By using sample standard deviation - (1) N or n = 20
(2) X or μ = 43.4
(3) σ = 9.78 and s = 10.04
Why does sample standard deviation exist?
When we talk about a sample standard deviation, we're not talking about population standard deviation. The average amount by which a group of values deviates from their mean is shown by the statistical measure of variability known as the standard deviation.
We are given with the following data set below;
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.
(2) The formula for calculating Mean of the data, i.e. X or μ is given by;
Mean = 51 +48+ 42+ 43+ 48 + 48 + 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42/20
= 868/20 = 43.4
So, the value of X or μ is 43.4.
(3) The formula for calculating population standard deviation () is given by;
Standard deviation, σ = √(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20
= 9.78
Similarly, the formula for calculating sample standard deviation (s) is given by;
Sample Standard deviation, s =
√(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20 - 1
= 10.04
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Management estimates that 5% of credit sales are eventually uncollectible. Of the collectible credit sales, 65% are likely to be collected in the month of sale and the remainder in the month following the month of sale. The company desires to begin each month with an inventory equal to 70% of the sales projected for the month. All purchases of inventory are on open account; 30% will be paid in the month of purchase, and the remainder paid in the month following the month of purchase. Purchase costs are approximately 60% of the selling prices. Budgeted January cash payments for December inventory purchases by Collection Corporation are:
Answer:
Step-by-step explanation:
Unfortunately, there is no information provided about the sales projections for the month of January or the selling prices of the inventory. Without this information, it is not possible to calculate the budgeted January cash payments for December inventory purchases.
What is the perimeter, P, of the rectangle?
Answer:
P = x(4x+7)/(x+2)(x+1)
Step-by-step explanation:
P = 2l + 2w. If x/x+2 = l and x/x+1 = w:
P = (2x/x+2) + (2x/x+1)
P = (2x(x+1)/(x+2)(x+1)) + (2x(x+2)/(x+1)(x+2))
P = (2x(x+1) + 2x(x+2))/(x+2)(x+1)
P = (4x squared + 7x)/(x+2)(x+1)
P = x(4x+7)/(x+2)(x+1)
the height y in feet of a ball thrown at a child
a) The initial height is 5 feet.
b) The maximum height is 17 feet.
c) The horizontal displacement is 26.3 feet
How high is the ball when it left the childs hands?The height of the ball is modeled by the given quadratic equation:
y = (-1/12)x² + 2x + 5
The ball leaves the child's hands at the beginning, so to get the height at that point we just need to evaluate this in x = 0, we will get:
y = (-1/12)*0² + 2*0 + 5
y = 5
The height is 5 feet.
b) To get the maximum height we need to find the vertex, in this case the vertex is at:
x = -(2/2)*-12 = 12
Then the maximum height is:
y = (-1/12)*12² + 2*12 + 5 = 17 feet.
Lastly, the ball will hith the ground when y = 0, then we need to solve:
(-1/12)*x² + 2x + 5 = 0
x² -12*2x - 12*5 = 0
x² -24x - 60 = 0
The quadratic formula gives:
[tex]x = \frac{24 \pm \sqrt{(-24)^2 -4*1*-60} }{2}[/tex]
The positive solution gives:
x = 26.3
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All of the following statements related to sample size are true characteristics of qualitative methodology except for which of the following?
The statement based on sample size representing true characteristics of qualitative methodology are smaller sample size, qualitative research and theoretical research of qualitative data.
Some general statements about sample size in qualitative methodology are as follow,
Qualitative research typically involves smaller sample sizes than quantitative research.
The sample size in qualitative research is not determined by statistical power calculations.
But rather by theoretical saturation and the quality of data collected.
The goal of qualitative research is to gain a deep understanding of the phenomenon being studied.
Rather than to generalize findings to a larger population.
Qualitative research often involves purposive or convenience sampling rather than random sampling.
All of these statements are generally true characteristics of qualitative methodology.
If any statement contradicts one of these characteristics,
Then that statement would not be true for qualitative methodology.
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The given question is incomplete, I answer the question in general according to my knowledge:
Write all the statement related to sample size representing true characteristics of qualitative methodology except for which of the following?
Use the conclusion of Exercise 15 to establish the following result. If f is analytic and never zero on a domain D, then |/(z)| has no local minima in D. That is, the graph (x, y, |/(x + iy)l) has no "pits."
If f is analytic and never zero on a domain D, then the graph (x,y,|f(x+iy)|) has no "pits". This follows from the fact that Re(f(z)) has no local minima in D.
Exercise 15 establishes the following result: if f is analytic and never zero on a domain D, then the the real part of f(z) has no local minima in D.
To use this result to establish the statement that |f(z)| has no local minima in D, we can use the fact that[tex]|f(z)|=\sqrt{real part of f(z))^2 + \ img part of f(z) )^2[/tex] . Since the sum of two non-negative functions is non-negative, it follows that if the real part of f(z) has no local minima in D, then |f(z)| has no local minima in D either.
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Let the Universal Set, S, have 158 elements. A and B are subsets of S. Set A contains 67 elements and Set B contains 65 elements. If Sets A and B have 9 elements in common, how many elements are in neither A nor B?
There are 92 elements in A but not in B.
What are sets?In mathematics, a set is a well-defined collection of objects or elements. Sets are denoted by uppercase symbols, and the number of elements in a finite set is denoted as the cardinality of the set enclosed in curly braces {…}.
Empty or zero quantity:
Items not included. example:
A = {} is a null set.
Finite sets:
The number is limited. example:
A = {1,2,3,4}
Infinite set:
There are myriad elements. example:
A = {x:
x is the set of all integers}
Same sentence:
Two sets with the same members. example:
A = {1,2,5} and B = {2,5,1}:
Set A = Set B
Subset:
A set 'A' is said to be a subset of B if every element of A is also an element of B. example:
If A={1,2} and B={1,2,3,4} then A ⊆ B
Universal set:
A set that consists of all the elements of other sets that exist in the Venn diagram. example:
A={1,2}, B={2,3}, where the universal set is U = {1,2,3}
n(A ∪ B) = n(A – B) + n(A ∩ B) + n(B – A)
Hence, There are 92 elements in A but not in B.
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Really need help asap !
The value of h(x) using exponents are as follows:
For -1, the value of h(x)=1/10
For 0, the value of h(x) = 1
For 1, the value of h(x) = 10
For 2, the value of h(x) = 100
For 3, the value of h(x) = 1000
What are exponents?The exponent of a number tells us how many times the original value has been multiplied by itself. For instance, 2×2×2×2 can be expressed as [tex]2^{4}[/tex] the result of 4 times multiplying 2 by itself. Thus, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."
Generally speaking, [tex]x^{n}[/tex] denotes that x has been multiplied by itself n times. Here x is the base and n is the power.
Now here, as we put the value of x in the equation, h(x) we can get the value of h(x) for each value of x.
So,
For -1, the value of h(x)=1/10
For 0, the value of h(x) = 1
For 1, the value of h(x) = 10
For 2, the value of h(x) = 100
For 3, the value of h(x) = 1000
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show that the properties of a probability distribution for a discrete random variable are satisfied.
The properties of a probability distribution for a discrete random variable ensure that the probabilities assigned to each possible value of the variable are consistent with the axioms of probability and allow for meaningful inference and prediction.
The properties of a probability distribution for a discrete random variable are.
The probability of each possible value of the random variable must be non-negative.
The sum of the probabilities of all possible values must equal 1.
The probability of any event A is the sum of the probabilities of the values in the sample space that correspond to A.
These properties are satisfied because the probabilities of each possible value of a discrete random variable are defined in such a way that they are non-negative and sum to 1. Additionally, any event A can be expressed as a collection of possible values of the random variable, and the probability of A is then computed as the sum of the probabilities of those values.
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Tutorial Exercise Find all the points at which the direction of fastest change of the function f(x, y) = x2 + y2 _ 8x 16y is i +j_ Step The direction in which the maximum rate of change of f(x, y) occurs at a point (a, b) is given by the vector Vfla, b) For flx,y) = x2 + y2 _ 8x - 16y, we have Vf(x, y) 2x 8)i + (2y - 16)jl (2x 8. 2y 16) Step 2 We need to find all points (x, Y) for which (2x 8)i + (2y 16)j is parallel to +j. So we must solve (2x 8)i + (2y 16)j k[i + j]- This means that k = 2x 8 and k = 2y 16. Equating these gives uS Submit
There are no points at which the function has its direction of fastest change along the vector i + j. This is because the equations lead to a contradiction.
The exercise asks to find all the points at which the function f(x, y) = x^2 + y^2 - 8x - 16y has its direction of fastest change along the vector i + j.
To find the points, we need to solve the equation:
(2x - 8)i + (2y - 16)j = k(i + j)
where k is a constant. Since the direction of fastest change is along the vector i + j, we know that the left-hand side of the equation represents the gradient vector of f(x, y).
Equating the x and y components of the gradient vector to the corresponding components of the vector i + j, we get:
2x - 8 = k
2y - 16 = k
Equating these two expressions for k, we get:
2x - 8 = 2y - 16
Solving for y in terms of x, we get:
y = x - 4
Substituting this expression for y into the equation of the gradient vector, we get:
2x - 8 = k
2(x - 4) - 16 = k
Simplifying, we get:
2x - 8 = k
2x - 24 = k
Substituting the first equation into the second, we get:
2x - 24 = 2x -
Simplifying, we get:
16 = 0
This is a contradiction, which means there are no points at which the function has its direction of fastest change along the vector i + j.
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Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
The expression (x < y) && (y == 5) is an alternative way of writing the original expression, and it will be true only if two conditions are met: first, x is smaller than y, and second, y is equal to 5.
The expression !(!(x < y) || (y != 5)) is equivalent to:
(x < y) && (y == 5)
To see why, let's break down the original expression:
!(!(x < y) || (y != 5))
= !(x >= y && y != 5) (by De Morgan's laws)
= (x < y) && (y == 5) (by negating and simplifying)
So, the equivalent expression is (x < y) && (y == 5). This expression is true if x is less than y and y is equal to 5.
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Complete question:
Assume that x and y have been defined and initialized as int values. The expression
!(!(x < y) || (y != 5))
is equivalent to which of the following?
(x < y) && (y = 5)
(x < y) && (y != 5)
(x >= y) && (y == 5)
(x < y) || (y == 5)
(x >= y) || (y != 5)
Find the matrix A of the linear transformationT(M)=[8097]M[8097]−1from U2×2 to U2×2 (upper triangular matrices) with respect to the standard basis for U2×2 given by{[1000],[0010],[0001]}.
The matrix A of the linear transformation T(M) with respect to the standard basis for U2×2 is given by:
T([1000]) = [8 0]
[0 0]
T([0010]) = [0 0]
[0 9]
T([0001]) = [0 1]
[0 0]
To find the matrix A of the linear transformation T(M), we need to apply T to each basis vector of U2×2 and express the result as a linear combination of the basis vectors for U2×2. We can then arrange the coefficients of each linear combination as the columns of the matrix A.
Let's begin by finding T([1000]). We have:
T([1000]) = [8097][1000][8097]^-1
= [8 0]
[0 0]
To express this result as a linear combination of the basis vectors for U2×2, we need to solve for the coefficients c1, c2, and c3 such that:
[8 0] = c1[1000] + c2[0010] + c3[0001]
Equating the entries on both sides, we get:
c1 = 8
c2 = 0
c3 = 0
Therefore, the first column of the matrix A is [8 0 0]^T.
Next, we find T([0010]). We have:
T([0010]) = [8097][0010][8097]^-1
= [0 0]
[0 9]
Expressing this as a linear combination of the basis vectors for U2×2, we get:
[0 0] = c1[1000] + c2[0010] + c3[0001]
Equating the entries on both sides, we get:
c1 = 0
c2 = 0
c3 = 0
Therefore, the second column of the matrix A is [0 0 0]^T.
Finally, we find T([0001]). We have:
T([0001]) = [8097][0001][8097]^-1
= [0 1]
[0 0]
Expressing this as a linear combination of the basis vectors for U2×2, we get:
[0 1] = c1[1000] + c2[0010] + c3[0001]
Equating the entries on both sides, we get:
c1 = 0
c2 = 1
c3 = 0
Therefore, the third column of the matrix A is [0 1 0]^T.
Putting all of this together, we have:
A = [8 0 0]
[0 0 1]
[0 0 0]
Therefore, the matrix A of the linear transformation T(M) is:
T([1000]) = [8 0]
[0 0]
T([0010]) = [0 0]
[0 9]
T([0001]) = [0 1]
[0 0]
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the formula for converting degrees fahrenheit (F) to degrees Kelvin is K= 5/9 (F = 459.67) Solve for F, terms of K
The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
What is degrees Fahrenheit and degrees Kelvin?Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.
The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.
Given that, K = 5/9 (F - 459.67).
To obtain F in term of K we isolate the value of F as follows:
K = 5/9 (F - 459.67)
Multiplying both sides by 9/5, we get:
(9/5) K = F - 459.67
Adding 459.67 to both sides, we get:
F = (9/5) K + 459.67
Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
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A company makes a mixture which contains 2% alcohol. If 10 litres of alcohol is added to the mixture, then the concentration increases to 5%. What is the approx. Quantity of the mixture?
To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63±$17.64.
Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?
The correct interpretation of the confidence interval is We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27 that is option A.
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific degree of confidence, this is the range of values you anticipate your estimate to fall inside if you repeat the test. In statistics, confidence is another word for probability.
Given,
Confidence interval, CI = 62.63 +/- 17.64
CI = ( 44.99 , 80.27 )
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
Most of the time, the confidence level is chosen before looking at the data. 95% confidence level is the standard degree of assurance. Nevertheless, additional confidence levels, such as the 90% and 99% confidence levels, are also applied.
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Complete question:
To investigate hospital costs for pets in a certain state, researchers selected a random sample of 46 owners of parrots who had recently taken their parrot to an animal hospital for care. The cost of the visit for each parrot owner was recorded and used to create the 95 percent confidence interval $62.63±$17.64.
Assuming all conditions for inference are met, which of the following is a correct interpretation of the interval?
We are 95 percent confident that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.We are 95 percent confident that the mean cost of a hospital visit for the parrot owners in the sample is between $44.99 and $80.27.For all parrot owners in the state, 95 percent of hospital visits for parrot care cost between $44.99 and $80.27.There is a 0.95 probability that the mean cost of a hospital visit for all parrot owners in the state is between $44.99 and $80.27.Find the area of 2 inches long times 1/4
By answering the question the answer is So the area of the rectangle is area 1/2 square inch.
What is area?The size of an area on a surface can be expressed as area. The open surface or boundary area of a three-dimensional object is called the surface area, and the area of the planar area or planar area refers to the area of the shape or planar layer. The total amount of space occupied by a planar (2-D) surface or shape of an object is known as its area. Draw a square on paper with a pencil. two-dimensional character. The area of a shape on paper is the space it occupies. Imagine a square made up of more compact unit squares.
It's not entirely clear what shape is being referred to here, but assuming it's a 2 inch by 1/4 inch rectangle, you can calculate the area by multiplying the length and width of the rectangle.
Area = Length x Width
Area = 2" x 1/4"
Area = (2/1) inch x (1/4) inch
Area = 1/2 square inch
So the area of the rectangle is 1/2 square inch.
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By answering the question the answer is So the area of the rectangle is area 1/2 square inch.
What is area?The size of an area on a surface can be expressed as area. The open surface or boundary area of a three-dimensional object is called the surface area, and the area of the planar area or planar area refers to the area of the shape or planar layer. The total amount of space occupied by a planar (2-D) surface or shape of an object is known as its area. Draw a square on paper with a pencil. two-dimensional character. The area of a shape on paper is the space it occupies. Imagine a square made up of more compact unit squares.
It's not entirely clear what shape is being referred to here, but assuming it's a 2 inch by 1/4 inch rectangle, you can calculate the area by multiplying the length and width of the rectangle.
Area = Length x Width
Area = 2" x 1/4"
Area = (2/1) inch x (1/4) inch
Area = 1/2 square inch
So the area of the rectangle is 1/2 square inch.
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Find the area of 2 inches long times 1/4
how many irrational numbers are there between 1 and 6 ? individual question 1 3 4 10 infinitely many
There are infinitely many irrational numbers between 1 and 6. This is because between any two distinct rational numbers, there is an infinite number of irrational numbers.
In the case of the interval between 1 and 6, there are infinitely many rational numbers between them, and therefore there must be infinitely many irrational numbers between them as well. This is due to the fact that the set of real numbers is uncountable, meaning that there is no finite or countably infinite list that contains all of its elements.
Thus, the answer is rather a statement about the infinite nature of the set of irrational numbers between 1 and 6.
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80 POINTS + BRAINLIEST!!
Jason bought a jacket on sale for 50% off the original price and another 25% off the
discounted price. If the jacket originally cost £88, what was the final sale price that
Jason paid?
Answer:
The first discount of 50% means Jason paid 50/100 x £88 = £44 for the jacket.
Then, the second discount of 25% means he paid 75/100 x £44 = £33 for the jacket.
Therefore, the final sale price that Jason paid for the jacket was £33.
Consider the following algebraic statements and determine the values of x for which each statement is true.
8=-|x|
Answer:
This is false.
Step-by-step explanation:
Since absolute value bars change negatives into positives and positive into themselves (positives) we can put the example:
[tex]-|8|\\[/tex]
When we remove the absolute value bars, 8 will still equal 8. But, we have a negative, therefore the 8 has a negative after being simplified with absolute value.
x = -8, not positive 8.
Answer:
Ther are no values of x that would make this statement true. There is no solution.
Step-by-step explanation:
Evaluate the expression for h = 6 and j = 5.
hj - h² =
Submit
Therefore, when h = 6 and j = 5, the value of hj - h² is -6.
What are arithmetic operations:Arithmetic operations are basic mathematical operations that involve manipulating numbers to perform calculations. There are four main arithmetic operations:
Addition: Adding two or more numbers together. The symbol used to represent addition is "+", and the result is called the sum.
Subtraction: Subtracting one number from another. The symbol used to represent subtraction is "-", and the result is called the difference.
Multiplication: Multiplying two or more numbers together. The symbol used to represent multiplication is "×" or "*", and the result is called the product.
Division: Dividing one number by another. The symbol used to represent division is "÷" or "/", and the result is called the quotient.
These operations can be combined to perform more complex calculations. Additionally, there are other arithmetic operations, such as exponentiation (raising a number to a power) and finding roots, which involve using arithmetic principles.
by the question.
To evaluate the expression hj - h² for h = 6 and j = 5, we simply substitute these values into the expression and perform the arithmetic operations:
hj - h² = (6)(5) - 6²
= 30 - 36
= -6
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factorise completely.
3x²-12xy
Answer:
Hence, factors are 3x,(x−4y).
Step-by-step explanation:
We need to factorise 3x 2 −12xy
Here we can take 3x common.
Thus we have 3x 2−12xy=3x(x−4y)
Hence, factors are 3x,(x−4y).
Answer: 3x ( x - 4y )
Step-by-step explanation:
Factorizing 3x²-12xy
3x ( x - 4y )
SOMEONE HELP PLEASE!!!
Find P(C|Y) from the information in the table.
To the nearest tenth, what is the value of P(C|Y)?
A. 0.4
B. 0.5
C. 0.7
D. 0.8
Answer:
The answer to your problem is, B, 0.5
Step-by-step explanation:
We are given the following table below;
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
As we know that the conditional probability formula of P(A/B) is given by:
P(A/B) = [tex]\frac{P(AnB)}{P(b)}[/tex]
P(C/Y) = [tex]\frac{P(CnY)}{P(Y)}[/tex]
P ( Y ) = [tex]\frac{30}{146}[/tex] and P(CnY) = [tex]\frac{15}{146}[/tex] [ because of the third column shown ]
Thus, the answer is, B. 0.5
Feel free to ask any questions down below \/ !
Find the measure of ACD
A - 36 degrees
B - 126 degrees
C - 162 degrees
D - 216 degrees
Answer:
C
Step-by-step explanation:
i assume its
C.
My question is the picture
Answer:
B. A student was most likely to have summer as their favorite season, whether or not they have allergies
Step-by-step explanation:
If you look at the chart. There is a majority under the summer column. Both those who have and don't have allergies favor summer.
can someone help me? please
evalute the following function h(x)=3x2+ax-1 for h(3) and find the value for a.
Answer:
Step-by-step explanation:
[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]
But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.
mr.woodstock has a plot of land 36 meter long and 16 meters wide. he uses the land for mixed farming- rearing animals and growing crop? What length of wire does mr.woodstock need to fence his land?
Mr. Woodstock will need to purchase 144 meters of wire to fully encircle his land. He will need to measure the length of the four sides of the land and add them together. The four sides measure 36 meters + 36 meters + 16 meters + 16 meters, which equals a total of 104 meters. He should buy enough wire to cover an additional 40 meters to account for any extra material he may need. Therefore, he needs to purchase 144 meters of wire for his fencing.
A small jet can fly 2040 miles in 4 hours with a tailwind but only 1560 miles into a headwind. Find the speed of the jet in still air and the speed of the wind
Answer:
Let's call the speed of the jet in still air "j" and the speed of the wind "w".
When flying with the tailwind, the effective speed of the jet is j + w. We know that it can travel 2040 miles in 4 hours, so:
2040 = 4(j + w)
Simplifying this equation, we get:
j + w = 510
When flying into the headwind, the effective speed of the jet is j - w. We know that it can only travel 1560 miles in 4 hours, so:
1560 = 4(j - w)
Simplifying this equation, we get:
j - w = 390
Now we have two equations with two variables:
j + w = 510
j - w = 390
We can solve this system of equations using elimination. Adding the two equations, we get:
2j = 900
Dividing both sides by 2, we get:
j = 450
So the speed of the jet in still air is 450 mph.
Now we can use either equation to solve for the speed of the wind. Let's use the first equation:
j + w = 510
Substituting j = 450, we get:
450 + w = 510
Subtracting 450 from both sides, we get:
w = 60
So the speed of the wind is 60 mph.
Step-by-step explanation:
6TH GRADE MATH FIND SLOPE IN THE EQUATION
Answer:
Step-by-step explanation:
answer is -2
Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation.
The result of the division in ordinary decimal notation is 300.
Scientific notation, also known as standard form or exponential notation, is a method of expressing very large or very small numbers in a compact and standardized way.
To perform the indicated operation, we need to divide 0.00036 by 0.0000012.
First, let's express both numbers in scientific notation
0.00036 = 3.6 x 10^(-4)
0.0000012 = 1.2 x 10^(-6)
Now we can divide the two numbers and simplify
3.6 x 10^(-4) / 1.2 x 10^(-6) = (3.6 / 1.2) x 10^(-4-(-6)) = 3 x 10^(2)
Finally, we can convert this result back to ordinary decimal notation
3 x 10^(2) = 300
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The given question is incomplete, the complete question is:
Convert each number to scientific notation and perform the indicated operations. Express the result in ordinary decimal notation. 0.00036/0.0000012
olivia and kieran share money in the ratio 2:5. Olivia gets £42. how much did kieran get?
[tex] \huge \: \tt \green{Answer} [/tex]
Olivia and kieran share ratio 2 : 5
[tex] \texttt{olivia's share \: of \: money = £42 }= \frac{2}{7} \\ [/tex]
Total Amount of Money = Olivia's share of money × Reciprocal of olivia's share
[tex] \tt \: = > 42 \times \frac{7}{2} \\ \\ = > 147[/tex]
Kieran's share of Money =
[tex] = > 147 \times \frac{5}{7} \\ \\ = > \sf{ \pink{£105}}[/tex]
In a GP the 8th term is 8748 and the 4th
term is 108. Find the sum of the 1st 10 terms.
The first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get 118096.
What is Geometric Progression?
A progression of numbers with a constant ratio between each number and the one before
Let the first term of the geometric progression be denoted by "a" and the common ratio be denoted by "r".
We know that the 4th term is 108, so we can use the formula for the nth term of a GP to write:
a*r³ = 108 .....(1)
We also know that the 8th term is 8748, so we can write:
a*r⁷ = 8748 .....(2)
To find the sum of the first 10 terms, we can use the formula for the sum of a finite geometric series:
S = a(1 - rⁿ)/(1 - r)
where S is the sum of the first n terms of the GP. We want to find the sum of the first 10 terms, so we plug in n = 10:
S = a(1 - r¹⁰)/(1 - r)
We now have two equations (1) and (2) with two unknowns (a and r). We can solve for a and r by dividing equation (2) by equation (1) to eliminate a:
(ar⁷)/(ar³) = 8748/108
r⁴ = 81
r = 3
Substituting r = 3 into equation (1) to solve for a, we have:
a*3³ = 108
a = 4
Therefore, the first term of the GP is 4 and the common ratio is 3. We can now substitute these values into the formula for the sum of the first 10 terms to get:
S = 4(1 - 3¹⁰)/(1 - 3)
S = 4(1 - 59049)/(-2)
S = 4(59048)/2
S = 118096
Therefore, the sum of the first 10 terms of the GP is 118096.
118096.
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