The probability that more than 91,000 cars will pass through the M50 toll is 0.2227, or 22.27% to 4 decimal places.
The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The probability mass function of the Poisson distribution is given by:
P(X = x) = (lambda^x * e^-lambda) / x!
Where lambda is the mean rate of occurrence and x is the number of occurrences. In this case, lambda = 90,000 and we want to find the probability that X > 91,000. We can use the cumulative distribution function (CDF) of the Poisson distribution to find this probability:
P(X > 91,000) = 1 - P(X <= 91,000)
Using the CDF of the Poisson distribution, we can calculate P(X <= 91,000) as follows:
P(X <= 91,000) = e^-lambda * sum_{i=0}^{91,000} (lambda^i / i!)
Using a calculator, we can find that P(X <= 91,000) = 0.7773. Therefore, the probability that more than 91,000 cars will pass through the M50 toll is:
P(X > 91,000) = 1 - 0.7773 = 0.2227
So the probability that more than 91,000 cars will pass through the M50 toll is 0.2227, or 22.27% to 4 decimal places.
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What is the value of x?
Answer:
x = 106 degrees
Step-by-step explanation:
we can create a triangle with angles x, 30, and 26+18.
that means x + 30 + (26 + 18) = 180.
move the constants to one side to get x = 180 - 30 - (26 + 18) = 106
Look at the relative frequency table above. What is P(X = 9) assuming the table represents all possible outcomes?
Using probability distribution, we can find that P(x=9) = 0.13
What do you mean by probability distribution?To determine the chance of each potential value that a random variable might have, a function known as the probability distribution is used. A discrete probability distribution can be defined using a probability distribution function and a probability mass function.
Both a probability density function and a probability distribution function can be used to define a continuous probability distribution. The geometric, Bernoulli, binomial, and Bernoulli distributions are examples of probability distributions.
Now in the given question,
P(3) = .04
P(6) = .62
P(12) = .21
Now,
p (3) + p (6) + p (9) + p (12) = 1
0.04 + 0.62 + p(9) + 0.21 = 1
p(9) = 0.13
Therefore, the value of P (9) = 0.13
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A box is being pushed up an incline of 58 degrees with a force of 150 N (which is parallel to the incline) and the force of gravity on the box is 40 N (gravity acts straight downward). Find the magnitude of the resultant force ||FR|| and round to two decimal places.
The magnitude of the resultant force ||FR|| is 80.55 N.
The weight of the box is acting straight downward, perpendicular to the incline, so it does not affect the magnitude of the resultant force parallel to the incline. Therefore, we only need to consider the force of 150 N pushing the box up the incline.
Let's call the angle between the force of 150 N and the incline "theta". We can find theta by subtracting 58 degrees from 90 degrees (since the incline is at an angle of 58 degrees with respect to the horizontal). So:
theta = 90 degrees - 58 degrees
theta = 32 degrees
Now we can use trigonometry to find the component of the force of 150 N parallel to the incline. We'll use sine, since we know the hypotenuse (the force) and the opposite side (the component parallel to the incline):
sin(theta) = opposite/hypotenuse
sin(32 degrees) = ||FR||/150 N
Solving for ||FR||, we get:
||FR|| = 150 N * sin(32 degrees)
||FR|| ≈ 80.55 N
Therefore, the magnitude of the resultant force is approximately 80.55 N.
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Info Sheet Math Definition
Power –
Base –
Exponent –
Coefficient –
Exponential Form –
Expanded Form –
Standard Form –
Exponent Laws –
Answer:
Power – A power is an expression that represents repeated multiplication of the same number or variable, such as a raised to the power of n, denoted by aⁿ.
Base – The base is the number or variable that is raised to a power or exponent in a power expression.
Exponent – The exponent is the number that indicates how many times the base is to be multiplied by itself in a power expression.
Coefficient – The coefficient is the numerical factor of a term that contains a variable in an algebraic expression.
Exponential Form – The exponential form is a way of writing a number using a base and an exponent, such as aⁿ, where a is the base and n is the exponent.
Expanded Form – The expanded form is a way of writing an expression as the sum or difference of its individual terms, such as (a+b)² = a² + 2ab + b².
Standard Form – The standard form is a way of writing a number using digits, such as 1234 or 1.234 x 10³.
Exponent Laws – The exponent laws are a set of rules that describe how exponents can be manipulated in algebraic expressions, including the product law, quotient law, power law, and negative exponent law. These laws help simplify and solve equations involving exponents.
A theater charges $10 for main-floor seats and $4 for balcony seats. If all seats are sold, the ticket income is $5800. At oneshow, 30% of the main-floor seats and 50% of the balcony seats were sold and ticket income was $1900. How many seats are on the main floor and how many are in the balcony?
To solve this problem, we can use a system of equations. Let's call the number of main-floor seats x and the number of balcony seats y.
The first equation can be written as:
10x + 4y = 5800
The second equation can be written as:
0.3x + 0.5y = 1900
Now we can use the elimination method to solve for one of the variables. Let's multiply the second equation by -10 to eliminate the x variable:
-3x - 5y = -19000
Adding the two equations together gives us:
7x - y = 3900
Now we can use substitution to solve for one of the variables. Let's solve for y in the first equation:
y = (5800 - 10x)/4
And substitute this value into the second equation:
7x - (5800 - 10x)/4 = 3900
Multiplying both sides by 4 gives us:
28x - 5800 + 10x = 15600
Solving for x gives us:
38x = 21400
x = 563.16
And plugging this value back into the first equation to solve for y gives us:
y = (5800 - 10(563.16))/4
y = 609.21
So there are approximately 563 main-floor seats and 609 balcony seats.
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Which statement below is TRUE about section b of the drive?
Group of answer choices
The time driven stayed the same
The distance driven stayed the same
The distance was increasing
The distance was decreasing
Answer: Im pretty sure its B
Step-by-step explanation:
I need help pls pls pls pls help quickly.
Answer:
-7/8
Step-by-step explanation:
The two coordinates shown are (0,5) and (8,-2).
The slope formula is (y2-y1)/(x2-x1).
Using that, the slope of a line passing through both points is (-2-5)/(8-0).
That reduces to -7/8.
Answer:
-7/
Step-by-step explanation:
9. Verify that each equation is an identity. a. sin 2x = 2 tan x / 1 + tan^2 x b. tan x + cot x = 2 csc 2x
a) Sin 2x = 2 tan x / 1 + tan^2 x is an identity.
b) Tan x + cot x = 2 csc 2x is an identity.
To verify that each equation is an identity, we will simplify both sides of the equation and show that they are equal.
For part a, we will use the double angle formula for sine and the Pythagorean identity.
sin 2x = 2 sin x cos x
2 tan x / 1 + tan^2 x = 2 sin x / cos x / 1 + sin^2 x / cos^2 x
= 2 sin x / cos x / cos^2 x / cos^2 x
= 2 sin x / cos x / 1 - sin^2 x
= 2 sin x / cos x / cos^2 x
= 2 sin x cos x
Therefore, sin 2x = 2 tan x / 1 + tan^2 x is an identity.
For part b, we will use the definitions of the trigonometric functions and the double angle formula for cosecant.
tan x + cot x = sin x / cos x + cos x / sin x
= (sin^2 x + cos^2 x) / (sin x cos x)
= 1 / (sin x cos x)
= 2 / (2 sin x cos x)
= 2 / sin 2x
= 2 csc 2x
Therefore, tan x + cot x = 2 csc 2x is an identity.
In conclusion, we have verified that both equations are identities.
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Find the effective interest rate for the specified
account.
nominal yield, 6.5%; compounded monthly
Question 10 answer options:
0.07%
6.70%
106.70%
0.54%
The effective interest rate for the specified account is 6.70%.
To find the effective interest rate, we can use the following formula:
Effective Interest Rate = (1 + Nominal Yield / Number of Compounding Periods) ^ Number of Compounding Periods - 1
In this case, the nominal yield is 6.5% and the number of compounding periods is 12 (since it is compounded monthly). Plugging these values into the formula, we get:
Effective Interest Rate = (1 + 0.065 / 12) ^ 12 - 1
Effective Interest Rate = (1.0054166666666667) ^ 12 - 1
Effective Interest Rate = 1.0670171619870418 - 1
Effective Interest Rate = 0.0670171619870418
Multiplying by 100 to convert to a percentage, we get:
Effective Interest Rate = 6.70%
Therefore, the effective interest rate for the specified account is 6.70%.
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F. Prime and Maximal Ideals LetAbe a commutative ring with unity, andJan ideal ofA. Prove each of the following:1 A/Jis a commutative ring with unity.2Jis a prime ideal iffA/Jis an integral domain. 3 Every maximal ideal ofAis a prime ideal. (HINT: Use the fact, proved in this chapter, that ifJis a maximal ideal thenA/Jis a field.) 4 IfA/Jis a field, thenJis a maximal ideal. (HINT: See Exercise 12 of Chapter 18.)
J is a maximal ideal.
1. To prove that A/J is a commutative ring with unity, note that the operations of addition and multiplication on A/J are well-defined and are commutative since they are inherited from the commutative ring A. Furthermore, the additive identity of A is the same as the additive identity of A/J, and therefore A/J has a unity.
2. Suppose first that J is a prime ideal of A. Then, if A/J is not an integral domain, there exist two nonzero elements x,y of A/J such that xy=0. This means that x and y are in the same coset of J in A. Thus, x-y is an element of J. Since J is prime, either x or y must be in J, which is a contradiction. Therefore, A/J is an integral domain. Conversely, if A/J is an integral domain, then the same argument can be reversed to show that J is a prime ideal.
3. If J is a maximal ideal of A, then A/J is a field by the fact proved in this chapter. Since a field is an integral domain, J is a prime ideal.
4. Suppose that A/J is a field. Then, for any ideal I of A, either I is contained in J or J is contained in I. This implies that J is a maximal ideal.
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Find the values of a, b, and c that make the equation true.
(2x - 1)(3x + 4) = ax² + bx+c
a =
b =
C =
Answer:
a = 6
b = 5
c = -4
Step-by-step explanation:
(2x-1)(3x+4) = [tex]6x^{2}[/tex]+8x-3x-4 = [tex]6x^{2}[/tex]+5x-4
If the equation is [tex]ax^{2}[/tex]+bx+c, then the values of a, b, and c, are 6, 5, and -4 as it makes the equation true.
danny is 22 year old. this is 6 year yonger than his sister terry write an equation that shows the relationship between the age of danny and terry. how old is terry
The equation that shows the relationship between the age of Danny and Terry is D = T - 6.
Let's represent Danny's age with the variable D and Terry's age with the variable T. We know that Danny is 22 years old, so we can write the equation D = 22.
We also know that Danny is 6 years younger than Terry, so we can write the equation D = T - 6. Now we can substitute the value of D from the first equation into the second equation to find the value of T.
D = T - 6
22 = T - 6
Add 6 to both sides of the equation:
22 + 6 = T
28 = T
So Terry is 28 years old.
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T-1.3 Let W be the subspace with dimension of n-1 within vector space V. Prove that there exists a basis in vector space V (denote as S), will satisfy the condition of SO W = 0.
The proof is complete.
To prove that there exists a basis in vector space V that satisfies the condition of $W = \{0\}$, we will use the dimension theorem. The dimension theorem states that if $V$ is an $n$-dimensional vector space, then any subspace of $V$ has a dimension that is less than or equal to $n$. In this case, the given subspace $W$ has a dimension of $n-1$ and so it must be a subspace of $V$. Since the dimension of $W$ is less than the dimension of $V$, the dimension theorem states that there exists a basis in $V$ that satisfies the condition of $W = \{0\}$. Therefore, the proof is complete.
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G is inversely proportional to the square of a. If a = -3 when g = 9, find two values for a, which will make g equal 25.
If a = -3 when g = 9, the two values for a, which will make g equal 25 will be ± 9/5.
If G is inversely proportional to the square of A, then we can write the relationship as:
G = k/A^2 Where k is a constant.
We can use the given values of A and G to find the value of k:
9 = k/(-3)^2
9 = k/9
k = 81
Now we can use the value of k and the desired value of G to find the values of A:
25 = 81/A^2
A^2 = 81/25
A = ± √(81/25)
A = ± 9/5
So the two values of A that will make G equal 25 are 9/5 and -9/5.
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An aerial photographer who photographs real estate properties has determined that the best photo is taken at a height of approximately 406 ft and a distance of 891 ft from the building. What is the angle of depression from the plane to the building?
The building's depression angle relative to the plane is found as 24.49°.
Explain about the Line of Sight?The straight path an observer's eyes take to view an item is known as the line of sight. The light that bounces off an item must travel along the line of sight to the eyes in order to be seen.According to an aerial photographer who specializes in taking pictures of real estate properties.
The ideal shot should be taken at a height of around 406 feet and a distance of 891 feet from the structure.
Height h = 406 ft
Distance d =891 ft
The building's depression angle relative to the plane:
tan Ф = Height / Distance
tan Ф = 406 / 891
tan Ф = 0.455
Ф = 24.49°
Thus, the building's depression angle relative to the plane is found as 24.49°.
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At the movie
theater, 8 tickets
cost $76.00.
How much is
each ticket?
USE A
Answer:
$9.50
Step-by-step explanation:
If there are 8 tickets and they all add up to $76, you have to divide 76 by 8 (the number of tickets)
The quotient is positive if the divisor and dividend have the same signs and negative if they have opposite signs. The quotient of any integers (with a nonzero divisor) will be a rational number
It is true that the quotient of two integers will always result in a rational numbers, as the quotient of two integers is in fact a fraction.
What are rational and irrational numbers?Rational numbers are numbers that can be represented by a ratio of two integers, which is in fact a fraction, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating. Examples are integers, fractions and mixed numbers.Irrational numbers are numbers that cannot be represented by a ratio of two integers, that is, they cannot be represented by fractions. They are non-terminating and non-repeating decimals, such as non-exact square roots.More can be learned about rational and irrational numbers at brainly.com/question/5186493
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The equation a = 6 000(1 + 0. 028t) represents the amount of money earned on a savings account with 2. 9% annual simple interest
Answer:
See below.
Step-by-step explanation:
This is the correct formula for simple interest, but be careful with the numbers.
a = 6 000(1 + 0. 028t)
0.028 means 2.8% interest rate.
For 2.9% interest rate it should be
a = 6 000(1 + 0. 029t)
k as the constant of variation for r varies directly as the square root of n and inversely as the square of y
The constant of variation k for this relationship is 4.
To find the constant of variation k for the given relationship, we can use the formula for direct and inverse variation:
k = (r * y^2) / √n
Where r is the variable that varies directly as the square root of n, and inversely as the square of y. To find the value of k, we can plug in the values of r, y, and n into the equation and solve for k.
For example, if r = 4, y = 2, and n = 16, we can plug these values into the equation to find k:
k = (4 * 2^2) / √16
k = (4 * 4) / 4
k = 16 / 4
k = 4
Therefore, the constant of variation k for this relationship is 4.
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Multiply and simplify: (4x-3)(-5x^(2)+2x-4) Choose your preferred method and submit the question.
The simplified form of [tex](4x-3)(-5x^(2)+2x-4)[/tex] is: [tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]
To multiply and simplify the given expression [tex](4x-3)(-5x^(2)+2x-4)[/tex], we can use the distributive property. This means we will multiply each term in the first parentheses by each term in the second parentheses and then combine like terms.
First, we will distribute the 4x to each term in the second parentheses:
[tex]4x * (-5x^(2)) = -20x^(3)4x * (2x) = 8x^(2)4x * (-4) = -16x[/tex]
Next, we will distribute the -3 to each term in the second parentheses:
[tex]-3 * (-5x^(2)) = 15x^(2)-3 * (2x) = -6x-3 * (-4) = 12[/tex]
Now we will combine all of the terms:
[tex]-20x^(3) + 8x^(2) - 16x + 15x^(2) - 6x + 12[/tex]
Finally, we will combine like terms:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]
So the simplified expression is:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]
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Toby, el perro de Julia, tuvo 5 cachorros. Cada cachorro come 0. 13 libras de alimento para perros todos los días. ¿Cuánto alimento para perros comen los cachorros en 1 día?
The amount of dog food consumed by five puppies every day as per given condition is equal to 0.65 pounds of food.
Total number of Julia dog Toby puppies = 5
Dog food eats by each pup = 0.13 pounds every day
Total dog food consume by puppies in one day
= ( total number of puppies ) × ( Dog food eats by each pup every day )
Substitute the value to get the total consumed food,
⇒ Total dog food consume by puppies in one day
= ( 5 ) × ( 0.13 ) pounds of dog food
⇒ Total dog food consume by puppies in one day
= ( 0.65 ) pounds of dog food
Therefore, every day total dog food eat by puppies is equal to 0.65 pounds of food.
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pleaseeeeeeee helppppppppp
Select the correct answer.
Which expression is equivalent to the given expression?
The equivalent expression is option D) [tex]81/m^7.[/tex]
What is the equivalent expression?
In mathematics, an equivalent expression is one that has the same value or meaning as another expression, even though it may look different. In other words, two expressions are equivalent if they simplify to the same value or form.
To simplify the expression [tex](3m^{(-4)})^3 * (3m^5)[/tex], we need to apply the power of a power property of exponents, which states that [tex](a^b)^c = a^(b*c)[/tex].
Using this property, we can rewrite [tex](3m^{(-4)})^3[/tex] as [tex]3^3[/tex] * [tex](m^{(-4)})^3 = 27 * m^{(-12)[/tex]. Similarly, we can rewrite (3m⁵) as 3 * m⁵.
Substituting these values back into the original expression, we get:
[tex](3m^{(-4)})^3 * (3m^5) = 27 * m^{(-12)} * 3 * m^5[/tex]
[tex]= 81 * m^{(-12+5)[/tex]
[tex]= 81 * m^{(-7)[/tex]
Therefore, the equivalent expression is option D) [tex]81/m^7.[/tex]
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Austin purchased a new laptop in 2018 for $1875. The laptop decreases in 7pm
value by 30% each year. What is the value of the laptop in 2022? Round to
the nearest whole dollar.
Answer:
There would be no value to the laptop. If you’re looking for the actual value, it would be worth $-375.
Step-by-step explanation:
Kathy saves $1 on the first day, $2 on the second day, $3 on the third day and so on,
saving an extra $1 on each subsequent day. On which day will she have $300 or more in total?
Answer:
Day 24 will be the day she'll reach $300
Step-by-step explanation:
Answer20th
Step-by-step explanation:
Find the value of the determinant of the coefficient matrix. You need to show the expansion of the determinant along the second row to get any credit. If you expand the determinant along any other row or column, you will get 0 points even if your answer is correct.
-3x + (0)y - 6z = 11
(5)x - 2y + 3z = 17
2x - y - (7)z = -3
The value of the determinant of the coefficient matrixis 102.
A coefficient matrix in linear algebra is a matrix made up of the coefficients of the variables in a group of linear equations. In order to solve systems of linear equations, the matrix is used.
The value of the determinant of the coefficient matrix can be found by expanding the determinant along the second row. The coefficient matrix is:
| -3 0 -6 |
| 5 -2 3 |
| 2 -1 -7 |
Expanding the determinant along the second row, we get:
= 5(-1)³(-3(-7) - (-6)(-1)) - (-2)(-1)⁴((-3)(-7) - (-6)(2)) + 3(-1)⁵((-3)(-1) - (0)(2))
= 5(21 - 6) - (-2)(21 - 12) + 3(3 - 0)
= 5(15) - (-2)(9) + 3(3)
= 75 - (-18) + 9
= 75 + 18 + 9
= 102
Therefore, the value of the determinant of the coefficient matrix is 102.
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Which shows how to multiply 2/5×4?
Responses
2×5÷4 you will be rewarded 10 points
2 times 5 divided by 4
2×4÷5
2 times 4 divided by 5
8×2÷5
8 times 2 divided by 5
4×5÷2
Answer:
i believe this is how you solve that problem... 2÷5×4
A band expects to put 16 songs on their next CD. The band writes and records 8.75% more songs than they expect to put on the CD. During the editing process, 60% of the songs are removed. How many songs will there be on the final CD?
Answer:
Step-by-step explanation:
Given that, There are 16 songs that are put on the next CD.And there are 8.75 more songs.Also, 60% of the songs are removed. Based on the above information, the calculation is as follows:
16+(0.875 x 16)=17.4
17.4(0.60 x 17.4)= 181.656 = 182 :)
Please help me i need the answer asap
The required slope of the line shown in the graph is 4/3, and the lines representing the rise and run are shown in the graph.
What is the slope of the line?The slope of a line is a measure of how steeply the line is inclined with respect to the horizontal axis.
Here,
To calculate the slope of a line from the rise and run values, we use the formula:
slope = rise/run
In this case, rise = 6 and run = 4.5. Substituting these values into the formula, we get:
slope = 6 / 4.5
Simplifying the fraction by dividing both the numerator and denominator by 1.5,
slope = 4/3
Therefore, the slope of the line is 4/3.
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Use PEMDAS to evaluate the expression:
8+(36 x 8-204) ÷ 6
Answer: 22
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
(36 x8-204)
multiply first
36(8)=288
then subtract
288-204=84
8+84 ÷6
divide first
84 ÷6=14
8+14=22
What are the necessary conditions to apply the SAS Triangle Congruence Theorem?
A. One angle and two sides of one triangle are congruent to the corresponding parts of another triangle.
B. Two angles and the included side of one triangle are congruent to the corresponding parts of another triangle.
C. An angle and the two sides collinear with the angle’s rays are congruent to the corresponding parts of another triangle.
D. Two sides and any angle of one triangle are congruent to the corresponding parts of another triangle.
Option A and C will be the correct answers based on the provided statement.
What is a triangle's three sides?A right triangle's hypotenuse is its longest side, its "opposing" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To define the side of right triangles, we utilize specific terminology.
Congruence of the SAS Triangle According to the theorem, two triangles are said to be congruent to one another if they have a single pair of corresponding sides and an incorporated angle that are equal to one another.
The image shows two triangles that are congruent by the SAS Congruence Theorem.
As a result, the following claims satisfy the requirements for two triangles to be regarded as congruent to one another by the SAS Congruity Theorem:
A. the corresponding two sides and the included angle in both triangles are congruent.
C. A pair of two sides that are congruent with the equivalent two sides and angle in the opposite triangle and are parallel to an angle's ray.
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