[tex]\boxed{\sf I=\dfrac{PRT}{100}}[/tex]
[tex]\\ \sf\longmapsto I=\dfrac{2000(12)(2.5)}{100}[/tex]
[tex]\\ \sf\longmapsto I=\dfrac{24000(2.5)}{100}[/tex]
[tex]\\ \sf\longmapsto I=\dfrac{60000}{100}[/tex]
[tex]\\ \sf\longmapsto I=600[/tex]
[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{S.I \: = \: \frac{P × R × T}{100} }}}}}\end{gathered} [/tex]
Basic TermsSimple Interest - Simple interest is the method of calculating interest charged on the amount invested in a fixed deposit.Principle - The principal is the amount due on any debt before interest, or the amount invested before returns.Rate - An interest rate is the percentage of principal charged by the lender for the use of its money.Time = Time is duration (in months or years) in Simple Interest.SolutionAs we know that , first we need to convert 2 years 6 months into years.
[tex] \sf \ \implies \: 1 \: \: year \: = \: 12 \: \: months[/tex]
[tex] \sf \implies \: 2 \: \: years \: \: and \: \: 6 \: \: months \: = \: 30 \: \:months[/tex]
[tex] \sf \implies \: \:\frac{ \cancel{30} \: \: ^{2.5 \: \: years} }{ \cancel{12 \: }} \\ [/tex]
[tex]\bf{\blue{ Time \: = \: 2.5 \: \: years}}[/tex]
Now , we have to find the Simple interest.[tex]\Large\rm{\orange{ \begin{cases} \large\begin{gathered} {\underline{\boxed{ \rm {\purple{S.I \: = \: \frac{P × R × T}{100} }}}}}\end{gathered} \end{cases}}}[/tex]
Substuting the values[tex] \tt \large \longrightarrow \: \: S.I \: = \: \frac{2000 \: × \: 12 × \: 2.5}{100} \\ [/tex]
[tex] \tt \large \longrightarrow \: \: S.I \: = \frac{60000}{100} \\ [/tex]
[tex]\tt \large \longrightarrow \: \: S.I \: = \frac{600 \cancel0 \cancel0}{1 \cancel0 \cancel0} \\ [/tex]
[tex]\tt \large \longrightarrow \: \: S.I \: = \: 600[/tex]
[tex]\large \underbrace{\textrm {{{\color{navy}{Simple Interest \: = \: 600}}}}}[/tex]
What are the solutions to the equation?
x3 – 6x2 – 9x + 54 = 0
Answer:
x = -3 or x = 3 or x = 6
Step-by-step explanation:
x3 – 6x2 – 9x + 54 = 0
There is no common factor to factor out. There are 4 terms. We try factoring by grouping. Factor a common factor out of the first two terms. Factor a common factor out of the last two terms.
x^2(x - 6) - 9(x - 6) = 0
x - 6 is a common factor, so we factor it out.
(x^2 - 9)(x - 6) = 0
x^2 - 9 is the difference of 2 squares, so we factor it.
(x + 3)(x - 3)(x - 6) = 0
x + 3 = 0 or x - 3 = 0 or x - 6 = 0
x = -3 or x = 3 or x = 6
Answer:
x=6 x=3 x=-3
Step-by-step explanation:
x^3 – 6x^2 – 9x + 54 = 0
Factor by grouping
x^3 – 6x^2 – 9x + 54 = 0
x^2(x-6) -9(x-6 ) =0
Factor out x-6
(x-6)(x^2 -9) =0
Notice x^2 -9 is the difference of squares
(x-6)(x-3)(x+3) = 0
Using the zero product property
x-6 =0 x-3 =0 x+3 =0
x=6 x=3 x=-3
What is the difference between the temperature - 7 Celsius and - 12 Celsius on a scatter diagram
Answer:
I have to go get my car from the doctor office today
What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?
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Answer:
opposite: 4.88adjacent: 14.18Step-by-step explanation:
SOH CAH TOA is a mnemonic intended to remind you of the relevant trig relations.
Sin = Opposite/Hypotenuse ⇒ opposite = 15×sin(19°) ≈ 4.88 units
Cos = Adjacent/Hypotenuse ⇒ adjacent = 15×cos(19°) ≈ 14.18 units
Answer:
For plato users the correct option is D.
Step-by-step explanation:
D. 4.9 units, 14.2 units
Identify the pattern in the list of numbers. Then use this pattern to find the next number.
2,4,6,10,16,26,___
Answer:
42
Step-by-step explanation:
2,4,6,10,16,26,___
The pattern is adding the previous two numbers to get the next number
2+4 = 6
4+6 = 10
6+10 = 16
10+16 = 26
16+26 =42
without drawing the graph, find the coordinates of its intersection with the x and y axes.
y=-5x+2
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Answer:
(0, 2), (2/5, 0)
Step-by-step explanation:
In this slope-intercept form, the y-intercept is the constant in the equation: 2. That is the point of intersection on the y-axis is (0, 2).
__
When y=0, the value of x is the x-intercept.
0 = -5x +2
5x = 2 . . . . . . add 5x
x = 2/5 . . . . . divide by 5
The point of intersection of the graph with the x-axis is (2/5, 0).
Which sets of values belong to the domain and range of a relation?
Answer:
Domain: input values, independent variables
Range: output vales, dependent variables
Step-by-step explanation:
Think of it like a graph: the domain are the x-values and the range is the y-values. if you're doing a problem with time, the time will go on the x-axis and cannot be influenced by the y-values, but the y-vales are depending on what the x-values are (independent/dependent). for the input/output, usually when solving equations on a graph, you plug in the x-value and find the y-value. you're INPUTTING the x-value to receive the OUPUT.
Domain = set of allowed inputs
The input x is the independent variable as it can do whatever it wants without relying on y.
-------------------------
Range = set of possible outputs
The output is the dependent variable. It depends on what the input x is. Often, we make y the output dependent variable.
-------------------------
For example, with y = 2x+5, we can plug in anything we want for x (it doesn't need to look to y for guidance or anything). Once we pick something for x, it will directly determine what y is.
Let's say we picked x = 10. That would mean y = 2x+5 = 2*10+5 = 25. The input x = 10 in the domain leads to y = 25 in the range. We see that the output y = 25 depends entirely on the independent input x = 10.
If the mean, median, and mode are all the same for 4, 9, 7, 8, and x, what is the value of x?
===========================================================
Explanation:
Since we have an odd number of values, this tells us that the median is part of the data set. It's the middle most item after we sort the values.
Recall that the mode is the most frequent item. Since the mode and median are the same, this must mean x can only be equal to one of the following
4, 9, 7 or 8
We can only pick one of those values.
----------------------
If x = 4, then the set {4,9,7,8,x} updates to {4,9,7,8,4} which sorts to {4,4,7,8,9}
The middle most item is in slot 3, which would be 7. So the median is 7.
The median 7 does not match with the mode 4.
So we cross x = 4 off the list.
-----------------------
If x = 7, then we have {4,7,7,8,9}
The mode is 7 and the median is 7. So far, so good.
Now let's compute the mean. Add up the values and divide by 5 because there are 5 items.
(4+7+7+8+9)/5 = 35/5 = 7
We've shown that the set {4,7,7,8,9} has mean 7.
Overall, that set has the same mean, median and mode. So the answer is confirmed.
I'll let you check the cases when x = 8 and x = 9.
HELP ME WITH THIS MATHS QUESTION
IMAGE IS ATTACHED
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Answer:
see attached
Step-by-step explanation:
Each point moves to the same distance on the other side of the mirror line. The slope of the mirror line is 1, so the points move along a line perpendicular to that, one with a slope of -1. You can make sure the distances are the same by counting the grid squares.
The lengths of two sides of the right triangle ABC shown in the illustration given
b= 8ft and c= 17ft
Answer:9oooooooooooooooooooooooooooooooooooo
Step-by-step explanation:
What is
the solution to the system of equations graphed below?
Evaluating linear piecewise functions
What is 10 + 15k equivalent
Plz hurry
Answer:
if you mean 15k as is 15 thousand then the answer would be 15,010
If the integer $152AB1$ is a perfect square, what is the sum of the digits of its square root?
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Answer:
13
Step-by-step explanation:
152AB1 is not a square in hexadecimal, so we assume A and B are supposed to represent single digits in decimal.
If A=B=0, √152001 ≈ 389.9
If A=B=9, √152991 ≈ 391.1
The least significant digit of 152AB1 being non-zero, we know it is not the square of 390. Hence, it must be the square of 391.
For 152AB1 to be a perfect square, we must have ...
152AB1 = 391² = 152881
The sum of the digits of the square root is 3+9+1 = 13.
SOMEONE HELP PLEASE ASAP!!! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
cto cto cto cto cto cto cto cto cto cto
Đối tượng của kế toán là:
Answer:
Đối tượng kế toán là sự hình thành và biến động của tài sản mà kế toán phải phản ánh và giám đốc trong quá trình hoạt động của đơn vị được thể hiện ở hai mặt là Tài sản và Nguồn vốn. Tài sản của đơn vị; Sự vận động của tài sản.
Perform the following series of rigid transformations on ∆ABC: Translate ∆ABC by moving it 5 units to the right and 2 units up. Draw the line y = -x, and reflect ∆A'B'C' across the line. Rotate ∆A''B''C'' counterclockwise about the origin by 270°.
Answer:
The answer is below
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is translated a units right and b units up, the new point is at A'(x + a, y + b).
If a point A(x, y) is reflected across the line y = -x, the new point is at A'(-y, -x).
If a point A(x, y) is rotated counterclockwise by 270 degrees, the new point is at A'(y, -x).
Let us assume that triangle ABC has vertices at A(-6, -1), B(-3, -3) and C(-1, -2).
If it is moved 5 units to the right and 2 units up, the new point is at A'(-1, 1), B'(1, -1) and C'(3, 0). If it is reflected across the line y = -x, the vertices are at A"(-1, 1), B"(1, -1) and C"(0, -3). If it is then rotated counterclockwise about the origin by 270°, the new point is at A'"(-1, -1), B"'(1, 1), C"'(3, 0)
Solve 2x2 - 9x - 5 = 0 by factoring.
AS IN THE PICTURE...........
What is the distance between U(-1,9) and V(4,7)leave answer in radical form
Answer:
[tex]d=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\\\=\sqrt{(4-(-1))^{2}+(7-9)^{2} } \\\\=\sqrt{(5)^{2}+(-2)^{2}} \\\\=\sqrt{25+4} \\\\=\sqrt{29}[/tex]
Jessica always uses the same ratio of green beads to blue beads when she makes necklaces. The graph shows these equivalent ratios.
Which table shows the same data?
3|3x+4|-7=5 please help
Answer:
[tex]x = 0[/tex]
Step-by-step explanation:
[tex]3 |3x + 4| - 7 = 5[/tex]
Add 7[tex]3 |3x + 4 | = 12[/tex]
Divide by 3.[tex] |3x + 4| = 4[/tex]
Remove the absolute value signs and left with:[tex]3x + 4 = 4[/tex]
Subtract[tex]3x = 0[/tex]
[tex]x = 0[/tex]
Henry wants to buy a new table saw for his carpentry shop. he saved $360 which is 2/3 of the price of the saw.how much does the table saw cost?
Answer:
Step-by-step explana
540
A linear regression equation and multiple linear regression equations can be used to calculate y if one is given the x values. However, a logistic regression equation cannot be used to calculate y when one is given x value.
a. True
b. False
Answer:
FALSE
Step-by-step explanation:
First, define y and x.
In statistics, we have what we call variables. Variables are items or symbols that can take on various values. We have dependent variables - whose values are derived from other variables in an equation - and independent variables - whose values are given and are used to determine the values of dependent variables.
Usually, y represents the dependent variable while x represents the independent variable. So the simplest form of regression equation is
y = f (x)
Said as "y is a function of x"
A logistic regression equation can be used to calculate y when x values are given.
Here, the independent variable function (the X function) is a logistic function and it is used to find a binary dependent variable (a Y value, out of two possible values).
In logistic regression equations, the value of Y is not numerical like 1, 0.2, 3/4, and so on. It is categorical, e.g.
Black/White, Gain/Lose, Pass/Fail, Eat/Drink, etc.
Need help due tomorrow
Answer:
[tex]Given:[/tex] Δ ABC ≈ ΔDEF
[tex]therefor:[/tex] A(ΔABC)/A(ΔDEF)=(BC)²/(EF)²
⇒ 34/A(ΔDEF)=9²/(13.5)²
⇒34/A(ΔDEF)=81/182.25
⇒A(ΔDEF)=34×182.25/81
⇒Area of ΔDEF=76.5 cm²
----------------------------------
Hope it helps...
Have a great day!!!
2 angles in a triangle are 82 and 76. What is the measure of the 3rd angle.
A. 38
B. 22
C. 82
D. 76
Answer:
22
Step-by-step explanation:
The sum of the angles in a triangle are 180
Let the third angle be x
82+76+x = 180
158 +x = 180
x = 180-158
x =22
Now keep the,
Third unknown angle as y.
The formula we use,
→ Sum of all angles of triangle = 180°
Let's solve for y,
→ y + 82 + 76 = 180°
→ y + 158 = 180°
→ y = 180 - 158
→ [y = 22°]
Thus, option (B) is the answer.
Class A has 9 pupils and class B has 24 pupils.
Both classes sit the same maths test.
The mean score for class A is 40.
The mean score for class B is 20.
What is the mean score (rounded to 2 DP) in the maths test across both classes?
Answer:
mean ≈ 25.45
Step-by-step explanation:
mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
We require the sum for both classes
class A
mean = [tex]\frac{sum}{9}[/tex] = 40 ( multiply both sides by 9 )
sum = 9 × 40 = 360
class B
mean = [tex]\frac{sum}{24}[/tex] = 20 ( multiply both sides by 24
sum = 24 × 20 = 480
Total sum for both classes = 360 + 480 = 840 , then mean for both classes is
mean = [tex]\frac{840}{33}[/tex] ≈ 25.45 ( to 2 dec. places )
Out of 100 people sampled, 42 had kids. Based on this, construct a 99% confidence interval for the true population proportion of people with kids. Give your answers as decimals, to three places.
Answer:
The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Out of 100 people sampled, 42 had kids.
This means that [tex]n = 100, \pi = \frac{42}{100} = 0.42[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.293[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 + 2.575\sqrt{\frac{0.42*0.58}{100}} = 0.547[/tex]
The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).
These 2 questions confuse me.
Can anyone help with some 3D trigonometry?
Answer:
Q2) 29 degree as unrounded to nearest degree is 28.95 degree
Q3) 69 degree as unrounded to nearest degree is 68.56 degree
Step-by-step explanation:
QU 2)
When they speak of plane we see ABCD and also see ABC
So we need the length of AB and BC to find the diagonal CA
AB^2 + BC^2 = CA^2
16.4^2 + 9.1^2 = sqrt 351.77
CA^2 = sqrt 351.77 = 18.8 cm
We know CG = 10.4cm
We identify the hypotenuse for ACG triangle
We do trig tan x = opp/adj for CGA angle
Tan x = tan-1 10.4/18.8 = 28.95099521 degree
Tan x = tan-1 18.8/10.4 = 61.04900479 degree
so we know one is much smaller than the other
We also know ACG angle is 90 degree and that angle from ABCD that meets line AG is the smaller angle.
Answer therefore must be 28.95 degree = or 29 degree
QU 3)
we are basically looking for angle where VB meets BC line or AVB meets ABC we have the slant length, so step 1 is find the height by first dividing square base by 2 then finding the height.
= 7.6/2 = 3.8 cm
Then Pythagoras
BV^2 - 1/2 BC = height
10.4^2 - 3.8^2 = height
Height = sq rt 93.72 =9.68090905 = 9.7cm
Which means V to midpoint VC = V to midpoint AB
They are the same and the midpoints are 90 degree angles.
To find the required angle for VB + BCmidpoint or we wont be able to determine the right angle hypotenuse.
We do the same as last question determine the hypotenuse and where the angle sought is is where we use the trig function = adj/hyp
Because if it was the midpoint angle then it would be opp/adj like the question 1 so this time its cos of x.
cos x = adj/hyp = cos-1 (3.8/ 10.4) = 68.5687455
Answer is 68.56 degree
The reason we show the height is so we can check by doing opp/hyp
= sin of x = sin-1 (9.68090905/3.8) = 23.11171135
and 90 -23.11171135 = 66.8882887
= 67 degree
So we go with the first one and assume 9.68 was already simplified to 9.7cm
= sin-1 (3.8/9.7) = 23 degree 90-23 = 67 degree
but when rounded to 10.4cm for slant we get the same
= sin-1 (3.8/10.4)
So we realise here trig functions -1 doesn't work on the same 90 degree angle for both lines that meet such 90 degree angle.
We try the sin-1 (10.4/ 9.68090905) = 68.5687455 = 69 degree
and that where the lines join away from the 90 degree angle we can always find true answer, and see it is a match with the first cos trig function we did.
This proves that cos line 1/line2 = sin line 1/line 2 are the same when the larger number is numerator for sin representing the hypotenuse slant for sin as shown and when the larger of the sides is numerator for cos di
and smallest side acts as denominator for both trig functions.
In the diagram attached, ΔABC has coordinates A(1,1), B(4,1), and C(4,5).
Given the function rule
f(x, y) → (x − 5, −y − 2)
Describe the transformation as completely as possible.
The diagram is attached-- Thanks in advance!
(No this is not homework, I was using a study guide I found online to study for a test.)
Answer:
Step-by-step explanation:
ΔABC has the vertices as A(1, 1), B(4, 1) and C(4, 5).
Rule for the transformation has been given as,
f(x, y) → (x - 5, -y - 2)
By this rule vertices of the transformed image will be,
A(1, 1) → A'(1 - 5, -1 - 2)
→ A'(-4, -3)
B(4, 1) → B'(4 - 5, -1 - 2)
→ B'(-1, -3)
C(4, 5) → C'(4 - 5, -5 - 2)
→ C'(-1, -7)
The probability I take a nap today is 4/5. The probability I will take a nap and a bubble bath today
is 1/5. What is the probability I will take a bubble bath today, given that I took a nap?
Use Bayes Theorem to compute that probability. I will denote bath as [tex]B[/tex] and nap as [tex]N[/tex], the probability will be denoted as [tex]P(B)[/tex] or [tex]P(N)[/tex].
By Bayes Theorem
[tex]P(B\mid N)=\frac{P(N\mid B)\cdot P(B)}{P(N)}[/tex]
Which reads,
"What is the probability of [tex]B[/tex] given [tex]N[/tex]".
We know that [tex]P(N\mid B)[/tex] is 1 because we already took a bath. So the formula simplifies to,
[tex]P(B\mid N)=\frac{P(B)}{P(N)}[/tex]
Now insert the data,
[tex]P(B\mid N)=\frac{1/5}{4/5}=\boxed{\frac{1}{4}}[/tex]
So the probability that you will take a bath is [tex]0.25[/tex] after you have taken a nap.
Hope this helps. :)
Suppose $1,000 was deposited into an account compounded quarterly that grew to $1,490 at rate of 6%. How long did it take for this to occur?
Answer:
A (1 + i)^n = 1490 time for amount to reach 1490
(1 + i)^n = 1.49 since A = $1000
n log (1 + .06/4) = log 1.49 take log of both sides at 1.5% per quarter
n = log (1.49) / log 1.015 = 26.78 periods or 6.695 years
(compare to 6.843 years compounded annually)
[tex]t = ln(A/P) / n[ln(1 + r/n)]\\t = ln(1,490.00/1,000.00) / ( 4 * [ln(1 + 0.06/4)] )\\t = ln(1,490.00/1,000.00) / ( 4 * [ln(1 + 0.015)] )\\t = 6.7 years[/tex]
It would take around 6 years 8 months to get $1,490 from $1,000 at 6%.
I hope I've helped! :)
