The simple interest on a principal amount is the function on time t.
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: Principal=$3200, Annual rate of interest =8% and time=5 years
Thus Simple interest is S.I= 3200×8×5 / 100
=$1280
Which is equal to the interest given in the question.
Thus the the interest rate forms a linear function or
Simple Interest is calculated using the following formula: SI = P × R × T /100,
where r and P are constant then S.I can be written as the function of time t
SI(t)= P×r×t/100
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Write an equation that passes through the points (1,8) and (3,4)
Answer:
[tex]y = -2x + 10[/tex]
Step-by-step explanation:
The slope-intercept form of equation of line:
y = mx + c
where:
m = slope
c = y-intercept
Slope, m: [tex]\frac{y_{2} - y_{1}}{x_{2} -x_{1}}[/tex]
= [tex]\frac{4 - 8}{3 - 1}[/tex]
= [tex]-\frac{4}{2}[/tex]
= [tex]-2[/tex]
[tex]y = -2x +c[/tex]
Substitute the coordinates of either of the two points in this equation to calculate the value of c:
8 = [tex]-2[/tex](1) + c
8 = [tex]-2[/tex] + c
c = 8 + 2
c = 10
Therefore, the equation is:
[tex]y = -2x +10[/tex]
Enlarge triangle T by a scale factor 1/2, centre (2, 0).
Answer:
To enlarge a triangle by a scale factor of 1/2 with the center (2, 0), each vertex of the triangle should be multiplied by 1/2 and then shifted so that the center of the new triangle is (2, 0).
Step-by-step explanation:
For example, if the original triangle has vertices at (a, b), (c, d), and (e, f), the vertices of the new triangle would be at ((a-2)/2 + 2, (b-0)/2 + 0), ((c-2)/2 + 2, (d-0)/2 + 0), and ((e-2)/2 + 2, (f-0)/2 + 0).
Jeremiah spins a spinner with 5 equal-sized section twice,
rolls a six-sided dice, and flips a coin. How many possible
outcomes there can be?
The total number of possible outcomes is the product of the number of outcomes for each event.
The spinner can land on any of its 5 sections on the first spin, and on any of the 5 sections again on the second spin. So there are 5 x 5 = 25 possible outcomes for the spinner.
The dice can land on any of its 6 sides.
The coin can land either heads or tails.
Therefore, the total number of possible outcomes is:
25 (spinner) x 6 (dice) x 2 (coin) = 300 possible outcomes.
5 tractors with the same power working together had not yet mowed 60% of the field when 3 of them left the job. How many hours did the other 2 tractors continue to work to finish harvesting the field, if it is known that exactly 0 of the field had been mowed after 6 hours 0,6
The information given is not sufficient to solve for the number of hours the remaining 2 tractors worked to finish harvesting the field.
How to solve similar problems with complete informationTo solve for this, additional information is required such as the mowing speed of each tractor, the size of the field, and the amount of the field that was mowed before the 3 tractors left the job.
With this information, you can determine the total mowing time required to mow the entire field, and then subtract the 6 hours the 5 tractors worked together to find the time the remaining 2 tractors worked.
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what is the reflection of the point (-8,7) across the x and y axis?
Step-by-step explanation:
We have the point (-8, 7)
When we reflect across the X-AXIS, then the Y coordinate changes signs
When we reflect across the Y-AXIS, then the X coordinate changes signs
So when we reflect (-8, 7) across the x-axis, it becomes (-8, -7) since we change signs for the Y coordinate from +7 to -7
Reflecting across the Y, it becomes (8, 7), because we change signs from -8 to +8
Tell me the explanation and the result of how to convert numbers into fractions Daisy is practicing trivia. She gets 12 out of 20 questions correct.
What percentage of the trivia questions do you get right? bone what is the percent of that
Answer:
60%
Step-by-step explanation:
12/20 = 0.6 multiply this by 100% = 60%
Negative sixteen plus the quotient of a number and 2 is 35.
If negative sixteen plus the quotient of a number and 2 is 35, the number is 102.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = x
Negative sixteen plus the quotient of a number and 2 is 35.
This can be written as,
Quotient of a number and 2.
x ÷ 2 = M (quotient)
So,
-16 + M = 35
Now,
Solve for M.
M = 35 + 16
M = 51
Now,
x ÷ 2 = 51
x/2 = 51
x = 51 x 2
x = 102
Now,
We can cross-check.
-16 + 51 = 35
35 = 35
Thus,
The number is 102.
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The mathematical constant pi is needed when calculating the area of a
When computing the area of a circle, the mathematical constant pi () is required. Pi is the circumference-to-diameter ratio of a circle and is approximately equal to 3.14159.
The area of a circle is calculated by multiplying pi by the radius squared (r2). To estimate the area of a circle, utilize pi in the calculation since it is a vital aspect of the relationship between the circumference and diameter of a circle.
Pi is not required when determining the area of a square, rectangle, or cube since the formulas for these shapes are different.
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The question is -
The mathematical constant pi is needed when calculating the area of a _.
a. circle
b. square
c. rectangle
d. cube
systems of two equations to solve systems of three equations.
Students are baking shortbread, croissants, and pound cakes.
• One group of students used a total of 3,525 grams of flour to make
5 batches of shortbread, 4 pound cakes, and 2 batches of croissants.
• Another group of students used 1,020 grams of flour to make one
batch each of shortbread and croissants and one pound cake.
• There is the same amount of flour in 4 pound cakes as there is
in 2 batches of croissants.
1. Let s = the amount of flour in a batch of shortbread, let c = the
amount of flour in a batch of croissants, and let p = the amount
of flour in a pound cake. Write an equation for each of the
3 statements above.
2. Multiply one equation, then add or subtract it with another
equation you wrote in Exercise 1 to eliminate the variable p.
3. Use the third equation and your result from Exercise 2 to write a
system of two equations with the variables p and c. Solve your system
and find the values for p and c.
4. What is the value of s? Explain what you did.
Step-by-step explanation:
Let s = the amount of flour in a batch of shortbread, let c = the amount of flour in a batch of croissants, and let p = the amount of flour in a pound cake.
The first statement can be written as 5s + 4p + 2c = 3525.
The second statement can be written as s + c + p = 1020.
The third statement can be written as 4p = 2c.
Multiplying the third equation by 2, we get 8p = 4c.
Subtracting this from the first equation, we get 5s + 4p + 2c - 8p = 3525 - 8p.
Simplifying, we get 5s - 6c = 3525 - 8p.
Now we have a system of two equations with the variables c and p:
5s - 6c = 3525 - 8p
s + c + p = 1020
We can use substitution to eliminate c. Solving the second equation for c, we get c = 1020 - s - p.
Substituting this into the first equation, we get 5s - 6(1020 - s - p) = 3525 - 8p.
Expanding the second equation and simplifying, we get 11s = 4545 - 8p.
Solving for s, we get s = (4545 - 8p) / 11.
Substituting the value of s into the second equation, we get c + p + (4545 - 8p) / 11 = 1020.
Expanding and simplifying, we get c + p + (4545 - 8p) / 11 = 1020.
Expanding, we get c + p = 1020 - (4545 - 8p) / 11.
Solving for c and p, we find that c = 664 grams and p = 356 grams.
Finally, the value of s is (4545 - 8 * 356) / 11 = 735 grams.
can you do it by telling
Answer:
Step-byoooooooooooo
-step explanation:
On the coordinate plan below, what is the length of AB?
I attached a photo please answer as quickly as possible.
The smallest integer value in the set is 7.
What is an integer?The grouping of positive and negative numbers is known as integers. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
Since an integer is a whole number, it can reach both positive and negative infinity. 0 is the smallest non-negative number.
Consider the given term as -3(x-4) = 12
Then, -3x + 12 = 12
or, -3x = 0
or, x = 0
So, the value of x is either x > 0 or x < 0
Based on the given option, the smallest integer value is 7.
So, the required answer is 7.
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if sammy has 900 fish and 200 dies and then he gets 500 × 8090 and gets divided by 2 how many fish dose sammy have
On solving the provided question, we can say that Sammy has 900 fish and 200 dies and equation will be => x - y = 700
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
Sammy has 900 fish and 200 dies
equation will be
x - y = 700
x = alive fishes
y = died fishes
remaining fishes are 700
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Pls help. Look at photo
Note that the line of Best fit is attached accordingly. See the definition below.
What is a Line of Best Fit and why is it important?A line of best fit is a straight line that represents the trend of a set of data.
It is used to summarize and analyze the relationship between two variables in a scatter plot. Note that the line of best fit can be used to approximate the trend or pattern of the data and make predictions for new observations that fall within the range of the data.
The line is drawn in a way that minimizes the distance between the observed data points and the line.
The line of best fit can be used to make predictions and identify outliers. It is important because it helps to reveal patterns and trends in data and allows us to make informed decisions based on the information.
Note that the line takes a position that gives an approximately equal amount of variables or data points on either side.
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If you flip a coin 12 times, what is the best prediction possible for the number of times it will land on heads?
The best prediction that the coin would land on heads wold be 6
If you flip a coin 12 times, what is the best prediction possible for the number of times it will land on heads?If you flip a fair coin 12 times, the best prediction for the number of times it will land on heads is 6. This is because each flip has an equal chance of landing on heads or tails, and if you flip a fair coin 12 times, the expected number of heads is 6. This is because each flip has a 50% chance of landing on heads.
In the coin, there are going to be 6 changes foe head and also 6 chains for tails. This is a 50 50 chance
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Find the midpoint of A and B
where A has coordinates (2, 7)
and B has coordinates (6, 3).
Answer:
(4, 5)
Step-by-step explanation:
Add the two x values and divide by two, add the two y values and divide by two. Then put them in brackets and those are your coordinates.
Complete the table using the function m = a + 20.
Answer:
26
28
29
Step-by-step explanation:
[tex]m = a + 20[/tex]
Anywhere you see the letter a, you'll plug in the given a number.
The first one is 6, meaning
[tex]m = 6 + 20 = 26[/tex]
Then we do the same for the others.
imagine you have a dataset at the individual level that reports how much tv an individual watches per week. you want to combine this with a dataset (also at the individual level) that reports how much each individual sleeps per week. what command in stata would be the most useful
The command in Stata would be the most useful is reg when you want to combine this with a dataset that reports how much each individual sleeps per week.
A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable. The data set includes values for each of the variables, such as the object's height and weight, for each set member. Data sets may also include a group of files or documents.
For data management, visualisation, statistics, and automated reporting, Stata is a general-purpose statistical software programme created by StataCorp. Researchers in a variety of disciplines, such as science, biomedicine, epidemiology, and sociology, use it.
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d=1/8t
t = time
d = distance
If d = 1/8t and t is a time and d is a distance then in this expression 1/8 is representing speed of the object.
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
Given that,
The expression,
d = 1/8t
where,
t = time
d = distance
which parameter 1/8 is indicating ?
The equation d = 1/8t describes a function that relates time (t) and distance (d) traveled.
The parameter 1/8 in the expression d = 1/8t is the rate of change of distance with respect to time.
It represents the amount of distance traveled in one unit of time.
In this case, 1/8 is the speed or velocity of the object being considered. It tells us that for every unit of time that passes, the distance traveled by the object increases by 1/8 units.
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What is the sign of
39
11
13
+
(
−
41
1
13
)
39
13
11
+(−41
13
1
)39, start fraction, 11, divided by, 13, end fraction, plus, left parenthesis, minus, 41, start fraction, 1, divided by, 13, end fraction, right parenthesis?
The sign of the expression is positive, since the result is positive.
What do you mean by algebraic expression?An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. Algebraic expressions are used to represent mathematical relationships and can be simplified, evaluated, and solved for particular values of the variables.
Algebraic expressions can be simple, such as a single variable or number, or complex, involving multiple variables, operations, and grouping symbols, such as parentheses. For example, the expression "x + 2" is a simple algebraic expression, where "x" is the variable and "2" is the constant term.
In algebra, variables are used to represent unknown values and the goal is often to find the value of these variables that satisfy a given condition or equation. Algebraic expressions can be simplified by combining like terms and applying the properties of arithmetic operations.
Algebraic expressions are also used to represent mathematical functions. A function is a relationship between an input value and an output value, where each input value corresponds to exactly one output value. Algebraic expressions can be used to define a function, and can also be used to find the value of the function for a particular input.
The expression 39 11 13 +(−41 131 )39, 11/13 + (−41/13) simplifies to 39 11 13 +(−41 131 )39, 11/13 + (−41/13) = 39 11 13 - 41 131 = (39 × 13 - 41 × 11) / 13 = (507 - 451) / 13 = 56 / 13 = 4.
The sign of the expression is positive, since the result is positive.
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Solve the system of linear equations by substitution.
y=4x
x+y=-10
We may determine that the values of x and y are -2 and -8, respectively, by replacing the linear equations.
What are linear equations?
A linear equation is a first-order (linear) term and a constant in an algebraic equation of the type y=mx+b, where m is the slope and b is the y-intercept.
The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."
The typical form for linear equations with two variables is Ax+By=C.
For instance, the linear equation 2x+3y=5 is in standard form.
Finding both intercepts of an equation in this style is quite easy (x and y).
The following is the equation:
y=4x ...(1)
x+y=-10 ...(2)
Now change equation (2) to y = 4x:
x+y=-10
x+4x=-10
5x = -10
x = -10/5
x = -2
Then, change equation (1) to read x = -2:
y = 4x
y = 4(-2)
y = -8
Therefore, we may determine that the values of x and y are -2 and -8, respectively, by replacing the linear equations.
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Photo attached in the description below
The reduction of the fraction is (y-3)/4.
How to interpret the fraction?Suppose the fraction is proper (the numerator is smaller than the denominator).
Let it be [tex]\dfrac{a}{b}[/tex]
Then, we can interpret it as:
[tex]\dfrac{a}{b}[/tex]= a parts out of b parts of a thing.
There is a fraction, containing numerator(upper value) and denominator(lower value).
When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction.
A proper fraction is also called fraction which is less than 1.
And an improper fraction is ≥ 1
A mixed fraction contains a sum of whole number and a proper fraction.
Given;
=y^2-9/4y+12
=y^2-3^2/4(y+3)
=(y+3)(y-3)/4(y+3)
=y-3/4
Therefor, the answer of fraction will be (y-3)/4
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We know
5 x 4 = 20
So, which of the following statements are also true?
(Choice A, )
5 is a factor of 20
(Choice B)
5 is a multiple of 20
(Choice C)
20 is a multiple of 4
Options A and C are correct for the condition 5 x 4 = 20.
What Is a Factor?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Factors can be found using either division or multiplication. Rules of divisibility can also be applied.
Given 5 x 4 = 20
factors of 20 are 2*2*5
so 5 is the factor of 20,
A is correct.
now multiples of 20 are 20, 40, 60.......
since all values are greater than 5,
so 5 is not a multiple of 20.
B is not correct.
now multiples of 4 are 4, 8, 12, 16, 20, 24 .......
so 20 is a multiple of 4,
C is correct.
Hence A and C are correct statements.
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Point A is at (-4, 8) and point B is at (6, 7).
What is the midpoint of line segment AB?
Answer:(1,7.5)
Step-by-step explanation:
Use Midpoint Formula
[tex]\lim_{x \to } 0 \frac{1-cosx\sqrt{cos2x} }{x^2} }[/tex]
Find the limit.
The limit of the function in this problem is given as follows:
lim x->0 f(x) = 1/2.
How to obtain the limit of the function?Following the standard procedure to obtain the limit of the function, merely obtaining the numeric value at x = 1, the limit is undetermined at x = 0, as follows:
0/0.
Hence the can apply the L'Hospital Rule, trying to find the derivative at the numerator and the denominator, hence:
[cos(x)sqrt(cos(2x))]' = [-sin(x)sqrt(cos(2x)) - 2sin(2x)cos(x)/sqrt(sin(2x))].[x²]' = 2x.At x = 0, the limit would again assume an undetermined value of 0/0, hence the L'Hospital Rule is applied again, hence:
[-sin(x)sqrt(cos(2x)) - 2sin(2x)cos(x)/sqrt(sin(2x))]' = cos(2x)sqrt(cos(2x)).[2x]' = 2.Now the function is:
f(x) = cos(2x)sqrt(cos(2x))/2.
Since cos(x) = 0, the numeric value at x = 0 is given as follows:
f(0) = 1/2.
Which is the limit.
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Hasan plans to choose a book from a section of the store where everything is 25% off. He writes the expression d−0.25d to find the sale price of the book if the original price is d dollars.
Bella correctly writes another expression, 0.75d, that will also find the sale price of the book if the original price is d dollars.
Drag each description to explain each part of both expressions.
Dragging each description to explain each part of Hasan's and Bella's expressions is as follows:
Hassan's Expression of d - 0.25d:d = Original price of book
0.25 = Percent Discount
0.25d = Amount of Discount
d - 0.25d = Sale price of book
Bella's Expression of 0.75d:0.75 = Percent of original price Bella will pay
d = original price
0.75d = Sale price of book
What is an algebraic expression?An algebraic expression is a combination of variables, constants, numbers, and values using the mathematical operands, including addition (+), subtraction (-), division (÷), and multiplication (×).
An algebraic expression does not have the equal symbol (=) unlike an equation.
Thus, the correct descriptions has been dragged to each part of both Hasan's and Bella's expressions.
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I’m on 1685 randomly selected high school students surveyed by public health organization, 437 said they were current smokers. Complete parts a through C below.
Answer: a. What is the proportion of current smokers among the 1685 high school students surveyed?
The proportion of current smokers among the 1685 high school students surveyed is 437/1685 = 0.259 or 26%.
b. What is the point estimate for the population proportion of all high school students who smoke?
The point estimate for the population proportion of all high school students who smoke is 0.259.
c. What is the 95% confidence interval for the population proportion of all high school students who smoke?
The 95% confidence interval can be calculated using the formula:
point estimate ± 1.96 * standard error
where standard error = square root of (point estimate * (1 - point estimate) / sample size)
standard error = square root of (0.259 * (1 - 0.259) / 1685) = 0.012
95% confidence interval = 0.259 ± 1.96 * 0.012
= 0.259 ± 0.023
= [0.236, 0.282]
So, the 95% confidence interval for the population proportion of all high school students who smoke is between 23.6% and 28.2%.
Step-by-step explanation:
PLSSS HELP IF YOUR TURLY KNOW THISSS
Answer:
The value of x =10
Step-by-step explanation:
2x+ 5 = 25
Subtract 5 from each side.
2x+5-5 = 25-5
2x = 20
Divide each side by 2.
2x/2 = 20/2
x =10
The value of x =10.
Answer:
10
Step-by-step explanation:
Move the 5 to the right so the equation is 2x = 25 - 5
Then its 2x = 20 and 20/2 is 10.
Find the inverse of the function f(x)=∛(x+2)-5. Please show all work in finding the inverse.
Answer:
Step-by-step explanation:
Let [tex]f(x) = y[/tex]
∴ [tex]y = \sqrt[3]{x + 2} -5[/tex]
x has to be isolated and made the subject of the formula:
[tex]y + 5 = \sqrt[3]{x + 2}[/tex]
Cube is applied to both sides of the equation to get rid of the cube root:
[tex](y + 5)^{3} = x + 2[/tex]
x = [tex](y + 5)^{3} -2[/tex]
Substitute [tex]f^{-1} (y) = x[/tex]:
[tex]f^{-1} (y) = (y + 5)^{3} - 2[/tex]
Replace y with x:
[tex]f^{-1} (x) = (x + 5)^{3} -2[/tex]
20 points if you help!
An equation of the line that passes through the given point and is perpendicular to the line shown in the graph are:
11. y = 5x - 1
12. y = 5x + 6
13. y = 5x + 23
14. y = 5x − 18
What is perpendicular line?If two geometric objects in fundamental geometry intersect at a right angle, they are perpendicular. The perpendicularity condition is graphically represented by the perpendicular symbol (║). It can be defined between two lines, between a line and a plane, or between two planes.
The slope of the line in graph
m = (3 -(-2))/(-2 - - 1)
m = − 5
For perpendicular to the given line the slope is always opposite sign and reciprocal i.e.
m = 3/5
11. (1, 4)
y - 4= 5(x - 1)
y - 4= 5x - 5 +4
y = 5x - 1
12. (0, 6)
y - 6 = 5(x - 0)
y = 5x + 6
13. (-5, -2)
y - (-2) = 5(x - (-5))
y = 5x + 23
14. (3, -3)
y - (-3) = 5(x - 3)
y = 5x − 18
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