Answer:
The amount of money after 8 years is $8448.69
Step-by-step explanation:
The rule of the compound interest is
[tex]A=p(1+r)^{t}[/tex] , where
A is the new valueP is the original valuer is the rate in decimalt is the time in years∵ There is $7500 in an account
∴ P = 7500
∵ The account paying 1.5% compound interest
∴ r = 1.5% = 1.5/100 = 0.015
∵ The money will invest for 8 years
∴ t = 8
→ Substitute all of these values in the rule above to find A
∵ [tex]A=7500(1+0.015)^{8}[/tex]
→ Use your calculator to find the answer
∴ A = 8448.69
∴ The amount of money after 8 years is $8448.69
The speed of a tidal wave, s, in hundreds of miles per hour can be modeled by the equation, [tex]s=\sqrt{t} -2t+6[/tex] , where t represents the time from its origin in hours. The graph of the tidal wave is shown.
Using it's concept, it is found that the domain of the function regarding the speed of the tidal wave is explained by:
[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.
What is the domain of a function?It is the set that contains all possible input values for the function. In a graph, it is given by the x-values, that is, the horizontal axis values.
In this graph, the horizontal axis assumes values between 0 and 4, which is the time after the wave, and considering that the wave cannot be less than zero. Hence, the correct option is:
[0, 4]: relating to the time of the tidal wave from it's origin in hours, restricted by the inability for the speed to be lees than zero.
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2. Get the difference between 7 and the sum of 1.0006 and 4.06.
3
Given:
The difference between 7 and the sum of 1.0006 and 4.06.
To find:
The mathematical expression for given statement and it value.
Solution:
Sum of 1.0006 and 4.06 = [tex](1.0006+4.06)[/tex]
The expression for the difference between 7 and the sum of 1.0006 and 4.06 is
[tex]7-(1.0006+4.06)[/tex]
On simplification, we get
[tex]7-(1.0006+4.06)=7-5.0606[/tex]
[tex]7-(1.0006+4.06)=1.9394[/tex]
Therefore, the difference between 7 and the sum of 1.0006 and 4.06 is 1.9394.
For a project in his Geometry class, Elijah uses a mirror on the ground to measure the height of his school building. He walks a distance of 8.25 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0.8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.45 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.
What is trigonometric ratio?Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let Ф represent the angle Elijah makes with the ground, hence:
tanФ = 1.45/0.8
Ф = 61.11°
The angle of elevation to the building is 61.11°. Let h represent the height of the building.
tan(61.11°) = h/8.25
h = 14.95
The school is about 14.95 meters tall, and the mirror is 8.25 meters from the school.
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Martin and Eva pool their loose change to buy snacks on their coffee break. One day, they spent $5.80 on 1 carton of milk, 2 donuts, and 1 cup of coffee. The next day, they spent $6.75 on 3 donuts and 2 cups of coffee. The third day, they bought 1 carton of milk, 1 donut and 2 cups of coffee and spent $6.05. How much is the price of a carton of Milk? (Write only the amount, example, $2.50)
Answer:
250
Step-by-step explanation:
gsv
Determine whether the pair of triangles is congruent.
Choose the correct answer below.
Congruent
Not congruent
Answer:
not congruent
Step-by-step explanation:
congruent is just a fancy way of saying the same in geometry. so to check if its congruent, see if all side lengths correspond to another side length on the other triangle. they do not, so they can't be congruent
hope this helped :)
Use the volume formula to find the volume of the prism.
A. 21 cubic units B. 42 cubic units C. 27 cubic units D. 9 cubic units
Answer:
D Because
Step-by-step explanation:
1/2 +1/2 is 1 so 1+1+3+4 is 9
HOPE THIS HELP! :)
A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 29 feet more
than the length of the shortest side. Find the dimensions if the perimeter is 141 feet.
What is the length of the shortest side?
The length of the shortest side is
(1)
What is the length of the second side?
The length of the second side is
(2)
What is the length of the third side?
The length of the third side is
(3)
Answer:
Step-by-step explanation:
8y8yy89y99u98u89y7t8y7i6u7i9jo
Which of the following is true?
A |−5| < 4
B |−4| < |−5|
C |−5| < |4|
D |−4| < −5
B is true
Step-by-step explanation:
because no number with them to lines can be a negative
A hall is thrown straight up, from 3 m above the ground, with a velocity of 14m/s. When does it hit the ground? Use the vertical motion formula.
In this question, to find the total height first, we must also take into consideration the acceleration due to gravity as well. To find the distance by which acceleration due to gravity pulls the ball down must know the Initial velocity.
In the answer key, it says that gravity changes the ball's height by a distance of -5t^2
Is initial velocity in this question 0 or 14m/s? Because if it is 14, then gravity should change the balls position by -(14+5t^2), not -5t^2, because if I remember correctly, the formula for finding distance is vt(initial velocity)+(1/2)at^2 ,and not just (1/2)at^2
Find the value of xxx, yyy, and zzz in the parallelogram below.
Answer:
Step-by-step explanation:
Opposite angles of a parallelogram are congruent, so:
[tex]112=y-9 \longrightarrow y=121[/tex]
and adjacent angles are supplementary, so:
[tex]112+x+1=112+z+3=180 \longrightarrow x=67, z=65[/tex]
Solve this system of equations algebraically:
y – 10 = 11x + x2
y – 12x = 30
The first solution is (–4, –18).
The second solution is
Answer:
5,90
Step-by-step explanation:
got it correct :)
The second solution for the system of equations is (5, 90).
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given the system of equations,
y - 10 = 11x + x² and
y - 12x = 30
Consider second equation.
y - 12x = 30
⇒ y = 30 + 12x
Substitute y = 30 + 12x in the equation y - 10 = 11x + x², we get,
(30 + 12x) - 10 = 11x + x²
12x + 20 = 11x + x²
12x - 11x - x² + 20 = 0
-x² + x + 20 = 0
x² - x - 20 = 0
Discriminant = [tex]\sqrt{(-1)^{2} -(4*1*-20)}[/tex] = √(1 + 80) = √81 = ±9
x = (1 + 9)/2 and x = (1 - 9) / 2
x = 5 and x = -4
The solution x = -4 and y = -18 is given.
Other solution is,
x = 5
y = 30 + 12x = 30 + 60 = 90
Hence the second solution is (5, 90).
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The mass of a carbon-12 atom is 1.99\times 10^{-23}1.99×10
−23
grams. The mass of a neutron is 1.68\times 10^{-24}1.68×10
−24
grams. How many times greater is the mass of a carbon-12 atom than the mass of a neutron? Write your answer in standard notation, rounding to the nearest tenth.
Answer:
If the mass of one electron is 9.11 x 10-28 g, and you are looking for the mass of a mole of electrons, you need to understand Avogadro's number. One mole is 6.02 x 1023 particles. So you will have to multiply (6.02 x 1023) x (9.11 x 10-28 g) to get your answer of 5.48 x 10-4 grams (answer rounded to significant figures)
Step-by-step explanation:
1.2 x 10¹ times greater is the mass of a carbon-12 atom than the mass of a neutron
What is Division?A division is a process of splitting a specific amount into equal parts.
To find the ratio of the mass of a carbon-12 atom to the mass of a neutron, we can divide the mass of carbon-12 by the mass of a neutron:
(1.99×10⁻²³ grams) / (1.68×10⁻²⁴ grams)
= 11.8 grams
This means the mass of a carbon-12 atom is 11.8 times greater than the mass of a neutron. Written in standard notation and rounded to the nearest tenth, the answer is 1.2 x 10¹
Hence, 1.2 x 10¹ times greater is the mass of a carbon-12 atom than the mass of a neutron
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The ratio of dogs to cats is 6:11. if i have 18 dogs, how many total animals do i have
Answer:
51
Step-by-step explanation:
6 dogs: 11 cats
12 dogs: 22 cats
18 dogs : 33 cats
18 + 33 = 51
Have an amazing day!!
PLEASE RATE!!
Do you know the tricks to multiplying variables?
Answer:
yes I know how to to multiple variables.
You buy cheese in 1lb bags. Your receipt for burritos requires 0.7 ounces of cheese per serving. How many servings can you make
Answer:
Step-by-step explanation:
Each batch of cookies is 8.9 oz. What is the weight of 2.5 batches of cookies
Answer:22.25 oz
Step-by-step explanation:
1 batch of cookies = 8.9 oz
2.5 batches of cookies = x oz
cross multiply
1x=8.9(2.5)
x=22.25 oz
Need help not sure if I got this right???????????
Working together, Bill and Tom painted a fence in 8 hours. Last year, Tom painted the fence by himself. The year before, Bill painted it by himself, but took 12 hours less than Tom took. How long did Bill and Tom take, when each was painting alone?
Answer:
Tom paints the fence in 24 hours and Bill paints the fence in 12
Step-by-step explanation:
T = 1 fence / x hours
B = 1 fence / x - 12 hours
B + T = 1 fence / 8 hours
( 1 fence / x - 12 hours ) + ( 1 fence / x hours ) = 1 fence / 8 hours
( 1 / x - 12 ) + ( 1 / x ) = 1 / 8
multiply through all the denominators to get:
8x + 8 (x - 12 ) = x( x - 12 )
8x + 8x - 96 = x^2 - 12x
combine like terms to get:
x^2 - 28x + 96 = 0
factor to get:
( x - 4 ) ( x - 24 ) = 0
x = 4, 24
4 won't work, because that would mean Bill would take a negative amount of time to paint the fence by himself, so that means
Tom paints the fence in 24 hours and Bill paints the fence in 12
Please help asap! I will gave brainlest!
Answer:
√2 + √6 / 4
Step-by-step explanation:
We know cos(-θ) = cosθ.
Therefore, cos(-15°) = cos15°.
cos15° = cos(45 - 30)
cos15° = cos45cos30 + sin45sin30cos15° = (1/√2)(1/2) + (1/√2)(√3/2)cos15° = 1/2√2 + √3/2√2cos15° = √3 + 1 / 2√2cos15° = (√3 + 1)(√2) / 4cos15° = √2 + √6 / 4Option 1what is the square root of 12?
A triangular pane of glass has a height of 44 inches and an area of 440 square inches. What is the length of the base of the pane?
Answer:
20 inches
Step-by-step explanation:
The base, height, and area of a triangle are related by the formula ...
A = 1/2bh
If you know two of these, you can use this formula to find the third.
440 in² = 1/2b(44 in)
(440 in²)/(22 in) = b = 20 in . . . . . . divide by the coefficient of b
The length of the base is 20 inches.
Please solve this linear algebra equation for 15 points.
Answer:
[6
-1.5]
the six and 1.5 are in the same bracket the 6 in ontop
When Gemma was born, her grandmother invested $200 000 in a building society for her. Find the value of this investment after 18 years if the interest rate is 4% per year and the interest is compounded quarterly.
Answer:
570.87
Step-by-step explanation:
please help me with this
Answer:
y-5=3/4(x-6)
Step-by-step explanation:
The picture you posted is a bit unclear and difficult to look at, but that's alright.
This is a simple question if you understand that the point slope for equation is: y-y1 = m(x-x1).
m is the slope and (x1,y1) is a point on the graph.
So, if you input the point (6,5) on the graph, it works.
You can double check with the other equations to see that they are all wrong!
A triangular prism with 5 faces.
A triangular prism has faces.
Answer:
Pentahedron
Step-by-step explanation:
A triangular prism with 5 faces is called Pentahedron.
It has 5 faces, 6 vertices and 9 edges.
5 faces - Two are triangular faces and three are rectangular faces.
Answer:
its has 5 faces
Step-by-step explanation:
What is the value of the expression?
(7 2/3−4 8/9)+(5 2/3−2 1/2)
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answer:
5 17/18
Step-by-step explanation:
Your calculator can help with this.
__
The integer parts of the mixed numbers can be dealt with separately. The fractional parts are added and subtracted using a common denominator. Here, that denominator is the least common multiple (LCM) of 2, 3, and 9, so is 18.
((7 2/3) -(4 8/9)) +((5 2/3)) -(2 1/2))
= (7 2/3) +(5 2/3) -((4 8/9) +(2 1/2))
= 12 4/3 -(6 +8/9 +1/2)
= 13 6/18 -(6 +16/18 +9/18)
= 13 6/18 -(6 +25/18) = 13 6/18 -(7 7/18)
= (13 -7) +(6/18 -7/18)
= 6 -1/18
= 5 17/18
__
Additional comment
Doing the math in the manner shown above means you can mostly do it without a calculator. If you like, you can convert all of the numbers to improper fractions, then add those. This often requires a calculator.
= (138/18 -88/18) +(102/18 -45/18)
= 50/18 +57/18
= 107/18 = 5 17/18
Question: In the expression: 4x-5+6x-8
a: Identify the third term (options listed)
- (-6x)
- (-5)
- (6x)
- (-8)
b: is it a constant or a variable term?
c: what is the coefficient? (options listed)
- (6)
- (-6)
- (8)
d: simplified (options listed)
- (10x-3)
- (-1x-2)
- (10x-13)
Answer:
a -(-6x)
b variay term
c-(-6)
d no answer
Two similar solid cones have their radii 15cm and 25cm respectively, if the volume of the bigger cone is 325cm³. Calculate (a) the linear scale factor (b) the volume scale factor (c) volume of the smaller cone
Answer:
The length scale factor = \(\frac{24}{6} = 4\)
The area scale factor = \(4^2 = 16\)
\[\text{Larger area} = 16 \times \text{smaller area}\]
\[50.3 \times 16 = 804.8\]
The area of the large clock face is approximately 804.8 cm2.
Step-by-step explanation:
The length scale factor = \(\frac{24}{6} = 4\)
The area scale factor = \(4^2 = 16\)
\[\text{Larger area} = 16 \times \text{smaller area}\]
\[50.3 \times 16 = 804.8\]
The area of the large clock face is approximately 804.8 cm2.
Answer:
a) the linear scale factor = 5/3
b) the volume scale factor = 125/27
c) 70.2 cm³
Step-by-step explanation:
r₁ = 15 cm, r₂ = 25 cm
r₂/r₁ = 25/15 = 5/3
They are similar, so h₂/h₁ = 5/3
a) the linear scale factor = 5/3
b) the volume scale factor = (5/3)³ = 125/27
c) V₂/V₁ = 125/27
Given V₂ = 325 cm³, V₁ = 325*27/125 = 70.2 cm³
HELP ME PLEASE I NEED HELP
Find the value of g(25) for the function below.
g(x) = 24(x − 39)
A.
561
B.
-14
C.
-336
D.
-911
Answer:
C.-336
Step-by-step explanation:
g(25)=24(25‒39)
=24(‒14)
=‒336
i hope it helps you
Step-by-step explanation:
g(x) =24(x-39)
g(25)=24(25-39)
=24(-14)
=-336
=c
QUESTION 1
The general term of the sequence is given by Tn= an + bn + c T2-T1 = 4; T3; -T2 = 6; T4-T3 = 8 and T2 = 6
1.1 Calculate a, b and c
Answer:
The general term of the sequence is given by
T
n
=
a
n
2
+
b
n
+
c
The general term of the sequence is given by
T
n
=
a
n
2
+
b
n
+
c
Calculate a,b and c
Determine the 12th term of the sequence.
grade12 general-term sequence series
Share your questions and answers with your friends.
answer comment
1 Answer
0
0
T3 - 6=6
T3=12
then T2-T1=4
6-T1=4
T1=2
T4-T3=8
T4-12=8
T4=20
Therefore terms= 2,6,12,20
1st difference= 4,6,8
2nd difference= 2,2,....
2a=2
a=1
3a+b=4
3(1) + b=4
b= 1
a+b+c= 2
c= 2-1- 1= 0
giving Tn= n^2 + n
T12 = 12^2 + 12 = 156