We have triangle ABC, the length of side AB is 16 inches and the length of side BC is 24 inches, the possible length of the side AC is less than 40 inches
To find the possible length of side AC, we need to use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side, that is, a + b > c, b + c > a, c + a > b.
Now, for the given triangle ABC:
a = AB = 16 inches
b = BC = 24 inches
c = AC
We know that a + b > c (using the triangle inequality theorem)
16 + 24 > cc < 40
Therefore, By using the triangle inequality theorem, the possible length of the side AC is less than 40 inches.
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The points (-3,-1) and (r,1) lie on a line with slope 1/4. Find the missing coordinate r.
The missing coordinate r for the slope is equal to 5.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and orientation. The symbol m is often used to represent slope. The ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line is used to determine slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two different points on the same line. A declining line has a negative "rise". The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a depiction or a plan.
by the question.
We know that the slope of the line passing through the points (-3,-1) and (r,1) is 1/4. Therefore, we have:
[tex](1 - (-1))/(r - (-3)) = 1/4[/tex]
Simplifying the above equation, we get:
[tex]2/(r + 3) = 1/4[/tex]
Multiplying both sides by 4(r + 3), we get:
[tex]8 = r + 3[/tex]
Subtracting 3 from both sides, we get:
[tex]r=5[/tex]
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ten drill bits are randomly selected from a process. the times to failure (i.e., loss of acceptable sharpness) for the bits are recorded as 37, 39, 42, 43, 49, 50, 54, 55, 59, and 63 hours. assuming the failure times have a weibull distribution, analyze the data using probability plotting. estimate the shape and scale parameters. plot the original data versus the cdf model corresponding to your parameter estimates. add confidence limits.
In probability plotting, a graph of the cumulative distribution function (CDF) is plotted against a transformed version of the data to determine if the data come from a particular distribution.
The distance between the two lines is equal to the product of the critical value of the t-distribution and the standard error estimate.
This can be used to analyze the times to failure (i.e., loss of acceptable sharpness) for a random selection of ten drill bits from a process that follows a Weibull distribution.
To estimate the shape and scale parameters
follow these steps:
Step 1: Rank the data from smallest to largest
Step 2: Calculate the failure probability of each data point using the formula: i/(n+1), where i is the rank of the data point and n is the number of data points.
Step 3: Transform the failure probabilities using the inverse Weibull distribution function: F^(-1)(p) = (−ln(1−p))^β for a given shape parameter β and scale parameter η.
Step 4: Plot the transformed data against the theoretical distribution, which is a straight line for the Weibull distribution.
Step 5: Find the best-fitting line by eye, or by using regression analysis.
The slope of the line is equal to the shape parameter β, and the intercept is equal to the logarithm of the scale parameter ln(η).
The Weibull distribution can be represented as:[tex]F(x) = 1 − e^(-(x/η)^β)[/tex], where β is the shape parameter and η is the scale parameter. The CDF model corresponding to your parameter estimates can be plotted by using the formula . This can be done by calculating the standard deviation of the residuals, and then calculating the upper and lower limits of the confidence interval using the t-distribution.
The confidence interval can be calculated as:β ± t(n−2,α/2) x SE(β)ln(η) ± t(n−2,α/2) x SE(ln(η))where SE(β) is the standard error estimate for the shape parameter, SE(ln(η)) is the standard error estimate for the logarithm of the scale parameter, and t(n−2,α/2) is the critical value of the t-distribution with n−2 degrees of freedom and a significance level of α/2.The confidence limits can be plotted as two parallel lines around the best-fitting line. The distance between the two lines is equal to the product of the critical value of the t-distribution and the standard error estimate.
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julie is a 14 year old student at odyssey charter high school. she is getting ready for beach season and wants to lose 3 pounds in four weeks. on average how many extra calories does julie need to burn each week to meet her goal?
To achieve her goal, Julie needs to burn an extra 2,625 / 7 = 375 calories every day.
Find how many extra calories neededTo calculate how many extra calories Julie needs to burn each week to lose 3 pounds in four weeks, we need to use the following formula:
1 pound of body weight = 3,500 calories
3 pounds of body weight = 3 x 3,500 = 10,500 calories
Julie wants to lose 3 pounds in 4 weeks.
Therefore, her weekly goal would be to lose 10,500 / 4 = 2,625 calories.
To burn 2,625 extra calories in a week, Julie needs to burn 375 calories extra each day.
Therefore, she needs to burn an extra 2,625 / 7 = 375 calories every day to achieve her goal.
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Solve the system of equations:
y = 2x – 5
y = x^2 – 5
A. (–1, –7) and (4, 3)
B. (–1, –4) and (3, 4)
C. (0, –5) and (2, –1)
D. (0, 5) and (2, 2)
Answer:
C. (0, –5) and (2, –1)
A machine at a company makes toy cars at a constant rate. The company received an order for toy cars that exceeded the number of toy cars that the company had in stock.
In order to make the additionaI 100 toy cars required to meet demand, the company wiII need to run the machine for 8 hours.
what is unitary method ?To answer mathematics issues invoIving proportionaI reIationships, utiIize the unitary method. It entaiIs determining the vaIue of a singIe unit or item and using that data to determine the vaIue of a specified number of units or items. When tackIing chaIIenges in business, finance, and science that require rates, ratios, and proportions, the unitary technique is very heIpfuI. The unitary technique, for instance, can be used to caIcuIate a singIe item's price given the price of aII the other products combined.
given
The formuIa beIow can be used to determine how Iong it wiII take to generate the requisite number of toy cars if we know the rate at which the machine produces them:
Time is caIcuIated as (Number of toy cars required - Number of toy cars in stock) / Production Rate.
For instance, if the machine can produce 10 toy cars per hour and the business needs to make an additionaI 100 to compIete the order, but they aIready have 20 toy cars on hand, the time needed to make the extra toy cars wiII be:
Time = (100-20) / 10 = 8 hours.
In order to make the additionaI 100 toy cars required to meet demand, the company wiII need to run the machine for 8 hours.
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Complete question:
1. A machine at a cοmpany makes toy cars at a constant rate. The company received an order for toy cars that exceeded the number of toy cars that the company had in stock.
Which three pieces of information are needed to determine the amount of time it will take the machine to make enough additional toy cars to fill the order?
Select the three pieces of information that are needed.
A. the cost to make each toy car
B. the rate that the machine makes toy cars
C. the number of toy cars requested in the order
D. the number of people needed to run the machine
E. the number of toy cars available when the order was received
Find the value of the expression x+|x| if x=7, 10, 0, -3, -8. write the expression without the absolute value symbol for these values of x: x≤0
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
What does the expression mean?When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The value of a function, given the value(s) assigned to its argument, is the sum that the function assumes for these input values (s).
For x =7,x+|x| =7+|7| =14
For x =10,x+|x|= 10+|10| =20
For x = 0,x+|x| =0+|0| =0
For x = -3, x + |x| = -3 + |-3| = 0
For x = -8, x + |x| = -8 + |-8| = 0
The expression's value is when x 0, and since |x| = -x when x 0, x + |x| simplifies to 0. In this case, x + |x| = x + (-x) = 0 for x 0.
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A hurries with a constant speed of 40km/h.How long will take to travel a distance of 80 kilometers
Answer:
2 hours
Step-by-step explanation:
80 ÷ 40 = 2
Check:
40 x 2 = 80
solve the following questions based on the information provided: i. six students a, b, c, d, e and f participated in a self-evaluation test of quants and data interpretation (d.i.). ii. the total marks of a in quants was just above c and in d.i. just above f. iii. b was just above c in d.i. but he scored less than d in quants. iv. f got more marks than d and e in d.i. but did not perform as well in quants as in d.i. as compared to d and e. v. no one is in between c and d in quant and c and a in d.i. 16.who got the highest marks in d.i.? a b c data inadequate 17.which of the following students has scored the least in d.i.? only d only e only d or e none of these 18.who was just below d in quants? b e c data inadequate 19.which of the given statements is not necessary to answer the questions? (ii) (iii) (iv) all are necessary
For all the following questions all the statements are required, It is possible to determine that c was just below d in quants based on the given information. Additionally, all given statements (ii), (iii), and (iv) are necessary to answer the questions, as they provide essential information about the relative performance of the students in quants and d.
The given statements which are not necessary to answer the questions are:
To answer this question, we need to find out who got the highest marks in d.i. According to statement (iv), F got more marks than D and E in d.i. Therefore, we can conclude that F got the highest marks in d.i. To answer this question, we need to find out who scored the least in d.i. However, the information provided does not tell us the score of any student in d.i., except that F got the highest marks. Therefore, we cannot determine which student scored the least in d.i. To answer this question, we need to find out who was just below D in quants. According to statement (v), no one is in between C and D in quants, which means that D got the highest marks in quants among the students listed. According to statement (ii), A's marks in quants were just above C's. Therefore, E must have been just below D in quants. To answer this question, we need to identify the statement that is not necessary to answer the questions. Statements (ii) and (iv) provide information about who got more marks in d.i. than certain other students, which is necessary to answer question 16. Statement (v) provides information about the order of marks in quants, which is necessary to answer question 18. Therefore, the statement that is not necessary to answer the questions is statement (iii), which only provides information about B's marks in quants relative to D and in d.i. relative to C. This information is not required to answer any of the questions.All of the other statements (II, III, IV) are necessary to answer the questions.
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To make a fruit smoothie, Olivia uses 4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango. What is the ratio of blueberries to banana?
Thus, the ratio for the number of blueberries to banana is 4:1.
Define about the ratios of the numbers?A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.
A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.
The given data for preparing fruit smoothie:
4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango.
Then,
ratio of blueberries to banana:
blueberries/banana = 4/1
Thus, the ratio for the number of blueberries to banana is 4:1.
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what is five more than x
Answer:
Step-by-step explanation:
x+5
Susan jogged for 1 1/2hours on Monday and 90 minutes on Tuesday. On which day did she jog longer?
Y = absolute value of x+5 if x > -5
Answer: y = ?
The absolute value of Y = X-5, with condition x > -5 is Y>-9.
The function of x is given to be,
Y = X-5, here a condition is given that, x > -5.
Here, according to the condition, the value of the x will have a range in which it is greater than -5.
Practically thinking, the number starting from -4, -3, -2, -1, 0, 1, 2, ...... all are greater than -5. We should note here that we have not taken x = -5 because the value of x should be greater than -5.
Now, the absolute value of the function y will be, putting x = -4,
Y = -4-5
Y = -9. Hence, the absolute value will always be more than -9. So, Y > -9.
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What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
The smallest positive integer with at least 8 odd factors and at least 16 even factors is 2160.
Use Euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y' = 4y + 3xy, y(2) = 1. Step 1 Euler's Method says that we can use a given step size h to approximate the solution to the initial-value problem y' = F(x, y), y(x) = yo by using the iterative formula Yn = Yn - 1 + HF(xn - 1. Yn - 1). To estimate y(2.5) for y' = 4y + 3xy, y(2) = 1 with step-size h = 0.1, we need 5 5 iterations.
The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size.
To estimate y(2.5) with step size 0.1 using Euler's Method, we need 5 iterations. The iterative formula is Yn = Yn-1 + hF(xn-1, Yn-1), where F(x, y) = 4y + 3xy. Using this formula and the initial condition Y(2) = 1, the 5 iterations are:
Therefore, the approximation of y(2.5) using Euler's method with step size 0.1 is
.
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Write an equation of the line that is parallel to y = 12
x + 3 and passes through the point (10, -5).
Answer:
y = 12x - 125
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 12x + 3 ← is in slope- intercept form
with slope m = 12
• Parallel lines have equal slopes , then
y = 12x + c ← is the partial equation
to fond c substitute (10, - 5 ) into the partial equation
- 5 = 12(10) + c = 120 + c ( subtract 120 from both sides )
- 125 = c
y = 12x - 125 ← equation of parallel line
Mei Mei wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box.
Mei Mei utilized wrapping paper that was 337.212 square inches in size.
What is the triangular pyramid formula?The formula V = 1/3AH, where H is the height of the pyramid or the distance from its base to its apex, may be used to calculate the volume of a triangular pyramid.
To find the amount of wrapping paper Mei Mei used
we need to find the surface area of the triangular pyramid.
The formula for an equilateral triangle's area is as follows:
[tex]A = (\sqrt{(3)/4}) \times s^2[/tex]
where s is a side of the triangle's length.
The base of the triangular base is 13 inches, so the sides of the triangles are also 13 inches.
The slant height of the pyramid is given as 11.26 inches.
Using the formula, we find that the area of each triangular face is:
[tex]A = (\sqrt{(3)/4)} \times s^2 = (\sqrt{(3)/4)} \times 13^2 = 84.303[/tex]
To find the total surface area of the pyramid, we add up the areas of all four triangular faces. There are four triangles, so:
total surface area =[tex]4 \times A = 4 \times 84.303 = 337.212[/tex]
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Complete question -
Mei Mei wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box.
2 ^ (3 ^ 2) =? Please explain also
Answer: 512
Step-by-step explanation:
2^ (3^2)
2^ (9)
512
A certain population is strongly skewed to the left. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one?
I. The distribution of our sample data will be closer to normal.
II. The sampling model of the sample means will be closer to normal.
III. The variability of the sample means will be greater.
A. I and II only
B. I only
C. III only
D. II and III only
E. II only
A. I and II only true if we use a large sample rather than a small one
sampling model
Define sampling modelA sampling model is a statistical model used to describe the behavior of a sample statistic. In other words, it is a model that describes the distribution of a particular sample statistic, such as the mean or standard deviation, as it is repeatedly sampled from a population.
When a sample is drawn from a population that is strongly skewed to the left, a small sample may not accurately represent the true population mean. However, if a large sample is taken, the sample mean is more likely to be normally distributed, due to the central limit theorem. This means that both statement I and II are true.
Statement III is false because as the sample size increases, the variability of the sample means actually decreases. This is because larger samples tend to have less sampling error and are more representative of the population as a whole.
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3.27 Underage drinking, Part II: We learned In Exercise 3.25 that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 year olds. (a) How many people in the sample would you expect to have consumed alcoholic beverages? (round to one decimal place) (b) Would you be surprised if the sample contained 45 or more people who have consumed alcoholic beverages? - No, it is just as likely as any other outcome - No, 45 or more accounts for six different events -- this wouldn't be surprising - Yes, 45 is more than two standard deviations above the expected value (mean) - Yes, 45 out of 50 is 90% (c) What is the probability that 45 or more people in this sample have consumed alcoholic beverages? Cound to forracina
The very low likelihood that there will be 45 or more people in the sample who have consumed alcoholic beverages.
a) The number of people in the sample expected to have consumed alcoholic beverages can be calculated as follows:First, we multiply the number of individuals in the sample by the proportion of people in that age group who drink alcohol.50 x 0.697 = 34.85Thus, we anticipate that about 34.85 people in the sample will have consumed alcoholic beverages.b) No, 45 or more accounts for six different events -- this wouldn't be surprising, you would not be surprised if the sample contained 45 or more people who have consumed alcoholic beverages. This is because it falls within the margin of error.c) To calculate the probability that 45 or more people in this sample have consumed alcoholic beverages, we will need to compute the z-score first.We use the following formula to calculate the z-score:$$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$$Where, x = 45μ = 0.697 x 50 = 34.85σ = √[(50 x 0.697 x 0.303)] = 3.77n = 50After plugging the values into the formula, we have:$$z=\frac{45-34.85}{\frac{3.77}{\sqrt{50}}}$$ = 3.89Since we are trying to determine the probability of having 45 or more people who have consumed alcoholic beverages, we will calculate the probability of having a z-score greater than or equal to 3.89.Instead of looking up the z-score in the z-table, we can use a calculator to determine the probability. From a standard normal distribution, the calculator provides the following output:P(Z ≥ 3.89) = 0.0000317Rounded to four decimal places, the probability is approximately 0.0000. Therefore, there is a very low likelihood that there will be 45 or more people in the sample who have consumed alcoholic beverages.
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I NEED ANSWERS ASAP….
Answer:
Step-by-step explanation:
It is set up
7x+5x+2y=20
7x+5x=12x
12x+2y=20
x=0
y=10
12(0)+2(10)=20
Ok so maybe this was not the same type of equation i thought it was it is not that easy!
6x+3y=−12 ? (0,−4) if x=−3 , what is the value of y?
In equation 6x+3y=−12, if value of x is -3 then by using substitution method the value of y is 2.
To find the value of y, we can use the substitute method with the given value of x = -3 in the equation 6x + 3y = -12 and solve for y:
6x + 3y = -12 (substitute x = -3)
6(-3) + 3y = -12
-18 + 3y = -12 (add 18 to both sides)
3y = 6
y = 2
Therefore, by using substitution method we find that the value of y when x = -3 is 2.
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____The given question is incorrect, the correct question is given below:
In equation 6x+3y=−12 if x=−3 , what is the value of y?
help me pls♀️♀️♀️. is the function linear, quadratic, or exponential
Answer: Quadratic (not 100% sure)
The sum of two expressions is x2-y2-2xy+y-7. if one of them is 2x2+3y2-7y+1, find the other.
I need proper step by step answer or else I will be terminating your answer.
Answer:
-x^2 - 2xy - 2y^2 + 8y - 8.
Step-by-step explanation:
Let the other expression be A. Then, we have:
x^2 - y^2 - 2xy + y - 7 = (2x^2 + 3y^2 - 7y + 1) + A
Simplifying the left side:
x^2 - y^2 - 2xy + y - 7 = 2x^2 + 3y^2 - 7y + 1 + A
Rearranging the terms:
A = x^2 - y^2 - 2xy + y - 7 - 2x^2 - 3y^2 + 7y - 1
Simplifying further:
A = -x^2 - 2xy - 2y^2 + 8y - 8
Therefore, the other expression is -x^2 - 2xy - 2y^2 + 8y - 8.
Which graph represents this equation? [tex]y=\frac{3}{2}x^{2}-6x[/tex]
I know the answer is C. What I want to know is WHY.
The x-intercepts are (0, 0) and (4, 0), and the y-intercept is (0, 0).
Why are equatiοns graphed?By graphing linear equatiοns, yοu can explain the relatiοnship between twο variables visually. We can easily see what happens tο οne variable as the οther grοws by using a graph. The value οf the x variable rises as we mοve tο the right οn a graph.
[tex]y = (3/2)x^2 - 6x[/tex] is the given equatiοn.
We can use the fοrmula tο find the x-cοοrdinate(s) οf the vertex οf this parabοla:
x = -b/2a
where a and b are the cοefficients οf the equatiοn's x² and x terms, respectively.
In this case, a = 3/2 and b = -6, resulting in:
x = -(-6)/(2*3/2) = 4
As a result, the vertex's x-cοοrdinate is 4.
Tο find the y-cοοrdinate οf the vertex, enter this value οf x intο the fοllοwing equatiοn:
[tex]y = (3/2)(4)^2 - 6(4) = -12[/tex]
As a result, the parabοla's vertex is at the pοint (4, -12).
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Which of the following would be the standard deviation for this sample data set: 5, 7, 6, 9, 6, 4, 4, 6, 5, 2, 5?
1.80
1.72
2.68
5.36
The standard deviation for this sample data set is 1.80.
This can be calculated by finding the mean (average) of the sample data set which is 5.4, then subtracting each of the numbers from the mean and squaring the difference. Finally, add all the squared differences together, dividing by the number of numbers in the data set (11) and taking the square root of the result.
Mean = 5.4
5 - 5.4 = -0.4 → (-0.4)² = 0.16
7 - 5.4 = 1.6 → (1.6)² = 2.56
6 - 5.4 = 0.6 → (0.6)² = 0.36
9 - 5.4 = 3.6 → (3.6)² = 12.96
6 - 5.4 = 0.6 → (0.6)² = 0.36
4 - 5.4 = -1.4 → (-1.4)² = 1.96
4 - 5.4 = -1.4 → (-1.4)² = 1.96
6 - 5.4 = 0.6 → (0.6)² = 0.36
5 - 5.4 = -0.4 → (-0.4)² = 0.16
2 - 5.4 = -3.4 → (-3.4)² = 11.56
5 - 5.4 = -0.4 → (-0.4)² = 0.16
Sum of squared differences = (0.16 + 2.56 + 0.36 + 12.96 + 0.36 + 1.96 + 1.96 + 0.36 + 0.16 + 11.56 + 0.16) = 28.8
Standard deviation = √(28.8/11) = √2.62 = 1.80
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Select the correct answer. Solve for x. x2 - 2x - 24 = 0
A.
-4, -6
B.
-4, 6
C.
2, -6
D.
4, 6
Answer:
B. -4, 6
Step-by-step explanation:
If the volume of a hexagonal prism is 3,660 ft³, what is the volume of a hexagonal pyramid in cubic feet
with the same dimensions?
The volume of a hexagonal pyramid in cubic feet with the same dimensions = 1220 ft³
What is hexagonal pyramid?A hexagοnal pyramid is a three-dimensiοnal geοmetric shape that cοnsists οf a base that is a regular hexagοn (a six-sided pοlygοn with all sides and angles equal) and six triangular faces that meet at a single pοint abοve the base, called the apex. The six triangular faces fοrm a pyramid shape with the base, which is why it's called a hexagοnal pyramid.
This relatiοnship can be derived using the fοrmula fοr the vοlume οf a pyramid V = (1/3)Bh, where B is area οf base and h is height οf pyramid. Since the base οf the pyramid is a hexagοn inscribed within the hexagοnal base οf the prism, the area οf the base is (3√3/2)a², where a is the side length οf the hexagοn. The height οf the pyramid is the same as the height οf the prism, which we can call h.
Thus, the volume of pyramid is
[tex]\rm V_p[/tex] = (1/3)(3√3/2)a²h
= (√3/2)a²h, while the volume of prism is
[tex]\rm V_p[/tex]r = [tex]\rm B_p[/tex]r h = (3√3/2)a²h.
Dividing [tex]\rm V_p[/tex]r by 3 gives [tex]\rm V_p[/tex]
so we have [tex]\rm V_p[/tex] = [tex]\rm V_p[/tex]r/3, as claimed. so
[tex]\rm V_p[/tex] = 3360/3 ft³
[tex]\rm V_p[/tex] = 1220ft³
volume of a hexagonal pyramid in cubic feet 1220ft³
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rory's castle measures 10 feet by 16 feet and has a perimeter of 52 ft mikes castle is 6 feet by 6feet what is the differecnce between permieters
The difference in perimeter between Rory's castle and Mike's castle is 16 feet. Rory's castle has a perimeter of 52 feet (10 feet + 10 feet + 16 feet + 16 feet), and Mike's castle has a perimeter of 24 feet (6 feet + 6 feet + 6 feet + 6 feet).
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The difference between the perimeters of these two castles is 28 ft.
Rory’s castle measures 10 feet by 16 feet and has a perimeter of 52 ft and Mike’s castle is 6 feet by 6 feet. Now, we are going to find the difference between the perimeters of these two castles.
The perimeter of a rectangle can be found by adding all the sides of a rectangle. Therefore, the formula of the perimeter of a rectangle is:
Perimeter of a rectangle = 2 × (Length + Breadth)
Length of Rory’s castle = 16 ft, Breadth of Rory’s castle = 10 ft
Perimeter of Rory’s castle = 2 × (Length + Breadth) = 2 × (16 + 10) ft
= 2 × 26 ft= 52 ft
Therefore, the perimeter of Rory’s castle is 52 ft.
Length of Mike’s castle = 6 ft, Breadth of Mike’s castle = 6 ft
Perimeter of Mike’s castle = 2 × (Length + Breadth) = 2 × (6 + 6) ft
= 2 × 12 ft = 24 ft
Therefore, the perimeter of Mike’s castle is 24 ft.
.Difference between the perimeters of these two castles= Perimeter of Rory’s castle − Perimeter of Mike’s castle
= 52 − 24= 28 ft
Therefore, the difference between the perimeters of these two castles is 28 ft.
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6 ft
Find the area.
8 ft
8 ft
Remember: A = πr²
A = [?] ft²
Round to the nearest
hundredth.
Use 3.14 for T.
The area of the figure is the collective sum of area of the square, rectangle and semi-circle which is 100.56 squared feet.
What is the area of the figureTo find the area of the figure, we need to find the area of the square, semi-circle and triangle.
A = Area of square + area of triangle + area of semi-circle
A = L² + 1/2(bh) + πr
A = 8² + 1/2(6 * 8) + 3.14(4)
A = 64 + 24 + 12.56
A = 100.56 ft²
The area of the figure is 100.56ft²
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Simplify the expression. csc^2x-1/1+sin x
A. csc x+1
B. csc x(csc x-1)
C. sin^2x-csc x
D. csc^2x-cos x tan x
Answer:
We can start by simplifying the numerator of the expression:
csc^2x - 1 = (1/sin^2x) - 1 = (1 - sin^2x) / sin^2x = cos^2x / sin^2x = cos^2x csc^2x
Now we can substitute this into the original expression:
csc^2x-1/1+sin x = (cos^2x csc^2x) / (1 + sin x)
We can then simplify this further by using the identity 1 + sin x = (sin^2x + cos^2x) / sin x:
(cos^2x csc^2x) / (1 + sin x) = (cos^2x csc^2x) / [(sin^2x + cos^2x) / sin x]
= cos^2x csc^2x sin x / (sin^2x + cos^2x)
= cos^2x csc^2x sin x / 1
= cos^2x csc^2x sin x
This expression can be simplified using the identity cos^2x = 1 - sin^2x:
cos^2x csc^2x sin x = (1 - sin^2x) csc^2x sin x = (1/sin^2x - 1) sin x = csc^2x - sin x
Therefore, the simplified expression is csc^2x - sin x. Answer: none of the given options.
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