The binomial probability distribution can be used to answer these questions. The formula for the binomial probability distribution is:
P(X=x) = C(n,x) * p^x * (1-p)^(n-x)
Where C(n,x) is the number of combinations of n items taken x at a time, p is the probability of success, and (1-p) is the probability of failure.
a. The probability that a single detection system will detect an attack is .86 (to 2 decimals).
b. If two detection systems are installed in the same area and operate independently, the probability that at least one of the systems will detect the attack is:
P(X>=1) = 1 - P(X=0)
P(X=0) = C(2,0) * .86^0 * (1-.86)^2 = .0196
P(X>=1) = 1 - .0196 = .9804 (to 4 decimals)
c. If three systems are installed, the probability that at least one of the systems will detect the attack is:
P(X>=1) = 1 - P(X=0)
P(X=0) = C(3,0) * .86^0 * (1-.86)^3 = .0027
P(X>=1) = 1 - .0027 = .9973 (to 4 decimals)
d. Based on the calculations, it is recommended that multiple detection systems be used. The probability of at least one system detecting an attack increases as the number of systems increases.
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Jazmin takes a ride share service home from the airport. The ride share service charges $5 as an initial cost to pick her up, and $2. 25 for every mile to her final destination. Jazmin's ride home cost a total of $38. 75. Write an equation to represent the situation. Let m represent the number of miles to her home
Answer ! :)
If Jazmin spent $38.75 on all
Then it would 15miles ( 15m ) to get home.
As your adding the extra $5 which starts the process.
Basically a equation could be:
(5 + 2.25 = 7.25) + ( 2.25 x 14 )
Extra info if needed more explanation: ( 2.25 x 14 = 31.5 ) Which 31.5 + 7.25 = 38.75
Info on counting:
7.25, 9.50, 11.75, 14, 16.25, 18.50, 20.75, 23, 25.25, 27.50, 29.75, 32, 34.25, 36.50, 38.75
The graphs below show the speed of a car over four different time periods. Which graph indicates the car slowing down and then stopping?
Answer:
(D)
Step-by-step explanation:
You want the graph that shows speed decreasing to zero.
Slowing"Slowing down" means speed is decreasing. On a graph of speed that is indicated by a negative slope.
StoppedWhen an object is stopped, its speed is zero. On a graph of speed, points on the horizontal axis indicate the speed is zero.
GraphThe attached graph shows the speed of a car that is slowing to a stop.
Need help with answer, than you!
Please help me with this and explain how you got it because I don’t really understand this.
Answer:YES
Step-by-step explanation:
you should write 1 instead of every x and 5 instead of every y.
6*1+2*5=6+10=16
1+3*5=1+15=16
there are two concentric circles, the radii for the circles are 15CM and 7CM. A diameter AB of the larger circle intersects the smaller circle at C and D. Find two possible values for AC.
Therefore, the two possible values for AC are approximately 13.266 cm and 16.734 cm.
In mathematics, what do circles represent?An assortment of similarly spaced out points in a plane make up a circle. The center is where the point is located, but the radius is the distance from the center. Two times the radius equals the diameter.
We can see that triangle ADC is a right triangle since it's inscribed in a semi-circle (the smaller circle). So we can use the Pythagorean theorem to find AC:
AC² = AD² - CD²
Since AD is the radius of the larger circle (15 cm) and CD is the radius of the smaller circle (7 cm), we have:
AC² = 15² - 7²
AC² = 176
AC = √(176)
AC ≈ 13.266 cm
So one possible value for AC is approximately 13.266 cm.
Now let's consider the other intersection point, D. We can see that triangle BDC is also a right triangle since it's inscribed in a semi-circle (the smaller circle). So we can use the Pythagorean theorem again to find BD:
BD² = BC² + CD²
Since BC is the radius of the larger circle (15 cm) and CD is the radius of the smaller circle (7 cm), we have:
BD² = 15² - 7²
BD² = 176
BD = √(176)
BD ≈ 13.266 cm
Since BD is a diameter of the larger circle, we have:
AC + BD = 2 * 15 = 30
So the other possible value for AC is:
AC = 30 - BD
AC ≈ 16.734 cm
Therefore, the two possible values for AC are approximately 13.266 cm and 16.734 cm.
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4. Kiran says that a solution to the equation x + 4 = 20 must also be a solution to the equation 5(x + 4) = 100. Write a convincing explanation as to why this is true.
Kiran is correct in saying that a solution to the equation x + 4 = 20 must also be a solution to the equation 5(x + 4) = 100. This is because the second equation is simply the first equation multiplied by 5. To see this, we can distribute the 5 on the left side of the second equation to get 5x + 20 = 100. We can then subtract 20 from both sides to get 5x = 80, and finally divide both sides by 5 to get x = 16.
Since x = 16 satisfies the first equation, it must also satisfy the second equation. This is because if we substitute x = 16 into the first equation, we get 16 + 4 = 20, which is true. If we substitute x = 16 into the second equation, we get 5(16 + 4) = 100, which is also true. Therefore, any solution to the first equation will also be a solution to the second equation when the second equation is just the first equation multiplied by a constant factor.
Answer:
Kiran is correct. To see why, let's first simplify the second equation, 5(x + 4) = 100, by multiplying both sides by 1/5:
5(x + 4) = 100
⇒ (1/5) * 5(x + 4) = (1/5) * 100
⇒ x + 4 = 20
Now we can see that the second equation simplifies to the first equation, x + 4 = 20. This means that any solution that satisfies the first equation (x + 4 = 20) will also satisfy the second equation (5(x + 4) = 100).
In other words, if we find a value of x that makes x + 4 = 20 true, then substituting that value of x into 5(x + 4) = 100 will also make it true. Therefore, any solution to the equation x + 4 = 20 will also be a solution to the equation 5(x + 4) = 100.
Step-by-step explanation:
Alberto compro 2 melones del mismo tamaño y juntos pesan 6kg.¿Cuántos gramos pesarán 7 melones iguales a los que compró Alberto?
Based on the above, the 7 melons together will weigh about 21,000 grams.
What is the melon about?We know that 2 melons of the same size together weigh 6 kg, therefore each melon weighs:
6kg / 2 = 3kg
To know how many grams the 7 melons weigh, we first need to know how many grams a kilogram weighs:
1kg = 1000g
So each melon weighs 3 kg * 1000 g/kg = 3000 g.
Therefore, 7 melons equal to the ones Alberto bought will weigh:
7 * 3000g = 21,000g
Therefore, the 7 melons together will weigh 21,000 grams.
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See text below
Alberto bought 2 melons of the same size and together they weigh 6 kg. How many grams will 7 melons equal to the ones Alberto bought weigh?
A cinema sells adult tickets and child tickets.
The cost of 2 adult tickets and 2 child tickets is £38.
The cost of 2 adult tickets and 5 child tickets is £59.
Work out how much the following cost:
a) 6 adult tickets and 6 child tickets.
b) 4 adult tickets and 7 child tickets.
c) 3 child tickets.
a) 6 adult tickets and 6 child tickets cost is £102. b) 4 adult tickets and 7 child tickets cost is £77 c) 3 child tickets cost is £21
Describe Elimination Method?The elimination method involves manipulating these equations to eliminate one of the variables. This is done by multiplying one or both of the equations by a constant so that the coefficients of one of the variables are equal in both equations, but with opposite signs. The equations are then added or subtracted, depending on the signs, to eliminate one of the variables.
Let x be the cost of one adult ticket and y be the cost of one child ticket.
From the given information, we can write two equations:
2x + 2y = 38 (equation 1)
2x + 5y = 59 (equation 2)
To solve for x and y, we can use elimination method.
Multiplying equation 1 by 5 and equation 2 by 2, we get:
10x + 10y = 190
4x + 10y = 118
Subtracting equation 2 from equation 1, we get:
6x = 72
x = 12
Substituting x = 12 into equation 1, we get:
2(12) + 2y = 38
2y = 14
y = 7
Therefore, one adult ticket costs £12 and one child ticket costs £7.
a) 6 adult tickets and 6 child tickets:
Cost = 6(£12) + 6(£7) = £102
b) 4 adult tickets and 7 child tickets:
Cost = 4(£12) + 7(£7) = £77
c) 3 child tickets:
Cost = 3(£7) = £21
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A coach buys 5 identical baseball bats for a total of $327.45 the bats are on sale for $14.50 off the regular price what is the regular price?
The regular price of one baseball bat is $80.40.
How is a discount calculated? What is a discount?A discount is a drop in a product's or service's price. It is often provided by the vendor as an inducement to lure customers into making a purchase. Often, the discount is indicated as a percentage or a dollar amount off the list price.
The standard price and the discount rate must be known in order to determine a discount. Often, the discount rate is expressed as a percentage. We multiply the usual price by the discount rate to determine the discount amount.
Given that, coach buys 5 identical baseball bats for a total of $327.45.
Thus,
5P = 327.45
P = 65.49
So one bat cost him 65.90.
Now, the regular cost of the bat will be:
Price = 65.90 + 14.50
Price = 80.40
Hence, the regular price of one baseball bat is $80.40.
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If LI = 25 cm and AC = 24 cm , what is the length of BC?
The length of the missing side of the given triangle ABC which is similar to triangle ILN would be = 7cm
How to calculate the length of the missing side of the given triangle?Given that triangle ILN and ABC are similar this shows that their sides are equal in measurement too.
Therefore, LI = 25cm = AB = c
AC = 24 cm = LN = b
BC = X = IN = a
Using the Pythagorean formula;
C² = a² + b²
25² = a² + 24²
625 = a² + 576
625 -576 = a²
a² = 49
a = √49
a = 7cm
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Evaluate using special products:
[tex]899^2-2*899*898+898^2[/tex]
please explain
The value of the given product or expression is =1,
An algebraic equation is said to have an algebraic identity if it is true regardless of the values of its variables. An equality that remains constant when the values of the variables change are known as an algebraic identity, to put it simply. Algebraic identities are routinely used to factor polynomials more rapidly and efficiently.
Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. The principles of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables. In an algebraic expression, both constants and variables can be employed. Any amount that is added before a variable and then multiplied by is a coefficient.
The given product can be solved by the algebraic identity,
[tex]a^2+2ab+b^2=(a+b)^2\\a^2-2ab+b^2=(a-b)^2[/tex]
[tex]899^2-2*899*898+898^2\\=(899-898)^2\\=1[/tex]
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The terminal side of an angle of 7 radians is in which quadrant?
According to the given information, the terminal side of an angle of 7 radians is in the second quadrant.
What is the terminal angle?
The terminal angle is the angle formed by the terminal side of an angle in standard position (i.e., with its initial side along the positive x-axis) and the nearest x-axis. It is typically measured in a counterclockwise direction from the positive x-axis.
An angle of 7 radians is greater than 2π radians (which is approximately 6.28 radians), so it corresponds to more than one full revolution around the unit circle.
To find the terminal side of an angle of 7 radians, we can subtract 2π radians (or 360 degrees) from 7 radians until the result is between 0 and 2π radians. We have:
[tex]$$7 \text{ radians} - 2\pi \text{ radians} \approx 1.716 \text{ radians}$$[/tex]
Since 1.716 radians is less than π radians (which is approximately 3.14 radians), the terminal side of an angle of 7 radians is in the second quadrant.
The terminal side of an angle of 7 radians is in the second quadrant.
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If A+B=O
then what's the relation between A and B
There are 52 cards in a standard deck of cards, with four of each type of card: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. Let event A be choosing a 7 out of a deck of cards. Identify the numbers of each of the following. Enter the probability as a fraction: Provide your answer below: There are cards in the sample space. There are cards in event A. There are cards in the sample space. There are cards in event A. P(A)=, is the probability that you choose a 7 out of the deck of cards.
The probability that you choose a 7 out of the deck of cards is P(A)= 1/13.
There are 52 cards in a standard deck of cards, with four of each type of card: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King. Let event A be choosing a 7 out of a deck of cards. Identify the numbers of each of the following:
There are cards in the sample space. There are cards in event A. There are cards in the sample space. There are cards in event A. Probability that you choose a 7 out of the deck of cards is P(A)= 1/13. There are 52 cards in a standard deck of cards, with four of each type of card: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.
We have to find out the probability of choosing 7 out of a deck of cards. The sample space is the total number of possible outcomes. Here, a standard deck of cards has 52 cards, so there are 52 possible outcomes. There are four 7s in the deck. So, there are 4 possible successful outcomes. Event A is defined as choosing a 7 out of a deck of cards.
Since there are four 7s, there are 4 possible outcomes in event A. Therefore, There are 52 cards in the sample space. There are 4 cards in event A. P(A) is the probability of choosing a 7 out of a deck of cards.
P(A) = number of successful outcomes/number of possible outcomes= 4/52= 1/13
Therefore, the probability that you choose a 7 out of the deck of cards is P(A)= 1/13.
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Jethro has sat 5 tests Each test was marked out of 100 and Jethro's mean mark for the 5 tests is 74 Jethro has to sit one more test that is also to be marked out of 100 Jethro wants his mean mark for all 6 tests to be at least 77 Work out the least mark that Jethro needs to get for the last test
Jethro must get a mark of 92 out of 100 for the last test to have a mean mark of at least 77 for all 6 tests.
To work out the least mark that Jethro needs to get for the last test, we can use the Mean formula: Mean = (Sum of all scores) / (Number of scores).
We know that the Mean of the 5 tests that Jethro has already sat is 74, so we can calculate the sum of the 5 test scores by multiplying the mean by the number of tests (74 x 5 = 370). We also know that Jethro wants his mean mark for all 6 tests to be at least 77, so the sum of all 6 test scores must be higher than (77 x 6 = 462).
To calculate the least mark Jethro needs to get for the last test, we can combine these two facts. We know the sum of the 5 test scores is 370, so the sum of all 6 test scores must be 462 or higher. This means the least mark Jethro needs to get for the last test must be (462 – 370) = 92. This means that Jethro must get a mark of at least 92 out of 100 for the last test to have a mean mark of at least 77 for all 6 tests.
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How do you find the surface area of the cone?
Answer:
A=[tex]\pi[/tex]r(r+h2+r2)=[tex]\pi[/tex]·7·(7+122+72)≈459.44884
rounded off to 500 square millimetres
Step-by-step explanation:
The total surface area of a cone is the combination of the curved surface as well as the base area of a cone. The formula to calculate the total surface area of the cone is:
TSA of cone = [tex]\pi[/tex]r^2 + [tex]\pi[/tex]r l = r (l + r) square units.
A triangle has sides 8 cm and 5 cm and an angle of 90° between them. Calculate the smallest angle of the triangle.
Step-by-step explanation:
let the smallest angle = x
tan x = 5/8
x = arctan 5/8
x = 32°
Answer: The smallest angle of the triangle is 32°
Step-by-step explanation:
Given:
one side of the triangle= 8 cm
The other side of the triangle = 5 cm
Angle between AB and BC = 90°
⇒ ∠ABC = 90°
ΔABC is a right angled triangle
Use trigonometric function: For X
tanx= AB/CB
tanx= 8/5
x=tan-1 (8/5)
x= 58°
Use trigonometric function: For Y
tany= BC/AB
tany=5/8
y=tan-1 (5/8)
y = 32°
Making 32° be the smallest angle of the triangle
3×4+(-7)×9 the answer
Answer:
-51 would be the answer for this equation.
Step-by-step explanation:
HELP ME PLEASE(HELP WITH BOTH PLEASE)
As a result, the answer to the following question, As a result, the length triangle of side JS is 18.
What precisely is a triangle?A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.
We must apply the Pythagorean theorem to answer question 19. We know that JN is the hypotenuse of a right triangle with legs of 6 and 8 lengths. As a result, we may apply the formula:
[tex]JN^2 = 6^2 + 8^2\\JN^2 = 36 + 64\\JN^2 = 100\\JN = square root (100)\\JN = 10\\[/tex]
As a result, the length of side JN is 10.
JS/NS = JM/JN
When we substitute the provided values, we get:
12/10 = JS/NS
When we simplify the left side, we get:
6/5 = JS/NS
When we multiply both sides by NS, we get:
JS = (6/5)NS
We also know that NS is 15, therefore we may substitute that number for:
[tex]JS = (6/5) * 15\sJS = 18[/tex]
As a result, the length of side JS is 18.
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Ronald bikes 6. 9 miles each day how far has ronald biked in seven days
Answer:
[tex]\huge\boxed{\sf 48.3 \ miles}[/tex]
Step-by-step explanation:
Given that,
1 day = 6.9 miles
Multiply 7 to both sides1 × 7 days = 6.9 × 7 miles
7 days = 48.3 miles[tex]\rule[225]{225}{2}[/tex]
Answer:
7 days = 48.3 miles
Step-by-step explanation:
Given information,
→ Ronald bikes 6.9 miles every day.
Now we have to,
→ Find the distance travelled in 7 days.
General formula we use,
→ Distance travelled × Number of days
Then the distance travelled will be,
→ Miles × Days
→ 6.9 × 7
→ 48.3 miles
Hence, the answer is 48.3 miles.
Suppose you bought a car for $63,765 and the value of the car has decreased by 44%. What is the new value of the car? Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
If the value of the car has decreased by 44%, it still retains 56% of its value. Thus, the solution for the depreciation is 63,765(.56) = $35,708.40
A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least 55% of the vote in the sample, that candidate will be forecast as the winner of the election. If you select a random sample of 100 voters, what is the probability that a candidate will be forecast as the winner when:___.
a. The population percentage of her vote is 50. 1%?
b. The true percentage of her vote is 60%?
c. The true percentage of her vote is 49% (and she will actually lose the election)?
d. Find a 95% confidence interval of the true percentage of her vote, if 55 voters in the sample of 100 indicated that they voted for her.
e. If 55% of a sample of 300 indicated that they have voted for her, is there sufficient evidence at 90% level of confidence that she has won the election? (Hint: If 0. 5 or less is within the C. I. , then no)
a. Probability of candidate being forecast as the winner ≈ 17.78%
b. Probability of candidate being forecast as the winner ≈ 99.65%
c. Probability of candidate being incorrectly forecast as the winner ≈ 1.58%
d. 95% confidence interval for the true percentage of the candidate's vote ≈ (0.449, 0.651)
e. No, there is not sufficient evidence at 90% level of confidence that she has won the election.
a. If the population percentage of the candidate's vote is 50%, then the probability of her receiving at least 55% of the vote in a sample of 100 voters can be calculated using the binomial distribution with n=100 and p=0.50:
P(X ≥ 55) = 1 - P(X < 55) = 1 - binomial distribution (54, 100, 0.50, true)
≈ 0.1778
b. If the true percentage of the candidate's vote is 60%, then the probability of her receiving at least 55% of the vote in a sample of 100 voters can be calculated using the binomial distribution with n=100 and p=0.60:
P(X ≥ 55) = 1 - P(X < 55) = 1 - binomial distribution (54, 100, 0.60, true)
≈ 0.9965
c. If the true percentage of the candidate's vote is 49%, then the probability of her receiving at least 55% of the vote in a sample of 100 voters can be calculated using the binomial distribution with n=100 and p=0.49:
P(X ≥ 55) = 1 - P(X < 55) = 1 - binomdist(54, 100, 0.49, true) ≈ 0.0158
d. The 95% confidence interval for the true percentage of the candidate's vote can be calculated using the following formula:
CI = p ± zα/2 × √(p×(1-p)/n)
where p is the sample proportion (55/100=0.55), zα/2 is the critical value for a 95% confidence interval (1.96), and n is the sample size (100).
Substituting the values, we get:
CI = 0.55 ± 1.96 × √(0.55×(1-0.55)/100) ≈ (0.449, 0.651)
e. If 55% of a sample of 300 indicated that they have voted for her, the sample proportion is p=0.55 and the sample size is n=300. We can calculate the standard error of the sample proportion using the following formula:
SE = √(p×(1-p)/n) ≈ √(0.55×(1-0.55)/300) ≈ 0.0316
The margin of error for a 90% confidence interval can be calculated by multiplying the standard error by the critical value for a 90% confidence interval, which is approximately 1.645:
ME = 1.645 × SE ≈ 0.052
The 90% confidence interval for the true proportion can be calculated as:
CI = p ± ME ≈ 0.55 ± 0.052 ≈ (0.498, 0.602)
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Challenging y’all a little
The dimensions of the inner square pyramid have a ratio 2:3 to the dimensions of the outer square pyramid. What are the dimensions of the inner square pyramid
a. The surface area of the outer square pyramid is 11.25 square centimeters. b. The side length of the inner square pyramid is 2.25 centimeters.
a. To find the surface area of the outer square pyramid, we need to calculate the area of each of its faces and add them together. The outer square pyramid has four triangular faces and a square base.
Area of a triangular face = (1/2) x base x height
Area of a triangular face = (1/2) x 1.5 cm x 3 cm = 2.25 cm²
The area of the square base can be found using the formula for the area of a square:
Area of square base = side length²
Area of square base = 1.5 cm x 1.5 cm = 2.25 cm²
Therefore, the total surface area of the outer square pyramid is:
Surface area = 4 x area of triangular face + area of square base
Surface area = 4 x 2.25 cm² + 2.25 cm²
Surface area = 11.25 cm²
Therefore, the surface area of the outer square pyramid is 11.25 square centimeters.
b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. Let's call the side length of the inner square pyramid "x". Since the ratio of the dimensions is 2:3, we know that the side length of the outer square pyramid is (3/2)x.
The volume of a square pyramid can be calculated using the formula:
Volume = (1/3) x base area x height
Since the two pyramids are similar, the ratio of their volumes is the cube of the ratio of their corresponding side lengths:
Volume of inner pyramid / Volume of outer pyramid = (x / (3/2)x)³ = (2/3)³
We also know that the volume of the outer pyramid is:
Volume of outer pyramid = (1/3) x base area x height
The height of the two pyramids is the same, since they are stacked on top of each other, so we can write:
Volume of inner pyramid / Volume of outer pyramid = (1/3) x base area of inner pyramid / (1/3) x base area of outer pyramid
Simplifying this expression, we get:
(x / (3/2)x)³ = (1/3) x² / (1/3) (3/2x)²
Solving for x, we get:
x = (3/2)²
x = 2.25
Therefore, the side length of the inner square pyramid is 2.25 centimeters.
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The complete question is :
a. For the outer square pyramid, the side length of the base is 1.5 centimeters and the height of one of the triangular faces is 3 centimeters. What is the surface area of the outer square pyramid?
b. The dimensions of the inner square pyramid have a ratio of 2:3 to the dimensions of the outer square pyramid. What are the dimensions of the inner square pyramid?
What is the value of x?
Answer:
x = 18
Step-by-step explanation:
[tex]\frac{6}{7}=\frac{x}{21} \\\\6*21=7*x\\\\126=7x\\\\x=18[/tex]
A plant grows at a constant rate. Lalita records the height of the plant each week. The unite rate is measured in inches per week. What is the constant of proportionality
A.1/2
B.3
C.7
D.2
The constant of proportionality between the plant's height and time in weeks is 2 inches/week. So,correct answer is (D) 2.
Define constant of proportionality?The constant of proportionality is a factor that relates two variables that are directly proportional, indicating the ratio of change between them.
We can use the given information to determine the constant of proportionality between the plant's height and time in weeks.
The plant's height increased by 6 - 0 = 6 inches in the first three weeks (from week 0 to week 3). Therefore, the rate of growth during this period was 6 inches / 3 weeks = 2 inches/week.
Similarly, the plant's height increased by 10 - 6 = 4 inches during the next two weeks (from week 3 to week 5), so the rate of growth during this period was 4 inches / 2 weeks = 2 inches/week.
Finally, the plant's height increased by 14 - 10 = 4 inches during the last two weeks (from week 5 to week 7), so the rate of growth during this period was also 4 inches / 2 weeks = 2 inches/week.
Since the plant grows at a constant rate, we can assume that the rate of growth was 2 inches/week throughout the entire period from week 0 to week 7.
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For what value of C is the function one-to-one?
(1,2) (2,3) (3,5) (4,7) (5,11) (6,C)
For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.
The basic definition of a one-to-one function is the mapping of two sets. If each element in the range of a function g matches precisely one in the domain of g, then the function g is one-to-one. 1-1 is another way to represent one-to-one. A function or formula, such as f() connects the values of two variables in such a way that the values of the first variable's elements determine the values of the second variable in exactly the same ways.
We have:
{(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)}
We can see the number of the 2nd position is prime and in sequence so, we can easily determine that 2, 3, 5, 7, 11, and next will be 13.
For the given options, the only element that not already appears in one of the pairs is c = 13, so that is the correct option.
When every element in a function's range and domain match exactly one another, the function is said to be one-to-one. 1-1 is also used to indicate one-to-one. A function or formula, such as f() links the elements and values of one variable to those of another in such a way that the elements of the first variable exactly predict the elements of the second variable.
The complete question is-
For what value of c is the function one-to-one?
{ (1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c) }
a)2
b) 5
c)11
d)13
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Find cos R and cos S.
The value of the trigonometric identities are;
1. cos R = 15/17
cos S = 8/17
2. cos R = 12/13
cos S = 5/13
What are trigonometric identities?
Trigonometric Identities are simply seen as the equalities involving trigonometry functions.
It also holds true for all the values of variables given in the equation.
There are various distinct trigonometric identities involving the side length as well as the angle of a triangle. They are;
sinetangentcosinecotangentsecantcosecantWe have cosine represented as;
cos θ = adjacent/hypotenuse
For the first triangle, we have;
cos R = 30/34 = 15/17
cos S = 16/34 = 8/17
For the second triangle;
cos R = 24/26 = 12/13
cos S = 10/26 = 5/13
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Write vector a in terms of other vectors using the following image:
Answer:
Step-by-step explanation:
2a = -b - d + c
= c - b - d
x = c/2 - b/2 - d/2
The vector a in terms of other vectors for the given vectors in the image is c/2 - b/2 - d/2.
A vector is a quantity that determines both an object, its magnitude, and its direction.
The resultant vector is obtained when the tail of one vector is attached to the head of another vector such the resultant vector is formed from the sum of the two vectors.
Let a be the total vector of the given figure.
The vectors are written as:
2a = -b - d + c
a = c - b - d
a = c/2 - b/2 - d/2
Hence, the vector a in terms of other vectors is c/2 - b/2 - d/2.
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4.02 Lesson check ! (3)
The given sequence 22, 12, 2, -8 is arithmetic, and the common difference is -10.
How to determine if the sequence is arithmetic?An arithmetic sequence is a sequence where the difference between any pair of consecutive terms is a constant knowed as the common difference, and if k is that common difference, we can write the recursive formula as:
a(n) = a(n - 1) + k
Here we have the sequence:
22, 12, 2, -8
Taking the differences between consecutive terms we get:
12 - 22 = -10
2 - 12 = -10
-8 - 2 = -10
The differences are all equal, then this is an arithmetic sequence, and the common difference is -10.
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