a) Hassan deposits $325 into an account that pays 4.7% annual interest compounded monthly. Write an equation to represent Hassanʼs account balance A after t years.
b) Use a system of equations to determine how many years it will take for the account reach $200. Round to the nearest year.
The equation will be written as [tex]A = 325[1.004]^{12t}[/tex]. The time taken to reach $200 will be 10 years.
What is compound interest?Compound interest is defined as the interest levied upon the interest. The formula to calculate the compound interest will be written as:-
[tex]A = P[1+\dfrac{r}{m}]^{rt}[/tex]
Given that Hassan places $325 into a savings account that offers a monthly compound interest rate of 4.7%.
The equation for the compounding on monthly basis,
[tex]A = 325[1+\dfrac{0.047}{12}]^{12t}[/tex]
[tex]A = 325[1.004]^{12t}[/tex]
The time will be calculated as:-
[tex]A = 325[1.004]^{12t}[/tex]
[tex]200 = 325[ 1.004]^{12t}[/tex]
log(0.615) = 12 x t x log(1.004)
12t = 121.77
t = 10 years
Therefore, the equation will appear as [tex]A = 325[1.004]^{12t}[/tex]. It will take 10 years for the price to reach $200.
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convert the following measurements into centimeters
A. 15m
B. 1.6km
C. 467mm
Answers:
A. 150 cmB. 160,000 cmC. 46.7 cm===========================================
Work Shown:
[tex]15 \text{ m} = (15 \text{ m})*\frac{100 \text{ cm}}{1 \text{ m}} = 1500 \text{ cm}\\\\\\1.6 \text{ km} = (1.6 \text{ km})*\frac{1000 \text{ m}}{1 \text{ km}}*\frac{100 \text{ cm}}{1 \text{ m}} = 160,000 \text{ cm}\\\\\\467 \text{ mm} = (467 \text{ mm})*\frac{1 \text{ cm}}{10 \text{ mm}} = 46.7 \text{ cm}[/tex]
Each conversion fraction is set up to cancel out any unit that isn't "centimeters".
Side notes:
1 m = 100 cm1 km = 1000 m1 cm = 10 mmSimplify (6x-15)/(4x^2-25)
Does the set of even integers have the density property? Explain.
Answer:
No
Step-by-step explanation:
You want to know if the set of even integers has the density property.
Density propertyThe density property states that for any two elements of a set, there are additional elements of the set between them.
There are no even integers between any two consecutive even integers, so the set of even integers does not have the density property.
17
What is the slope of the line that contains the points (-1, 9) and (5, 21)?
slope found by rise over run or m = (y2 - y1) / (x2 - x1)
orientation is important to not mix either values order.
( 9 - 21) / ( -1 - 5) => ( -12 ) / ( - 6 )
negatives cancel and simplify to find
m = 2
The area of the trapezoid is 36 ft².
Find the height of the trapezoid.
4 ft
8 ft
Answer:
6ft
Step-by-step explanation:
area of trapezoid formula: 1/2h(a+b)
height=x
x/2(4+8)=36
x/2*12=36
2 and 12 will get cancelled
6x=36
x=36/6
x=6
hope it helped!!!
3= g/-4 -5
tysm for helping me
For the equation 3 = (g/-4) - 5, the value of g is g = -32.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The given equation is -
3 = (g/-4) - 5
The equation contains a fractional component.
Simplify the equation to get the value of g.
First collect all the like terms -
g/-4 = 3 + 5
Then use arithmetic operation of addition -
g/-4 = 8
Then move the denominator of the fraction to right hand side of the equation -
g = 8 × -4
Then use arithmetic operation of multiplication -
g = -32
Therefore, the value of g is -32.
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Kenji is deep-sea diving with two friends. Ezra is exploring a coral reef 12 meters in front of Kenji, and Tori is floating on the surface directly above Kenji. If Tori and Ezra are 20 meters apart, how far apart are Kenji and Tori?
Answer:
Step-by-step explanation:
We know that the hypotenuse is 20m and one leg is 12m.
Pythagorean Theorem= a^2 + b^2 = c^2
12^2 + b^2 = 20^20
144 + b^2 = 400
b^2 = 256
Square root of 256 = 16
Kenji and Tori are 16 meters away from each other.
1 Colour three parts green. Colour five parts yello a What fraction of the circle is green?
Answer:
3/8
Step-by-step explanation:
1. If there are three parts green and 5 parts yellow, you can add them to find the total parts
2. 5+3 is 8
3. Then to find the green, which is three, we can divide it
4. 3 green parts/ total which is 8
5. 3/8
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
The Pythagorean theorem describes the relationship between the lengths of legs a and b and the hypotenuse c of any
right triangle.
a² + b² = c²
Complete the equation below by writing an expression equivalent to the length of a, the leg of a right triangle.
Completing the equation below by writing an expression equivalent to the length of a, the leg of a right triangle is given below
a^2 + b^2 = c^2a^2 = c^2 - b^2a = square root of (c^2 - b^2)What is Pythagoras' Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Hence, the complete equation according to this theorem is given above.
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nonononononononnnono
-2/5(15-5) is equivalent to what value?
Alan and betty collected cans for recycling. Alan collected 154 cans. Betty collected 215 cans. How many cans did they collect?
Answer:
369 cans
Step-by-step explanation:
Add the two numbers of cans collected by each:
Alan: 154 cans
Betty: 215 cans
Total: 369 cans
A STORY OF RATIOS
A positive, finite decimal s is said to be written in scientific notation if it is expressed as a product d x 10", where d
is a finite decimal so that 1 ≤ d < 10, and n is an integer.
The integer n is called the order of magnitude of the decimal d x 10".
Are the following numbers written in scientific notation? If not, state the reason.
Exercise 1
1.908 x 1017
Exercise 2
0.325 x 10-2
Exercise 3
7.99 x 10³2
EUREKA
MATH
Lesson 9:
Scientific Notation
© 2019 Great Mindeurekamath.org
Exercise 4
4.0701 +10
Exercise 5
18.432 x 5
Lesson 9 Classwork 8.1
Exercise 6
8x 10-¹1
85
Exercise 1: Yes, 1.908 x 10^17 is written in scientific notation.
Exercise 2: Yes, 0.325 x 10^-2 is written in scientific notation.
Exercise 3: No, 7.99 x 10^32 is not written in scientific notation. The decimal d must be between 1 and 10, not between 10 and 100.
Exercise 4: No, 4.0701 + 10 is not written in scientific notation. The correct format is d x 10^n.
Exercise 5: No, 18.432 x 5 is not written in scientific notation. The correct format is d x 10^n.
Exercise 6: No, 8x 10^-11 is not written in scientific notation. The correct format is d x 10^n.
can rectangle corner perpendicular diagonal lines of the rectangle?
if so can you draw a picture
Answer:
yes
Step-by-step explanation:
1. Polygon ABCDE is congruent to polygon TVSRK.
The angle that VSR would correspond to, given that polygon ABCDE is congruent to polygon TVSRK, is 2. Angle C.
How to find the angle ?When polygons are said to be congruent, then it means that their sides are the same lengths, and they have the same angles which means that they are corresponding.
This therefore means that the angle at A in polygon ABCDE would be congruent to the angle at T in TVSRK.
This therefore means that the angle VSR would correspond to the angle C in ABCDE because S is the third letter in TVSRK and C is the third letter in ABCDE.
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The full question is:
Polygon ABCDE is congruent to polygon TVSRK. what do angle VSR correspond to _____?
1. Angle B
2. Angle C
3. Angle D
4. Angle A
Combine the like terms to simplify this expression: ( the 2 to the right of the x, is an exponent)
2x² + 3x-4-x² + x + 9
Answer:
x^2 +4x +5
Step-by-step explanation:
2x^2 -x^2 will be x^2
3x+x is 4x
-4+9 is 5
If
D=1−s^2 −s and C=3+3s, find an expression that equals 2D−3C in standard form.
The expression that equals 2D−3C in standard form is -2s² - 11s - 7
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of coefficients, variables, terms, factors and constants.
From the information given, we have that;
D=1−s^2 −s and C=3+3s,
To determine the expression for 2D - 3C
substitute the values of the expressions, we get;
2(1-s² - s) - 3(3 + 3s)
expand the bracket
2 - 2s² - 2s - 9 -9s
collect the like terms or factors, we get;
-2s² - 2x - 9s - 9 + 2
Add or subtract the values
-2s² - 11s - 7
Hence, the expression is -2s² - 11s - 7
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Question in picture! Thanks
Answer:
~ generally is substituted by negation
Hence, option D (Even numbers are not divisible by 2) would be the correct answer.
If you get paid $13 per hours and work 8 hours and 45 minutes how much money did you earn? round your answer to the nearest hundred?
Answer:
113.75
Step-by-step explanation:
13$ x 8.75 h (45 minutes is 3/4 of an hour) = $113.75
keeping in mind that an hour has 60 minutes, so you're really getting paid $13 per 60 minutes, so now, 8 hours and 45 minutes is just 8*60 + 45 = 525 minutes.
[tex]\begin{array}{ccll} \$&minutes\\ \cline{1-2} 13 & 60\\ x& 525 \end{array} \implies \cfrac{13}{x}~~=~~\cfrac{60}{525} \\\\\\ \cfrac{ 13 }{ x } ~~=~~ \cfrac{ 4 }{ 35 }\implies 455=4x\implies \cfrac{455}{4}=x\implies 113.75=x[/tex]
I need to find the value of x and it's a horizontal line or whatever the cross over like a x (3x-3)°147°
In parallelogram ABCD, AB = 5x * 3 and CD = 15 * x. FInd the value of x
In a parallelogram, opposite sides are equal. Therefore, AB = CD.
5x * 3 = 15 * x
15x = 15
x = 1
Therefore, the value of x is 1.
If the height of parallelogram ABCD is 6, what is the area of the parallelogram?To find the area of parallelogram ABCD, we can use the formula A = base x height, where the base is the length of side AB and the height is the perpendicular distance between side AB and the opposite side CD. Since the height of parallelogram ABCD is given as 6, we need to find the length of side AB.
From the given information, we know that AB = 5x * 3, where x = 1. Therefore, AB = 15. Now we can calculate the area of parallelogram ABCD as:
A = base x height
A = 15 x 6
A = 90 square units
Therefore, the area of parallelogram ABCD is 90 square units.
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There were 10 games work out the mean number of goals per game
Answer:
Step-by-step explanation:
Add all the number of goals and then divide by 10.
convert 1hour 38 min 14 second to seconds
Answer:
5894 seconds
Step-by-step explanation:
Convert 1 hour 38 min 14 seconds to seconds
1 hour = 3600 seconds
1 min = 60 seconds
38 mins = 60 x 38 = 2280 seconds
Now add all numbers together
3600 + 2280 + 14 = 5894 seconds
So, 1 hour 38 minutes 14 seconds is 5894 seconds.
Mia invests $7500 at a rate of 3.5% per year simple interest
Calculate the total amount she has after 5 years.
Answer:
$8812.50
Step-by-step explanation:
To calculate the simple interest earned on Mia's investment, we can use the formula:
I = Prt
where I is the interest earned, P is the principal amount invested, r is the interest rate as a decimal, and t is the time in years.
Plugging in the values, we have:
I = $7500 * 0.035 * 5
I = $1312.50
The total amount Mia has after 5 years is the sum of her original investment and the interest earned:
$7500 + $1312.50 = $8812.50
Hey! I need help with these 2 questions! Thanks.
8. The depth of the water is solved to be = 2.9 cm (one decimal place).
9 The ratio r: s =√3 : 2.
How to find the depth of the waterThe depth of water is calculated by first using Pythagoras theorem to get the level between water level 7 cm and water level when completely full which is 10 cm
= √(10² - 7²)
= √(100 - 49)
= √51
The next step is to subtract from the radius
= 10 - √51
= 2.8586 cm
= 2.9 cm
9. The length of diagonal of a cube is given by the formula
= (√3)·s
The diameter of the sphere is equal to length of diagonal of a cube.
radius of a sphere = diameter / 2
r = (√3)*s / 2
r / s = √3 / 2
hence the ratio is
r : s = √3 : 2
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complete question is attached
A dust particle weighs around 7.53 x 10-16 grams.
grams
O 7,530,000,000,000,000,000
0.0000000000000753 grams
75, 300,000,000,000,000 grams
O 0.0000000000000000753 grams
O'0.0
0.000000000000000753 grams
Answer:
It would be 3.765 pounds. You have to do 7.53 x 10 to the -10= 0.000000000753. Then do 0.000000000753 x 5 billion to get 3.765.
Step-by-step explanation:
solve for x -8= x+27/-6
Answer:
x=-7/2 (exact form)
x=-3.5 (decimal form)
x=-3 1/2 (mixed number form)
Step-by-step explanation: :)
What percent of Jemma's answers did she get incorrect?
If Jemma got 2 out of 20 questions wrong on her most recent math quiz, then the incorrect percent is 10% .
Total number of questions in the Math's quiz is = 20 ;
Number of incorrect questions done by Jemma is = 2 ;
Number of correct questions done by Jemma are = 18 ;
So , to find the percentage she got incorrect, we divide ; (number of incorrect answers) by (total number of questions) and then multiply by 100 ;
that means ⇒ (2/20) × 100 = 10% ;
Therefore, Jemma got 10% of the questions incorrect on her most recent math quiz.
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The given question is incomplete , the complete question is
If Jemma got 2 out of 20 questions wrong on her most recent math quiz, what percent did she get incorrect ?
Find the lower bound for the following weights
b) 21. 58 g correct to 2 decimal place
The lower bound for the weight 21.58 g correct to 2 decimal places is 21.57 g. This is because the next smallest value based on the rounding is obtained rounding down the number in second decimal place, which is 5.
To find the lower bound for the weight 21.58 g correct to 2 decimal places, we need to consider the next smallest number that can be represented to 2 decimal places.
Since the second decimal place is 8, the next smallest number is obtained by rounding down the number in the second decimal place, which is 5. Therefore, the lower bound for 21.58 g correct to 2 decimal places is: 21.57g
Note that the weight could be more precise than what we are given, but to represent it to 2 decimal places we have to make an assumption about the last digit.
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f(x) = -x² + 5 and g(x) = -2x+2, find all values of x for which f(x) = g(x).
Answer:
The values of x for which f(x) = g(x) are:
x = -1x = 3Step-by-step explanation:
To find all the values of x for which f(x) = g(x), equate the given functions:
[tex]\implies f(x)=g(x)[/tex]
[tex]\implies -x^2+5=-2x+2[/tex]
Rearrange the equation so that it is in the quadratic form ax²+bx+c=0:
[tex]\implies -x^2+5+2x-2=0[/tex]
[tex]\implies -x^2+2x+3=0[/tex]
Divide both sides by -1:
[tex]\implies x^2-2x-3=0[/tex]
Factor the quadratic equation:
[tex]\implies x^2-3x+x-3=0[/tex]
[tex]\implies x(x-3)+1(x-3)=0[/tex]
[tex]\implies (x+1)(x-3)=0[/tex]
To solve for x, apply the zero-product property:
[tex](x+1)=0 \implies x=-1[/tex]
[tex](x-3)=0 \implies x=3[/tex]
Therefore, the values of x for which f(x) = g(x) are:
x = -1x = 3We can check the solutions by substituting each found value of x into the functions.
[tex]f(-1)=-(-1)^2+5=4[/tex]
[tex]g(-1)=-2(-1)+2=4[/tex]
[tex]f(3)=-(3)^2+5=-4[/tex]
[tex]g(3)=-2(3)+2=-4[/tex]
As f(-1) = g(-1) and f(3) = g(3), this proves that the values of x for which f(x) = g(x) are x = -1 or x = 3.
Equate Both equatios and find x
f(x)=g(x)-x²+5=-2x+2x²-5=2x-2x²-2x-3=0(x+1)(x-3)=0The points are -1,3
