Answer:
12 years
Explanation:
For an investment whose interest is compounded continuously, the amount in the account after t years is determined using the formula:
[tex]A(t)=P_oe^{rt}\text{ where }\begin{cases}{P_o=\text{ The amount invested}} \\ r=Interest\text{ }{Rate} \\ {t}=Time\end{cases}[/tex]In our given problem:
• A(t) = $6,000
,• Po = $4000
,• r = 3.5% = 0.035
We want to find the value of t.
Substitute the given values into the formula:
[tex]6000=4000e^{0.035t}[/tex]Then solve for t:
[tex]\begin{gathered} \text{ Divide both sides by 4000} \\ \frac{6000}{4000}=\frac{4000e^{0.035t}}{4000} \\ 1.5=e^{0.035t} \\ \text{ Take the ln of both sides:} \\ \ln(1.5)=\ln(e^{0.035t}) \\ 0.035t=\ln(1.5) \\ \text{ Divide both sides by }0.035 \\ \frac{0.035t}{0.035}=\frac{\operatorname{\ln}(1.5)}{0.035} \\ t=11.58 \\ t\approx12\text{ years} \end{gathered}[/tex]It will take Dennis 12 years (rounded to the nearest year) before he has $6,000 in his account.
The following table is a function.х15725354 9у-3 27-4 5971 0
a For any relation to be a function, an independent variable x cannot produce different dependent varible y
From the table,
when x = 5, y = 2
Also, when x = 5, y = 5
and when x = 5, y = 7
We can see that x= 5 produces 3 different values of y ( that is 2, 5, and 7). This has disobeyed the rule of a function
Hence, the table is not a function
The answer is False
which is the better buy and provide the unit price for your answer! $5.28 for 6 candy bars or $12.75 for 15 candy bars?
Answer:
Explanation:
Given:
$5.28 for 6 candy bars
$12.75 for 15 candy bars
To determine the better buy, we simplify each option first:
For $5.28 for 6 candy bars:
5.28/6 = $0.88 per candy bar
For $12.75 for 15 candy bars:
12.75/15 = $0.85 per candy bar
Therefore,
(7 x 10^-5) x (5 * 10^-8)= ?x 10^
1) Let's calculate that. Start by multiplying the factors 7, and 5.
[tex]\begin{gathered} 7\cdot10^{-5}\text{ x 5 }\cdot10^{-8}= \\ 35\cdot10^{-13} \end{gathered}[/tex]After that, we use the property of the exponents when multiplying. Repeat the base and then add the exponents -8 + (-5) = -8 -5 = -13.
Multiply the pair conjugates using the Product of Conjugates Pattern (simplify) (rs-2/5)(rs+2/5)
In order to calculate the product of a pair of conjugate terms, we can use the pattern below:
[tex](a+b)(a-b)=a^2-b^2[/tex]So we have:
[tex]\begin{gathered} (rs-\frac{2}{5})(rs+\frac{2}{5}) \\ =(rs)^2-(\frac{2}{5})^2 \\ =r^2s^2-\frac{4}{25} \end{gathered}[/tex]What is the LCM of 10 and 4?
One way to find the least common multiple of two numbers is to first list the prime factors of each number.
[tex]\begin{gathered} 10=2\cdot5 \\ 4=2\cdot2 \end{gathered}[/tex]Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor by the greatest number of times it occurs.
[tex]undefined[/tex]is rational or irrational v2
The square root of 2 is irrational
Here, we want to check if the square root of 2 is rational or not
When we talk of rational numbers, we mean numbers that can be expressed as the ratio of two integers
Roots of non-perfect squares such as two are not rational. They are referred to as irrational numbers. The special name they are called is surd
ВС: Round your answer to the nearest hundredth. B 2 7
opposite to angle 65 = BC
adjacent to angle 65 = 7
[tex]\tan \text{ }\theta\text{ = }\frac{\text{opposite }}{\text{adjacent}}[/tex][tex]\tan \text{ 65 =}\frac{BC}{7}[/tex][tex]\begin{gathered} BC\text{ = 7 x tan 65} \\ =\text{ 7 x 2.1445} \\ BC\text{ = 15.0115} \\ BC\text{ }\approx\text{ 15.01 (nearest hundreth)} \end{gathered}[/tex]What is an obtuse angle?A) Angle COAB) Angle BOAC) Angle DOBD) Angle DOA
An obtuse angle is an angle that measures more than 90° but not eauql or greater than 180°.
COA is the sum of COB and BOA, which is 90°, so COA is not obtuse.
BOA is 60°, so it is not obtuse.
DOA is a straight line, so it is 180°, so not obtuse.
DOB is COD plus COB. Since COA is 90°, DOC is also 90°, so DOC ples COB is 120°, which is between 90° and 180°, so DOB is obtuse and the correct alternative is C.
What is the probability of rolling a die (ordinary, 6-sided die with numbers 1, 2,3, 4, 5, 6) and getting a 7?
Let:
A = Getting a 7
a = Number of sides with 7
N = Number of sides
so:
[tex]\begin{gathered} P(A)=\frac{a}{N} \\ P(A)=\frac{0}{6} \\ P(A)=0 \end{gathered}[/tex]Graph the solution to the following system of inequalities.ys-2x-3y> 4x + 710-8-4-Х?10
Explanation
[tex]\begin{gathered} y\leq-2x-3 \\ y>4x+7 \end{gathered}[/tex]Step 1
First, graph the inequality 1
[tex]y\leq-2x-3[/tex]the related equation is
[tex]y=-2x-3[/tex]now, get 2 coordinates of the line
a) when x=1
[tex]\begin{gathered} y=-2x-3 \\ y=-2(1)-3 \\ y=-2-3 \\ y=-5 \\ so,\text{ the coordinate is (1,-5)} \end{gathered}[/tex]b)when x=0
[tex]\begin{gathered} y=-2x-3 \\ y=-2\cdot0-3 \\ y=0-3 \\ y=-3 \\ \text{coordinate P2}\Rightarrow(0,-3) \end{gathered}[/tex]now, draw a line that pases trought the coordinates we found.
Since the inequality is ≤ , not a strict one, the border line is solid
Step 2
Now, do the same for inequality 2
so
[tex]y>4x+7[/tex]the related equation is
[tex]y=4x+7[/tex]find 2 coordinates of the line
a)when x=0
[tex]\begin{gathered} y=4x+7 \\ y=4\cdot0+7 \\ y=0+7 \\ y=7 \\ so,\text{ the coordinate 3 is (0,7)} \end{gathered}[/tex]b) when x=-2
[tex]\begin{gathered} y=4x+7 \\ y=4\cdot-2+7 \\ y=-8+7 \\ y=-1 \\ so,\text{ the coordinate 4 is (-2},-1) \end{gathered}[/tex]now, draw the line 2, this lines passes trougth the coordiantes 3 and 4
Since the inequality is >, a strict one, the border line is dotted
Step 3
Graph:
in inequality (1) we need the values smaller r than -2x-3, it measn all values under the line,
and in Inequality 2 we need the values greater than 4x+7, it means all values over the line
so, the solution is the dark purple zone
I hope this helps you
Find the 55th term of the arithmetic sequence -7, -5, -3,
The given numbers are -7,-5,-3.
The common differen
I need help ASAP please can you help you help
OPTION C
A quartic function is a fourth-degree polynomial: a function that has, as its highest order term, a variable raised to the fourth power.
From our question, it was easy to
I need to write and simplify an algebraic expression for the perimeter of each shape.please help!
For the square, we have that each side's length is 2p, since the perimeter is the sum of the length of all sides of a geometric figure, this means that we have to add all the lengths of the square like this:
[tex]\begin{gathered} P=2p+2p+2p+2p_{} \\ \Rightarrow P=8p \end{gathered}[/tex]And we can do the same with the 3 sides of the triangle:
[tex]\begin{gathered} P=2x+2x+3x+1 \\ \Rightarrow P=7x+1 \end{gathered}[/tex]Where x is the horizontal distance in feet from the point at which the ball is thrown.How far from the child does the ball strike the ground?
To calculate the maximum distance that the ball takes, we can use the first and second derivatives of y to find out this. We have:
[tex]\begin{gathered} y=-\frac{1}{14}x^2+4x+3 \\ \Rightarrow y^{\prime}=-\frac{2}{14}x+4=-\frac{1}{7}x+4 \\ \Rightarrow y^{\doubleprime}=-\frac{1}{7} \end{gathered}[/tex]Using the second derivative criterion, we have that y'' < 0, therefore, we have a maximum in the root of the first derivative. For that, we get the following:
[tex]\begin{gathered} y^{\prime}=0 \\ \Rightarrow-\frac{1}{7}x+4=0 \\ \Rightarrow\frac{1}{7}x=4 \\ \Rightarrow x=7\cdot4=28 \\ x=28 \end{gathered}[/tex]Therefore, at x=28 is where the maximum distance is. Now we only substitute x=28 in y to find out:
[tex]\begin{gathered} y=-\frac{1}{14}(28)^2+4(28)+3 \\ \Rightarrow y=-\frac{1}{14}(784)+112+3 \\ \Rightarrow y=-56+112+3=59 \\ y=59 \end{gathered}[/tex]Finally, we have that the ball will go 59 feet from the child
if H & J equals 7 and 10s equals 10 find LK
The trapezoid HJKL has T and S as midpoints of the legs
The length of TS can be calculated as the mean or average of the lengths of HJ and LK, i.e.:
[tex]TS=\frac{HJ+LK}{2}[/tex]We are given the lengths HJ=14, LK=42, thus:
[tex]TS=\frac{14+42}{2}=\frac{56}{2}=28[/tex]Now if we have HJ=7 and TS=10, we can find LK by solving the equation for LK
[tex]LK=2TS-HJ[/tex][tex]LK=2*10-7=20-7=13[/tex]The length of LK is 13
Find the distance between vertices A and C of a regular hexagon whose sides are 20 cm each angle of the hexagon is 120 degrees
Use cosine law to find b:
[tex]b^2=a^2+b^2-2ac*cosB[/tex][tex]\begin{gathered} b^2=(20cm)^2+(20cm)^2-2(20cm)(20cm)*cos120º \\ b^2=400cm^2+400cm^2-800cm^2*(-0.5) \\ b^2=400cm^2+400cm^2+400cm^2 \\ b^2=1200cm^2 \\ b=\sqrt{1200cm^2} \\ b=20\sqrt{3}cm \\ b\approx34.64cm \end{gathered}[/tex]Then, the distance between A and C is 20√3 cm or approximately 34.64 cmCan you pls help with 7 I need to do 8 more packets like these by tomoghy
The daily rate can be found by dividing the total number of books over the number of calendar days.
15,260 / 28 = 545
545 books per day
"The distributive Property"
Using the distributive property, the maximum number of players that can be in the NBA is; 450 players
How to use distributive property?The distributive property is a property of algebra that states that you can distribute the contents of one parentheses into another to find an answer. For example;
a(b + c) = ab + ac
Now, we are told that there are 30 teams in the national basketball association and that each team has 12 healthy players plus three on injured reserve. Thus;
Number of players on each team = (12 + 3)
Now, for the 30 teams;
Total number of players for the teams = 30(12 + 3)
Applying distributive property, we have;
(30*12 + 30*3) = 450
Read more about distributive property at; https://brainly.com/question/2807928
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Glven: Circle P with center at (-2, 3) and a radius of 23. Identify the equation that could represent circle P. (3 – 2) + (y - 3)2 = 23 (2+2) + (y + 3)' = 23 (2 – 2)2 + (y + 3) = 23 (2+2)² + (y – 3)2 =23
The correct option is:
[tex](x+2)^2+(y-3)^2=23[/tex]Because we need to remember that the equation for a circumference centered in (h,k) and with radius r is:
please help. due today! will mark as brainliest!
Answer:
which question you want to be answered
Answer:
[tex]\textsf{13.\;a)}\quad d=\dfrac{P}{0.5 \pi +1}[/tex]
[tex]\textsf{13.\;b)}\quad d=14\; \sf inches[/tex]
Step-by-step explanation:
Question 13The perimeter, P inches, of a semicircle of diameter, d inches, is represented by the equation:
[tex]\boxed{P=0.5 \pi d+d}[/tex]
Part (a)
To express d in terms of P, rearrange the equation to isolate d.
Factor out the common term d from the right side of the equation:
[tex]\implies P=d(0.5 \pi +1)[/tex]
Divide both sides by (0.5π + 1):
[tex]\implies \dfrac{P}{0.5 \pi +1}=\dfrac{d(0.5 \pi +1)}{0.5 \pi +1}[/tex]
[tex]\implies \dfrac{P}{0.5 \pi +1}=d[/tex]
[tex]\implies d=\dfrac{P}{0.5 \pi +1}[/tex]
Part (b)
Given:
Perimeter = 36 in[tex]\pi \approx \dfrac{22}{7}[/tex]Substitute the given values into the equation derived in part (a) and solve for d:
[tex]\implies d=\dfrac{36}{0.5 \left(\frac{22}{7}\right) +1}[/tex]
[tex]\implies d=\dfrac{36}{\frac{11}{7} +1}[/tex]
[tex]\implies d=\dfrac{36}{\frac{11}{7} +\frac{7}{7}}[/tex]
[tex]\implies d=\dfrac{36}{\frac{18}{7}}[/tex]
[tex]\implies d=36 \times \dfrac{7}{18}[/tex]
[tex]\implies d=\dfrac{252}{18}[/tex]
[tex]\implies d=14[/tex]
Therefore, the diameter is 14 inches.
Enter an algebrak expression for the word expression. twice a number, minus 19 The expression is ?
x is an unknown number
twice a number means: 2x
and twice a number minus 19 means: 2x - 19
(x² + 5x - 2)-(3x²-x+4)
Given: (x² + 5x - 2)-(3x²-x+4)
Remove the parentheses:
[tex]=x^2+5x-2-3x^2+x-4[/tex]Add like terms:
[tex]\begin{gathered} =x^2-3x^2+5x+x-2-4 \\ =-2x^2+6x-6 \end{gathered}[/tex]Answer:
[tex]\begin{equation*} -2x^2+6x-6 \end{equation*}[/tex]Find the area of the shaded sector of the circle. Leave your answers in terms of pi
Answer:
D. 8pi yd^2
Explanation:
Area of a sector is expressed as;
[tex]A\text{ = }\frac{\theta}{360}\times\pi r^2[/tex]r is the radius of the circle
theta is the angle substended at the centre
Given the following
r = 9yd
theta = 360-200
theta = 160degrees
Substitute
A = 160/360 * pi(9)^2
A = 4/9*18pi
A = 72pi/9
A = 8pi yd2
Hence the area of the shaded sector is 8pi yd2
I need help with part b please
we have that
interval (-infinite,0) ------> f(x)=5x+4
interval [0, infinite) ------> f(x)=x+7
Part B
f(0)
For x=0 ------> belong to the interval [0, infinite)
so
f(x)=x+7
substitute
f(0)=0+7
f(0)=7Part C
f(3)
For x=3 ---> belong to the interval [0, infinite)
so
f(x)=x+7
substitute
f(3)=3+7
f(3)=10Write each equation in slope intercept form. Then graph .
ANSWER
EXPLANATION
Given;
[tex]y=-\frac{5}{6}x+4[/tex]Recall, the general formula for slope - intercept form is;
[tex]\begin{gathered} y=mx+c \\ m=slope \\ c=y-intercept \end{gathered}[/tex]comparing the given equation with the standard slope intercept form formula;
[tex]\begin{gathered} y=mx+c \\ y=-\frac{5}{6}x+4 \\ m=-\frac{5}{6} \\ c=4 \end{gathered}[/tex]Hence, the graph of the given equation is;
Giving a test to a group of students, the grades and gender are summarized below A B C TotalMale214 4 20Female1018 13 41Total1232 17 61If one student is chosen at random,Find the probability that the student did NOT get an "C". Round your answer to 3 decimal places_____.
Given:
⇒There are 61 students in total.
⇒12 of them got an A while 32 of them got a B.
⇒In total, 44 students did not get a C.
⇒So, 44 out of 61 students did not get a C.
Convert 44/61 into decimal form.
[tex]\frac{44}{61}=44\div61=0.721311\approx0.721[/tex]Answer:
The probability that a randomly chosen student did not get a C is 0.721 approximately.
3 batteries cost $5r and 8 folders cost $2r. Jason bought6 batteries and 4 folders. How much does he pay?Give your answer in terms of the
We are asked to determine the total amount paid for 6 batteries and 4 folders. To do that we need to determine the unit price of each item. We do that by dividing the amount spent by the number of items that were bought. That is:
[tex]\begin{gathered} n_b=\frac{5\text{ dollars}}{3\text{ batteries}} \\ \\ n_f=\frac{2\text{ dollars}}{8\text{ folders}} \end{gathered}[/tex]Now we multiply the desired number of items by each of the corresponding unit prices:
[tex]N=\frac{5}{3}\times6+\frac{2}{8}\times4[/tex]Solving the operations:
[tex]\begin{gathered} N=10+1 \\ N=11 \end{gathered}[/tex]Therefore, the total amount paid is $11.
I need help finding the angle measurements of 1 and 2
To find the angles 1 and 2:
In the above triangle, the angles opposite to the equal sides are equal.
Let us take,
[tex]\angle1=\angle2=x[/tex]So, using the angle sum property of a triangle
[tex]\begin{gathered} 55+x+x=180 \\ 2x=180-55 \\ 2x=125 \\ x=62.5^{\circ} \end{gathered}[/tex]Hence, the angles are
[tex]\begin{gathered} \angle1=62.5^{\circ} \\ \angle2=62.5^{\circ} \end{gathered}[/tex]If $163,300 is invested in an account earning 3.75% annual interest compounded semi-annually, how much interest is accrued in the first 4 years? Round to the nearest cent?
Solution:
An amount compounded is given as;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{Where;} \\ P=\text{ amount invested;} \\ r=\text{ interest rate;} \\ n=\text{ number of times interest applied per time period;} \\ t=\text{ number of time period elapsed.} \end{gathered}[/tex]Given that;
[tex]\begin{gathered} P=163,300 \\ r=0.0375 \\ n=2 \\ t=4 \end{gathered}[/tex]Thus, we have;
[tex]\begin{gathered} A=163300(1+\frac{0.0375}{2})^{2\times4} \\ A=163300(1.01875)^8 \\ A=189464.20 \end{gathered}[/tex]Thus, the interest accrued in the first 4 years is;
[tex]\begin{gathered} I=A-P \\ I=189464.20-163300 \\ I=26164.20 \end{gathered}[/tex]FINAL ANSWER: $26,164.20
Which of the following represents the factorization of the trinomial below?x2 – X-20A. (x-4)(x-5)B. (X + 4)(x-5)oC. (x-2)(x-10)0D. (x+2)(x-10)
Answer:
(x+4)(x-5)
Step-by-step explanation:
Second order polynomial in the following format:
ax² + bx + c = 0
Has roots x¹ and x².
Can be factored as:
(x - x¹)(x - x²)
So, we have to find the roots.
Finding the roots:
Bhaskara formula, which is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]In the polynomial given in this question:
a = 1, b = -1, c = -20
So
[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4\ast1\ast(-20)}}{2}=\frac{1\pm\sqrt{81}}{2}[/tex]The roots are:
[tex]x^1=\frac{1+9}{2}=5,x^2=\frac{1-9}{2}=-4[/tex]The factored form is:
(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)