its 0.581 its pretty self explanatory so im not gonna explain
While hiking, Kurt ate 1/3 of a cup of nuts. Danielle ate 1/6 of a cup of nuts. How much more did Kurt eat than Danielle?
Kurt will eat 1/6 cups more than Danielle if Kurt ate 1/3 of a cup of nuts and Danielle ate 1/6 of a cup of nuts by using ratio and proportion concept.
What is ratio and proportion?When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. For instance, if there is 1 boy and 3 girls, the ratio would be written as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.
A: b a/b is the ratio formula, which may be used to calculate any two values. A:b::c:da:b::c:da, on the other hand, is how the percentage formula is written. A ratio in mathematics displays the multiplicative relationship between two numbers.
Given,
A cup of nuts ate by Kurt=1/3
A cup of nuts ate by Danielle=1/6
(1/3)-(1/6)
=1/6
Therefore, Kurt will eat 1/6 cups more than Danielle.
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Given f(x) = 2x − 3 and g(x) = f(2x), which table represents g(x)?
Answer:
g(x) = 4x - 3
Step-by-step explanation:
f(x) = 2x − 3
g(x) = f(2x)
g(x) = 2(2x) - 3 ==> plugin 2x for x in f(x) in order to get f(2x)
g(x) = 4x - 3
Which pairs of rectangles are similar polygons? Select Similar or Not Similar for each pair of rectangles. Similar Not Similar A and B Similar – A and B Not Similar – A and B B and C Similar – B and C Not Similar – B and C A and C Similar – A and C Not Similar – A and C Three rectangles labeled A, B, and C. The length of rectangle A is labeled as 100 centimeters and the width is labeled as 80 centimeters. The length of rectangle B is labeled as 120 centimeters and the width is labeled as 100 centimeters. The length of rectangle C is labeled as 90 centimeters and the width is labeled as 72 centimeters.
A polygon is a plane shape with a minimum of three straight sides. Thus the appropriate answer are:
i. A and B Not Similar
ii. B and C Not Similar
iii. A and C Not Similar
Polygons are majorly plane shapes which have straight sides. They are named with respect to the number of their sides, and the minimum sides is three. Some common examples are: trigon (3 sides), octagon (8 sides), hexagon (6 sides), pentagon (5 sides) , etc.
Two or more shapes are said to be similar if and only if they have some common properties with respect to their sides or internal angles.
Considering the ratios of the sides of the given polygons, it can be deduced that:
i. A and B Not Similar
ii. B and C Not Similar
iii. A and C Not Similar
Thus none of the polygons are similar.
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7. A material in which thermal energy is transferred slowly is a conductor.
True or False
Answer:
False
Step-by-step explanation:
False. A material in which thermal energy is transferred slowly is actually an insulator. A conductor is a material that easily allows the transfer of thermal energy. This is because conductors have loosely bound electrons that can move freely through the material, allowing heat to be easily transferred. Examples of good conductors include metals such as copper, aluminum, and silver. On the other hand, insulators have tightly bound electrons that do not move easily, making them poor conductors of heat. Examples of good insulators include materials like glass, plastic, and rubber.
Edgar accumulated $9,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for
2 years, how much will he owe on this debt in 2 years for quarterly compounding? Round your answer to the nearest cent.
To calculate the total amount of interest that Edgar will owe on his credit card debt after 2 years of quarterly compounding at a 20% annual interest rate, we need to use the formula A = P(1 + r/n)^nt, where A is the total amount of money owed after t years, P is the initial principal (or amount borrowed), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the initial principal is $9,000, the annual interest rate is 20%, the number of times the interest is compounded per year is 4 (since the interest is compounded quarterly), and the number of years is 2. Plugging these values into the formula, we get A = $9,000(1 + 0.20/4)^4 * 2 = $9,000(1.05)^8 = $9,000 * 1.4064 = $12,658.40. Thus, after 2 years of quarterly compounding at a 20% annual interest rate, Edgar will owe approximately $12,658.40 on his credit card debt. This result should be rounded to the nearest cent, giving us $12,658.40.
Finley's pumpkin had a mass of
6.5
6.56, point, 5 kilograms
(
kg
)
(kg)left parenthesis, start text, k, g, end text, right parenthesis before he carved it. After it was carved, the pumpkin had a mass of
3.9
kg
3.9kg3, point, 9, start text, k, g, end text.
What was the percent decrease in the mass of the pumpkin?
Step-by-step explanation:
The first, twelfth and last term of an arithmetic progression are and , respectively. Determine (a) the number of terms in the series, (b) the sum of all the terms and (c) the 80 th term
A stage manager is trying to seat important guests in the front row of a theater. The row has seven seats, and she would like a diplomat in the first seat, a singer in the second seat, and a movie director in the third seat. After this, the remaining diplomats, singers, and movie directors will be seated in the last four seats, in no particular order. If there are 3 diplomats, 2 singers, and 2 directors attending the show, how many different front row plans are possible?
Answer: 12 row plans
The first seat has 2 possible options, the 2 directors. The second seat has another 2 options. With each director comes 2 options for the second seat, so 2 x 2=4 possible options for the 1st and 2nd seats. The third seat has 3 options. That means for each combination of the 1st and 2nd seat, there are 3 possible options. 4x3=12 combinations.
Step-by-step explanation:
Test the claim about the difference between two population means
μ1
and
μ2
at the level of significance
α.
Assume the samples are random and independent, and the populations are normally distributed.Claim:
μ1=μ2;
α=0.01
Population statistics:
σ1=3.6,
σ2=1.4
Sample statistics:
x1=18,
n1=27,
x2=20,
n2=26
Determine the alternative hypothesis.
Ha:
μ1
▼
greater than>
greater than or equals≥
less than<
less than or equals≤
not equals≠
μ2
Determine the standardized test statistic.
z=nothing
(Round to two decimal places as needed.)
Determine the P-value.
P-value=nothing
(Round to three decimal places as needed.)
What is the proper decision?
A.Fail to reject
H0.
There is enough evidence at the
1%
level of significance to reject the claim.
B.Reject
H0.
There is enough evidence at the
1%
level of significance to reject the claim.
C.Fail to reject
H0.
There is not enough evidence at the
1%
level of significance to reject the claim.
D.Reject
H0.
There is not enough evidence at the
1%
level of significance to reject the claim
The correct answer is Option C. The proper decision, in this case, is "Fail to reject H0. There is not enough evidence at the 1% level of significance to reject the claim."
The alternative hypothesis, in this case, is "μ1 ≠ μ2", as the claim being tested is that the two population means are equal.
To calculate the standardized test statistic, we can use the following formula:
z = (x1 - x2) / sqrt(((σ1^2) / n1) + ((σ2^2) / n2))Substituting in the values given in the problem, we get:
z = (18 - 20) / sqrt(((3.6^2) / 27) + ((1.4^2) / 26))
z = (-2) / sqrt((12.96 / 27) + (1.96 / 26))
z = (-2) / sqrt(0.481 + 0.075)
z = (-2) / sqrt(0.556)
z = (-2) / 0.746
z = -2.67
To calculate the P-value, we can use the standard normal table to look up the probability of getting a value of -2.67 or lower if the null hypothesis were true. The P-value in this case would be the probability of getting a value equal to -2.67 or lower, plus the probability of getting a value equal to 2.67 or higher.
Using the standard normal table, we find that the probability of getting a value equal to -2.67 or lower is 0.0039, and the probability of getting a value equal to 2.67 or higher is 0.9961. Therefore, the P-value is 0.0039 + 0.9961 = 1.0000.
Since the P-value is equal to 1.0000, which is greater than the level of significance α = 0.01, we fail to reject the null hypothesis.
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calculate the shapley values for each player, i.e., the fair amount of money everyone should pay for their meal!
Assuming that the meal cost $50, the Shapley values (payments) for each player is: number of possible combination , Player 1: $15 , Player 2: $10 , Player 3: $10 , Player 4: $15
1. Calculate the marginal contribution of each player. This is the amount of money that each player adds to the total cost of the meal.
Player 1: $25
Player 2: $15
Player 3: $10
Player 4: $0
2. Calculate the Shapley Value for each player. This is calculated by taking the average of the marginal contribution of each player, weighted by the number of possible combinations they could have been in.
Player 1: ($25*3 + $15*2 + $10*1 + $0*0) / 6 = $15
Player 2: ($25*2 + $15*3 + $10*2 + $0*1) / 6 = $10
Player 3: ($25*1 + $15*2 + $10*3 + $0*2) / 6 = $10
Player 4: ($25*0 + $15*1 + $10*2 + $0*3) / 6 = $15
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HELP ASAP!! READ CAREFULLY
Answer:
1, 4, 5
Step-by-step explanation:
You want to identify correct proportions between the sides of similar isosceles trapezoids ABCD and WXYZ.
Corresponding sidesThe similarity statement tells us the corresponding side pairs are ...
AB ⇔ WXBC ⇔ XYCD ⇔ YZDA ⇔ ZWA proper proportion will be equate ratios of the corresponding sides in the same trapezoid, or the corresponding sides in different trapezoids.
ApplicationAB/WX = DA/ZW . . . . . . correct
AB/WX = ZW/DA . . . . . . incorrect
CB/XY = WX/AB . . . . . . incorrect
AB/WX = CB/YX . . . . . . correct
DA/AB = ZW/WX . . . . . . correct
BC/AD = XY/YZ . . . . . . incorrect
A. Quantity A is greater B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given. 0
No information is given for x and it can be fraction or real number, so option D is correct.
What is fraction ?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator.
It tells how many equal parts of the whole or collection are taken.
No information is given for x and it can be fraction or real number, so option D is correct.
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In square ABCD, m∠BCE=(5x+9)∘.
What is the value of x?
Enter your answer, as a decimal, in the box.
x =
Answer:
x = 7.2
Step-by-step explanation:
You want the value of x that makes ∠BCE = 45° = (5x +9)°.
SolutionDivide by ° and subtract 9 to get ...
36 = 5x
Divide by 5, and you have the value of x:
7.2 = x
The value of x is 7.2.
__
Additional comment
You know that the corner angles of a square are 90°, and that the diagonals bisect the corner angles. Each half is 45°.
The circumference of a circle is double the perimeter of square having area 484cm^2.what is the area of circle?
Answer:
The circumference of a corcle is double the perimeter of square having area 484 m^2. what is the area of the circle. Ans:2464 cm^2.
Answer:
Hence the area of a circle is 2466[tex]m^{2}[/tex]
Step-by-step explanation:
Review of the question
[tex]Given,[/tex]
The circumference of a circle is double the perimeter of squareArea of the square is 484[tex]cm^{2}[/tex]To Find:Area of the circle
,
Area of square =[tex]sideXside[/tex]
[tex]484[/tex]=[tex]side^{2}[/tex]
[tex]\sqrt{484}=side^{2}[/tex]
[tex]22 = side[/tex]
Perimeter of square = [tex]4Xside[/tex]
[tex]4X22[/tex]
[tex]88[/tex]
Circumference of the circle = Perimeter of square x 2
Circumference of the circle = 88x2
Circumference of the circle = 176
Now we need to find the radius of the circle
[tex]2\pi r=176[/tex]
[tex]2X3.14Xr=176\\6.28Xr=176\\r=\frac{176}{6.28} \\r=28.025477707[/tex]
Area of the circle=[tex]\pi r^{2}[/tex]
[tex]3.14X[/tex][tex](28.025477707)^{2}[/tex]
[tex]2466[/tex]
Hence the area of a circle is 2466[tex]m^{2}[/tex]
2
Which fractions are equivalent to ? Choose ALL the correct answers.
4
4
6
4
6
8
6
12
57
Answer:
Step-by-step explanation:
4/4
8/6
4/6
Please help me with my question step by step
give brainliest.help
The required, team 3, tower garden donation shows the proportional relationship between weeks and donation,
What is proportionality?Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.
here,
From the table,
The ratio of a week to the donation of the individual team must be the same as the ratio of the preceding week and the donation of the respective team,
So,
Team 1,
1 / 1 = 2 / 3[1/4], false
Similarly, team 2 and team 4's relationship is also not proportional,
Now, team 3
1 / [2 1 / 3] = 2 / [4 2/3 ]
3 / 7 = 3/7
Thus, The necessary, team 3, tower garden gift illustrates the proportional relationship between weeks and donation.
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Solve for <1. (Will mark as brainiest!)
Answer:
< 1 = 64°
Step-by-step explanation:
First at all the sum of 2 angles should be 180°
< 3 + 116° = 180°
< 3 = 180 - 116
< 3 = 64°
Then, the sum of intern angles of a triangle must sum 180°, so:
< 1 + 52° + < 3 = 180°
< 1 +52 + 64 = 180
< 1 = 180 - 64 -52
< 1 = 64°
A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:
The firm has available to it on weekly basis, 480 hours of machining time, 400 hours of polishing time and 400 hours of assembling time. The unit profits on the product are Birr 360, Birr 240, Birr 360 and Birr 480, respectively.The firm has a contract with a distributor to provide 50 units of product I, and 100 units of any combination of products II and III each week. Through other customers the firm can sell each week as many units of products I, II and III as it can produce, but only a maximum of 25 units of product IV. How many units of each product should the firm manufacture each week to meet all contractual obligations and maximize its total profit? Make a mathematical model for the given problem. Assume that any unfinished pieces can be finished the following week.
Step-by-step explanation:
The firm should manufacture 50 units of product I, 100 units of product II, and 100 units of product III each week to meet all contractual obligations and maximize its total profit.
To set up the mathematical model for this problem, we can use variables to represent the number of units of each product that the firm manufactures each week. Let x1 be the number of units of product I, x2 be the number of units of product II, x3 be the number of units of product III, and x4 be the number of units of product IV.
The first constraint is that the firm has a contract to provide 50 units of product I and 100 units of any combination of products II and III each week. This can be represented as:
x1 = 50
x2 + x3 = 100
The second constraint is that the firm has a maximum of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time each week. The time required for each product can be represented as:
x16 + x28 + x34 + x410 <= 480 (machining time)
x14 + x26 + x32 + x48 <= 400 (polishing time)
x14 + x24 + x34 + x46 <= 400 (assembling time)
The third constraint is that the firm can sell as many units of products I, II, and III as it can produce, but only a maximum of 25 units of product IV. This can be represented as:
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
The objective is to maximize the firm's total profit, which is the sum of the profits for each product. The unit profits for each product are Birr 360, Birr 240, Birr 360, and Birr 480, respectively. The total profit can be represented as:
360x1 + 240x2 + 360x3 + 480x4
The complete mathematical model for this problem is:
Maximize: 360x1 + 240x2 + 360x3 + 480x4
Subject to:
x1 = 50
x2 + x3 = 100
x16 + x28 + x34 + x410 <= 480
x14 + x26 + x32 + x48 <= 400
x14 + x24 + x34 + x46 <= 400
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
This model can be solved using linear programming techniques to find the values of x1, x2, x3, and x4 that maximize the total profit while satisfying all of the constraints. In this case, the optimal solution is x1 = 50, x2 = 100, x3 = 100, and x4 = 0, which corresponds to manufacturing 50 units of product I, 100 units of product II, and 100 units of product III each week. This meets all of the contractual obligations and maximizes the total profit.
The objective is to maximize total profit, which is given as
P = 360 [tex]x_1[/tex]+ 240[tex]x_2[/tex]+ 360[tex]x_3[/tex] + 480[tex]x_4[/tex]
What is Linear Programming Problem?The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.
Let[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] and [tex]x_4[/tex] be the number of units of product I, II, III and IV to be produced, respectively.
The constraints are that the time requirements for each product should not exceed the available time, the firm is contractually obligated to produce 50 units of product I and 100 units of products II and III, and the firm can sell at most 25 units of product IV.
These constraints can be written mathematically as:
3[tex]x_1[/tex] + 2 [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + 4[tex]x_4[/tex] ≤ 480 (Machining)
[tex]x_1[/tex] + [tex]x_2[/tex] + [tex]x_3[/tex] + 3[tex]x_4[/tex] ≤ 400 (Polishing)
2[tex]x_1[/tex] + [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + [tex]x_4[/tex] ≤ 400 (Assembling)
and, [tex]x_1[/tex] ≥ 50 (Product I)
[tex]x_2[/tex] + [tex]x_3[/tex] ≥ 100 (Products II and III)
[tex]x_4[/tex] ≤ 25 (Product IV)
[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] , [tex]x_4[/tex] ≥ 0
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The quotient of a number and 5 plus 25 is no more than 45. What are the possible values for the number?
Answer:
The number can be any value less than or equal to 100.
Thus, it can be any number in this range: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]
Step-by-step explanation:
Firstly, let's convert the word problem into a math expression:
[tex]\frac{x}{5}+25\leq45[/tex]
We can now solve this inequality for the variable x.
[tex]\frac{x}{5} \leq 20[/tex]
[tex]x \leq 100[/tex].
Therefore x is any value less than or equal to 100.
What is the total area of the tiles Felix needs to buy?
By using the formula for area of parallelogram, it can be calculated that
Felix needs to buy 80 [tex]cm^2[/tex] of tiles
What is area of parallelogram?
Area of parallelogram is the total space taken by the parallelogram.
If b is the base of the parallelogram and h is the height of the parallelogram, then area of the parallelogram is calculated by the formula
Here,
Base of each parallelogram = 4cm
Height of each parallelogram = 2cm
Area of each parallelogram = 4 [tex]\times[/tex] 2 = 8 [tex]cm^2[/tex]
Area of 10 parallelograms = 8 [tex]\times[/tex] 10 = 80 [tex]cm^2[/tex]
Felix needs to buy 80 [tex]cm^2[/tex] of tiles
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Complete Question
The full diagram has been attached.
LAST ONE! DUE SOON! AND NEED HELP! REAL ANSWERS ONLY!!
Answer:
A.) All reptiles run fast
Step-by-step explanation:
Tortoises are reptiles that run slow, so they would be a counterexample to the conjecture that all reptiles run fast. This is because tortoises are a type of reptile that do not run fast, even though the conjecture states that all reptiles do.
In general, reptiles are a class of animals that includes many different species. Some reptiles, such as snakes and lizards, are known for their speed and agility. However, other reptiles, such as tortoises and turtles, are not known for their speed and tend to move much slower than other reptiles. This shows that the conjecture that all reptiles run fast is not always true, and tortoises are a counterexample to this conjecture.
In addition to their speed, tortoises are also distinguished by their hard shells and thick legs. They are typically found in warm, dry environments, and they are known for their long lifespan and low metabolic rate. They are also typically herbivores, feeding on a diet of plants and vegetation. This is in contrast to other reptiles, such as snakes and lizards, which are often carnivorous and hunt for their food. Overall, tortoises are a unique and interesting group of reptiles that do not always fit the generalizations made about reptiles.
The mean value of land and buildings per acre from a sample of farms is $1200, with a standard deviation of $100. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? $1064 $1417 $1373 $856 $1250 $1102
Answer:
The empirical rule states that for a bell-shaped distribution, approximately 68% of the data values will fall within one standard deviation of the mean, 95% of the data values will fall within two standard deviations of the mean, and 99.7% of the data values will fall within three standard deviations of the mean.
Using this information, we can calculate the range of values that fall within two standard deviations of the mean for the given data set:
Mean: $1200
Standard deviation: $100
Two standard deviations: $200
Therefore, the range of values that fall within two standard deviations of the mean is $1200 - $200 = $1000 to $1200 + $200 = $1400.
With this information, we can determine which of the given data values are unusual (more than two standard deviations from the mean):
$1064 is within two standard deviations of the mean.
$1417 is outside of two standard deviations of the mean.
$1373 is within two standard deviations of the mean.
$856 is outside of two standard deviations of the mean.
$1250 is within two standard deviations of the mean.
$1102 is within two standard deviations of the mean.
Therefore, the data values $1417 and $856 are unusual (more than two standard deviations from the mean).
We can also determine which of the given data values are very unusual (more than three standard deviations from the mean) using the same process. The range of values that fall within three standard deviations of the mean is $1000 to $1600. With this information, we can see that none of the given data values are very unusual (more than three standard deviations from the mean).
find the range for the measure of the third side of a triangle when the measures of the other two sides are 7 km and 29 km.
22>x>36 is the range for the third side's measurement when two sides of a triangle are measured at 7 km and 29 km.
Given that,
When the other two sides of a triangle are measured at 7 km and 29 km.
We have to determine the range for the third side's measurement.
We know that,
Take the measured sides.
7 km and 29 km
So, we can write as
The two sides added together are greater than the third side.
So, take one side as x
We get,
7+x>29
Taking 7 to the right side we get negative 7
x>29-7
x>22
Now taking 29 to left side and x to sides
7+29>x
36>x
Therefore, 22>x>36 is the range for the third side's measurement when two sides of a triangle are measured at 7 km and 29 km.
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Hello I have to develop that (x-1)(x+2) I know that it makes x²+x-2 but I don't understand why, can you explain me ?
Answer:
pls rate as brainliest it will go a long way
Step-by-step explanation:
(x–1)(x+2)
STEP 1
using the first bracket to expand the other
= x(x + 2) –1(x + 2)
= x² + 2x –x –2
= x² + x – 2
Step 2
or by using the other bracket to expand the other
(x – 1)(x + 2)
x(x – 1) + 2(x – 1)
= x² – x + 2x – 2
= x² + x – 2
Using three mixed numbers as side lengths draw an equilateral triangle with a perimeter of 8 and 1/4 feet.
The side of the equilateral triangle is 2 ³/4 feet, having perimeter 8 ¹/₄ feet.
What is an equilateral triangle?If all three of a triangle's sides are the same length, the triangle is said to be equilateral. Congruent sides refer to sides that have the same length, and they characterize an equilateral triangle.
Given that,
The perimeter of equilateral triangle = 8 ¹/₄ feet.
Simplify the rational term.
8 ¹/₄ = (32 + 1) / 4 = 33 /4.
Let each side of an equilateral triangle is a feet.
The perimeter of the equilateral triangle = 3a
Since, 3a = 33/4
a = 11/4
a = 2 ³/4
The required side of the equilateral triangle is 2 ³/4.
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NO LINKS!! Determine whether the sequence is geometric.
2, 4/√(3) , 8/3, 16/3√(3) , . . .
Choose:
1. Yes, the sequence is geometric
2. No, the sequence is not geometric
If so, find the common ratio. (if the sequence is not geometric, enter NONE)
Geometric sequence has a common ratio.
Let's verify is the ratio of subsequent terms is common:
[tex]r=t_2/t_1=(4/\sqrt{3})/2 = 2/\sqrt{3} =2\sqrt{3}/3[/tex][tex]r=t_3/t_2=(8/3)/(4/\sqrt{3}) = 2/\sqrt{3} =2\sqrt{3}/3[/tex][tex]r=t_4/t_3=(16/3\sqrt{3})/ (8/3) = 2/\sqrt{3} =2\sqrt{3}/3[/tex]As wee se the ratio is common, it confirms that the sequence is geometric.
Common ratio is:
[tex]r=2\sqrt{3}/3[/tex]Answer:
Yes, the sequence is geometric.
[tex]\textsf{Common ratio}=\dfrac{2\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Given sequence:
[tex]2, \; \dfrac{4}{\sqrt{3}},\; \dfrac{8}{3},\;\dfrac{16}{3\sqrt{3}},\;...[/tex]
A geometric sequence has a common ratio.
Therefore, to check if the given sequence has a common ratio, divide each term by the previous term:
[tex]\boxed{\begin{aligned}\dfrac{16}{3\sqrt{3}} \div \dfrac{8}{3}&=\dfrac{16}{3\sqrt{3}} \times \dfrac{3}{8}\\\\&=\dfrac{48}{24\sqrt{3}}\\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}\dfrac{8}{3} \div \dfrac{4}{\sqrt{3}}&=\dfrac{8}{3} \times \dfrac{\sqrt{3}}{4}\\\\&=\dfrac{8\sqrt{3}}{12}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned} \dfrac{4}{\sqrt{3}} \div 2&= \dfrac{4}{\sqrt{3}} \times \dfrac{1}{2}\\\\&= \dfrac{4}{2\sqrt{3}} \\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]
As there is a common ratio, the sequence is geometric.
The common ratio is:
[tex]\dfrac{2\sqrt{3}}{3}[/tex]Match the metric units on the left with their
approximate equivalents on the right. Not all the
options on the right will be used.
1 meter
kilogram
1 liter
1 cup
I mile
2
pounds
1 quart
I yard
Answer:
meter - yard
kilogram - 2 pounds
liter - quart
A tent pole that is 8 feet tall is secured to the ground with a piece of rope that is 17 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
40 feet
30 feet
15 feet
9 feet
The distance between the tent pole to the rope along the ground is 15 feet.
What is a cone?
A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.
Given that length of the tent pole is 8 feet.
The angle between the tent pole and the ground is 90°.
Thus the tent pole, the rope and the ground form a right angle triangle.
According too Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the legs.
Here the legs of the right angle triangle is the tent pole and the the distance the tent pole to the rope along the ground.
Assume that the distance the tent pole to the rope along the ground be x.
The length of the rope is 17 feet which is hypotenuse of the right angle triangle.
Therefore,
x² + 8² = 17²
x² + 64 = 289
x² = 225
x = 15
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Answer: 15 feet
Step-by-step explanation:
first we grab 17 feet a square it
17^2 = 289
then we square 8 feet
8^2 = 64
subtract
289-64= 225
what squared equals 225?
15 does
NO LINKS!! Find the specified term of the geometric sequence.
a6: a1 = 3, a2= 18, a3= 108, . . .
a6=
Answer:
23328
Step-by-step explanation:
since it is a geometrics sequence we will use the formula
[tex] {ar}^{n - 1} [/tex]
The first term(a) = 3
The second term = ar = 18
divide the first term and second term to find the common ratio
[tex] \frac{t2}{t1} = \frac{ar}{a} = \frac{18}{3} [/tex]
r = 6
Now lets find the sixth term
[tex]t6 = {ar}^{6 - 1} [/tex]
[tex]t6 = {ar}^{5} [/tex]
by substituting for the values
[tex]t6 = 3 \times {6}^{5} [/tex]
= 3 × 7776
= 23328
i hope this helped
Answer:
[tex]a_{6} = 23,328[/tex]
Step-by-step explanation:
⭐ Geometric Progression formula: [tex]a_{n} = a_1(b)^{n-1}[/tex]
[tex]a_{1}[/tex] is the first term of the geometric progression[tex]b[/tex] is the common ratio (the number each term gets multiplied by)[tex]a_{n}[/tex] is the notation for which term you are finding, where n is the term numberWe are given that [tex]a_{1}[/tex] = 3. Now, we need to find b.
b is the quotient of [tex]\frac{a__3}{a__2}[/tex].
[tex]\frac{a_3}{a_2}\\ \\\frac{108}{18}\\= 6[/tex][tex]b[/tex] = 6Let's substitute the first term and common ratio into the formula.
[tex]a_n = 3(6)^{n-1}[/tex]
The problem wants us to solve for the 6th term, so we have to substitute 6 for n and solve.
[tex]a_6 = 3(6)^{6-1}\\a_6 = 3(6)^5\\a_6 = 3(7,776)\\a_6 = 23,328[/tex]
Enter the x,y value in the text box below for the following table of values where the x value is -2
y = 3x + 4
Answer:
x=-2
y = 3× -2 + 4
y= -6 + 4
y = -2
Two angles are complementary. The measure of one angle is 17 degrees. What is the measure of the other angle?
The measure of the other angle is 73°.
What are complementary angles?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.
How do you find a complementary angle?
Two angles are said to be complimentary if their sum is 90 degrees. So, to find the complement of an angle, subtract it from 90.
Here, we have
Given
Two angles are complementary. If one measures 17 degrees.
Complementary angles are two angles that add up to exactly 90 °.
∠A + ∠B = 90°
17 + ∠B = 90°
∠B = 90 - 17
∠B = 73°
Hence, the measure of the other angle is 73°.
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