Determine whether the following series converges or diverges using any test. Be sure to clearly state what test(s) you are using and check any conditions needed to apply that test.
Answers
According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.
How to determine whether a series converges by ratio criterioHerein we have a series in rational form, whose convergence can be proved by the ratio criterion, whose defintion is shown below:
x = lim (n → ∞) |aₙ/aₙ₊₁| (1)
The series converges if x < 0 and diverges when x > 1. If x = 1, the criterion cannot be used and another criterion must be used instead. Now we proceed to apply it on the expression behind the series:
|aₙ/aₙ₊₁| = [(2 · n + 1) · (2 · n + 2)] / [5 · (n + 1)²]
|aₙ/aₙ₊₁| = [4 · n² + 5 · n + 2] / [5 · n² + 10 · n + 5]
Then, by applying the limit property for rational equations we find that limit of the expression within the series is:
L = 4 / 5
According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.
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By the ratio test, the series diverges.
[tex]\displaystyle \lim_{k\to\infty} \left| \frac{5^{k+1} ((k+1)!)^2}{(2(k+1))!} \cdot \frac{(2k)!}{(5^k (k!)^2}\right| = 5 \lim_{k\to\infty} \frac{(k+1)^2}{(2k+2)(2k+1)} = \frac54 > 1[/tex]
Related Questions
f(x)
Which type of function describes f(x)?
•
Rational
Polynomial
O Logarithmic
• Exponential
Answers
Answer:
Exponential function
[tex]y=1.25(2)^x[/tex]
Step-by-step explanation:
Definitions
Asymptote: a line that the curve gets infinitely close to, but never touches.
Hole: a point on the graph where the function is not defined.
Polynomial Function[tex]f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_2x^2+a_1x+a_0[/tex]
An equation containing variables with non-negative integer powers and coefficients, that involves only the operations of addition, subtraction and multiplication.
A continuous function with no holes or asymptotes.
Rational Function[tex]f(x)=\dfrac{h(x)}{g(x)}[/tex]
An equation containing at least one fraction whose numerator and denominator are polynomials.
A rational function has holes and/or asymptotes.
A rational function has holes where any input value causes both the numerator and denominator of the function to be equal to zero.A rational function has vertical asymptotes where the denominator approaches zero.If the degree of the numerator is smaller than the degree of the denominator, there will be a horizontal asymptote at y = 0.If the degree of the numerator is the same as the degree of the denominator, there will be a horizontal asymptote at y = ratio of leading coefficients.If the degree of the numerator is exactly one more than the degree of the denominator, slant asymptotes will occur. Logarithmic Function[tex]f(x) =\log_ax[/tex]
A continuous function with a vertical asymptote.
A logarithmic function has a gradual growth or decay.
Exponential Function[tex]f(x)=ab^x[/tex]
The variable is the exponent.
A continuous function with a horizontal asymptote.
An exponential function has a fast growth or decay.
Answer: exponential
Step-by-step explanation:
A locker combination consists of two non-zero digits. the digits in a combination are not repeated and range from 2 through 9. event a = the first digit is less than 5 event b = the second digit is less than 5 if a combination is picked at random, with each possible locker combination being equally likely, what is p(b|a) expressed in simplest form?
Answers
Answer:
1/3.
Step-by-step explanation:
P(event a occurs) = 3/9 = 1/3
P(event b occurs) = 3/9 = 1/3
P(a) ∩ P(b) = 1/3 * 1/3 = 1/9
P(b|a) = P(a) ∩ P(b) / P(a)
= 1/9 / 1/3
= 1/3.
math help pleasee!!!!
Answers
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Since this is an algebraic problem
⇒let's solve it like one
[tex]2*3^{x+5} < 14\\3^{x+5} < 7\\ x+5 < log_37\\x < -5 + log_37\\x < -3.2288[/tex]
Answer: x < -3.2288
Hope that helps!
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im pulling my hair out with this problem my calculator simplified it to [tex]\frac{1+/-\sqrt{14}}{10}[/tex]
What am i doing wrong?? :')
Answers
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ 0=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{-5} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (2) \pm \sqrt { (2)^2 -4(3)(-5)}}{2(3)} \implies x = \cfrac{ -2 \pm \sqrt { 4 +60}}{ 6 } \\\\\\ x= \cfrac{ -2 \pm \sqrt { 64 }}{ 6 }\implies x=\cfrac{ -2 \pm 8}{ 6 }\implies x= \begin{cases} ~~ 1\\ -\frac{5}{3} \end{cases}[/tex]
Answer:
-5/3 and -1
Step-by-step explanation:
I am not sure what you mistake is, but here is my solution. I hope that it helps. I am sorry that you are frustrated. We have all been there.
pllllllllllllllllllllleasee one guys i neeed ur help one
Answers
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Calculate discriminant :
[tex]\qquad \sf \dashrightarrow \: 3 {x}^{2} + 6x - 1[/tex]
a = 3b = 6c = 1[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (6) {}^{2} - (4 \times 3 \times 1)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 36 - 12[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 24[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d} = 2 \sqrt{6} [/tex]
Now, let's calculate it's roots ( x - intercepts )
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - b \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{2 \times 3} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6\pm 2 \sqrt{6} }{6} [/tex]
So, the intercepts are :
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6 - 2 \sqrt{6} }{6} [/tex]
and
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{ - 6 + 2 \sqrt{6} }{6} [/tex]
Answer:
[tex]\left( \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ 0\right), \ \left(\dfrac{ -3 - 2\sqrt{3}}{ 3}, \ 0\right)[/tex]
Explanation:
Given expression:
f(x) = 3x² + 6x - 1
To find x intercepts, set f(x) = 0Use quadratic formula:
[tex]\sf x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ where \ ax^2 + bx + c = 0[/tex]
Here after finding coefficients:
a = 3, b = 6, c = -1Applying formula:
[tex]x = \dfrac{ -6 \pm \sqrt{6^2 - 4(3)(-1)}}{2(3)}[/tex]
[tex]x = \dfrac{ -6 \pm \sqrt{48}}{6}[/tex]
[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{6}[/tex]
[tex]x = \dfrac{ -6 \pm 4\sqrt{3}}{2 \cdot 3}[/tex]
[tex]x = \dfrac{ -3 \pm 2\sqrt{3}}{ 3}[/tex]
[tex]x = \dfrac{ -3 + 2\sqrt{3}}{ 3}, \ \dfrac{ -3 - 2\sqrt{3}}{ 3}[/tex]
Which is a recursive formula for the sequence 99.4, 0, –99.4, –198.8, where f(1) = 99.4? f(n 1) = f(n) 99.4, n ≥ 1 f(n 1) = f(n) – 99.4, n ≥ 1 f(n 1) = 99.4f(n), n ≥ 1 f(n 1) = –99.4f(n), n ≥ 1
Answers
The recursive formula for the given sequence is [tex]f(n+1)=f(n)-99.4[/tex]
What is recursive formula?Any term of a series can be defined by its preceding term in a recursive formula (s). For instance: An arithmetic series has the recursive formula [tex]a_n = a_{n-1} + d[/tex]. [tex]a_n = a_{n-1}r[/tex] is the recursive formula for a geometric sequence.
We are given a sequence as:
99.4,0,-99.4,-198.8, and so on
We can see that the sequence is constantly getting decreased by -99.4
i.e. f(1)=99.4
Then, f(2)=f(1)-99.4
=99.4-99.4
=0
f(3)=f(2)-99.4
=0-99.4
=-99.4
Therefore, the recursive formula of the given series is [tex]f(n+1)=f(n)-99.4[/tex]
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A square of sides 6cm has been removed from regular pentagon of sides 12cm. Calculate the perimeter of the shape
Answers
The perimeter of the shape is 52 cm
How to determine the perimeter of the shape?The shape is given as:
Regular pentagon
The length of the sides are
Length = 12 cm
So, the perimeter of the regular pentagon is
P = 5* Length
This gives
P = 5 * 12cm
Evaluate
P = 60 cm
When the square of sides 6cm is removed from the regular pentagon, the perimeter becomes
P = 60cm - 6cm
Evaluate the difference
P =52 cm
Hence, the perimeter of the shape is 52 cm
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Which of these expressions demonstrates the identity property? 25(0) = 25 25(1) = 25 25 + 0 = 25 25 + 1 = 25
Answers
The expressions which demonstrates the identity property of multiplication is; 25(1) = 25 option B
Identity Property
Identity Property of Multiplication states that any number multiplied by 1 does not change, that is, it is constant or remains the same
Check all options
25(0) = 25
0 = 25
Not true
25(1) = 25
25 = 25
True (identity property of multiplication holds)
25 + 0 = 25
25 = 25
True (Not identity property of multiplication)
25 + 1 = 25
26 = 25
Not true
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Identify the 7th term of the geometric sequence in which a2 = 324 and a4 = 36.
Answers
Answer:
a7=4/3 or a7=-4/3
Step-by-step explanation:
using the geometric sequences formula
an=ar^n-1
a2=ar
a4=ar³
when a2=324 and a4=36
324=ar...........(1)
36=ar³............(2)
from equation (1) a=324/r substitute in equation (2)
we have :
36=324/r *r³
36=324r²
r²=36/324
r²=1/9
r=±1/3
substitute when r=±1/3 in (1)
324=a(±1/3)
a=±972
so the 7th term is
when r=±1/3
we have
a7=ar^6
a7=±972(±1/3)^6
a7=972/729
a7=4/3 or a7=-4/3
The following table represents a relation. X Y -3 0 0-2 5 -3 11-2 Does the table represent y as a function of c? Why or why not? No, because a number in the input is the same as a number in the output. Yes, because there are no x-values with more than one y-value. Yes, because every x-value has at least one y-value. No, because there are two inputs that have the same output.
Answers
The table represent y as a function of c, Yes because every x-value has at least one y-value.
According to the question,
X -3 0 5 11
Y 0 2 -3 -2
In order to find the table represent y as a function of c, When x = -3; y=0; x= 0 ;y=2; x= 0 y=2; x= 5 y=-3; x= 11 y=-2.
No, because a number in the input is the same as a number in the output.⇒ Above option is wrong, because a number in the input is not same as a number in the output.
Yes, because there are no x-values with more than one y-value.⇒ Above option is wrong, because there are many x-values with more than one y-value.
Yes, because every x-value has at least one y-value.⇒ Above option is correct, because every x-value has at least one y-value.
No, because there are two inputs that have the same output.⇒ Above option is wrong, because there are not two inputs that have the same output
Hence, the table represent y as a function of c, Yes, because every x-value has at least one y-value. Above option is correct, because every x-value has at least one y-value.
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The area of a circle is 9pi cm². Find its radius.
Please do this question with full solution:)
Answers
Answer:
3 cm
Step-by-step explanation:
The formula for the area of a circle is:
[tex]A = \pi r^2[/tex]
Where "r" represents the radius of the circle. We can substitute the given value for Area into the equation to solve for the radius.
Solve for Radius[tex]A=\pi r^2\\9\pi = \pi r^2[/tex]
Divide both sides by π
[tex]9=r^2[/tex]
Take the square root of both sides
[tex]\sqrt9=\sqrt {r^2}\\r=3[/tex]
The radius of the circle is 3 cm.
PLEASE HELP!!!!!!!!!!!!!!!!!!
Answers
Answer:
[tex]\sin\left(x+\frac{\pi}{7} \right)[/tex]
Step-by-step explanation:
[tex]\sin\left(x+\frac{\pi}{7} \right)=\sin \frac{\pi}{7}\cos x +\cos \frac{\pi}{7} \sin x[/tex]
HELPPPP!!!!! Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each given function with the description of its graph.
Answers
Answer:
y = 2(1/2)^x --> Second choice
y = (1/4)^x --> First choice
y = 3^x --> Third choice
Step-by-step explanation:
Take a look at the images uploaded for the reasons why.
y = 2(1/2)ˣ is y intercept (0,2) second choice, y = (1/4)ˣ is y intercept (0,1) first choice, y = 3ˣ is y intercept (0,1), fourth choice.
Let's break down each of the given exponential functions and understand their y-intercepts:
y = 2(1/2)ˣ :
When x = 0, the value of (1/2)ˣ is 1, since any number raised to the power of 0 is 1. Therefore, y = 2 * 1 = 2 when x = 0. This gives us the y-intercept (0, 2).
y = (1/4)ˣ :
Similarly, when x = 0, the value of (1/4)ˣ is 1, since any number raised to the power of 0 is 1. Therefore, y = 1 when x = 0. This gives us the y-intercept (0, 1).
y = 3ˣ :
Again, when x = 0, the value of 3ˣ is 1. Therefore, y = 1 when x = 0. This gives us the y-intercept (0, 1).
The y-intercept is the point where the graph of the function intersects the y-axis, which occurs when x is zero. In all three cases, when x = 0, the exponent becomes zero, resulting in the base being raised to the power of zero, which is always equal to 1. The graph is given below.
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s in
Squaring both sides of the equation
√√x+1=√x+6-1 and simplifying, the equation
becomes 3 = √√x+6.
The solution of the equation is
Answers
The value of x in given linear equation is x = 3.
According to the statement
we have given that the equation and we have to find the solution of that equation.
So, For this purpose,
The given equation is :
[tex]\sqrt{ x+1} = \sqrt{ x+6} -1[/tex]
From this equation it is clear that the it is a linear equation.
So, for find the value of x
To solve this equation squaring on both sides then equation become
x+1 = x+6 +1 -2√x+6.
Then
-2√x+6 = -6
then
[tex]\sqrt{x + 6} = 3[/tex]
Now remove the square by S.B.S.
Then the equation become
x +6 = 9
x = 3.
In this equation the value of x is 3.
So, The value of x in given linear equation is x = 3.
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Solve for d.
5+d > 5−d
Answers
Answer:
d>0
Step by Step Explanation:
Let's solve your inequality step-by-step.
5+d>5−d
Step 1: Simplify both sides of the inequality.
d+5>−d+5
Step 2: Add d to both sides.
d+5+d>−d+5+d
2d+5>5
Step 3: Subtract 5 from both sides.
2d+5−5>5−5
2d>0
Step 4: Divide both sides by 2.
2d/2>0/2
d>0
Answer:
3
Step-by-step explanation:
You could put 3 because 5+3 is greater than 5-3.
John, Jim and Joe each went for a medical examination. Their combined height was 5.25 m. If John was 12 cm shorter than Jim and Jim was 0.09 m taller than Joe, how tall, in metres, was Joe?
Answers
The 5.25 m combined height of John, Jim, and Joe, the 12 cm height difference between John and Jim and the 0.09 m difference in height between Jim and Joe, indicates that solution to the word problem is Joe was 1.73 meters tall
What is a word problem?A word problem is a presentation of a math problem using verbal description rather than numbers, variables and operators.
The combined height of John, Jim and Joe = 5.25 m
John's height = Jim's height - 12 cm = Jim's height - 0.12
Jim's height = Joe's height + 0.09 m
Let h represent Joe's height, we get;
Jim's height = h + 0.09
John's height = h + 0.09 - 0.12 = h - 0.03
John's height = h - 0.03
The sum of the heights is therefore; h + h + 0.09 + h - 0.03 = 3·h + 0.06
The sum of their heights = Their combined height = 5.25 meters
Therefore; 3·h + 0.06 = 5.25
h = (5.25 - 0.06)/3 = 1.73
Joe's height, h = 1.73 meters
Jim's height = 1.73 + 0.09 = 1.82
Jim's height = 1.82 meters
John's height = 1.73 - 0.03 = 1.7
John's height is 1.7 meters
Joe was 1,73 meters tall
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In triangle r s t, angle r = 63 degrees, angle t = 90 degrees, side r s = 23 and side s t = 10.4. which ratios are correct?
Answers
The correct ratios are: cos 27=23/RT, sec 27= 23/10.4 and cot 63 = RT/10.4
What is trigonometry ratio in tringle?
Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.In triangle RST, angle T= 90° and angle R= 63°
As the total of all angle in any triangle is 180°, so the measure of the angle S = 180°- (90°+63°)
S= 180°- 153°
S= 27°
According to the rule of trigonometric ratios,
cos(θ) = [tex]\frac{hypotenuse}{opposite}[/tex]
sec(θ) = [tex]\frac{hypotenuse}{adjacent}[/tex]
cot(θ) = [tex]\frac{adjacent}{opposite}[/tex]
In respect of angle R (63°), side RS(23) is hypotenuse , ST(10.4) is opposite and RT is adjacent.
cos(63°) = [tex]\frac{23}{10.4}[/tex]
sec(63°) = [tex]\frac{23}{RT}[/tex]
cot(63°) = [tex]\frac{RT}{10.4}[/tex]
Now, in respect of angle S(27°), hypotenuse is RS(23), adjacent is ST(10.4) and opposite is RT.
So, cos(27°) = [tex]\frac{23}{RT}[/tex]
sec(27°) = [tex]\frac{23}{10.4}[/tex]
cot(27°) = [tex]\frac{10.4}{RT}[/tex]
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Pick the correct answer
Help me please thanks so much
Answers
Answer:
E
Step-by-step explanation:
line I slopes downwards from left to right and has a negative slope.
line K is a horizontal line and has a slope of zero
line J slopes upwards from left to right and has a positive slope
slopes from least to greatest are therefore I, K, J
3. If the geometric mean of a and 25 is 20,
find the value of a.
Answers
Answer:
Value of a is 16.
Step-by-step explanation:
Solution Given:
we know that
Geometric mean=[tex]\sqrt{a*b}[/tex]
By using this formula
20=[tex]\sqrt{a*25}[/tex]
20=5[tex]\sqrt{a}[/tex]
dividing both side by 5, we get
20/5=5/5* [tex]\sqrt{a}[/tex]
4=[tex]\sqrt{a}[/tex]
squaring both side
4²=a
:. a=16
A kite has vertices at (2, 4), (5, 4), (5, 1), and (0, –1).
What is the approximate perimeter of the kite? Round to the nearest tenth.
11.3 units
13.6 units
16.8 units
20.0 units
Answers
Answer:
16.8
Step-by-step explanation:
here is that kite on a graph. you can see there are 2 sides of length 5, and 2 sides of length 3, so closest perimeter is 16.8
Find the solution for the system of linear equations by substitution: 2x - y = 3 y − x = 1
Answers
The solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x- y = 3
y - x = 1
Make y the subject in the second equation, by adding x to both sides of the equation
y - x + x = x + 1
This gives
y = x + 1
Substitute y = x + 1 in 2x- y = 3
2x- x - 1 = 3
Evaluate the like terms
x = 4
Substitute x = 4 in y = x + 1
y = 4 + 1
Evaluate
y = 5
Hence, the solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5
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Find the distance in nm between two slits that produces the first minimum for 405-nm violet light at an angle of 57. 5°
Answers
The distance between two slits is d =2.89*10^-7 m
Distance between slits, d=2.89*10^-7 m
It is given that,
Wavelength, λ = 410nm= 410*10^-9 m
Angle, θ =45
We need to find the distance between two slits that produces first minimum. The equation for the destructive interference is given by :
dsinθ =(n+1/2) λ
For first minimum, n = 0
dsinθ =(1/2) λ
So, d is the distance between slits
d ={1/2 λ}sinθ
=2.89*10^-7 m
So, the distance between two slits is d =2.89*10^-7 m. Hence, this is the required solution.
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How does the mean absolute deviation (mad) of the data in set 1 compare to the mean absolute deviation of the data in set 2? set 1: 12, 8, 10, 50 set 2: 13, 9, 8 the mad of set 1 is 13 less than the mad of set 2. the mad of set 1 is 13 more than the mad of set 2. the mad of set 1 is 2 more than the mad of set 2. the mad of set 1 is 2 less than the mad of set 2.
Answers
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
How to estimate the Mean Absolute Deviation from the given data?Set 1: 12, 8, 10, 50
Set 2: 13, 9,8
To determine the mean for each set
Mean = totality of elements/number of elements
Mean of Set 1:
[tex]$=\frac{12+8+10+50}{4}[/tex]
[tex]$=\frac{80}{4}=20$[/tex]
Mean of Set 2:
[tex]$=\frac{13+9+8}{3}[/tex]
[tex]$=\frac{30}{3}=10$[/tex]
To determine the mean absolute deviation (MAD) of the data in each set.
M.A.D of Set 1:
[tex]$=\frac{|12-20|+|8-20|+|10-20|+|50-20|}{4}[/tex]
[tex]$=\frac{8+12+10+30}{4}=\frac{60}{4}=15$$[/tex]
M.A.D of Set 2:
[tex]$=\frac{|13-10|+|9-10|+|8-10|}{3}[/tex]
[tex]$=\frac{3+1+2}{3}=\frac{6}{3}=2$[/tex]
The Mean Absolute Deviation of Set 1 exists 13 more than the mean absolute deviation of Set 2.
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Oscar corporation is planning to construct an elliptical gate at its headquarters. the width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. the company wants to place two bright spots at the foci of the ellipse. how far from the center of the ellipse will the spots be located?
Answers
The distance from the center of the ellipse to where the spots are located will be 2 feet.
What is Distance?
Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.The distance from the center of the ellipse to where the spots are located will be -
= 5 - 3
= 2 feet.
Therefore, the distance from the center of the ellipse is 2 feet.
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Which of the following scatter plots does not have a zero correlation?
Answers
The first scatter plot does not have a zero correlation.
Option(a) is correct.
A statistic called correlation gauges how much two variables change in connection to one another.
Correlation quantifies correlation but cannot determine whether x causes y or vice versa, or whether a third component is responsible for the association.
A scatterplot may make it easier to spot correlation, particularly when the variables have a non-linear but nevertheless significant association.
Zero means there is no correlation between the two variables under comparison.
A 0 correlation indicates that there is no relationship between the two variables according to the correlation statistic. This merely indicates that there isn't a linear relationship, not that there isn't any link at all. The first scatter plot does not represent a linear relationship, thus, it has zero correlation.
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Brass is an alloy made by melting and mixing copper and zinc. A metallurgist has two brass
alloys, one that is 65% copper and one that is 90% copper. He would like to combine a
portion of each alloy to produce 500 g of a new alloy that is 75% copper.
Write a system of equations for this problem
Answers
Answer:
x +y = 5000.65x +0.95y = 0.75(500)solution: (x, y) = (300, 200)Step-by-step explanation:
A system of equations for the problem can be written using the two given relationships between quantities of brass alloys.
SetupLet x and y represent the quantities in grams of the 65% and 90% alloys used, respectively. There are two relations given in the problem statement.
x + y = 500 . . . . . . quantity of new alloy needed
0.65x +0.90y = 0.75(500) . . . . . quantity of copper in the new alloy
These are the desired system of equations.
SolutionThis problem does not ask for the solution, but it is easily found using substitution for x.
x = 500 -y
0.65(500 -y) +0.90y = 0.75(500)
(0.90 -0.65)y = 500(0.75 -0.65) . . . . . . subtract 0.65(500)
y = 500(0.10/0.25) = 200
x = 500 -200 = 300
300 grams of 65% copper and 200 grams of 90% copper are needed.
Tim, paco, maria, and jenny are standing in line for lunch. jenny is standing between paco and maria, and paco’s position in line is an odd number. tim is not standing on either end of the line, and he is in front of jenny. which friend is standing third in line?
Answers
Answer:
the order is Paco, Tim, Jenny, Maria
Step-by-step explanation:
Answer:
b.
Paco, Tim, Jenny, Maria
Step-by-step explanation:
Solve the equation the square root of the quantity x plus 4 minus 3 equals 1 for the variable.
Answers
Answer:
x = 12
Step-by-step explanation:
sqrt(x+4) - 3 = 1
First get the sqrt all by itself on one side of the equation. Add 3 to both sides of the equation.
sqrt(x+4) = 1 + 3
sqrt(x+4) = 4
To "fix" the sqrt, that is, "undo it" and get rid of it, you have to SQUARE both sides of the equation.
(sqrt(x+4))^2 = 4^2
x + 4 = 16
subtract 4 to finish up.
x = 12
Check:
sqrt(12 + 4) - 3 = 1
sqrt16 - 3 = 1
4 - 3 = 1
1 = 1 Check!
[tex]\frac{12}{20} =_____% = _____ hundredths
Answers
The percentage form of given fraction is 60% and the hundredths form is 0.60
According to the statement
we have given that the a fraction and we have to find the percentage of that fraction and write in the form hundredths.
So, For this purpose,
The given fraction is 12/20.
Then the definition of the percentage is that
The Percentage, a relative value indicating hundredth parts of any quantity.
so, the percentage of given fraction is :
Percentage fraction = 12/20 * 100
After solving it, The percentage fraction will become:
Percentage fraction = 60%
and Now convert into the hundredths form then
In the hundredths form it will become
from 60% to 0.60.
So, The percentage form of given fraction is 60% and the hundredths form is 0.60
Learn more about Percentage here
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can someone help me with this?
Answers
Answer:
Step-by-step explanation:
Beatrice's conclusion is wrong
All of these points are not on the same line, because are different parallel lines
The slope between (-2,-1) and (1,0) is equal to 1/2
Answer:
Beatrice is incorrect. All of these points are not on the same line because the slope between (-2,-1) and (1,0) which are coordinates fr each of the pairs above, are equal to 1/2
Step-by-step explanation:
Let m1 be first slope
[tex]m1 \: = \frac{y2 - y1}{x2 - x1}= \frac{0 - ( - 2)}{4 - ( - 2)}= \frac{0 + 2}{4 + 2} \\ = \frac{2}{4} = \frac{1}{2} [/tex]
Let m2 be second slope
m2 = (y2 - y1)/ (x2 - x1)
= (2-(-1)) / (4-(-2)
= (2+1) / (4+2)
= 3/6 =1/2
Thus, the slopes are different parallel lines because m1 =m2