Let's use the simple interest formula:
[tex]FV=PV\cdot r\cdot t[/tex]Where:
FV = Future value = $6050
PV = Present value = $5000
r = interest rate
t = time = 3
Replacing the data into the equation:
[tex]\begin{gathered} 6050=5000\cdot r\cdot3 \\ 6050=15000r \\ \text{Solving for r:} \\ \frac{6050}{15000}=r \\ \\ r\approx0.4033\approx40.33 \end{gathered}[/tex]r = 40.33%
The formula for the area of the shaded
region on the diagram is:
Area of the circle - Area of the square
The area of the circle is 67.1 cm² rounded to
1 decimal place.
The area of the square is 12.3 cm² truncated
to 1 decimal place.
Write the error interval for the area, a, of the
shaded region
The error interval of the area a of the shaded region
What is Error Interval?
Error intervals are the limits of accuracy when a number has been rounded or truncated. They are the range of possible values that a number could have been before it was rounded or truncated.
Given,
Area of the circle = 67.1cm²
Area of the square = 12.3cm²
According to the question:
The formula for the area of the shaded
region on the diagram is:
Area of the circle - Area of the square
Putting the value of Area of circle and Area of square
= 67.1cm² - 12.3cm²
= 54.8cm²
The Error interval of area a = 54.8 + 0.5 and 54.8 - 0.5
= 54.85 and 54.75
Hence, Area of shaded region is 54.85< a < 54.75
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Find the slope of the line graphed below
Answer:
Go up 8 and right 2
8/2
Step-by-step explanation:
(a) An angle measures 60°. What is the measure of its supplement?
measure of the complement:
(b) An angle measures 31°. What is the measure of its complement?
Answer:
(a) 120°
(b) 149°
Step-by-step explanation:
Supplementary angles add up to 180°
So to find the supplement of a given angle just subtract its measure from 180
(a) 180 - 60 = 120°
(b) 180- 31 = 149°
a) the supplementary angle of 60 degree is 120 degrees.
b) the complimentary angle of 31 degree is 59 degrees.
Supplementary angles are those angles whose sum comes out to be 180 degrees. to find a supplement of an angle we need to subtract the given angle from 180 degree.
supplement of 60 degree (here given angle is 60 degree)
= 180 - given angle = 180 - 60 = 120 degree
Complimentary angles are those angles whose sum comes out to be 90 degrees. To find a compliment of an angle we need to subtract the given angle from 90 degree.
compliment of 31 degree (here given angle is 31 degree)
= 90 - given angle = 90 - 31 = 59 degree
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Question
The manufacturer of pencils spends $0.05 to make each pencil and sells them for 0.25. The manufacturer also has fixed
costs each month of $2000.
Find the revenue function R when x pencils are manufactured.
Answer:C(x) = 2000+ 0.05 x
Step-by-step explanation: Cost (C) = fixed cost + (cost per pencil x number of pencils)
Since:
Fixed cost: $2000
Cost per pencil : $0.05
Replacing with the values given:
C(x) = 2000+ 0.05 x
Where x is the number of pencils manufactured.
Feel free to ask for more if needed or if you did not understand something.
Is the shape a polygon?
Answer:
Yes
Step-by-step explanation:
Because a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
Find the mystery number. If you multiply it by 1, then add 5, and finally subtract 2 you get 3. What is the mystery number?
The mystery number is y = 0.
A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), operations, variables, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Let's assume the mystery number to be y.
When we multiply it by 1, add 5, and finally subtract by 2 we obtain 3.
Using the statement we obtain the expression,
y × 1 + 5 - 2 = 3
y + 5 - 2 = 3
y + 3 = 3
Subtracting 3 from each side of the equation,
y + 3 - 3 = 3 - 3
y = 0
Hence the mystery number is 0.
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What is 2 1/2 ÷ 2 5/8
Answer: THE ANSWER IS 20/21
Step-by-step explanaTion:
Answer:
[tex]5\frac{1}{8}[/tex]
Step-by-step explanation:
[tex]=\frac{5}{2} +\frac{21}{8}[/tex]
[tex]=\frac{40+42}{16}[/tex]
[tex]=\frac{82}{16}[/tex]
[tex]=\frac{41}{8}[/tex]
[tex]=5\frac{1}{8}[/tex]
Hope this helps
The temperature in a town is 26.2F during the day and -11.2F during the night Find the difference in the temperatures.
what is the differience
The difference in the temperatures of the town is -37.4 degrees Fahrenheit.
What is the difference between the two values?The difference between two values refers to the result of a subtraction operation.
A subtraction operation has the following parts: minuend, subtrahend, and difference.
In this situation, the minuend is 26.2F while the subtrahend is -11.2F.
Thus, the difference results from subtracting -11.2F from 26.2F, which is -37.4F, showing that the temperature is reduced by -37.4F to reach -11.2F during the night.
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using long division
helo me please show your complete ssolutions
Step-by-step explanation:
Make the facts and then you can get the answer easily
math is hard ok
attachments below
The measurement that does not represent the dimension of the triangle is 15, 30 and 45cm
The measurement that does represent the dimension of the triangle is 4, 8 and 10 cm.
What are the measurements?Two triangles are similar if the ratio of the side lengths of the triangle are equal.
The ratio of the length of the triangles are 6 cm : 12 cm : 15 cm
Express the ratio in its simplest form - 2 cm : 4 cm : 5 cm
Ratio of 12, 24 cm and 30cm in its simplest form - 2 : 4 : 5
Ratio of 10, 20 and 25cm in its simplest form - 2 : 4 : 5
Ratio of 18, 36, 45cm in its simplest form - 2 : 4 : 5
Ratio of 15, 30 and 45cm in its simplest form - 1 : 2 : 3
Ratio of 4, 8 and 10 in its simplest form - 2 : 4 : 5
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A train travels 16 miles in 20 minutes . At this rate ٫ how many minutes will it take to travel 12 miles
We will establish simple proportions. If [tex]16[/tex] miles takes [tex]20[/tex] minutes, how many minutes for [tex]12[/tex] miles?
[tex]16miles/20min[/tex][tex]0.8miles/min[/tex]That makes [tex]12[/tex] miles in [tex]15[/tex] minutes.
[tex]0.8(12)=12miles/?min[/tex][tex]?=15min[/tex]45 divided by 3 to the power of 2 minus 37
Answer:
-32
Step-by-step explanation:
Answer:
-32
Step-by-step explanation:
45:3=15:3=5-37=-32
hope it helps
have a nice night with apples))
Helppppp please!!! Immediately
Barbara, Mark, and Carlos participated in the third heat of “The Big Race.” Barbara thought she could win with a 3 meter head start even though she only pedaled 3 meters every 2 seconds. Mark began at the starting line and finished the 20 meter race in 5 seconds. Meanwhile, Carlos rode his tricycle so that his distance (y) from the starting line in meters could be represented by the equation y= 5/2x+1 where x represents time in seconds.
1)What is the dependent variable?
2)What is the independent variable?
3)Write an equation that discribes Barbara's motion. HINT: Write the equation in y=mx+by=mx+b form, where mm is the rate of change and bb is the starting point.
4)Write an equation that discribes Mark's motion. HINT: Write the equation in y=mx+by=mx+b form, where mm is the rate of change and bb is the starting point.
5)How fast did Carlos pedal? Write your answer as a unit rate
6)When did Carlos pass Barbara?
The measure of a supplement of an angle is 35 more than twice the complement of the angle. Find the measures of the angle, its supplement, and its complement.
The measure of the angle is 35°. The complement is 55° and the supplement is 145°.
How to calculate the angle?Let's measure of the angle = x
Supplementary angle of x = 180° - x
Complementary angle of x = 90° - x
By the given condition
180° - x = 2(90° - x) + 35°
Find the measure of the angle
180° - x = 2(90° - x) + 35°
⇒ 180° - x = 180° - 2x + 35°
⇒ - x = - 2x + 35°
⇒ - x + 2x = 35°
⇒ x = 35°
The measure of the angle = 35
The complement will be:
= 90° - 35° = 55°
The supplement will be:
= 180° - 35° = 155°
The concept illustrates how angles are calculated.
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f(x) = 6 - 1/(x-4)
Determine the value that the function f approaches as the magnitude of x increases. (If you need to use or –, enter INFINITY or –INFINITY, respectively.)
The value of the function as x increases comes closer to 6 and at limit x→∝ the value is 6.
In mathematics, a limit is the value that such a function (or sequence) gains as the input (or index) gets closer to a particular value.
Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.The concept of a limit of a series is further generalized to encompass the concept of such a limit of a topological net, in addition to being strongly related to limit and indirect limit in category theory.Several different converging ideas can be defined on function spaces. This sometimes relies on how frequently the area is set up. Two well-known examples of function spaces having a notion of convergence are Lp spaces and Sobolev space.Given the function is [tex]f(x) = 6-\frac{1}{x-4}[/tex]
Now we put the limit to the function as [tex]lim_{x\rightarrow \infty} f(x)[/tex]
Therefore :
[tex]lim_{x\rightarrow \infty} (6-\frac{1}{x-4})\\=lim_{x\rightarrow \infty} 6 - lim_{x\rightarrow \infty}\frac{1}{x-4}\\=6 - 0\\=6[/tex]
Hence the value of the function is 6.
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The sales tax rate is 5%. If Abdul buys a wheelbarrow priced at $79, how much tax will he
pay?
Answer:
$3.95Step-by-step explanation:
GivenPrice = $79,Sales tax = 5%.SolutionFind 5% of $79:
79 * 5/100 = 395/100 = 3.95Answer:
Abdul must pay $ 3.95.
Step-by-step explanation:
Now we have to,
→ find the amount of tax he must pay.
Then the amount will be,
→ (79/100) × 5
→ 0.79 × 5 = $ 3.95
Hence, he must pay $ 3.95.
Simplify (4x −3+2x²) + (2x + 1)
Answer: 2x^2 + 6x - 2
Step-by-step explanation:
4x - 3 - 2x^2 + 2x + 1 =
2x^2 + 6x - 2
Find the non-extraneous solutions of the square root of the quantity x plus 7 minus 4 equals quantity x plus 3
The non-extraneous solutions of the square root of the quantity x plus 7 minus 4 equal quantity x plus 3 is: x = -7 and x =-6.
How do we find the non-extraneous solutions?
The non-extraneous solution can be found with this calculation:
[tex]\sqrt{x} + 7 - 4 = x + 3\\\\\sqrt{x} + 7 = x + 7\\\\[/tex]
Now, we will square both sides:
[tex](x + 7) = (x + 7)^{2} \\\\(x + 7) = (x+7) (x+7)\\\\x + 7 = x^{2} + 14x + 49\\\\x = x^{2} + 13x + 42\\\\0 = (x + 7) (x+6)\\[/tex]
Thus, we have; x = -7 and x = -6
Note that we collected like terms from the figures on the left-hand-side to the figures on the right-hand side. When the lowest common multiple betwen 14 and 42 was checked, figures 7 and 6 were gotten.
When we plug figure x into both equations, we get the same figures and this confirms the solution.
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Caleb lost 32 of his marbles when playing against his brother. if he began the game with 56 marbles, what fraction of his original marbles does he have left as a fraction?
Answer:
3/7
Step-by-step explanation:
Hey there!
To find this out, we have to put the numerator of the fraction as the number of marbles he has left, and the denominator as the number of marbles he had in total before he played
# of marbles in total - 56
# of marbles he has left - (56 - 32) 24
Fraction - 24/56
Simplify - 24/56 --> 3/7
So, the fraction of his original marbles he has left as a fraction is 3/7
find the sum or difference 6 3/5 - (-2 1/5)
A. -4 2/5
B. 8 4/5
C. -8 2/5
D. 4 2/5
Answer:
B
Step-by-step explanation:
Fraction subtraction:
[tex]\sf 6 \dfrac{3}{5}-(-2\dfrac{1}{5})=6\dfrac{3}{5}+2\dfrac{1}{5}[/tex]
Convert mixed fraction to improper fraction,
[tex]\sf = \dfrac{33}{5}+\dfrac{11}{5}[/tex]
Now, add.
[tex]\sf = \dfrac{33+11}{5}\\\\=\dfrac{44}{5}[/tex]
Covert improper fraction to mixed fraction.
[tex]\sf = 8\dfrac{4}{5}[/tex]
And the question below
Answer:
(a) 2nd Choice: The amount of time he has walked (in hours) when he is x kilometers from Glen City
(b) [tex]D^{-1}(x) = \dfrac{11.6 - x }{4}[/tex]
(c) [tex]D^{-1}(6.4) = 1.3 \;\text{hours}[/tex]
Step-by-step explanation:
(a)
Since D is distance in km from Glen City after t hours of walking, the inverse D⁻¹ would be the time taken in hours to walk x kilometers from the city. So the second choice
(b)
[tex]D^{-1}(x) = \dfrac{11.6 - x }{4}[/tex]
To find the inverse of a function y = f(x), interchange y and x and solve
y = 11.6 - 4x (using x instead of t)
Interchange y and x ==> x = 11.6 - 4y
Add 4y to both sides ==> 4y + x = 11.6 - 4y + 4y = 11.6
Subtract x from both sides ==> 4y = 11.6 - x
Divide both sides by 4 ==> y = (11.6 - x)/4
(c) [tex]D^{-1}(6.4) = \dfrac{11.6 - 6.4 }{4} = \dfrac{5.2}{4} = 1.3 \;\text{hours}[/tex]
What is the avrage length finger nails will grow in 12 months
The average length by which finger nails will grow in 12 months will be 60mm, considering that they grow by an average of 5mm every month.
As per the question statement, there is no information provided about the average monthly growth of fingernails, and we required to calculate the average length by which finger nails will grow in 12 months.
To solve this question, we assumed that, the fingernails grow by an average of 5mm every month.
Now, using the unitary method, we can form a series of Mathematical statements to solve this question, which goes as follows:
If the average monthly growth of fingernails is 5mm,
It means that, fingernails grow in 1 month, by an average of 5mm.
Therefore, they will grow in 12 months, by an average of (5 * 12) = 60mm.
Average: In Mathematics and Statistics, the mean or average refers to a central tendency among a set of values in a sample or observation, calculated by the sum of all the values in the set, divided by the number of elements in that set.To learn more about Average, click on the link below.
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The monthly sale (in thousands of units) for the t^th month after the introduction of a product in the market is given by S = 135t/(t^2 + 50). In which earliest month would the sale (S) have been 9?
Given the following equation:
[tex]\text{ S = }\frac{135t}{t^2\text{ + 50}}[/tex]Let's determine t at S = 9.
We get,
[tex]\text{ 9 = }\frac{135t}{t^2\text{ + 50}}[/tex][tex]\frac{9(t^2+50\rparen}{9}\text{= }\frac{135t}{9}[/tex][tex]\text{ t}^2\text{ + 50 = 15t}[/tex][tex]\text{ t}^2\text{ -15t + 50}[/tex]a = 1, b = -15 and c = 50
Apply the quadratic formula:
[tex]\text{ t = x = }\frac{-\text{b }\pm\text{ }\sqrt{\text{b}^2\text{ - 4ac}}}{\text{ 2a}}[/tex][tex]\text{ = }\frac{\text{ -\lparen-15\rparen }\pm\text{ }\sqrt{(-15)^2\text{ - 4\lparen1\rparen\lparen50\rparen }}}{\text{ 2\lparen1\rparen}}[/tex][tex]=\text{ }\frac{\text{ 15 }\pm\text{ }\sqrt{\text{ 225 - 200}}}{\text{ 2}}[/tex][tex]\text{ = }\frac{\text{ 15 }\pm\text{ }\sqrt{\text{25}}}{\text{ 2}}[/tex][tex]\text{ = }\frac{\text{ 15 }\pm\text{ 5}}{\text{ 2}}[/tex][tex]\text{ x}_1\text{ = }\frac{\text{ 15 + 5}}{\text{ 2}}\text{ = }\frac{20}{2}\text{ = 10th month}[/tex][tex]\text{ x}_2\text{ = }\frac{\text{ 15 - 5}}{\text{ 2}}\text{ = }\frac{\text{ 10}}{\text{ 2}}\text{ = 5th month}[/tex]Therefore, the earliest month will be either the 5th or 10th month.
Among the given choices, only the 10th month is in the choices.
Therefore, the answer is CHOICE B : 10th
pls help will mark brainliest
The simplest form of the graph is 3x + 0y = 0
And the values of A and B are 3 and 0 respectively.
The point which is plotted in the graph : (3, 0)
What is the general form of linear equation?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). Additionally, when resolving systems of two linear equations, this form is highly helpful.
The given general form of equation is Ax+By+C= 0
So as in this graph it is clearly visible that:
A= 3 and B= 0
Thus we can write it as 3x + 0y = 0
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use the trapezoidal rule, the midpoint rule, and simpson's rule to approximate the given integral with the specified value of n. (round your answers to six decimal places.) 4 0 ln(3 ex) dx, n
a. Trapezoidal Rule- 9.413607
b. Midpoint Rule-9.393861
c. Simpson's Rule -9.400407
a. We use n=8 for this integral, .Δt=4-0/8=0.5
Therefore the integral range is[0,0.5,1.0,1.5......3.0,3.5....4.0 ]
#For the Trapezoidal Rule:
[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Tn=[/tex]Δr/2[∫([tex]x0[/tex])+2∫(x1)+....+∫(xn)]
=[tex]\int\limits^4_0[/tex][tex]In(2+ex[/tex])dx≈[tex]T8[/tex]
=0.5/2[[tex]In[/tex](2+[tex]e0.0[/tex])+2In(2+e0.5)+2In(2+e1.0)+....+2In(2+e3.5)+In(2+e4.0)]
=0.25[1.098612+2.588754+3.102889+3.737962+4.479090+5.304017+6.189846+7.117283+4.035976]
≈9.413607
Hence, the approximate integral value using Trapezoidal rule is 9.413607
b.For the Midpoint Rule, we calculate the integral as:
[tex]\int\limits^a_b[/tex]∫(x)dx≈[tex]Mn=[/tex]Δx[∫[tex](x1)[/tex]+∫([tex]x2)[/tex]........∫([tex]xn)}[/tex]
x1 is the midpoint of the ith interval.
From our interval ,[0,0.5,1.0,1.5....3.0,3.5,4.0]the applicable intervals are
[0.25,0.75,1.25,2.25,2.75,3.25,3.75]
We therefore have the integral value as:
=4/8[[tex]In[/tex](2+[tex]e0.25[/tex])+In(2+[tex]e0.72[/tex])+In(2+[tex]e1.25[/tex])+....+In(2+[tex]e1.75[/tex])+In(2+[tex]e2.25[/tex])[tex]In[/tex](2.75)+In(2+e0.5)+In(2+e1.0)]
Hence, the approximate integral value using the Midpoint Rule is 9.393861
c. For the Simpson's Rule, we calculate the integral rule as follows:
Hence, the approximate integral value using the Simpson's Rule is 9.400407
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what is (tan x + cot x) sin x * cos x ?
pls helppp
(tan x + cot x) sin x * cos x is 1
(tan x + cot x) sin x * cos x
= (tan x + 1 / tan x) sin x * cos x because cot x = 1 / tan x
= (((tan x) ^2 + 1) / tan x) sin x * cos x because (tan x) ^2 +1= (sec x) ^2
= (sin x / cos x) tan x
= tan x / tan x
= 1
Use the scatter plot to answer the question.
A scatter plot with points at (negative 16, negative 7), (negative 9, negative 5), (negative 3, negative 3), (1, 2), (5, 4), (8, 3) & (14, 6).
Which function best fits the data in the scatter plot?
f(x)=2x−3f of x is equal to 2 x minus 3
f(x)=2x+1f of x is equal to 2 x plus 1
f(x)=12x−3f of x is equal to 1 half x minus 3
f(x)=12x+1
Using linear regression, the function that best fits the data in the scatter-plot is given by:
f(x) = 1/2x + 1.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the context of the problem.
The scatter-plot in this problem contains these following points:
(-16, -7), (-9, -5), (-3, -3), (1, 2), (5, 4), (8, 3) and (14,6).
Inserting these points into a calculator, the equation is given by:
f(x) = 0.46835x + 1.
Approximating the slope to 1/2 considering the given options, the function is given by:
f(x) = 1/2x + 1.
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PLEASE HELP ASAP
The math counts club had a party at school. There were cookies and 40 slices pizza with nothing left pizza to be shared equally. Each students had the same number of whole cookies and the name number of slices of pizza with nothing left over. How many students How many students could have been at the party? (There is more than one answer. List as many as you can)
Answer:
There could have been 5, 10, or 20 students at the party.If there were 5, each student got 4 cookies and 8 slices of pizza if there were 10, each student got 2 cookies and 4 slices of pizza if there were 20, each student got 1 cookie and 2 slices of pizza
elrond is organizing a council in rivendell. he has invited two men, two dwarves, and two elves, and plans to seat them along with himself in a circle with seven seats. he knows that dwarves and elves do not get along, so he plans to seat them so that no dwarf is sitting next to an elf. the circle has a head chair. if elrond (himself an elf) must sit at the head of the circle, in how many ways can he seat the other six guests? all beings are distinguishable from one another, and the head chair is distinguishable from the other chairs.
Elrond can sit his guest in 15 ways around the circle such that all conditions are fulfilled.
A cycle is a shape made up of all the points in a rectangle that are a certain distance from the center. It is the curve drawn by a moving location in a rectangle so that the radius from a given stage remains constant.
The radius of a circle is the distance between any two locations on the circle and the canter.
In most cases, the radius must be positive. A circle with r=0 is a degenerate instance. This section is about rounds in Euclidean geometry, primarily the Euclidean plane, unless otherwise noted.
Now we have to consider the conditions:
Elrond is holding a council at Rivendell. He's invited two men, two dwarves, and two elves, and plans to seat them all in a circle with seven seats, including himself. so 5+6=11
He understands that dwarves and elves do not get along, therefore he plans to arrange them so that no dwarf seats next to an elf. In the center of the circle is a chair. Hence 2=2 = 4
Number of ways = 11+4 = 15
Therefore Elrond can sit his guest in 15 ways around the circle such that all conditions are fulfilled.
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The radius of the wheel of a unicycle is 14 inches. What is the
distance, in inches, that the unicycle covers after 10 full
rotations of the wheel? Use 3.14 for pi
Step-by-step explanation:
We need to find the circumference of the equation.
One circle circumference is a circle full rotation.
[tex]c = \pi(d)[/tex]
[tex]d = 2r[/tex]
[tex]c = 2r\pi[/tex]
R is 14.
[tex]c = 28\pi[/tex]
We need a rotation 10times so
[tex]10 \times 28\pi = 280\pi[/tex]
