Answer:
The time required is of 17.53 years.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Find the time required for an investment of 7,000 dollars to grow to 14,000 dollars at an interest rate of 4% per year, compounded monthly.
This is t for which [tex]A(t) = 14000[/tex], considering [tex]P = 7000, r = 0.04, n = 12[/tex]. So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]14000 = 7000(1 + \frac{0.04}{12})^{12t}[/tex]
[tex](1.0033)^{12t} = 2[/tex]
[tex]\log{(1.0033)^{12t}} = \log{2}[/tex]
[tex]12t\log{1.0033} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{12\log{1.0033}}[/tex]
[tex]t = 17.53[/tex]
The time required is of 17.53 years.
3x + 1 over 4y2
What is the value of the expression above when x = 3 and y = 4? You must show all work and calculations to receive full credit.
Answer:
5/32
Step-by-step explanation:
(3x+1)/4y^2
(3(3)+1)/[4(4)^2]
(3*3+1)/[4(4)(4)]
(9+1)/[4*16]
10/64
simplify
5/32
The value of the expression at x = 3 and y = 4 is [tex]\frac{5}{32}[/tex] .
Concept:Firstly we will convert the expression into numerical form.Then, we will substitute the value of x & y respectively in the expression and simplify it.How to solve the given question?Converting the expression into numerical form.Thus, the value of the expression at x = 3 and y = 4 is [tex]\frac{5}{32}[/tex] .
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What is the exponential regression equation that fits these data? x у 1 4 2 9 3 27 4 90 5 250 6 580 O A. y = 39.16x2 - 169.38x+ 158.9 O B. y = 1.31(2.804) O C. y = 2.80(1.31") O D. y = 104.74x - 206.6
Answer:
1.31(2.80)^x
Step-by-step explanation:
Given the data :
x : 1 2 3 4 5 6
y : 4 9 27 90 250 580
Using technology, the exponential regression data obtained by fitting the data is :
y = 1.31(2.80)^x
Where, y = predicted value
1.31 = Initial value
2.80 = growth fractor
x = period
Answer:
1.31(2.80)^x
trust me i just did the cst
Step-by-step explanation:
Two triangles have the same area. One triangle has a base of 4 cm and a height of 7 cm. If the height of the other triangle is 14 cm, then what is its base length?
3 cm
2 cm
4 cm
5 cm
Answer:
x = 2
Step-by-step explanation:
→ Work out the area of the first triangle
0.5 × 4 × 7 = 14
→ Set up an equation for the second base
0.5 × x × 14 = 14
→ Simplify
7x = 14
→ Divide both sides by 7
x = 2
Answer:
option B = 2cm
Step-by-step explanation:
[tex]Area \ of \ first \ triangle = \frac{1}{2} \times base_1 \times height_1 \ [ \where base_1 = 4\cm \ height_1 \ = 7cm \ ][/tex]
[tex]=\frac{1}{2} \times 4 \times 7 \\\\= 14 \ cm^2[/tex]
Given area of second triangle is same as first.
[tex]Area \ of \ second \ triangle = \frac{1}{2} \times base_2 \times height_2 \ [ \ where \ height _ 2 = 14cm \ ][/tex]
[tex]14 = \frac{1}{2} \times base_2 \times 14\\\\14 = 7 \times base_2\\\\base_2 = 2 \ cm[/tex]
Please help! Which interval describes where the graph of the function is positive?
Answer:
c. -oo < x < -1
Step-by-step explanation:
according to the graph the function possitive
=> y > 0 , and x < -1
Find the general value of log(1 + i) + log(1 - i)
Answer:
the answer would be log 2
Eighty members of a bike club were asked whether they like touring bikes and whether they like mountain bikes. A total of 70 like touring bikes, 47 like mountain bikes, and 5 do not like either.
A 4-column table with 3 rows. The first column has no label with entries likes mountain bikes, does not like mountain bikes, total. The second column is labeled liking touring bikes with entries a, c, 70. The third column is labeled does not like touring bikes with entries b, 5, e. The fourth column is labeled total with entries 47, d, 80.
What are the correct values of a, b, c, d, and e?
a = 42, b = 28, c = 33, d = 5, e = 10
a = 42, b = 5, c = 28, d = 33, e = 10
a = 5, b = 42, c = 28, d = 10, e = 33
a = 5, b = 10, c = 28, d = 33, e = 42
Answer: Choice B
a = 42, b = 5, c = 28, d = 33, e = 10
====================================================
Explanation:
Refer to the diagram below. We have a table of values in which some values (if not most) are unknown. We have variables as placeholders until we can figure out which numbers replace them.
Along the bottom row, we see that 70+e = 80, which solves to e = 10. I subtracted 70 from both sides.
That must mean the answer is between choice A or choice B.
--------------------------
Since e = 10, and b+5 = e (third column), we can replace the 'e' with 10 to get the equation b+5 = 10. That solves to b = 5. This rules out choice A.
The final answer is choice B
---------------------------
If you want to keep going to find a, c and d, then let's solve a+b = 47 which is the same as a+5 = 47 after replacing letter b with 5.
a+5 = 47 solves to a = 42 after subtracting both sides by 5.
Then along the first column, we see that a+c = 70 which is the same as 42+c = 70. Isolating c gets us c = 28
Lastly, c+5 = d is shown along the second row. Plug in c = 28 to find that d = c+5 = 28+5 = 33
So overall we have:
a = 42, b = 5, c = 28, d = 33, e = 10
Answer:
b is correct
Step-by-step explanation:
Graph the set on a number line. {-1/2, -1 3/4}
Answer:
D
Step-by-step explanation:
Each dot is 1/4 and we are going from 0 to -2
A right triangle has side lengths 5, 12, and 13 as shown below. Use these lengths to find tanB, sin B, and cos B. (WORK INCLUDED GIVING BRAINLEST TO BEST ANSWER)
9514 1404 393
Answer:
tan(B) = 12/5sin(B) = 12/13cos(B) = 5/13Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships.
Sin = Opposite/Hypotenuse ⇒ sin(B) = 12/13
Cos = Adjacent/Hypotenuse ⇒ cos(B) = 5/13
Tan = Opposite/Adjacent ⇒ tan(B) = 12/5
a person can type 800 words in 10 minutes.how many words can be type in 1 minute?
Answer:
Yes they can type about 130 each minute
Step-by-step explanation:
I learned this in a book
Answer:
the person can type
80 wpm
What base makes the equation below true?
Note: A number should be entered, not a word.
Answer:
4
Step-by-step explanation:
in base 4
21 = (2 * 4) + (1 * 1) = 9
The table contains the lengths of the sides of different triangles. Do the given side lengths form a right triangle?
Drag and drop Yes or No into the box next to the side lengths.
5 cm, 12 cm, 13 cm
8 cm, 9 cm, 10 cm
3 cm, 4 cm, 4 cm
7 cm, 24 cm, 25 cm
1 cm, 4 cm, 9 cm
Answer:
ans: it's order wise
a) yes
b) no
c) no
d) no
Step-by-step explanation:
use pythagoras theorem
h² = p² + b²
data given satisfying the theorem form right angled triangle
Answer this math gods
Answer:
y = 4x^2
Hope that this helps!
Savannah needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 694 knives. There are currently 262 knives. If each set on
sale contains 12 knives, which inequality can be used to determine s, the minimum
number of sets of knives Savannah should buy?
Answer:
[tex]s\geq 36[/tex]
Step-by-step explanation:
Step 1, how many knives to buy?
The restaurant already has 262 knives. We can subtract this number from their needed 694 knives to find how many they still need:
[tex]694-262=432[/tex] knives.
Step 2, how many sets of knives?
The restaurant needs to buy 432 knives. We know the knives come in sets of 12, so we can divide to find the # of packs she needs to buy, determined by variable s.
Notice how the restaurant needs to buy a minimum of 694 knives, hence we use a greater or equal than symbol:
[tex]\fbox{\frac{432}{12} \geq s}\\[/tex][tex]s\geq \frac{432}{12}[/tex]
[tex]s\geq 36[/tex]
I hope this helps! Let me know if you have any questions :)
The inequality that can be used to determine s, the minimum number of sets of knives Savannah should buy is 694 ≥ 262 + 12s.
Given that;
The restaurant needs at least 694 knives. There are currently 262 knives.
Here, each set on sale contains 12 knives.
Let us assume that;
The minimum number of sets of knives Savannah should buy = s
Hence the inequality for the given condition is,
694 ≥ 262 + 12s
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Encontrar X..................
PLEASE HELP ASAP For each expression below, select the letter that corresponds to the equivalent expression from the given list.
(4x^3 – 4 + 7x) – (2x^3- 8)
is equivalent to expression___
(-3x^2 + x^4 + x) + (2x^4 - 7 + 4x) is equivalent to expression ____
(12 – 2x)(2x + 3) is equivalent to expression___
The blanks are for the letters in the picture
BAnswer:
B-D-A
Step-by-step explanation:
-
Question 4 of 5
How many solutions does 8 + 6
=
– 4 + have?
A. Two solutions
B. One solution
C. No solutions
D. Infinitely many solutions
SUBMIT
Total employment for sheet metal workers in 2016 is projected to be 201,000. If this is a 6.3% increase from 2006,
approximately what was the tctal employment in 2006?
a. 214,000
b. 187,000
C. 195,000
d. 189,000
Answer:
D 189,000
Step-by-step explanation:
х
9) -5 +
-6
-16
please help!
Answer:
x = 16
Step-by-step explanation:
[tex]-5+\frac{x}{-16} =-6[/tex]
[tex]-5+\frac{16}{-16} =-6[/tex]
[tex]-5-1=-6[/tex]
[tex]-6=-6[/tex]
Answer:
101
Step-by-step explanation:
-5 + ×/-16=-6
-5+x=96
x= 101
A bacteria culture is growing at a rate of
r(t) = 7e^0.6t
thousand bacteria per hour after t hours. How much did the bacteria population increase during the first two hours? (Round your answer to three decimal places.)
Answer:
[tex]{ \bf{r(t) = 7e {}^{0.6t} }} \\ { \tt{r(2) = 7 {e}^{0.6 \times 2} }} \\ = { \tt{7 {e}^{1.2} }} \\ = 23.241 \: thiusand bacteria \: per \: hour[/tex]
Help me please asap!!
Answer:
angle BCA = 45 degree
Step-by-step explanation:
since it is an isosceles triangle , it's one angle is 90 degree whereas other two angles are 45 degree each.
Prove formally. Step by step with statements and reasons.
Answer:
K
K -> H
H
B -> ~H
H not B (sorry I couldn't type out the symbol)
~B
Step-by-step explanation:
Verbally, what's happening is this:
We have an assertion of K. Since K -> H (K implicates H), and B -> ~H (B implicates a negation of H), a negation of B (~B) is proven. (In this entire process, nothing is given about the symbols except K is true, hence the assertion, which then implicates that H is true and that B is negated since B implicates that negated H is true when in fact it is the opposite.)
Formally, the answer would be the following:
K
K -> H
H
B -> ~H
H not B (sorry I couldn't type out the symbol)
~B
Hope this helped!
If y= 5x- 2 were changed to y = x-2, how would the graph of the new
function compare with the first one?
O A. It would be less steep.
O B. It would be steeper.
O C. It would be shifted down.
OD. It would be shifted left.
Given right triangle ABC with altitude BD drawn to hypotenuse AC
Given:
In right triangle ABC, BD is the altitude drawn to hypotenuse AC.
[tex]AD=20, DC=45[/tex]
To find:
The length of BD.
Solution:
According to geometric mean theorem of triangles, if an altitude is drawn to the hypotenuse of a triangle, then the altitude is the geometric mean of the segments of the hypotenuse.
Using geometric mean theorem of triangles, we get
[tex]BD^2=AD\times DC[/tex]
[tex]x^2=20\times 45[/tex]
[tex]x^2=900[/tex]
Taking square root on both sides, we get
[tex]x=\dfrac{900}[/tex]
[tex]x=30[/tex]
Therefore, the length of BD is 30 units and the correct option is C.
Write the following sentence using mathematical symbols.
The product of 9 and x is less than or equal to - 40.
The answer is
Fran swims at a speed of 2.1 km/h in still water. The Lazy River flows at a speed of 0.7 km/h. How long will it take Fran to swim 10 km upstream?
What is Fran's speed while swimming upstream?
Answer: Fran's speed while swimming upstream = 1.4 km/h
Step-by-step explanation:
Given: Fran's swimming speed = 2.1 km/h
Speed of river = 0.7 km/h
The direction against the stream is called upstream.
Speed in Upstream = Fran's swimming speed - Speed of river
= 2.1-0.7 km/h
= 1.4 km/h
hence, Fran's speed while swimming upstream = 1.4 km/h
PLEASE HELP ME ASAP!
Answer:
A
Step-by-step explanation:
escribe un acto bueno de las personas y explica por qué es bueno
Answer:
Un buen acto o acción podría ser el donar dinero a la caridad, o contribuir con alimentos a comedores sociales. Estas serían buenas acciones porque, sin ninguna duda, ayudarían a contribuir con el bienestar de la sociedad, a través de la realización de medidas efectivas para luchar contra la pobreza, el hambre y la desigualdad de la población.
Find the difference of (4.2x10^3)-(2.7x10^3)
Show work!
Step-by-step explanation:
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The perimeter of a rectangle 6 5/7 ft and 2 5/6 ft
Which of the data sets below has a mean of 48? Select all that apply.
A) 51, 53, 43
B) 24, 91, 18, 65, 52
C) 65, 18, 72, 33, 52
D) 72, 18, 56, 46