choice of related or unrelated samples will determine the type of statistical test you should use.
For related samples, you can use tests like the paired t-test, Wilcoxon signed-rank test, or repeated measures ANOVA. For unrelated samples, you can use tests like the independent t-test, Mann-Whitney U test, or one-way ANOVA.
In summary, assuming that two or more groups are from separate populations means they are considered unrelated or independent samples, not related samples, for conducting statistical tests.
The choice of related or unrelated samples will guide you in selecting the appropriate statistical test for your analysis.
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Work out the values of a, b, c and d.
Justify each of your answers.
The values of a, b, c ,d are 54,31,28,67 respectively
What is circle geometry?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed shape, two-dimensional shape, curved shape.
There are different theorems that can be used to determine various missing angles In a circle.
angle c = 28°( angle in the same segment are equal)
angle b = 31( angle in the same segment)
angle d = 180-( 82+31) ( sum of angle in a triangle)
d = 180 - 113
d = 67°
angle a = 180-( 98+28) ( sum of angle Ina triangle)
a = 180- 126
a = 54°
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What is halfway between 3/5 and 8/10
Answer:
7/10 because 3/5 is equal to 6/10.
The median between 6/10 and 8/10 is 7/10
Therefore that is the answer.
"The beautiful thing about learning is that no one can take it away from you." :)
our environment is very sensitive to the amount of ozone in the upper atmosphere. the level of ozone normally found is 5.5 parts/million (ppm). a researcher believes that the current ozone level is not at a normal level. the mean of 13 samples is 6.0 ppm with a standard deviation of 0.9 . assume the population is normally distributed. does the data support the researcher's claim at the 0.05 level? make the decision to reject or fail to reject the null hypothesis.
The data support the researcher's claim that the current ozone level is not at a normal level, at the 0.05 level of significance, concluded with the help of a one-sample t-test.
To test whether the current ozone level is significantly different from the normal level of 5.5 ppm, we can use a one-sample t-test.
The null hypothesis is that the mean ozone level is equal to 5.5 ppm:
H0: mu = 5.5
The alternative theory is that the average ozone level exceeds 5.5 ppm:
Ha: mu > 5.5
The significance threshold will be set at 0.05.
t = (x - mu) / (s / sqrt(n)) is the test statistic for a one-sample t-test.
where x is the sample mean, is the hypothesized population mean, s represents the sample standard deviation, and n represents the sample size.
When we substitute the provided values, we get:
t = (6.0 - 5.5) / (0.9 / sqrt(13)) = 1.936
Using a t-table with 12 degrees of freedom (n-1=13-1=12) and a significance level of 0.05, the critical value is 1.782. Since our calculated t-value (1.936) is greater than the critical value (1.782), we reject the null hypothesis.
Therefore, we can conclude that the data support the researcher's claim that the current ozone level is not at a normal level, at the 0.05 level of significance.
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What is the value of x? Enter your answer in the box.
Thus, the value of the variable x for the given one variable linear equation is found as: x = 8.5.
Explain about the one variable linear equation:A linear equation is a one-variable equation of such a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.
All values which it make this equation true are included in the solution set. All real numbers make up the solution set for this equation because, when a real number is used in place of x, the equation is proved to be true.
Given one variable linear equation :
3x + 8 = 5x - 9
Isolate the variable and the constants on the different sides;
5x - 3x = 8 + 9
2x = 17
x = 17/2
x = 8.5
Thus, the value of the variable x for the given one variable linear equation is found as: x = 8.5.
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Complete question:
What is the value of x? The given equation is: 3x + 8 = 5x - 9.
how many solutions does −5x+12=−12x−12 have
Answer:
one solution, x = - [tex]\frac{24}{7}[/tex]
Step-by-step explanation:
- 5x + 12 = - 12x - 12 ( add 12x to both sides )
7x + 12 = - 12 ( subtract 12 from both sides )
7x = - 24 ( divide both sides by 7 )
x = - [tex]\frac{24}{7}[/tex]
*60 POINTS FOR FOUR CORRECT GEOMETRY ANSWERS*
Please answer these for me. Thank you
The length of the altitude is
B. 7.5The similarity statement about the triangles is
c. triangle MON ~ triangle MPO ~ triangle OPNThe value of x in the pentagon is 21
How to find the value of xThe value of x is solved by applying the the proportions of the pentagon
20 / 15 = 18 / 13.5 = 4/3
therefore, 12 * 4/3 = x - 5
16 = x - 5
16 + 5 = x
x = 21
The altitude of the right triangle
h / 14 = 4 / h
h^2 = 14 * 4
h^2 = 56
h = sqrt (56)
h = 7.5
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Math help
Nyssa made the table below to show the relation between the side length and the areas of various poster boards
The relation between the area (a) and the side length (s) in the table is:
A. a = s²
What is an area?
To see this relationship, we can observe that the areas of the poster boards are the square of their respective side lengths. For example, when the side length is 2 feet, the area is 4 square feet (2²).
Similarly, when the side length is 4 feet, the area is 16 square feet (4²). This pattern holds true for all the side lengths listed in the table. Therefore, we can conclude that the area of each poster board is equal to the square of its side length.
Calculation:
Side Length (s) | Area (a)
1 | 1
2 | 4
3 | 9
4 | 16
As we can see, the area of each poster board is equal to the square of its side length. Thus, the relation between the area (a) and the side length (s) in the table is a = s².
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Answer:
A
Step-by-step explanation:
[tex]a = s {}^{2} \\ 1. \: + - \sqrt{a = s} \\ 2. \: s = + - \sqrt{a} [/tex]
Write the equation of a line that contains the given point and has the given slope:
(-8,-8), slope is 3
Answer:
Ok
Step-by-step explanation:
Y = mx + c
Slope is for the gradient =m therefore we have +3 as our gradient
Now we are going to substitute pont - 8mac- 8 on the above equation
Y = mx +c
-8=3(-8) +c
-8=-24 +c
-8+24 =c
16=c
This means that the y intecept of this straight line is 0 mac 16
Meaning that when the line touches the y axis at 16 x will be equal to zero
Therefore our equation is
Y =3x +16
For each of the figures write an absolute value equation that has the following solution set.
The absolute value equation | x - (-5) | = 3 has a solution set corresponding to a straight horizontal line with marked points -8, -2, and x in left to right manner.
How to write an absolute value equation that has the following solution set?
The solution set given as a straight horizontal line passing through the points -1/2 and 3/2 can be represented as:
| x - 1 | = 1/2
Explanation:
The absolute value function | x - 1 | gives the distance between x and 1 on the number line.Since the given solution set is a straight horizontal line passing through -1/2 and 3/2, the midpoint of the two points would be 1.The distance between the midpoint (1) and one of the points (-1/2 or 3/2) would be 1/2.Therefore, the equation | x - 1 | = 1/2 represents the set of all values of x that are at a distance of 1/2 units away from the midpoint 1, which is the straight horizontal line passing through -1/2 and 3/2.To learn more about horizontal line, visit: brainly.com/question/30197744
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assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.74. (a) compute a 95% ci for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (round your answers to two decimal places.) , (b) compute a 98% ci for true average porosity of another seam based on 18 specimens with a sample average porosity of 4.56. (round your answers to two decimal places.) , (c) how large a sample size is necessary if the width of the 95% interval is to be 0.37? (round your answer up to the nearest whole number.) specimens (d) what sample size is necessary to estimate true average porosity to within 0.21 with 99% confidence? (round your answer up to the nearest whole number.) specimens
The required confidence interval for the given sample size and sample mean is,
95% confident interval which is true average porosity of the seam lies between 4.49 and 5.20 percent.
98% confident interval which is true average porosity of the other seam lies between 4.10 and 5.02 percent.
Sample size with 95% confidence interval with a width of 0.37 is 16 .
Sample size with 99% confidence interval with a width of 0.21 is 11 .
Sample size 'n' = 19
Confidence interval = 95%
Sample mean = 4.85
True average porosity of a certain seam is , we use the formula,
CI = sample mean ± t(α/2, n-1) ×(standard deviation / √(n))
where t(α/2, n-1) is the critical t-value.
α level (0.05 for a 95% confidence interval)
Degrees of freedom (n-1 = 18).
Plugging in the values, we get,
CI
= 4.85 ± t(0.025, 18) × (0.74 / √(19))
Using a t-table ,
t(0.025, 18) = 2.101.
So the confidence interval is,
CI
= 4.85 ± 2.101 × (0.74 / √(19))
= (4.49, 5.20)
95% confident that the true average porosity of the seam lies between 4.49 and 5.20 percent.
Compute a 98% confidence interval for the true average porosity of another seam .
Sample size = 18
Sample mean = 4.56,
Use the same formula as above but with a different t-value,
CI = 4.56 ± t(0.01, 17) ×(0.74 / √(18))
Using a t-table
t(0.01, 17) = 2.898.
So the confidence interval is,
CI
= 4.56 ± 2.898 × (0.74 / sqrt(18))
= (4.10, 5.02)
98% confident that the true average porosity of the other seam lies between 4.10 and 5.02 percent.
Sample size to obtain a 95% confidence interval with a width of 0.37,
Use the formula,
n = (t(α/2, n-1) × standard deviation / (width / 2))^2
Solving for n, we get,
n = [(t(α/2, n-1) × standard deviation) / (width / 2)]^2
Substituting the given values, we get,
n = [(t(0.025, n-1) × 0.74) / 0.37]^2
Using trial and error or a t-table,
t(0.025, n-1) is approximately 2 for large sample sizes.
So we have,
n = [(2 × 0.74) / 0.37]^2
= 16
A sample size of at least 16 specimens is necessary to obtain a 95% confidence interval with a width of 0.37.
Sample size to estimate the true average porosity to within 0.21 with 99% confidence,
Use the same formula as above but solve for n with the given width and confidence level,
n = [(t(α/2, n-1) ×standard deviation) / (width / 2)]^2
Substituting the given values, we get,
n = [(t(0.005, n-1) × 0.74) / 0.21]^2
Using trial and error or a t-table,
t(0.005, n-1) is approximately 3 for large sample sizes.
So we have
n = [3 × 0.74) / 0.21]^2
= 11.17
≈ 11
Sample size to estimate the true average porosity to within 0.21 with 99% confidence is 11.
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Write 8,360,000 in scientific notation
[tex] \bf Question[/tex]
Write 8,360,000 in scientific notation
Step- by -step explanation8,360,000
After one digit you should mark decimal then count after decimal how many digits are remaining after you get Ans then put your Ans always on 10.
Like this,
8.36× 100,000 = as 8.36 × 10⁶
Am mark decimal after one digit and count how many digits are remaining then am put my ans on 10
So, 8,360,000 written as 8.36 × 10⁶ in scientific notation
See this, there are two pairs one is 8.36 and one is 100,000 in first one we can't write zeros. We write numbers like 1,2,3,4,5,6,7,8,9 but not 0. Like this question is 8,360,000 , our first work is to mark decimal after one digit 8. then we have to notice that after decimal how many number are remaining like 360,000 As, we know we can't write zeros in first pair so we can write only 8.36× now our first pair is done , Second pair is so easy only you have to count digits after decimal 8360,000 So digits are 6 so our final answer is 8.36×10⁶
Always remember in second pair we write remaining no. of digits only on 10 like this 10⁶
Required Answer :8.36 × 10⁶
Extra InformationThe purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.
Examples :-Now, can you express 40,000,000,000 in the similar way ?
Count the number of zeros in it. It is 10.
So, 40,000,000,000 = 4.0×10¹⁰
Do you agree with the fact, that the number when written in scientific notation is much easier to read and understand.
The scientific notation of the given number is 8.36×10⁶.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
The given number is 8,360,000.
In scientific notation
8,360,000 = 8.36×10⁶
Therefore, the scientific notation of the given number is 8.36×10⁶.
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Determine the discriminant of 3x² - 5x+4=0.
PLEASE HELP THIS IS URGENT
Answer:
7 hours and 2 hours longer
Model Real Life You arrange eight chairs around a circle that has eight sections. Find the sum of the angle measures of 7 of the sections.
The sum οf the angle measures οf 7 οf the sectiοns is 315 degrees.
What are Angles?An angle is a geοmetric figure fοrmed by twο rays that share a cοmmοn endpοint, called the vertex. It is usually measured in degrees οr radians and describes the amοunt οf rοtatiοn between the twο rays.
If we arrange eight chairs arοund a circle that has eight sectiοns, each sectiοn will have a central angle οf 360 degrees / 8 = 45 degrees.
Tο find the sum οf the angle measures οf 7 οf the sectiοns, we can add the central angles οf thοse 7 sectiοns:
7 x 45 degrees = 315 degrees.
Therefοre, the sum οf the angle measures οf 7 οf the sectiοns is 315 degrees.
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O is the center of the regular decagon below, the radii equals 16. Find its perimeter. Round to the nearest tenth if necessary.
The length of the side is 67.8 which gives us the perimeter as 67.8 x 10 = 678units
We are given a decagon, which is a 10-sided polygon with center O, and a radius of 11 units.
We are required to find the perimeter of the decagon and round the answer to the nearest tenth.
We begin by calculating the interior angle of e decagon.
We use the formula;
S = (n-2) 180, where,
S = sum of interior angles,
n = number of sides
therefore, S = (10 - 2) 180
S = 8 x 180
S = 1440
For a 10-sided polygon, each interior angle will now measure;
Interior angle = 1440/10 = 144
take note that the radius of the polygon divides the angle at the vertex (that is, the interior angle) into two equal halves.
With that in mind we can now construct the following triangle:
Take note that the line from the center to the side is the apothem, while the side labeled 11 is the radius (which was given). We can now extract one of the right angled triangles and use that calculate the apothem as follows:
The side labeled a; the apothem can be calculated using the angle 72 degrees as the reference angle:
reference angle = 72
opposite = a
hypotenuse = 11
therefore when we use the formula of sin, we get a = 10.46
Also, for the side labeled s (half the length of one side of the decagon); s = 3.39
For the length of one side of the decagon, we have the side s times 2. Hence, the length of the side is 67.8
67.8 x 10 = 678units
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Some states, such as Oregon, do not have a state imposed sales tax like other states. However, the state government has to make up that financial difference in another way. Which option is better for the individual: a state with sales tax or a state without sales tax? Explain why. Which option is better for the state government? Explain why. Give an opinion in your own words, using complete sentences.
A state with a sales tax is a better option for both individuals and state governments.
WHAT IS SLES TAX?
A state without a sales tax may seem preferable since they do not have to pay additional taxes on purchases. However, in such states, the government often imposes higher income taxes or property taxes to compensate for the lack of sales tax revenue. Therefore, it ultimately depends on the individual's financial situation and spending habits.
From the state government's perspective, having a sales tax is generally more beneficial as it provides a consistent and reliable revenue stream. Sales tax revenue is collected on a regular basis and is not subject to fluctuations in the economy or changes in demographics. Additionally, sales tax revenue is not as heavily reliant on the state's residents and can be partially collected from tourists and visitors who make purchases within the state.
In my opinion, a state with a sales tax is a better option for both individuals and state governments. While paying additional taxes may not seem appealing, it allows the state to fund essential services such as education, healthcare, and infrastructure. Additionally, sales tax revenue is spread across a wider population, making it more equitable and less burdensome on individual taxpayers. Overall, having a sales tax system in place helps to ensure that the state government can continue to provide essential services and maintain a stable economy.
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jane is planning to offer a groupon for inner tube rentals that she will distribute on hot, sunny, summer days by the river that runs through her town. based on her past experience with groupon, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day. if jane would like her expected revenue to be at least $390 per day, what should the groupon price be? (round your answer up to the nearest whole dollar amount.)
The price of Groupon for revenue of $300 is $4 if the expected revenue is at least $390 per day.
Probability is assigned as
x =30, 60, 120, 180
P(x) = 0.10,0.40, 0.40, 0.10
Expected sales volume:
Number of tubes x =30, 60, 120, 180
Probability P(x)= 0.10,0.40, 0.40, 0.10
Expected values are 3, 24,48,18
Total = 93 tubes
Groupon price = $390/$93 = $4.19
Jane's price for each Groupon is the daily rental income divided by the expected number of tubes rented per day. The expected number of tubes is derived by multiplying the expected number of each tube by its probability and then summing the results.
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