To explain why A + B is irrational, we need to show that it cannot be expressed as a ratio of two integers.
Suppose that A + B is rational, which means we can write it as the ratio of two integers p and q (where q is not zero):
A + B = p/q
Now, we can substitute the values of A and B and simplify:
√363 + √27 = p/q
We can then rearrange the terms to isolate one of the square roots:
√363 = p/q - √27
We can square both sides of this equation to eliminate the square roots:
363 = p^2/q^2 + 27 - 2(p/q)√27
Notice that the right-hand side of this equation has a term with a square root. This means that if we assume that A + B is rational, we arrive at a contradiction: we have shown that √363 (which is equal to A) is irrational, which means that p^2/q^2 + 27 must also be irrational. However, the left-hand side of the equation is rational. Therefore, our assumption that A + B is rational must be false, and we conclude that A + B is irrational.
To explain why AB is rational, we can use the fact that the product of two rational numbers is rational.
We can rewrite A and B as follows:
A = √(363) = √(121 x 3) = √(11^2 x 3) = 11√3
B = √(27) = √(9 x 3) = √(3^2 x 3) = 3√3
Therefore, AB = 11√3 x 3√3 = 33 x 3 = 99.
Since 99 is a rational number (which can be expressed as the ratio of the integers 99 and 1), we conclude that AB is rational.
The mean monthly salary of female employees of a company is 3750 Birr, while the mean monthly salary of male employees is 4500 Birr. It is known that the mean monthly salary of male and female employees combined is 4000 Birr. a) What is the ratio of the number of female employees to male employees? b) What percentage of employees are females?
what is 45 x 6 i need help
Answer:
270
Step-by-step explanation:
I am showing my mental math, hope this helps you:
45 x 6 is the same as 4 x 6 = 10s place value and 5 x 6 = 1s place value:
4 x 6 = 24
5 x 6 = 30
Therefore, the answer is:
2 (4 + 3) 0
270
The value of the expression 45 x 6 is 270.
We have,
To calculate the product of 45 multiplied by 6, you can follow these steps:
- Start by multiplying the units digits of the two numbers: 5 x 6 = 30.
- Write down the units digit of the result, which is 0, and carry over the tens digit, which is 3.
- Multiply the tens digit of the first number by the second number: 4 x 6 = 24.
- Add the carried-over value from step 2 to this result: 24 + 3 = 27.
- Write down the tens digit of the result, which is 7, and carry over the hundreds digit, which is 2.
- Multiply the hundred digit of the first number by the second number: 4 x 6 = 24.
- Add the carried-over value from step 5 to this result: 24 + 2 = 26.
- Write down the hundred digit of the result, which is 6.
- Combine the hundreds, tens, and units digits together: 6, 7, 0.
- The final product of 45 multiplied by 6 is 270.
So, 45 x 6 = 270.
Thus,
The value of the expression 45 x 6 is 270.
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If GI and JL are parellel lines and m
The measure of angle IHE is 23°.
Since DF and GI are parallel, we know that angle HJF is congruent to angle GHJ. Therefore, we have:
mHJF = mGHJ = 134°
We can now use this information to find the measure of angle IHE. To do this, we need to use the fact that the sum of the angles in a straight line is 180°. Since H, J, F, and I lie on a straight line, we have:
mHJF + mFJI + mIHE = 180°
Substituting the values we know, we get:
134° + mFJI + mIHE = 180°
Simplifying the equation, we get:
mFJI + mIHE = 46°
We still need to find the measure of angle FJI. To do this, we can use the fact that the angles in a triangle add up to 180°. Triangle GHJ is a straight line, so its angles add up to 180°. Therefore, we have:
mGHJ + mHJF + mFJI = 180°
Substituting the values we know, we get:
134° + mFJI + mFJI = 180°
Simplifying the equation, we get:
2mFJI = 46°
Dividing both sides by 2, we get:
mFJI = 23°
Finally, we can substitute this value back into our earlier equation to find the measure of angle IHE:
mFJI + mIHE = 46°
23° + mIHE = 46°
Subtracting 23° from both sides, we get:
mIHE = 23°
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Complete Question:
If DF and GI are parallel lines and mGHJ = 134°, what is mIHE?
PLEASE HELP ME QUICK!!!
Answer:
Option D. [tex]g(x)=5(0.8)^{x}+2[/tex]
Step-by-step explanation:
Main concepts
Concept 1: identifying horizontal asymptote
Concept 2: assuring decreasing exponential function
Concept 1. identifying horizontal asymptote
Any exponential function of the form [tex]y=a*b^x[/tex] has a horizontal asymptote on the x-axis. A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number. Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units. Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.
Concept 2. assuring decreasing exponential function
Exponential functions of the form [tex]y=a*b^x[/tex] increase or decrease based on the value of "b".
If "b" is between 0 and 1 (a "small" number), the function will decrease.If "b" is larger than 1 (a "big" number), the function will increase.Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.
To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.
Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.
Models that represent z+9=14 ASAP
To represent z+9=14, we can start by subtracting 9 from both sides of the equation:
z + 9 - 9 = 14 - 9
Simplifying the left side of the equation gives:
z = 5
Therefore, the solution to the equation z+9=14 is z=5.
Plsss help meeee quick
Answer:
B
Step-by-step explanation:
Lateral surface contains B,C and D (because A and E are bases)
A (lateral surface area) = 70 + 70 + 56 = 196 cm^2
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A population of rabbits is increasing at a rate of 1.5% per month. If there are 60 rabbits today, how many will there be after 10 months? Round to the nearest whole.
If population of rabbits is increasing at a rate of 1.5% per month, after 10 months, there will be approximately 71 rabbits in the population.
To solve this problem, we need to use the formula for exponential growth:
A = P(1 + r)ᵗ
where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time period. In this case, we have P = 60, r = 0.015 (1.5% expressed as a decimal), and t = 10.
Plugging these values into the formula, we get:
A = 60(1 + 0.015)¹⁰
A ≈ 71
t's important to round to the nearest whole, so we can't be exact, but we know the answer will be somewhere between 70 and 72 rabbits.
Exponential growth is a model that assumes continuous growth over time, which may not be entirely accurate in real-world scenarios.
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A spinner divided into three equal sections marked A A and Z is spun 570 times approximately how many times will it be expected to land on an A
If a spinner divided into three equal sections marked A A and Z is spun 570 times . The number of times it will be expected to land on an A is 380 times.
How to find the Expected number of time ?Since the spinner has three equal sections in which two of them are marked A. The probability of landing on an A in a single spin will be 2/3 while the probability of landing on Z will be 1/3.
So,
Expected number of time E(A) =Number of spins x Probability of landing on A
Expected number of time E(A) = 570 x (2/3)
Expected number of time E(A) = 380
Therefore the Expected number of time E(A) is 380 times.
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Find the exact value of each of the remaining trigonometric functions of θ.
tan θ= -3/5, sec θ>0.
If given trigonometric functions of θ are tan θ= -3/5, sec θ>0, the exact value of sin θ is 3/√(34).
To find the value of sin θ, we can use the Pythagorean identity: sin²θ + cos²θ = 1.
First, we need to find the value of cos θ. We know that sec θ = 1/cos θ and sec θ > 0, which means that cos θ > 0. Therefore, we can use the identity: tan²θ + 1 = sec²θ to find the value of cos θ.
tan θ = -3/5
tan²θ = 9/25
sec²θ = tan²θ + 1 = 34/25
cos²θ = 1/sec²θ = 25/34
cos θ = √(25/34) = 5/√(34)
Now, we can use the Pythagorean identity to find sin θ:
sin²θ + cos²θ = 1
sin²θ = 1 - cos²θ
sin²θ = 1 - 25/34
sin²θ = 9/34
sin θ = √(9/34) = 3/√(34)
In trigonometry, the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) are used to relate the angles of a triangle to its sides. The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words, sin θ = opposite/hypotenuse.
Knowing the value of sin θ is important because it allows us to calculate the values of the other trigonometric functions. For example, cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse, so we needed to find the value of cos θ to calculate sin θ.
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Use the Law of Sines. Find the measure x to the nearest tenth.
Answer:
Step-by-step explanation:
Law of sines states that the lengths of the sides of a triangle are proportional to the sines of the corresponding angles.
sinM/17 = sinx/10
sin M = .94551
.94551/17 = sin x /10
cross mulitply and then divide.
.954551 · 10/17 = sin x
9.4555/17 = .5562
sin inverse is 33.793 ° or rounded to 33.8°
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two serving of blueberry pie provides 1290 calories
The caloric content for ice cream C is 250 calories while the caloric content for ice cream B is 270 calories.
How to determine the caloric contentTo determine the caloric content, we will assign algebraic notations to each of the dessert types.
1 Icecream + 2 Blueberry pie = 790 calories
3 icecream + 2 Blueberry pie = 1290 calories
Now the first equation will be subtracted from the second equation as follows:
2 icecream = 500 calories
So, 1 ice cream is 250 calories.
Also, since, 1 icecream serving equals 250 calories, 2 Blueberry pies = 790 - 250 = 540 calories, and 1 Blueberry pie equals 270 calories.
Complete question:
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two servings of blueberry pie provides 1290 calories. Find the caloric content of each item.
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Rosie earns $25 for travel time plus $18 an hour working at her uncle’s shop. Write an expression that can be used to find the amount Rosie will earn for working, 7, hours.
Answer:
Earned = 25 + 18h
Earned = 151
Step-by-step explanation:
The amount earned is the travel time plus the amount per hour times the hours
Earned = 25 + 18h
She works 7 hours
Earned = 25 + 18*7
Earned = 25 + 126
Earned = 151
In each diagram, one square unit represents 10 square centimeters. Find the area of each figure. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
Lines and Angles
10) In the figure below BD is the perpendicular bisector of AC. Find the value of x.
3(2x-8)
4425
Enter your answer in the box.
x=
Since BD is the perpendicular bisector of AC, then AB = BC, which implies 2x - 8 = 5x - 17.
Solving for x, we have:
3(2x - 8) = 4425
6x - 24 = 4425
6x = 4451
x = 741.83
Rounding to the nearest whole number, we have x = 742.
Therefore, x = 742.
S = [10, 11, 13, 19, 21, 23, 29, 30]
A = The number is At least 21
B = the number is Between 12 and 25
O = number is Odd
L = number is a Less than 25
Which events are independent.
After considering all the given options we conclude that the number is atleast 21 and the less than 25, which is Option C.
It is given to us that two events are independent if they take place then one event does not trigger the probability of the other event.
Now if the taking place of a certain event triggers the other event then it is referred as dependent
For the given case, we have four events A, B, Q and L.
A = the state when the given number is At least 21
B = is the sate when the given number is Between 12 and 25
Q = is the sate when the given number is Odd
L = is the state when the given number is a Less than 25
It is clearly visible that events A and L are independent due to the number being at least 21, it doesn't affect whether it's less than 25 or not. So, events B and Q are independent because if we know that a number is between 12 and 25, it doesn't affect whether it's odd or not.
Hence, option C) A and L is correct.
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The complete question is
S = [10, 11, 13, 19, 21, 23, 29, 30]
A = The number is At least 21
B= the number is Between 12 and 25
Q = number is Odd
L= number is a Less than 25
Which events are independent.
Question options:
A) A and B
B) A and O
C) A and L
D) Band O
E) Land B
F) Land O
G) None of the 2 events are independent
.If $10,000 is deposited in an account earning 5 ¾ % interest compounded monthly. How much money will be in the account in 5 years.
The total amount in the acount in 5 years is approximately $13,321.76.
What is the accrued amount in the account in 5 years?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n} )^{n*t}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $10,000Compounded monthly n = 12Time t = 5 yearsInterest rate r = 5 3/4% = 5.75%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 5.75/100
r = 0.0575
Plug the given values into the above formula and solve for A.
[tex]A = P( 1 + \frac{r}{n} )^{n*t}\\\\A = 10000( 1 + \frac{0.0575}{12} )^{(12*5)}\\[/tex]
A = $13,321.76
Therefore, the accrued amount is $13,321.76.
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A map shows the vertices of a campsite are (25,10), (25,-5), (-5,-5), and (-5,10). The vertices of your tent are (0,-3), (0,6), (10,6), and (10,-3). The coordinates are measured in feet. What percent of the campsite is not covered by your tent?
The percent of the area that is not covered is 80 percent
How to calculate the area that is not coveredIn mathematics area is defined as the absolute or total space that an object or shape occupies. It is usually measured using centimeters, cm ² square or the use of meter square m ².
area of tent
= (10 - 0) * (6 - (-3))
= 90
The area of the campsite would be:
(25 - (-5) x (10 - (-5))
= 450
Then the area would be 450 - 90
= 360
the percentage that is not covered by tent = 360 / 450 x 100
= 80 percent
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Find the probability that
event A or B takes place.
The probability that event A or B takes place is P ( A ∪ B ) = 6/17
Given data ,
Let the probability that event A or B takes place is P ( A ∪ B )
Now , the probability of A is P ( A ) = 2/17
And , the probability of B is P ( B ) = 4/17
where P ( A ∩ B ) = 0
On simplifying the equation , we get
P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )
So , P ( A ∪ B ) = 2/17 + 4/17
P ( A ∪ B ) = 6/17
Hence , the probability is 6/17
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what is – 7n + –3 – 6n + 3 + 5 is simpified
Answer:
-13n + 5
Step-by-step explanation:
Give:
– 7n + –3 – 6n + 3 + 5
To Find:
simplify
Explanation:
– 7n + –3 – 6n + 3 + 5
= (-7n - 6n) + (-3 + 3 + 5)
= - 13n + 0 + 5
= -13n + 5
Final Answer:
-13n + 5
A swimming pool holds 450, 000 L
of water and has two drainage
pipes.
Pipe A, by itself, can drain the pool
in 150 minutes. Pipe B, by itself, can
drain the pool in 225 minutes.
If you turned on both pipes at the
same time, how many minutes
would it take to drain the pool?
Using a linear equation, the minutes it would take both pipes to drain the swimming pool that holds 450,000 liters is 90 minutes.
What is a linear equation?A linear equation is an equation of a straight line written in the form of y = mx +b, where m is the slope.
The quantity of water the swimming pool holds = 450,000 liters
The drainage time of Pipe A working alone = 150 minutes
Drainage rate of Pipe A = 3,000 liters per minute (450,000 ÷ 150)
The drainage time of Pipe B working alone = 225 minutes
Drainage rate of Pipe B = 2,000 liters per minute (450,000 ÷ 225)
The drainage rate of the combined pipes = 5,000 liters per minute (3,000 + 2,000)
Let the number of minutes for both pipes to drain the pool = x
Therefore, the linear equation is 5,000x = 450,000
x = 90 minutes (450,000 ÷ 5,000)
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if my circular garden requires 2 cups of water per 10 square feet, how many cups of water do i need when the radius is 3 feet
Can you guys help me out?
Step-by-step explanation:
For f(3) 3 is >= 2 so you use the second portion of the function :
f(3) = 5x+2 = 5(3) + 2 = 17
If Charlie invested $1,000 in an account paying 10% compounded monthly, how much will be in the account at the end of 10 years?
Answer:
Compound Interest Formula: A = P (1 + R/100)^t
P = Principle ($1,000)R = Rate (10%)T = Time (10 years)A = 1000 (1 + 10/100)^10
A = $2593.74
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Let u = - 2i + 5j v = 6i - j and w oplus=81 Find 3u - (5v - w)
Answer: ⬇️
Step-by-step explanation:
Given, u=(2,4,−5) and v=(1,−6,9).Now,3u−5v=3(2,4,−5)−5(1,−6,9)=(1,42,−60).
please help for this question
The single transformation that maps shape A to shape B is: Reflection about the line x = -2
What is the transformation rule?There are different ways of carrying out transformation of objects and they are:
Reflection whereby all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection
Rotation whereby all points are rotated about a point.
Dilation where the object is reduced or increased by a scale factor.
Translation where the object is moved from one point to another.
Looking at the given image, we can tell that this denotes a reflection because it is the exact same shape and looks like a mirror image which was reflected over the line x = -2
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‼️HELP CUZ IM SO LOST PLEASE‼️
Using two column proof we have been able to show that AB ║ EC
by definition of alternate interior angles
How to use two column proof?A two-column proof is defined as a two-column table labeled with statements on the left-hand side and reasons on the right-hand side.
The two column proof of the given diagram is as follows:
Statement 1: ΔADE is an Isosceles Triangle
Reason 1: Given
Statement 2: ∠DEA ≅ ∠DAE
Reason 2: Properties of Isosceles Triangles
Statement 3: ∠ADE = 20°
Reason 3: Sum of angles in a triangle
Statement 4: ∠BAD ≅ ∠EDA
Reason 4: Congruent Angles
Statement 5: ∠BAD and ∠EDA are alternate angles
Reason 5: Alternate angles are congruent
Statement 6: AB ║ EC
Reason 6: Definition of alternate interior angles
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A new television set was recently purchased for the common room in a Residence Hall for $451.50 including tax. If the tax rate is 5%, find the price of the television set before taxes.
Answer:
430
Step-by-step explanation:
Let's call the price of the television set before taxes "x".
The total cost including tax is $451.50, which is equal to x plus 5% of x (the tax). In other words:
x + 0.05x = $451.50
Simplifying the left side by factoring out x, we get:
1.05x = $451.50
Dividing both sides by 1.05, we get:
x = $430
Therefore, the price of the television set before taxes was $430.
Find the volume of the cone shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer: 100.48 cubic feet
Step-by-step explanation:
Find the real or imaginary solutions of the following equation by factoring.
w³-512=0
Choose the correct answer below.
OA. -8,4+4√3i, 8-4√3i
OB. 64,- 64+8i, 64-8√3i
O C. -512, -4+4√3i, -8-4√3i
OD. 8, -4+4√3i, -4-4√3i
