The sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954
What is Pythagoras's theorem?
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle or in standard algebraic notation, a² + b² = c², is equal to the squares on the legs.
What is the sum of numbers?
The outcome or conclusion we arrive at when we add two or more integers is known as the sum. Addends are the numbers that are added.
Here, we calculate the sum of the given numbers
= (1³)^²⁰ + (1³)²⁰ + (2³)²⁰ + (-2³)²⁰
= 2,305,843,009,213,693,954
Hence, the sum of the numbers they wrote on the piece of paper is 2,305,843,009,213,693,954.
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The ____ of 12 is -12.
Answer; the Negative of 12 is -12
Step-by-step explanation: first of all the reciprocal of 12 is 1 over 12. so that's not it. The absolute value of 12 is still 12 so that's not it. So the only thing that it can be is the Negative of 12 is -12
a sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. determine the decision rule for rejecting the null hypothesis, h0, at the 0.10 level.
The alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
Given that;
A sample of 900 computer chips revealed that 34% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature states that 31% of the chips do not fail in the first 1000 hours of their use. the quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage.
To get decision rule for rejecting the null hypothesis, h0, at the 0.10 level;
n = 900
P = 0.34
p = 0.31
α = 0.10
Claim: More than 31% do not malfunction within the first 1000 hours of operation.
The null and alternative hypothesis must be stated.
This is a right-tailed test because the claim is directional to the right side (> type).
Therefore, the alternative hypothesis and null are:
H₀ : p = 0.31 vs H₁ : p > 0.31
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Here you go LOL didn't get all the files. I need help TWT
Answer:
First option
Step-by-step explanation:
→ Define domain
The set of x values a function can take
→ Identify
2 to negative infinity
A family of four goes to a movie theater and spends $26.50. They buy 2 children's tickets at
$3.50 per ticket, 2 adult tickets, and 3 boxes of popcorn at $2.50 per box. What is the cost of
an adult ticket?
(Algebra)
Answer:
$6.50
Step-by-step explanation:
3.50(2)+2x+2.50(3)=26.50
6.00+2x+7.50=26.50
13.50+2x=26.50
2x=13.00
x=6.50
Ms. Grace bought 3 bags of dog treats for $7.38. What is the cost per bag of dog treats?
Answer:
$2.46
Step-by-step explanation:
7.38/3 = 2.46
2.46 x 3 = 7.38
(2sin(x) - 1)(tan(x) - 1) = 0 for 0 ≤ x ≤ 2 pi
Answer: x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4
Step-by-step explanation:
2sin(x)-1=0
tan(x)-1=0
sin(x)=1/2
tan(x)=1
x=π/6
x=5π/6
x=π/4
x=5π/4
x1=π/6 ,x2 = π/4, x3 = 5π/6, x4 5π/4
Sam catches a sale on airline tickets that are being discounted 15%. He purchases a flight that normally costs $235. What is the new price of the flight?
The new price of the flight is $208.25
How to determine the new price of the flight?In this question, we have the following parameters
Discount proportion = 15%
Cost of flight = $245
This means that
New price = Cost of flight x (1 - Discount proportion)
Substitute the known values in the above equation, so, we have the following representation
New price = $245 x (1 - 15%)
Evaluate the product
New price = $208.25
Hence, th new price is $208.25
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if a password is to have 4 digits, each from 0 to 9, what is the probability that there will be no repeats on the digits?
The probability that there will be no repeats on the digits is 0.504.
What is meaning of probability?
The ratio of favorable outcomes with the total number of outcomes is known as probability of that event.
The number of digits of the password is 4.
The numbers from 0 to 9 is 10.
If the digit can repeat, then we can chose first digit in 10 ways, the second digit in 10, third digit in 10 ways and fourth digit in 10 ways.
The total number of ways is 10 × 10 × 10 × 10 =10000.
If the digit can't repeat, then we can chose first digit in 10 ways, the second digit in 9 (because we can't use first digit) , third digit in 8 ways (because we can't use first digit and second digit) and fourth digit in 7 ways(because we can't use first digit, second digit, and third digit).
The total number of ways is 10 × 9 × 8 × 7 =5040.
The favorable outcomes for this event is 5040.
The total number of outcomes is 10000.
The required probability is 5040/10000 = 0.504.
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Need help asap
Solve by using elimination. Express your answer as an ordered pair.
3x−2y=11
3x−y=7
The solution to the given set of systems of equations is (x, y) = (1, -4).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let's determine the solution using the elimination Method
3x−2y=11 (Equation 1)
3x−y=7(Equation 2)
Multiply the second equation by 2.
6x - 2y = 14 (Equation 3)
Now subtract the first equation from third to eliminate the y.
6x - 2y - (3x - 2y) = 14 - 11
3x = 3
x = 1
Now to find the value of y,
3x−y=7
3(1) − y = 7
y = 7 - 3
y = -4
Therefore, the solution to the given set of systems of equations is (x, y) = (1, -4).
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Solve using proportions: If a 4-pound roast takes 140 minutes to cook, how long should a 5-pound roast take to cook?
Step-by-step explanation:
[tex]4pound \: roast \: = 140 \: minutes \\ 5 \: pounds \: roast \: = {?} \\ then cross multiplication \\ 140 \times 5 \: divide \: by \: 4 \\ 700 \div 4 = 175 \\ 5 \: pound \: roast \: take \: 175 \: minutes[/tex]
you want to obtain a sample to estimate a population proportion. based on previous evidence, you believe the population proportion is approximately 40%. you would like to be 90% confident that your estimate is within 1.5% of the true population proportion. how large of a sample size is required?
The largest sample size required is 2886.4.
Here we have to calculate how large of a sample size is required.
The formula:
(Z ∝I2/ E)² × P( 1- P)
The given data:
Margin error (E) = 1.5%
=0.015
As it is given that 90% confident that your estimate is within 1.5% of the true population proportion, therefore we have:
The level of significance(∝) = 1 - 0.90
= 0.10
The z value for the 90% confidence is 1.645
Therefore the largest of a sample size is required = ( 1.645/ 0.015)²× ( 0.4)(1- 0.4)
= 2886.4
The largest a sample size required is 2886.4
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4. A park charges $8 for adults and $4 for kids. How many of each type of ticket was sold if a total of 325 tickets were sold for a total of $1812?
Answer:
1300 and 750
Step-by-step explanation:
mark me on brainliest please follow me to
Y+4=2(x-7)
In standard form
Answer:
2x-y=18
Step-by-step explanation:
y + 4 = 2(x - 7) (open brackets)
y + 4 = 2x - 14 (re arrange)
4 + 14 = 2x - y
2x - y = 18
I (O,6), J (-1,1)
Help me find the slope please
Answer:
The slope is 5.
Step-by-step explanation:
[tex]m = \frac{1 - 6}{ - 1 - 0} = \frac{ - 5}{ - 1} = 5[/tex]
Solve for n.
5(n+4)
3
O-24
24
22
O-22
=n-8
The value of n is -22.
What is a variable?
Any traits, figures, or amounts that may be gauged or counted are considered variables.
Given:
5(n+4)/3=n-8
Move 3 to the right
5(n+4)=3(n-8)
5n+20=3n-24
5n-3n= -24-20
2n=-44
n=- 44/2=-22
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plsssssssshelpppppppppp
a) The correct equation to represent the given condition is;
⇒ 4 (x + $3) = $36
Where, x represents the amount Pablo parents added in each day.
b) The amount to added by his parents in his account = $6
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
For 4 days, Pablo put $3 into his account.
And, His parent also add the some money to his saving account.
In the end, there was a total $36 in his account.
Now,
Let the amount Pablo parents added in each day = x
So, We can formulate;
⇒ 4 (x + $3) = $36
Solve for x as;
⇒ 4x + $12 = $36
⇒ 4 x = $36 - $12
⇒ 4x = $24
Divide by 4 both side, we get;
⇒ x = $6
Thus,
a) The correct equation to represent the given condition is;
⇒ 4 (x + $3) = $36
Where, x represents the amount Pablo parents added in each day.
b) The amount to added by his parents in his account = $6
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PLEASE HELP MEEE!!!!!!!!!
Each function operation should be matched with what it is equivalent to as follows:
f(x) + g(x) = -2x² + x + 6.
g(x) - f(x) = -2x² - 5x + 2.
f(x) · g(x) = -6x³ - 10x² + 8x + 8.
h(x) - f(x) = 3x² - 7x - 2
f(x) · h(x) = 9x³ - 6x² - 8x.
f(x) + g(x) + h(x) = x² - 3x + 6.
How to determine the solutions of the given function?In order to determine the solutions of the given function, we would have to evaluate each of the function based on the required mathematical operations as follows.
From the information provided, we have the following functions:
f(x) = 3x + 2
g(x) = -2x² - 2x + 4
h(x) = 3x² - 4x
f(x) + g(x) = 3x + 2 + (-2x² - 2x + 4)
f(x) + g(x) = 3x + 2 - 2x² - 2x + 4
Next, we would rearrange the function by collecting like terms as follows:
f(x) + g(x) = -2x² + (3x - 2x) + (2 + 4)
f(x) + g(x) = -2x² + x + 6 (solution).
g(x) - f(x) = -2x² - 2x + 4 - (3x + 2)
Opening the bracket, we have:
g(x) - f(x) = -2x² - 2x + 4 - 3x - 2
Next, we would rearrange the function by collecting like terms as follows:
g(x) - f(x) = -2x² + (-2x - 3x) + (4 - 2)
g(x) - f(x) = -2x² - 5x + 2 (solution).
f(x) · g(x) = (3x + 2) × (-2x² - 2x + 4)
Opening the bracket, we have:
f(x) · g(x) = -6x³ - 6x² + 12x - 4x² - 4x + 8
Next, we would rearrange the function by collecting like terms as follows:
f(x) · g(x) = -6x³ + (-6x² - 4x²) + (12x - 4x) + 8
f(x) · g(x) = -6x³ - 10x² + 8x + 8 (solution).
h(x) - f(x) = 3x² - 4x - (3x + 2)
h(x) - f(x) = 3x² - 4x - 3x - 2
h(x) - f(x) = 3x² - 7x - 2 (solution).
f(x) · h(x) = (3x + 2) × (3x² - 4x)
f(x) · h(x) = 9x³ - 12x² + 6x² - 8x
f(x) · h(x) = 9x³ - 6x² - 8x (solution).
f(x) + g(x) + h(x) = 3x + 2 + (-2x² - 2x + 4) + (3x² - 4x)
f(x) + g(x) + h(x) = -2x² + x + 6 + 3x² - 4x
f(x) + g(x) + h(x) = x² - 3x + 6 (solution).
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Find the total amount given the original price and tax rate. Round to the nearest cent if necessary. $31.69, 6%
The total amount given the original price and tax rate is $33.59
How to determine the total amount?From the question, we have the following parameters:
Original price = $31.69
Sales tax rate = 6%
In order to determine the total sales amount, we make use of the following total sales equation
Total sales = original price + original price * sales tax rate
Substitute the known values in the above equation
So, we have the following equation
Total sales = 31.69 + 31.69 * 6%
Evaluate
Total sales = 33.59
Hence, the total amount is $33.59
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Find the slope of the line that passes through the pair of points (8, −2), (1, 1)
The slope of the line that passes through the given pair of points is, -3/7.
What is slope of the line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. where "m" represents a line's slope. So, the slope of a line is tanθ.
Given: (8, -2), (1, 1)
Since, if two points [tex](x_1, y_1), (x_2, y_2)[/tex] are given then slope (m) is defined as,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex].
Here,
[tex](x_1, y_1) = (8, -2)\\(x_2, y_2)=(1, 1)[/tex]
So, the slope can be defined as,
[tex]m = \frac{1-(-2)}{1-8} \\m=\frac{3}{-7} \\m=-\frac{3}{7}[/tex]
Hence, the slope of the line that passes through the given pair of points is, -3/7.
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Which of the following equations have exactly one solution?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
6
x
−
6
=
15
x
+
15
6x−6=15x+156, x, minus, 6, equals, 15, x, plus, 15
(Choice B)
B
6
x
+
15
=
6
x
+
15
6x+15=6x+156, x, plus, 15, equals, 6, x, plus, 15
(Choice C)
C
6
x
−
15
=
6
x
+
15
6x−15=6x+156, x, minus, 15, equals, 6, x, plus, 15
(Choice D)
D
6
x
−
6
=
6
x
+
15
6x−6=6x+156
The equation which has exactly one solution is 6x - 6 = 15x + 15.
The correct answer option is option A
Solving equations with one solutionCheck all that applies:
6x - 6 = 15x + 15
6x - 15x = 15 + 6
- 9x = 21
divide both sides by -9
x = 21/-9
x = -2.33
6x + 15 = 6x + 15
6x - 6x = 15 - 15
0 = 0
False
6x - 15 = 6x + 15
6x - 6x = 15 + 15
0 = 30
False
6x - 6 = 6x + 15
6x - 6x = 15 + 6
0 = 21
False
In conclusion, the 6x - 6 = 15x + 15 has only one solution.
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(jk−1)÷j when j=−4 and k=−0.9
The evaluation of the expression for the given values of j and k is -0.65
Evaluating an ExpressionFrom the question, we are to evaluate the given expression for the given values of j and k.
From the given information,
The given expression is
(jk - 1) ÷ j
and
j = -4 and k = -0.9
Now, substitute the values of j and k into the expression
(jk - 1) ÷ j
((-4)(-0.9) - 1) ÷ -4
= (3.6 - 1) ÷ -4
= 2.6 ÷ -4
= - 0.65
Hence, the value of the expression is -0.65
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14. the mean price of a pound of ground beef in 75 cities in the midwest is $2.11 and the standard deviation is $0.56. suppose the histogram of the data shows that the distribution is unimodal and symmetrical. a local grocer is selling a pound of ground beef for $3.50. what is this price in standard units? assuming the empirical rule applies, would this price be unusual or not? round to the nearest hundredth.
For a unimodal distribution which is symmetrical with a mean price of $2.11 and standard deviation of $0.56, a local grocer’s price of $3.50 in standard units would be 2.282 and it is unusually expensive.
A unimodal distribution refers to a distribution with one clear peak as the values increase to a single highest point after which they. It can be symmetrical or non-symmetrical. A symmetrical distribution refers to a distribution whose mean, mode, and median are all equal.
The standard score (z) is given by:
z = (x - µ)/σ where µ is the mean and σ is the standard deviation.
To determine the value of z for $3.50 price:
z = (3.5 – 2.11)/0.56 = 2.482
From the z-table, the probability of z ≥ 2.282
P (z ≥ 2.282) = 1 – P (z < 2.282) = 1 – 0.98876 = 0.0112 or 1.12%
Hence, the price of $ 3.50 is unusually high.
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Help find the Perimeter of 4,5,6 please
The perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm and 28 inches respectively.
We need to find the perimeter of given figures.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
4) Now, sum of all the sides
= 5+3.5+1.5+3.5+5+3.5+1.5+3.5 m
= 27 m
5) Here, radius = Diameter/2 = 17 cm
Perimeter = 2 semicircles+2(17) cm
= 2 × 1/2 πr + 2×17
= 2 × 3.14 × 17 + 34
= 140.76 cm
6) In the given figure here, there are 4 similar triangles
= 4(4+3) inches
= 4 × 7
= 28 inches
Therefore, the perimeters of the given figures 4, 5, 6 are 27 m, 140.76 cm and 28 inches respectively.
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Is x + 1/y = 7 a linear equation?
[tex]x + \frac{1}{y} = 7[/tex]
The equation ; x + 1/y = 7 as given in the task content is a linear equation.
What are linear equations?It follows from the task content that the equation given in the task content is to be identified as linear or not.
Since the given equation is; x + 1/y = 7;
It is noteworthy to know that a linear equation is one in which case, the greatest exponent of the variable is; 1.
Therefore, since the greatest exponent of a variable in the given equation is 1; it follows that the equation is a linear equation.
Hence, the equation given in the task content; x + 1/y = 7 is a linear equation.
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pls help! Last year, 180 new houses were built in a neighborhood. So far this year, 5/6 of them have been sold. How many new houses have been sold this year? Write your answer in simplest form.
Answer:
150 Houses
Step-by-step explanation:
180/6=30. Every 1/6 is 30 houses. Therefore you multiply 30x5 to get 150. 150 is 5/6 of the houses sold.
Sabrina needs more than 42 ft.³ of soil to top up her raised garden bed. each bag of soil contains 1.75 ft.³. Write and solve any inequality to find how many bags of soil Sabrina needs
The inequality that represents the quantity of bags of soil Sabrina needs is 1.75x > 42
The bags of soil needed is 24 bags
What is inequality?Inequality as used in math refers to relations that are not precisely equal
How to determine the bags of soil Sabrina needsSabrina needs more than 42 ft.³ of soil to top up her raised garden bed
> 42 ft³
each bag of soil contains 1.75 ft.³
let the number of bags of soil be x, such that
1.75x > 42
x > 42 / 1.75
x > 24
Sabrina needs at least 24 bags of soil
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Find X in all three problems below
The lengths for the missing side of each case, determined by the use of trigonometric functions, are listed below:
Case D: 50.513
Case E: 46.165
Case F: 2.052
How to determine missing lengths of right triangles by trigonometric functions
In this problem we have three cases of right triangles, each of which has an unknown side length. Each length can be found by using trigonometric functions. Now we proceed to determine it for each case:
Case D
tan 29° = 28 / x
x = 28 / tan 29°
x ≈ 50.513
The missing side length is approximately 50.513 units.
Case E
tan 18° = 15 / x
x = 15 / tan 18°
x ≈ 46.165
The missing side length is approximately 46.165 units.
Case F
cos 70° = x / 46
x = 46 · cos 70°
x ≈ 2.052
The missing side length is approximately 2.052 units.
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an old-model machine can stamp 1000 parts in four hours. a newmodel machine can stamp 1000 parts in just two hours. how long will it take one old-model and one new-model machine to stamp 1000 parts working together?
It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.
Given that;
Finding the hourly cost of stamping parts for each machine is one way to approach this issue.
In 4 hours, the outdated equipment can stamp 1000 pieces. That means that it produces 250 parts per hour (1000 divided by 4). The new machine produces 1000 parts in two hours, which translates to 500 components every hour of stamping (1000 divided by 2).
If t is the amount of time that both machines are simultaneously stamping, then to determine the output, which must be 1000 parts, we simply multiply the rates of the two machines by t.
By multiplying the unknown time, t, by each of the two machines' rates and setting the result equal to 1000, it is possible to determine the precise amount of time required. Equation form of this is;
250t + 500t = 1000
750t = 1000
t = 1000/750
t = 1.333
It will take 1 hour 20 mins for one old-model and one new-model machine to stamp 1000 parts working together.
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What does negative 3 over 5 > −2 indicate about the positions of negative 3 over 5 and −2 on the number line? (1 point) a negative 3 over 5 is located on the right of −2 b negative 3 over 5 is located on the left of −2 c negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 d negative 3 over 5 is located on the left of 0 and −2 is located on the right of 0
This is worth 40 points pls help
Answer:
−2 c negative 3 over 5 is located on the right of 0 and −2 is located on the left of 0 d negative 3 over 5
Step-by-step explanation:
A construction company is planning the foundation for a house. Stakes have been placed in the ground to mark the corners of the foundation. The four sides formed are measured as 20 feet, 20 feet, 48 feet, and 48 feet. The diagonal of the quadrilateral formed is measured to be 54 feet.
What type of triangle is formed by the diagonal and two sides of the current foundation plan?
Answer:
See below
Step-by-step explanation:
It is NOT a right triangle or the diagonal would measure 52 feet (instead of 54 feet) ....it is an OBTUSE triangle