[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$20953.80\\ P=\textit{original amount deposited}\dotfill & \$18000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &6 \end{cases} \\\\\\ 20953.80=18000[1+(\frac{r}{100})(6)]\implies \cfrac{20953.80}{18000}=1+\cfrac{6r}{100}[/tex]
[tex]\cfrac{20953.80}{18000}=\cfrac{100+6r}{100}\implies \cfrac{2095380}{18000}=100+6r\implies \cfrac{11641}{100}=100+6r \\\\\\ \cfrac{11641}{100}-100=6r\implies \cfrac{1641}{100}=6r\implies \cfrac{1641}{600}=r \\\\\\ \cfrac{547}{200}=r\implies \stackrel{\%}{2.735} = r[/tex]
The amount of Jake’s paycheck is directly proportional to the hours he works. After working 23 hours, his paycheck was $180.55. Determine the number of hours Jake needs to work to receive a paycheck of $290.45.
Answer:
35 hours
Step-by-step explanation:
What is the area of the beach ball with a diameter of 14 in. ?
Answer:
The answer is 675.75 square Inches
Step-by-step explanation:
Given;Diameter (d) = 14 in.To Find;Area of beach ball = ?Formula;Area = 4πr²Now,
Radius (r) = diameter ÷ 2
r = 14/2 in.
r = 7 in.
Now,
A = 4πr²
A = 4 × 22/7 × (7)² in.
A = 4 × 22 × 7 in.
A = 615.75 square in.
Thus, The area of the beach ball with a diameter of 14 in. is 615.75 square in.
Answer:
615.8 in²
Step-by-step explanation:
The area of a sphere is given by the formula ...
A = 4πr² . . . . . sphere of radius r
In terms of diameter, the area is ...
A = 4π(d/2)² = πd²
__
For a diameter of 14 inches, the area of the beach ball is ...
A = π(14 in)² = 196π in² ≈ 615.8 in²
The area of the ball is about 615.8 square inches.
Bob shoots off a small rocket from the balcony of his apartment. The balcony is 30 ft above the ground and the rocket travels at 40 ft/second. When does it reach the highest point? What is the highest point? When does it hit the ground (seconds)?
From the calculations;
The highest point above the ground is 112 feetThe time taken to reach this height is 8 secondsEquations of motionThe equations of motion are used in kinematics to obtain the various variables that has to do with motion.
In this case;
distance covered = 30 ft
initial velocity = 40 ft/second
Final velocity = 0 m/s at the maximum height
Hence;
v^2 = u^2 - 2gh
since v = 0
u^2 = 2gh
h = u^2/2g
h = (40)^2/2(9.8)
h = 82 feet
highest point above the ground = 82 feet + 30 feet = 112 feet
Now;
v = u - gt
since v = 0
u = gt
t = u/g
t = 40/9.8
t = 4 seconds
Time taken to hit the ground = 2(4 seconds) = 8 seconds
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A $70,000 mortgage is $629.81 per month. What was the percent and for how many years?
9%, 20 years
9%, 30 years
7%, 20 years
9%, 25 years
The interest percent and the maturity period of the $70,000 mortgage with a monthly payment of $629.81 are A. 9%, 20 years.
How can the monthly payments be calculated?The monthly payments can be computed using the present value annuity table or formula.
However, to compute the percent interest and the maturity period, we can use an online finance calculator as below by inputting the calculated monthly payments.
Thus, at an interest rate of 9% for 20 years and a monthly payment of $629.81, the present value of $70,000 will be equal.
Data and Calculations;N (# of periods) = 240 (20 years x 12)
I/Y (Interest per year) = 9%
PMT (Periodic Payment) = $629.81
FV (Future Value) = $0
Results:
PV = $70,000.20
Sum of all periodic payments = $151,154.40 ($629.81 x 240)
Total Interest $81,154.20
The interest percent and the maturity period of the $70,000 mortgage with a monthly payment of $629.81 are A. 9%, 20 years.
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HELPPPPPP PLEASE! URGENT
Answer:
x=59 y= 81 z= 99
Step-by-step explanation:
z=
180-(57+24)=99
y=180-99=81
x= 40+81=121
180-121=59
whats 2+7
a. 14
b. 19
c.88383838837
Answer:
9
Step-by-step explanation:
Was this a joke or something
Pythagorean Theorem
(Rounding)
Find the length of the third side. If necessary, round to the nearest tenth.
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER AND POINTS!!!!
IMAGE DOWN BELOW!!
Answer:
19.2 or 19.20
Step-by-step explanation:
Side 25=hypotenuse because it is across from the rightness of the triangleThis means that teh unknown side is a leg, as well as the side that says 16This makes our equation: a²+16²=25²Next we solve16²=256 and 25² is 625 so now our equation is a²+256=625We then subtract 256 from both sides which leaves us with x²=369To find the value of x, we take the square root of both sides. This leaves us with X=19.2What is the volume of this cone? use 3.14 for π and round your answer to the nearest tenth. in your answer, give the volume of the cone rounded to the nearest tenth, and then explain how you calculated it.
Answer:
Volume of a cone = 1/3•pi r•r•h
V = 1/3•pi•2•2•8
V = 33.49333333333333
V = 33.5 inches squared
I hope this helps! Have a good day! :)
The volume of the considered cone whose heigth is 8 inches and radius of the base is 2 inches is 33.5 cubic inches approximately.
How to find volume of a right circular cone?Suppose that the radius of considered right circular cone be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \dfrac{1}{3} \pi r^2 h \: \rm unit^3[/tex]
Right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
The missing image for this problem is attached below.
For this case, the radius is of 2 inches, and height is of 8 inches, thus, the volume of the considered cone is:
[tex]V = \dfrac{1}{3} \pi r^2 h \: \rm unit^3 \approx \dfrac{1}{3} \times 3.14 \times (2)^2 \times 8 \approx 33.51 \approx 33.5 \: \rm in^3[/tex]
(rounded to the nearest tenth, which is first place to right of the decimal point.
Thus, the volume of the considered cone whose heigth is 8 inches and radius of the base is 2 inches is 33.5 cubic inches approximately.
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Which of the objects below best holds 1 quart? A. gas tank pitcher C. coffee mug D. pool
simplify (2^3)^-2
urgent need for answers
Answer:
0.015625Step-by-step explanation:
I would REALLY try to explain, but I can't find any explanation.
If this is my best, give other person brainliest.
Answer:
Exact form would be 1/64
Decimal form would be 0.015625
Step-by-step explanation:
of The marked price of a pair of shoe is Rs480. Shopkepper allow discount 10% on shoe find how much should for the shoes after discount a customer pay.
Answer:
$48.
Step-by-step explanation:
$480-$48
=$432
after the discount
a. translation; four units right and six units down
b. translation; four units left and six units down
c. rotation; 90 degrees
d. reflection; across y=-4
Answer:
b. translation; four units left and six units down
On a TV game show, a contestant makes $700 for every correct answer but loses $400 for every wrong answer. After answering 22 questions, Sarah broke even. How many questions did she answer correctly?
Answer:
She answered 8 of them correctly.
Step-by-step explanation:
help me out please ty!
Answer:
a5 = 2604
Step-by-step explanation:
a1 = 4
a2 = -5(4)-1 = -21
a3 =-5(-21)-1 = 104
a4 = -5(104)-1 =-521
a5 =-5(-521)-1 = 2604
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \tt \dashrightarrow \:a1 = 4[/tex]
Now, let's proceed next till we get[tex] \tt a_5 [/tex]
[tex]\qquad \tt \dashrightarrow \: a_2 = - 4a_{(2 - 1)}+ 5[/tex]
[tex]\qquad \tt \dashrightarrow \: a_2 = - 4a_{1}+ 5[/tex]
[tex]\qquad \tt \dashrightarrow \: a_2 = (- 4 \times 4)_{}+ 5[/tex]
[tex]\qquad \tt \dashrightarrow \: a_2 = - 16_{}+ 5[/tex]
[tex]\qquad \tt \dashrightarrow \: a_2 = - 11[/tex]
Similarly,
[tex]\qquad \tt \dashrightarrow \: a_3 = 49[/tex]
[tex]\qquad \tt \dashrightarrow \: a_4= - 191[/tex]
Now, let's solve for [tex]\tt a_5 [/tex]
[tex]\qquad \tt \dashrightarrow \: a_5= - 4( - 191) + 5[/tex]
[tex]\qquad \tt \dashrightarrow \: a_5= 764 + 5[/tex]
[tex]\qquad \tt \dashrightarrow \: a_5= 769[/tex]
i need answer please
Answer:
Below in bold.
Step-by-step explanation:
Radius of the pizza = 1/2 * 8 = 4 in.
Area of the whole pizza = π r^2
= π * 4^2
= 8 π
So if you take 1/8 away
the area left = 7/8 * 8 * π
= 7π
Taking π to be 22/7:
= 7 * 22/7
= approximately 22 in^2.
Theresa blended 30 lbs of orange pekoe tea worth $6.00 per pound with 70 lbs of green tea worth of $3.20 per pound. what is the cost per pound of the blend?
$4.04 is the answer.
30 x $6.00 = $180
70 x $3.20 = $224
$180 + $224 = $404
404/100 = $4.04
The cost per pound of the blend will be $4.04.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
Theresa blended 30 lbs of orange pekoe tea worth $6.00 per pound with 70 lbs of green tea worth $3.20 per pound.
Then the cost per pound of the blend will be
⇒ 30 x $6.00 + 70 x $3.20
⇒ $180 + $224
⇒ $404
The cost per pound of the blend will be
⇒ $404 / 100
⇒ $4.04
The cost per pound of the blend will be $4.04.
More about the Algebra link is given below.
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Round of to the numbers as indicated:
1. 48521
To nearest 10:
To nearest 100:
To nearest 1000:
1. 674502
To nearest 10:
To nearest 100:
To nearest 1000:
3. 3875
To nearest 10:
To nearest 100:
To nearest 1000:
Answer:
See below.
Step-by-step explanation:
1. 48521
To nearest 10: 48520
To nearest 100: 48500
To nearest 1000: 49000 (8 goes up to 9 becasue of the 5)
1. 674502
To nearest 10: 674500
To nearest 100: 674500
To nearest 1000: 675000
3. 3875
To nearest 10: 3880
To nearest 100: 3900
To nearest 1000: 4000
To nearest 10:
= 48520
To nearest 100:
= 48500
To nearest 1000:
= 49000
1. 674502To nearest 10:
= 674500
To nearest 100:
= 674500
To nearest 1000:
= 676000
3. 3875To nearest 10:
= 3880
To nearest 100:
= 3900
To nearest 1000:
= 4000
(if the number your rounding is higher than 5, round the number up)
If the sample regression equation is found to be yˆ = 10 + 2x, what is the estimated value of Y if x = 5?
The sample regression y = 10 + 2x is a linear regression equation
The estimated value of y if x = 5 is 20
How to estimate the value of y?The sample regression equation is given as:
y = 10 + 2x
When x = 5, the equation becomes
y = 10 + 2 * 5
Evaluate the product
y = 10 + 10
Evaluate the sum
y = 20
Hence, the estimated value of y if x = 5 is 20
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A clothing store sells shirts with long, short, or no sleeves. Each style is available in gray, red, or pink. A clerk incorrectly states the sample space for the possible color and sleeve styles as (gray, long), (gray, short), (red, long), (red, short), (pink, long), and (pink, short). Use a table to show the sample space. What error did the clerk make?
Need asap
A buoy starts at a height of 0 in relation to sea level and then goes up. its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. which of the following equations can be used to model h, the height in feet of the buoy in relation to sea level as a function of time, t, in seconds? h = 4 sine (startfraction pi over 6 endfraction t) h = 4 sine (startfraction pi over 3 endfraction t) h = 6 sine (startfraction pi over 4 endfraction t) h = 6 sine (startfraction pi over 2 endfraction t)
The equation of the model h will be h = 6 × sin(2πt/8). Then the correct option is C.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
A buoy starts at a height of 0 in relation to sea level and then goes up.
Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds.
Then we have
[tex]h=A \times \sin \omega t, \ \ at=0, \ \ h =0[/tex]
The maximum displacement of the buoy in either direction is 6 ft, then we have
[tex]h=6 \times \sin \omega t[/tex]
The time it takes the buoy to get from the lowest to the highest point is 4 seconds then the oscillation time period will be 8 seconds.
Then we have
[tex]\omega T = 2\pi\\\\\omega = \dfrac{2\pi}{8}[/tex]
Then the h will be given as
[tex]h =6\times \sin (\dfrac{2\pi}{8}t)[/tex]
More about the function link is given below.
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pls help me wat is 10 × 3 + 4
Answer:
34
Step-by-step explanation:
10 x 3 = 30
30 + 4 = 34
34 is the answer.
Answer:
10×3+4
=30+4
=34
hope this helps you
What is the length of BD?
A. 53.3 units
B. 30 units
C. 67.5 units
D. There is not enough information to determine the length of BD.
Answer: B
Step-by-step explanation:
Which postulate proves these two
triangles are congruent?
A. SSA
B. HL
C. ASA
D. SAS
Answer:
B
Step-by-step explanation:
Remark
If the Hypotenuse and a corresponding leg in one right triangle = the Hypotenuse and corresponding leg of the second right triangle, then the triangles are congruent.
Answer
HL
Help me please I do not understand this assignment
Answer:
Step-by-step explanation:
Equation: y = 20x
y = # of gallons
x = minutes
6.
So, you substitute (0, 1, 2, 3 and 4 minutes) for x, to find the number of gallons:
x = 0 mins:
y = 20x
y = 20(0)
y = 0 gallons
(0, 0)
x = 1 min.
y = 20x
y = 20(1)
y = 20 gallons
(1, 20)
x = 2 mins.
y = 20x
y = 20(2)
y = 40 gallons
(2, 40)
x = 3 mins.
y = 20x
y = 20(3)
y = 60 gallons
(3, 60)
x = 4 mins.
y = 20x
y = 20(4)
y = 80 gallons
(4, 80)
7. View the attached graph
8. Predict the amount of water in the tank after 6 mins.
We use the same equation, y = 20x for this question
y = 20x
y = 20(6)
y = 120 gallons
(6, 120)
8. Linear ==> straight line
Non-linear ==> anything other than a straight line (curved line)
As you can see from my attached graph, the relationship between x and y and linear, because the graph has a straight line.
Hope this helps!
Khalil is 1.65 meters tall. At 3 p.m., he measures the length of a tree's shadow to be
34.55 meters. He stands 30.4 meters away from the tree, so that the tip of his shadow
meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
1.65 m
30.4 m
34-55 m
Answer:
Step-by-step explanation:
The height of the tree to the nearest hundredth of a meter is 1.875 meters.
Given that:
Khalil is 1.65 meters tall. At 3 p.m., he measures the length of a tree's shadow to be 34.55 meters. He stands 30.4 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow.
Let h be the height of khalil h = 1.65 , H be the tree height , L be the length of the tree's shadow L = 34.55 and l be the length of khalil shadow l = 30.4
Using equivalent ratios of heights:
h : H = l : L
H : 1.65 = 34.55 : 30.4
H/1.65 = 34.55/30.4
H = 34.55/30.4 * 1.65
on solving
H = 1.875 meters which is tree height
Therefore the height of the tree to the nearest hundredth of a meter is 1.875 meters.
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six bags of flour and 4 bags of sugar weighs 64 pounds 8 bags of flour weigh 64. all bags of flour weigh the same and all bags of sugar weigh the same. what is the ratio of one bag of flour to one bag of sugar ?
Answer:
the ratio of one bag of flour is 8
.
The dimensions of a triangle are shown below.
What is the area of the triangle?
Step-by-step explanation:
pls put the image as well becoz the dimensions are not shown
plss help me noww if you can
Answer:
i cant see the picture at all
Step-by-step explanation:
The mean length of 10 childrens' index finger is 12.6cm.
The mean length of 6 adults' index finger is 16.1cm.
What is the mean length (rounded to 2 DP) of these 16 people's index finger?
Get total lengths by multiplying:
10 x 12.6 = 126
6 x 16.1 = 96.6
Add the total lengths together and divide by 16:
126 + 96.6 = 222.6
222.6 / 16 = 13.9125
Rounded to 2 decimal places = 13.91
answer: 13.91
find the exact value of 2sin30 cos30
Answer:
[tex]\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
Let's take a look at the unit circle below.
Remmeber that cos represents the x-value and that sin represents the y-value.
We see that:
[tex]sin(30)= \frac{1}{2}\\\text{and}\\ cos(30) = \frac{\sqrt{3}}{2}[/tex]
Now we just multiply all the together and we get:
[tex]2*\frac{1}{2}*\frac{\sqrt{3}}{2} =\frac{\sqrt{3}}{2}[/tex]
