[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$10000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]10000=P\left(1+\frac{0.05}{4}\right)^{4\cdot 4} \implies 10000=P(1.0125)^{16} \\\\\\ \cfrac{10000}{(1.0125)^{16}}=P\implies 8197.46\approx P[/tex]
Number between 50 and 80 that has exactly 4 factors one which is 2
58, 62 and 74 are the numbers between 50 and 80 that has exactly 4 factors with 2 being one of them 4.
As per the question statement, we are required to find out the numbers between 50 and 80 that has exactly 4 factors with 2 being one of the factors.
To solve this question, we need to know that every or any number in the number system as has at least 2 factors: 1 and the number itself.
Since we are to find numbers with exactly 4 factors, 2 being one of the factors and as per the above mentioned concept, two of the remaining three factors will be 1 and the number itself, the fourth factor has to be a prime number as prime numbers have no other factors than 1 and itself.
That is, we will have to find prime numbers (say "n") which when multiplied by 2 lies within the range of 50 and 80,
[tex]or, 50\leq (n*2) \leq 80\\or, \frac{50}{2}\leq n\leq \frac{80}{2}\\ or, 25\leq n\leq 40[/tex]
That is, we will need to find the prime numbers between 25 and 40; They are 29, 31 and 37.
Hence, our required numbers are [(29 * 2) = 58], [(31 * 2) = 62] and
[(37 * 2) = 74]. They lie between 50 and 80 that has exactly 4 factors with 2 being one of them.
Factors: In mathematics, a factor "x" of a number, say "y" is such a number that, "y" when divided by "x", the division leaves no remainder.Prime Numbers: Any number greater than 1, that has only two factors, 1 and the number itself is known as a prime number.To learn more about Factors, click on the link below.
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5, 32, 229, 1016, 3133, 7780, 16,757 whats the next term
Answer: 32604
Step-by-step explanation:
Part A: Wilson bought fruit that weighs 2 and 1 over 2 pounds. How many ounces does the fruit weigh? Show your work. (5 points) [16 ounces = 1 pound] Part B: A running tap dispenses 0.14 gallons of water every second. How many pints of water is dispensed after 50 seconds? Show your work. (5 points) [1 gallon = 4 quarts, 1 quart = 2 pints]
The weight of the fruits in ounces is 40 ounces
The pints of water dispensed after 50 seconds is 56 pints
What are the converted units?The mathematical operations that would be used to determine the answer is multiplication. Multiplication is the process of determining the product of two or more numbers. Multiplication is represented with the sign - x.
A mixed fraction is a non-integer that is made up of a whole number and a proper fraction. An example of a mixed fraction is 2 1/2.
Weight of the fruits in ounces = 2 1/2 x 16
5/2 x 16 = 40 ounces
Pints of water dispensed after 50 seconds = gallon per second x 50 x 4 x 2
0.14 x 50 x 4 x 2 = 56 pints
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Question Collapse ^ Given slope (gradient) of a line is 3 and two points that lie on that line are N(-2,3) and D(3, d). Find the value of d.
The value of d is 18.
Given, the slope of the line is 3.
Slope equals a height change (Change in width) You may also say that a slope is a climb or a run. This formula changes if the graph's horizontal axis is represented by x and the vertical axis by y: Slope is equal to (y-change)/ (Change in x)
Two points which lie are N(₋2 , 3) and D(3,d)
slope of the line = y₂ ₋ y₁/x₂ ₋ x₁
let the points N(₋2 , 3) be (x₁ , y₁)
and D(3,d) be (x₂ , y₂)
therefore, 3 = d ₋ 3/3 ₋ (₋2)
3 = d ₋ 3/3 ₊ 2
3 = d ₋ 3 / 5
15 = d ₋ 3
d = 15₊3
d = 18
Hence we get the value of d as 18.
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what is 4 multiplied by pi multiplied by 4.6 to the power of 3
Answer:
193,153.72460551
Step-by-step explanation:
Multiply 4 times pi or 3.14 if you are rounding. Then multiply that number by 4.6
Lastly once you done all of put it to the po wer of 3
What raw score best corresponds to the top 20% for each distribution?
What raw score best corresponds to the 30th percentile for each distribution?
Major Hours ZHours
1 15 -1.59248
1 24 .42616
1 25 .65045
1 18 -.91960
1 30 1.77192
1 18 -.91960
1 22 -.02243
1 23 .20186
1 26 .87474
1 20 -.47102
2 21 1.95475
2 12 -.71082
2 13 -.41464
2 10 -1.30317
2 17 .77005
2 12 -.71082
2 12 -.71082
2 20 1.65858
2 12 -.71082
2 12 -.71082
2 15 .17770
2 12 -.71082
2 15 .17770
2 14 -.11847
2 19 1.36240
The raw score from the given table that corresponds with the 20th and 30th percentiles are;
First distribution;
20th percentile; 1830th percentile; 22Second distribution;
20th percentile; 1230th percentile; 14How can percentile values be found from Z–Score?The Z–Score percentile normal distribution table can be used to find the Z–Score that gives the percentile value of a raw score.
The Z–Score, also known as the standard score, gives the number of standard deviations, a raw score is far from the mean.
The mathematical equation for the Z–Score is as following; [tex]Z = \frac{x - \mu}{ \sigma} [/tex]
Therefore, a positive value of Z is obtained when the raw score, x, is larger than the mean, [tex] \mu[/tex]
and negative Z value is given by raw scores lower than the mean.
Using the standard normal distribution table, raw score corresponds to the 1th percentile when the Z–Score = -2.326, while the Z–Score for the 99th percentile is 2.326.
The Z–Score of the 20th percentile is -0.842, while for the 30th percentile it is -0.524
Comparing the standard values with the values in the given table, we have;
First distribution;
The raw score that corresponds with the 20th percentile in the first distribution is 18, given that the Z-Hours for 18 is -0.91960, and we have;-0.91960-(-0.842) = -0.0776
-0.71082 -(-0.842) = 0.13118
The smaller difference is given by -0.91960.
Similarly;
The raw score that corresponds to the 30th percentile is 22.Second distribution;
The raw score that corresponds with the 20th percentile in the second distribution is 12While;
The raw score that corresponds to the 30th percentile is 14Learn more about the Z–Score of a normal distribution here:
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There are 43 jazz songs, 56 rock songs, and 16 country songs on your music player. If you set your music player on random, what is the probability that the next song will be a country song? Give your answer as a decimal rounded to the nearest thousandth
Answer:
0.139
Step-by-step explanation:
total = 43 + 56 + 16 = 115
country songs = 16
p(country song) = 16/115 = 0.139
find the value of the variable and the measure of each labeled angle
value=
measure=
find the equation of the line with slope −6 which goes through the point (−9,−6).
Give your answer in slope-intercept form y=mx+b.
The equation of the line with slope −6 which goes through the point (−9,−6) = y = -6x + 9.
How do you calculate slope intercept?When you know the slope of something like the line to be investigated and the point given also contains the y-intercept, you can utilize the slope-intercept formula y = MX + b. (0, b). The y value of the y-intercept point is represented by b in the formula.
What is the definition of a slope?A line's slope is the ratio of how much y grows as x increases by a certain amount. The slope of a line indicates how steep it is, or how much y grows as x increases.
According to the given information:The slope of the line = -6 = m
The points (−9,−6). x = -9 , y = -6
Find the y-intercept.
y=mx+b
Substituting the value we get:
-6 = (-6 x -9) + b
-6 = -54 x b
b = 54/6
b = 9.
The equation in slope intercept form as:
y=mx+b
y = (-6)x + 9
y = -6x + 9
The equation of the line with slope −6 which goes through the point (−9,−6) = y = -6x + 9.
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Employees of the store in the Example wear shirts with the logo on the back. The
scale from the original logo in inches to the shirt in inches is 1 : 8. What is the area
of the logo on their shirts? Show your work.
The original logo is a triangle and measures
1.5in x 1.5in
Magnification is
Original shirt = 1:8
Shirt logo area
A = 1/2bh
A = 1 / 2 * (1.5 * 8) (1.5 * 8) = 72 square inches
The area is a quantity that describes the extent of an area on a plane or curved surface. Planar region or planar region area refers to the area of a shape or planar layer, and surface area refers to the open surface or boundary area of a three-dimensional object.
The area is defined as the total space occupied by a planar (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. A two-dimensional character. The space a shape occupies on paper is called its area. Now imagine that the square is made up of smaller unit squares.
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A dolphin dives from the surface into the ocean at a rate of 6.2 feet per second estimate the approximate location of the dolphin after 25 seconds
The approximate location of the dolphin is 155 feet as it moves at the rate of 6.2 feet per second.
Rate in defined as the speed or the distance travelled by the dolphin in unit time.
rate or speed is calculated by dividing the distance travelled by the total time taken to cover that distance.The units of rate is given by unit of distance/unit of time .The units of rate are meter/second , miles/hour , feet/second etc..Velocity is defined as the rate in a specified direction. Velocity is a vector quantity while speed or rate is a scalar quantity.Given the rate of the dolphin is feet per second .
Time taken by the dolphin is 25 seconds.
∴ distance travelled is given by rate × time
Hence distance travelled is 6.2 × 25 = 155 feet
Therefore the approximate location is given by 155 feet from the starting point.
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Find the measures of the central tendency of the data: (Round the answer to 2 decimal places)
7 14 9 10 10 7 13
Mode:
(Enter DNE if there are no modes)
Mean:
Median:
can someone tell me what the asnwer is thanks (geometry)
the perimeter P. of any rectangle is given by the formula P = 21 + 2w, where I represents the length if the rectangle and w represents the width. let the length of a rectangle equal 3 ft more than 3 times its width and the perimeter equal 54 ft
Answer:
width = 6 ft
length = 21 ft
Step-by-step explanation:
Forming algebraic expressions and finding the dimensions of a rectangle:
Width = w ft
length = 3*w + 3 = (3w + 3) ft
2l +2w = P
2(3w + 3) + 2w = 54
Use distributive property to open the brackets,
2*3w + 2*3 + 2w = 54
6w + 6 + 2w = 54
Combine like terms,
6w + 2w + 6 = 54
8w + 6 = 54
Subtract 6 from both sides,
8w = 54 - 6
8w = 48
Divide both sides by 8
w = 48 ÷ 8
[tex]\sf \boxed{\bf w = 6 \ ft}[/tex]
l = 3w + 3
= 3*6 + 3
= 18 + 3
l = 21 ft
Aida starts the week with $18.00. The table below shows the change in the amount of money she has each day.
Day Change in Amount ($)
Monday -5.15
Tuesday +12.40
Wednesday -11.20
Thursday +2.50
Friday x
Aida declares that she ended the week with the same amount of money with which she started the week. Determine the value of x for which Aida's statement is true.
Answer:
+ 1.45
Step-by-step explanation:
the end result is 16.55, therefore you add 1.45 to get $18 again.
What is the mean of the data set rounded to the nearest tenth
0.7,1.1,0.8,1.6,2.2,1.1
Answer:
1.3 is the correct answer
Step-by-step explanation:
Which expression is equivalent to the given expression [tex]\sqrt{45}[/tex]
Answer:
6.7
Step-by-step explanation:
√45 = 6.7
.................
The minimum temperature of mercury is approximately -275 F.The minimum temperature of Mars is approximately -195 F.Which is the following best compares the minimum temperature of two planets?
A. -195 > -275
B. -275 > -195
C. -195 > -275
D. -275 < -195
The expression that best compares the minimum temperature of the two planets is -195 > -275
Magnitude of temperaturesFrom the question, we are to determine which of the given options best compares the minimum temperature of the two planets
From the given information,
"The minimum temperature of mercury is approximately -275 F"
and
"The minimum temperature of Mars is approximately -195 F"
NOTE: The number -195 is greater than the number -275
Thus,
The minimum temperature of Mars is greater than the minimum temperature of Mercury
Hence, the expression that best compares the minimum temperature of the two planets is -195 > -275
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A certain substance in an experiment was being stored at −2.4°F. It was then placed on a table where the temperature was raised by 5.3°F.
What was the new temperature of the substance?
A. 7.2.9°F
B. 2.9°F
C. −2.9°F
D. −7.7°F
Given f(x)=x²-9, find the indicated values.
f(-1)
Answer: -8
Step-by-step explanation:
First, you plug -1 in for x
[tex]f(x)=f(-1)=(-1)^2 -9[/tex]
[tex]=1-9=-8[/tex]
X over 3 = 6
Solve for X
I will give brainlist
Choose an equivalent expression for two thirds to the fourth power times two thirds raised to the third power comma all raised to the second power.
four ninths raised to the fourteenth power
four ninths raised to the twenty fourth power
two thirds raised to the fourteenth power
two thirds raised to the twenty fourth power
Using exponent properties, the equivalent expression is given as follows:
[tex]\left(\frac{2}{3}\right)^14[/tex]
What is the equivalent expression?Two thirds to the fourth power is given by:
[tex]\left(\frac{2}{3}\right)^4[/tex]
Two thirds to the third power is given by:
[tex]\left(\frac{2}{3}\right)^3[/tex]
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:
[tex]\left(\frac{2}{3}\right)^4 \times \left(\frac{2}{3}\right)^3 \left(\frac{2}{3}\right)^{4 + 3} = \left(\frac{2}{3}\right)^7[/tex]
Then, this entire expression is raised to the second power, meaning that:
[tex]\left[\left(\frac{2}{3}\right)^7\right]^2 = \left(\frac{2}{3}\right)^7 \times \left(\frac{2}{3}\right)^7 = \left(\frac{2}{3}\right)^{7+7} = \left(\frac{2}{3}\right)^14[/tex]
[tex]\left(\frac{2}{3}\right)^14[/tex] is the equivalent expression.
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How do you write 14 programming errors for every 56 programmers as a rational number? Select the simplified rational number that represents this scenario.(1 point)
14
56
14/56
1/4
The simplified rational number that represents this scenario is 1/4
How to determine the simplified rational number that represents this scenario?The given parameters are:
14 programming errors for every 56 programmers
The above means:
Error : Actual = 14 : 56
Express as fraction
Error/Actual = 14/56
Simplify the ratio
Error/Actual = 1/4
Hence, the simplified rational number that represents this scenario is 1/4
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35. What is the equation of the line that is parallel to y = 4x + 3 and passes through the point (2, 6) ?
The equation of the line that is parallel to y = 4x ₊ 3 and passes through the point (2,6) is y = 4x ₋ 2.
The slope of the preceding equation is 4 because it is in slope intercept form. The slope of an equation is always equal for parallel lines, hence the slope of the equation we are requested to create is also 4. We are given that this line passes through (2,6).
In the absence of intersection, two lines are said to be parallel. Each line has the same slope. In the event where m₁=m₂, f(x)=m₁x+b₁ and g(x)=m₂x+b₂ are. parallel
In order to write in y = mx +b form, we need to solve for b (the y-intercept).
Given, x=2, y=6, and m = 4.
6 = (4) (2) ₊ b
simplify
6 = 8 ₊ b
solve for b.
b = 6 ₋ 8
b = ₋2
So the equation of the parallel line is y = 4x ₋ 2
Hence we get the equation of the line that is parallel to y = 4x ₊ 3 and passes through the point (2,6) is y = 4x ₋ 2
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Sep 20, 8:10:23 AM
The sum of three consecutive integers is 51. Find the value of the greatest of the
three.
The first integer is 16 and the next two integers are 17 and 18. The largest one is 18
What in math is an integer?
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.Three categories of integers exist: Zero (0) Good integers (Natural numbers) Integer Negatives (Additive inverse of Natural Numbers)The first integer will be called x. Consequently, the second integer is x+1 and the third is x+2 (this is because they are consecutive integers). The total of these three numbers is 51, so build up the following equation and answer it.
x+(x+1)+(x+2)=51
3x+3=51
3x=48
x=16
Therefore, the first integer is 16 and the next two integers are 17 and 18. The largest one is 18 and this is the answer.
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Answer if you know your right, bur dont answer just for the points
Answer: 6.7% 0.67 6
-
9
Step-by-step explanation:
Answer:
[tex]\sf 6.7\% < 6/9 < 0.67[/tex]
Explanation:
You would think 6.7% is a lot bigger than both, but it is not. Remember 6.7 is a percentage out of 100, thus, 6.7% actually is 0.067.
Determine the interval(s) for which f(x) ≥ 0. f(x) = x − 2
The interval(s) for which f(x) ≥ 0. is x ≥ 2
How to determine the interval(s)?The function is given as:
f(x) = x - 2
Also, we have:
f(x) ≥ 0
This means that
x − 2 ≥ 0
Add 2 to both sides of the inequality
x ≥ 2
Hence, the interval(s) for which f(x) ≥ 0. is x ≥ 2
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what are the possible values of x such that 10[x] =2.5
There is no solution for the given equation i.e.10[x] =2.5
Equation:
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Greatest integer function:
The largest integer function is one that yields an integer that is closest to the specified real value. Additionally known as the step function. The closest integer is used to round off the input using the biggest integer function. Thus, the equation to determine the largest integer is fairly straightforward. It is symbolised by [x] where x can take on any value.
⇒10[x] =2.5
⇒[x] =[tex]\frac{2.5}{10}[/tex]
⇒[x] =0.25
⇒[x] will be always a interger.As a result there is no solution for the given equation.
Therefore,There is no solution for the given equation i.e.10[x] =2.5
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Is this a linear or nonlinear?
Answer:
non
Step-by-step explanation:
bc its not a straight line
Answer: Non-linear
Step-by-step explanation:
It’s not a straight line and there is no pattern.
Solve the inequality.
2(4x-3) ≥-3(3x) +5x?
Answer:
Step-by-step explanation:
2(4x-3)≥-3(3x)+5x
8x-6≥-9x+5x
8x≥-4x+6
8x+4x≥6
12x≥6
x≥6/12
or
x≥1/2