Answer:
integer of course
Step-by-step explanation:
an integer can either be negative or positive.
i need help will rate you branliest
Answer:
D. the bottom one is the answer, because hyperbola is two curves that curve infinitely
Find the measure of c.
Answer:
149 degrees
Step-by-step explanation:
This shape is a cyclic, so opposite angles add up to 180 degrees.
180-31 = 149
Century Roofing is thinking of opening a new warehouse, and the key data are shown below. The company owns the building that would be used, and it could sell it for $100,000 after taxes if it decides not to open the new warehouse. The equipment for the project would be depreciated by the straight-line method over the project's 3-year life, after which it would be worth nothing and thus it would have a zero salvage value. No new working capital would be required, and revenues and other operating costs would be constant over the project's 3-year life. What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.)
Question Completion:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Answer:
Century Roofing
Project's NPV is: ($6,578)
Step-by-step explanation:
a) Data and Calculations:
WACC = 10.0%
Opportunity cost = $100,000
Net equipment cost (depreciable basis) = $65,000
Straight-line deprec. rate for equipment = 33.333%
Sales revenues, each year = $123,000
Operating costs (excl. deprec.), each year = $25,000
Tax rate = 35%
Cash outflow in year 0 = $165,000 (Opportunity and new equipment costs)
Annual Cash inflow = $123,000 - $25,000 - $34,300 = $63,700
PV of annuity for 3 years at 10% = $158,422 ($63,700 x 2.487)
NPV = Cash inflow minus Cash outflow
= $158,422 - $165,000
= ($6,578)
Negative NPV
b) Since Century Roofing could have realized $100,000 from the sale of the building if it decides not to open the new warehouse, this opportunity cost is factored into the calculation of the Net Present Value. It becomes a present cash outflow. Century Roofing's opportunity cost is defined as the loss of $100,000 being the future return from the best alternative project when it chooses to build the new warehouse instead of selling off the building.
BRAINLEST , If y varies inversely with the square of x, and y = 26 when x = 4, find y when x = 2.
Answer:
Question 18: B. 104
Question 19: [tex] x = \frac{3}{2} [/tex]
Step-by-step Explanation:
Question 18:
Step 1: express the inverse relationship with an equation
[tex] y = \frac{k}{x^2} [/tex] ,
where k is constant
y = 26 when x = 4,
Constant, k, = [tex] y*x^2 = k [/tex]
[tex] k = 26*4^2 = 416 [/tex]
The equation would be [tex] y*x^2 = 416 [/tex]
Step 2: use the equation to find y when X = 2.
[tex] y*x^2 = 416 [/tex]
[tex] y*2^2 = 416 [/tex]
[tex] y*4 = 416 [/tex]
Divide both sides by 4
[tex] \frac{y*4}{4} = \frac{416}{4} [/tex]
[tex] y = 104 [/tex]
Question 19:
[tex] \frac{x}{3} = \frac{x + 2}{7} [/tex]
Cross multiply
[tex] x(7) = 3(x + 2) [/tex]
[tex] 7x = 3x + 6 [/tex]
Subtract 3x from both sides
[tex] 7x - 3x = 3x + 6 - 3x [/tex]
[tex] 4x = 6 [/tex]
Divide both sides by 4
[tex] \frac{4x}{4} = \frac{6}{4} [/tex]
[tex] x = \frac{3}{2} [/tex]
Answer: D.) 52
Explanation: I guessed and got it right lol
Rhombus J K L M is shown. The length of J K is 2 x + 4 and the length of J M is 3 x. What is the length of a side of rhombus JKLM? 4 units 8 units 12 units 16 units
Answer:
12 units
Step-by-step explanation:
Since all of the sides of a rhombus are congruent, JK = JM which means:
2x + 4 = 3x
-x = -4
x = 4 so 3x = 3 * 4 = 12
BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Answer:
$935.76
Step-by-step explanation:
BOND VALUATION Asiana Fashion's bonds have 10 years remaining to maturity. Interest is paid annually; they have a $1,000 par value; the coupon interest rate is 8% and thebyield to maturity is 9%.What is the bond's current market price?
Step 1
We find the Present value factor of sum
The formula =
(1 + i)^n
Where
i = maturity rate = 9% = 0.09
n = number of years = 10 years
Present Value = ( 1 + 0.09)^-10
= 0.4224
Step 2
We find the present value factor of annuity
The formula is given as:
1 - (1+i)^-n / i
i = maturity rate = 9% = 0.09
n = number of years = 10 years
= 1 - (1 + 0.09)^-10 /0.09
= 1 - 0.4224 /0.09
= 0.5775 /0.09
= 6.417
Step 3
The bond's current market price is calculated as:
= PV factor of Sum × Par Value + PV factor of annuity × coupon payment
Coupon payment is calculated as:
= Coupon interest × par value
= 8% × 1000
= 80
Hence,
= 0.4224 × 1,000 + 6.417 × 80
= 422.4 + 513.36
= 935.76
In this exercise we have to use the knowledge of finance to calculate the corrective value of the market place, in this way we find that:
[tex]\$935.76[/tex]
We find the Present value factor of sum, by the formula of:
[tex](1 + i)^n[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]Present \ Value = ( 1 + 0.09)^{-10} = 0.4224[/tex]
We find the present value factor of annuity, by the formula as:
[tex]1 - (1+i)^{-n} / i[/tex]
Where:
i = maturity rate = 9% = 0.09 n = number of years = 10 years
Substituting the values in the formula as;
[tex]= 1 - (1 + 0.09)^{-10} /0.09\\= 1 - 0.4224 /0.09\\= 0.5775 /0.09\\= 6.417[/tex]
The bond's current market price is calculated as:
[tex]= PV \ factor\ of\ Sum * Par\ Value + PV\ factor\ of\ annuity * coupon\ payment[/tex]
Coupon payment is calculated as:
[tex]= Coupon\ interest * par\ value\\= 8\% * 1000= 80[/tex]
So continue the calcule;
[tex]= 0.4224 *1,000 + 6.417 * 80\\= 422.4 + 513.36\\= 935.76[/tex]
See more about market place at brainly.com/question/24518027
Enter an expression that is equivalent to (6x2−1)+(x2+3)−2(x2−5)−15x2, combining all like terms. Use the on-screen keyboard to type the correct polynomial in the box below.
Answer:
Its 10x^2+12
Step-by-step explanation:
Answer:
-10X^2+12
Step-by-step explanation:
3
BO
Evaluate the function f(x) = x2 + 4x + 1 at the given values of the independent variable and simplify.
a. f(6)
b. f(x +9)
c. f(-x)
Answer:
a) f(6)=(6)^2+4(6)+1=65
b)f (x+9)=(x+9)^2+4 (x+9)+1=(x^2+18x+81)+(4x+36)+1=x^2+22x+117
f (-x)=(-x)^2-4x+1
Choose the situation that represents a function.
A) The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie.
B) The inches of rainfall is a function of the day’s average temperature.
C) The time it takes to cook a turkey is a function of the turkey’s weight.
D) The number of sit-ups a student can do in a minute is a function of the student’s age.
Answer:c
Step-by-step explanation:
Answer: The answer is C.
Hope this helps you!
Solve x/10 = -7 A. x = 3 B. x = -0.7 C. x = -17 D. x = -70
Answer:
x = -70
Step-by-step explanation:
x/10 = -7
Multiply each side by 10
x/10*10 = -7*10
x = -70
in the diagram, find the values of a and b.
Answer:
m∠a = 67° , m∠b = 42°Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
PLEASE HELP!!! The question is.. [tex]163-y=-5[/tex] ANSWER GETS BRAINLIEST
Answer:
y = 168Step-by-step explanation:[tex]163 -y =-5\\Collect\:Like\:terms\\163+5 = y\\Simplify\\168 =y\\\\y = 168[/tex]
Hello There!
Answer: [tex]163-168=-5[/tex]Explanation:[tex]163-y=-5[/tex]
To solve your equation, you can just change the -5 to 5 and move it to where y is. After that, change the minus sign to addition.
[tex]163+5=y[/tex]
Now all you have to do is sum it up.
[tex]163+5=168[/tex]
So y = to 168
So your answer is
[tex]163-168=-5[/tex]
Hope this Helps!
Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked.Required:a. What is the (approximate) probability that X is at most 30?b. What is the (approximate) probability that X is less than 30?c. What is the (approximate) probability that X is between 15 and 25 (inclusive)?
Answer:
(a) The probability that X is at most 30 is 0.9726.
(b) The probability that X is less than 30 is 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.
Step-by-step explanation:
We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.
Let X = the number among these that are nonconforming and can be reworked
The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).
Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.
Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).
So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]200 \times 0.11[/tex] = 22
and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{200 \times 0.11 \times (1-0.11)}[/tex]
= 4.42
So, X ~ Normal([tex]\mu =22, \sigma^{2} = 4.42^{2}[/tex])
(a) The probability that X is at most 30 is given by = P(X < 30.5) {using continuity correction}
P(X < 30.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{30.5-22}{4.42}[/tex] ) = P(Z < 1.92) = 0.9726
The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.
(b) The probability that X is less than 30 is given by = P(X [tex]\leq[/tex] 29.5) {using continuity correction}
P(X [tex]\leq[/tex] 29.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{29.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] 1.70) = 0.9554
The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = P(X < 25.5) - P(X [tex]\leq[/tex] 14.5) {using continuity correction}
P(X < 25.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{25.5-22}{4.42}[/tex] ) = P(Z < 0.79) = 0.7852
P(X [tex]\leq[/tex] 14.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{14.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] -1.70) = 1 - P(Z < 1.70)
= 1 - 0.9554 = 0.0446
The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.
Therefore, P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = 0.7852 - 0.0446 = 0.7406.
A human factor expert recommends that there be atleast 9 square ft of floor space in a classroom for every student in the class. Find the min space required for 49 students
Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?
Answer:
The percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 100[/tex]
The percent of people who write this exam obtain scores between 350 and 650
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
[tex]P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )[/tex]
[tex]P(350 < X 650 ) = P(-1.5<Z < 1.5 )[/tex]
[tex]P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)[/tex]
From the z-table [tex]P(Z < -1.5 ) = 0.066807[/tex]
and [tex]P(Z < 1.5 ) = 0.93319[/tex]
=> [tex]P(350 < X 650 ) = 0.93319 - 0.066807[/tex]
=> [tex]P(350 < X 650 ) = 0.866[/tex]
Therefore the percentage is [tex]P(350 < X 650 ) = 86.6\%[/tex]
Mark is buying supplies for his students. He is buying a notebook (n) and a pack of pencils for each of his 25 students. Each pack of pencils costs $1.25. If Mark's total cost is $156.25, which of the following equations can be used to find how much each notebook cost? Select TWO that apply.
Answer:
$5
Step-by-step explanation:
Note. There are no options to select.Let the notebook cost x, then Mark spent:
25x + 25*1.25 = 156.2525x + 31.25 = 156.2525x = 156.25 - 31.2525x = 125x= 125/25x= 5Notebook costs $5
A planet rotates on an axis through its poles and 1 revolution takes 1 day 1 day is 24 hours. The distance from the axis to a location the planet 30 degrees north latitude is about 3387.5 miles. Therefore, a location on the planet at 30 degrees north latitude is spinning on a circle of radius 3387.5 miles.
Compute the linear speed on the surface of the planet at 30 degrees north latitude.
Answer:
The velocity is [tex]v = 886.96 \ m/s[/tex]
Step-by-step explanation:
From the question we are told that
The period of each revolution is [tex]T = 1\ day = 24 \ hours[/tex]
The angle is [tex]\theta = 30^o[/tex]
The radius is [tex]r = 3387.5 \ miles[/tex]
Generally the linear speed is mathematically represented as
[tex]v = w * r[/tex]
Where [tex]w[/tex] is the angular speed which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 *3.142 }{24}[/tex]
[tex]w = 0.2618 \ rad/s[/tex]
Thus
[tex]v = 0.261833 * 3387.5[/tex]
[tex]v = 886.96 \ m/s[/tex]
Please answer this correctly without making mistakes
Step-by-step explanation:
Option A and B are the correct answer because it equal to 688.5 and 688.05
Answer:
it is 1377/2 and 688 1/17 thats the answer
Step-by-step explanation:
Suppose the following data show the prices of 4 cars with similar characteristics that sold at a recent auction (in thousands of dollars): 6.6, 5, 10.7, 7.3. Calculate the standard deviation of the sample of selling prices. (please express your answer using 2 decimal places)
Answer: 2.40
Step-by-step explanation:
Given: The prices of 4 cars with similar characteristics that sold at a recent auction (in thousands of dollars): 6.6, 5, 10.7, 7.3.
Let x: 6.6, 5, 10.7, 7.3.
n= 4
Mean : [tex]\overline{x}=\dfrac{\sum x}{n}[/tex]
[tex]\Rightarrow\ \overline{x}=\dfrac{6.6+5+10.7+7.3}{4}\\\\=\dfrac{29.6}{4}\\\\=7.4[/tex]
Now , standard deviation = [tex]\sqrt{\dfrac{\sum(x-\overline{x})^2}{n-1}}[/tex]
[tex]=\sqrt{\dfrac{(6.6-7.4)^2+( 5-7.4)^2+( 10.7-7.4)^2+( 7.3-7.4)^2}{4-1}}\\\\=\sqrt{\dfrac{0.64+5.76+10.89+0.01}{3}}\\\\=\sqrt{\dfrac{17.3}{3}}\approx2.40[/tex]
Hence, the standard deviation of the sample of selling prices = 2.40
A type of related samples design in which participants are observed more than once is called a
A. repeated measures design
B. matched pairs design
C. matched samples design
D. both matched pairs design and matched samples design
Answer:
Option A (repeated measures design) is the correct option.
Step-by-step explanation:
Researchers as well as statisticians vary in terms of methods used mostly for repetitive measurements. Besides illustration, repeated models of measurements are however recognized as repeated analyzes of variance measurements, standardized considerations of measurements, or layouts of objects throughout them.The other three options are not related to the given instance. So that alternative A would be the correct choice.
The formula for the area of a square is s2, where s is the side length of the square. What is the area of a square with a side length of 6 centimeters? Do not include units in your answer.
Answer:
36
step by step
given length=6
so area of square is given by s2 i.e 6^2
=6×6
=36 (Ans)
Question
Consider this expression.
4/2² - 6²
Type the correct answer in the box. Use numerals instead of words. For help, see this worked example e.
When a =
-5 and b = 3, the value of the expression is
Submit
Answer:
16
Step-by-step explanation:
4 * sqrt( a^2 - b^2)
Let a = -5 and b =3
4 * sqrt( (-5)^2 - 3^2)
Do the squaring first
4 * sqrt( 25 - 9)
Subtract inside the square root
4 * sqrt( 16)
Take the square root
4 * 4
Multiply 16
Answer:
[tex]\Large \boxed{16}[/tex]
Step-by-step explanation:
[tex]4\sqrt{a^2-b^2 }[/tex]
[tex]\sf Plug \ in \ the \ values \ for \ a \ and \ b.[/tex]
[tex]4\sqrt{-5^2-3^2 }[/tex]
[tex]4\sqrt{25-9 }[/tex]
[tex]4\sqrt{16}[/tex]
[tex]4 \times 4=16[/tex]
name all the pairs of angles which are vertical angles , alternate interior angles , alternate exterior angles , co interior angles , co exterior angles , and corresponding angles from the given figure . (co interior - interior angles on the same side of transversal)
Answer:
Step-by-step explanation:
Since m and k are the parallel lines and a transverse 'l' is intersecting these lines at two different points.
- Opposite angles at the point of intersection of parallel lines and the transverse will be the vertical angles.
∠1 ≅ ∠3, ∠2 ≅ ∠4, ∠5 ≅ ∠8 and ∠6 ≅ ∠7 [Vertical angles]
- Pair of angles between parallel lines 'k' and 'm' but on the opposite side of the transversal are the alternate interior angles.
∠4 ≅ ∠6 and ∠3 ≅ ∠5 [Alternate interior angles]
- Angles having the same relative positions at the point of intersection are the corresponding angles.
∠2 ≅ ∠6, ∠3 ≅ ∠8, ∠4 ≅ ∠7 and ∠1 ≅ ∠5 [Corresponding angles]
- Co interior angles are the angles between the parallel lines located on the same side of the transversal.
∠4 and ∠5, ∠3 and ∠6 [Co interior angles]
- Co exterior angles are the angles on the same side of the transverse but outside the parallel lines.
∠2 and ∠8, ∠1 and ∠7 [Co exterior angles]
PLEASE HELP ASAP Madelyn drove a race car in a race. She averaged 55 mph and began the race 0.5 hours ahead of the other drivers. The variable d represents Madelyn's distance driven, in miles. The variable t represents the number of hours since the other drivers began to race. Which equation can be used to determine the distance Madelyn drove t hours into the race? d=55t−0.5 d=55(t+0.5) d=55(t−0.5) d = 55t + 0.5
Answer:
d=55(t+0.5)
Step-by-step explanation:
d=55(t+0.5)
Answer:
27.5
Step-by-step explanation:
Marine ecologists estimate the reproduction curve for swordfish in a fishing ground to be f(p) = −0.01p2 + 9p, where p and f(p) are in hundreds. Find the population that gives the maximum sustainable yield, and the size of the yield.
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?
Answer:
92 inches squared
Step-by-step explanation:
T/P = 8 * 3
L/R = 3 * 2
F/B = 8 * 2
Solving for surface area!
2(24) + 2(6) + 2(16) = 92
Find the work W done by a force of 7pounds acting in the direction 30 degreesto the horizontal in moving an object 7feet from (0 comma 0 )to (7 comma 0 ).
Answer:
The work done by the force is 42.4 Joules
Step-by-step explanation:
The force F = 7 pounds
angle to the horizontal that the force acts ∅ = 30°
The object is moved a distance d = 7 feet
The coordinate (0 comma 0 )to (7 comma 0 ), indicates that the movement started from the origin, and is along the x-axis.
The work done by this force = F cos ∅ x d
==> 7 cos 30° x 7
==> 7 x 0.866 x 7 = 42.4 Joules
Given the following hypotheses: H0: μ = 490 H1: μ ≠ 490 A random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9. Using the 0.01 significance level:
a.) State the decision rule.
b.) Compute the value of the test statistic.
c.) What is your decision regarding the null hypothesis?
Answer:
We conclude that the population mean is equal to 490.
Step-by-step explanation:
We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490 {means that the population mean is equal to 490}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490 {means that the population mean is different from 490}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_1_4[/tex]
where, [tex]\bar X[/tex] = sample mean = 495
s = sample standard deviation = 9
n = sample of observations = 15
So, the test statistics = [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex] ~ [tex]t_1_4[/tex]
= 2.152
The value of t-test statistics is 2.152.
Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.
Therefore, we conclude that the population mean is equal to 490.
5/7 minus 2/9 please
Answer:
[tex]\large \boxed{31/63}[/tex]
Step-by-step explanation:
5/7 - 2/9
Make denominators equal by LCM.
(5 × 9)/(7 × 9) - (2 × 7)/(9 × 7)
45/63 - 14/63
Subtract fractions since denominators are equal.
(45 - 14)/63
31/63
Answer:
[tex]\frac{31}{63}[/tex]
Step-by-step explanation:
Find the LCM of 7 and 9: 63Find how much we increased each number to get to 63: we increased 7 by 9, and we increased 9 by 7Multiply the numerators by the corresponding increase numbers: 5 × 9 = 45, and 2 × 7 = 14Put the new numerators over the new denominators, so it looks like this: [tex]\frac{45}{63}[/tex] and [tex]\frac{14}{63}[/tex] Finally, subtract one from the other and here's what you get: [tex]\frac{31}{63}[/tex]Therefore, the answer is [tex]\frac{31}{63}[/tex].
Evaluate 2/3 + 1/3 + 1/6 + … THIS IS CONTINUOUS. It is NOT as simple as 2/3 + 1/3 + 1/6.
[tex]a=\dfrac{2}{3}\\r=\dfrac{1}{2}[/tex]
The sum exists if [tex]|r|<1[/tex]
[tex]\left|\dfrac{1}{2}\right|<1[/tex] therefore the sum exists
[tex]\displaystyle\\\sum_{k=0}^{\infty}ar^k=\dfrac{a}{1-r}[/tex]
[tex]\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{1}{6}+\ldots=\dfrac{\dfrac{2}{3}}{1-\dfrac{1}{2}}=\dfrac{\dfrac{2}{3}}{\dfrac{1}{2}}=\dfrac{2}{3}\cdot 2=\dfrac{4}{3}[/tex]
