Using the scale factors obtained the values are -
The value of k is 8, since g(−2) = 8.
The value of k is 8, since g(−2) = 8.
The value of k is 8, since g(−2) = 1.
The value of k is 4, since g(−2) = 2.
What is scale factor?
The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.
For each part, we can use the given table to determine how the transformation affects the function values -
g(x) = f(2x)
This transformation is a horizontal compression by a factor of 2.
To see this, notice that when we evaluate g at x = -1, we get the same value as f evaluated at x = -2.
Similarly, when we evaluate g at x = 0, we get the same value as f evaluated at x = 0.
And so on. In other words, the function values of g(x) are the same as the function values of f(x) at every other point (starting with x = -2).
So, g(x) is a compressed version of f(x) horizontally by a factor of 2.
Therefore, the value of k is 8, since g(−2) = 8 = f(2×(-2)).
g(x) = 2f(x)
This transformation is a vertical stretch by a factor of 2.
To see this, notice that every value of g(x) is twice the corresponding value of f(x).
So, g(x) is a stretched version of f(x) vertically by a factor of 2.
Therefore, the value of k is 8, since g(−2) = 2f(−2) = 2×4 = 8.
g(x) = f(x/2)
This transformation is a horizontal stretch by a factor of 2.
To see this, notice that when we evaluate g at x = -2, we get the same value as f evaluated at x = -4.
Similarly, when we evaluate g at x = -1, we get the same value as f evaluated at x = -2.
And so on. In other words, the function values of g(x) are the same as the function values of f(x) at every other point (starting with x = -4).
So, g(x) is a stretched version of f(x) horizontally by a factor of 2.
Therefore, the value of k is 8, since g(−2) = f(−1) = 1.
g(x) = (1/2)f(x)
This transformation is a vertical compression by a factor of 2.
To see this, notice that every value of g(x) is half the corresponding value of f(x).
So, g(x) is a compressed version of f(x) vertically by a factor of 2.
Therefore, the value of k is 4, since g(−2) = (1/2)f(−2) = (1/2)×4 = 2.
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Division involving a whole number and a Divide. Write your answer in simplest form. 3-:(2)/(3)
The answer in simplest form is 9/2
The division involving a whole number and a fraction can be simplified by multiplying the whole number by the reciprocal of the fraction.
The reciprocal of a fraction is obtained by flipping the numerator and denominator.
In this case, the division is 3 ÷ (2/3). The reciprocal of (2/3) is (3/2).
So, we can multiply 3 by (3/2) to simplify the division:
3 × (3/2) = (3/1) × (3/2) = (3 × 3) / (1 × 2) = 9/2
Therefore, the answer in simplest form is 9/2.
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A retailer sells model solar systems for $72 that were acquired at a cost of $24. What is the mark-up percentage?
Therefore, the mark-up percentage for the model solar system is 200%. This means that the selling price is twice the cost price.
I have to figure out a percentage.We must divide the value by the entire value to find the percentage, then increase the resulting number by 100.
The mark-up percentage is the percentage by which the selling price exceeds the cost price.
In this case, the cost price of the model solar system is $24 and the selling price is $72. The mark-up amount is the difference between the selling price and the cost price, which is:
$72 - $24 = $48
To find the mark-up percentage, we divide the mark-up amount by the cost price and multiply by 100:
Mark-up percentage = (Mark-up amount / Cost price) x 100%
Mark-up percentage = ($48 / $24) x 100%
Mark-up percentage = 200%
Therefore, the mark-up percentage for the model solar system is 200%. This means that the selling price is twice the cost price.
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Step-by-step explanation:
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Thank You!
Find the inverse of each function:
y = log5 (4x + 1)
y = log3 (2^x + 8)
y = log4 (-2x + 9)
y = 5^x + 9/2
y = 10^x + 3/ -3
y = log5 (-4x + 10)
Taking the given functions, we will obtain the following inverse functions
1)[tex]f^-1(x) = (5^x - 1)/4[/tex]2) [tex]f^-1(x) = log2 (3^x - 8)[/tex]3)[tex]f^-1(x) = (9 - 4^x)/2[/tex]4)[tex]f^-1(x) = log5 (x - 9/2)[/tex]5) [tex]f^-1(x) = log10 (x - 3/ -3)[/tex]6) [tex]f^-1(x) = (10 - 5^x)/4[/tex]To find the inverse of each function, we need to switch the x and y values and solve for y. This will give us the inverse function.
1) [tex]y = log5 (4x + 1)[/tex]
Switch x and y:
[tex]x = log5 (4y + 1)[/tex]
Solve for y:
[tex]5^x = 4y + 1\\4y = 5^x - 1\\y = (5^x - 1)/4[/tex]
Inverse function:
2) [tex]y = log3 (2^x + 8)[/tex]
Switch x and y:
[tex]x = log3 (2^y + 8)[/tex]
Solve for y:
[tex]3^x = 2^y + 8\\2^y = 3^x - 8\\y = log2 (3^x - 8)[/tex]
Inverse function: [tex]f^-1(x) = log2 (3^x - 8)[/tex]
3) [tex]y = log4 (-2x + 9)[/tex]
Switch x and y:
[tex]x = log4 (-2y + 9)[/tex]
Solve for y:
[tex]4^x = -2y + 9\\-2y = 4^x - 9\\y = (9 - 4^x)/2[/tex]
Inverse function: [tex]f^-1(x) = (9 - 4^x)/2[/tex]
4) [tex]y = 5^x + 9/2[/tex]
Switch x and y:
[tex]x = 5^y + 9/2[/tex]
Solve for y:
[tex]5^y = x - 9/2\\y = log5 (x - 9/2)[/tex]
Inverse function: [tex]f^-1(x) = log5 (x - 9/2)[/tex]
5) [tex]y = 10^x + 3/ -3[/tex]
Switch x and y:
[tex]x = 10^y + 3/ -3[/tex]
Solve for y:
[tex]10^y = x - 3/ -3\\y = log10 (x - 3/ -3)[/tex]
Inverse function: [tex]f^-1(x) = log10 (x - 3/ -3)[/tex]
6) [tex]y = log5 (-4x + 10)[/tex]
Switch x and y:
[tex]x = log5 (-4y + 10)[/tex]
Solve for y:
[tex]5^x = -4y + 10-4y = 5^x - 10y = (10 - 5^x)/4[/tex]
Inverse function: [tex]f^-1(x) = (10 - 5^x)/4[/tex]
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Let f and g be polynomials of degree 3. Is it true that f ∘ g = g ∘ f?
A. Yes, always
B. No, it's only with polynomials with a degrees of 1
C. It is true in some cases
D. No, never
The true statement about the polynomials is (b) No, it's only with polynomials with a degrees of 1
How to determine the true statementGiven that the polynomials f and g have a degree of 3
The composition of two functions, f ∘ g (read as "f composed with g"), is not commutative in general, meaning that f ∘ g is not necessarily equal to g ∘ f.
This holds true for polynomials of degree 3 as well.
In fact, if f and g are two different polynomials of degree 3, then f ∘ g and g ∘ f will be different polynomials in general.
The equation f ∘ g = g ∘ f holds true is when f and g are constant polynomials, that is, polynomials of degree 0 or 1.
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Find the area of the shaded segment of the circle.
The area of shaded region is 0.15 ft².
What is the area of the shaded region?
The area of the shaded region is calculated by subtracting the area of the triangle from the area of the entire sector.
The angle subtended by the sector is calculated as;
θ = ¹/₂ (55⁰)
θ = 27.5⁰
The area of the triangle is calculated as;
A₁ = ¹/₂r² sinθ
where;
r is the radiusA₁ = ¹/₂ x 4² sin(27.5)
A₁ = 3.69 ft²
Area of the sector is calculated as;
A_t = θ/360 x πr²
A_t = ( 27.5 / 360) x π x 4²
A_t = 3.84 ft²
Area of shaded region = 3.84 ft² - 3.69 ft² = 0.15 ft².
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find the 12th term of the geometric sequence 2,-12,8, ...
The 12th term of the geometric sequence 2, -12, 8, ... is -111,974,400.
What is Geometric Progression?A geometric progression is a sequence of numbers in which each term after the first is found by multiplying the preceding term by a fixed number, called the common ratio.
To find the 12th term of the geometric sequence, we need to use the formula:
[tex]an = a1 * r^{(n-1)[/tex]
where:
an = the nth term
a1 = the first term
r = the common ratio
We can see that the common ratio is -6, since:
-12/2 = 8/-12 = -6
So, we have:
[tex]a12 = 2 * (-6)^{(12-1)[/tex]
[tex]a12 = 2 * (-6)^{11}[/tex]
a12 = -111,974,400
Therefore, the 12th term of the geometric sequence 2, -12, 8, ... is -111,974,400.
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Need Hotp? [-it.19 peints] spitcAtC7 6.5.02. is wmaller than aAy.? \[ \begin{array}{l} b=49, \quad c=46, \quad=C=26^{\circ} \\ \Delta A_{1}=1 \quad \therefore A_{2}= \\ x d_{1}= \\ \text { - }+B_{2}=
Without further clarification on the terms and the relationship between the variables and the given information, it is difficult to provide a complete and accurate answer to the problem.
It seems that there are several typos and irrelevant parts in the question, making it difficult to understand the problem and provide a clear and accurate answer. However, I will do my best to answer the question based on the information given.
In terms of "wmaller" and "aAy.", it is unclear what these terms are referring to or how they relate to the problem. It is also unclear what "peints" is referring to. Without further clarification on these terms, it is difficult to provide a complete answer.
Based on the given information, it seems that the problem is asking to solve for the unknown variables A2, x, and B2 in a triangle with sides b=49, c=46, and angle C=26 degrees. However, without knowing the relationship between these variables and the given information, it is difficult to provide a step-by-step explanation for solving the problem.
In conclusion, without further clarification on the terms and the relationship between the variables and the given information, it is difficult to provide a complete and accurate answer to the problem.
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1. arithmetic mean of the sample is:
a. 3.47
b. 3.75
c.3.0
d.3.50
Dato (x) Frecuencia
2 3
3 6
4 8
5 2
2. The average age of the children (x) is: a. 8.00 b.65.60 c. 7.81 d.62.57
Edad frecuencia xf x²f
6 7 42 252
7 12 84 588
8 10 80 640
9 8 72 648
10 5 50 500
Total 42 328 2628
3. standard desviation
a. 0.79
b. 2.01
c. 0.89
d. 2.45
Dato (x) Frecuencia
3.2. 3
1.3 4
2.4 2
1. The arithmetic mean of the sample is: d. 3.50
To calculate the arithmetic mean, you need to add up all of the numbers in the sample and divide it by the total number of numbers in the sample. Using the given data, the total number is 20 (3+6+8+2=20). The total of the numbers in the sample is 31 (2+3+4+5=14). Therefore, the arithmetic mean of the sample is 31/20 = 3.50.
2. The average age of the children (x) is: c. 7.81
To calculate the average age of the children, you need to find the sum of the products of age and frequency (xf) and divide it by the total frequency (42). The sum of the products of age and frequency is 2628 (42+84+80+72+50=2628). Therefore, the average age of the children is 2628/42 = 7.81.
3. Standard deviation: a. 0.79
To calculate the standard deviation, you need to find the sum of the squares of the frequency multiplied by the square of the deviation (x²f) and divide it by the total frequency (42). The sum of the squares of the frequency multiplied by the square of the deviation is 6790 (252+588+640+648+500=6790). Therefore, the standard deviation is 6790/42 = 0.79.
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Suppose the annual interest rate is 7.5% and the interest is compounded annually. How much will an investment of $1,000 be worth after 3 years?
An investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.
What is value?Value is a term used to describe the worth of something, either in terms of money, or in terms of importance or usefulness. Value can be determined in terms of the amount of money something is worth, or the level of importance or usefulness it has to someone. When something has a high value, it means that it is worth a lot of money or has a high level of importance or usefulness.
The value of an investment of $1,000 after 3 years at an annual interest rate of 7.5%, compounded annually, can be calculated using the following formula:
Future Value (FV) = Present Value (PV) × (1 + r)ⁿ
Where PV is the present value of the investment ($1,000 in this case), r is the annual interest rate (7.5%) and n is the number of years (3).
Using this formula, we can calculate the future value of the investment after 3 years as follows:
FV = $1,000 × (1 + 0.075)³
FV = $1,000 × 1.23228
FV = $1,232.28
Therefore, an investment of $1,000 at an annual interest rate of 7.5%, compounded annually, will be worth $1,232.28 after 3 years.
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help me i don't understand
The volume of the fully inflated balloon is [tex]\frac{19652}{3}[/tex]π inch³ and volume of half inflated balloon is [tex]\frac{19652\pi }{6}[/tex].
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
Diameter of a fully inflated balloon = 34 inch
Radius is half the diameter.
Radius of fully inflated balloon = 34 / 2 = 17 inches
Volume of a sphere = [tex]\frac{4}{3}[/tex] π r³, where r is the radius.
(a) Volume of fully inflated balloon = [tex]\frac{4}{3}[/tex] π (17)³
= [tex]\frac{19652}{3}[/tex]π inch³
(b) Volume of the half inflated balloon = Half of the fully inflated volume
= ([tex]\frac{19652}{3}[/tex]π / 2) inch³
= [tex]\frac{19652\pi }{6}[/tex] inch³
(c) Volume of half inflated balloon = [tex]\frac{19652\pi }{6}[/tex]
[tex]\frac{4}{3}[/tex] π r³ = [tex]\frac{19652\pi }{6}[/tex]
[tex]\frac{4}{3}[/tex] r³ = [tex]\frac{19652}{6}[/tex]
r³ = [tex]\frac{19652}{8}[/tex]
r = 13.49 inch
Hence the volume and radius are found.
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Helpppp ! The A, C, and J Trains stop at the Fulton Street station. The table shows data for trains that
arrived at the station.
What is the likelihood that a randomly
selected A Train will arrive on time?
? %
Late
On Time
Total
A Train C Train J Train
28
17
30
22
8
50
25
15
45
Total
75
45
120
Likelihood that a randomly selected A Train will arrive on time is 0.44 or 44%.
What is the randomly selection?
Random selection is a process of choosing individuals, items, or samples from a population in a way that every member of the population has an equal chance of being selected.
To find the likelihood that a randomly selected A Train will arrive on time, we need to determine the number of A Trains that arrived on time and divide that by the total number of A Trains that arrived at the station.
From the table, we can see that there were a total of 50 trains that were A Trains, out of which 22 arrived on time. Therefore, the probability that a randomly selected A Train will arrive on time is:
P(A Train arrives on time) = Number of A Trains that arrived on time / Total number of A Trains
= 22 / 50
= 0.44
Therefore, likelihood that a randomly selected A Train will arrive on time is 0.44 or 44%.
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Q1.Identify the percent of change as an increase or a decrease. 9 points to 4 points
Q2.Find the percent of change. Round to the nearest tenth of a percent if necessary
The percent of change from 9 points to 4 points is a decrease of 55.56%.
What is the difference between a dependent and independent variable?In an experimental research, an independent variable is one that you change or alter to examine its effects. It is named "independent" because it is unaffected by any other research factors.
A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.
The percent change is given as:
Percent change = (Difference)/(Original) (100)
Percent change = (9 - 4) / 9 (100) = 55.56%.
Hence, the percent of change from 9 points to 4 points is a decrease of 55.56%.
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Abbreviations Length Conversions - Inches = in 1ft=12 in - Feet =ft - 1yd=3ft - Yards =yds1yd=36in - Miles =mi1mi=5,280ft.
Find the perimeter in feet and area in square feet of the figure below. If needed, round to 1 decimal place.
The perimeter of the figure is 5,287 ft and the area is 15,840 sq ft.
The perimeter of a figure is the sum of the lengths of its sides. The area of a figure is the product of its length and width.
To find the perimeter of the figure below, we need to add the lengths of all the sides together:
Perimeter = 12 in + 3 ft + 36 in + 5,280 ft
To convert all the lengths to feet, we can use the following conversion factors:
1 ft = 12 in
1 yd = 3 ft
1 mi = 5,280 ft
Using these conversion factors, we can convert the lengths to feet:
Perimeter = (12 in / 12 in/ft) + 3 ft + (36 in / 12 in/ft) + 5,280 ft
Perimeter = 1 ft + 3 ft + 3 ft + 5,280 ft
Perimeter = 5,287 ft
To find the area of the figure, we need to multiply the length and width together:
Area = Length x Width
Assuming that the figure is a rectangle, the length is 5,280 ft and the width is 3 ft:
Area = 5,280 ft x 3 ft
Area = 15,840 sq ft
Therefore, the perimeter of the figure is 5,287 ft and the area is 15,840 sq ft.
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Let X and Y be independent, geometrically distributed random
variables, each with parameter p, p ∈(0, 1). Set N = X + Y.
(a) Find the joint PMF of X, Y, and N.
(b) Find the joint PMF of X and N.
(a) The joint PMF of X, Y, and N can be found by multiplying the two independent PMFs of X and Y. The joint PMF is: P(X=x, Y=y, N=n) = P(X=x) * P(Y=y) = (1-p)^x * p * (1-p)^y * p = (1-p)^(x+y) * p^2.
(b) The joint PMF of X and N can be found by marginalizing over Y. The joint PMF is: P(X=x, N=n) = P(X=x, Y=n-x) = (1-p)^(x+(n-x)) * p^2 = (1-p)^n * p^2.
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find the median of 3,5,6,8,8,9,10
Answer:
the meadian is 8
Step-by-step explanation:
The value of the middle-most observation is called the median of the data.
Gavin wants to buy a skateboard that sells for $49.99. An advertisement says that next week the skateboard will be on sale for $42.50 how much will Gavin save if he waits until next week to buy the skateboard.
Answer:
$7.49
Step-by-step explanation:
49.99-42.50=7.49
the distance between LONDON and CARDIFF is 150 miles . what is the distance in kilometers
The distance between London and Cardiff is approximately 241.4 kilometers.
What is conversion factor?A conversion factor is a ratio in mathematics that is used to change a quantity's unit of measurement. We may represent the same quantity in many units thanks to this link between the two units of measurement. For instance, 1 mile equals 1.60934 kilometres, thus we may multiply the number of miles by this conversion ratio to find the corresponding distance in kilometres. In science, engineering, and daily life, conversion factors are frequently employed to translate units of length, volume,
We know that,
1 mile = 1.60934 kilometers
Thus,
150 miles x 1.60934 kilometers/mile = 241.4 kilometers
Hence, the distance between London and Cardiff is approximately 241.4 kilometers.
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A chemist has 10% and 50% solutions of acid available. How many
liters of each solution should be mixed to obtain 400 liters of 11%
acid solution?
liters of 10% acid
liters of 50% acid
To obtain 400 liters of 11% acid solution, you need to mix 390 liters of the 10% acid solution and 10 liters of the 50% acid solution to obtain 400 liters of 11% acid solution.
Let x be the number of liters of 10% acid solution and y be the number of liters of 50% acid solution.
We can set up a system of two equations to represent the given information:
x + y = 400 (total volume of the mixture is 400 liters)
0.10x + 0.50y = 0.11(400) (the amount of acid in the mixture is 11% of the total volume)
Simplifying the second equation:
0.10x + 0.50y = 44
We can now use either substitution or elimination method to solve for x and y.
Using substitution, we can solve for y in terms of x from the first equation:
y = 400 - x
Substituting this into the second equation:
0.10x + 0.50(400-x) = 44
Simplifying and solving for x:
0.10x + 200 - 0.50x = 44
-0.40x = -156
x = 390
So the chemist needs 390 liters of the 10% acid solution and 10 liters of the 50% acid solution to obtain 400 liters of 11% acid solution.
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Micah has 6565 feet of fencing to make a dog run in his yard. He wants the length to be 4.54.5 feet more than the width. Find the length, L�, by solving the equation 2L+2(L−4.5)=652�+2(�-4.5)=65.
The length of the dog run is 18.5 feet and the width is 14 feet. Micah can use his 65 feet of fencing to make a dog run with these dimensions.
To find the length of the dog run, we need to solve the equation for L. Here are the steps:
1. Start with the given equation: 2L + 2(L - 4.5) = 65
2. Distribute the 2 on the right side of the equation: 2L + 2L - 9 = 65
3. Combine like terms: 4L - 9 = 65
4. Add 9 to both sides of the equation: 4L = 74
5. Divide both sides of the equation by 4: L = 18.5
So, the length of the dog run is 18.5 feet. Since the length is 4.5 feet more than the width, we can find the width by subtracting 4.5 from the length:
W = L - 4.5
W = 18.5 - 4.5
W = 14
Therefore, the width of the dog run is 14 feet.
In conclusion, the length of the dog run is 18.5 feet and the width is 14 feet. Micah can use his 65 feet of fencing to make a dog run with these dimensions.
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Today, everything at a store is on sale. The store offers a 20% discount.
The regular price of a T-shirt is $16. What is the discount price?
36 flowers in 3 bouquets
This is called the unit rate.
Answer: Yes, you are correct.
Step-by-step explanation:
The relationship between the number of flowers and the number of bouquets is an example of a unit rate.
Answer:
yes
Step-by-step explanation:
it is a unit rate
Calculate the fluid intake in milliliters for the following meal
(assume a cup = 6oz and a glass = 8oz)
1/3 glass of orange juice
1/2 cup of tea
1/2 pt milk
1 tuna fish sandwich
1 popsicle (3oz)
TOTAL = _____ mL
*I need this answered quickly please and thank you.*
The total fluid intake for the meal is 493.04 mL.
How to find the total fluid intake for the meal?We first need to convert the volume of each beverage to ounces, and then to milliliters.
1/3 glass of orange juice = (1/3) x 8 oz = 2.67 oz = 79.01 mL (assuming 1 oz = 29.57 mL)
1/2 cup of tea = (1/2) x 6 oz = 3 oz = 88.72 mL
1/2 pt milk = (1/2) x 16 oz = 8 oz = 236.59 mL (assuming 1 pt = 16 oz and 1 oz = 29.57 mL)
1 popsicle (3oz) = 3 oz = 88.72 mL
The total fluid intake for the meal is
79.01 mL + 88.72 mL + 236.59 mL + 88.72 mL = 493.04 mL
Therefore, the fluid intake for the meal is approximately 493.04 mL.
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120 rupees 5 paise = — ( 120. 50 / 120. 05) rupees
The expression of one hundred twenty rupees and five paise in rupees is equals to the rupees 120.05.
We have, 120 rupees and 5 paise and we will express as rupees using decimals.
We have been given 5 paise. As we see 120 rupees so it's remain as it but we have to change 5 paise in rupees. Using the conversation factor, as we know that 100 paise = rupee 1
=> 1 paisa = Rs. 1/100
so, here conversation factor is = 1/100
The required value is obtained by multiplying the observed values by conversion factor. Therefore,
5 paise = Rs. (5×1/100)
= 5/100
= Rs. 0.05
Therefore, in decimals 5 paise = Rs. 0.05. Now, 120 rupees 5 paise = Rs. 120 + Rs. 0.05 = Rs. 120.05
Hence, required value is Rs. 120.05.
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Complete question:
Express in form of rupees
120 rupees 5 paise = — rupees.
Let S1, S2 ⊂ V be two sets of vectors which each span V , show
that S1 ∪ S2 span V
If S1 and S2 are two sets of vectors that each span V, then S1 ∪ S2 also spans V.
Let S1 and S2 be two sets of vectors that each span V. We need to show that S1 ∪ S2 also spans V.
Let v be any vector in V. Since S1 spans V, there exist vectors u1, u2,..., un in S1 and scalars a1, a2,..., an such that:
v = a1u1 + a2u2 + ... + anun
Similarly, since S2 spans V, there exist vectors w1, w2,..., wm in S2 and scalars b1, b2,..., bm such that:
v = b1w1 + b2w2 + ... + bmwm
Now, since S1 ∪ S2 contains all the vectors in S1 and S2, we can write v as a linear combination of the vectors in S1 ∪ S2:
v = a1u1 + a2u2 + ... + anun + b1w1 + b2w2 + ... + bmwm
Therefore, S1 ∪ S2 spans V.
In conclusion, if S1 and S2 are two sets of vectors that each span V, then S1 ∪ S2 also spans V.
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You go to the park on a windy day to fly a kite. You have released 40 feet of string. The string makes an angle of 30°with the ground. How high is the kite in the air?
Answer:
20 feet
Step-by-step explanation:
You can use trigonometry to solve this problem. The height of the kite can be found using the sine function. The sine of an angle in a right triangle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the side opposite the 30° angle is the height of the kite (h), and the hypotenuse is the length of the string (40 feet). So we have:
sin(30°) = h / 40
Solving for h, we get:
h = 40 * sin(30°)
Since sin(30°) = 0.5, we have:
h = 40 * 0.5
So, h = 20 feet.
The kite is 20 feet high in the air.
Answer:
To solve this problem, we can use trigonometry. Let's assume that the height of the kite from the ground is h. Then, we can use the tangent function to find the value of h.
We know that the tangent of an angle is equal to the opposite side over the adjacent side. In this case, the opposite side is the height of the kite (h) and the adjacent side is the distance from you to the point directly below the kite on the ground, which is 40 feet.
So we have:
tan(30°) = h/40
Multiplying both sides by 40, we get:
h = 40 tan(30°)
Using a calculator, we can find the value of tangent of 30 degrees, which is approximately 0.5774. So:
h = 40 × 0.5774 ≈ 23.1
Therefore, the height of the kite in the air is approximately 23.1 feet.
6. General questions 1. volume of pyramid b) progress , ideas • some people remembered a formula for volume of pyramid V = 1/3 lwh MAIN PROBLEM: where dues this come from? Why 1/3 ? • one strategy: dissect cube (orrectangule box) (assume for now l=w=h= 1) what is volume of negative space, compared to pyramid ? • second strategy glut multiple priemies together • third strategy: Slice pyramid horizontally Problems: • Keep thinking about strategy one and the • For strategy 3, fiad fald volume for four blocks that I drew above. (That is an overestimat) • Also we smiler stratey to set can underestimate That give range? • Try ti make more
These three strategies can help you understand why the volume of a pyramid is 1/3 lwh.
The formula for the volume of a pyramid is V = 1/3 lwh and the reason why the value is 1/3 is because of the three different strategies that can be used to calculate it.
The first strategy is to dissect a cube (a 3-dimensional rectangle) into the pyramid and the remaining negative space (assuming l=w=h=1). Comparing the volume of the pyramid to the negative space will show that the pyramid takes up 1/3 of the cube.
The second strategy is to stack multiple pyramids together. This will show that the sum of their volumes is equal to one third the total volume of the base they are stacked on.
The third strategy is to slice the pyramid horizontally, and calculate the volume of the four blocks. This will overestimate the volume of the pyramid, but by subtracting this volume from the total volume of the base, you can get a lower limit for the volume of the pyramid.
These three strategies can help you understand why the volume of a pyramid is 1/3 lwh.
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Find sin tetha if cos tetha=-5/17 and tetha is in Q III Find cos tetha if sin tetha=1/4 and tan tetha = √3
Find all other trigonometric function values lif sec tetha =-4 and tetha is in Q II
If cos tetha = -5/17 and tetha is in Q III, then sin tetha can be found using the Pythagorean identity: sin^2 tetha + cos^2 tetha = 1.
Substituting the given value for cos tetha and solving for sin tetha gives:
sin^2 tetha + (-5/17)^2 = 1
sin^2 tetha = 1 - 25/289
sin^2 tetha = 264/289
sin tetha = √(264/289)
sin tetha = ±√264/17
Since tetha is in Q III, where sin is negative, the correct answer is:
sin tetha = -√264/17
If sin tetha = 1/4 and tan tetha = √3, then cos tetha can be found using the definition of tan tetha: tan tetha = sin tetha/cos tetha.
Substituting the given values for sin tetha and tan tetha and solving for cos tetha gives:
√3 = (1/4)/cos tetha
cos tetha = (1/4)/√3
cos tetha = √3/12
If sec tetha = -4 and tetha is in Q II, then cos tetha can be found using the definition of sec tetha: sec tetha = 1/cos tetha.
Substituting the given value for sec tetha and solving for cos tetha gives:
-4 = 1/cos tetha
cos tetha = -1/4
Once we have cos tetha, we can find sin tetha using the Pythagorean identity: sin^2 tetha + cos^2 tetha = 1.
Substituting the value for cos tetha and solving for sin tetha gives:
sin^2 tetha + (-1/4)^2 = 1
sin^2 tetha = 1 - 1/16
sin^2 tetha = 15/16
sin tetha = ±√(15/16)
Since tetha is in Q II, where sin is positive, the correct answer is:
sin tetha = √15/4
Once we have sin tetha and cos tetha, we can find the other trigonometric function values using their definitions:
tan tetha = sin tetha/cos tetha = (√15/4)/(-1/4) = -√15
cot tetha = 1/tan tetha = -1/√15 = -√15/15
csc tetha = 1/sin tetha = 4/√15 = 4√15/15
sec tetha = 1/cos tetha = -4 (given)
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20 points hurry and mark brainly
Jennifer bought three of the same shirt and paid $63 after the 30% discount. What was the original price of each shirt? Show your work or explain in words how did you get the answer.
Answer:
.7x 63 = 90 (.7 is the same as 70%. If they took off 30%, they left on 70%)
90 ÷ 3 = 30
Jennifer originally paid $30.00 a shirt.
Check
30 x .3 = 9 This is the amount of the discount per shirt.
30 - 9 = 21 Discounted cost per shirt.
21 x 3 = 63 The cost of three shirts.
This checks.
Helping in the name of Jesus.
On Martin's first stroke, his golf ball traveled
4
5
5
4
start fraction, 4, divided by, 5, end fraction of the distance to the hole. On his second stroke, the ball traveled
79
7979 meters and went into the hole. How many kilometers from the hole was Martin when he started?
As per the given distance, Martin was 79 kilometers from the hole when he started.
Let's call the initial distance between Martin and the hole "x". According to the problem statement, on Martin's first stroke, the golf ball traveled 4/5 of this distance. This means that the distance the ball traveled on the first stroke was:
distance traveled on first stroke = (4/5)x
After the first stroke, Martin was left with a distance of:
distance left after first stroke = x - (4/5)x = (1/5)x
On Martin's second stroke, the ball traveled 79 meters and went into the hole. This means that the total distance the ball traveled was:
total distance traveled = distance traveled on first stroke + distance left after first stroke + distance traveled on second stroke
total distance traveled = (4/5)x + (1/5)x + 79
total distance traveled = x + 79
Since the ball went into the hole after the second stroke, the total distance traveled is equal to the initial distance between Martin and the hole:
x + 79 = initial distance between Martin and the hole
Therefore, the initial distance between Martin and the hole was:
x = initial distance between Martin and the hole = (79 km)
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