Answer:
principal (p)=$1300
Interest (I) =$28.67
Time( T) = 1 year
R=?
we have,
R = I*100/T*R
II. The following figure shows an infinite zigzag path with each zag
occurs at an angle of π/4. Find the total length of this infinite zigzag
path.
T/4
1
T/4/
I need help please, it would greatly appreciated!!
The length of the infinite zigzag path is 1
How to determine the length
Note that the infinite zigzag path is embedded in an isosceles triangle
Using angle π/4, we have that
Tan π/4 = opposite/ adjacent
[tex]tan \frac{3. 412}{4} = \frac{x}{1}[/tex]
[tex]tan 0. 7855 = x[/tex]
[tex]x = 0. 014[/tex]
To find the longer part 'y', use the Pythagorean theorem
[tex]y^{2} = (0.014)^2 + (1)^2[/tex]
[tex]y^2 = 1.879 * 10^-4 + 1[/tex]
[tex]y^2 = 1. 00[/tex]
[tex]y = \sqrt{1. 000}[/tex]
[tex]y = 1. 000[/tex]
The length of the infinite zigzag path is the same as the length of the longer part of the triangle which equals 1.
Thus, the length of the infinite zigzag path is 1
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Which degenerate conic is formed when a double cone is sliced through the a pex by a plane parallel to the slant edge of the cone?
Circle
Parabola
One line
Two lines
One line will be formed which will be parallel to the slant edge option third is correct.
What is a conic section?It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (circle is a special type of ellipse).
We have a statement:
Which degenerate conic is formed when a double cone is cut through the top by a plane parallel to the slant edge of the cone?
As we can see in the attached picture if the double cone is cut through the top by a plane parallel to the slant edge of the cone one line will be formed which will be parallel to the slant edge.
Thus, one line will be formed which will be parallel to the slant edge option third is correct.
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For all a and b, what is the sum of (a-b)² and (a+b)²
Answer:
2a² + 2b²
Step-by-step explanation:
(a - b)² + (a + b)² ← expand both factors using FOIL
= a² - 2ab + b² + a² + 2ab + b² ← collect like terms
= 2a² + 2b²
Step-by-step explanation:
Expand both classic quadratics and combine like terms to find the sum:
(a−b)2+(a+b)2
Which pair represents equivalent ratios?
A.2/3,95
B.5/8,15/21
C.3/12,6/18
D.4/10,12/30
Answer:
D
Step-by-step explanation:
We can test each pair making each ratio into its simplest form.
For A 2/3 is already in its simplest form and 9/15=3/5. they are not equivalent.
For B, 5/8 is already in its simplest form and 15/21=5/7. they are not equivalent.
For C, 3/12=1/4, and 6/18=1/3. They are not equivalent.
For D, 4/10=2/5, and 12/30=2/5. They are equivalent.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Let's see which ones are equivalent}\\\huge\textbf{to each other, shall we?}\\\\\\\huge\textbf{We will convert the given fractions to}\\\huge\textbf{decimals or make the fractions on the}\\\huge\textbf{right to easier to solve or comparing it}\\\huge\textbf{to the one on the left.}[/tex]
[tex]\huge\textsf{Option A.}[/tex]
[tex]\mathsf{\dfrac{2}{3}, \dfrac{9}{15}}[/tex]
[tex]\mathsf{\dfrac{2}{3}}\\\\\mathsf{= 2\div3}\\\\\mathsf{= 0.66\overline{6}7}\\\\\\\mathsf{\dfrac{9}{15}}\\\\\mathsf{= \dfrac{9\div3}{15\div3}}\\\\\mathsf{= \dfrac{3}{5}}\\\\\\\\\mathsf{\dfrac{2}{3} \neq \dfrac{9}{15}}[/tex]
[tex]\huge\textsf{Option B.}[/tex]
[tex]\mathsf{\dfrac{5}{8}, \dfrac{15}{21}}[/tex]
[tex]\mathsf{\dfrac{5}{8}}\\\\\mathsf{= 5\div8}\\\\\mathsf{= 0.625}\\\\\\\mathsf{\dfrac{15}{21}}\\\\\mathsf{= \dfrac{15\div3}{21\div3}}\\\\\mathsf{= \dfrac{5}{7}}\\\\\mathsf{\dfrac{5}{8}\neq \dfrac{15}{21}}[/tex]
[tex]\huge\textsf{Option C.}[/tex]
[tex]\mathsf{\dfrac{3}{12}.\dfrac{6}{18}}[/tex]
[tex]\mathsf{\dfrac{3}{12}}\\\\\mathsf{= 3 \div 12}\\\\\mathsf{= 0.25}\\\\\\\\\mathsf{\dfrac{6}{18}}\\\\\\\mathsf{= \dfrac{6\div3}{18\div3}}\\\\\\\mathsf{= \dfrac{2}{6}}\\\\\\\mathsf{= \dfrac{2\div2}{6\div2}}\\\\\\\mathsf{= \dfrac{1}{3}}\\\\\\\mathsf{\dfrac{3}{12}\neq \dfrac{6}{18}}[/tex]
[tex]\huge\textsf{Option D.}[/tex]
[tex]\mathsf{\dfrac{4}{10}, \dfrac{12}{30}}[/tex]
[tex]\mathsf{\dfrac{4}{10}}\\\\\mathsf{= 4\div10}\\\\\mathsf{= 0.40}\\\\\\\mathsf{\dfrac{6}{18}}\\\\\mathsf{= \dfrac{12\div3}{30\div3}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4}{10}}\\\\\mathsf{= \dfrac{4\div2}{10\div2}}\\\\\mathsf{= \dfrac{2}{5}}\\\\\mathsf{\dfrac{4}{10} = \dfrac{12}{20}}[/tex]
[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{Option\ D. \dfrac{4}{10}, \dfrac{12}{30}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Last year over 10,000 students took an entrance exam at a certain state university. Ivanna's score was at the 36th percentile. Aldo's score was at the 19th percentile.
Ivanna's score was at the 36th percentile, will be 99.64 and Aldo's score was at the 19th percentile, will be 99.81.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Last year, over 10,000 students took an entrance exam at a certain state university.
Let the maximum score be 100.
Ivanna's score was at the 36th percentile, will be
⇒ [(10,000 – 36) / 10,000] x 100
⇒ 99.64
Aldo's score was at the 19th percentile, will be
⇒ [(10,000 – 19) / 10,000] x 100
⇒ 99.81
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two variables x and y have corresponding values as shown in the table below. x=2,3,a and y=20,40,104 given that y varies directly as x power 2+1 find (a) value of k (b) value of a
The value of k is 4 and the value of a is 5
How to determine the value of k?The table of values is given as:
x=2,3,a
y=20,40,104
The variation is given as:
[tex]y\ \alpha\ x^2+1[/tex]
Express as an equation
y = k(x^2 + 1)
When x = 2, y = 20.
So, we have:
[tex]20 = k(2^2 + 1)[/tex]
Evaluate the sum
20 = 5k
Divide by 5
k = 4
Hence, the value of k is 4
How to determine the value of a?In (a), we have:
y = k(x^2 + 1)
Substitute 4 for k
y = 4(x^2 + 1)
When x = a, y = 104.
So, we have:
104 = 4(a^2 + 1)
Divide by 4
26 = a^2 + 1
Subtract 1 from both sides
a^2 = 25
Take the square root
a = 5
Hence, the value of a is 5
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Which linear equation has a slope of 3 and a y-intercept of -2?
y = 3x + 2
y = 3x - 2
y = -2x + 3
y=-2x-3
Answer:
y = 3x - 2
Step-by-step explanation:
The number beside the x is the slope. The number at the end of the equation is the y-intercept.
All the answers are in this form:
y = mx + b
m is the slope.
b is the y-intercept.
With a 3 filled in for slope and -2 filled in for the y-intercept, you get:
y = 3x + -2
is the same as,
y = 3x - 2
Evaluate the integral
-7x³
x³ +1
Note: Use an upper-case "C" for the constant of integration.
I
dx
The value of the integration is
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex], where C is an integrating constant.
We know that finding the area of the curve's undersurface is the process of integration. To do this, cover the area with as many tiny rectangles as possible, then add up their areas. The sum gets closer to a limit that corresponds to the area under a function's curve. Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral over the domain is finite with the given bounds, then the integration is definite.
Here, we have to determine the value of the given integral
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx[/tex].
So,
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx = 7 \int {\frac{1-x^{3}-1 }{x^{3}+1} } \, dx[/tex][tex]= 7 \int [{1-\frac{1 }{x^{3}+1} } ]\, dx =7\int \, dx - 7 \int {\frac{1 }{x^{3}+1} } \, dx[/tex] ...(1)
Now,
[tex]\frac{1}{x^{3} +1} = \frac{1}{(x+1)(x^{2} -x+1)}[/tex]
We can write
[tex]\frac{1}{(x+1)(x^{2} -x+1)}=\frac{A}{(x+1)} + \frac{Bx+C}{(x^{2} -x+1)}[/tex]
i.e. [tex]1 = A(x^{2} -x+1)+(Bx+C)(x+1)[/tex]
i.e. [tex]1 = Ax^{2} -Ax + A+Bx^{2} +Bx+Cx+C[/tex]
i.e. [tex]1=(A+B)x^{2} +(-A+B+C)x +(A+C)[/tex]
Comparing both sides, we get
[tex]A+B=0 \implies B = -A[/tex] ...(2)
[tex]-A+B+C = 0 \implies -A+(-A)+C=0 \implies -2A+C=0[/tex] ...(3)
[tex]A+C=1[/tex] ...(4)
Subtracting (3) from (4),
[tex]A+C+2A-C=1-0 \implies 3A=1 \implies A=\frac{1}{3}[/tex]
From (4), [tex]C= 1-\frac{1}{3} =\frac{3-1}{3} =\frac{2}{3}[/tex]
From (2), [tex]B =-\frac{1}{3}[/tex]
We get
[tex]\frac{1}{x^{3}+1 } =\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{3} \frac{x-2}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-4}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1-3}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1}{x^{2} -x+1}+\frac{3}{6} \frac{1}{x^{2} -x+1}[/tex]
[tex]=\frac{1}{3} \frac{1}{(x+1)} - \frac{1}{6} \frac{2x-1}{x^{2} -x+1}+\frac{1}{2} \frac{1}{x^{2} -x+1}[/tex]
Integrate both sides,
[tex]\int \frac{1}{x^{3}+1 }\, dx =\frac{1}{3} \int \frac{1}{(x+1)} \, dx - \frac{1}{6} \int \frac{2x-1}{x^{2} -x+1}\, dx+\frac{1}{2} \int \frac{1}{x^{2} -x+1}\, dx[/tex]
i.e. [tex]\int \frac{1}{x^{3}+1 }\, dx =\frac{1}{3} \ln(x+1) - \frac{1}{6} ln (x^{2} -x+1)+\frac{\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })[/tex]
From (1),
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex]
Therefore, the value of the integration is
[tex]\int {\frac{-7x^{3} }{x^{3}+1} } \, dx =7x - \frac{7}{3} \ln(x+1) + \frac{7}{6} ln (x^{2} -x+1)-\frac{7\sqrt{3} }{3} tan^{-1} (\frac{2x-1}{\sqrt{3} })+C[/tex], where C is an integrating constant.
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HELP STAT:
Graph the function F(x)= -sec (x/4) +3 on the interval [-2pi,6pi]
Answer:
Step-by-step explanation:
Is the graph increasing, decreasing, or constant?
Answer:
jxdhjsssdddddsssssdd
Answer:
increasing
Step-by-step explanation:
look left to right, line goes up
ABC Bank requires a 20% down payment on all its home loans. If the house is
priced at $145,000, what is the amount of the down payment required by the
bank?
A. $18,000
B. $290,000
• C. $29,000
D. $14,500
Answer:
c. $29,000
Step-by-step explanation:
since 20% of 145,000 = 29,000
to calculate use
(20/100) * 145,000
or
(y/100) * x
y = the precentage
x = the price of the house
therefore your answer is c. $29,000
hope this helps:)
Select the correct statement about the function represented by the table. x y 1 34 2 41 3 48 4 55 5 62 A. It is a linear function because the difference y – x for each row is constant. B. It is an exponential function because the y-values increase by an equal factor over equal intervals of x-values. C. It is an exponential function because the factor between each x- and y-value is constant. D. It is a linear function because the y-values increase by an equal difference over equal intervals of x-values.
Answer:
sorry
Step-by-step explanation:
What is the following answer to 2+2
Answer:
well the answer is 4 have a good day
solve the equation uding the most direct method: 3x(x+6)=-10?
To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.
DistributeUse the distributive property to distribute 3x into the term (x + 6):
[tex]3x(x+6)=-10[/tex]
[tex]3x^2+18x=-10[/tex]
RearrangeTo create a quadratic equation, add 10 to both sides of the equation:
[tex]3x^2+18x+10=-10+10[/tex]
[tex]3x^2+18x+10=0[/tex]
Use the Quadratic FormulaThe quadratic formula is defined as:
[tex]\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.
Therefore:
a = 3b = 18c = 10Set up the quadratic formula:
[tex]\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}[/tex]
Simplify by using BPEMDAS, which is an acronym for the order of operations:
Brackets
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Use BPEMDAS:
[tex]\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}[/tex]
Simplify the radicand:
[tex]\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}[/tex]
Create a factor tree for 204:
204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.
The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:
[tex]\sqrt{4\times51}[/tex]
Then, using the Product Property of Square Roots, break this into two radicands:
[tex]\sqrt{4} \times \sqrt{51}[/tex]
Since 4 is a perfect square, it can be evaluated:
[tex]2 \times \sqrt{51}[/tex]
To simplify further for easier reading, remove the multiplication symbol:
[tex]2\sqrt{51}[/tex]
Then, substitute for the quadratic formula:
[tex]\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}[/tex]
This gives us a combined root, which we should separate to make things easier on ourselves.
Separate the RootsSeparate the roots at the plus-minus symbol:
[tex]\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}[/tex]
[tex]\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}[/tex]
Then, simplify the numerator of the roots by factoring 2 out:
[tex]\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}[/tex]
[tex]\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}[/tex]
Then, simplify the fraction by reducing 2/6 to 1/3:
[tex]\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}[/tex]
[tex]\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}[/tex]
The final answer to this problem is:
[tex]\displaystyle x=\frac{-9 + \sqrt{51}}{3}[/tex]
[tex]\displaystyle x=\frac{-9 - \sqrt{51}}{3}[/tex]
Given m = -1/2 and the point (3, -6), which of the following is the point-slope form of the equation
Answer:
y + 6 = -1/2(x-3)
Step-by-step explanation:
let me know if you want an explanation
Question 2
A) 800 cents
A laptop computer consumes about 40 watts of electricity per hour when operating. At $0.20 per kilowatt-hour, how much does.
laptop cost to operate for 10 hours?
B) 40 cents
200 cents
8 cents
19 OF 20 QUESTIONS REMAIN
Question 3
10 Point
10 Points
Answer: $80
Step-by-step explanation:
Given:
The laptop consumes 40 watts/hour
The operating cost is $0.20 per kilowatt - hour
So,
The cost for 1 hour of consumption = 40 * 0.20 = $8
The cost for 10 hours of consumption = $8 * 10 hours = $80
how do i work this on calculator
2x-10=8
Answer:
x = 9Step-by-step explanation:
2x-10=8
2x = 10 + 8
2x = 18
x = 18 : 2 =
x = 9
-----------------------
check
2 * 9 - 10 = 8 (remember PEMDAS)
18 - 10 = 8
8 = 8
the answer is good
Find the value of x.
Answer:
7x-1 + 2x-1 =7 ..... given
9x-2 = 7
9x = 9
x = 1
Step-by-step explanation:
This is the answer of the above condition.
Please mark as BRAINLIEST and THANK ME.
The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Find the range, sample variance, and sample standard deviation of the numbers of medals won by these countries. 1 2 3 3 4 9 9 11 11 11 14 14 19 22 23 24 25 29
The range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
What is a Range?A range is given to a parameter to allow maximum leverage to the parameter. for example, if a vendor wants a rod of diameter 20 cm, then he may give a range of ±1 cm., which means he will accept the rod of 19(20-1) cm to 21(20+1) cm.
The range of the numbers of medals won by these countries is,
Range = Max - Min = 29 - 1 = 28
To find the standard deviation we need to know the following details,
Sum of the number of medals = ∑x = 234Sum of the square of the number of medals = ∑x² = 4372Number of observations = n = 18Now, the standard deviation of medals won by these countries is,
[tex]\sigma = \sqrt{\dfrac{\sum x^2 - \frac1n (\sum x)^2}{n-1}}\\\\\sigma = \sqrt{\dfrac{\4372 - \frac{234^2}{18}}{18-1}}\\\\\sigma = 8.845[/tex]
The variance of the numbers of medals won by these countries is,
v = σ²
v = 78.2353
Hence, the range, standard deviation, and variance of the numbers of medals won by these countries are 28, 8.845, and 78.2353, respectively.
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Please help !! I will give 20 points for correct answer !!!!
The table below shows the average SAT math scores from 1993-2002.
Year
SAT math scores
1993
503
1994
504
1995
506
1996
508
1997
511
1998
512
1999
511
2000
514
Using the data from the table determine if there is a linear trend between the year and the average SAT math scores and determine if there is an exact linear fit of the data. Describe the linear trend if there is one.
a.
Positive linear trend, an exact linear fit.
b.
Positive linear trend, not an exact linear fit.
c.
Negative linear trend, not an exact linear fit.
d.
Negative linear trend, an exact linear fit.
Please select the best answer from the choices provided
A
B
C
D
Mark this and return
According to the information in the table, it can be inferred that the trend of the results is positive but does not have an exact linear fit (option B).
How to calculate the average of the results?To calculate the average of the results we must add all the results and divide the result by the number of years as shown below.
503 + 504 + 506 + 508 + 511 + 512 + 511 + 514 = 40694069 ÷ 8 = 508.6Additionally, to identify if the trend is positive or negative, we must see if the results increase or decrease year after year. From the above, it is possible to infer that it is a positive trend.
On the other hand, it can be stated that it does not have an exact linear fit because the increase is not constant each year.
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Hassan used the iterative process to locate StartRoot 0.15 EndRoot on the number line.
A number line going from 0 to 0.9 in increments of 0.1. A point is between 0.4 and 0.5.
Which best describes Hassan’s estimation?
Hassan is correct because StartRoot 0.15 EndRoot almost-equals 0.4
Hassan is correct because the point is on the middle of the number line.
Hassan is incorrect because StartRoot 0.15 EndRoot is less than 0.4.
Hassan is incorrect because the point should be located between 0.1 and 0.2
Hassan is incorrect because √0.15 is less than 0.4, and the value of √0.15 is 0.3872 option third is correct.
What is the iteration method?Iteration is the process of repeating a procedure in order to produce a series of results.
We have:
= √0.15
[tex]= \rm \sqrt{{\dfrac{15}{100}}}[/tex]
[tex]= \rm \sqrt{{\dfrac{3}{20}}}[/tex]
= (1.732)/(4.472)
= 0.3872
√0.15 is less than 0.4.
Thus, Hassan is incorrect because √0.15 is less than 0.4, and the value of √0.15 is 0.3872 option third is correct.
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Answer:
C
Step-by-step explanation:
the length of a cll is 2/3 mm. if the area of the cell is 1/12 square mm, what is the width of the cell
The width of a cell with the length (l) of the cell is [tex]\frac{2}{3}[/tex] mm and area (A) of the cell is [tex]\frac{1}{12}[/tex] mm² is [tex]\frac{1}{8}[/tex].
Given that, the length (l) of the cell is [tex]\frac{2}{3}[/tex] mm and area (A) of the cell is [tex]\frac{1}{12}[/tex] mm².
We need to find the width of the cell.
What is the area of a rectangle?The area of a rectangle is the product of its length and width. So, the area of the rectangle = Length×Width square units.
Now, the area of a cell = [tex]\frac{2}{3}[/tex] ×Width= [tex]\frac{1}{2}[/tex] mm².
⇒Width=[tex]\frac{\frac{1}{12} }{\frac{2}{3} } ={\frac{1}{12} \times {\frac{3}{2}=\frac{1}{8}[/tex]
Therefore, the width of a cell with the length (l) of the cell is [tex]\frac{2}{3}[/tex] mm and area (A) of the cell is [tex]\frac{1}{12}[/tex] mm² is [tex]\frac{1}{8}[/tex].
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Giving you the brainliest!
Answer:
The answer will be J
Step-by-step explanation:
Since you see, that the 67,896 will need to be rounded. It rounds up to 70,000 so you can elinmate M & N. 22% can be converted as a decimal to 0.2, also equals to 0.20. So elinmate L. Now you have J and K. You always times with these kinds of percentage.
Therefore the Answer Will Be J: 70,000 timed by 0.20.
Expert-Certifieder of Cousin.
joseph drove from his summer home to his place of work. To avoid the road construction, joseph decided to travel the gravel road. After driving 20 minutes, he was 62 miles away from work, and after driving 40 minutes, he was 52 miles away from work. this situation is shown in the graph below. determine the slope of the line and describe what it means in this situation
The slope of the line and describe is the negative 0.5 which means in this situation will be negative 0.5 miles per minute.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall, and the difference between the abscissa is called run.
Joseph drove from his summer home to his place of work.
To avoid the road construction, Joseph decided to travel the gravel road.
After driving 20 minutes, he was 62 miles away from work, and after driving 40 minutes, he was 52 miles away from work.
This situation is shown in the graph below.
Then the slope of the line and describe what it means in this situation will be
Slope = (52 – 62) / (40 – 20)
Slope = – 10 / 20
Slope = – 0.5 miles per minute
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How much of an alloy that is 30% copper should be mixed with 200 ounce of an alloy that is 70% copper in order to get an alloy that is 40% copper?
The alloy of copper will be 600 ounces.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Let us represent
Number of ounce of 30% copper = x
Hence, our Equation will be given below:-
x × 30% + 200 × 70% = (x + 200) × 40%
0.3x + 140 = (x + 200)0.4
0.3x + 140 = 0.4x + 80
Collect like terms
0.4x - 0.3x = 140 - 80
0.1x = 60
x = 60/0.1
x = 600 ounces
Therefore the alloy of copper will be 600 ounces.
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what is the value of the rational expression below when is equal to 5?
15-(5)/5-10=10/-5=-2 hope it helps!
a. The Gap purchased inventories totaling $10,392 million for the fiscal year ended February 2, 2019. Use the financial statement effects template to record cost of goods sold for The Gap's fiscal year ended February 2, 2019. (Assume accounts payable is used only for recording purchases of inventories and all inventories are purchased on credit.)
b. What amount did the company pay to suppliers during the year? Record this with the financial statement effects template.
I'm not sure how to show these amounts on the financial statement effects template.
The cost of goods sold is $10,258 million and the Cash paid to supplier is $10,447 million.
Cost of goods solda. Cost of goods sold
Cost of Goods Sold=Beginning Inventories + Purchases – Ending Inventories
Cost of goods sold = $1,997 + $10,392 - $2,131
Cost of goods sold = $10,258
b. Cash paid to supplier
Cash paid=2015 Beginning balance + Purchases - 2015 Ending balance
Cash paid = $1,181 + $10,392 - $1,126
Cash paid = $10,447
Therefore the cost of goods sold is $10,258 million and the Cash paid to supplier is $10,447 million.
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Assume that t varies jointly as r and q2². If t=320 when r=5 and q = 4, what is the value of q when r= 1 and t= 196?
q=
Step-by-step explanation:
[tex]t = k(r)( {q}^{2} )[/tex]
[tex]320 = k(5)( {4}^{2} )[/tex]
[tex]320 = 80k[/tex]
[tex]k = 4[/tex]
[tex]196 = 4(1)( {q}^{2} )[/tex]
[tex]49 = {q}^{2} [/tex]
[tex]q = 7[/tex]
I NEED HELP ON THESE 2 PROBLEMS. pls good anawers or bad rating and report
Answer:
1.a. skew
1.b. parallel
1.c. none of the above
1.d. perpendicular
1.e. parallel
1.f. skew
2.a. never
2.b. always
2.c. always
2.d. sometimes, sometimes, sometimes
Step-by-step explanation:
For these questions, it is critical to know the definitions of each of the terms.
DefinitionsPerpendicular: Two intersecting lines that form a right angle.Parallel: Two non-intersecting lines that are coplanar.Skew: Two non-intersecting lines that are not coplanar.Problem Breakdown
1.a. skew [tex]\overset{\longleftrightarrow}{AB} \text{ and } \overset{\longleftrightarrow}{EF}[/tex]
Point E is not on line AB. Any three non-linear points form a unique plane (left face), so A, B, and E are coplanar. Point F is not in plane ABE. Since line EF and line AB do not intersect and are not coplanar, they are skew.
1.b. parallel [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{EH}[/tex]
Line CD is parallel to line AB, and line AB is parallel to line EH. Parallel lines have a sort of "transitive property of parallelism," so any pair of those three lines is coplanar and parallel to each other.
1.c. none of the above [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{GA}[/tex]
Line AC and line GA share point A, necessarily intersecting at A. Therefore, line AC and line GA cannot be parallel or skew.
Any three points form a unique plane, so these two lines are coplanar, however, do they form a right angle? If the figure is cube-shaped, as depicted, then no.
Note that each line segment AC, AG, and CG are all the diagonal of a cube face. A cube has equal edge lengths, so each of those diagonals would be equal. Thus, triangle ACG is an equilateral triangle.
All equilateral triangles are equiangluar, and by the triangle sum theorem, the measures of the angles of a planar triangle must sum to 180°, forcing each angle to have a measure of 60° (not a right angle). So, lines AC and GA are not perpendicular. (If the shape were a rectangular prism, these lines still aren't perpendicular, but the proof isn't as neat, there is a lot to discuss, and a character limit)
"none of the above"
1.d. perpendicular [tex]\overset{\longleftrightarrow}{DG} \text{ and } \overset{\longleftrightarrow}{HG}[/tex]
Line DG and line HG share point G, so they intersect. Both lines are the edges of a face, so they intersect at a right angle. Perpendicular
1.e. parallel [tex]\overset{\longleftrightarrow}{AC} \text{ and } \overset{\longleftrightarrow}{FH}[/tex]
Line AC is a diagonal across the top face, and line FH is a diagonal across the bottom face. They are coplanar in a plane that cuts straight through the cube from top to bottom, but diagonally through those faces.
1.f. skew [tex]\overset{\longleftrightarrow}{CD} \text{ and } \overset{\longleftrightarrow}{AG}[/tex]
Point A is not on line CD, and any three non-linear points form a unique plane (the top face), so C, D, and A are coplanar. Point G is not in plane ACD. Since line CD does not intersect and is not coplanar with line AG, by definition, the lines are skew.
2.a. Two lines on the top of a cube face are never skew
Two lines are on a top face are necessarily coplanar since they are both in the plane of the top face. By definition, skew lines are not coplanar. Therefore, these can never be skew.
2.b. Two parallel lines are always coplanar.
If two lines are parallel, by definition of parallel lines, they are coplanar.
2.c. Two perpendicular lines are always coplanar
If two lines AB and CD are perpendicular, they form a right angle. To form a right angle, they must intersect at the right angle's vertex (point P).
Note that A and B are unique points, so either A or B (or both) isn't P; similarly, at least one of C or D isn't P. Using P, and one point from each line that isn't P, those three points form a unique plane, necessarily containing both lines. Therefore, they must always be coplanar.
2.d. A line on the top face of a cube and a line on the right side face of the same cube are sometimes parallel, sometimes skew, and sometimes perpendicular
Consider each of the following cases:
Parallel: Consider line CD (top face), and line GF (right face). They are coplanar and don't intersect. By definition, parallel.Skew: Consider line AD (top face), and line GF (right face). They aren't coplanar and don't intersect. By definition, skew.Perpendicular: Consider line AD (top face), and line GD (right face). They do intersect at D, and form a right angle. By definition, perpendicular.None of the above: Consider line AC (top face), and line GC (right face). These lines intersect at C, but as discussed in part 1.c, they form a 60° angle, not a right angle. By definition, "none of the above".These 4 cases prove it is possible for a pair of top face/right face lines to be parallel, perpendicular, skew, or none of the above. So, those two lines are neither "always", nor "never", one of those choices. Therefore, they are each "sometimes" one of them.