Answer:
They are not equivalent expressions
Step-by-step explanation:
Let's expand each expression and see if they are the same
6(-b + 8) = 6 x (-b) + 6 x 8 = -6b + 48
2(-3b + 4) = 2 x (-3b) + 2 x 4 = -6b + 8
So while the terms -b are the same, the constants are different
Hence the two expressions are not equivalent
Select the false statement involving p, and the arbitrary events A and B. a) P( A^c n B^c)=P(A^c) P(B^c) b). P( A n B)=P( A) + P( B) -P( A U B). c). P(A^) + P(A)=1.d). P(A n B^c)= P(A)-P(A n B).e). P(A^c n B)=P(B)-P(A n B). f). None of the above.
The false statement is (a) P( A^c n B^c)=P(A^c) P(B^c). The probability of the intersection of complements is generally not equal to the product of individual complements.
The misleading assertion including p, and the erratic occasions An and B is (a) P( A^c n B^c)=P(A^c) P(B^c).
This assertion is bogus in light of the fact that by and large, the likelihood of the convergence of the supplements of two occasions, A^c and B^c, isn't equivalent to the result of their singular supplements.
For instance, assume we flip a fair coin. Let A be the occasion of getting heads and B be the occasion of getting tails. Then, P(A) = P(B) = 1/2, so P(A^c) = P(B^c) = 1/2. In any case, A^c and B^c are a similar occasion (getting heads or tails, separately), so P(A^c n B^c) = P(A^c) = 1/2. Then again, P(A^c) P(B^c) = (1/2)(1/2) = 1/4, which isn't equivalent to P(A^c n B^c).
Consequently, proclamation (a) is misleading.
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suppose v varies directly as g , and = 70 when v=30. Find v when g=9
Answer:
v = 21
Step-by-step explanation:
Suppose v varies directly as g, meaning that there is a constant k such that v = kg. If v = 70 when g = 30, then we can use this information to find the value of k:70 = k * 30k = 70 / 30k = 7 / 3Now that we have the value of k, we can use it to find v when g = 9:v = kgv = (7 / 3) * 9v = 21So when g = 9, v = 21.In conclusion, by finding the value of the constant of proportionality k and using the formula v = kg, we determined that when g = 9, v = 21.
I need help with this question
The amount of Tylenol remaining after 8 hours is 47.1g
What is half life?half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive.
R = A(0.5)^t/3
R = 300(0.5)^8/3
R = 300( 0.157)
R = 47.1
therefore after 8 hours 47.1 g of Tylenol is is left
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Can anyone help in number 12 pls… I don’t have to draw anything just have to write down the equation of a and b
Answer:
y=3x-2
Step-by-step explanation:
s=n/2(a+l) make a the subject
Answer: a = (2S)/(n + l)
Step-by-step explanation:
a = (2S)/(n + l)
In this equation, 'a' is the subject, which means that it is the value being solved for. To solve for 'a', we can divide both sides by the denominator of the fraction on the right-hand side (n + l). This leaves us with the answer of a = (2S)/(n + l).
Choose the correct sum of the polynomials (3x3 − 5x − 8) + (5x3 + 7x + 3).
8x3 + 2x + 5
2x3 − 12x − 11
2x3 + 12x − 5
8x3 + 2x − 5
Answer:
8x3 + 2x − 5
Step-by-step explanation:
A flag is shown. Determine the area of the shaded part of the flag.
Answer:
84 square inches
Step-by-step explanation:
The shaded region comprises of two same trapeziums:
∴Area of shaded region = 2 × (Area of a trapezium)
= 2 × [tex]\frac{1}{2}[/tex] × (Sum of parallel sides) × (perpendicular height of trapezium)
= [tex]\frac{2}{2}[/tex] × (4 + 8) × (6)
= 84 square inches
please answer!!!!!!!!!!!!!!!!!
The value of t is,
⇒ t = 28
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
The circle is shown in figure.
Now, From the figure we can formulate;
t = 1/2 (3t - 28)
2t = 3t - 28
3t - 2t = 28
t = 28
Thus, The value of t is,
⇒ t = 28
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How do you check the factorization of a polynomial?
Completely factorize the polynomial using any methods that are appropriate, then look for shared factors and the polynomial's roots. Next, double-check your work to confirm accuracy.
Follow these steps to determine a polynomial's factorization:
Completely factor the polynomial using any relevant techniques, including grouping, utilizing the difference of squares or cubes, or using the quadratic formula.
By multiplying them all together, you can verify that each factor is accurate. The final figure must match the initial polynomial.
Look for shared factors among the polynomial factors. If the polynomial has common components, remove them from the equation and rewrite it as the product of the common factors and the other factors.
The polynomial's roots can be verified by setting each factor to zero and calculating the variable. The roots ought to correspond to the original polynomial.
Verify your work a second time to make sure all relevant elements have been identified and taken into consideration.
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help. I’m stuck with this
Answer:
$14
Step-by-step explanation:
i multiplied 2.80 times 5 and got 14.
i hope this helped :)
Write a short essay to explain how you would guide learners to move from the concrete level, to the semi-concrete level and finally to the abstract level in relation to their understanding of the more than/less than concept. -8
In order to guide learners to move from the concrete level to the semi-concrete and finally to the abstract level in relation to their understanding of the more than/less than concept, I would use a step-by-step approach.
At the concrete level, I would introduce the concept of more than/less than with a hands-on activity. For example, I would have students compare the number of counters or blocks and have them determine which group has more or less. This would help them develop a fundamental understanding of the concept.At the semi-concrete level, I would introduce the concept of more than/less than with written numerals. I would have students compare numbers on paper, such as 4 and 6, and have them determine which number is more or less. I would also ask them to use concrete objects to represent the numbers, such as using four counters for 4 and six counters for 6.At the abstract level, I would introduce the concept of more than/less than with larger numbers. I would ask students to compare numbers such as 12 and 15, and determine which number is more or less. I would also ask them to use abstract symbols, such as 12 + and 15 -, to represent the numbers.By using this step-by-step approach, students will be able to move from the concrete level to the semi-concrete and finally to the abstract level of understanding the more than/less than concept. This will help them develop a strong foundation of the concept, which will allow them to solve more complex problems in the future.
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Find the measure of the missing angles.
x[tex]x^{4} -41x^{2} +400=0[/tex]
Answer:
Values of x are ±4 and ±5
Step-by-step explanation:
Let y = [tex]x^{2}[/tex]
Which means: [tex]y^{2} = x^{4}[/tex]
Therefore:
A quadratic equation is formed:
[tex]y^{2} - 41y + 400 = 0[/tex]
The above quadratic equation can be simplified either by The Double Bubble Method or using the quadratic formula
Double Bubble Method:
[tex]y^{2} - 41y + 400 = 0[/tex]
The pair of factors of 400 that add together to give 41 are 25 and 16. Use these two factors to rewritre -41y:
[tex]y^{2} - 25y - 16y + 400 = 0[/tex]
Then do Factorization by grouping (i.e group the terms with common factors before factorizing):
[tex]y(y -25) - 16(y - 25) = 0[/tex]
[tex](y - 25)(y - 16) = 0[/tex]
The product of two expressions is zero, which means either of the two expressions is equal to Zero:
Either: [tex]y - 25 = 0[/tex]
Substituting [tex]y = x^{2}[/tex]:
= [tex]x^{2} - 25 = 0[/tex]
= [tex]x^{2} = 25[/tex]
= [tex]\sqrt{x^{2}} = \sqrt{25}[/tex]
∴ x = ±5
Or: [tex]y - 16 = 0[/tex]
Substituting [tex]y = x^{2}[/tex]
[tex]= x^{2} - 16 = 0[/tex]
[tex]= x^{2} = 16[/tex]
[tex]= \sqrt{x^{2}} = \sqrt{16}[/tex]
∴ x = ±4
∴Values of x are ±4 and ±5
At the beginning of a snowstorm, Abigail had 12 inches of snow on her lawn. The snow then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow was melting, how much snow would Abigail have on her lawn 5 hours after the snow began to fall? How much snow would Abigail have on her lawn after tt hours of snow falling?
The snow on the lawn after 5 hours is 14.50 inches.
The snow on the lawn after tt hours is 12 + 0.5tt inches
How much snow is on the lawn?The equation that represents the amount of snow after a number of hours is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
The form of the equation is:
Total snow = snow on the lawn + (rate at which the snow falls x number of hours)
Snow after 5 hours = 12 + (0.5 x 5)
= 12 + 2.5 = 14.50 inches
Snow after tt hours = 12 + (0.5 x tt)
= 12 + 0.5tt inches
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Select all the expressions that show breaking the addends 7 5/12 and 11 2/3 apart to make a whole.
A. 7 + 5/12 + 11 + 2/3
B. 7 + 5/12 + 8/12 + 11
C. 7 + 5/12 + 7/12 + 11 1/12
D. 7 + 5/12 + 5/12 + 11 3/12
E. 7 + 1/12 + 4/12 + 8/12 + 11
10. Find the original price of an antique which was sold at £545 at a profit of 9%.
495.95
convert the percentage into a decimal
0.09
then do b=1-r
1 - 0.09 = 0.91
Now do 545 x 0.91
Answer: 495.95
Let's assume that the original price of the antique was x.
We know that the antique was sold at a profit of 9%, which means that the selling price is 109% of the original price:
[tex]Selling \: price = Original \: price + Profit[/tex]
[tex]£545 = x + 0.09x \\ £545 = 1.09x[/tex]
To find the original price, we can divide both sides of the equation by 1.09:[tex]x = \frac{545}{1.09} [/tex][tex]x = 500[/tex]
Therefore, the original price of the antique was £500.How do I find the slope of the image below??!!
Answer:
Step-by-step explanation:
How much 5000000 won to usd?
Answer:
3,975.16 United States Dollar
Step-by-step explanation:
what’s the answer to this question? i’ve been having a hard time figuring it out
Answer:
10.305
Step-by-step explanation:
First you calculate for the angle of 12ft down the wall secondly you calculate for the angle of 8ft down the wallthirdly you subtract the angle of the 8ft frpm the 12ftthe remainder it the angle that the projector needs to be tilted to focus on 8ft down the wallCharles is flying a kite
that is on a string that
112 feet long. If the
angle of depression from
the kite to the ground is
27°, how high off of the
ground is the kite?
The height of the kite is 56 feet.
Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.
Let h represent the height of the kite. Hence, using trigonometric ratios:
[tex]sin(30)=\frac{h}{112}[/tex]
h = 56 feet
Therefore, the height of the kite is 56 feet.
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Find the solution of the system of equations
8x+2y=38
2x-4y=-4
The solution of the system of equations is (4, 3)
How to solve the system of equations?Here we want to solve the system below:
8x+2y=38
2x-4y=-4
If we add 2 times the first equation and the second equation we will get:
2*(8x + 2y) + (2x - 4y) = 2*38 - 4
16x + 4y + 2x - 4y = 72
18x = 72
x = 72/18 = 4
And the vale of y is given by inputing x = 4 in one of the two equations.
2*4 - 4y = -4
8 - 4y = -4
-4y = -4 - 8
y = -12/-4 = 3
The solution is (4, 3)
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find x. show your work.
Please help out on question 1
1. Cosx = 5/√(41)
2. An equation {tan(x) + cot(x)}/{tan(x)} =csc²(x)
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
1. tanx = -4/5
and tanx = perpendicular/adjacent leg
So, P = -4 and A = 5
So, H = √(-4)² + (5)²
H = √(41)
So, Cosx = 5/√(41)
2. A trigonometric identity,
{tan(x) + cot(x)}/{tan(x)}
Simplifying,
= {tan(x)/tan(x) + cot(x)/{1/tan(x)}
= 1 + cot²(x)
= csc²(x)
Therefore, Cosx = 5/√(41)
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According to a Manila police, two people were killed when the 1,000 kg car illegally drag racing at a speed of 30 m/s had a head on collision with a 2,000 kg truck whose driver fell asleep as it traveled 20 m/s. Which vehicle has received the greater force?
Answer: To determine which vehicle received the greater force, we need to calculate the momentum change for each vehicle during the collision. The force experienced by a vehicle during a collision is equal to the rate of change of its momentum.
First, let's calculate the initial momentum for each vehicle:
The car has a mass of 1,000 kg and a velocity of 30 m/s, so its initial momentum is 1,000 kg * 30 m/s = 30,000 kg m/s.
The truck has a mass of 2,000 kg and a velocity of 20 m/s, so its initial momentum is 2,000 kg * 20 m/s = 40,000 kg m/s.
Next, let's calculate the final momentum for both vehicles after the collision:
The car and truck collide head-on, so their velocities will become zero after the collision. So the final momentum for both vehicles will be zero.
Finally, we can calculate the rate of change of momentum for each vehicle:
The rate of change of momentum for the car is equal to its final momentum minus its initial momentum, or 30,000 kg m/s - 0 kg m/s = 30,000 kg m/s.
The rate of change of momentum for the truck is equal to its final momentum minus its initial momentum, or 0 kg m/s - 40,000 kg m/s = -40,000 kg m/s.
Since the magnitude of the rate of change of momentum for the truck is greater than the magnitude of the rate of change of momentum for the car, the truck has received the greater force.
Step-by-step explanation:
(SAT Prep) Find the value of x
2x
3x
Answer:
36°
Step-by-step explanation:
2x+3x=5x
5x=180°
x=180°:5=36°
Determine the slope and the y-intercept of the equation. b=3.99a
The equation b = 3.99a has a slope of 3.99 and the y intercept is 0.
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
The standard form of a linear equation is:
y = mx + b
Where y, x are variables and b is the y intercept
Given an equation:
b = 3.99a
Comparing with the standard linear equation:
The slope is 3.99 and the y intercept is 0.
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Elish was required to write a 600 word Literature essay. After working away for one hour, the word count on her computer showed that she had typed 240 words. What fraction of the essay does Elish still need to complete? Write your answer in simplest form
If Elish was required to write a 600 word Literature essay and word count on her computer showed that she had typed 240 words Elish still needs to complete 3/5 of the essay.
To find the fraction of the essay that Elish still needs to complete, we need to determine how many words she has left to write. We can do this by subtracting the number of words she has already written from the total required word count:
Words left to write = Total word count - Words already written
Words left to write = 600 - 240
Words left to write = 360
Now, to find the fraction of the essay that Elish still needs to complete, we can express the remaining words as a fraction of the total word count:
Fraction of essay left to complete = Words left to write / Total word count
Fraction of essay left to complete = 360 / 600
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 120:
Fraction of essay left to complete = (360 ÷ 120) / (600 ÷ 120)
Fraction of essay left to complete = 3 / 5
This means that she has completed 2/5 of the essay so far (which is the equivalent fraction of 240/600).
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There are 32 students in a 5th grade classroom. Each table seats 6 students. How many tables are needed so that every student has a seat?
5 tables 30 tables 6 tables 7 tables
To sit comfortably, the students need a total of 6 tables. The correct option is 3.
There are 32 students in a classroom. In 5th grade. Now to sit comfortably, the students need 6 tables. In each table, a total of 6 students can fit. In 5 tables, only 30 students can sit but two students will remain table less. With 1 extra table, 2 students can sir and each student from a table can sit in the las bench, i.e., 6th table.
The number of pupils in the classroom is 32. in grade five. The pupils now require 6 tables in order to sit comfortably. A total of 6 pupils can fit at each table. Only 30 pupils can fit at 5 tables, however 2 students will be tableless. With one extra table, two students can sit at the sixth table and each student from a table can use the last bench. Therefore, students need a total of 6 tables.
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Which phrase describes the algebraic expression Three-fourths x + 2?
The phrase to describes the algebraic expression Three-fourths x + 2 is three-fourths of a number plus two.
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 in question;
The algebraic expression;
Three-fourths x + 2
Now,
The phrase that describes the algebraic expression Three-fourths x + 2;
three-fourths of a number plus two.
Therefore, the phrase of expression will be three-fourths of a number plus two.
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Josh and Chris are training for baseball season. Josh did 36 pushups in 30 seconds. Chris did 56 pushups in 50 seconds
Who will do more pushups in 2 and a half minutes?
Josh will do more push ups than Charis in 2 1/2 minutes. This can be solved by using the concept of multiplication.
What is multiplication?Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. Multiply in mathematics refers to the continual addition of sets of the same size. One of the fundamental mathematical processes is multiplication. The result of multiplying two or more integers together is known as the product. The first number used in a multiplication operation between two numbers is referred to as the multiplicand.
Given that,
Josh did 36 push ups in 30 seconds
Josh did push ups in 2 1/2 minutes:
= (36/30) × 150
= 180 push ups
Chris did 56 push ups in 50 seconds
Chris did push ups in 2 1/2 minutes:
= (56/50)× 150
= 168 push ups
Thus, Josh will do more push ups than Charis in 2 1/2 minutes.
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