The compound interest on $1240 at 8% for 2 years is $205.8
What is compound interest?Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.
The Amount on a compound interest is expressed as: A = P(1+r/100)^t
where P is the principal and r is the rate, t is the time
A = 1240( 1+8/100)²
A = 1240(1+0.08) ²
A = 1240(1.08)²
A = 1240× 1.166
A = $1445.8
A = P+I
I = A-P
I = 1445.8-1240
I = $ 205.8
therefore the interest on the $1240 compounded for 2 years is $205.8
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ms tunnicliffe is making jam for the county fair blackberries cost 5.50 per kg sugar cost 65c per kg 15 glass jars cost 5.85 she uses 16kg of blackberries and 10kg of sugar to make 15 jars of jam calculate the total cost to make the 15 jars
Therefore , the solution of the given problem of unitary method comes out to be total cost for to make 15 jars is 12,386.25 euroes.
What exactly is a unitary method?After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.
Here,
Given :
cost of blackberry = 88 euroes
cost of sugar = 650 euroes
Jam bottles costs =87.75
total cost for to make 15 jars is
=> 15 * (87.75+650+88)
=> 15 * 825.75
=> 12,386.25 euroes
Therefore , the solution of the given problem of unitary method comes out to be total cost for to make 15 jars is 12,386.25 euroes.
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you watch a roulette wheel spin 7 consecutive times and the ball lands on a red slot each time. what is the probability that the ball will land on a red slot on the next spin?
The probability that the ball will fall into a red slot during the following spin is 0.14.
To calculate the probability of an occurrence, divide the total number of outcomes by the total number of possible outcomes. The concepts of probability and odds are distinct. Odds are determined by dividing the probability of a situation happening by the probability that it won't happen. Probability is a metric used to determine how likely an event is to occur. When we toss the coin in the air, the probability that it will land with the heads side up is calculated. Here is a practical use of probability that you are probably already familiar with. We always check the weather forecast before a significant outing.
[tex]\frac{1}{7}=0.142857[/tex]
The probability is 0.14
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The probability of the ball landing on a red slot in a single spin of a fair roulette wheel is 1/2, as there are an equal number of red and black slots.
The outcome of each spin is independent, meaning that the outcome of one spin does not affect the outcome of another. Therefore, the probability that the ball will land on a red slot in the next spin is still 1/2, regardless of the results of the previous seven spins.
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Write a
linear function f with f (5) = -1 and
f (0) = -5.
f(x) =
[tex]\huge\begin{array}{ccc}f(x)=\dfrac{4}{5}x-5\end{array}[/tex]
The linear function.
We have:
[tex]f(5)=-1\\\\f(0)=-5[/tex]
therefore we have two points on the line:
[tex](5,-1),\ (0,-5)[/tex]
Use the two points-slope formula:
[tex]A(x_a,\ y_A),\ B(x_B,\ y_B)\\\\y-y_A=\dfrac{y_B-y_A}{x_B-x_A}(x-x_A)[/tex]
Substitute:
[tex](5,-1)\to x_A=5,\ y_A=-1\\(0,-5)\to x_B=0,\ y_B=-5[/tex]
[tex]y-(-1)=\dfrac{-5-(-1)}{0-5}(x-5)\\\\y+1=\dfrac{-5+1}{-5}(x-5)\\\\y+1=\dfrac{-4}{-5}(x-5)\\\\y+1=\dfrac{4}{5}(x-5)\\\\y+1=\dfrac{4}{5}x-4\\\\y+1-1=\dfrac{4}{5}x-4-1\\\\\boxed{y=\dfrac{4}{5}x-5}[/tex]
Answer:
f(x) = 0.8x - 5
Step-by-step explanation:
the equation of a linear function is of the form
f(x) = ax + b
to find a and b use the given points
f(5) = - 1 ⇒ (5, - 1)
f(0) = - 5 ⇒ (0, - 5 )
substituting into the standard form , (0, - 5 )
- 5 = a(0) + b
- 5 = b
then
f(x) = ax - 5
substitute the other point (5, - 1 )
- 1 = 5a - 5 ( add 5 to both sides )
4 = 5a ( divide both sides by 5 )
[tex]\frac{4}{5}[/tex] = a
f(x) = [tex]\frac{4}{5}[/tex] x - 5
or
f(x) = 0.8x - 5
Y is inversely proportional to the square of x. If Y = 6 when x = 2, then Y =1/2 when x is ______.
Marcy works as a server at the Cass Restaurant. The amount of money she earns during a shift depends on the number of tables she serves. m = the amount of money Marcy earns t = the number of tables Marcy serves Which of the variables is independent and which is dependent?
If you divide $320 by 40 your answer is 8, so Mary probably earns 8 dollars an hour.
Geometry, I’m unsure. Please help it is due tomorrow.
Question 5(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 30 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
A . graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 20
B. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40
C. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one third comma 0
D. graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 40
The graph represents this situation:
B) graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
y= 30+ 10x
Now, take x= 0
y= 30
and, x= 1
y= 30+ 10
y= 40
and, x= 2
y= 30+ 20
y= 50
and, graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars.
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Choose ALL answers that describe the polygon KLMN if KL = 10, LM = 17, MN = 10, NK = 17, KL // MN, and LM // NK
In the polygon KLMN KL = 10, LM = 17, MN = 10, NK = 17 and
KL || MN, and LM || NK hence the polygon KLMN is a parallelogram.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
Given, A polygon in which KL || MN, and LM || NK and also from the given information opposite sides are of equal length.
We know in a parallelogram opposite sides are parallel and equal in length.
Now, If in this parallelogram all individual interior angles measures
90° then this parallelogram would be a rectangle.
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in the extensive-form game that follows, how many strategies does player 2 have? c 2 f 2 g 8, 0 0, 2
If we consider all possible mixed strategies for player 2, then the number of strategies that player 2 has is infinite.
In the extensive-form game provided, player 2 has two decision points where they can choose between two actions, C and F in the first decision point and G and not-G in the second decision point. Therefore, player 2 has 2 x 2 = 4 pure strategies.
However, player 2 can also mix their strategies in each decision point, choosing a probability distribution over the available actions. For example, in the first decision point, player 2 can play a mixed strategy where they choose C with some probability and F with the complementary probability. Similarly, in the second decision point, player 2 can mix their strategies by choosing to play G with some probability and not-G with the complementary probability.
So, if we consider all possible mixed strategies for player 2, then the number of strategies that player 2 has is infinite.
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In the extensive-form game that follows, how many strategies does player 2 have?
Which equations could verify the solution to the equation − 48 = − 7 x − 13 ? Select two answers.
A.-48 = -7(-5) - 13
B.-48 = -35 - 13
C.-48 = 7(-5) - 13
D.-48 = -7(5) - 13
E.48 = 35 + 13
F.48 = 7(5) + 13
The equations that can verify the solution.
-48 = -35 - 13
-48 = 7(-5) - 13
-48 = -7(5) - 13
Options B, C, and D are the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 6 is an equation.
We have,
-48 = -7x P - 13
-48 + 13 = -7P
-35 = -7P
P = 5
The solution is 5.
This means,
-48 = - 7 x 5 - 13
-48 = -35 - 13
-48 = -48
Verified.
Now,
A.
-48 = -7(-5) - 13
-48 = 35 - 13
-48 = 22
Not true.
B.
-48 = -35 - 13
-48 = -48
Verified.
C.
-48 = 7(-5) - 13
-48 = -35 - 13
-48 = -48
Verified.
D.
-48 = -7(5) - 13
-48 = -35 - 13
-48 = -48
Verified.
E.
48 = 35 + 13
48 = 48
True.
F.
48 = 7(5) + 13
48 = 35 + 13
48 = 48
True.
Thus,
-48 = -35 - 13
-48 = 7(-5) - 13
-48 = -7(5) - 13 equations can verify the solution.
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Please help!!! Answer the following questions for f(x) = -x4 + x3 - 7x2 + 9x + 18
A.) How many total zeros does this function have? Explain how you know. (1 point)
B.) Using p/q, list all possible rational zeros. (3 points)
C.) Using Descartes' Rule of Signs, how many possible positive, negative, and complex (imaginary) zeros are possible... list all possibilities. It would be helpful to make a table (4 points)
D.) Describe the end behavior of this graph. (2 points)
The total zeros the function has is 4
See below for other solutions
How many total zeros does this function have?This is the degree of the function
The degree of f(x) = -x^4 + x^3 - 7x2 + 9x + 18 is 4
So, the number of zeros is 4
The possible rational zerosStart by writing out the factors of the leading coefficient and the constant term
p = ±(1, 2, 3, 6)
q = ±1
So, we have
p/q = ±(1, 2, 3, 6)/±1
p/q = ±(1, 2, 3, 6)
How many types of zeros are possibleHere, we find the number of changes in sign in the coefficients of the polynomial function.
f(x) = -x^4 + x^3 - 7x2 + 9x + 18
Number of sign changes = 3
Calculate f(-x) for the negative zeros
f(-x) = -(-x)^4 + (-x)^3 - 7(-x)^2 + 9(-x) + 18
f(-x) = -x^4 - x^3 - 7x^2 - 9x + 18
Number of sign changes = 1
This means that there is the possibility of 3 positive zeros, 1 negative zero, and 1 complex zero.
The end behavior of the graph of the functionHere, we make use of the leading term, -x4, which is negative.
This implies that the graph will approace -∝ as x approaches +∝ and will approach +∝ as x approaches -∝.
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suppose there is a 10% chance of raining, and there is a 2% chance that the midterm exam is cancelled. assume that these two events (raining and cancelling the exam) are independent. what is the probability that neither events happen? please select the best answer.
TLDR: 88%
The probability of neither event happening is the complement of the probability of either event happening, which is 100 - 12 = 88.
Cheers,
qxxi
Determine if the system has a nontrivial solution. Try to use as few row operations as possible. 4x^1-6x^2 + 13x^3 = 0 -4x^1-10x^2-x^3 = 0 8x^1+4x^2 +14x^3 = 0 Choose the correct answer below. A. It is impossible to determine. B. The system has only a trivial solution. C. The system has a nontrivial solution.
The correct answer is option C. The system has a nontrivial solution.
One way to determine if a system has a nontrivial solution is to use Gaussian elimination to reduce the augmented matrix to row echelon form. If the row echelon form has a row of zeros except for the last entry in the augmented part, then the system has only a trivial solution.
If there is a row of zeros in the row echelon form that corresponds to a free variable, then the system has a nontrivial solution. In this case, it is possible to use Gaussian elimination to see that the row echelon form of the augmented matrix has a row of zeros except for the last entry in the augmented part, which is not zero, indicating that the system has a nontrivial solution.
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a coin is tossed times. (a) how many different outcomes are possible? (b) how many different outcomes have exactly heads? (c) how many different outcomes have at least heads ?
different outcomes have at least heads 2048, 165, 2036, 1816,
1. total number of different outcomes for 11 times toss
=2048
2. exactly 8 heads can be found by combination ( exactly n heads possiblity can be found by 11Cn
= 165
3. number of outcomes with atleast 2 heads can be found by subtracting number of outcomes with with 0 and 1 heads from total number of outcomes
= total number of outcomes - outcomes with 0 heads - outcomes with 1 heads
= 2036
4. number of outcomes with atmost 7 heads can be found by subtracting number of outcomes with 8, 9, 10, 11 heads from total number of outcomes
= total number of outcomes - outcomes with 8 heads - outcomes with 9 heads - outcomes with 10 heads -outcomes with 11 heads
=1816
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assuming that nothing is known about the shape of the distribution for the data, what percentage of dentists use less than 102 units of local anesthetics per week?\
If the data has a mound-shaped distribution, then percentage of dentists who use less than 102 units of local anesthetics per week is 84% .
The Distribution is mound shaped and symmetric
we have to find percentage of dentists use less than 102 units of local anesthetics per week ;
Since the distribution is mount shaped , 68% of the data values are within 1 standard deviations of the mean (by the empirical rule) and 32% of data values are more than 1 standard deviations (23) from mean (79) .
Since , Distributions is symmetric, we expect about 16% of the data values to be more than 1 standard deviations below the mean, and about 16% of data values to be more than 1 standard deviations above mean.
So , 68% + 16% = 84% of the data values is expected to be less than 102.
Therefore , 84% of dentists use less than 102 units of local anesthetics per week .
The given question is incomplete , the complete question is
A study published in Current Allergy & Clinical Immunology (Mar. 2004) investigated allergic reactions of dental patients to local anesthetics. Based on a survey of dental practitioners, the study reported that the mean number of units (ampoules) of local anesthetics used per week by dentists was 79, with a standard deviation of 23. Suppose we want to determine the percentage of dentists who use less than 102 units of local anesthetics per week.
Assuming that the data has a mound-shaped distribution, what percentage of dentists use less than 102 units of local anesthetics per week ?
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g a runner wants to run 10.1 km . her running pace is 6.8 mi/hr . how many minutes must she run?
I runner is running at the speed of 6.8 miles/hr and he wants to run 10.1 km then he runner must run for 9.3 minutes.
To calculate this, we first need to convert the given speed from miles per hour to kilometers per hour. 6.8 mi/hr is equal to 10.9 km/hr.
Then, we need to divide the total distance (10.1 km) by the speed (10.9 km/hr) to get the total time it will take for the runner to complete the 10.1 km run.
10.1 km/10.9 km/hr = 0.922 hr = 9.3 minutes.
Therefore, the runner must run for 9.3 minutes in order to complete the 10.1 km run.
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state the degree and leading coefficient of each polynomial in one variable. if it is not a polynomial in one variable, explain why
The degree and leading coefficient of each polynomial in one variable is given below :- (2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial
The "leading coefficient" is the coefficient of the highest-degree term in the sum of terms that makes up a polynomial.
These expressions all have one variable, so the number of variables is not an issue in any case. All of the exponents are positive integers, so that is not an issue in any case. However, the variable appears in the denominator in the expression of problem 6, so that sum is not a polynomial.
______
(2). In order to put this into the form we recognize as a polynomial, the expression must be "simplified' by performing the multiplication of the two factors:
= 8x³ -4x² +6x -3
The leading coefficient is the coefficient of the highest-degree term, which is the product of the highest-degree terms of the factors. That product is ...
(2x)(4x²) = 8x³
so the leading coefficient is 8. The variable is to the 3rd power, so the degree is 3.
______
(4). The expression is already written as a sum, so we only need to find the term of highest degree. That is the last one: 7y^6. Its degree is 6 and its leading coefficient is 7.
_____
(6). Variables are not allowed in the denominator of a polynomial. This expression is not a polynomial.
Hence the degree and leading coefficient of each polynomial in one variable is given below :-
(2). degree 3; leading coefficient 8 | (4). degree 6; leading coefficient | (6). not a polynomial
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----------- Correct format of the question is given below --------
(Q). State the degree and leading coefficient of each polynomial in one variable. if it is not a polynomial in one variable, explain why?
*equations of each polynomial is given below in image.*
If x1 and x2 are solutions to 3x^2+15x+9=0 quadratic equation, then
x1+x2=
Answer:
[tex]x_1 + x_2 = \boxed{-5}[/tex]
Step-by-step explanation:
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\implies x_{1,\:2}=\dfrac{-b}{2a}\pm\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]
Let's have
[tex]x_{1}=\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]\
[tex]x_{2}=\dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x_1 + x_2 =\dfrac{-b}{2a}+\dfrac{\sqrt{b^{2}-4ac}}{2a} + \dfrac{-b}{2a}-\dfrac{\sqrt{b^{2}-4ac}}{2a}\\[/tex]
[tex]\dfrac{\sqrt{b^{2}-4ac}}{2a} - \dfrac{\sqrt{b^{2}-4ac}}{2a} = 0\\\\[/tex]
Leaving us with
[tex]\dfrac{-b}{2a} + \dfrac{-b}{2a}\\\\\implies 2 \cdot \left(\dfrac{-b}{2a}\right)\\\\\implies -\dfrac{b}{a}\\\\[/tex]
The given equation is
[tex]3x^2+15x+9=0[/tex]
Here a = 3, b = 15
So
[tex]-\dfrac{b}{a} = --\dfrac{15}{3} = -5\\[/tex]
Answer:
[tex]x_1 + x_2 = \boxed{-5}[/tex]
An item on sale costs 15% of the original price. If the original price was $20, what is the sale price?
Timed again, 100 points
remember: ONLY 5 stars, thanks, and brainliest IF correct!
Answer:
17
Step-by-step explanation:
The original price was $20, so the discount price would be 20 * 15% = $3.
Therefore, the sale price would be 20 - 3 = $17.
List the decimal numbers 2.36, 2.4, 2.04, and 2.3 in order from least to greatest.
A 2.3, 2.4, 2.04, 2.36
B 2.3, 2.36, 2.4, 2.04
C 2.04, 2.3, 2.36, 2.4
D 2.04, 2.36, 2.4, 2.3
Answer:
C 2.04, 2.3, 2.36, 2.4
Step-by-step explanation:
Start comparing from left to right.
2.36
2.4
2.04
2.3
The ones digit has a 2. All numbers have a 2 in the ones digit, so so far they are all the same.
Now move over one digit to the right. It is the first digit to the right of the decimal point. It is the tenths digit. Compare the numbers in the tenths digit.
2.36
2.4
2.04
2.3
The tenths digit contains a 3, a 4, a 0, and a 3. Now put the numbers in increasing order by the tenths digit.
2.04
2.36
2.3
2.4
The digits in the tenths place are now in increasing order. Now we look at the next digit to the right, the hundredths digit. If a number has no digit in the hundredths place, put a zero there.
2.04
2.36
2.30
2.40
The only change we see that we need to make is the two middle numbers.
2.04
2.30
2.36
2.40
Answer: 2.04, 2.30, 2.36, 2.40
Use synthetic division to evaluate f(x)=x4+6x2−7x+1 for x=3.
Mia had $22 Then she started to receive $4 a week as an allowance. She plans to save all of her money for a bicycle and draws a graph of her planned savings. Mia lets x represent the number of weeks she has received her allowance, and y represent her total amount of money. Which of the following ordered pairs is on Mia's graph?
A. (2,44)
B. (1,22)
C. (6,24)
D. (5,42)
Answer:
(5, 42)
Step-by-step explanation:
22 + 4x= 42
There is only one that will work.
42 - 22 = 20
4x = 20
x= 5
" X is the number of weeks they have gotten the allowance "
Answer: D. (5,42)
Step-by-step explanation:
If x is representing the weeks that she received her allowance, this means that we would need to add 4 to her starting amount (22) for every week.
So, if she got an allowance for 5 weeks, we would need to multiply her earning amount (4 per week) by the number of weeks (5).
5 x 4 = 20
But, we aren't done just yet! We still need to add this amount to her starting balance, which is $22. So, 20 + 22 = 42.
So, if x is 5, y would be 42, just like in the answer!
Another way of solving this answer would be 22 + 4x = 42.
I hope this helped you :)
Cheers!
Please I need help on this immediately!!!
The value of the element t11 is 34 and the value of the element at d12 is 15.
When are two matrices called being equal?Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.
M + W = Indoor= [26 55] Outdoor = [32 49]
The value indicates the sum of the indoor volunteers ages 18-39,\
34.
To create a matrix by subtracting the women's matrix from the mens matrix.
Now the difference;
M – W = Indoor = 8 15 Outdoor = -16 3
This value indicates the difference of the volunteers indoors 40 so
Therefore the value would be 15.
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what is true about an equation with infinite solutions
The solutions for the infinite solutions have the same set of coefficients on both sides of the equations
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A be
ax + by = 0
Let the second equation be represented as B
Now , the value of B be
cx + dy = 0
For the system of equations to have infinite solutions , the coefficients of both the equations should be same
So , when a = c and b = d
ax + by = cx + dy
Hence , when the coefficients of the equations are same , the system has infinite solutions
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given that the mean number of book read per child is 1, the value of x.
Since the mean number of book read per child is 1, the value of x is 4.
What is a mean?In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
How to calculate the mean for the number of book read?Mathematically, the mean for this set of scores can be calculated by using the following formula:
Mean = [F(x)]/n
For the total number of books, we have;
Total number of book = 0(4) + 12(1) + 2(x)
Total number of book = 12 + 2x
Mean = (12 + 2x)/(16 + x)
1 = (12 + 2x)/(16 + x)
16 + x = 12 + 2x
2x - x = 16 - 12
x = 4.
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the expression $y^2 10y 33$ can be written as a combination of a square of a binomial and an integer. find the integer.
When the expression y² + 10 y + 33 is written as a combination of a square of a binomial expression and an integer, the value of the integer is 8
We are given an expression y² + 10 y + 33 and this expression can be written as a combination of a square of a binomial and an integer. we need to find the value of the integer.
= y² + 10 y + 33
Write 10 y = 2 (5) (y)
= y² + 2 (5) (y) + 33
Write 33 = 25 + 8
= y² + 2 (5) (y) + 25 + 8
Write 25 = 5²
= y² + 2 (5) (y) + 5² + 8
Write y² + 2 (5) (y) + 5² = (y + 5)²
= (y + 5)² + 8
So, here (y + 5)² is the square of the Binomial expression and 8 is the integer.
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Can I please get help anyone
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 3000e^{0.06\cdot 2} \implies A \approx 3382.49~\hfill \underset{interest~only}{\stackrel{3382.49~~ - ~~3000}{\approx\text{\LARGE 382.49}}}[/tex]
does anything in the plot of the semimajor axis versus the period change when the eccentricity is changed?
Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.
What is eccentricity?In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.
Here,
In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.
As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.
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suppose a system of equations has 3 equations and 5 variables. additionally, suppose the coefficient matrix for the system has 3 pivot columns. based on this information alone, is the system consistent or inconsistent? why or why not?
Suppose a system of equations has 3 equations and 5 variables. additionally, suppose the coefficient matrix for the system has 3 pivot columns. Based on the information provided, it is consistent.
The number of pivot columns in the coefficient matrix of a system of equations determines the rank of the matrix, which is a measure of the number of linearly independent rows or columns. A system of equations is consistent if and only if the rank of the coefficient matrix is equal to the number of unknowns in the system.
In this case, the system has 3 equations and 5 variables, so it is not immediately clear if the rank of the coefficient matrix is equal to the number of unknowns. Additionally, the number of pivot columns alone is not enough to determine the consistency of the system, as there may be additional relationships between the variables that affect the rank.
So, Based on the information provided, it is consistent.
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Zack's biology lab group is studying how quickly bacteria grow when exposed to sunlight. At the beginning of the experiment, Zack looked at the sample under a microscope and counted 5 bacteria. After the sample was exposed to sunlight for one hour, Zack looked again and counted 35 bacteria. Write an exponential equation in the form y=a(b)x that can model the number of bacteria, y, after x hours in sunlight. Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential function that models the number of bacteria after x hours is given as follows:
y = 5(7)^x.
How to model the exponential function?An exponential function is defined as follows:
y = a(b)^x.
In which the parameters are given as follows:
a is the initial amount.b is the rate of change.The initial amount of bacteria was of 5, hence the parameter a is obtained as follows:
a = 5.
After one hour, the number of bacteria was multiplied by 7, as 35/5 = 7, hence the parameter b is obtained as follows:
b = 7.
Thus the function is given as follows:
y = 5(7)^x.
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