Find the surface area of the equilateral triangular pyramid.
A 180cm^2
B 228cm^2
C 268cm^2
D 456cm^2
Answers
The surface area of a triangular pyramid is the sum of areas of all faces of a triangular pyramid. Here, the surface area of a triangular pyramid with side 12 cm, base height 10 cm is equals to the 228 cm². So, the option (b) is correct choice.
Generally, a triangular pyramid has a triangular base and is bounded by three lateral triangular faces with one vertex. The units of measured surface area are square units like cm², m², ft² or cubit². The Formula for the surface area of a pyramid is calculated by adding up the area of all triangular faces of a pyramid. Mathematically,
Surface area = 1⁄2(a × b) + 3⁄2(b × s).
Where b --> the side of a pyramid
a --> the height of a base triangle, and
s --> the slant height of a pyramid. We have a triangular pyramid as present in above figure. Here height of base, a = 8 cm
slant height , s = 10 cm
side of a pyramid, b = 12 cm
So, Area of base triangle is, A1 = 1⁄2(a × b)
= (1/2)(8×12) = 48 cm²
Area of one triangular face = 1/2( b×s)
= 1/2( 12 × 10) = 60 cm²
Area of all triangular faces of a pyramid, A2 = 3× 60 = 180 cm²
The surface area of a pyramid = A1 + A2
= 48 + 180 = 228 cm²
Hence, required area is 228 cm².
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Complete question:
Find the surface area of the equilateral triangular pyramid. See the above
A 180cm^2
B 228cm^2
C 268cm^2
D 456cm^2
Related Questions
Anyone know this and can help?
Answers
Answer: A. ; [tex]2x-3=7[/tex]
Step-by-step explanation: We are solving for when the value of x is equal to five. Here is proving that the answer to the first question is correct.
[tex]2x-3=7[/tex]
Add 3 to both sides
[tex]2x=10[/tex]
Divide both sides by 2
[tex]x=5[/tex]
Please Mark Brainliest
Answer: A
Step-by-step explanation:
When an equation has a solution for x = some number n, that means the equation is true when you substitute for x=n. In this case, n=5, so we substitute x=5 in all 4 equations. We can notice that A yields 2*5-3=7 -> 10-3=7, which is true. Therefore, A yields a solution for x=5. We can also put in x=5 for the other 3 equations and we can spot that the equation does not hold for x=5 for any of them.
Jobs arriving to a computer server have been found to require CPU
time that can be modeled by an exponential distribution with a mean of 140 ms
(milliseconds). The CPU scheduling discipline is quantum-oriented so that a job not
completed within a quantum of 100ms will be routed back to the tail of the queue of waiting
jobs.
a. What is the probability that an arriving job is forced to wait for a second quantum (that is,
it will be forced to wait for more than 100ms)?
b. What is the probability that the fifth arriving job of a day will be the first one that is
forced to wait for a second quantum (that is, it will be forced to wait for more than
100ms)
Answers
The probability of the fifth job being the first one that is forced to wait for a second quantum is 0.0266.
What is probability?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability is calculated by taking all possible outcomes into consideration and then dividing the number of favourable outcomes by the total number of possible outcomes.
The probability that an arriving job is forced to wait for a second quantum is the probability of that job requiring more than 100ms of CPU time. This probability can be calculated by taking the cumulative distribution function of the exponential distribution and subtracting the probability of the job requiring 100ms or less of CPU time. The probability of the job requiring more than 100ms of CPU time is 0.6853.
This probability can be calculated by taking the probability of the first four jobs requiring less than 100ms of CPU time and multiplying it by the probability of the fifth job requiring more than 100ms of CPU time.
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2100 dollars is placed in an account with an annual interest rate of 5%. To the nearest year, how long will it take for the account value to reach 5100 dollars?
Answers
Therefore, it will take about 11 years for the account value to reach 5100 dollars.
What is percent?Percent is a way of expressing a quantity as a fraction of 100. The symbol "%" is used to represent percent. For example, if we say that an interest rate is 5%, it means that the interest is 5/100 or 0.05 as a decimal. Percentages are commonly used in finance, economics, and everyday life to express rates, proportions, and changes in quantities.
Here,
We can use the formula for compound interest to solve this problem:
A = P(1 + r/n)ⁿˣ
where A is the amount of money in the account after x years, P is the principal amount (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and x is the time (in years).
We are given that P = 2100, r = 0.05, and we want to find the value of x when A = 5100. Let's assume that the interest is compounded annually (n = 1). Substituting the given values into the formula, we get:
5100 = 2100(1 + 0.05)ˣ
Dividing both sides by 2100, we get:
(1 + 0.05)ˣ = 5100/2100
Simplifying the right-hand side, we get:
(1 + 0.05)ˣ = 2.42857
Taking the natural logarithm of both sides, we get:
ln(1 + 0.05)ˣ = ln 2.42857
Using the power rule of logarithms, we can simplify the left-hand side:
x ln(1 + 0.05) = ln 2.42857
Dividing both sides by ln(1 + 0.05), we get:
x= ln 2.42857 / ln(1 + 0.05)
Using a calculator, we get:
x≈ 11.4
Rounding this to the nearest year, we get:
x ≈ 11 years
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4. (Odds / Ends p. 125 #7) Martha is trying to decide where to go to university. She applied to three schools: UTM, Western, and Queens. UTM is her first choice, Queens is her last choice. So far Martha has only heard back from Western. They are offering her early admission: they’ll admit her but only if she agrees right now to go there (she can’t wait until she finds out if the other two schools will admit her). Based on her grades, Martha knows that if she waits she’ll be admitted to Queens for sure. But her chance of getting into UTM is only 6/10. After thinking about it a while, she can’t decide: a guaranteed spot at Western seems just as good to her as the gamble on UTM vs. Queens. a. If the utility of going to Queens is 5/10 for Martha, and the utility of going to UTM is 9/10, what is the utility of going to Western? b. Martha’s friend is considering York University. Martha didn’t apply to York, but if she had she would be indifferent between these options: - Accept an early-admissions offer from York and go there. - Gamble on a 3/4 chance at going to Western vs. a 1/4 chance of having to go to Queens. How much utility does going to York have for Martha?
Answers
a. The utility of going to Western is 6.4/10
b. The utility of going to York would also be 5.15/10
Define the term decision theory?Decision theory is a branch of mathematics that deals with decision making in the face of uncertainty.
a. If Martha accepts the early admission offer from Western, her utility would be 5/10, since that is the utility of going to Queens.
If Martha waits and gets admitted to Queens, her utility would be 5/10 as well, since that is the utility of going to Queens.
If Martha waits and gets admitted to UTM, her utility would be 9/10.
The probability of getting admitted to Queens is 1, since she is guaranteed admission. The probability of getting admitted to UTM is 6/10. The probability of accepting the early admission offer from Western is 4/10, since it is the complement of the probability of getting admitted to UTM.
Therefore, the expected utility of waiting is ⇒ (1 * 5/10) + (6/10 * 9/10) = 8.4/10. The expected utility of accepting the early admission offer is
⇒ (4/10 * 5/10) = 2/10.
Since Martha is indifferent between the two options, the utility of going to Western is 8.4/10 - 2/10 = 6.4/10
b. If Martha is indifferent between accepting an early-admissions offer from York and gambling on a 3/4 chance at going to Western vs. a 1/4 chance of having to go to Queens, then the utility of going to York must be the same as the expected utility of gambling.
If Martha gambles, her expected utility would be (3/4 * 6.4/10) + (1/4 * 5/10) = 5.15/10.
Therefore, the utility of going to York would also be 5.15/10.
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Four envelopes contain four different amounts of money. You are allowed to open them one by one, each time deciding whether to keep the amount or discard it and open another envelope. Once an amound is discarded, you are not allowed to go back and get it later. Compute the probability that you get the largest amount under the following different strategies: a) You take the first envelope b) You open the first envelope, note that it contains the amount x, discard it, and take the next amount which is larger than x( if no such amount shows up, you must take the last envelope). c) You open the first two envelopes, cal the amounts x and y, and discard both and take the next amount that is larger than both x and y.
Answers
1. If the first envelοpe cοntains the largest amοunt, then yοu take it and stοp. The prοbability οf this happening is 1/4.
What is prοbability?Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.
a) If yοu take the first envelοpe, the prοbability that it cοntains the largest amοunt is 1/4.
b) If yοu οpen the first envelοpe, nοte that it cοntains the amοunt x, and take the next amοunt which is larger than x (if nο such amοunt shοws up, yοu must take the last envelοpe), the prοbability that yοu get the largest amοunt is 1/3.
Tο see why, cοnsider the fοllοwing cases:
2. If the first envelοpe dοes nοt cοntain the largest amοunt, but the secοnd envelοpe dοes, then yοu discard the first envelοpe and take the secοnd οne. The prοbability οf this happening is (3/4) x (1/3) = 1/4.
3. If the first twο envelοpes dο nοt cοntain the largest amοunt, but the third οne dοes, then yοu discard the first twο envelοpes and take the third οne. The prοbability οf this happening is (3/4) x (2/3) x (1/2) = 1/4.
4. If the first three envelοpes dο nοt cοntain the largest amοunt, then yοu must take the last envelοpe, which has the largest amοunt with prοbability 1/4.
c) If yοu οpen the first twο envelοpes, call the amοunts x and y, and discard bοth and take the next amοunt that is larger than bοth x and y, the prοbability that yοu get the largest amοunt is 1/2.
Tο see why, cοnsider the fοllοwing cases:
1. If the largest amοunt is in the first twο envelοpes, then yοu must take the last twο envelοpes, and the prοbability οf getting the largest amοunt is 1/2.
2. If the largest amοunt is nοt in the first twο envelοpes, then yοu must take the third οr fοurth envelοpe, and the prοbability οf getting the largest amοunt is 1/2.
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Bert can paddle his kayak at a maximum speed of 270metersperminute. If he paddles across a lake at one-third of his top speed for 8minutes, how far will he move?
Answers
After calculating, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.
Considering that Bert's maximum speed is 270 meters per minute, then his speed when he is paddling at one-third of his top speed is:
270 m/min * (1/3) = 90 m/min
If he is paddling at this speed for 8 minutes, then the distance that he covers is:
distance = speed * time = 90 m/min * 8 min = 720 meters
Therefore, Bert will move 720 meters when paddling across the lake at one-third of his top speed for 8 minutes.
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trapezoid ABCD has an area of 450 square cm MA=MB, NC=ND, CD = AB x 2..a) Calculate ACD. b) Calculate AMCN . c) lengthen DA and CB intersect at k , calculate the area ABK
Answers
According the question given above the area of ABK is 100 square cm.
a) ACD = 50 square cm
b)AMCN = 225 square cm
c)ABK = 100 square cm
a) Tο calculate ACD, we need tο use the fοrmula fοr the area οf a trapezοid, which is:
Area = (base1 + base2) × height ÷ 2
Since CD is twice the length οf AB, we can let AB = x and CD = 2x. Let's alsο call the height οf the trapezοid h.
Then we have:
450 = (AB + CD) × h ÷ 2
450 = (x + 2x) × h ÷ 2
450 = 3xh ÷ 2
300 = 3xh
100 = xh
Nοw, we can use the fact that MA = MB tο find the area οf triangle ACD:
ACD = AB × h ÷ 2
ACD = xh ÷ 2
ACD = 100 ÷ 2
ACD = 50 square cm
b) Tο calculate AMCN, we need tο first find the length οf MN. Since MA = MB and NC = ND, we can use the fact that οppοsite sides οf a trapezοid are parallel tο find that AMCN is a parallelοgram. Therefοre, MN is equal tο AB.
Using the fοrmula fοr the area οf a parallelοgram, which is base × height, we have:
AMCN = AB × CD
AMCN = x × 2x
[tex]AMCN = 2x^2[/tex]
AMCN = 900 ÷ 2
AMCN = 225 square cm
c) Tο find the area οf triangle ABK, we need tο find the length οf BK. Since AB = x and CD = 2x, we knοw that AK and KC are alsο equal tο x. Therefοre, BK is equal tο DA, which is 2x.
Using the fοrmula fοr the area οf a triangle, which is base × height ÷ 2, we have:
ABK = AB × BK ÷ 2
ABK = x × 2x ÷ 2
[tex]ABK = x^2[/tex]
ABK = 100 square cm
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Pls help me. I cant figure this out.
Answers
Answer:
Step-by-step explanation:
You can do 6x+the number of the amount of squares. Then find find the units of the square unit.
The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%. What will the probability be? Or is the proportion satisfied?
Answers
satisfied=88%
The program director estimated that the proportion of MGMT650 students that are very satisfied is 88% ±5%.What is probability?Probability is the branch of mathematics that studies the probability of an occurrence, as well as the likelihood of its occurrence. Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.Probability formula is P(E) = n(E) / n(S), where P(E) refers to the probability of occurrence of event E, n(E) is the number of outcomes in event E, and n(S) is the total number of possible outcomes.What is proportion?The proportion is a percentage, a fraction, or a ratio that compares the number in the group to the total number. When looking at a sample from the population, the sample proportion is calculated as the number in the sample with the attribute of interest divided by the total number of people in the sample. It gives us the proportion of people who have the attribute of interest in the sample.Answer:Therefore, the probability will be 88% ±5% and the proportion satisfied is 88%.
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Mr. Stenfanski's class has 7 boys and 10 girls. If two students are randomly selected, what is the probability they are both girls? After selecting the first student, she does not go back in the room before the second student is selected.
A. 10/17
B. 59/143
C. 10/7
D. 45/136
Answers
Answer:
[tex] \frac{45}{136} [/tex]
Step-by-step explanation:
The probability of selecting a girl on the first pick is 10/17, since there are 10 girls out of 17 students in total.
After the first pick, there are 16 students remaining, including 7 boys and 9 girls. So the probability of selecting a girl on the second pick, given that a girl was not selected on the first pick, is 9/16, since there are now only 9 girls and 16 total students left to choose from.
To find the probability of both events occurring (i.e., both students being girls), we need to multiply the probabilities of each event. Therefore, the probability of selecting two girls in a row is:
[tex] \frac{10}{17} \times \frac{9}{16} = \frac{90}{272} [/tex]
So the probability of selecting two girls in a row is
[tex] \frac{90}{272} [/tex]
which can be simplified to
[tex] \frac{45}{136} [/tex]
Complete the problem. Let f(x)=(1)/(x) and g(x)=(1)/(x+3). Describe the transformation from f(x) to g(x).
Answers
The transformation from f(x) to g(x) involves a horizontal shift and a change in the slope of the graph.The function g(x) is obtained from the function f(x) by a vertical shift of 3 units to the left.
Specifically, the denominator of g(x), x+3, represents a horizontal shift of 3 units to the left compared to the denominator of f(x), x. As a result, g(x) is shifted to the left relative to f(x). Furthermore, the shift causes the graph of g(x) to be steeper than that of f(x) at x=0. This is because, for small values of x, the difference between (1)/(x) and (1)/(x+3) becomes larger as x gets smaller. Therefore, the transformation from f(x) to g(x) involves a horizontal shift and a change in the slope of the graph.
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What is the elevation at point b? question 6 options: 700 ft 740 ft 780 ft 800 ft
Answers
The elevation at point B is 740 ft. So, option B is correct.
The elevation is the height above or below a specified reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation.
There are Four points that are displayed on the given map whose range are from A to D. There are few additional lines in between these four places. The height between these points and lines is indicated on the map in feet, and from point A onwards there is an elevation difference of 20 feet. Point A is at the 700 ft and there is one more line between A and B, and the elevation difference in between one line is 20. So the elevation difference at point B is = 700 + 20 +20= 740 ft. So, option answer is B.
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2
8. ¿Cuál es la factorización de x² + 2x?
(A) x²(2x)
(B) x(x + 2)
(C) x(x + 2x)
(D) x²(1 + 2x)
Answers
Answer:
B.) x(x+2)
Step-by-step explanation:
Hope this helps! :)
If the sixth term of an(AP) is 37 and the sum of the first six terms is 147 find the
I) first term
I) the sum of the first fifteen terms
Answers
As a result, the arithmetic progression's first term is 22 and its first fifteen terms add up to 735. The AP's initial term is 22 and its first fifteen terms add up to 735.
The total of the first seven terms is seventy-five.
The formulae for the nth term and the sum of an arithmetic progression can be used to solve the issue.
We have the following using the nth term formula:
a + 5d = 37\s(6/2)(2a + 5d) = 147
3a + 15d = 147\sa + 5d = 49
We may find a by substituting d into either equation and finding:
a + 5(-3) = 37\sa = 22
Hence, the first term of the arithmetic progression is 22 and the formula for the total of the first fifteen terms is (15/2)(2a + 14d) = 735.
(15/2)(2(22) + 14(-3)) = 735
If we simplify, we get:
15 terms added together is 735
As a result, the AP's first term is 22 and its first fifteen terms add up to 735.
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what is the radius if a circle with diameter 3cm
Which diagram shows how to set a pair of compasses to draw a circle with diameter 3cm
Answers
Answer: The radius of a circle is half of its diameter. Therefore, if the diameter of the circle is 3 cm, then the radius is 1.5 cm.
To set a pair of compasses to draw a circle with diameter 3 cm, open the compasses to a distance of 1.5 cm (which is the radius of the circle). The correct diagram in the link provided shows the compasses set to the correct radius.
So its A
The radius of the circle is 1.5cm.
A circle's diameter is divided in half by its radius. Thus, if the circle's diameter is 3 cm, the radius is:
radius = diameter/2 = 3cm/2 = 1.5cm
what is the radius?Any circular object's radius is the measurement from the centre to its outermost border or boundary. A radius is a dimension that applies to spheres, semispheres, cones with circular bases, and cylinders with circular bases in addition to circles.
It is possible to define a circle as the locus of a point travelling on a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its centre. The fixed point is referred to as the centre of the circle.
The distance along a line drawn between two points on a circle and through the centre of the circle is the diameter of the circle. It is equivalent to double the circle's radius. It is typically indicated with a d or a D.
Diameter = 2 x Radius
Or
Radius = diameter / 2.
The circle's longest chord equals its diameter.
Moreover, we may relate a circle's area and circumference to its diameter.
Circle circumference equals (Diameter)
Circle area equals /4 (Diameter[tex])^2.[/tex]
from the question;
A circle's diameter is divided in half by its radius. Thus, if the circle's diameter is 3 cm, the radius is:
radius = diameter/2 = 3cm/2 = 1.5cm
Therefore, the radius of the circle is 1.5cm.
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I drove 175 miles in 5 hours. What was my speed
Answers
The speed at which the driver travelled the 175 miles in 5 hours is 35 miles/hour.
The speed can be calculated by dividing the distance travelled (175 miles) by the amount of time taken (5 hours).
Formula: Speed = Distance/Time
Speed = 175/5 = 35 miles/hour
Therefore, my speed was 35 miles/hour.
To calculate the speed, the formula mentioned above is used. The formula states that speed is equal to the distance travelled divided by the amount of time taken. In this case, the distance travelled was 175 miles, and the time taken was 5 hours. When the distance travelled is divided by the time taken, the result is 35 miles/hour. This is the speed at which the driver travelled the 175 miles in 5 hours.
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HELP PLEASE
THANK YOU SO MUCH
I APPRECATE THE HELP
Answers
Answer:
103
Step-by-step explanation:
157-54= 103
Answer: 103
Step-by-step explanation:
subtract 54 from 157
pls help me this is also due on Saturday!!!!!
Answers
Answer:
u=4
Step-by-step explanation:
u+6/12 = 4+6/12 = 10/12 ÷ 2/2 = 5/6
Answer: u = 4
Step-by-step explanation:
Please ASAP Help
Will mark brainlest due at 12:00
Answers
Answer:
plot the point at -3
Step-by-step explanation:
-3 is 6 points away from t and 4 away from s. thus 3/5
Pls help ASAP 100 pts (sisters 7th grade homework) but considered highschool level.
please post reasonable answers. Also the answer is also not 6.5 or 7
Answers
Answer:
Let's assume Karl rents the bike for x hours. Then the cost of renting the bike can be expressed as:
Cost = 7x + 9.5
We know that the maximum cost Karl can afford is $55. So we can set up an equation:
7x + 9.5 ≤ 55
Subtracting 9.5 from both sides:
7x ≤ 45.5
Dividing both sides by 7:
x ≤ 6.5
Since Karl can only rent the bike for whole hours, the maximum number of hours he can rent the bike is 6 hours (which costs $49 plus the $9.5 flat fee, for a total of $58.5). If he rented it for 7 hours, it would cost $60.5, which is over his budget.
In a consumer research study, several Meijer and Walmart stores were surveyed at random and the average basket price was recorded for each. You wish to determine if the average basket price for Meijer is different from the average basket price for Walmart. It was found that the average basket price for 25 randomly chosen Meijer stores (group 1) was $60.345 with a standard deviation of $10.8968. Similarly, a random sample of 20 Walmart stores (group 2) had an average basket price of $67.635 with a standard deviation of $12.936. Perform a two independent samples t-test on the hypotheses Null Hypothesis: μ1 = μ2, Alternative Hypothesis: μ1 ≠ μ2. What is the test statistic and p-value of this test? You can assume that the standard deviations of the two populations are statistically similar.
Question 3 options:
1) Test Statistic: -2.052, P-Value: 1.977
2) Test Statistic: -2.052, P-Value: 0.0461
3) Test Statistic: -2.052, P-Value: 0.023
4) Test Statistic: -2.052, P-Value: 0.977
5) Test Statistic: 2.052, P-Value: 0.0461
Answers
From the given data, the test statistic is -2.052 and the p-value is 0.0461. The correct answer is option 5.
To perform a two independent samples t-test, we can use the following formula to calculate the test statistic:
t = (x₁ - x₂) / (s_p × √(1/n₁ + 1/n₂))
where x₁ and x₂ are the sample means, n₁ and n₂ are the sample sizes, s_p is the pooled standard deviation, calculated as:
s_p = √(((n₁ - 1) × s₁² + (n₂ - 1) × s₂²) / (n₁ + n₁ - 2))
Let's calculate the test statistic:
x₁ = 60.345, s₁ = 10.8968, n₁ = 25
x₂ = 67.635, s₂ = 12.936, n₂ = 20
s_p = √(((25 - 1) × 10.8968² + (20 - 1) × 12.936²) / (25 + 20 - 2)) = 11.8074
t = (60.345 - 67.635) / (11.8074 × √(1/25 + 1/20)) = -2.052
The degrees of freedom for the t-distribution can be calculated as:
df = n₁ + n₂ - 2 = 43
Using a two-tailed t-test at a significance level of 0.05, the critical t-value is ±2.016.
The p-value for the test is the probability of obtaining a t-value as extreme or more extreme than the calculated t-value, assuming the null hypothesis is true. Since the calculated t-value is outside the critical region (|t| > 2.016), the p-value is less than 0.05 and we can reject the null hypothesis in favor of the alternative hypothesis.
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solve this question
Answers
Step-by-step explanation:
(a + 1/a)³ = a³ + 3a + 3/a + 1/a³
We are given that a + 1/a = 4, so we can substitute that into the identity and simplify:
(a + 1/a)³ = (4)³ = 64
a³ + 3a + 3/a + 1/a³ = 64
a³ + 1/a³ + 3(a + 1/a) = 64
a³ + 1/a³ + 3(4) = 64
a³ + 1/a³ = 52
Therefore, we have proved that a³ + 1/a³ = 52 when a + 1/a = 4.
Picture not drawn to scale. Make sure you show all your work for full points.
What is w, m, and n?
Answers
Answer:
w = 102
m = 78
n = 58
Step-by-step explanation:
Three angles of a triangle add up to 180°
∴ w = 180 - (36 + 42)
= 180 - 78
= 102
w and m are supplementary angles:
m + w = 180
m + 102 = 180
m = 180 - 102 = 78
Three angles of a triangle add up to 180°
m + 44 + n = 180
78 + 44+ n = 180
122 + n = 180
n = 180 - 122
n = 58
5.83. the probabilities are 0.40, 0.50, and 0.10 that, in city driving, a certain kind of compact car will average less than 28 miles per gallon, from 28 to 32 miles per gallon, or more than 32 miles per gallon. find the probability that among 10 such cars tested, 3 will average less than 28 miles per gallon, 6 will average from 28 to 32 miles per gallon, and 1 will average more than 32 miles per gallon.
Answers
The probability that among 10 such cars tested, 3 will average less than 28 miles per gallon, 6 will average from 28 to 32 miles per gallon, and 1 will average more than 32 miles per gallon is given by 0.0020125
Let X be the number of cars among ten that averages less than 28 miles per gallon. Let Y be the number of cars among ten that average from 28 to 32 miles per gallon. Let Z be the number of cars among ten that average more than 32 miles per gallon. We are to find P(X = 3, Y = 6, Z = 1).
Firstly, let us find the probability of getting 3 cars among 10 cars that will average less than 28 miles per gallon.
The probability of getting exactly 3 cars among 10 cars that will average less than 28 miles per gallon is given by the probability mass function:
P(X = 3) = (10C3) (0.4)³ (0.6)⁷
= (10 x 9 x 8 / 3 x 2 x 1) (0.064) (0.096)
= 0.23 (approximately)
Similarly, the probability of getting 6 cars among 10 cars that will average from 28 to 32 miles per gallon is given by the probability mass function:
P(Y = 6) = (10C6) (0.5)⁶ (0.5)⁴
= (10 x 9 x 8 x 7 x 6 x 5 / 6 x 5 x 4 x 3 x 2 x 1) (0.156) (0.063)
= 0.25 (approximately)
Finally, the probability of getting 1 car among 10 cars that will average more than 32 miles per gallon is given by the probability mass function:
P(Z = 1) = (10C1) (0.1)¹ (0.9)⁹
= (10) (0.1) (0.348)
= 0.035
Therefore, the answer is:
P(X = 3, Y = 6, Z = 1) = P(X = 3) P(Y = 6) P(Z = 1)
= 0.23 x 0.25 x 0.035
= 0.0020125 (approximately)
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-7 - 4 is equivalent to?
-11
11
-3
3
Answers
A small manufacturer makes two types of motors, models A and B. The assembly process for each is similar in that both require a certain amount of wiring, drilling, and assembly. Each model A takes 3 hours of wiring, 2 hours of drilling, and 1. 5 hours of assembly. Each model B must go through 2 hours of wiring, 1 hour of drilling, and 0. 5 hours of assembly. During the next production period, 240 hours of wiring time, 210 hours of drilling time, and 120 hours of assembly time are available. Each model A sold yields a profit of $22. Each model B can be sold for a $15 profit. Assuming that all motors that are assembled can be sold, find the best combination of motors to yield the highest profit
Answers
The maximum profit of $3330 can be obtained by manufacturing 80 model A motors and 70 model B motors.
Let A and B denote the number of model A and model B motors to be manufactured, respectively. The goal is to maximize the total profit, which is given by the expression 22A + 15B
The given constraints imply that [tex]$3A + 2B \le 240$, $2A + B \le 210$, and $1.5A + 0.5B \le 120$.[/tex]
We can solve this problem using linear programming. Let P = 22A + 15B denote the total profit. Then, the optimization problem can be written as follows:
Maximize P = 22A + 15B
Subject to [tex]$3A + 2B \le 240$, $2A + B \le 210$, and $1.5A + 0.5B \le 120$.[/tex]
Using the Simplex Method, we obtain the optimal solution: A = 80, B = 70, and P = 2280 + 1050 = 3330$. This implies that the maximum profit is 3330, which is obtained by manufacturing 80 model A motors and 70 model B motors.
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round each number to the nearest hundred
124= 2,311= 48=
Answers
Answer:
124= 100
2,311= 2,300
48= 0
Step-by-step explanation:
A hardware store rents vacuum cleaners that customers may use for part of a day before returning. The function f(x) = 6x + 14 models the total rental cost of a vacuum cleaner.
What is the flat fee that the store charges?
Answers
The flat fee that the stοre charge $14 and the cοst fοr 7 hοurs is $56. we sοlve this questiοn using linear equatiοn.
What is linear equatiοn?An equatiοn is said tο be linear if the maximum pοwer οf the variable is cοnsistently 1. A linear equatiοn with οne variable has the cοnventiοnal fοrm Ax + B = 0. In this case, the variables x and A are variables, while B is a cοnstant.
let f be the tοtal rental cοst οf a vacuum cleaner fοr x hοurs
And, f(x) = 6x + 14 (Given)
Sο The flat fee that the stοre charge $14.
Reasοnable dοmain is 1 ≤ x ≤ 12
The cοst fοr 7 hοurs is,
f(7) = 6(7) + 14 = 56.
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PLS ANSWER ASAP!!!
While driving on 1-10, Geoffrey used his cruise control so that the number of miles he
traveled was proportional to the time he spent driving. After five hours, Geoffrey had driven 340
miles. Determine the constant of proportionality and explain its meaning in the context of this
situation
Answers
Answer:
68
Step-by-step explanation:
Si O es el centro de la circunferencia de la figura y el ∡ ABC = 40°, halla la medida del ∡X
Answers
As in the given circle, the measure of the value of ∠X is 115°.
Now, let's look at point X. This point is on the same line as point B and is also on the circle. Since the angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any point on the circle, we can find the measure of ∠AXB by first finding the measure of arc ACB. Since arc ACB is subtended by ∠AOC, which measures 90°, we can find the measure of arc ACB by subtracting 40° (the measure of ∠ABC) from 90°. Therefore, arc ACB measures 50°. This means that ∠AXB is half the measure of arc ACB, so ∠AXB measures 25°.
Therefore, the measure of ∠X is 180° minus the sum of ∠AXB and ∠ABC, which gives us:
∠X = 180° - (25° + 40°) = 115°.
So, the measure of ∠X is 115°.
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Complete Question:
If O is the center of the circle of the figure and the ∠ABC = 40°, then the measure of ∠X