The amount you will have $6,500 with 5% in six years using continuous compounding is of:
$8,774.
The amount you will need to have the entire $32000 in the 6 years is of:
$18,890.46.
What is continuous compounding?The balance of an account after t years, using continuous compounding, is given as follows:
[tex]B(t) = Pe^{kt}[/tex]
In which the parameters are given as follows:
P is the principal, which is the initial investment.k is the APR, as a decimal.Putting the $6,500 into the account, the values of the parameters are given as follows:
P = 6500, k = 0.05, t = 6.
Hence the balance will be of:
B(6) = 6500 x e^(0.05 x 6) = $8,774.
The balance to have the entire $32,000, considering what you already have, will be of:
32000 - 6500 = 25500
Hence the principal is obtained as follows:
Pe^(0.05 x 6) = 25500
P = 25500/e^(0.3)
P = $18,890.46.
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Find the slope of the line that passes through all of the points
on the table.
8
2
5
8
11
14
Y
2
-6
-14
-22
-30
Only need the answer
Answer:
-8/3
Step-by-step explanation:
PLEASE HELP IM SCREWED
Number 13 and 15
Answer:7
Step-by-step explanation:
y=-3x-17 y=x-1 solving linear equations by substitions
x=-4, y=-5
You can substitute equation 2 into equation 1 since it's easier. After that, just substitute x=-4 back into equation 2.
x/7= -10 what is the answer????
The answer is x = -70.
To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.
Multiply all terms by the same value to eliminate fraction denominators
/7 = −10
7⋅/7 = 7(−10)
Cancel multiplied terms that are in the denominator
7⋅/7 = 7 (−10)
x =7(-10)
Multiply the numbers
=7(−10)
=−70.
Hence The answer is x = -70.
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78900 grams into kilograms
78.9 kg.
To convert 78,900 grams to kilograms, we can divide the number of grams by 1,000. Since 1 kilogram is equal to 1,000 grams, dividing the number of grams by 1,000 will give us the equivalent number of kilograms.
Therefore, 78,900 grams is equivalent to 78,900 / 1,000 = 78.9 kilograms.
Susan runs 6 miles in 50 minutes. At the same rate, how many miles would she run in 35 minutes?
Answer:
Step-by-step explanation:
4.2 miles
Two angles of a triangle have the same measure and the third one is 60 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
The Largest Angle has a measure of 100 degrees and measure of other two angles is 40 degrees each.
What is angle sum property of a triangle?
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
According to the given question:
In triangle ABC, angle ABC equals to angle ACB and BAC is the largest angle.
Let angle measure of ABC and ACB angles be x degree then, measure of third angle BAC will be x + 60 degrees.
Since sum of all angles of any triangle is 180 degree.
x + x + (x + 3) = 180
3x = 180 - 60
3x = 120
x = 40 degrees
So, First angle = 40 degree
Second angle = 40 degree
Third Angle = 100 degree.
The Largest Angle angle has a measure of 100 degrees.
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Determine whether the following graphs describe relations, and whether they describe functions.
Answers: A.function B.Relation C.Neither D.Both
Answer: D
Step-by-step explanation:
The table shows the number of cars washed each hour during a fundraiser hour 1, 22 cars, hour 2, 30 cars, hour 3, 35 cars, To the nearest tenth, what was the percent of increase in cars washed from hour 2 to hour 3
The percentage increase in the number of cars from hour 2 to hour 3 is 16.7%
How to determine the percentage increase in the number of cars?In this question, we have the given figures that can be used in our computation:
Hour 1 = 22 cars
Hour 2 = 30 cars
Hour 2 = 35 cars
We want to calculate the percentage increase in the number of cars
So, we make use of only the following parameters
Hour 2 = 30 cars
Hour 2 = 35 cars
These figures can be represented as
Initial amount = 30
Final amount = 35
The percentage of the increase of the cars is then calculated using the following percentage equation
Increase percentage = (Final amount - Initial amount)/Initial amount * 100%
Substitute the known values in the above equation, so, we have the following representation
Increase percentage = (35 - 30)/30* 100%
Evaluate
Increase percentage = 16.7%
Hence, the increase percentage is 16.7%
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Which graph best represents a function with a domain of all real numbers greater than or
equal to 5?
Answer:
(c)
Step-by-step explanation:
You want the graph that has a domain of x ≥ 5.
DomainThe domain of a function is the set of x-values for which the function is defined. A domain of x ≥ 5 means the function is defined for x-values at least 5. The graph of the function will extend from x=5 indefinitely to the right.
Graph C is like that.
The figure below will be rotated 90º clockwise about the origin, translated 9 units down, and then reflected about the y-axis.
When the figure passed through the transformations the image formed is similar to the image at B as attached
How to get the image of the transformationThe figure is in the second quadrant
clockwise rotation 90degrees about the origin will being the figure to the first quadrant
Translation 9 units down will bring an image to the -6 of the y direction in the fourth quadrant
reflection over the y axis will create a mirror image of the figure and make the image at the third quadrant
The option B correctly shows the final image
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What triangle congruence theorem proves the triangles congruent? Type in the LETTER abbreviations NOT the full words. EXAMPLE: SSS
Answer:
HL
Step-by-step explanation:
the two triangles are right and have the same hypotenuse (the diagonal side) and one congruent leg (the horizontal side)
Mrs. Williams assigned her class a project to find the height of a flagpole. The students could not measure the height, so they used a mirror to determine the height of the flagpole. Jerrica placed a mirror on the ground 20 feet from the base of the flagpole and backed up until the top of the pole was centered in the mirror. Jerrica is 5.6 feet tall and is standing 7.4 feet from the mirror.
What is the height of the flagpole?
With the help of similar triangles the height of Flagpole is 15.13 feet
what is similar triangle?
Triangles that are similar in shape but differ in size are known as similar triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size.
solution:
let C is the point of reflection in triangle ABC and EDC
∠ ABC = ∠ EDC ( 90 Degree)
∠ ACD = ∠ ECD ( Reflective angle )
By symmetry,
AB/ED = BC/CD
5.6/ x = 7.4 / 20
x = 15.13 feet
Hence the height of flagpole is 15.13 feet
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Simplify (√2)(3/2) N/A 2 23 26 26 Look at the picture Its Better
PLEASE HELP
Answer:
C
Step-by-step explanation:
(√2) can be interpreted as 2^(1/2) and the second term can be interpreted as 2^(1/3). The law of exponents tells us that we must add the exponents when multiplying two numbers with the same base. 1/2 + 1/3 is 3/6+2/6 = 5/6 so the final answer would be 2^(5/6)
Sarah spent 30 minutes practicing her spelling words. She spent 3 times as much time reading. How many minutes did Sarah spend reading?
Sarah spends reading 30 min + [tex]0.05 min^{2}[/tex].
What is a mathematical expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. To assist identify the sequence of operations and other features of logical syntax, mathematical symbols can denote numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.
However, in modern mathematics, and particularly in computer algebra, formulae are considered expressions that may be evaluated as true or false based on the values assigned to the variables in the expressions.
The problem is in a mathematical expression.
30 min+3s min did Sarah spend reading
Convert s to min
.30min+3s min× 1min/60s
Cancel the common units and simplify.
Cross-cancel units.
30 min + [tex]0.05 min^{2}[/tex]
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please help me out! im very confused
Answer: C
Step-by-step explanation:
38520 *.12 = $4,622.40
Solve
-3(2x+1)= 4(x-1)
Answer: x = 1/0 in exact form. x = 0.1 in decimal form.
First step, distribute:
[tex]-6x-3 = 4x-4[/tex]
Next, isolate x to one side :
[tex]-6x - 4x=-4+3[/tex]
[tex]-10x=-1[/tex]
Last step, divide both sides by -10:
[tex]x=\frac{1}{10}[/tex]
Thus, the answer is [tex]\frac{1}{10}[/tex]
Hope this helped :)
The following table shows the speeds at which Jeff does 4 activities. For example, Biking has a rate of 19 miles in 2 hours.
Activity Miles Hours
Biking 19 2
Walking 14 4
Running 15 3
Swimming 18 4
Which type of activity does Jeff do at a speed of 4.5 miles per hour?
Choose 1 answer:
(Choice A)
Biking
(Choice B)
Walking
(Choice C)
Running
(Choice D)
Swimming
Answer:
Step-by-step explanation:
option 2 since it equals 14/4
What is the answer 4(16)3 / 103=
The value of numerical expression 4(16)³ / 10³ will be 16.384.
What is the value of the expression?When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ 4(16)³ / 10³
Simplify the expression, then we have
⇒ 4(16)³ / 10³
⇒ 4 x 4096 / 1000
⇒ 16384 / 1000
⇒ 16.384
The value of numerical expression 4(16)³ / 10³ will be 16.384.
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PS Unit 02: Prove These Triangles are Congruent
please help I need this ASAP
The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
If two lines intersects, then the opposite angle of the line will be congruent to each other.
In ΔBAE and ΔCDE,
AB = DC, (Given)
∠BAE = ∠CDE, (Right angle)
∠BEA = ∠DEC, (Opposite angle)
The triangle ΔBAE is congruent to the triangle ΔCDE by ASA postulate.
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the diameter of earth is about 13,000 kilometer the diameter of the moon is about 3000 kilometer about how many times greater is the diameter of earth than the diameter of the moon?
13000 divided by 3000 = 4.33 repeating meaning the 33 keps going like 4.33333333333333333333333333333333333333333333333333
NO LINKS!! Each table below represents an exponential function of the form y = ab^x. Complete each table and find the corresponding equation.
Answer:
[tex]\textsf{a)} \quad y=1.8(3.2)^x[/tex]
[tex]\textsf{b)} \quad y=5(7)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Part (a)Given ordered pairs:
(0, 1.8)(1, 5.76)(2, 18.432)The y-intercept is the y-value when x = 0.
Therefore, as the y-intercept is 1.8, a = 1.8.
[tex]\implies y=1.8b^x[/tex]
Substitute point (1, 5.76) into the equation and solve for b:
[tex]\begin{aligned} y&=1.8b^x\\\implies 5.76&=1.8 \cdot b^1\\5.76&=1.8b\\b&=\dfrac{5.76}{1.8}\\b&=3.2\end{aligned}[/tex]
Therefore, the exponential equation is:
[tex]\boxed{y=1.8(3.2)^x}[/tex]
To complete the given table, simply substitute the values of x into the found equation:
[tex]\begin{array}{c|l}x&\phantom{189}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{18}1.8\\\vphantom{\dfrac12}}1&\phantom{18}5.76\\\vphantom{\dfrac12}}2&\phantom{1}18.432\\\vphantom{\dfrac12}}3&\phantom{1}58.9824\\\vphantom{\dfrac12}}4&188.74368\end{array}[/tex]
Part (b)Given ordered pairs:
(0, 5)(2, 245)The y-intercept is the y-value when x = 0.
Therefore, as the y-intercept is 5, a = 5.
[tex]\implies y=5b^x[/tex]
Substitute point (2, 245) into the equation and solve for b:
[tex]\begin{aligned} y&=5b^x\\\implies 245&=5 \cdot b^2\\49&=b^2\\b&=\sqrt{49}\\b&=7\end{aligned}[/tex]
Therefore, the exponential equation is:
[tex]\boxed{y=5(7)^x}[/tex]
To complete the given table, simply substitute the values of x into the found equation:
[tex]\begin{array}{c|l}x&\phantom{11}y\\\cline{1-2} \vphantom{\dfrac12}}0&\phantom{1111}5\\\vphantom{\dfrac12}}1&\phantom{111}35\\\vphantom{\dfrac12}}2&\phantom{11}245\\\vphantom{\dfrac12}}3&\phantom{1}1715\\\vphantom{\dfrac12}}4&12005\end{array}[/tex]
is - 5/1 a integer?
evaluate the expression for x=-3 Thank you
[tex] {x}^{2 } - 2x + 4[/tex]
Answer: 7
Step-by-step explanation:
3 x 3 = 9 - 2(3)+4
9-6+4
=7
Y varies directly as x if y=4 when x=3 find x when y=-12
Answer:x=-9
Step-by-step explanation:-12/4=-3 then do 3*-3=-9
One year in Ferndale, California, it rained on 79 days. If one day of that year is randomly selected, what is the probability of rain on that day? (Assume that this was not a leap year.)
Answer:
21.64 % probability of rain at a random year
Step-by-step explanation:
79/365 * 100
21.64 %
Given h of x equals x squared minus 2 x minus 35, which statement is true?
The zeros of the quadratic equation: h(x) = x^2 - 2x - 35
are -5 and 7, thus the correct option is B.
What are the true statements?Here we have the quadratic equation:
h(x) = x^2 - 2x - 35
Using the quadratic formula we will get the two solutions:
[tex]x = \frac{2 \pm \sqrt{(-2)^2 - 4*1*-35} }{2*1} \\\\x = \frac{2 \pm 12 }{2} \\\\[/tex]
The solutions are:
x = (2 + 12)/2 = 7
x = (2 - 12)/2 = -5
Then the factors of the quadratic are (x - 7) and (x + 5), the correct option is B.
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Michael and Imani go out to eat for lunch.
Part A
If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill? Enter your answer to the nearest cent.
Part B
After adding a tip, the total lunch cost was $32.24. What percentage tip did they give? Enter your answer to the nearest percentage.
Answer:
Part A: The bill is $27.32
Part B: The percentage is 19%
My work:
Part A
? 8
--------- = ---------
25.30 100
equals 2.02400
then round to get the tax amount which is $2.02
to find the bill cost we need to add the tax and the cost of the meal:
2.02 + 25.30 = 27.32
Part B
to find the tip we need to subtract the bill from the total lunch cost:
27.32 + t = 4.92 (t = tip)
32.24 - 27.32 = 4.92
So now that we know the tip we can figure out how much percentage that is of the cost of the meal:
4.92 ?
-------- = --------
25.30 100
which equals 19.4466403/100
the percentage is 19%
3,000 divided by 48 x 4
Answer:500 I hope this helpful
Step-by-step explanation:
3000 divided by 48 times 8
To make the calculation easier, first multiply the numbers that result in multiples of 10
24000 divided by 48
Divide the numbers
=500
Answer:
250
Step-by-step explanation:
If we follow the rules of PEMDAS, we go from left to right. Therefore, first, do 3,000 divided by 48.
3,000/48=62.5
Now, multiply 62.5 by 4.
62.5x4= 250
250 is your answer :D
Hope this helps and have a wonderful day!
Humans can distinguish up to 18,400,000 individual dots called pixels on a typical computer display. Can a human distinguish pixels on a same sized HDTV with 2 x 10 to the 6th power pixels
Yes, human can distinguish pixels on a same-sized HDTV with 2 times 10 to the 6th power pixels.
What is Scientific Notation?Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
In the scientific form, we write a number in the form of base×10ⁿ.
Where 0 ≤ base < 10 and n can be any rational number.
Given,
Humans can distinguish up to 18,400,000 individual dots called pixels on a typical computer display
We need to check whether human distinguish pixels on a same sized HDTV with 2 x 10 to the 6th power pixels
2×10⁶ pixels.
= 2000000 pixels.
As 2000000 < 18400000
Hence, human can distinguish pixels on a same-sized HDTV with 2 times 10 to the 6th power pixels.
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