Money with Nathan in his savings account = $40
Rate of interest per annum = 5%
We know that :
[tex]\color{hotpink}\tt \: simple \: interest \color{plum}= \frac{principal \times rate \times time}{100} [/tex]
In this case :
Principal = $40
Rate = 5%
Time = 1 year
Simple interest he will earn in 1 year :
[tex] =\tt \frac{40 \times 5 \times 1}{100} [/tex]
[tex] = \tt \frac{200}{100} [/tex]
[tex]\color{plum} =\tt\$ \: 2[/tex]
Amount = Principal + Interest
Amount Nathan has to pay at the end of one year :
[tex] = \tt40 + 2[/tex]
[tex]\color{plum} =\tt \$42[/tex]
Thus, at the end of 1 year Nathan has to pay $42.
Therefore, simple interest Nathan will earn in 1 year = $2
find the sample standard deviation
Answer:
Step 1: Calculate the mean of the data—this is xˉx, with, \bar, on top in the formula.
Step 2: Subtract the mean from each data point. ...
Step 3: Square each deviation to make it positive.
Step 4: Add the squared deviations together.
Step 5: Divide the sum by one less than the number of data points in the sample.
Step-by-step explanation:
X-4/x-3 is less than 2x-1/2
Answer:
yes
Step-by-step explanation:
yes
2. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, (iii) BD and (iv) AC.
Answer:
The answer is below.
Step-by-step explanation:
A square is a quadrilateral (has four sides and four angles) in which all the sides are equal. Also all the angle of a square are equal and measure 90°. The diagonals of a square are equal.
In square ABCD:
AB = BC = CD = AC
Given that P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b.
a) In triangle ABP:
BC = AB (all sides of a triangle are equal)
BP = 1/2 (BC) = 1/2(AB) = 0.5AB
Using Pythagoras theorem:
AB² + BP² = AP²
substituting:
AB² + (0.5AB)² = a²
AB² + 0.25AB² = a²
1.25AB² = a²
AB² = a² / 1.25
AB² = 0.8a²
AB = √(0.8a²)
AB = a√0.8
b) In triangle ADQ:
AD = CD (all sides of a triangle are equal)
DQ = 1/2 (CD) = 1/2(AD) = 0.5AD
Using Pythagoras theorem:
AD² + DQ² = AQ²
substituting:
AD² + (0.5AD)² = b²
AD² + 0.25AD² = b²
1.25AD² = b²
AD² = b² / 1.25
AD² = 0.8b²
AD = √(0.8b²)
AD = b√0.8
c) In triangle ABD, Using Pythagoras theorem:
AB² + AD² = BD²
Substituting:
0.8a² + 0.8b² = BD²
But AB = AD (all sides of a triangle are equal). Hence AB = AD = 0.8a² = 0.8b²
BD = √(0.8a² + 0.8b²)
BD = √(1.6a²) 0.8a² = 0.8b²
BD = a√1.6
D) AC = AD (diagonal are equal)
AC = √(0.8a² + 0.8b²)
AC = √(1.6b²) 0.8a² = 0.8b²
AC = b√1.6
Which of the following is an example of an irrational number? Question 5 options: A) 3∕4 B) C) D) 74∕99
Answer:
happy to help, but c and d are not included in your question
helppp!! For the given solid figure, find the value of the variable.
9514 1404 393
Answer:
10 cm
Step-by-step explanation:
The diameter of the cylinder is 6 cm, so the length designated 'c' is the hypotenuse of a right triangle with legs 6 cm and 8 cm.
The Pythagorean theorem tells you the hypotenuse is ...
c^2 = (6 cm)^2 + (8 cm)^2 = 100 cm^2
c = √(100 cm^2) = 10 cm
The value of c is 10 cm.
_____
You may recognize these numbers as double those of a 3-4-5 right triangle.
A submarine was situated 832 feet below sea level. If it descends 289 feet, what is its new position?
It's new position is 1121 feet below sea level.
(In this problem u are descending into a negative value so it made sense for me to add for some reason).
Hope this helps and have a good day.
Also, as proof I included my calculator showing the logic behind it. Sorry for bad Camera quality.
-R3TR0 Z3R0
the equations are
A. y=5/3 x -5
B. y=3/5 x -5
C. y=5/3 x +5
D. y=3/5 x +5
Answer:
A
Step-by-step explanation:
Lester's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 100 espressos in all, 40% of which were single-shot. How many single-shot espressos did the cafe sell?
Answer:
The cafe sold 40 single shot espressos.
Step-by-step explanation:
A nature center has a fish tank in the shape of a rectangular prism. The tank is 10 feet long, 8 ¼ feet wide, and 6 feet tall. The nature center's caretaker filled 80% of the tank with water. What was the volume of the water in the tank, in cubic feet?
Answer:
Do you know theh answer??
Step-by-step explanation:
Answer:
Step-by-step explanation:
The answer is...
Find the surface area of this rectangular prism: Don't forget to show the unit of measure.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as the attachment of the prism is not given.
From the attachment:
[tex]L =10cm[/tex] -- Length
[tex]W = 4cm[/tex] -- Width
[tex]H=5cm[/tex] -- Height
Required
Determine the volume
So, the volume is:
[tex]Volume = Length * Width (* Height[/tex]
[tex]Volume = 10cm * 4cm * 5cm[/tex]
[tex]Volume = 200cm^3[/tex]
Draw the proble. give me steps. Please
Answer:
I cant draw 4 u sry
Answer:
A. c = 3.5h + 15
Step-by-step explanation:
I can't exactly draw the problem BUT I can still help.
C represents the cost altogether but we do not know how much the total cost would be.
So we're paying $15 as a fee, no more from that.
Next, there's another fee that costs $3.50 per hour but since we wouldn't know how long we would use the kayak, hours would represent h.
Now, c = 3.5h + 15.
(In other words, the cost to rent a kayak would be $3.5 PLUS the additonal 15 one time cost.)
MNOP is a trapezoid with bases MN and OP. If MN = 25 and OP = 23, what is the length of the midsegment of MNOP?
Answer:
24
Step-by-step explanation:
you can get the answer from the attachment
The midsegment of a trapezoid divides the trapezoid into equal parts.
The length of the midsegment of MNOP is 24
The lengths of the base are given as:
[tex]\mathbf{MN = 25}[/tex]
[tex]\mathbf{OP = 23}[/tex]
Let the midsegment be x.
So, we have:
[tex]\mathbf{x=\frac{1}{2}(MN + OP)}[/tex]
Substitute values for MN and OP
[tex]\mathbf{x=\frac{1}{2}(25 + 23)}[/tex]
[tex]\mathbf{x=\frac{1}{2}(48)}[/tex]
[tex]\mathbf{x=24}[/tex]
Hence, the midsegment of MNOP is 24
Read more about midsegments of trapezoids at:
https://brainly.com/question/7511906
the EXACT value of 2÷(0.01)2 is
The EXACT value of 2÷(0.01)2 is 100.
The question asks that we divide 2 by (0.01)2. Division is a basic mathematical operation. The expression in the question can be rewritten as [tex]\frac{2}{(0.01)2}[/tex].
The first step to take in order to determine the answer is to simplify the denominator. Bracket means to multiply. So, 0.01 would be multiplied by 2. 0.01 x 2 = 0.02. Now that the denominator has been simplified, divide the numerator by the denominator.
2 / 0.02 = 100
A similar question was answered here: https://brainly.com/question/22357901
The EXACT value of 2÷(0.01)2 is 100.
The question asks that we divide 2 by (0.01)2.
Division is a basic mathematical operation.
The expression in the question can be rewritten as : 2/ (0.01)2
now, we get,
The first step to take in order to determine the answer is to simplify the denominator.
Bracket means to multiply.
So, 0.01 would be multiplied by 2.
i.e. 0.01 x 2 = 0.02.
Now that the denominator has been simplified, divide the numerator by the denominator.
we get,
2 / 0.02 = 100
Learn more about the Division here:
brainly.com/question/22357901
#SPJ6
Jonas is buying fencing to surround his garden. If his garden has a perimeter of 36 feet, and fencing costs
$10.00 a yard, how much money will he need for the fencing?
Answer:
Step-by-step explanation:
$120
-8m – 6(1 - 4m) = -102
Answer:
Step-by-step explanation:
Here you go mate
Step 1
-8m – 6(1 - 4m) = -102 Question
Step 2
-8m – 6(1 - 4m) = -102 Remove parenthesis
16m-6=-102
Step 3
16m-6=-102 add 6 to sides
16m=-96
Step 4
16m=-96 Divide sides by 16
Answer
m=-6
Hope this helped
Answer:
Step-by-step explanation:
I can help
Step 1
-8m – 6(1 - 4m) = -102 Simplify
Step 2
-8m – 6(1 - 4m) = -102 Add 6 to the sides
16m=−96
Step 3
16m=−96 Divide the sides by 16
Answer
m=-6
Hope this helps
Find GK pls help with this problem
Answer:
Step-by-step explanation:
IH:GH = 45:30 = 3:2
JK:GK = 36:GK = 3:2
GK = 24
What is the ratio of a:b, knowing that a-b/a+b = 3/5.
Answer:
4:1
Step-by-step explanation:
[tex]\frac{a-b}{a+b}[/tex] = [tex]\frac{3}{5}[/tex]
4-1 = 3
4+1 = 5
Ana has won a lottery. She was offered two options to receive the award: She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now. Assuming (a) interest at an annual rate of 5% compounded annually, or (b) interest at an annual rate of 6% compounded continuously, which option should she choose under the consideration of cash value only?
A) If the interest is at the annual rate of 5%, compounded annually, then the present value of the five installments is $______. B) If the interest is at the annual rate of 6%, compounded continuously, then the present value of the five installments is $______.
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
She can either take it in five installments of $60,000 annually, starting from now; or she can take a lump-sum of $255,000 now.
First, we determine the value of the 5 installments using a 5% annual compounded rate.
We calculate the future value, and then the present value:
FV= {A*[(1+i)^n-1]}/i
A= annual payments
FV= {60,000*[(1.05^5) - 1]} / 0.05
FV= $331.537.88
PV= FV/(1+i)^n
PV= $259,768.60
At an annual rate of 5% compounded annually, she should choose the five installments instead of the $255,000.
Now, if the annual rate is 6% continuously compounded.
First, we need to calculate the effective interest rate:
r= e^i - 1
r= effective inerest rate
r= e^0.06 - 1
r= 0.0618
FV= {60,000*[(1.0618^5) - 1]} / 0.0618
FV= 339,443.23
PV= 339,443.23/1.0618^5
PV= $251,509.01
At an annual rate of 6% compounded continuously, she should choose the $255,000.
The enrollment of students in evening classes at a local university decreased by 6% between two recent years. If the total number of students attending evening classes in both years was 13,925 , find how many students enrolled in evening classes in each of the years.
Answer:
First year: 13925; Second year: 13090
I need help with this
look at picture
Complementary angles
Answer:
77
Step-by-step explanation:
48 + (x-35) = 90
x-35 = 90-48
x-35 = 42
x = 42+35
x = 77
Select the algebraic expression for the word expression.
24 less than h
24 - h
24 - h
h - 24
h - 24
24 ÷ h
24 ÷ h
h
Step-by-step explanation:
The Answer Is 24 - h
As, 24 Is Less Than "h"
Help me plssssssssssss
Answer:
6
Step-by-step explanation:
6 is the answer
Please show work so i know how you got your answer..thank you and have a nice day<3
Answer:
V=whl=2·2.5·4=20
Step-by-step explanation:
Answer:
2880 feet³
Step-by-step explanation:
since the question is asking for cubic feet we know we're finding volume.
v=l·w·b
v=4·24·30
=2880
6(x - 1) = 6x - 1
what’s the answer ^^
Answer:
this is an identity which is true for all x values
Step-by-step explanation:
Perform the indicated multiplication. We get:
6x - 1 = 6x -1
and see that this is an identity which is true for all x values.
Please help I need this answer!
Answer: 16
Step-by-step explanation: Good luck! :D
Answer:
It’s 16
Good luck
I honestly lost most of my brain cells Bc of quarantine so I’m glad I figured this out
What is the common ratio of 7, -14, 28, -56
Answer:
multiplied by -2 I believe
Step-by-step explanation:
Find the measure of each missing angle.
9514 1404 393
Answer:
35°145°55°125°55°Step-by-step explanation:
The right triangles are similar, so angle 1 is congruent to the given angle, and angles 3 and 5 are complements of that.
Angles 2 and 4 are the supplements of angles 1 and 5, respectively.
∠1 = 35°
∠2 = 180° -35° = 145°
∠3 = ∠5 = 90° -35° = 55°
∠4 = 180° -55° = 125°
HELP ASAP PLEASE! GIVING AWAY 30 POINTS AND BRAINLIEST!
Answer:
DB!
Step-by-step explanation:
Question a: 3+3+2+2 = 10 dinners
Question b: 15-30 and 30-45, because most people choose that range.
Hope I helped!
Answer:
a) 10 b) 2-3 dollars
Step-by-step explanation:
a) 3+3+2+2
b) (2+2+3+3)/2 equal 2.5 mean, range between them is 2 to 3
please help and explain , HURRY PLEASE !
WILL GIVE BRAINLIEST GIVE CORRECT ANSWER
Answer:
everything u chose is right
Step-by-step explanation:
50 = 20 + 4h
-20. -20
30/4= 4h/4
7.5 = h
So 50 = 20 + 4(7.5)
50 = 30 + 20
50 = 50