Mathematics High School
Answers
Answer 1
18x²y⁶ is the third term in the binomial expansion .
What does binomial expansion mean?
The process of extending an expression that has been raised to any finite power uses the Binomial Theorem.
A binomial Theorem is a potent expansionary tool with applications in probability, algebra, and other fields. binary expression An algebraic expression with two terms that are not the same is known as a binomial expression.
We have been given with the expression [tex]( 3x + y^{3} )^{4}[/tex]
We have general formula for binomial expansion which is
[tex]a^{n} + na^{n - 1} + ............................................. + b^{n}[/tex]
a = 3x b = y³
n = 4
Substituting the values in the formula we will get
3x⁴ + 4(3x)⁴⁻¹ y₃ + (4)(4 - 1)/2 * 3x⁴⁻² (y³)²
( 3x)⁴ + 4(3x)³y³ + 6(3x)²y⁶
(3x)⁴ + 12x³y³ + 18x²y⁶
we can clearly see that third term of the expansion will be
18x²y⁶
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Related Questions
Jamie is playing a card game. Jamie score changes by -12 for 8 turns in row. What is the total change in jamie's score?
Answers
The total change in Jamie's score is -96
The term total in math is defined as the result of arithmetically adding numbers or quantities.
Here we have given that Jamie is playing a card game.
Here we also know that Jamie score changes by -12 for 8 turns in row.
Then the value of Each turn score = -12
And the Number of turn = 8
Then then total of Jamie's score is calculated by using the following formula,
=> Total of Jamie's score = Each turn score × Number of turn
Apply the value on the formula, then we get
=> Total of Jamie's score = -12 × 8
Therefore the total of Jamie's score is written as -96
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Why is repetition used in epic poetry?
Answers
Answer: It allows poets to remember and retell the poem and helps the audience absorb the poem. It also creates a rhythmic pattern.
Step-by-step explanation: Hope this helps! Please let me know if it's correct ;)
Andy earns $62,000 a year at an accounting firm. each year, he receives a raise.
andy has determined that the probability that he receives a 10% raise is 0.5, the probability that he
earns a 5% raise is 0.4, and the probability that he earns a 2% raise is 0.1.
a competing company has offered andy a similar position for $68,000 a year. andy wonders if he
should take the new job or take his chances with his current job.
a) find the mathematical expectation of the dollar amount of his raise at his current job.
Answers
The mathematical expectation of the dollar amount of raise at his current job is $4464.
What is mathematical expectation?
The summation or integration of potential values from a random variable is mathematical expectation, often known as the expected value.
What is probability?
Probability is a way to gauge how likely something is to happen.
Let us consider the percentage rise as x and the probability of raise as p(x) and find x. p(x)
For 10% increase:
x= 10
p(x) = 0.5.
x.p(x) = 5
For 5% increase:
x=5
p(x)=0.4
x.p(x) = 2
For 2% increase:
x=2
p(x) = 0.1
x.p(x) = 0.2
Calculate the expected raise by adding all the values of x.p(x):
∑x.p(x) = 5+2+0.2
x.p(x) = 7.2%
Now the expected raise is calculated as:
expected raise = (62000) (7.2%)
= $4464
Hence, the mathematical expectation of the dollar amount of his raise is $4464, and the total earning is $66464 at current job. He should have chosen new job.
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7. a distribution centre sends three different types of parcels. one consignment has 6 small, 8 medium and 9 large parcels which cost $173.20 to post. another consignment has 7 small, 13 medium and 17 large parcels with total postage $291.05. a large parcel costs twice as much to post as a small one. work out the total cost of posting 3 small parcels, 9 medium parcels and 2 large parcels.
Answers
we multiplied the cost of each parcel type by the number of each parcel type in the consignment to get the total cost of posting 3 small parcels, 9 medium parcels and 2 large parcels, which is $88.83.
Total cost = (3 x Small) + (9 x Medium) + (2 x Large)
= (3 x ($173.20 / 23)) + (9 x ($291.05 / 29)) + (2 x (2 x ($173.20 / 23)))
= $88.83
1. Calculate the cost of 1 small parcel:
Cost of 1 consignment = $173.20
Total number of parcels = 6 + 8 + 9 = 23
Cost of 1 small parcel = $173.20 / 23 = $7.54
2. Calculate the cost of 1 medium parcel:
Cost of 1 consignment = $291.05
Total number of parcels = 7 + 13 + 17 = 37
Cost of 1 medium parcel = $291.05 / 37 = $7.88
3. Calculate the cost of 1 large parcel:
Cost of 1 large parcel = 2 x Cost of 1 small parcel = 2 x $7.54 = $15.08
4. Calculate the total cost of posting 3 small parcels, 9 medium parcels and 2 large parcels:
Total cost = (3 x Small) + (9 x Medium) + (2 x Large)
= (3 x $7.54) + (9 x $7.88) + (2 x $15.08)
= $88.83
To calculate the total cost of posting 3 small parcels, 9 medium parcels and 2 large parcels, we first calculated the cost of 1 small parcel ($7.54), 1 medium parcel ($7.88) and 1 large parcel ($15.08) using the cost and number of parcels of the two consignments. Then we multiplied the cost of each parcel type by the number of each parcel type in the consignment to get the total cost of posting 3 small parcels, 9 medium parcels and 2 large parcels, which is $88.83.
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hector received three a's and one b in his college courses. what is his grade point average?assume each course is three credits. a
Answers
The grade point average received by hector is 3.75.
What is GPA?
Your grade point average (GPA) is calculated by dividing the total number of credits you have earned in high school by the sum of all of your course grades. The majority of colleges and secondary schools use a 4.0 scale to report grades. A perfect score, or an A, is a 4.0.
The unit value for each course in which a student obtains one of the grades mentioned above is multiplied by the grade point total for that grade to determine the GPA. Then, divide the sum of these products by the sum of the units. The cumulative GPA is calculated by dividing the total grade points by the total number of units.
3 a and one is B received by Hector.
The A = 4.0, B = 3.0, C = 2.0, D = 1.0 is given by college
We have GPA= A+A+A+B/4
GPA=4+4+4+3/4
GPA= 15/4
GPA=3.75
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Complete question
Hector Ramirez received three A's and one B in his college courses. What is his grade point average? Assume each course is three credits. A = 4.0, B = 3.0, C = 2.0, D = 1.0
What is the circumference of a circle? How do you find it using a formula or a measurement? Give an example and show your work.
Answers
In other words, if a circle is opened to produce a straight line, the circle's diameter will be equal to the length of that line.
what is circle ?
A circle is a circular shape that can be created by tracing a moving point in a plane so that its distance from a specified point remains constant. From the Greek word kirkos, which means hoop or ring, comes the term circle.
Example
the circle's circumference if the radius is 28 cm. The circle's radius is 28 cm, hence that is the answer.
The circumference formula is 2[tex]\pi[/tex]r = 2 22/7 28 = 176 cm, and it will be used to determine the circle's circumference.
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A farmer wants to divide ha of grazing into 9 or 15 camps if equal size how did he know without a division calculation that the 15 camp is an easier practical solution than the 9 camps division
Answers
15 is a factor of 8085, it follows that it is easier to divide the land in to 15 camps of equal size.
What is Division?
A division is a process of splitting a specific amount into equal parts.
In mathematics, the term factor has to do with a number that can be able to divide another number without remainder.
In order to know which way is easier, we must ask ourselves which of 9 and 15 is a factor of 8085.
Since 15 is a factor of 8085, it follows that it is easier to divide the land in to 15 camps of equal size.
Hence, as 15 is a factor of 8085, it follows that it is easier to divide the land in to 15 camps of equal size.
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choose the correct answers. which equation models the relationship? is there a viable solution when time is 30 minutes?
Answers
When t=30, w=0, hence there is no workable solution. It implies that there is no longer any water after 20 minutes. So it is illogical for t=30 minutes.
what is equation ?
Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship.
calculation
A linear relationship exists here. The linear equation's slope-intercept form is as follows: where m is the rate of change (positive if increasing rate and negative if decreasing rate)
2.5 quarts per minute are changed (it is decreasing so m is -2.5)
C is 50 since the initial value is 50 quarts.
incorporating the results' values. y = -2.5x +50
We get y = -2.5x +50 by swapping the variables w and t for y and x, respectively. Where w is the remaining water in the bathtub and t is the passing time in minutes.
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Drag and drop the correct choice into the drop areas on the image above
y= -5x +10
y=4x+3
y=2x+4
y=8
Answers
Drag and drop the correct choice into the drop areas on the image:
y= -5x +10 (red line, line 1)
y=4x+3 (blue line, line 3)
y=2x+4 (purple line, line 2)
y=8 (green line, line 4)
Match the step with the correct line of working.
A
√9×√8
B
3√8
C
√9×8
D
√72
Write down the question.
Write √72 in the form √a×b where a is the biggest possible square number.
The root of the product is the same as the product of the roots.
Work out √9then write down your answer.
Answers
Answer:
[tex]\sqrt{72}[/tex] = 6 × [tex]\sqrt{2}[/tex]
Step-by-step explanation:
given
[tex]\sqrt{72}[/tex]
the largest factor of 72 which is a square number is 36
using the property of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{72}[/tex]
= [tex]\sqrt{36(2)}[/tex]
= [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex]
= 6 × [tex]\sqrt{2}[/tex]
When computed using an effective interest rate of i, it is known that the present value of $2,000 at the end of each year for 2n years plus an additional $1,000 at the end of each of the first n years is $52,800. using this same interest rate, the present value of an n year deferred annuity-immediate paying $4,000 per year for n years is $27,400. find n. [hint: first find an i and a2n i, then vn and i.]
Answers
The present value of an n year deferred annuity-immediate paying $4,000 per year for n years in $27,400. is 8.47
How do you find n present value?
The present value formula PV = FV/(1+i)^n states that present value is equal to the future value divided by the sum of 1 plus interest rate per period raised to the number of time periods.
What does N stand for in present value?
The caret symbol stands for exponentiation; n is the number of years; the negative n is the negative value of the year. Thus year 1 is -1, year 2 is -2 and so on. When present value is calculated for multiple years of projected income, for example, two numbers in the formula would change.
The present value of n year deferred annuity immediate paying dollar 4000 per month is
v^n*1000anl=27400
4000v^n*an=27400
Hence,
3000an+4000v^n*an=52800
3000an+27400=52800
3000an=25400
an=25400/3000
an=8.47
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a surprising number of young adults (ages 19 to 25) still live in their parents' homes. the national institutes of health surveyed independent random samples of
2253 men and 2629 women in this age group. the survey found that 986 of the men and 923 of the women lived with their parents. let p1-the true proportion of
young men who live in their parents' homes and p2 - the true proportion of young women live in their parents' homes.
1
construct and interpreta 99% confidence interval for the difference in the true proportions of men and women aged 19 to 25 who live in their parents homes
Answers
At 99 percent confidence level, the difference in the true proportions are:
(0.0505, 0.1226). The interval in part a gives the convincing evidence.
What means 95% confidence level?
The 95% confidence interval is a range of values that you can be 95% confident contains the true mean of the population. Due to natural sampling variability, the sample mean (center of the CI) will vary from sample to sample. The confidence is in the method, not in a particular CI.
What are the 3 common confidence level?
The most common confidence levels are 90%, 95% and 99%. The following table contains a summary of the values of corresponding to these common confidence levels. (Note that the"confidence coefficient" is merely the confidence level reported as a proportion rather than as a percentage.)
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In an all boys school, the heights of the student body are normally distributed with a
mean of 68 inches and a standard deviation of 4.5 inches. using the empirical rule,
what percentage of the boys are between 54.5 and 81.5 inches tall?
Answers
Using the empirical rule, approximately 95% of the boys in the all boys school are between 54.5 and 81.5 inches tall.
What is standard deviations?
Standard deviation is a measure of how spread out numbers in a data set are from the mean, or average. It is the measure of the amount of variation or dispersion of a set of values from the mean. The larger the standard deviation, the greater the dispersion of values from the mean.
This is calculated by finding the area under the normal distribution curve that falls between 1.5 standard deviations (68 - (1.5 × 4.5)) and 1.5 standard deviations (68 + (1.5 ×4.5)). The empirical rule states that approximately 95% of the data should fall between 1.5 standard deviations of the mean.
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movie tickets cost $3 for children and $7 for adults how much will tickets cost for a family of 3 children and 2 adults
Answers
When tickets for movies were $3 for kids and $7 for adults, a family of 3 kids and 2 adults had to pay $ 23.
what is equation ?
Equations are mathematical expressions with two algebraic expressions on either side of the equals (=) symbol. This relationship is proven by showing that the expressions on the left and right are equivalent to one another.
calculation
considering that kids' cinema tickets cost $3
Adult movie tickets cost $3,
Adult movie tickets cost $3,
therefore a family of three children and two adults would pay three times that much
= 2 * ( $7 ) + 3 * ( $3 }
= $9 + $14
= $ 23
When tickets for movies were $3 for kids and $7 for adults, a family of 3 kids and 2 adults had to pay $ 23.
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Triangle ABC and triangle PQR are similar and have the same orientation. The endpoints of the hypotenuse of triangle ABC are B(-5, -7) and C(-3, -3). The hypotenuse of triangle PQR is on the same line as the hypotenuse of triangle ABC and is twice the length of BC. What is the slope of the hypotenuse of triangle PQR? What are the coordinates of the hypotenuse of triangle PQR?
Answers
The slope of the hypothenuse PQR is 5 and its endpoints are (-10, -14), (-6,6)
Slope of a Line
This is the ratio of the rise to run of the graph function. It is simply said as the ratio between the change in y - axis to the change in x - axis.
The triangle ABC have it's hypothenuse with endpoints at B(-5, -7) and C(-3, 3)
However, the hypothenuse of PQR is twice the length of ABC
The coordinate will change as
PQR = 2ABC
PQR = 2[(-5, -7), (-3, 3)]
PQR = (-10, -14), (-6, 6)
Using this coordinate, we can find the slope of the line with the formula
m = y₂ - y₁ / x₂ - x₁
m = 6 - (-14) / -6 - (-10)
m = 6 + 14 / -6 + 10
m = 20 / 4
m = 5
The slope of the hypothenuse is 5
B) The coordinates of the hypothenuse PQR are (-10, -14), (-6, 6)
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divide : (x^3-2x^2-9x+4) ÷ (x^2+2x-1)
Answers
The result of divide : (x³ - 2x² - 9x + 4) ÷ (x² + 2x - 1) is x - 4
How to carry out the division of the polynomials
From the question, we have the following parameters that can be used in our computation:
divide : (x^3-2x^2-9x+4) ÷ (x^2+2x-1)
Rewrite the above parameters properly
So, we have the following representation
divide : (x³ - 2x² - 9x + 4) ÷ (x² + 2x - 1)
This means that
Divisor = x² + 2x - 1
Dividend = x³ - 2x² - 9x + 4
Using the long division, we have the following setup
x² + 2x - 1 | x³ - 2x² - 9x + 4
Divide x³ by x²
So, we have
x
x² + 2x - 1 | x³ - 2x² - 9x + 4
Multiply x² by x² + 2x - 1
This gives
x
x² + 2x - 1 | x³ - 2x² - 9x + 4
x³ + 2x² - x
Evaluate the difference
x
x² + 2x - 1 | x³ - 2x² - 9x + 4
x³ + 2x² - x
------------------------------------------------
-4x² -8x + 4
Repeat the above steps
So, we have
x - 4
x² + 2x - 1 | x³ - 2x² - 9x + 4
x³ + 2x² - x
------------------------------------------------
-4x² -8x + 4
-4x² -8x + 4
------------------------------------------------
This means that
Quotient = x - 4
Hence, the result is x - 4
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The length of a new rectangular playing field is 6 yards longer than quadruple the width. if the perimeter of the rectangular playing field is 452 yards, what are its
dimensions?
the width is
yards
Answers
Therefore , the solution to the given problem of the area comes out to be
the dimensions of the playing field are 118 yards × 56 yards.
Specify the area.
When calculating area, multiply length by breadth. L times B is the formula for area. Area = r2(=3.14), or area = radius. The area of different quadrilaterals, a special kind of polygon having four sides and an angle of less than 90 degrees, can also be calculated using these methods. Application. Since its inception, geometry has been built on the idea of area.
Here,
We determine that w = 56, meaning that the rectangle has a width of 56 yards.
Since the length is equal to 2w + 6, we may simplify the calculation by substituting 56 for w in order to determine the rectangle's length.
We learn that the rectangle is 118 yards long.
The playing field is therefore 118 yards by 56 yards in size.
Therefore , the solution to the given problem of the area comes out to be
the dimensions of the playing field are 118 yards × 56 yards.
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A department store receives a shipment of 3 boxes of glass ornaments in each box. Lucas opens the boxes and finds that 6 of the ornaments are broken. Based on this shipment, what prediction can Lucas make about the next shipment of ornaments?
Answers
If Luca received 6 broken ornaments from 3 boxes of glass ornaments received each containing 25 ornaments, then there can be 2 broken ornaments in every box received.
There are 25 ornaments in each 3 boxes received. So total number of ornaments received is
= 25 × 3
= 75
The number of ornaments that were broken is 6. So the probability that an ornament received is broken is
Probability = 6/ 75
Probability = 2/ 25
That is every 2 out of every 25 ornament received can be broke. As each box has 25 ornaments, 2 ornaments can be broken for every box received.
--The question is incomplete, answering to the question below--
"A department store receives a shipment of 3 boxes of glass ornaments. There are 25 ornaments in each box. Lucas opens the boxes and finds that 6 of the ornaments are broken. Based on this shipment, what prediction can Lucas make about the next shipment of ornaments?"
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What is the equation of the line that passes through the point (-8, -6) and has a slope of 1/2
Answers
Answer:
y = 1/2x - 2
Step-by-step explanation:
you can use the point-slope formula, which is y = mx + b
'y' can represent -6
'x' can represent -8
'm' represents the slope of 1/2
we can plug these values into the formula to find 'b' (which is the y-intercept)
-6 = -8(1/2) + b
-6 = -4 + b
add 4 to each side and the value of 'b' is -2
now fill in the slope and y-intercept to get the equation
Wyatt invests $1200 into an account that earns 6.2% simple interest for 4 years. he does not make any other deposits or withdrawals.
at the end of 4 years, wyatt invests the entire account balance into a different account that earns 8% simple interest. he leaves the money in the account for 5 years without making any additional deposits or withdrawals.
what is the new account balance at the end of 5 years?
Answers
If Wyatt initially invests an amount of $1200 for 4 years at a simple interest of 6.2% and then the amount from that is invested for 5 years at a simple interest of 8%, the new account balance at the end is 2096.64 dollars.
Therefore the answer is $2096.64
The amount when invested an initial amount of P for n years at annual simple interest rate of r is given by
A = P + Pnr
As Wyatt invest an amount of $1200 at 6.2% simple interest, at the end of 4 years he will have an amount equal to
A = 1200 + 1200×4×0.062
A = 1497.6
Now as Wyatt invest an amount of $1497.6 at 8% simple interest, at the end of 5 years he will have an amount equal to
A = 1497.6 + 1497.6×5×0.08
A = 2096.64
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When given a set of cards laying face down that spell M, A, T, H, I, S, F, U, N, determine the probability of randomly drawing a vowel.
three tenths
three sixths
one ninth
one third
Answers
The probability of randomly drawing a vowel is D. one third.
How to calculate the probability?
It should be noted that probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.
When given a set of cards laying face down that spell M, A, T, H, I, S, F, U, N, There are 3 vowels out of 9.
The probability of randomly drawing a vowel is:
= 3/9
= 1/3.
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Answer: D: One Third (1/3).
Step-by-step explanation: The regular answer would be 3/9 (Three Ninths) but that is not an answer so the alternative is 1/3 (One Third) knowing it is the equal to 3/9 (Three Ninths).
Saving a certain amount for future is a good habit. ramesh
is a student of class x and he inculcated the habit of saving.
recently, ramesh have received a prize money of rs 10000
in an art competition. he deposited it with a bank. the bank
offers him a simple interest at the rate of 6.5% per year.
he has a plan to use this money to some books and
stationary.
based on the given information, answer the following questions:
(i) write the sequence of amount of money at the ends of each year. what kind of sequence is it and why?
(ii) if ramesh continue this for 16 years, what will be the amount he gets at the end of 16 years.
will give free brainliest to everyone who answers
Answers
Answer:
Below
Step-by-step explanation:
i) Money he has at end of each year = 10 000 + 10 000 ( .065) * n
where n = number of years .065 = decimal interest per year
this can be reduced to : 10 000 ( 1 + .065 *n) = amount
ii) put 16 in for 'n'
10 000 ( 1 + .065 * (16) ) = Rs 20 400
Calculate and interpret the residual for the high school senior with a foot length of 20 cm.
Answers
On solving the provided question, Actual minus anticipated value equals residual, [tex]or 160 minus 157.06.[/tex] [tex]=2.94 cm[/tex]
what is standard deviation?
Standard deviation, or variance in a collection of values, is a measure of variation or variance in statistics. A low standard deviation suggests that the values are more likely to be close to the set's mean, whereas a large standard deviation suggests that the values are widely dispersed. The standard deviation, abbreviated as, expresses how much the data deviate from the mean. When the standard deviation is low, the data tend to be grouped around the mean, but when the standard deviation is large, the data are dispersed more widely.is expressed in the form y = mx + b.
The first stage involves computing the regression equation.
height equals [tex]105.08 + 2.599[/tex] times the length of the foot.
Height at foot length of [tex]20[/tex] cm is equal to [tex]105.08 + 2.599[/tex] times [tex]20.[/tex]
[tex]= 157.06 cm[/tex]
Actual minus anticipated value equals residual, [tex]or 160 minus 157.06.[/tex]
[tex]=2.94 cm[/tex]
The residual standard deviation often provides an indication of how well the regression equation fits the data. We can determine how much the projected values from the model will differ from the actual values by looking at the magnitude. The linear model makes sense.
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The lengths of the diagonals of a rhombus are 2x and 10x. What expression gives the perimeter of the rhombus?.
Answers
P = 4x√26 unitsis the required expression that determines the rhombus's perimeter.
What is a rhombus?
A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry.
The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
A quadrilateral with two sets of parallel sides is referred to as a parallelogram.
Every rhombus is a parallelogram because its opposite sides are all parallel.
So, a rhombus's diagonals are perpendicular bisectors of each other and its sides are all congruent.
The Pythagorean Theorem in use:
c² = a² + b²
We have:
a = 2x/2 = x units
b = 10x/2 = 5x units
Insert the values as follows:
c² = x² + (5x)²
c² = 26x²
x = x√26
The perimeter of the rhombus can be calculated by multiplying the length side by 4:
P = 4(x√26)
P = 4x√26 units
Therefore, P = 4x√26 unitsis the required expression that determines the rhombus's perimeter.
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A weather balloon is being filled. the linear equation
v = 6 + 0.04t
models the volume v (in cubic feet) of hydrogen in the balloon at any time t (in seconds). (see exercise 55 in section 2.2.) how many minutes will it take until the balloon contains 58 ft3 of hydrogen? (round your answer to one decimal place.)
Answers
It takes 21.67 minutes to fill up the balloon by this amount of hydrogen gas.
What is linear equation?
Mathematical statement that shows equality between two expressions.
Expressions are formed by variables, numbers and operator. The linear equations are one where maximum power of any variable is one.
How to solve the given equation?
we are given a linear equation that models the volume V of hydrogen in the balloon at time t in second
V = 6+0.04t
in the above equation, 6 is constant number
0.04 is a number but a coefficient of variable t
V is a variable denotes the volume of gas
V= 58 ft³
we need to determine the time taken to fill up the balloon by this amount of gas.
58 = 6 + 0.04t
0.04t = 52
t = 1300 second = 21.67 minutes
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Question 5 (1 point)
an advertisem*nt for a lawn service claims their fertilizer treatment kills weeds in half the time. when you read the
small print at the bottom of the ad, you see that they asked 20 of their long-term customers to estimate how long it
took until their weeds died out before employing the lawn service. on average, the customers said it took 4 weeks
for all the weeds to die before the service. the company knows that their fertilizer treatment can kill weeds in 2
weeks.
why is this advertisem*nt misleading?
Answers
On solving the question, we have - The sample size needed to draw this conclusion, which is 20, is quite large.
What is sample size?
The number of observations utilized to estimate a particular population is referred to as the sample size. The sample size was calculated based on the population.
Advertising is the practice of spreading knowledge about a product in order to boost sales. The commercial is deceptive based on the situation provided for the following reasons:
20 samples is a relatively tiny sample size for this result to be accurate. Customers claimed that it would take 4 weeks for all of the weeds to die, yet the corporation was aware that the fertilizer treatment could eliminate weeds in about 2 weeks. In light of this, the commercial is deceptive because: The sample size needed to draw this conclusion, which is 20, is quite large.
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22. MODELING You have a total of 42 math and science problems for homework.
You have 10 more math problems than science problems. How many 201
problems do you have in each subject? Use a system of linear equations
to justify your answer.
Answers
Answer:
16 science problems and 26 math problems.
Step-by-step explanation:
I think that 201 might be typo.
Let m = number of math problems
Let s = number of science problems.
m + s = 42
m = s+ 10 Substitute s + 10 for m in the first equation
s + 10 + s = 42 Combine line terms
2s + 10 = 42 Subtract 10 from both sides
2s + 10 - 10 = 42 - 10
2s = 32 Divide both sides by 2
[tex]\frac{2s}{2}[/tex] = [tex]\frac{32}{2}[/tex]
s = 16
m + s = 42 Substitute 16 for s and solve for m
m + 16 = 42 Subtract 16 from both sides
m + 16 - 16 = 42 - 16
m = 26
What are the 7 tips for successful group work participation?
Answers
Working with others enables you to pool your ideas and see problems from different perspectives.
What are the 7 tips for successful group work participation?
Meet as a group and introduce yourself before the group project even starts. Ask each person what they had for breakfast or what their favourite book was as a quick icebreaker.
A leader gives everyone of you someone to turn to if issues emerge, even though it's crucial to keep everyone in the group on an equal footing. Some groups struggle to accomplish their goals because the members are unclear about their specific responsibilities.
Each group member ought to ideally be given a task that plays to his or her skills. As a result, the final product is of superior quality, and the project gives everyone participant a chance to shine.
Start off the group project on the right foot.Designate a group leader. Set clear expectations for all group membersBe honest about your abilitiesSet deadlines and stick to them.Meet regularly to check inBe respectful to all members
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medical researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic mental illness established two independent test groups. the first group consisted of 13 people with the illness, and the second group consisted of 9 people with the illness. the first group received treatment 1 and had a mean time until remission of 154 days, with a standard deviation of 7 days. the second group received treatment 2 and had a mean time until remission of 162 days, with a standard deviation of 6 days. assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. can we conclude,
Answers
Our calculated t-value of -5.88 is less than the critical t-value of 2.201, we have sufficient evidence to reject the null hypothesis that there is no difference in the mean time until remission between the two treatments.
To determine whether there is a significant difference in the mean time until remission for the two treatments, we can use an independent t-test.
First, we need to calculate the mean difference between the two groups:
Mean difference = mean time until remission for treatment 1 - mean time until remission for treatment 2
= 154 days - 162 days
= -8 days
Next, we need to calculate the standard deviation of the difference:
Standard deviation of difference = √((standard deviation for treatment 1²/sample size for treatment 1) + (standard deviation for treatment 2²/sample size for treatment 2))
= √(7²/13 + 6²/9)
= √(49/13 + 36/9)
= √(3.77 + 4)
= 2.86
Now that we have the mean difference and standard deviation of the difference, we can calculate the t-value:
t-value = (mean difference)/(standard deviation of difference/√(sample size for treatment 1 + sample size for treatment 2))
= (-8)/(2.86/√(13 + 9))
= (-8)/(1.36)
= -5.88
Finally, we need to find the critical t-value from a t-table using the appropriate degrees of freedom (13-1=12 for treatment 1 and 9-1=8 for treatment 2) and alpha level (typically 0.05). For a two-tailed test (assuming we are interested in whether there is any difference in mean time until remission between the two treatments), the critical t-value at an alpha level of 0.05 is 2.201.
Since our calculated t-value of -5.88 is less than the critical t-value of 2.201, we have sufficient evidence to reject the null hypothesis that there is no difference in mean time until remission between the two treatments. This means that we can conclude that there is a significant difference in mean time until remission between the two treatments. However, we cannot determine which treatment is more effective based on this test alone. Additional analysis would be needed to determine the direction of the difference and whether one treatment is more effective than the other.
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consider joint probability distribution given below. x y ( ),xyf x y 1.0 1 1/32 1.5 2 11/32 1.5 3 1/4 2.5 4 1/4 3.0 5 1/8
Answers
On solving the provided question we can say that - E = event that tails come F = event that head comes then, the Probability (head comes) = 1/2
What is probability?
A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1.
let us assume that
E = event that tails come
F = event that head comes
then,
the P (head comes) = 1/2
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