From the principal mathematical induction, the inequality, 2ⁿ > n², where n belongs to integers, is true for all integers greater than four, i.e., n > 4.
We have to prove the inequality 2ⁿ > n², for all integer greater than 4. For this we use mathematical induction method. The principle of mathematical induction is one of method used in mathematics to prove that a statement is true for all natural numbers.
Step 1 : first we consider case first for n= 5 , here 2⁵ = 32 and 5² = 25, so 2⁵ > 5²
Thus it is true for n = 5.
Step 2 : Now suppose it's true for some integer k such that n≤ k, that is 2ᵏ > k²--(1)
Step 3 : Now, we have to prove it's true for n = k + 1. So, 2ᵏ⁺¹ = 2ᵏ. 2
2ᵏ⁺¹ = 2ᵏ.2 > 2k² ( since, 2ᵏ > k² )
> 2k² = k² + k²
> k² + 2k + 1 ( since, k² > 2k + 1 ,k > 3)
> ( k +1)² = k² + 2k + 1
=> 2ᵏ⁺¹ > (k+1)²
So, we proved it for n = k + 1. Hence, this theorem is true for all n.
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Write the number in standard form 7. 1x10^4=
The number 7.1 x 10⁴ in standard form is: 71,000
In standard form, a number is expressed as a coefficient multiplied by a power of 10, where a coefficient is a number greater than or equal to 1 and less than 10, and the power of 10 represents the number of places the decimal point must be moved to obtain the number's value.
In this case, the coefficient is 7.1, which is greater than or equal to 1 and less than 10. The power of 10 is 4, which means that the decimal point must be moved 4 places to the right to obtain the value of the number. Therefore, we get 71,000.
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a large sports supplier has many stores located world wide. a regression model is to be constructed to predict the annual revenue of a particular store based upon the population of the city or town where the store is located, the annual expenditure on promotion for the store and the distance of the store to the center of the city.
The use of regression modeling in retail analytics can help businesses make data-driven decisions that ultimately lead to increased profits and growth.
Based on the information given, it seems that the large sports supplier is interested in predicting the annual revenue of a particular store based on various factors, such as population, promotion expenditure, and distance from the city center. This is a common approach in retail analytics, where regression models are often used to predict sales or revenue based on different variables.
By constructing a regression model, the sports supplier can gain valuable insights into which factors are most strongly associated with revenue, and how they can optimize their operations to increase sales. For example, they may find that stores located closer to the city center tend to have higher revenue, or that increased promotion expenditure leads to a greater increase in revenue in smaller towns.
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How many different simple random samples of size 4 can be obtained from a population whose size is 48? The number of simple random samples which can be obtained is ____. (Type a whole number.)
The number of simple random samples of size 4 that can be obtained from a population of size 48 is 194,580.
To find the number of different simple random samples of size 4 that can be obtained from a population whose size is 48, we can use the combination formula. The combination formula is written as:
C(n, k) = n! / (k!(n-k)!)
where n is the population size (48), k is the sample size (4), and ! denotes a factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1).
So, in this case:
C(48, 4) = 48! / (4!(48-4)!)
C(48, 4) = 48! / (4!44!)
C(48, 4) = (48 × 47 × 46 × 45) / (4 × 3 × 2 × 1)
C(48, 4) = 194580
Therefore, the number of simple random samples of size 4 that can be obtained from a population of size 48 is 194,580.
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1. Find the component form and magnitude of the vector AB with
the following initial and terminal points.
i. A(12, 41), B(52, 33)
ii. A(8, 14), B(12, 3)
iii. A(9, -2, 5), B(8, 5, 11) (3D space)
i. To find the component form of the vector AB, we subtract the coordinates of A from the coordinates of B:
AB = <52 - 12, 33 - 41> = <40, -8>
To find the magnitude of the vector AB, we use the formula:
|AB| = sqrt((40)^2 + (-8)^2) = sqrt(1600 + 64) = sqrt(1664) ≈ 40.79
ii. Similarly, we find the component form of AB:
AB = <12 - 8, 3 - 14> = <4, -11>
And the magnitude of AB:
|AB| = sqrt((4)^2 + (-11)^2) = sqrt(157) ≈ 12.53
iii. To find the component form of AB in 3D space, we subtract the coordinates of A from the coordinates of B:
AB = <8 - 9, 5 - (-2), 11 - 5> = <-1, 7, 6>
To find the magnitude of AB, we use the formula:
|AB| = sqrt((-1)^2 + (7)^2 + (6)^2) = sqrt(86) ≈ 9.27
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an auditorium can see 1800 and there's always a capacity for shells the owner wants to increase revenue by raising ticket prices tickets currently cost $6.00 and he estimates that for each $0.50 increase in price 100 few people were 10 what pressure he said it takes to make the most money based on this scenario
HELPP
Answer:
Step-by-step explanation:
To find the optimal ticket price that will maximize revenue, we need to determine the price point where the increase in revenue from selling each ticket at a higher price is greater than the decrease in revenue from selling fewer tickets due to the higher price.
Let's start by calculating the current revenue generated at the current ticket price of $6.00:
Current revenue = 1800 x $6.00 = $10,800
Now, we need to determine the effect of increasing ticket prices by $0.50 on the number of tickets sold:
For each $0.50 increase in ticket price, 100 fewer people will attend. So, for a $0.50 increase, the new ticket price will be $6.50, and the number of attendees will be:
1800 - 100 = 1700
For a $1.00 increase, the new ticket price will be $7.00, and the number of attendees will be:
1700 - 100 = 1600
And so on.
We can create a table to calculate the revenue at different price points:
Ticket Price Number of Tickets Sold Revenue
$6.00 1800 $10,800
$6.50 1700 $11,050
$7.00 1600 $11,200
$7.50 1500 $11,250
$8.00 1400 $11,200
$8.50 1300 $11,050
$9.00 1200 $10,800
As we can see from the table, the optimal ticket price that will maximize revenue is $7.50, where the revenue is $11,250. Beyond this point, the decrease in attendance outweighs the increase in ticket price, resulting in a decrease in revenue.
Therefore, the owner should increase the ticket price to $7.50 to maximize revenue.
How do I solve for the angle and X
The measure of angle x in the given right triangle is 71.8°
Calculating the measure of an angle x in the right triangleFrom the question, we are to determine the measure of angle in the given triangle
The given triangle is a right triangle
We can determine the value of angle x by using SOH CAH TOA
sin (angle) = Opposite / Hypotenuse
cos (angle) = Adjacent / Hypotenuse
tan (angle) = Opposite / Adjacent
In the given triangle,
Adjacent = 5
Hypotenuse = 16
Thus,
cos (x) = 5/16
x = cos⁻¹ (5/16)
x = 71.7900°
x ≈ 71.8°
Hence, the measure of angle x is 71.8°
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The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.6% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick nine first-time, full-time freshmen from the survey. You are interested in the number that believes that same-sex couples should have the right to legal marital status. What is the standard deviation (σ)?
The standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.
To find the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students, we need to use the binomial distribution.
Given that 71.6% of all first-time, full-time freshmen believe that same-sex couples should have the right to legal marital status, the probability (p) that a randomly selected student from this population believes this is:
p = 0.716
Since we are interested in the number of students in a sample of nine who believe this, we can model this using the binomial distribution with parameters n = 9 and p = 0.716.
The formula for the standard deviation of a binomial distribution is:
σ = sqrt(n * p * (1 - p))
Substituting in the values of n and p, we get:
σ = sqrt(9 * 0.716 * (1 - 0.716))
σ = 1.168
Therefore, the standard deviation (σ) of the number of students who believe that same-sex couples should have the right to legal marital status among a random sample of nine students is approximately 1.168.
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Find all real zeros of the function.
h(x)=-5x(x−2)(16)
If there is more than one answer, separate them with commas.
zero(s):
00
X
The zeroes of the function as required to be determined in the task content are; 0, 2, -4, 4.
What are the real zeroes of the function?It follows from the task content that the zeroes of the given function; f(x) = -5x (x - 2) (x² - 16) is to be determined.
To determine the zeroes; we have;
-5x = 0; x = 0
x - 2 = 0; x = 2
x² - 16 = 0; x² = 16; x = ± 4.
Ultimately, the zeroes of the function are; 0, 2, -4, 4.
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which equation is true when n = 5? A) 2n = 7 B) n + 3 =8 C) 9 -n = 14 D) n/15 = 3
The answer is B.
In order to get the answer, you replace the letter n to 5 and workout the problems to see which one is true.
B is the answer because n + 3 = 8
5 + 3 = 8
Answer:
B
Step-by-step explanation:
n+3 =
5+3=
Triangle BHY is shown, where m
mLNYB= (3x +81)°.
H
B
a. Determine the value of x. Show your work.
Y
N
The value of x is equal to 17.
What is the exterior angle theorem?In Mathematics, the exterior angle theorem or postulate is a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.
By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the triangle BHY is equal to the measure of angle x (∠NYB);
m∠BHY + m∠HBY = m∠NYB
(2x + 7)° + (8x - 18)° = (4x + 91)°
10x - 11 = 4x + 91
10x - 4x = 91 + 11
6x = 102
x = 102/6
x = 17.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
a 6. Let Xn be a bounded martingale and let T be a stopping time (NOT necessarily bounded). Prove that E[XT] = E[X] by considering the stopping times Tn= min(T, n).]
For a bounded martingale Xₙ and stopping time T (not necessarily bounded), E[XT] = E[X] is proved by considering the stopping times Tₙ= min(T, n) and using the Optional Stopping Theorem.
To prove that E[XT] = E[X], we can utilize the Optional Stopping Theorem.
First, we know that since Xₙ is a bounded martingale, it satisfies the conditions for the Optional Stopping Theorem stating that for any stopping time T, [tex]E[X_{T}] = E[X_{0}][/tex], where [tex]X_{0}[/tex] is the initial value of Xₙ.
Now, taking into consideration stopping times Tn = min(T, n). As Tn is a bounded stopping time, we utilize the Optional Stopping Theorem to get:
[tex]E[X_{Tn}] = E[X_{0}][/tex]
We can rewrite this as:
[tex]E[X_{Tn}] - E[X_{0}] = 0[/tex]
Now, if we take the limit as n→∞.As Xn is a bounded martingale, it follows that E[|Xn|] < infinity for all n. Thus, utilizing Dominated Convergence Theorem, we get:
[tex]lim_{n} E[X_{Tn}] = E[lim_{n} X_{Tn}] = E[XT][/tex]
Similarly, [tex]lim_{n} E[X_{0}] = E[X].[/tex]
Therefore, taking the limit as n→∞ in our previous equation, we get:
E[XT] - E[X] = 0
Or, equivalently:
E[XT] = E[X]
So, E[XT] = E[X] by considering the stopping times Tn= min(T, n)].
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Parker has 9 gallons of water. How many quarts of water does he have?
Answer: 36 quarts
Step-by-step explanation:
pretty much just do 9 * 4 qts
hope this helped!!
Answer: Parker has 36 Quarts of water.
We are given the following:
Parker has 9 gallons of water.We are asked to find:
How many Quarts of Water does he have.This question strictly revolves the around the conversion of units. In other words, in order to answer this question, we must know how many quarts are in a gallon.
Fortunately, we know that 4 quarts = 1 gallon.
Since Parker possesses 9 gallons of water, we would do [tex]4*9=36[/tex]. Arriving us at our answer of 36 quarts of water.
Parker has 36 quarts of water.
(b) What is the probability of obtaining x= 126 or more individuals with the characteristic? That is, what is P(p20.63)?
P(p≥ 0.63)=
(Round to four decimal places as needed.)
in example
Get more help.
G
The probability of obtaining 126 or more individuals with the characteristic, P(p ≥ 0.63) is 0.5.
What is the probability?The binomial distribution is used to approximate the probability.
The mean of the binomial distribution is np is 200 * 0.63
mean = 126
The standard deviation is √(np(1-p)) = √(200 * 0.63 * 0.37)
standard deviation = 5.18.
Standardize the random variable p as follows:
z = (x - μ) / σ
z = (126 - 126) / 5.18 = 0
Using a calculator to find the probability of z being greater than or equal to 0, the given probability is 0.5.
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Q.5.f(x,y) = x + y; if both x & y are even f(x,y) = x - y; if both & y are odd f(x, y) = 2x – y2, if any one of them is odd & other is = even. Find f(2,3) - f(2,4) a)-31 b) -56 c)-11 d) -13
f(x,y) = x + y; if both x & y are even f(x,y) = x - y; if both & y are odd f(x, y) = 2x – y2, if any one of them is odd & other is = even. Then the result of f(2,3) - f(2,4) is -11, which corresponds to option c).
Determining f(2,3)
Since x = 2 (even) and y = 3 (odd)
Then, the function definition for this case is f(x,y) = 2x - y²
f(2,3) = 2(2) - 3² = 4 - 9 = -5
Determining f(2,4)
Since x = 2 (even) and y = 4 (even)
Then, the function definition for this case is f(x,y) = x + y.
f(2,4) = 2 + 4 = 6
Now, Calculating f(2,3) - f(2,4)
f(2,3) - f(2,4) = -5 - 6 = -11
Therefore, the answer is option c) -11.
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2) A gho with a cost price of Nu 750 was sold for Nu 900. What was the percent markup?
The percent markup is 20%
The selling price of the Nu is 900
The cost price of the Nu is 750
The percent markup can be calculated as follows
= 900-750/750 × 100
= 150/750 × 100
= 0.2 × 100
= 20%
Hence the percent markup is 20%
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Nayeli has a points card for a movie theater.
• She receives 40 rewards points just for signing up.
• She earns 14.5 points for each visit to the movie theater.
• She needs at least 185 points for a free movie ticket.
Use the drop-down menu below to write an inequality representing v, the number of
visits she needs to make in order to get a free movie ticket.
An inequality representing v, the number of visits Nayeli needs to make to get a free movie ticket is 40 + 14.5v ≥ 185.
What is inequality?Inequality describes a mathematical statement that states that two or more algebraic expressions are unequal.
Inequalities are represented as:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The rewards points Nayeli has just for signing up = 40
The points earned per visit to the movie theater = 14.5
The total number of points required for a free movie ticket ≥ 185
Let the number of visits Nayeli needs to make too get a free movie ticket = v
Inequality:40 + 1.45v ≥ 185
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The probability assigned to each experimental outcome must be
a. one
b. between zero and one
c. smaller than zero
d. any value larger than zero
The probability assigned to each experimental outcome must be: b. between zero and one
The probability assigned to each experimental outcome must be between zero and one. This is because probability is a measure of how likely an event is to occur, and it cannot be negative or greater than 100%. A probability of zero means that the event will not occur, while a probability of one means that the event is certain to occur. Probabilities between zero and one indicate the likelihood of an event occurring, with higher probabilities indicating greater likelihood. It is important for probabilities to add up to one across all possible outcomes, as this ensures that all possible events are accounted for and that the total probability is normalized. Probability theory is used in many fields, including statistics, finance, and engineering, and is essential for making informed decisions based on uncertain events. By assigning probabilities to different outcomes, we can calculate expected values and make predictions about future events, helping us to better understand the world around us.
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Show your calculation steps dearly Correct you answer to 4 decimal places and report the measurement unit when applicable. Question 1 (10 marks) A salad shop is selling fruit cups. Each fruit cup consists of two types of fruit, strawberries and blue berries. The weight of strawberries in a fruit cup is normally distributed with mean 160 grams and standard deviation 10 grams. The weight of blue berries in a fruit cup is normally distributed with mean u grams and standard deviation o grams. The weight of strawberries and blue berries are independent, and it is known that the weight of a fruit cup with average of 300 grams and standard deviation of 15 grams. (a) Find the values of u and o (b) The weights of the middle 96.6% of fruit cups are between (300 - K. 300 + K) grams. Find the value of K.
C) The weights of the middle 96.6% of fruit cups are between (L1, L2) grams. Find the values of LI and L2.
(a) The values of u is 140 g and o is 13.42 g. (b) The value of K in (300 - K. 300 + K) grams is 27.15 g. C) The weights of the middle 96.6% of fruit cups are between (L1, L2) grams. The values of LI is 272.85 g and L2 is 327.15 g.
(a) The mean weight of blueberries is:
300 g - 160 g = 140 g
The standard deviation of the weight is:
Var(X + Y) = Var(X) + Var(Y)
Adding the variances:
15^2 = 10^2 + o^2
Solving for o:
o = sqrt(15^2 - 10^2) = 13.42 g
Therefore, the values of u and o are u = 140 g and o = 13.42 g.
(b) Since the distribution is normal, we can use the standard normal distribution to find K.
The middle 96.6% of a standard normal distribution corresponds to the interval (-1.81, 1.81) (using a table or calculator). Therefore,
K = 1.81 * 15 = 27.15 g
Therefore, the weights of the middle 96.6% of fruit cups are between 300 - 27.15 = 272.85 g and 300 + 27.15 = 327.15 g.
(c) Using the standard normal distribution to find the corresponding interval on the standard normal scale:
(-1.81, 1.81)
We can then scale this interval to the distribution of the weight of fruit cups by dividing by the standard deviation and multiplying by 15 g:
L1 = 300 + (-1.81) * 15 = 272.85 g
L2 = 300 + 1.81 * 15 = 327.15 g
Therefore, the weights of the middle 96.6% of fruit cups are between 272.85 g and 327.15 g.
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Tom bought $72 worth of merchandise at a yard sale and sold it for $84 at a flea market. To the nearest percent, by what percent did he increase his investment?
Tom increased his investment by 16.67% percent when he sold the merchandise at the flea market.
Given that Tom bought $72 worth of merchandise at a yard sale
Tom sold it for $84 at a flea market.
We have to find the percent did he increase his investment
Tom's initial investment was $72, and he sold the merchandise for $84. The difference between these amounts is:
$84 - $72 = $12
To express this difference as a percentage of his initial investment, we can use the formula:
percent increase = (difference / initial investment) x 100%
Substituting the values we have:
percent increase = ($12 / $72) x 100%
= 0.1667 x 100%
= 16.67%
Hence, Tom increased his investment by approximately 16.67% when he sold the merchandise at the flea market.
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Look at picture! It is all written there
Answer:
In/out
-18, -19
-17, -18
-15, -16
-7, -8
0, -1
14, 13
Step-by-step explanation:
the rule states "subtract 1" so if you look at the In, -15 for example goes to -16 for the out which proves that -15-1 is -16. so for all the In's you subtract each number by 1. to FIND a In from the out you just add 1. So just follow the rules and look at the rules carefully!
in (x-2)+in(x+1)=2
x = -2.6047
x = 4.2312
x = 3.652
x = 3.6047
Answer:
Step-by-step explanation:
The number in your question is expressed in scientific notation, which is typically used to express numbers that are either too large or too small. The number in scientific notation is expressed as a power of 10. A positive exponent means the # is large whereas if the exponent is negative, then the # is small.
3.652 x 10-4 --> negative exponent, therefore, # is small.
All you need to do is to convert this number to standard notation by moving the decimal 4 places to the left.
3.652 x 10-4 = 0.0003652
Part B What will be the area, in square inches, of the piece of sheet metal after both sections are cut and removed?
The dimensions of section B are 36 inches by 48 inches, and the area of the piece of sheet metal after both sections are cut and removed is 6336 square inches.
Given the width and length of a rectangular piece of sheet metal as 60 inches and 44 inches, we need to find the dimensions of section B and the area of the piece of sheet metal after both sections are cut and removed.
The length of rectangle B can be found as TR = SR - ST = PQ - ST, where SR and PQ are opposite sides of the rectangle. Here, PQ is the length of the rectangular sheet metal, which is 60 inches, and ST is the width of the rectangle WVTX, which is 24 inches. Therefore, the length of rectangle B is:
TR = PQ - ST = 60 - 24 = 36 inches
The breadth of rectangle B can be found as UR = QR - QV - VT - TU. Here, QR and PS are opposite sides of the rectangle PQRS, so QR = PS = 144 inches. Also, QV is the width of rectangle WVTX, which is 36 inches, and VT and TU are the lengths of rectangle WVTX, which are both 24 inches. Therefore, the breadth of rectangle B is:
UR = QR - QV - VT - TU = 144 - 36 - 24 - 36 = 48 inches
So, the dimensions of section B are 36 inches by 48 inches.
Next, we need to find the area of the piece of sheet metal after both sections are cut and removed.
The area of rectangle B is the product of its length and breadth, which is:
Area of rectangle B = length × breadth = 36 × 48 = 1728 square inches
The area of rectangle WVTX is the product of its length and breadth, which is:
Area of rectangle WVTX = length × breadth = 24 × 24 = 576 square inches
The area of rectangle PQRS is the product of its length and breadth, which is:
Area of rectangle PQRS = PQ × PS = 60 × 144 = 8640 square inches
Therefore, the area of the piece of sheet metal after both sections are cut and removed is:
Area of the piece of sheet metal = Area of rectangle PQRS - Area of rectangle B - Area of rectangle WVTX
= 8640 - (1728 + 576)
= 8640 - 2304
= 6336 square inches
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Kim made 3 batches of this fruit punch recipe. Combine: 70 milliliters of strawberry juice 500 milliliters of pineapple juice 2 liters of apple juice How many liters of fruit punch did Kim make?
For made a fruit punch, Kim used the 3 batches of this fruit punch recipe. From unit conversion, the total quantity in litres used to fruit punch is equals to the 2.570 L.
We have Kim made 3 batches of this fruit punch recipe. It includes the combination of following,
quantity of strawberry juice = 70 mL
quantity of apple juice = 2 L
quantity of pineapple juice = 500 mL
We have to determine the number of liters of fruit punch he made. Using the unit conversion,
one liters = 1000 mililiters
=> 1 mL = 0.001 L ( conversion factor)
so, quantity of strawberry juice = 70 mL = 70× 0.001 L = 0.070 mL
quantity of pineapple juice = 500 mL = 500× 0.001 L = 0.500 L
So, total quantity of fruit punch made by Kim in liters = strawberry juice + pineapple juice + apple juice
= 0.070 L + 0.500 L + 2 L
= 2.570 L
Hence, the required value is 2.570 liters.
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on a coordinate plane, kite h i j k with diagonals is shown. point h is at (negative 3, 1), point i is at (negative 3, 4), point j is at (0, 4), and point k is at (2, negative 1).
On a coordinate plane, kite HIJK with diagonals is shown. Point H is located at (-3, 1), point I is at (-3, 4), point J is at (0, 4), and point K is at (2, -1). The diagonals of this kite connect points H and J, and points I and K, creating an intersecting pattern within the shape.
Based on the information provided, we know that a kite shape has been loaded onto a coordinate plane with points h, i, j, and k located at specific coordinates. The coordinates for point h are (-3, 1), for point i are (-3, 4), for point j are (0, 4), and for point k are (2, -1). Additionally, we know that the kite has diagonals, but we are not given any information about their lengths or intersection points.
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Answer:
B is the answer
Step-by-step explanation:
Find the volume of the prism
Answer:
Volume formal= L × W × W
Volume formal= 6 × 8 × 9
Answer= 6×8×9= 432
Use polar coordinates to find the volume of the given solid.
Enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3
-x2 - y2 + 9 = 6 >>> x2 + y2= 3 so r2 = 3 >>> squart 0<=r <=3
My question is that why negative square root of 3 is not included in the range???
In polar coordinates, the radial distance "r" is defined as the distance from the origin to a point in the plane. Since distance cannot be negative, we only consider the positive square root of 3 in the range for this problem. So, the correct range for "r" is 0 ≤ r ≤ √3, and negative square root of 3 is not included because it doesn't represent a valid distance in polar coordinates.
To find the volume of the given solid enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3 using polar coordinates, we need to express the equation of the hyperboloid in terms of polar coordinates.
Substituting x = rcosθ and y = rsinθ, we get:
−r2cos2θ − r2sin2θ + z2 = 6
Simplifying, we get:
z2 = 6 - r2
Since the plane z = 3 intersects the hyperboloid, we have:
3 = √(6 - r2)
Solving for r, we get:
r = √3
Hence, the range for r is 0 ≤ r ≤ √3.
In summary, the negative square root of 3 is not included in the range of r because r represents a distance and cannot be negative. The volume of the solid can be found by integrating the function f(r,θ) = √(6 - r2) over the range 0 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π using polar coordinates. The result will be in cubic units and can be obtained by evaluating the integral.
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Which table shows a linear function
The table that shows a linear function include the following: B. table B.
What is a linear function?In Mathematics, a linear function is a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.
In this context, we have:
Slope = (0 - 2)/(-3 + 5) = (2 - 0)/(-3 + 1) = -1
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A pole 12 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Jamal measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
Answer:
The given question is on trigonometry which requires the application of required function so as to determine the value known. So that the length of the guy wire is 67.0 feet.
Trigonometry is an aspect of mathematics that requires the application of some functions to determine the value of an unknown quantity.
Let the length of the guy wire be represented by l, and the angle that the guy wire makes with the stake be θ. So that applying the appropriate trigonometric function to determine the value of θ, we have:
Tan θ =
�
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�
�
�
�
�
�
�
�
�
�
�
�
�
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adjacent
opposite
=
11
4
4
11
Tan θ = 2.75
θ =
�
�
�
−
1
Tan
−1
2.75
= 70.0169
θ =
7
0
�
70
o
Considering triangle formed by the tower and the stake to determine the value of l, we have;
Cos θ =
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�
�
�
�
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�
ℎ
�
�
�
�
�
�
�
�
�
hypotenuse
adjacent
Cos
7
0
�
70
o
=
23
�
l
23
l =
23
�
�
�
7
0
�
Cos70
o
23
=
23
0.3420
0.3420
23
l = 67.2515
l = 67 feet
The length of the guy wire is 67 feet.
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Find the value of sin N rounded to the nearest hundredth, if necessary
The value of the identity sin N = 3/5
How to determine the valueTo determine the value of the identity, we need to know the different trigonometric identities. These identities are;
cosinesinetangentcotangentsecantcosecantFrom the information given, we have that;
The angle of the triangle is N
The opposite side of angle N is 3
The hypotenuse side of angle N is 5
Using the sine identity, we have;
sin N = 3/5
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Which is the area of the rectangle?
A rectangle of length 150 and width 93. Inside the rectangle, there is one segment from one opposite angle of base to the base. The length of that segment is 155.
The area of the rectangle is 13, 950 square unit.
We have,
length = 150
width= 93
So, Area of rectangle
= length x width
= 150 x 93
= 13950 square unit.
Thus, the required Area is 13, 950 square unit.
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