By trignometric property, The 630 .18 feet tall is the gateway arch .
What is the definition of trigonometry?
Trigonometry is a discipline of mathematics that examines certain functions of angles and how to use them in computations. A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc).
As given
The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.
Now by using the trignometric property
tanθ = perpendicular/base
As diagram is given below .
θ = 39
tan39° = AB/CB
CB = 778 feet
tan39° = 0.81 (approx)
0.81 = AB/778
AB = 0.81 × 778
AB = 630 .18 feet
Therefore, the 630 .18 feet tall is the gateway arch .
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Akio has succeeded as a public communications specialist. He likes to think
cooperative behavior. Akio likes to achieve objectives with coworkers using
of himself as a friendly person who places a high priority on friendships and
understanding and mutual respect. This reflects that Akio fits the
social style.
Akio is a public communication specialist with skill sets to influence and raise awareness for public.
What do you mean by public communication specialist?
Specialists in public-relations develop and uphold a positive public image for the people, groups, or organisations they represent. To influence how the public perceives their clients and to raise awareness of each client's efforts and objectives, they prepare press releases and create social media strategies.
Public relations, information output, and media requests are handled by communications specialists. They can also plan an organization's social media or advertising campaigns.
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the incomes of all families in a particular suburb can be represented by a continuous random variable. it is known that the median income for all families in this suburb is $60,000 and that 40% of all families in the suburb have incomes above $72,000. (a) for a randomly chosen family, what is the probability that income will be between $60000 and $72000?
For a randomly chosen family in the suburb, the probability of having an income between $60,000 and $72,000 is 40%. This is because 40% of all families in the suburb have incomes above $72,000, and the median income for all families in the suburb is $60,000.
Therefore, the probability of having an income between [tex]$60,000[/tex] and $72,000 is 40%.
This information can also be interpreted in a graphical representation. The graph will have a vertical line at $60,000 and a horizontal line at 40%. The area between these two lines will represent the probability of having an income between $60,000 and $72,000, which is 40%.
In conclusion, for a randomly chosen family in the suburb, the probability of having an income between $60,000 and $72,000 is 40%.
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Assuming all necessary accessor functions are defined for a class, the comparison operator (<) can be overloaded for this class as a function. a. member b. friend c. global (non-member, non-friend) d. b) and c) only e. all three (a, b, and c)
The comparison operator (<) can be overloaded for a class as a function in all three ways: member, friend, and global (non-member, non-friend). Therefore, the correct answer is e. all three (a, b, and c).
When overloading the comparison operator (<) as a member function, it is defined within the class and has access to all the members and functions of the class.
When overloading the comparison operator (<) as a friend function, it is defined outside of the class but is given access to all the members and functions of the class.
When overloading the comparison operator (<) as a global (non-member, non-friend) function, it is defined outside of the class and does not have access to the members and functions of the class. However, it can still be used to compare objects of the class by using the accessor functions defined for the class.
The comparison operator (<) can be overloaded for a class as a function in all three ways: member, friend, and global (non-member, non-friend).
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Mai is visiting Paris to see the Eiffel Tower. She is 80 feet away when she spots it. To see the top, she has to look up at an angle of 85. 7 degrees. How tall is the Eiffel Tower to the nearest foot?
The Eiffel Tower is approximately 919 feet tall to the nearest foot.
We can use trigonometry to solve this problem.
Let's assume that the height of the Eiffel Tower is h feet.
From the problem, we know that Mai is 80 feet away from the base of the tower and looking up at an angle of 85.7 degrees. We can use the tangent function to relate the height of the tower to the angle and distance:
tan(85.7) = h/80
We can solve for h by multiplying both sides by 80:
h = 80 × tan(85.7)
Using a calculator, we get:
h ≈ 919.4 feet
Therefore, the Eiffel Tower is approximately 919 feet tall to the nearest foot.
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please help me. I need help
Answer:5 3/8
Step-by-step explanation:
[tex]3\frac{1}{8} =\frac{25}{8}\\4\frac{7}{28} =4\frac{1}{4}=\frac{17}{4}\\1\frac{5}{6} =\frac{11}{6}=\frac{33}{18}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{17}{18}+\frac{33}{18}=\frac{50}{18}=\frac{25}{9}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{\frac{25}{9}}{1}\\\frac{25}{8}=\frac{25}{9}*(x-\frac{17}{4})\\(x-\frac{17}{4})=\frac{25}{8}:\frac{25}{9}=\frac{25}{8}*\frac{9}{25}=\frac{9}{8}\\x=\frac{9}{8}+\frac{17}{4}=\frac{9}{8}+\frac{34}{8}=\frac{43}{8}=5\frac{3}{8}[/tex]
Which number makes the statement true?
0.42 < ?
A 0.4
B 0.45
C 0.415
D 0.4008
Answer:
b.0.45
Step-by-step explanation:
Answer: B 0.45
0.42 < 0.45
Step-by-step explanation:
I would appreciate if someone could help
Answer:
this is actually about derivatives,
the answer would be simply 10x-6
if they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true.Are the vectors 4 1 and 16 nearly independent? 45 Choose If they are linearly dependent, find scalars that are not all zero such that the equation below is true. If they are linearly independent, find the only scalars that will make the equation below true 171 01 45
The vectors 4 1 and 16 are linearly dependent because they can be expressed as multiples of each other. This means that there are scalars that are not all zero that will make the equation below true:
4a + 16b = 0
To find the scalars, we can set one of them to any non-zero value and solve for the other. For example, if we set a = 1, then we can solve for b:
4(1) + 16b = 0
16b = -4
b = -4/16
b = -1/4
So the scalars that will make the equation true are a = 1 and b = -1/4. These are not all zero, which confirms that the vectors are linearly dependent.
If the vectors were linearly independent, then the only scalars that would make the equation true would be all zero. In other words, a = 0 and b = 0 would be the only solution. However, since we found scalars that are not all zero that make the equation true, we know that the vectors are not linearly independent.
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Bobo and the Bouncing Ball Bobo was walking down the street one day, minding his own business, when a ball feil right in front of him and bounced straight up. It soared to tremendous height and came down again. Bobo caught the ball and climbed to the top of the 64 foot tall building to investigate _ On the roof, he saw a little girl peering over the edge. "What's wrong, little girl?" he asked, The girl answered without turning around, "I dropped my special magic ball; It always bounces exactly half its previous height and it'Il bounce forever if nobody catches it:" "Wowl" exclaimed Bobo. "Id give anything for a ball like thatl" "Il make a deal with you, sald the little girl, "If you answer two questions for me, I'Il give you the ball.Please help Bobo find the answers to these questions: (1) How high did the ball bounce on its 10t bounce? (2) How far had the ball traveled altogether by the time it reached its peak after its 10th bounce. 5 EINSTEIN POINT EXTENSION: If Bobo drops his magic ball from the top of the Empire State Building, how far will it have traveled when it hits the pavement for the 7h time? Explain your solution in detail.
1) The ball bounced 0.125 feet high on its 10th bounce.
2) The total distance traveled by the ball by the time it reached its peak after its 10th bounce is 255.75 feet.
3) If Bobo drops his magic ball from the top of the Empire State Building, the ball will have traveled 382 feet by the time it hits the pavement for the 7th time.
1) To find out how high the ball bounced on its 10th bounce, we can use the fact that the ball always bounces to half its previous height. We can start by finding the height of the first bounce, which we know is 64 feet since that's the height of the building. Then, we can keep dividing by 2 to find the height of each subsequent bounce. So, the height of the 2nd bounce is 32 feet, the height of the 3rd bounce is 16 feet, and so on. Continuing this pattern, we can find that the height of the 10th bounce is:
64 feet / 2^(10-1) = 64 feet / 512 = 0.125 feet
2) To find out how far the ball had traveled altogether by the time it reached its peak after its 10th bounce, we can use the fact that the distance traveled is equal to the sum of the distances of each bounce. The distance of each bounce is equal to twice the height of the bounce (since the ball travels up and then back down). So, the distance of the first bounce is 264 = 128 feet. The distance of the second bounce is 232 = 64 feet, and so on. Continuing this pattern, we can find that the distance of the 10th bounce is:
2×0.125 = 0.25 feet
So the total distance traveled by the ball by the time it reached its peak after its 10th bounce is:
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 + 0.5 + 0.25 = 255.75 feet
3) We know that the height of each bounce is half the height of the previous bounce, so we can use this to find the height of the 7th bounce. Starting with the height of the first bounce (which is the height of the Empire State Building), we can keep dividing by 2 to find the height of each subsequent bounce. So, the height of the 2nd bounce is 64/2 = 32 feet, the height of the 3rd bounce is 32/2 = 16 feet, and so on. Continuing this pattern, we can find that the height of the 7th bounce is:
64/2^(7-1) = 1 foot
Since the ball bounces up and down, it travels twice the height of each bounce. So, the distance traveled by the ball on each bounce is 2 feet. To find out how far the ball will have traveled by the time it hits the pavement for the 7th time, we can add up the distances traveled on the first 7 bounces:
2×(64 + 32 + 16 + 8 + 4 + 2 + 1) = 382 feet
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ASAP!! ITS URGENT
Solve these problems. (Use a calculator with a square root function, and round off answers to two decimal places.)
Answer:
10. To find the area of rhombus ABCD, we can use the formula:
Area = (diagonal 1 x diagonal 2) / 2
We need to find the length of both diagonals. Since the diagonals of a rhombus are perpendicular and bisect each other, we can use the Pythagorean theorem to find the length of each diagonal.
AC is one diagonal, AB is a side of the rhombus, and BD is the other diagonal divided by 2 (since BD bisects AC):
BD = AC/2 = 10/2 = 5 cm
Using the Pythagorean theorem with AC and BD:
AC^2 = AB^2 + BD^2
AC^2 = 13^2 + 5^2
AC^2 = 169 + 25
AC^2 = 194
AC = sqrt(194) ≈ 13.93 cm
Now that we have the lengths of both diagonals:
Area = (AC x BD) / 2
= (13.93 x 5) / 2
≈ 34.83 cm^2
Therefore, the area of rhombus ABCD is approximately 34.83 cm^2.
11. We know that the area of rhombus ABCD is 96 cm^2, and that BD is 8 cm. To find the length of AC, we can use the formula:
Area = (diagonal 1 x diagonal 2) / 2
Solving for diagonal 1 (AC):
AC = (2 x Area) / BD
= (2 x 96) / 8
= 24 cm
Therefore, the length of AC is 24 cm.
12. We know that AB is a side of the rhombus and that AB = 16 m. We also know that mZABD = 60 degrees. We can use trigonometry to find the length of the diagonals.
First, we can find the length of AD using the law of cosines:
AD^2 = AB^2 + BD^2 - 2(AB)(BD)cos(mZABD)
AD^2 = 16^2 + (2x)^2 - 2(16)(2x)cos(60)
AD^2 = 256 + 4 - 32x
AD^2 = 260 - 32x
AD = sqrt(260 - 32x)
Then, we can find the length of AC using the law of sines:
AC / sin(mZBAD) = AD / sin(mZABD)
AC / sin(120) = AD / sin(60)
AC = (AD x sin(120)) / sin(60)
AC = (sqrt(260 - 32x) x sqrt(3)) / 2
Now that we have the lengths of both diagonals:
Area = (AC x BD) / 2
= [(sqrt(260 - 32x) x sqrt(3)) / 2] x 8 / 2
= 2(sqrt(260 - 32x) x sqrt(3))
≈ 67.29 m^2
Therefore, the area of rhombus ABCD is approximately 67.29 square meters.
13. We know that the perimeter of the rhombus is 20 mm, so each side is 5 mm. We also know that AC is one of the diagonals. To find the length of the other diagonal, we can use the Pythagorean theorem.
Let x be half the length of the other diagonal:
AC^2 = (2x)^2 + 5^2
x^2 = (AC^2 - 25) / 4
x = sqrt((AC^2 - 25) / 4)
Now that we have the lengths of both diagonals:
Area = (AC x BD) / 2
= (AC x 2x) / 2
= xAC
= sqrt((AC^2 - 25) / 4) x AC
≈ 19.80 mm^2
Therefore, the area of rhombus ABCD is approximately 19.80 square millimeters.
Ruth is making Lemonade. For 1 cup of water she uses 3 lemins, for 2 cups 6 lemons, ect. If this pattern continues, how many lemons will she need for 10 cups of water?
Ruth will need 30 lemons to make lemonade with 10 cups of water.
Ruth is making Lemonade. For 1 cup of water she uses 3 lemins, for 2 cups 6 lemons, ect. The formula to calculate the number of lemons needed for a given cups of water is:
Lemons = 3 × Cups of Water
Therefore, the number of lemons needed for 10 cups of water is:
Lemons = 3 × 10
Lemons = 30
Hence, Ruth will need 30 lemons to make lemonade with 10 cups of water.
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10.A trader bought a screwdriver set for R90. He added 20% to the cost price for profit and expenses. Calculate the amount a customer will pay for the screwdriver set. 1000 (3) [9]
The customer will pay R108 for the screwdriver set.The trader bought a screwdriver set for R90 and added 20% to the cost price for profit and expenses. To calculate the amount a customer will pay for the screwdriver set, we need to add the profit and expenses to the cost price.
First, let's calculate the profit and expenses added by the trader. Since the trader added 20% to the cost price, the profit and expenses will be:
20% of R90 = 0.2 x R90 = R18
Now, we can calculate the selling price of the screwdriver set by adding the cost price and the profit and expenses:
Cost price = R90
Profit and expenses = R18
Selling price = Cost price + Profit and expenses = R90 + R18 = R108
Therefore, the customer will pay R108 for the screwdriver set.
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solve by elimination
5x-3y=16
4x+5y=-2
The value is x in the equation is -2
The value of y in the equation is -8.67
How to calculate the value of x and y using elimination method?5x - 3y= 16...........equation 1
4x + 5x= -2..........equation 2
Multiply equation 1 by 4 and equation 2 by 5
20x - 12y= 64
20x + 25x= -10
-37x= 74
x= -74/37
x= -2
Substitute -2 for x in equation 1
5x - 3y= 16
5(-2) - 3y= 16
-10 -3y= 16
-3y= 16+10
-3y= 26
y= -26/3
y= -8.67
Hence the value of x is -2 and the value of y is -8.67
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7 The time in minutes (7) taken to cook a joint of beef is given by T-35w +25,
where w is the weight of the joint in kg.
a) How long would it take to cook a 1.5 kg joint?
b) Make w the subject of the formula.
c) What weight of beef needs to be cooked for 207 minutes?
d) What weight of beef needs to be cooked for 3 hours and 48 minutes?
1:11
In conclusion for part A it would take T - 32.5 minutes to cook a 1.5 kg joint. For part B w is given by the formula w = (T - 25) / (-35). For part C 6.6 kg of beef needs to be cooked for 207 minutes. For part D 5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.
How to solve?
a) To find how long it would take to cook a 1.5 kg joint, we can substitute w = 1.5 into the formula:
T - 35w + 25 = T - 35(1.5) + 25 = T - 32.5
So, it would take T - 32.5 minutes to cook a 1.5 kg joint.
b) To make w the subject of the formula, we need to isolate w on one side of the equation. We can start by subtracting 25 from both sides:
T - 35w = T - 25
Next, we can divide both sides by -35:
w = (T - 25) / (-35)
Therefore, w is given by the formula w = (T - 25) / (-35).
c) To find the weight of beef that needs to be cooked for 207 minutes, we can substitute T = 207 into the original formula:
T - 35w + 25 = 207
Simplifying this equation, we get:
-35w = -232
Dividing both sides by -35, we get:
w = 6.6 kg
Therefore, 6.6 kg of beef needs to be cooked for 207 minutes.
d) To find the weight of beef that needs to be cooked for 3 hours and 48 minutes (which is equivalent to 3 × 60 + 48 = 228 minutes), we can substitute T = 228 into the original formula:
T - 35w + 25 = 228
Simplifying this equation, we get:
-35w = -207
Dividing both sides by -35, we get:
w = 5.91 kg
Therefore, 5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.
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I NEED HELP ON THIS ASAP!!!
The constraints as a system of linear inequalities include the following;
x + y ≤ 180
x ≥ 40
y ≥ 40
3x + 4y ≤ 640
75x + 60y ≤ 12,900
The solution set for the system of linear inequalities is shown in the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of SOS Smartcall produced in one day and number of SOS Basic produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the SOS Smartcall produced in one day.Let the variable y represent the number of SOS Basic produced in one day.Based on the information provided about this cell phone company, the constraints can be written as a system of linear inequalities as follows;
x + y ≤ 180
x ≥ 40
y ≥ 40
3x + 4y ≤ 640.
75x + 60y ≤ 12,900
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3. If 55% of a number is 11, find the number?
Answer:
20
Step-by-step explanation:
[tex]55% of a number = 11[/tex]% of a number = 11
[tex]\frac{55}{100} * x = 11[/tex]
solve for x
[tex]55x = 1100[/tex]
[tex]x = 20[/tex]
Hope this helps!
Answer:20
Step-by-step explanation:
55%---------11
100%------x
x=100*11/55=20
Determine the intercepts of the line.
Do not round your answers
Kayla wants to purchase some new clothes for the school year and has a budget of $200. The sales tax rate that will apply when she makes her purchases is 7%. Here are the items she wants to purchase:
2 T-shirts, $9. 98 each
1 pair of pants, $25. 99
3 dresses, $24. 99 each
1 pair of shoes, $89. 99
Kayla’s budget be enough to purchase all of the clothing items listed after sales tax is applied because the total will
Kayla would ultimately spend $210.91 + $14.76 = $225.67 for all the clothing items, including sales tax.
To determine if Kayla's budget will be enough to purchase all the clothing items listed after sales tax is applied, we need to calculate the total cost of the items first.
The cost of 2 T-shirts would be 2 x $9.98 = $19.96.
The cost of 3 dresses would be 3 x $24.99 = $74.97.
The cost of 1 pair of pants would be $25.99.
The cost of 1 pair of shoes would be $89.99.
Therefore, the total cost of the clothing items is $19.96 + $74.97 + $25.99 + $89.99 = $210.91.
Next, we need to add the sales tax rate of 7% to the total cost to find the final price that Kayla would pay.
7% of $210.91 = $14.76
Therefore, the final price that Kayla would pay for all the clothing items, including sales tax, is $210.91 + $14.76 = $225.67.
Since Kayla's budget is $200, she would not have enough money to purchase all of the clothing items listed after sales tax is applied.
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Can someone help me with this problem
Step-by-step explanation:
If I=Prt
I is interest earned
P is principal
R is the interest rate
T is time in years
Then substitute the values into the equation
Plug into your calculator
I= 100 x 6% x 3 = 18
Answer for the first one is $18
For the others, it requires you to rearrange the equation.
Good luck!
a large diamond with a mass of 4289.6 grams was recently discovered in a mine. if the density of the diamond is 3.51 grams over centimeters cubed, what is the volume? round your answer to the nearest hundredth. 142.78 cm3 384.96 cm3 1221.9 cm3 33759.15 cm3
If a large diamond with a mass of 4289.6 grams was recently discovered in a mine and the density of the diamond is 3.51 grams over centimeters cubed, the volume is 1221.9 cm³.
To find the volume of the diamond, we need to use its mass and density. The density of the diamond is given as 3.51 grams per cubic centimeter. This means that every cubic centimeter of diamond has a mass of 3.51 grams.
We can use this information to find the volume of the diamond by dividing its mass by its density. Plugging in the given values, we get:
Volume = Mass / Density
Volume = 4289.6 g / 3.51 g/cm³
Volume = 1221.86 cm³
This means that the diamond has a volume of 1221.86 cubic centimeters. However, the question asks us to round the answer to the nearest hundredth, so we round this value to: Volume = 1221.9 cm³
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in this question, we will show the existence and uniqueness of solutions to systems of differential equations with inputs in particular,we previously considered the scalar differential equation
Existence and uniqueness of solutions to systems of differential equations depend on the number of equations and the order of each equation. For example, a system of two first-order equations has a unique solution, while a system of three first-order equations may not have a unique solution.
Previously, we considered the scalar differential equation, which is a single differential equation involving only one independent variable. In this case, the solution to the equation is unique. This is because there is only one equation and only one variable, so the solution must be unique for a given set of initial conditions.
For a system of differential equations, the existence and uniqueness of solutions depend on the number of equations and the order of each equation.
Systems of differential equations with higher order equations or more equations than unknowns may not have a unique solution. On the other hand, if there are more unknowns than equations, then there is always a unique solution. To find the solution, the equations must be solved simultaneously.
In conclusion, A scalar differential equation always has a unique solution.
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By applying the compound angles and without using a calculator, Determine the value of: 1.7.1 cos 15°
Answer:
this is the answer to that problem
Which algebraic expressions are polynomials? Check all that apply.
0 2x³ - -/-/
X
0x³y - 3x² + 6x
□ y² + 5y -√3
02-√4x
0 -x + √6
0-32³-12-2²+1
The algebraic expressions that are polynomials are:
1. 2x³ -/-/-
2. 0x³y - 3x² + 6x
3. -x + √6
What are polynomials?Polynomials are a type of algebraic expression that consists of variables and coefficients, combined using mathematical operations of addition, subtraction, and multiplication, and non-negative integer exponents. The term "poly" means many, and "nomial" means term. Hence, a polynomial is a sum of many terms.
What are algebraic expressions?Algebraic expressions are mathematical expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used in algebra to represent relationships between variables and to solve mathematical problems.
The algebraic expressions that are polynomials are:
1. 2x³ -/-/- (a polynomial of degree 3)
2. 0x³y - 3x² + 6x (a polynomial of degree 3)
3. -x + √6 (a polynomial of degree 1)
The expressions that are not polynomials are:
1. y² + 5y -√3 (not a polynomial because it contains a square root)
2. 02-√4x (not a polynomial because it contains a square root)
3. 0-32³-12-2²+1 (not a polynomial because it contains a negative exponent)
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Adam received a bonus of 15% of his weekly wage of $600. How much of a bonus was given to him?
Answer:
90$
Step-by-step explanation:
We need to find 15% of the number 600:
[tex] \frac{600 \times 15\%}{100\%} = 90 [/tex]
So, the answer is 90$
log4 n=1/4 log4 81 + 1/2 log4 25
Solve and show work
(I cannot for the life of me figure this one out, so please help me !!)
Answer:
Step-by-step explanation:
We can start by using the logarithmic rule that states:
log a (mn) = log a (m) + log a (n)
And also the property:
log a (b^c) = c*log a (b)
With these rules, we can simplify the given expression as follows:
log4 n = 1/4 log4 81 + 1/2 log4 25
log4 n = log4 81^(1/4) + log4 25^(1/2) (using the above properties)
log4 n = log4 (3^4)^(1/4) + log4 (5^2)^(1/2) (81 = 3^4 and 25 = 5^2)
log4 n = log4 3 + log4 5 (using the rule log a (b^c) = c*log a (b))
log4 n = log4 (3*5) (using the rule log a (mn) = log a (m) + log a (n))
log4 n = log4 15
Therefore, the solution to the equation log4 n=1/4 log4 81 + 1/2 log4 25 is:
n = 15
What is 3x+y over z when x=21, y = 36, and z= 49?
Answer:
Step-by-step explanation:
2.02
x=21 so replace x with 21
3(21)+y/z
then do the same with y and z
3(21)+36/49
63+36/49
99/49
SOLUTION 2.02
what is the value expression
1/4 (16 + g) -h
when g=4 and h=2
a 16/3
b 4/5
c 3
d 5
[tex] \bf Question :- \\ [/tex]
what is the value of expression
1/4 (16 + g) -hwhen g=4 and h=2
[tex] \bf Solution :- \\ [/tex]
[tex] \longrightarrow \: \: \frac{1}{4} (16 + g) - h \\ \\ \longrightarrow \: \: \frac{1}{4} (16 + 4) - 2 \\ \\ \longrightarrow \: \: \frac{1}{{ \cancel{4} }} \times( \cancel{ 20)} - 2 \\ \\ \longrightarrow \: \: 1 \times 5 - 2 \\ \\ \longrightarrow \: \: 1 \times 3 \\ \\ \longrightarrow \: \: 3 \\ [/tex]
Henceforth, Option c is the required answer.
What is the equation of the function that is graphed as line b?
ут
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Answer:
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The equation of the function that is graphed as line b is,
⇒ y = - 2x - 1
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line b are (- 1, 1) and (- 2, 3).
Now,
Since, The equation of line passes through the points ( (- 1, 1) and (- 2, 3).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 1)) / (- 2 + 1)
m = 2 / - 1
m = - 2
Thus, The equation of line with slope - 2 is,
⇒ y - 1 = - 2 (x + 1)
⇒ y - 1 = - 2x - 2
⇒ y = - 2x - 1
Therefore, The equation of the function that is graphed as line b is,
⇒ y = - 2x - 1
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When Aaron runs the 400 m dash is finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 2. 5 seconds using the elliptical rule determine the interval of times that represent the middle 99. 7% of his finishing times in the 400 m race
The interval of times that represent the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].
Using the empirical rule or the elliptical rule, we know that in a normal distribution:
approximately 68% of data falls within one standard deviation of the meanapproximately 95% of data falls within two standard deviations of the meanapproximately 99.7% of data fall within three standard deviations of the meanIn this case, we want to find the interval of times that represents the middle 99.7% of Aaron's finishing times, which means we need to find the range of values that fall within three standard deviations of the mean.
So, using the formula for finding the interval of values within k standard deviations of the mean:
lower bound = mean - k * standard deviation
upper bound = mean + k * standard deviation
where k = 3 for this problem, we get:
lower bound = 80 - 3 * 2.5 = 72.5
upper bound = 80 + 3 * 2.5 = 87.5
Therefore, the interval of times that represents the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].
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A turtle and a snail are 300 feet apart when they start moving towards each other. The turtle is moving at a speed of 5 feet per minute, and the snail is moving at a speed of 1 foot per minute. How fast are the turtle and snail approaching each other
The turtle and snail are apprοaching each οther at a rate οf 6 feet per minute.
Let's use the cοncept οf relative speed tο sοlve this prοblem. The relative speed οf twο οbjects mοving tοwards each οther is the sum οf their individual speeds.
What is relative speed?Relative speed is the speed οf an οbject οr persοn in relatiοn tο anοther οbject οr persοn. It is the difference between the velοcities οf twο οbjects mοving relative tο each οther. The relative speed can be calculated by subtracting the velοcity οf οne οbject frοm the velοcity οf the οther οbject.
Let's call the rate at which the turtle and snail are apprοaching each οther "r".
Relative speed = turtle's speed + snail's speed
r = 5 + 1
r = 6 feet per minute
Sο the turtle and snail are apprοaching each οther at a rate οf 6 feet per minute.
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