[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&19000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases}[/tex]
[tex]\bf 19000=P\left(1+\frac{0.08}{2}\right)^{2\cdot 5}\implies 19000=P(1.04)^{10} \\\\\\ \cfrac{19000}{1.04^{10}}=P\implies 12835.72\approx P[/tex]
To have $19,000 in 5 years with an 8% interest rate compounded semiannually, you should deposit approximately $12,840.72 now.
The question is about calculating the present value of an investment to reach a future sum of money with a given interest rate, compounded semiannually. To find out how much you should deposit now to have $19,000 in the future, we can use the formula for the present value of an investment for compound interest:
PV = FV / (1 + r/n)(nt)
FV = $19,000
r = 8% or 0.08
n = 2 (because interest is compounded semiannually)
t = 5 years
We can substitute these values into our formula:
PV = $19,000 / (1 + 0.08/2)(2*5)
Doing the math:
PV = $19,000 / (1 + 0.04)10
PV = $19,000 / 1.48024
PV = $12,840.72
So, you would need to deposit approximately $12,840.72 now in order to have $19,000 in 5 years, given an 8% interest rate compounded semiannually.
For which of the following statements is the inverse false? A. If a triangle is an equilateral triangle, then one angle equals 60°. B. If a triangle is a right triangle, then the other two angles add up to 90°. C. If a triangle is an equilateral triangle, then each of the angles equals 60°. D. If a triangle is a right triangle, then one angle equals 90°.
The statement for which the inverse is false is A, because if one angle of a triangle equals 60°, the triangle is not necessarily equilateral.
The question asks for which statement the inverse is false. To answer this, we analyze each statement and its inverse:
A. If a triangle is an equilateral triangle, then one angle equals 60°. Inverse: If one angle of a triangle equals 60°, then the triangle is equilateral. This could be false if the triangle is not equilateral but one angle happens to be 60°.
B. If a triangle is a right triangle, then the other two angles add up to 90°. Inverse: If two angles of a triangle add up to 90°, then it is a right triangle. This is true, given the geometric principle that the sum of angles in a triangle is 180°.
C. If a triangle is an equilateral triangle, then each of the angles equals 60°. Inverse: If each angle of a triangle equals 60°, then it is an equilateral triangle. This is true, as by definition, an equilateral triangle has all angles equal.
D. If a triangle is a right triangle, then one angle equals 90°. Inverse: If one angle of a triangle equals 90°, then it is a right triangle. This is true, as by definition, a right triangle has one 90° angle.
Therefore, the statement for which the inverse could be false is A.
4 miles 999 feet = in feet
Answer:
approximately = 26394.72
Convert between the 2 units.
Can i plz have the brainliest answer plz!!!!!!!!!!!
In order for an atom to have a zero charge every proton which has a change of +1, must be matched with an electron which has a change of -1 a helium atom has 2 protons and 2 electrons explain why a helium atom has a zero change
A helium atom has a zero charge because the number of protons equals the number or protons. The positive and negative charges add together to reach zero.
The formula for the circumference of a circle is C = 2πr, where r is the radius. Rearrange the formula to solve for r and select the correct option below.
Evaluate f(x) = -4x + 7 when x = 2 and x = -2.
Answer:
f(x)=-1 and 15
Step-by-step explanation:
What you do is you put -2 and 2 into the x.
f(x) = -4(-2) + 7 = -1
f(x) = -4(2) + 7 = 15
f(x)=-1 and 15 are your answers.
After substituting the values of x into the function f(x)=-4x + 7, when x = 2 the result is -1, and when x= -2 the result is 15, indicating specific points on the graph of the function.
Explanation:To evaluate the function f(x) = -4x + 7 for specific values of x, we need to substitute the x values provided into the function.
When x = 2, f(2) = -4(2) + 7 = -8 + 7 = -1.
When x = -2, f(-2) = -4(-2) + 7 = 8 + 7 = 15.
So, f(2) = -1 and f(-2) = 15. These values represent specific points on the graph of the function f(x) = -4x + 7.
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cos12sin78+cos78sin12
Sin 12 x cos 78 + cos 12 x sin 78
= sin 12 x cos (90-12) + cos 12 x sin (90-12)
=sin 12 x sin 12 + cos 12 x cos 12
=sin^2 12 + sin^2 12
=1
Y/-7=10 solve and check
Always write y in lower case
y/-7 = 10
y = 10(-7)
y = -70
Check:
Let y = -70
(-70)/-7 = 10
10 = 10
Done!
there are 18 oranges in box A and 36 in box B, what is the ratio of box A to box B
Answer:
1 : 2
Step-by-step explanation:
Express the ratio as the number of oranges in each box, that is
box A : box B
= 18 : 36
Simplify the ratio by dividing both parts by 18, thus
ratio = 1 : 2 ← in simplest form
Adhy, Ben and Clayson shared a bag of chocolates. The ratio of Adhy's share to Ben's share is 3:4 while
the ratio of Ben's share to Clayson's share is 3:5.
Given that Ben has 9 more chocolates than Adhy, find the difference between the number of chocolates
that Adhy and Clayson has.
Answer: 33
Step-by-step explanation:
The ratio of Adhy's to Ben's is 3:4 so let
Adhy = 3x
Ben = 4x
Since Ben = Adhy + 9
then 4x = 3x + 9
--> x = 9
So, Adhy = 3x = 3(9) = 27
Ben = 4x = 4(9) = 36
*************************************************************
The ratio of Ben's to Clayson's is 3:5
How do we get Ben's ratio of 3 equal to 36? by multiplying by 12
Ben : Clayson
3 x 12 5 x 12
36 60
So, Clayson = 60
***********************************************************
The difference between Adhy and Clayson is:
Clayson - Adhy
60 - 27 = 33
Please help me i really need it
Answer:
B and C
Step-by-step explanation:
It can't be A because that would equal 5b.
For C, you multiply 2b by 2 and get 4b.
For B, you add b to 3b to get 4b.
Which of the following polynomials is equivalent to the expression above?
A) x² + 5
B) x² +7
C) 4x² +7
D) x² + 4x + 7
Answer:
D) x² + 4x + 7
Step-by-step explanation:
2x + 6 + x² + 2x + 1
x² + 2x + 2x + 6 + 1
x² + 4x + 7
The equivalent expression for the given polynomial is x² + 4x + 7.
Option D is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
(2x + 6) + (x² + 2x + 1)
Removing the parenthesis.
2x + 6 + x² + 2x + 1
Adding the like terms.
4x + 7 + x²
x² + 4x + 7
Thus,
The final expression is x² + 4x + 7.
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Solve the equation for Y 4x-10y = 12
4x - 10y = 12
4x - 12 = 10y
y = (4x - 12)/10
y = 2x/5 - 6/5
If two is added to four times a certain number, the result
is 26. What is the number?
For this sort of question you have to work backwards.
.
26 - 2 = 24.
24 / 4 = 6
.
The number would be 6
Given the function below, select all the equalities that are true.
f(x) = x2 + 3
Answer:
a&c
Step-by-step explanation:
because you can multiply to numbers and reach 0 or 2, but no number times another equals 7 and no number times 0 equals three (multiplicative identity of 0)
Find the value of C. m^2+7/12m+c
Use b^2 - 4ac = 0.
Let a = 1
Let b = 7/12
(7/12)^2 - 4(1)c = 0
Take it from here.
evaluate 4 square root 9 square root 9 over 4 square root 9^5
[tex]\frac{\sqrt[4]{9}.\sqrt{9}}{\sqrt[4]{9^5}}[/tex]
[tex]\frac{9^\frac{1}{4}.9^\frac{1}{2}}{9^\frac{5}{4}}[/tex]
[tex]\frac{9^\frac{6}{8}}{9^\frac{5}{4}}[/tex]
[tex]9^{\frac{6}{8}-\frac{5}{4}}[/tex]
[tex]9^\frac{-1}{2}[/tex]
Word expression to match 24-6+3
Answer:
I think itśn 5
Step-by-step explanation:
Please help me with this
the answer is true it is a rational number
As a fraction, 2 is 2/1
Oh no, there is always an odd exponent. So it could not have been made by squaring a rational number! This means that the value that was squared to make 2 (ie the square root of 2) cannot be a rational number. In other words, the square root of 2 is irrational.
x + 10 = 2x
PLEASE SHOW EXPLANATION + WORK
Answer:
X=10
Step-by-step explanation:
x+10-10=2x-10
x=2x-10
x-2x=2x-10-2x
-x= -10
-x/-1= -10/-1
x=10
6 x 7 - 3 + 2 = __
Insert parentheses to make the expression equal 26.
A) 6 x (7 - 3 + 2)
B) 6 x (7 - 3) + 2
C) (6 x 7 - 3) + 2
D) 6 x 7 - (3 + 2)
Answer:
B is the correct answer
2(2X-3)-10 <_ 6(X-2)
Answer:
x<14/5
Step-by-step explanation:
expand
4x-6-10 < -6x+12
4x-16 < -6x+12
4x < -6x+12+16
4x < -6x+28
4x+6x < 28
10x < 28
x < 28/10
hope this helps
Answer:
[tex]\large\boxed{x\geq-2\to x\in[-2,\ \infty)}[/tex]
Step-by-step explanation:
[tex]2(2x-3)-10\leq6(x-2)\qquad\text{use the distributive property}\ a(b+c)\\\\(2)(2x)+(2)(-3)-10\leq(6)(x)+(6)(-2)\\\\4x-6-10\leq6x-12\\\\4x-16\leq6x-12\qquad\text{add 16 to both sides}\\\\4x\leq6x+4\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-2x\leq4\qquad\text{change the signs}\\\\2x\geq-4\qquad\text{divide both sides by 2}\\\\x\geq-2[/tex]
Jenny’s Gift Shop sells candles in a variety of packages. The cost per candle is the same in every package. A package of 8 candles costs $12.96. Determine the cost of a package of 3 candles.
Answer:
8 candle = $12.96
1 candle =($12.96/8)
= $1.62
package of 3 candles =3×$(1.62)
: =$4.86
Find the slope of the line that passes through the points (-8,-3), (2,3)
Answer:
⅗
Step-by-step explanation:
-y₁ + y₂\-x₁ + x₂ = m
[tex] \frac{3 + 3}{8 + 2} = \frac{6}{10} = \frac{3}{5} [/tex]
I am joyous to assist you anytime.
For f(x) = 3x +1 and g(x) = х2 - 6, find (f-g)(x).
Answer:
(f-g)(x) = -x^2 + 3x + 7
Step-by-step explanation:
Note that -g(x) = -x^2 + 6.
Thus, (f-g)(x) = f(x) + [-x^2 + 6]: Add the following:
f(x) = 3x + 1
-g(x) = -x^2 + 6
--------- ------------------
(f-g)(x) = -x^2 + 3x + 7 (answer)
Roselyn wants to drive her car at a speed of 606060 miles per hour for 1.251.251, point, 25 hours. Her car has a fuel efficiency of 151515 miles per gallon.
How many gallons of fuel does Roselyn need for her journey?
Answer:
Hence, there is 5 gallons of fuel Roselyn needed for her journey.
Step-by-step explanation:
Since we have given that
Speed at which Roselyn wants to drive her car = 60 miles per hour
Time taken by her car = 1.5 hours
As we know the formula for "Distance-Speed " :
Her car has fuel efficiency = 15 miles per gallon
Number of gallons of fuel is given by
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Answer:
5 gallons.
Step-by-step explanation:
Roselyn wants to drive her car at a speed of 60 mph
Speed of car, S = 60 mph
She drives for 1.25 hours.
Time travel, t = 1.25 hours
Total distance travel = s × t
= 60 × 1.25
= 75 miles
The fuel efficiency of car is 15 miles per gallon.
[tex]\text{Number of gallon used}=\dfrac{\text{Total distance travel}}{\text{Fuel efficiency}}[/tex]
[tex]\text{Number of gallon used}=\dfrac{75}{15}[/tex]
[tex]=5\text{ gallons}[/tex]
Hence, she needs 5 gallons.
-9.5 as a mixed number
You know that .5 = 0.5 = 5/10 = 1/2.
Mixed number sought: -9_1/2.
Select the correct answer.
Anton is approved for overtime at his job. Last week, he worked a total of 45 hours. How many hours of overtime did he work?
3 hours
B. 5 hours
C. 15 hours
D.45 hours
Answer: 15 hours
Step-by-step explanation: full time is 30 hours so if he worked 45 that’s 30+15=45 so 15hrs over time
categorize the following graph as linear increasing, linear decreasing, exponential growth, or exponential decay
Answer:
Linear decreasing
Step-by-step explanation:
We are given that a graph
We have to find the type of graph.
Increasing function: If [tex]x_1 \leq x_2[/tex]
Then ,[tex]f(x_1)\leq f(x_2)[/tex]
Decreasing function:If [tex]x_1\leq x_2[/tex]
Then, [tex]f(x_1)\geq f(x_2)[/tex]
The given graph is not exponential graph because exponential graph is type of curve.
But given graph is line graph.
The equation of line
[tex]y=mx+c[/tex]
The equation of line is linear equation.
When x increasing then value of function decreasing with increasing value of x.
Hence, the graph is linear decreasing.
Final answer:
The graph depicts a logistic growth model, signified by an S-shaped curve, which represents population growth that begins exponentially, slows as resources deplete, and stabilizes at the carrying capacity.
Explanation:
The graph you are referring to seems to describe a logistic growth model, which is characterized by an S-shaped curve. This type of growth is common in populations where initially there is exponential growth due to plenty of resources and few individuals. However, as the population increases, resources become limited, slowing the growth rate; eventually, the population size stabilizes at the carrying capacity of the environment. When categorizing the graph:
Initially, the growth is exponential.
Over time, as resources become scarce, the growth rate decreases.
Finally, growth becomes nearly zero as the population reaches the environment's carrying capacity.
At different time intervals, we can annotate changes in the growth rate:
During the first phase, growth rate increases linearly with the number of individuals (exponential growth).
During the second phase, the growth rate decreases in proportion to the square of the number of individuals.
In the third phase, when carrying capacity is reached, the rate of growth is zero (no net increase in population).
This can be contrasted with the exponential growth model which is represented by a J-shaped curve and shows unbounded growth over time.
The perimeter of a rectangle is 44 m. The length is 4 m more than the twice the
width. Find the dimensions.
Final answer:
The dimensions of the rectangle with a perimeter of 44 m, where the length is 4 m more than twice the width, are 6 m for the width and 16 m for the length.
Explanation:
The perimeter of a rectangle is given as 44 m, and the length (L) is said to be 4 m more than twice the width (W). To find the dimensions, we can set up the following equations based on the properties of a rectangle:
Perimeter P = 2(L + W)
L = 2W + 4
Since the perimeter is 44 m, we can substitute the length expression into the perimeter equation:
44 = 2((2W + 4) + W)
By solving this equation for width (W), we get:
44 = 2(3W + 4)
44 = 6W + 8
36 = 6W
W = 6 m
Now that we have the width, we can determine the length using the expression for L:
L = 2(6) + 4 = 16 m
Therefore, the final answer for the width is 6 m and the length is 16 m.
7X²-26X-8=0
Solving polynomial equations with factoring, algebra. Please help me!
Answer: [tex]\bold{x=\bigg\{4,-\dfrac{2}{7}}\bigg\}[/tex]
Step-by-step explanation:
7x² - 26x - 8 = 0
Find two numbers whose product equals (7)(-8) and sum equals -26.
-28 × 2 = 56, -28 + 2 = -26
Replace -26x with -28x + 2x: 7x² - 28x + 2x - 8 = 0
Factor the left two terms & right two terms: 7x(x - 4) + 2(x - 4) = 0
Notice that both sides have a common factor of (x - 4) --> This is one of the factors. The other factor is what is on the outside of (x - 4) --> 7x + 2
Rewrite the expression as two factors: (x - 4)(7x + 2) = 0
set each factor equal to zero and solve for x.
x - 4 = 0 7x + 2 = 0
x = 4 7x = -2
x [tex]=-\dfrac{2}{7}[/tex]