Answer:
23e+3
Step-by-step explanation:
Answer:
Step-by-step explanation:
Elijah opened a checking account with $588 and deposits $25 into it every week. He
opened another checking account with $385 and deposits $35 into it every week. Write a
simplified expression to represent how much he will have in both accounts after w weeks.
Show your work below!
t-
Expression to represent total amount Elijah will have in both accounts after two weeks is 60w + 973
What is expression?An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
Given,
Elijah opened a checking account with $588 and deposits $25 into it every week.
Expression for the amount in w weeks = 25w + 588
He opened another checking account with $385 and deposits $35 into it every week.
Expression for the amount in w weeks = 35w + 385
Total amount in both bank accounts in w weeks
= 25w + 588 + 35w + 385
Adding like terms
= 60w + 973.
Hence, expression, 60w + 973 represents the amount Elijah will have in both accounts after w weeks.
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Let S be a sample space for an experiment in which every outcome is both equally likely and mutually exclusive. What can you conclude about the sum of the probabilities for all of the outcomes? Give an example.
The conclusion abput the sum of the probabilities is that the sum for all outcomes in a sample space for the experiment is equal 1.
How to make conclusion about the sumThe sum of the probabilities for all outcomes in a sample space for an experiment must equal 1.
This is because the probability of an event is the number of favorable outcomes divided by the number of total outcomes in the sample space,
And since all outcomes are equally likely and mutually exclusive, the sum of their individual probabilities must equal 1.
Example:
Consider a fair die, the sample space S is the set of all possible outcomes {1, 2, 3, 4, 5, 6}.
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solve the proportion 5x/3 = 80/12
Answer:
x=4
Step-by-step explanation:
pls tell me if wrong have a good day/night<3
what must be the probability that a randomly chosen young adult has some education beyond high school but does not have a bachelor's degree? why?
Probability: P(education beyond high school but not a bachelor's degree) = (number of young adults with education beyond high school but not a bachelor's degree) / (total number of young adults).
The probability that a randomly chosen young adult has some education beyond high school but not a bachelor's degree would be:
P(education beyond high school but not a bachelor's degree) = (number of young adults with education beyond high school but not a bachelor's degree) / (total number of young adults)
where "number of young adults with education beyond high school but not a bachelor's degree" refers to the count of individuals in the population who meet this criteria, and "total number of young adults" refers to the count of all individuals in the population who are considered young adults.
The formula calculates the probability of a certain event by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the event is a randomly chosen young adult having some education beyond high school but not a bachelor's degree. The numerator, "number of young adults with education beyond high school but not a bachelor's degree," represents the favorable outcomes, while the denominator, "total number of young adults," represents all possible outcomes.
By dividing the favorable outcomes by the total number of possible outcomes, we get the probability of the event occurring, which is a value between 0 and 1. The closer the value is to 1, the higher the probability that the event will occur. The closer the value is to 0, the lower the probability that the event will occur. This formula allows us to quantify the likelihood of an event occurring in a population based on the available data.
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-2/3 in its simplest form
Answer:
Step-by-step explanation:Find the GCD (or HCF) of numerator and denominator GCD of 2 and 3 is 1
Divide both the numerator and denominator by the GCD 2 ÷ 1 3 ÷ 1
Reduced fraction: 2 3 Therefore, 2/3 simplified to lowest terms is 2/3.
Which statement below compares the decimals correctly?
A 0.63 < 0.48
B 0.48 = 0.63
C 0.63 > 0.48
D 0.48 > 0.63
Answer:
C 0.63 > 0.48
Step-by-step explanation:
Not A, Because: 0.63 Is GREATER than 0.48 not less
Not B, Because: Like I said up top 0.63 is GREATER
Yes C, Because: 0.63 Is GREATER than 0.48
Not D, Because: 0.48 is LESS than 0.63
suppose 3% of cotton fabric rolls and 2% of nylon fabric rolls contain flaws. of the rolls used by a manufacturer, 70% are cotton and 30% are nylon. what is the probability that a randomly selected roll used by the manufacturer contains flaws? round your answer to three decimal places (e.g. 0.987).
The probability that a roll chosen at random and utilized by the manufacturer has problems is 0.032.
Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics. Probability is a mathematical representation of the likelihood or potential that an event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%. Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics.
So, the probability
[tex]=\frac{80}{100}*0.03+\frac{20}{100}*0.04\\=0.8*0.03+0.2*0.04\\=0.024+0.008\\=0.032[/tex]
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Which property is represented by the equation below? 1/3 + (2/3 + 1/7) = (1/3 + 2/3) + 1/7
A property which is represented by the equation above is
What is the Associative Property of Addition?The Associative Property of Addition states that when three (3) numbers are added, the end result would always be the same regardless of the way the numbers are grouped.
Generally speaking, the Associative Property of Addition allows the addends to be re-grouped without causing a change in the result, output, or outcome.
By applying the Associative Property of Addition, we have the following;
1/3 + (2/3 + 1/7) = (1/3 + 2/3) + 1/7
8/7 = 8/7
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Match the sentences below to the correct vocabulary word.
1. If x is not a rational number, it must be a(n) _______.
2. 0.7 is a
3. x is a terminating decimal, so it must also be a
4. A decimal that ends in zero is a
irrational number
rational number
repeating decimal
terminating decimal.
The required match of the sentence to the correct vocabulary has been shown below.
What is a rational number?In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.
Here,
1. If x is not a rational number, it must be a(n) irrational number.
2. 0.7 is a rational number.
3. x is a terminating decimal, so it must also be a rational number.
4. A decimal that ends in zero is a terminating decimal.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
The probability of landing on yellow is less than the probability of landing on blue.
==========================================================
Explanation:
We have the following:
There are 2 purple sections labeled "1" and "8". The probability of getting purple is 2/8.There are 2 yellow sections labeled "2" and "3". The probability of getting yellow is 2/8.There are 3 blue sections labeled "4", "5", and "6". The probability of getting blue is 3/8.There's only one orange section (labeled "7"). The probability of getting orange is 1/8.In short,
Probability of purple = 2/8Probability of yellow = 2/8Probability of blue = 3/8Probability of orange = 1/8Normally the goal is to reduce the fractions, but in this case it's better to keep them as they are. This allows for easier comparisons of other fractions.
------------
Now to look through the answer choices to see which are true, and which are false.
A) This is false because the probability of orange is 1/8, while the probability of purple is 2/8. We're twice as likely to get purple compared to orange. Statement A is backwards and therefore false.B) This is true. The probabilities of yellow and blue are 2/8 and 3/8 respectively. Compare the numerators to see that 2 < 3, so 2/8 < 3/8. Choice B is the final answer.C) This is false. We found that the probability of orange was 1/8, while the probability of yellow was 2/8. It's clear that 1/8 and 2/8 aren't equal. Or you could say [tex]1 \ne 2 \rightarrow 1/8 \ne 2/8[/tex]D) This is false. The probabilities of purple and blue are 2/8 and 3/8 respectively. Like with choice C, it's clear that 2/8 and 3/8 aren't equal.5. Which number is the square of 5√2-1? A. 23 - 5√2 B. 15√2-2 C. 51 - 10/2 D. 20√2-5 E. 100 + 4√2
Answer:
C. 51 -10√2
Step-by-step explanation:
You want the square of 5√2 -1.
SquareThe square of 5√2 -1 can be found using the distributive property.
[tex](5\sqrt{2}-1)^2=(5\sqrt{2}-1)(5\sqrt{2}-1)\\\\=5\sqrt{2}(5\sqrt{2}-1) -1(5\sqrt{2}-1)\\\\=(5\sqrt{2})(5\sqrt{2}) -5\sqrt{2}-5\sqrt{2}+1\\\\=25(\sqrt{2})^2-10\sqrt{2}+1\\\\=25\cdot2+1-10\sqrt{2}=\boxed{51-10\sqrt{2}}[/tex]
jasmine and ron drive away from pat's diner at the same time. jasmine drives west at 42 mi/h and ron drives south at 56 mi/h. find the rate (in mi/h) at which is the distance between jasmine and ron is increasing after four hours.
After 4 hours, the distance between Jasmine and Ron is increasing at a rate of 54 mi/h.
To find the rate at which the distance between Jasmine and Ron is increasing after four hours, we need to use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the distance between them and their respective speeds.
The distance between them after 4 hours is given by the square root of the sum of the squares of their respective distances traveled:
[tex]\sqrt{((42 * 4)^2 + (56 * 4)^2)}[/tex]
The rate at which this distance is increasing is equal to the magnitude of the velocity vector of their relative motion, which can be found using the hypotenuse formula:
[tex]\sqrt{(42^2 + 56^2)} = \sqrt{(2916) }= 54 mi/h[/tex]
So, after 4 hours, the distance between Jasmine and Ron is increasing at a rate of 54 mi/h.
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a mathematics professor wishes to schedule an appointment with each of her 7 teaching assistants, four men and three women, to discuss her calculus course. suppose that all possible orderings of appointments are equally likely to be selected. a) how many possible orderings of appointments are there if each person is identified by their name? count of possible orderings
The number of possible orderings of appointments is 720.
The number of possible orderings of appointments can be calculated using the formula n!/(n-r)! where n is the number of teaching assistants (7) and r is the number of appointments (7). Therefore, the total number of possible orderings of appointments is 5040.
To explain this formula, we can think of it in terms of permutations. A permutation is an arrangement of a set of items in a specific order. In this case, the set of items are the 7 teaching assistants (4 men and 3 women). The number of possible permutations (orderings) of these 7 teaching assistants is 7!. This is because there are 7 possible choices for the first appointment, 6 for the second, 5 for the third, and so on. This simplifies to 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
However, since each appointment is a unique one-time meeting, the order in which the teaching assistants are appointed does not matter, so the number of possible orderings of appointments is reduced to 7!/7 = 5040/7 = 720.
Therefore, in this case, the number of possible orderings of appointments is 720.
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if a feather is dropped from the top of a bridge 75 feet above a river, how long does it take the feather to reach the water? your answer is seconds.
The answer can be solved by using the kinematic equation, S= ut+at²/2. Here the time taken by the feather to fall from 75 feet will be 2.16 s.
Here a feather is dropped from a height of 75 ft. All other units are in SI system. So we have to convert the height to meters.
75 ft = 75/ 3.281 = 22.86 m.
We are neglecting the frictional force, or any other force acting on the feather. If the feather is under free fall, we can use the kinematic equation,
S = ut + at²/2
S is the displacement, here the height = 22.86 m
u is the initial velocity, which is 0
t is the time
a is acceleration, here a= g, acceleration due to gravity = 9.8 m/s².
S = 0×t + 9.8t²/2
22.86 = 4.9t²
t² = 22.86/4.9
= 4.665
t = √4.665 = 2.159 s = 2.16 s
So the time taken for the feather to reach water will be 2.16 s.
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not really sure how to do this
a quality-control program at a plastic bottle production line involves inspecting finished bottles for flaws such as microscopic holes. the proportion of bottles that actually have such a flaw is only 0.0002. if a bottle has a flaw, the probability is 0.993 that it will fail the inspection. if a bottle does not have a flaw, the probability is 0.96 that it will pass the inspection. if a bottle passes inspection, what is the probability that it does not have a flaw? round the answer to seven decimal places.
The probability that a bottle passes inspection and does not have a flaw is 0.9598067.
Let P(f) = 0.0002 be the probability of a bottle having a flaw, and P(s|f) = 0.993 be the probability of a bottle failing the inspection given that it has a flaw. Also, let P(s|~f) = 0.96 be the probability of a bottle passing the inspection given that it does not have a flaw. We want to find P(~f|s).
We can use Bayes' Theorem to find P(~f|s):
P(~f|s) = P(s|~f) * P(~f) / P(s)
P(s) = P(s|f) * P(f) + P(s|~f) * P(~f)
P(s) = 0.993 * 0.0002 + 0.96 * (1 - 0.0002)
P(s) = 0.0001986
P(~f|s) = 0.96 * (1 - 0.0002) / 0.0001986
P(~f|s) = 0.9598067
Therefore, the probability that a bottle passes inspection and does not have a flaw is 0.9598067.
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please help (look at photo)
The expression that represents the length of the rectangular computer chip is 14ab².
How to find the length of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
Therefore, the area of the rectangular computer chip is 112a²b³ square microns. The expression that represents the length of the rectangular computer chip can be represented as follows:
Area of the rectangular computer chips = lw
where
l = lengthw = widthTherefore,
w = 8ab microns
Hence,
Area of the rectangular computer chips =112a²b³
112a²b³ = 8ab × length
Therefore, let's divide both sides of the equation by 8ab
length = 112a²b³ / 8ab
length of the rectangular computer chip = 14ab²
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54. how many integers between, but not including, 20 and 30 have a prime factorization with exactly 3 factors that are not
Integers between, but not including, 20 and 30 have a prime factorization with exactly 3 factors is 0 integers.
To find the integers between 20 and 30 with a prime factorization with exactly 3 factors that are not 1, we can start by listing out all the prime numbers up to 30.
The prime numbers up to 30 are 2, 3, 5, 7, 11, 13, 17, 19, and 23.
Next, we can list out all the integers that have exactly 3 factors in their prime factorization that are not 1. This can be done by finding all the products of exactly 3 primes. For example, the product of
2 * 3 * 5 = 30 has 3 prime factors.
However, 30 is not between 20 and 30, so we need to find another example.
The product of 2 * 3 * 7 = 42 is not between 20 and 30 either, so we need to keep finding examples until we find one that falls between 20 and 30.
The product of 2 * 5 * 7 = 70 is too large, but the product of 2 * 3 * 5 = 30 is between 20 and 30, so we have found one example.
We can continue this process to find all the examples and count how many there are. In this case, there is only 1 example, so the answer is 1.
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The scatter plot shows the relationship between the amount of time students in a mathematics class studied for an exam and their score on the exam.
Which of the following describes the pattern of association for the graph?
There is a positive linear association.
There is a positive nonlinear association.
There is a negative linear association.
There is a negative nonlinear association.
The pattern associated with the scatter plot is given as follows:
There is a positive nonlinear association.
How to classify the pattern?The scatter plot shows a series of points in (input, output) format, in which the input is the time studying in minutes and the output is the grade.
As the increasing graph shows, the more a person studies, the better the grade, hence there is a positive relationship among the variables.
The increase is slow initially while it has a higher rate for a higher number of minutes, hence the association is also nonlinear.
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Sarah has been working at her new job for 2 weeks now and she just got her first paycheck for the amount of $875. If Sarah had worked for 35 hours per week during those 2 weeks, how much does she get paid per hour?
Therefore , the solution of the given problem of fraction comes out to be $25 she get paid per hour.
Define fraction.A whole can be represented by any class of similar sums or fractions. A fraction is used to express the amount of a particular size in standard English. 8, 3/4. Fractions are also wholes. In mathematics, numbers are represented by the fraction to numerator ratio. All of these fractions are simple integers. The fraction of a challenging fraction contains a fraction. due to the variations in actual fraction calculations, numerators, and numerators.
Here,
Given :
=> new job 2 weeks
=> amount = $875
35 hours work per week
So,
Per hour she get paid is :
=> 875/35
=> 25
Thus,
$25 she get paid.
Therefore , the solution of the given problem of fraction comes out to be $25 she get paid per hour.
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Kyle is walking away from his house at a rate of 3 km/hr in the positive direction. After ten minutes, he turns around and walks home at 3 km/hr. In these two motion scenarios,
which statement best describes the difference between in his velocity vectors?
Answer:
Hi
Kyle's velocity vectors have opposite directions.
Step-by-step explanation:
When Kyle is walking away from his house, his velocity vector is pointing in the positive direction, representing the movement of his position in a specific direction. But after ten minutes, when he turns around and walks home, his velocity vector changes direction to point in the opposite direction, now representing his movement towards his house. The difference between the two velocity vectors is that they are in opposite directions.
please help me with this!
The scale factor for the given dilation transformation is 1/3
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given that, a triangle ABC is being dilated to form a new triangle A'B'C'
We are asked to the scale factor,
The length of sides of triangle ABC is 6 units
And, length of sides of triangle A'B'C' is 2 units,
Since, the figure id shrinking, therefore, the dilation is a reduction, and scale factor must be less than 1,
Scale factor = 2/6
= 1/3
Hence, the scale factor for the given dilation transformation is 1/3
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Write as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats
please write it out in long form. Thank you
25/6
The decimal with the bar is 4.1[tex]\over6[/tex].
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
25/6
= 4.16666666
6 is the repeating number so we put the bar on 6.
= 4.1[tex]\over6[/tex]
Thus,
The decimal is 4.1[tex]\over6[/tex].
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a number cube is rolled 24 times and lands on 6 three times. find the experimental probability of not landing on a 6. express your answer as a fraction in simplest form.
If a cube is rolled 24 times and lands on 2 four times and on 6 three times , then the experimental probability of not landing on a "6" is 0.171 .
on a cube there are total 6 outcomes ,
the probability of getting "2" on a single cube is = P(2) = 1/6 ;
the probability of getting "6" on a single cube is = P(6) = 1/6 ;
the probability of the cube not landing on 6 is = P'(6) = 5/6 ;
Since the cube is rolled 24 times , the experimental probability of not landing on "6" is
⇒ P(not 6) = ²⁴C₅×(1/6)⁵×(5/6)¹⁹ ;
On simplifying ,
we get ;
⇒ P(not 6) = 0.171 .
Therefore , the experimental probability of not landing on a 6 is 0.171 .
The given question is incomplete , the complete question is
A number cube is rolled 24 times and lands on 2 four times and on 6 three time. Find the experimental probability of not landing on a 6 .
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an experimenter surveyed two acres of a desert preserve and found six cactus wren nests. assuming that the habitat is fairly uniform, how many nests would he expect to be in the entire 200-acre preserve?
600 cactus wren nests the experimenter would expect to be in the entire 200-acre preserve.
To estimate the number of cactus wren nests in the entire 200-acre preserve, we can use the ratio of the area surveyed to the number of nests found.
Let's call the number of nests in the entire 200-acre preserve "N".
The ratio of the area surveyed to the number of nests found is:
2 acres / 6 nests = 200 acres / N nests
We can use this ratio to find the number of nests in the entire 200-acre preserve:
N nests = 200 acres * (6 nests / 2 acres)
N nests = 200 * 3
N nests = 600
So the experimenter would expect to find approximately 600 cactus wren nests in the entire 200-acre preserve, assuming that the habitat is fairly uniform.
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Find the area of the surface generated when the given curve revolved about the xx-axis.y=8√xy=8x on [9,20][9,20]
As a result, the area of the surface formed by rotating the given curve about the x-axis throughout the period [9, 20] is 864π.
What is area?The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
The area of the surface generated when a curve is revolved about an axis is known as the surface area of revolution and can be calculated using the formula:
A = 2π ∫ y dx
where y is the equation of the curve being revolved and the integral is taken over the interval [a,b] in which the curve is being revolved.
In this case, the curve is given by y = 8√x on the interval [9, 20]. So, the surface area of revolution is:
A = 2π ∫_9^20 8√x dx
This integral can be evaluated using substitution. Let u = √x, so that du = dx / 2√x and x = u^2. Then:
A = 2π ∫_3^4 8u * 2u du
= 2π * 8 * ∫_3^4 u^2 du
= 2π * 8 * [u^3/3]_3^4
= 2π * 8 * (64/3 - 27/3)
= 2π * 8 * (37/3)
= 864π
So, the area of the surface generated when the given curve is revolved about the x-axis over the interval [9, 20] is 864π.
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HELP pls will mark u the brainliest
Step-by-step explanation:
Multiplying the kites by 2 then adding 20
For 4 kites, 4 times 2 is 8. Adding 20 is 28
For 7 kites, 7 times 2 is 14. Adding 20 is 34
For 10 kites, 10 times 2 is 20. Adding 20 is 40
For the equation we have to multiply kites purchased by 2, so 2x. They also said to add 20, making it 2x + 20. Doing this will get the total cost, which they indicate as y
Equation; y = 2x + 20
sin(180+0) =
a. sin 0
b. -sin 0
c. cos 0
please explain thoroughly and in basic concepts I’m really bad at math thank you!
b.
because if you use math it tells you b
The graph shows a linear relationship between x and y, where x represents the number of comic books, all at the same price, Priya buys at the store, and y represents the amount of money (in dollars) Priya has after buying the comic books.
a) The y - intercept of the graph is, 20.
b) The slope of the line is, - 4
c) The equation of line is, y = - 4x + 20
d) The cost of 3 comics = $8.
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)
We have to given that;
The graph shows a linear relationship between x and y, where x represents the number of comic books, all at the same price, Priya buys at the store, and y represents the amount of money (in dollars) Priya has after buying the comic books.
Now, By the graph;
Let two points on the graph are (5, 0) and (0, 20).
Since, The equation of line passes through the points (5, 0) and (0, 20).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (20 - 0) / (0 - 5)
m = 20 / - 5
m = - 4
Thus, The equation of line with slope - 4 is,
⇒ y - 0 = - 4 (x - 5)
⇒ y = - 4x + 20
Thus, The y - intercept of the graph = 20
Now, When Priya buy 3 comics, then the cost of comics are,
⇒ y = - 4x + 20
⇒ y = - 4 × 3 + 20
⇒ y = -12 + 20
⇒ y = $8
Thus, We get;
a) The y - intercept of the graph is, 20.
b) The slope of the line is, - 4
c) The equation of line is, y = - 4x + 20
d) The cost of 3 comics = $8.
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P=(t -w)/y
t = 9.7 correct to 1 decimal place
w = 5.9 correct to 1 decimal place
y = 3 correct to 1 significant figure
Calculate the upper bound for the value of P.
Show your working clearly.
The value of the expression correct to 1 decimal place is P = 1.3.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The given expression is, P = (t - w)/y.
Where, t = 9.7 correct to 1 decimal place, w = 5.9 correct to 1 decimal place
and y = 3 correct to 1 significant figure.
Therefore, P = (9.7 - 5.9)/3.
P = 3.8/3.
P = 1.26 or P = 1.3.
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