[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6425\\ P=\textit{initial amount}\dotfill &3500\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &8\\ \end{cases}[/tex]
[tex]6425=3500(1 + \frac{r}{100})^{8} \implies \cfrac{6425}{3500}=\left( \cfrac{100+r}{100} \right)^8\implies \cfrac{257}{140}=\left( \cfrac{100+r}{100} \right)^8 \\\\\\ \sqrt[8]{\cfrac{257}{140}}=\cfrac{100+r}{100}\implies 100\sqrt[8]{\cfrac{257}{140}}=100+r \\\\\\ 100\sqrt[8]{\cfrac{257}{140}}-100=r\implies {\LARGE \begin{array}{llll} \stackrel{\%}{7.89}\approx r \end{array}}[/tex]
Gen need help pls plsss
Answer:
Choice a
y = 2x -5
Step-by-step explanation:
The slope-intercept form of a line is y = mx + b where m is the slope and b the y-intercept
The given line has slope = 2
A parallel line will have slope = 2 also
So the only choice is 2x + 5 which is choice a
8. Why is "How many continents are there?" not a statistical question? (1 point)
there is only one answer
O the answer is unknown
Othe answer is less than ten
Oeveryone knows the answer
Answer: The answer is unknown
Step-by-step explanation: 7 continents, so you would only have 1 data.
I have a test coming up, and I think I will have questions like 7a+5a+4b-b etc. please help!
Answer:
12a + 3b = no solution
Step-by-step explanation:
You have to add like terms here!
7a + 5a = 12a
12a + 4b - b
4b - b = 3b
And now you're left with 12a and 3b, you can't go any further because 12 a and 3b are not like terms, you cannot add, or subtract them. Which means there is no solution.
I hope this helped :)
Simplify the expression. Write your answer as a power 6^2/6 • 6^12 / 6^8
The simplified form of the expression is 6^(-3)
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
6^2/6 • 6^12 / 6^8
Simplifying
6^2/6 • 6^12 / 6^8
Applying the division law of indices
6^(2 -1 ) • 6^(12 - 8)
6^(1) • 6^(4)
Applying the multiplication law of indices
6^(1 - 4)
6^(-3)
Hence, the simplified form of the expression is 6^(-3)
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Suppose that (x₁, y₁) and (x₂, y₂) are values from an inverse variation. Show that x₁/x₂=y₂/y₁.
It can be proved using the method of inverse variation.
What is inverse variation?
In mathematics, inverse variation refers to the relationships between variables expressed as y = k/x, where x and y are two variables and k is a constant. According to this statement, if the value of one item rises, the value of the other quantity falls.
Given,
(x₁, y₁) and (x₂, y₂) are values from an inverse variation.
inverse function of x and y will be -
y1 = k. 1 / x1
k = y1 / x1 ....(1)
y2 = k. 1 / x2
k = y2 / x2 ....(2)
from (1) , (2)
we can say that,
y1 / x1 = y2 / x2
⇒ y2 / y1 = x1 / x2
Hence proved.
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Solve the system of equations using elimination: − 2 x − 4 y = − 30 −2x−4y=−30 and − x + y = 6 −x+y=6.
Answer:
(1, 7 )
Step-by-step explanation:
- 2x - 4y = - 30 → (1)
- x + y = 6 → (2)
multiplying (2) by 4 and adding to (1) will eliminate y
- 4x + 4y = 24 → (3)
add (1) and (3) term by term to eliminate y
- 6x + 0 = - 6
- 6x = - 6 ( divide both sides by - 6 )
x = 1
substitute x = 1 into either of the 2 equations and solve for y
substituting into (1)
- 2(1) - 4y = - 30
- 2 - 4y = - 30 ( add 2 to both sides )
- 4y = - 28 ( divide both sides by - 4 )
y = 7
solution is (1, 7 )
What is the coordinate of G' if triangle E'F'G' is created by dilating EFG with factor of 4 about the origin?
Answer:
G' (8, - 8 )
Step-by-step explanation:
since the dilatation is centred at the origin then multiply each of the coordinates by the scale factor of 4
G (2, - 2 ) → G' (4(2), 4(- 2)) → G' (8, - 8 )
Two thirds equals negative eight times a number
Answer:
Step-by-step explanation:
25/3
Which function will have the steepest graph
The linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines. (Correct choice: D)
How to find the linear equation with the steepest graph?
Linear equations are equations of the form y = m · x + b, where m, b are the slope and the intercept of the equation, respectively. As slopes may be positive, null or negative, then we should use absolute values to determine the grade of steepness of a linear equation, where |m| ≥ 0. A line is steeper than other line when the absolute value of the former is greater than the absolute value of the latter.
According to this criterion, the linear equation y = (5 / 2) · x exhibits the steepest graph in comparison with the other three lines.
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Let f(x)=2 x+5 and g(x)=x²-3 x+2 . Perform each function operation, and then find the domain.
f(x) \cdot g(x)
The values for f(x).g(x) = 2x² -6x +9
What is the domain of the function f(x). g(x)?
Given:
f(x)=2 x+5 and g(x)=x²-3 x+2
(f.g)x = f(g)x)
g(x) = x²-3 x+2
f(x²-3 x+2) = 2 (x²-3 x+2) +5
f(x²-3 x+2) = 2x² -6x +9
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20 POINTS! Can someone help me? The question is located below!
A. 12cm x 8cm
B. 12cm x 9cm
C. 13cm x 8cm
D. 13cm x 9cm
The dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.
What are Whole Numbers?Whole numbers are numbers that do not have any fractional part and represents a whole quantity.
What are Mixed Numbers?A mixed number consist of an whole number and a proper fraction or fractional part.
How to Convert Mixed Numbers to Improper Fractions?Given the dimensions of the rectangular photo as, 12 11/16 cm by 8 3/4cm, convert each dimension to improper fractions:
12 11/16 would be converted to 203/16
8 3/4 would be converted to 35/4
203/16 = 12.6875 ≈ 13 [nearest whole number of cm]
35/4 = 8.75 ≈ 9 [nearest whole number of cm]
Therefore, the dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.
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Answer the 2 question in the photo
[easy points]
Mr. Lawson needs to borrow 8000 to help pay his son's college tuition. He explored options from several banks. Which option allows Mr. Lawson to pay the smallest amount of interest?
BANK: INTREST RATE: LOAN TERM:
United Bank 4% simple interest. 6 years
Nations First 3.8% simple interest. 7 years
City Credit Union 5.1% simple interest. 4 years
Priority Bank 4.2% simple interest. 5 years.
Mr. Lawson is to pay the smallest amount of interest that is allowed in the City Credit Union which is a simple interest would be 1632.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
To determine the smallest amount of interest.
We have to calculate the simple interest of each bank
United Bank : 4% interest rate and 6 years
S.I. of United Bank = 8000 × 4/100 × 6 = 1920
Nations First :3.8% interest rate and 7 years
S.I. of Nations First = 8000 × 3.8/100 × 7 = 2128
City Credit Union :5.1% interest rate and 4 years
S.I. of City Credit Union = 8000 × 5.1/100 × 4 = 1632
Priority Bank : 4.2%interest rate and 5 years.
S.I. of Priority Bank = 8000 × 4.2/100 × 5 = 1680
So the smallest amount of interest would be City Credit Union which is 1632.
Therefore, Mr. Lawson is to pay the smallest amount of interest that is allowed in the City Credit Union which is a simple interest would be 1632.
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HELP ME PLEASE!!!
I will give brainlist to whoever helps me!!!!
Answer: t=15
Step-by-step explanation:
ST=9. BC=3
ST/BC=
9/3=3 ==> with this information, we can conclude that triangle ABC needs to be stretched by a scale factor of 3 in order to become triangle RST.
t=RS
RS=AB*3
RS=5*3
RS=15
t=15
A family spends ; of their monthly income
on food,
5
14
on clothing and ‡on rent.
What fraction of the family's income is
spent on other things? If in a particular
month, the family spends GH&2,400 on
other things, how much did the family
spend on clothing? What was the family's
income for the month.
They spent 1/70 of their monthly income on other things.
The family spent GH¢60,000 on clothing.
The monthly income of the family is GH¢168,000.
What is Fraction?
The number is expressed as a quotient in which the numerator is divided by the denominator is called fraction.
Since, The family spend;
On food = (3/7)*x
On clothing = (5/14)*x
On rent = (1/5)*x
Let the family's monthly income = x
Now, To find the fraction of the family's income is spent on other things, we can assume that y is spent on other things, then we should have;
(3/7)*x + (5/14)*x + (1/5)*x + y*x = x
We can divide both sides by x, we get:
(3/7) + (5/14) + (1/5) + y = 1
Now, we can solve this for y as;
3/7 + 5/14 + 1/5 + y = 1
6/14 + 5/14 + 1/5 + y = 1
(6 + 5)/14 + 1/5 + y = 1
11/14 + 1/5 + y = 1
The smallest common factor of 14 and 5 = 14*5 = 70
So, we can multiply in the first fraction by 5/5 and the second by 14/14,
(5/5)*(11/14) + (14/14)*(1/5) + y = 1
55/70 + 14/70 + y = 1
69/70 + y = 1
y = 1 - 69/70
y = 1/70
Hence, They spent 1/70 of their monthly income on other things.
And, On a particular month, the family spends GH¢2,400 on other things, then if the monthly income is x, we have:
(1/70)*x = GH¢2,400
x = 70* GH¢2,400
x = GH¢168,000
So, The monthly income of the family is GH¢168,000
And, we know that they spend (5/14)*x on clothing,
Then this month they spent on clothing,
⇒ (5/14)*GH¢168,000 = GH¢60,000
So, They spent 1/70 of their monthly income on other things.
The family spent GH¢60,000 on clothing.
The monthly income of the family is GH¢168,000.
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The complete question is this,
A family spends 3/7 of their monthly income on food,5/14 on clothing and 1/5 on rent. What fraction of the family's income is spent on other things? If in a particular month, the family spends GH&2,400 on other things, how much did the family spend on clothing? What was the family's income for the month.
In cooking class, the instructor divided 1/2 of an ounce of salt evenly to make 4 servings of a dish. How much salt did he put in each serving? Write your answer as a fraction or as a whole or mixed number.
During the cooking class, the instructor put 1/8 of the salt in each serving
How to calculate the number of salt placed in each serving ?The instructor divided 1/2 of an ounce of salt evenly
The instructor needs to 4 servings in a dish
Therefore the number of salt in each serving can be calculated as follows
= 1/2 ÷ 4
change the expression to multiplication
1/2 × 1/4
= 1/8
Hence 1/8 of the salt was placed in each serving of the dish
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Use the properties of logarithms to simplify and solve each equation. Round to the nearest thousandth.
ln (x+1)+ln (x-1)=4
The simplified form of the given logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).
What precisely are logarithms?A logarithmic term represents a number in log form. A log term is another name for it.
A quantity can also be the sum of two or so more quantities. As a result, a term can be the product of 2 or more quantities, one of which must be in logarithmic form. In those kind of instances, the terms are recognized as log terms.
A quantity can also be defined as the quotient of two quantities. So, if a term includes a quotient of quantities, or at least each of the quantities could be expressed in log form, this same terms are known as log terms.
Quotient Rule: ㏒(A/B) = ㏒A - ㏒BProduct Rule : ㏒A + ㏒B = ㏒(AB)Power Rule: n㏒A = ㏒AⁿBase Rule = ㏒ₐb = ㏒ₓb/㏒ₓaExponent Rule = e∧lnx = xNow, according to the stated condition in question;
ln (x+1)+ln (x-1) = 4
Applying the Product Rule on the left side of the equation;
ln (x+1)/ (x-1) = 4
Convert the obtained expression in the exponent form.
Thus,
e∧[ln (x+1)/ (x-1)] = e⁴
Now, apply the exponent rule.
(x+1)/ (x-1) = 4
Now, simplifying the equation.
(x+1) = 4 (x-1)
x+1 = 4x - 1
4x - x = 1 + 1
3x = 2
x = 2/3
x = 0.666...
x = 0.67 (to the nearest thousandth).
Therefore, the solution for the stated logarithmic expression ln (x+1)+ln (x-1)= 4 is x = 0.67 (to the nearest thousandth).
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4^3+/(3+1)x2 please solve 15 points dude
Carl brownstein is a golf course groundkeeper whose annual gorss pay is 45,500, he has exemptions of 3000. the state tax on the first 2500 is 1.5% and 3% on amounts over 2,500.
If Carl Brownstein is a golf course groundskeeper whose annual gross pay is 45,500, and he has exemptions of 3000, and the state tax on the first 2500 is 1.5% and 3% on amounts over 2,500 then the state income tax of Carls is C- 1237.50.
The state income tax of Carls can be calculated as follows;
First, we subtract the exemption of 3000 from the annual gross pay as follows;
45500 - 3000 = 42500
As the percentage tax on the first 2500 is 1.5%, it can be calculated as follows;
1.5/100 × 2500 = 0.015 × 2500 = 37.50
The percentage tax on amounts over 2500 is 3%, therefore we can calculate the tax on the remaining amount as follows;
42500 - 2500 = 40000
3/100 × 40000 = 0.03 × 40000 = 1200
The total state income tax can be calculated by addition;
Tax on the first 2500 + Tax on the amount over 2500
37.50 + 1200 = 1237.50
Hence the state income tax of Carl is calculated to be 1237.50
Although a part of your question is missing, you might be referring to this question:
Carl Brownstein is a golf course groundskeeper whose annual gross pay is 45,500, he has exemptions of 3000. The state tax on the first 2500 is 1.5% and 3% on amounts over 2,500. What is the state income tax of Carl's?
A- 3233
B- 1200
C- 1237.50
D- 1588
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pls pls help whoever gets it right gets a crown
Answer:
No Solution
Step-by-step explanation:
0.3(6y+15)=1.8y+4.5
Step 1: Simplify both sides of the equation.
0.3(6y+15)=1.8y+4.5
(0.3)(6y)+(0.3)(15)=1.8y+4.5(Distribute)
1.8y+4.5=1.8y+4.5
Step 2: Subtract 1.8y from both sides.
1.8y+4.5−1.8y=1.8y+4.5−1.8y
0y+4.5=4.5
Step 3: Subtract 4.5 from both sides.
0y+4.5−4.5=4.5−4.5
0y=0
Step 4: Divide both sides by 0.
0y/0 = 0/0
y=0
How many pieces of string each measuring 10cm can be cut from a length measuring 2.5metres
Jenna works for the Parks Department and just completed some maintenance work at the baseball fields in Memorial Park. She needs to drive to the playground at Veteran’s Park next. In which general direction will she drive?
a map of a town showing two parks
A.
southwest
B.
northwest
C.
southeast
D.
northeast
Answer:North west, the roads should have stopped this answer but north alone wasn’t an option so just pretend Jenna is a lawless maniac ig♂️
Step-by-step explanation:
Find y.
Round to the nearest tenth:
y
x
27°
350 ft
y = [? ]ft
The value of y or the perpendicular of the is 180 rounded to nearest tenth.
Here we have to use Trigonometry
Trigonometry is basically the study of the relationship between the sides and angles of the right-angle triangle. Thus , trigonometry helps to find the missing or unknown angles or sides of a right-angle triangle using the trigonometric formulas, functions or trigonometric identities. In trigonometry, the angles can be are generally measured in degrees
Here we will use Tan α
Tan α = Perpendicular / Base
From the given figure we know that base is given as 350 feet and α is 27°
Tan 27° = y/ 350
0.509 = y / 350
y = 350 × 0.509
y = 178.15
Hence, The value of y or the perpendicular of the is 180 rounded to nearest tenth
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The number of new bicycles must be more than 13 times the number of new treadmills. Each bicycle costs $340 and each treadmill costs $670. He must spend less than $5,650.
Select all of the constraints for this situation.
y>13x
y greater than fraction 1 over 3 end fraction x
x>0
x is greater than 0
340x+670y<5650
340 x plus 670 y less than 5650
x>13y
x greater than fraction 1 over 3 end fraction y
340x+670y≤5650
340 x plus 670 y less than or equal to 5650
y>0
The constraints of the equation will be x > 13 y and 340 x + 670 y < 5650.
Let the number of new bicycles be x
Let the number of new treadmills be y.
Cost of 1 new bicycle = $ 340
Cost of 1 new treadmill = $ 670
Also, he must spend less than $ 56,50
Now, the constraints for this will be:
x > 13 y
x greater than 13 y
340 x + 670 y < 5650
340 x plus 670 y less than or equal to 5650
Therefore, the constraints of the equation will be x > 13 y and 340 x + 670 y < 5650 .
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Work out the perimeter of a regular octagon with side length 1.7mm.
Answer:
13.6mm
Step-by-step explanation:
1.7mm x 8 sides =
. You get paid on the first day of each month. You cash your check and pay
all of your essential expenses. You keep the balance in your "discretionary
spending" envelope. A scatter plot shows the number of days that have passed
since you were paid and the amount left in your discretionary spending
envelope. The explanatory x-variable is the number of days that have passed.
The response y-variable is the amount left in your envelope. Is there a positive
or negative correlation? Explain.
From the given scatter plot with x and y variables, we can say that the correlation is; Negative Correlation.
How to interpret scatter plot correlation?We are told that you kept the balance in your "discretionary spending" envelope.
Now, we are further told that a scatter plot shows the number of days that have passed since you were paid and the amount left in your discretionary spending envelope.
Now, In this case, the day of the salary increases the money spent, that is, the amount of money in the envelope decreases. Thus, as the variable increases and the other decreases, it is a negative correlation.
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FINANCE
A financial advisor handles the a customer's stock
portfolio. For every transaction, a certain financial advisor
gets a 1% commission, regardless of whether the transaction
is a purchase or sale. Write a formula for the advisor's
commission. Let D represent the value of one transaction.
Give two examples of how this financial advisor could earn a
commision of $1000 by completing two transactions.
Answer:
whether the transaction
is a purchase or sale. Write a formula for the advisor's
commission. Let D represent the value of one transaction.
Give two examples of how this financial advisor could earn a
commision of $1000
Step-by-step explanation:
Answer:
gove two examples of how this financial advisor could earn a
Step-by-step explanation:
fluctuates
increases
stays the same
decreases
Answer:
d)decreases
Step-by-step explanation:
Paolo purchased a shirt at store A. He paid $19.50 for the shirt. Raoul purchased the same shirt at store B for $22.35.
How much money did Paolo save by purchasing the shirt at store A instead of at store B?
Answer:
2.85
Step-by-step explanation:
Reason 19.50 - 22.35 = 2.85
I really need help on this Math homework
Answer:
x + 3x + 56 = 180
x + 3x = 124
4x = 124
x = 31
Step-by-step explanation:
A: 31
B: 3(31) = 91
C: 56
Total: 180