The number of years the amount has been in the venture account with 12% interest per year is 4.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
A sum of $2,500 was deposited in a venture account, which pays 12% compounded per year and it accumulated to $3,950.
Then the number of the years will be
We know the compound interest formula
[tex]\rm A = P(1+r)^t[/tex]
where
A = Accumulated amount
P = Deposited value
r = rate of interest
t = time
Then we have
[tex]3950 = 2500 (1.12)^t\\\\1.58\ =1.12^t[/tex]
Taking log both sides, then we have
[tex]\rm \ln 1.58 = t \times \ln 1.12\\\\or \ \ \ \ t = 4.036 \approx 4 \ years[/tex]
Then the number of the years is 4.
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What is the value of x?
Please help me
Answer:
54=x
Step-by-step explanation:
2x+2=3x-52
this is because they are opposite alternating angles so now we can re arrange the equation.
54=x
Step-by-step explanation:
The both angles are vertically opposite angle so
[tex](2x + 2) = (3x - 52)[/tex]
By moving x on left side
[tex]2x - 3x = - 52 - 2[/tex]
So
[tex] - x = - 54[/tex]
Negative sign in both side are canceled so we got
[tex]x = 54[/tex]
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASEWhat is the RANGE of the function shown in the graph?
A.
B.
C.
D.
Answer:
D
Step-by-step explanation:
you can see can graph intersects the y axis at -3 and it goes upward forever.So minimum for y is
-3 so it is -3<y<infinity.
what is the domain of the function f(x)=6x+3
Answer:
All Real Numbers
Step-by-step explanation:
This is a linear function, so the domain is All Real Numbers, or (-∞, ∞). In other words, the all numbers on the x-axis are defined on the graph. We have no points where x is undefined or imaginary. Domain contains all real numbers.
BRAINLIEST please if this helped!Which ordered pair is a solution to the following system of inequalities? y ≤ –x2 + 8x y > x2 – 3 (–1, 4) (0, 9) (2, 7) (4, 3)
Answer:
(2, 7)
Step-by-step explanation:
(2, 7) are the coordinate which ordered pair is a solution to the following system of inequalities [tex]y \leq -x^2 + 8x \\[/tex] and [tex]y > x^2 - 3[/tex].
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
we want to find which ordered pair is a solution to the following system of inequalities.
[tex]y \leq -x^2 + 8x \\[/tex]
[tex]y > x^2 - 3[/tex]
The solution of a inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the inequality is the graph of all solutions of the system.
Graph one line at the time in the same coordinate plane and shade the half-plane that satisfies the inequality.
[tex]y \leq -x^2 + 8x \\\\y = -x^2 + 8x\\\\y > x^2 - 3\\\\[/tex]
x = 2 and y = 7
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50 points each question. Please help. How do I solve?
[tex]~~~~y= \sec^{-1} (14x)\\\\\\\implies \dfrac{dy}{dx} = \dfrac{1}{14x \sqrt{(14x)^2 -1}} \cdot 14\\\\\\\implies \dfrac{dy}{dx}=\dfrac{1}{x\sqrt{196x^2 -1}}\\\\\\\text{At point,}~~ (x_1,y_1) = \left(\dfrac{\sqrt2}{14}, \dfrac{\pi}4} \right), \text{slope of the tangent line,}\\\\\\m = \dfrac{dy}{dx} = \dfrac{1}{\dfrac{\sqrt 2}{14} \sqrt{196 \left(\dfrac{\sqrt 2}{14} \right)^2-1}} \\\\\\~~~~~~~~~~~=\dfrac{14}{\sqrt 2 }\\\\\\~~~~~~~~~~~=\dfrac{7\sqrt 2 \sqrt 2}{\sqrt 2}\\\\\\[/tex]
[tex]=7\sqrt 2\\\\\\\text{Equation of tangent line,}\\\\\\~~~~~y-y_1 = m(x -x_1)\\\\\\\implies y- \dfrac{\pi}4 = 7\sqrt 2 \left(x - \dfrac{\sqrt 2}{14} \right)\\ \\\\\implies y= 7x\sqrt 2 - 1+ \dfrac{\pi}4[/tex]
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Suppose the goal is to raise $600. One equation relating the calendar and poster sales to the $600 goal is 3c + 2p= 600. Suppose the company donating the calendars and posters said they would provide a total of $250 items.
Answer:
100 calendars and 150 postersStep-by-step explanation:
Note it seem the "$" shouldn't be in front of 250 as it is the numbe of itemsa) The second equation is
c + p = 250b) The graph of both equations is attached
The intersection point of the lines is (100, 150)
It indicates 100 calendars and 150 posters to be donated to meet both of targets $600 and 250 items.
Answer:
Given equation:
[tex]3c+2p=600[/tex]
where:
c = number of calendarsp = number of postersPart (a)If the company donating the calendars and posters said they would provide a total of 250 items then:
[tex]c+p=250[/tex]
Part (b)To graph:
Rewrite both equations to make p the subjectFind the c-interceptFind the p-interceptConnect the two points with a straight line[tex]3c+2p=600 \implies p=300-\dfrac{3}{2}c[/tex]
[tex]\textsf{x-intercept}: \quad 300-\dfrac{3}{2}c=0 \implies c=200 \implies (200,0)[/tex]
[tex]\textsf{y-intercept}: \quad 300-\dfrac{3}{2}(0)=300 \implies (0,300)[/tex]
[tex]c+p=250 \implies p=250-c[/tex]
[tex]\textsf{x-intercept}: \quad 250-c=0 \implies c=250 \implies (250,0)[/tex]
[tex]\textsf{y-intercept}: \quad 250-0=250 \implies (0,250)[/tex]
Point of intersection (equate equations):
[tex]\begin{aligned}300-\dfrac{3}{2}c &=250-c\\50 & =\dfrac{1}{2}c\\ c & =100\end{aligned}[/tex]
[tex]p=250-100=150[/tex]
[tex]\implies \left(100,150}\right)[/tex]
The point of intersection tells us that they need to sell 100 calendars and 150 posters to reach their goal of raising $600. Therefore, the company needs to provide 100 calendars and 150 posters (or 250 items in the ratio of calendars to posters of 2 : 3).
Fill in the blank with the correct number to balance the equation: 4Cr + 3O2 → Cr2O3
Answer:
2
Step-by-step explanation:
which expression is equivalent to 2^-5?
Answer:
1/32
Step-by-step explanation:
Basic theory: x ^ (-a) = 1 / x^ (+a)
2^(-5) = 1 / 2^(+5) = 1/ 32
Find the length of a using
the Pythagorean Theorem.
B
8
a
C
A
6
Hint: a² + b² = c²
Round your answer to the nearest tenth
Answer:
8.3
Step-by-step explanation:
8 square = 6 square + x square
square them
64 = 36 + x square
minus 64 with 36
64 - 36 = 28
cancel the square with square root
x square = 28
square root of 28 is 5.3
5.3 x 5.3 = 28.09
hope this helped you!
The profits earned in a year by some companies in a city are shown $160,000 $140,000 $130,000 $1120,000 $150,000 based on the data should the mean, or the median Be used to make the inference about the profits earned by the companies
Answer:
Median
Step-by-step explanation:
In this data set, there's a huge outlier ($1,120,000) which would skew the results upwards. Using the mean to make an inference about the profits would better represent the whole data set since you'd get $150,000 which is more in line with the rest of the data point.
John jumped 32 inches. Ella jumped 1 foot farther than John jumped. How far did Ella jumped?
2 ft 8 in
8 ft 6 in
3 ft 8 in
7 ft 2 in
The following table shows the low temperatures and the high temperatures, in degrees Fahrenheit, in four different cities on the same day. Find the difference between the low and the high temperatures in each city.
Answer:
Read explanation
Step-by-step explanation:
1st city. 8.1-(-17) OR 8.1+17 which is 25.1 degrees
2nd city. 3.2+16.8 is 20
3rd city. 33.1-3.9 is 29.2
4th city. -6+29 is 23 degrees
43. Find an equation of the tangent line to the curve [tex]y=10^{x}[/tex] at the point (1,10)
Answer:
23x-y=13
Step-by-step explanation:
we need to find the derivative with respect to x
In(y) =In(10^x)
In(y)=xIn(10)
now we have to take the derivative with respect to x
Therefore, y'=yIn(10)
where y'=10^xIn(10), Chain rule!
note: First derivative function always give us the gradient value when x value is substituted in
Therefore, at x=1, our gradient will be m= 10^1In(10)
Gradient m=23.0 to the nearest tenth
Finding the equation of the line
y-y1=m(x-x1)
y-10=23(x-1)
y-10=23x-23
y-23x=-23+10
y - 23x = -13
so, the equation of the line tangent line is
23x - y =13
13-28 Sketch the region enclosed by the given curves and find its area.
24. [tex]y=\cos x, \quad y=1-\cos x, \quad 0 \leqslant x \leqslant \pi[/tex]
Answer:
rea (A) 0.0682
Step-by-step explanation:
The sketch for the region enclosed by the given curves can be found in the image attached below.
From the image below;
The two curves intersect in the area of tan 9x = 2 sin 9x
Recall that:
making x the subject; then:
The subdivision of the domain is in two intervals
where;
Area (A) =
Area (A) = 0.06818
Area (A) 0.0682
Find - 3a - 6 when a = - 2. Write the answer in simplest form.
Answer:
-3(-2) - 6
6 - 6
= 0
Answer:
0
Step-by-step explanation:
-3a-6=-3×-2-6=6-6=0
Solve the equation by using the quadratic formula.
8x2 – 2x - 15 =0
Answer:
x = 3/2 or x = -5/4
Step-by-step explanation:
Solve for x over the real numbers:
8 x^2 - 2 x - 15 = 0
Using the quadratic formula, solve for x.
x = (2 ± sqrt((-2)^2 - 4×8 (-15)))/(2×8) = (2 ± sqrt(4 + 480))/16 = (2 ± sqrt(484))/16:
x = (2 + sqrt(484))/16 or x = (2 - sqrt(484))/16
Simplify radicals.
sqrt(484) = sqrt(4×121) = sqrt(2^2×11^2) = 2×11 = 22:
x = (2 + 22)/16 or x = (2 - 22)/16
Evaluate (2 + 22)/16.
(2 + 22)/16 = 24/16 = 3/2:
x = 3/2 or x = (2 - 22)/16
Evaluate (2 - 22)/16.
(2 - 22)/16 = -20/16 = -5/4:
Answer: x = 3/2 or x = -5/4
One positive integer is 1 less than twice another. The sum of their squares is 461. Find the integers.
Answer:
10 and 19
Step-by-step explanation:
In Algebra, an even number = 2x, because anything multiplied by 2 is even.There are two numbers in the question, I'll define the first one as 2xthe other number is 1 less than twice of the first, so I'm going to define it in algebra as 2(2x) - 1, which is just 4x - 1the square of the first is [tex]4x^2[/tex]the square of the second is [tex]16x^2-8x+1[/tex]add them together: [tex]20x^2-8x+1[/tex]this equation = 461, so [tex]20x^2-8x+1 = 461[/tex]simplify to [tex]20x^2-8x-460 = 0[/tex]I wont explain how to solve this here, since it is very complicated, if you don't know search up solving quadratics.the solutions are 5 or -4.6, it cannot be -4.6 since the question says positive, so the solution for x = 5substitute x into our equations for the two numbers in steps 1 and 2the first number = 10, the second = 19complete the table of values for y=x^2-4x+3
x=1
y=1²-4(1)+3=1-4+3=0x=2
y=2²-4(2)+3=4-8+3=7-8=-1x=3
y=3²-4(3)+3=9-12+3=12-12=0Colleen is cutting pieces of string to tie around party bags for her sister’s
birthday party. The length of each piece of string needs to be 8.75 inches.
If she has 100 party bags, what is the length of string Colleen needs to tie
all the bags?
Answer:
875 inches
Step-by-step explanation:
almost 73 feet!
What is the determinant of this matrix:
[tex]\left[\begin{array}{ccc}0&8\\7&0\end{array}\right][/tex]
Answer:
-56
Step-by-step explanation:
Formula to get determinant is::
[tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] = ad-bc[/tex]
0(0)-8(7)
0 - 56
-56
[tex]\\ \rm\Rrightarrow \left|\begin{array}{ccc}0 &8 \\ 7& 0\end{array}\right|[/tex]
[tex]\\ \rm\Rrightarrow 0-8(7)[/tex]
[tex]\\ \rm\Rrightarrow 0-56[/tex]
[tex]\\ \rm\Rrightarrow -56[/tex]
Is x = 0 a valid potential solution to the equation log(x + 2) + log(x + 5) = 1? (You don't need to solve this equation, just determine if x = 0 is a valid solution) Question 22 options: No, because log(0) is undefined. No, because the logarithm of a negative value is undefined. It can't be determined from the information given. Yes, since log(2) and log(5) both exist as valid values for the logarithm.
Answer:
Yes, since log(2) and log(5) both exist as valid values for the logarithm.
didnt check if ur equation is correct though
HELP PLEASE I BEG U - 10MIN LEFT
A rectangle is shown on a coordinate plane with vertices A(Negative 4, 8), B(1, 8), C(1, Negative 1), and D(Negative 4, Negative 1).
On a coordinate plane, a rectangle has 4 points. Point A is (negative 4, 8), point B is (1, 8), point C is (1, negative 1), point D is (negative 4, negative 1).
What are the dimensions of the rectangle?
The base is 4 units and the height is 9 units.
The base is 5 units and the height is 7 units.
The base is 5 units and the height is 9 units.
The base is 9 units and the height is 3 units.
The base is 5 units and the height is 9 units.
Base:
-4 to 1
=====
1 -(-4)
5 units
Height:
-1 to 8
=====
8 -(-1)
8 + 1
9 units
Simplify 2x-- yfor x = 3 and y=-2.
•20
•14
•16
•10
Answer:
8 (none of the above)
Step-by-step explanation:
Given that,
→ x = 3
→ y = -2
Let's solve the equation,
→ 2x - y
→ 2(3) -(-2)
→ 6 + 2
→ 8 is the answer.
Subtraction is the reverse operation of_____
Answer:
addition !
Step-by-step explanation:
Answer: subtraction is the reverse operation of Addition
Step-by-step explanation: Hope this helps,
Please help on math.
Answer:
[tex]\fbox{625 \: dollars }[/tex]
Step-by-step explanation:
Given:
from circular graph,
Savings by Oliver's = 25% of Total budget
Monthly budget = $ 2500
To find:
How much money does Oliver save?
Solution:
From diagram we came to know that,
Oliver's saving is 25% of total monthly budget.
Hence the money he saves each month will be 25% of $2500(Monthly budget)
To calculate the X percent of any given real number multiply the number with X and divide it by 100.
[tex] \sf \hookrightarrow \: 25 \% \: of \: 2500 \\ \sf \hookrightarrow 2500 \times \frac{25}{100} \\ \sf \hookrightarrow 2500 \times \cancel\frac{25}{100}_4 \\ \sf \hookrightarrow \: \frac{2500}{4} \\ \sf \hookrightarrow \cancel{\frac{2500}{4}} \: ^{625} \\ \sf \hookrightarrow \fbox{625 \: dollars }[/tex]
625$ does Oliver saves each month.
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The area of a rectangle is 72 square inches. The length is
12 inches. What is the width?
Answer: 6 inches
Step-by-step explanation: the area of a rectangle is width times length, that is [tex]A = w.l[/tex]
In this case we have:
Area A = 72 square inchesWidth w = 12 inchesSo to get the Lenght l we need to divide [tex]l = \frac{A}{w}[/tex]
[tex]l = \frac{72}{12}[/tex]
[tex]l = 6[/tex]
f(x)= 4/5x +7
What is the value of f(5)?
Answer: 11
Step-by-step explanation:
Can someone tell me the formula of this shape so that i can solve it and would it be the ² or the ³ and last what number in this problem do i not use thank u
Answer:
660 ft³
Step-by-step explanation:
The way I'm thinking of it, we can think of it as a triangle and then extruding out from that triangle for the length.
First, the triangle:
area = base * width / 2 = 12 * 10 / 2 = 60 ft²
volume = the triangle for the length
the length is 11 feet,
so we extrude that triangle for 11 feet to get
60 ft² * 11 ft = 660 ft³
we multiply 10 ft by 12 ft by 11 ft. there are 3 instances of ft, so the corresponding exponent is therefore ³.
another way to think of the extrusion is like a rectangular prism, the formula for a rectangular prism's volume is length * width * height. we're extruding from the bottom rectangle for the whole of the height, so we multiply the area of the bottom triangle (length * width) by height.
this might be confusing so let me know if you have any questions!
The transformation (x, y) to (x+4, y-3) is preformed on the line segment AB. The image is the line segment A'B' where point A' = (3, -3) and point B' = (5, -3). What are the coordinates of A and B in line segment AB?
A) A = (-1, 6), B = (1, -6)
B) A = (-1, 0), B = (1, 0)
C) A = (7, 6), B = (9, -6)
D) A = (7, 0), B = (9, 0)
Answer:
B) A = (-1, 0), B = (1, 0)
Step-by-step explanation:
If the transformation of AB to A'B' is (x+4, y-3),
then the transformation of A'B to AB is the reverse: (x-4, y+3)
Given
A' = (3, -3) → A = (3-4, -3+3) = (-1, 0)
B' = (5, -3) → B = (5-4, -3+3) = (1, 0)
Therefore:
A = (-1, 0), B = (1, 0)
Fred bought 5 pounds of ground beef. He will share the ground beef equally with Janice and Ralph. How much ground beef will each person get.
The question is an illustration of ratio, each person will get 1.67 pounds of ground beef
How to determine each person's share?The given parameters are:
Ground beef = 5 pounds
People = 3 i.e. Fred, Janice and Ralph
The amount gotten by each person is:
Share = 5 pounds/3
Evaluate the quotient
Share = 1.67 pounds
Hence, each person will get 1.67 pounds of ground beef
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