Answer:
The answer is
[tex]y = 3[/tex]
[tex]y = - 4[/tex]
Step-by-step explanation:
We must find a solution where
[tex] \frac{6}{y + 1} + \frac{y}{y - 2} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]
Consider the Left Side:
First, to add fraction multiply each fraction on the left by it corresponding denomiator and we should get
[tex] \frac{6}{y + 1} \times \frac{y - 2}{y - 2} + \frac{y}{y - 2} \times \frac{y + 1}{y + 1} [/tex]
Which equals
[tex] \frac{6y - 12}{(y -2) (y + 1)} + \frac{ {y}^{2} + y }{(y - 2)(y + 1)} [/tex]
Add the fractions
[tex] \frac{y {}^{2} + 7y - 12 }{(y - 2)(y + 1)} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]
Simplify the right side by multiplying the fraction
[tex] \frac{6y}{(y + 1)(y + 2)} [/tex]
Set both fractions equal to each other
[tex] \frac{6y}{(y + 1)(y - 2)} = \frac{ {y}^{2} + 7y - 12}{(y + 1)(y - 2)} [/tex]
Since the denomiator are equal, we must set the numerator equal to each other
[tex]6y = {y}^{2} + 7y - 12[/tex]
[tex] = {y}^{2} + y - 12[/tex]
[tex](y + 4)(y - 3)[/tex]
[tex]y = - 4[/tex]
[tex]y = 3[/tex]
Answer:
Step-by-step explanation:
[tex]\frac{6}{y+1}+\frac{y}{y-2}=\frac{6}{y+1} \times \frac{y}{y-2} \\multiply ~by~(y+1)(y-2)\\6(y-2)+y(y+1)=6y\\6y-12+y^2+y=6y\\y^2+y-12=0\\y^2+4y-3y-12=0\\y(y+4)-3(y+4)=0\\(y+4)(y-3)=0\\y=-4,3[/tex]
A 27% solution ( 27mg per 100 mL of solution) is given intravenously. Suppose a total of 1,36 L of the solution is given over a 10 -hour period. Complete parts (a) through (c) below.
a. What is the flow rate in units of mL/hr?
nothing mL/hr (Type an integer or decimal rounded to the nearest thousandth as needed.)
What is the flow rate in per hour?
nothing mg/hr (Type an integer or decimal rounded to the nearest thousandth as needed.)
b. If each mL contains 13 drops (the drop factor is expressed as gtt/mL), what is the flow rate in units of 13gtt/hr?
nothing gtt/hr (Type an integer or decimal rounded to the nearest thousandth as needed.)
c. During the 10 -hour period, how much is delivered?
nothing mg (Type an integer or decimal rounded to the nearest thousandth as needed.)
Answer:
Step-by-step explanation:
a.
(1.36 L)/(10 hr) = (0.136 L)/(hr)
Flow rate = (0.136 L)/(hr) × (1000 mL)/L = (136 mL)/(hr)
136 mL × (27 mg)/(100 mL) = 36.72 mg
Delivery rate = (36.72 mg)/(hr)
b.
(136 mL)/(hr) × (13 gtt)/(mL) = (1868 gtt)/(hr)
c.
10 hr × (36.72 mg)/)hr) = 367.2 mg
How much fabric is needed to make a tent in the shape of a triangular prism with the following measures?
Answer:
The fabric needs 196.4 ft²
Step-by-step explanation:
∵ The tent formed formed from 4 faces
two equilateral triangles with side length 7 ft
two rectangles with dimensions 11 ft and 7 ft
∵ Area equilateral Δ = 1/4 S²√3
∵ Area rectangle = L × W
∴ The area of the prism = 2 × 1/4 × (7)²√3 + 2 × 7 × 11
= 196.4 ft²
Note:
If you find the area of the triangle by the rule 1/2 × base × height
∴ Area Δ = 1/2 × (7) × 6 = 21 ft²
∴ Area tent = 2 × 21 + 2 × 77 = 196 ft²
Two answer very closed
Answer:
273 ft^2 (apparently you have to cover the ground)
Step-by-step explanation:
Match each equation with its graph.
Carin opened a money market account with a deposit of $3,000. This account earns 2% simple interest annually. How many years will it take for her $3,000 deposit to earn $420 in interest, assuming she does not withdraw any of the money?
Answer: 7 years
2% = 0.02
3000·0.02=60.00
1 year simple interest = $60.00
420/60=7
7 years
evaluate the expression when b= -6 and c=3
-4c+b
Answer:
-18
Step-by-step explanation:
b = -6
c = 3
-4c + b = ?
Plug in the value of each variable into the equation
-4c + b = ?
= -4(3) + (-6)
= -12 - 6
= -18
The sum of an a.p is 340. the first term is 7 and the common difference is 6. Cal the number of terms in the sequence.
anyone?
Common difference: 6
First term: 7
Second term: 13
Third term: 19
Fourth term: 25
Fifth term: 31
I hope this is correct and helps!
Answer to the following question is as follows;
Number of term in AP (N) = 10
Step-by-step explanation:
Given:
Sum of arithmetic progression (Sn) = 340
First term of AP (a) = 7
Common difference of AP (d) = 6
Find;
Number of term in AP (N)
Computation:
Sn = [n/2][2a + (n-1)d]
340 = [n/2][2(7) + (n-1)6]
340 = [n/2][14 + 6n - 6]
680 = n[6n + 8]
6n² + 8n - 680
Using Quadratic Formula
n = 10
Number of term in AP (N) = 10
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The function f(x) = 7x + 1 is transformed to function g through a horizontal compression by a factor of 3. What is the equation of function &
Substitute a numerical value for k into the function equation.
Step-by-step explanation:
The horizontal stretch or compression for a function f(x) is given by g = f(bx) where b is a constant. If b> 0 then the graph of a function is compressed.
As it is given in the question that the function is transformed by a compression factor of 3.
Given function
The value of k will be 3 if the function is transformed by a compression factor of 3
The foot of a ladder is placed 9 feet away from a wall. If the top of the ladder rests 13 feet up on the wall, find the length of the ladder.
4 feet
15.81 feet
8.81 feet
13 feet
Answer:
15.81 ft .
Step-by-step explanation:
This question is based on " Pythagoras Theorem " . If we imagine the given situation as a right angled triangle , then the base will be " 9ft " , and the perpendicular will be " 13 ft" . And the length of the ladder will be equal to hypontenuse of the triangle.
Using Pythagoras Theorem :-
[tex]\implies\rm h^2= p^2+b^2 \\\\\implies\rm h^2 = (9ft)^2+(13ft)^2 \\\\\implies\rm h^2 = 81 ft^2 + 169 ft^2 \\\\\implies\rm h^2 = 250ft^2 \\\\\implies \boxed{ \rm Ladder's \ Length = 15.81 \ ft }[/tex]
Hence the length of the ladder is 15.81 ft.
A computer disk that once sold for $2.25 now sells for 25% less. How much does the computer.
Answer:
$ 1.6875 or $1.69 or $1.70
1^2 +2^2+••••+n^2=1/6n(n+1)(2n+1)
using maths induction
Hello,
[tex]if\ n=1\ then\ 1^2=1\ and\ \dfrac{1}{6}*1*2*3=1:\ true\ for\ n=1\\[/tex]
We suppose the property true for n:
1²+2²+...+n²=n(n+1)(2n+1) / 6
and we are going to demonstrate that the property is true for n+1:
1²+2²+..+(n+1)²=(n+1)*(n+2)*(2n+3)/6
[tex]1^2+2^2+...+n^2+(n+1)^2\\\\=n*(n+1)*(2n+1)/6+(n+1)^2\\\\=(n+1)/6*[n(2n+1)+6n+6]\\\\=(n+1)/6*(2n^2+7n+6)\\\\=(n+1)(n+2)(2n+3)/6\\[/tex]
Find the area of the figure
Answer:
24
Step-by-step explanation:
divide the area in 2 regions
4 x 2 = 8 (area of one region)
4 x 4 = 16 (area of second region)
8 + 16 = 24 (sum of areas of the two regions)
In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 21% of your total grade, each major test is worth 25%, and the final exam is worth 29%. Compute the weighted average for the following scores: 60 on the lab, 81 on the first major test, 69 on the second major test, and 79 on the final exam. Enter your answer as a whole number.
Answer:
[tex]Weighted\ Average = 73[/tex]
Step-by-step explanation:
Given
[tex]Lab = 21\%[/tex]
[tex]Tests = 25\%[/tex]
[tex]Exam = 29\%[/tex]
[tex]Lab\ Score = 60[/tex]
[tex]First\ Test = 81[/tex]
[tex]Second\ Test = 69[/tex]
[tex]Exam = 79[/tex]
Required
The weighted average
To do this, we simply multiply each score by the corresponding worth.
i.e.
[tex]Weighted\ Average = Lab\ worth * Lab\ score + Tests\ worth * Tests\ score.....[/tex]
So, we have:
[tex]Weighted\ Average = 21\% * 60 + 25\% * 81 + 25\% * 69 + 29\% * 79[/tex]
Using a calculator, we have:
[tex]Weighted\ Average = 73.01[/tex]
[tex]Weighted\ Average = 73[/tex] --- approximated
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
Answer:
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
The null and alternative hypothesis would be: H 0 : μ M = μ F H 1 : μ M < μ F H 0 : μ M = μ F H 1 : μ M > μ F H 0 : p M = p F H 1 : p M ≠ p F H 0 : p M = p F H 1 : p M < p F H 0 : p M = p F H 1 : p M > p F H 0 : μ M = μ F H 1 : μ M ≠ μ F
The test is:
right-tailed
left-tailed
two-tailed
Based on a sample of 40 men, 25%Based on a sample of 40 men, 25% owned cats
Based on a sample of 40 women, 40% owned cats
The test statistic is:
The p-value is:
Based on this we:
Reject the null hypothesis
Fail to reject the null hypothesis
To make a salad dressing you mix vinegar and olive oil in the ratio 2:5 how much olive oil is needed with 20 ml of vinegar
Answer:
Step-by-step explanation:
Set this up as a proportion with the ratios being
[tex]\frac{vinegar}{oil}[/tex] If there is a 2:5 ratio of vinegar to oil, that ratio looks like this:
[tex]\frac{v}{o}:\frac{2}{5}[/tex] and if we are looking for how much oil, x, is needed for 20 ml of vinegar, then that ratio completes the proportion:
[tex]\frac{v}{o}:\frac{2}{5}=\frac{20}{x}[/tex] and cross multiply.
2x = 100 so
x = 50 ml of oil
Triangle A'B'C' is formed by a reflection over x = 1 and dilation by a scale factor of 2 from the origin. Which equation shows the correct relationship between AABC
and A'B'C'?
Answer:
[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]k = 2[/tex] --- scale factor
Required
Relationship between ABC and A"B"C"
[tex]k = 2[/tex] implies that the sides of A"B"C" are bigger than ABC
i.e.
[tex]A"B" = 2AB[/tex]
[tex]A"C" = 2AC[/tex]
[tex]B"C" = 2BC[/tex]
In [tex]A"B" = 2AB[/tex]
Divide both sides by A"B"
[tex]1 = \frac{2AB}{A"B"}[/tex]
Divide both sides by 2
[tex]\frac{1}{2} = \frac{AB}{A"B"}[/tex]
Rewrite as:
[tex]\frac{AB}{A"B"}=\frac{1}{2}[/tex]
(a) is correct
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated samplingg distribution.
The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.5 years and a standard deviation of 2.1 years. Random samples of size 17 are drawn from the population and the mean of each sample is determined.
a. 1.33 years, 2.1 years
b. 5.5 years, 0.12 years
c. 5.5 years, 0.51 years
d. 1.33 years, 0.51 years
Answer:
c. 5.5 years, 0.51 years
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Mean of 5.5 years and a standard deviation of 2.1 years.
This means that, for the population, [tex]\mu = 5.5, \sigma = 2.1[/tex]
Random samples of size 17.
This means that [tex]n = 17[/tex]
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.
The mean is the same as the mean for the population, that is, 5.5 years.
The standard deviation is:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{17}} = 0.51[/tex]
This means that the correct answer is given by option c.
A line has a slope of -2/3 and passes through the point (-3, 8). What is the equation of the line?
y= -2/3x + 6
y= -2/3x + 8
y= 6x- 2/3
y= 8x- 2/3
Answer:
y= -2/3x+6
Step-by-step explanation:
Using slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -2/3x +b
Substitute the point into the equation
8 = -2/3(-3) +b
8 = 2+b
8-2 =b
6=b
y= -2/3x+6
A plumber charges $50 for the first visit plus $8 per hour of work. If the total bill is $290, how many hours did the plumber work?
30 hours
40 hours
80 hours
None of these choices are correct.
Answer:
Step-by-step explanation:
50 + 8x = 290
8x = 240
x = 30 hours
Solve using the quadratic equation 3x^2+x-5=0
Answer:
comparing with ax²+bx+c=0
a=3, b=1 , c= -5
Solve using the formula now ,,
The formula for the lateral area of a right cone is LA = pi rs, where is the radius of the base and s is the slant height of the cone.
Answer:
r is the radius of the base and s is the slant height of the cone. From the options given, We can make s the subject of the formula. Hence: Option a) s equals StartFraction L A Over pi r EndFraction
Two equivalent equations are s = LA/πr and r = LA/πs
What is cone?A cone is a shape formed using a series of line segments or lines that connect a common point, called a apex or vertex, to all points on the base of a circle that do not contain a vertex. The distance from the apex of the cone to the base is the height of the cone. A circular base has a measured radius value. And the length from the apex of the cone to any point around the base is the height of the slope. Equations for the surface area and volume of a cone can be derived from these quantities
Volume(V) = ⅓ πr²h cubic units
The total surface area of the cone = πrs + πr²
where, r is radius of the base, s is slant height and h is height of the cone
Given,
Lateral area of cone is denoted by LA
Lateral area of cone = πrs
where r is radius and s is slant height
⇒ LA = πrs
⇒ s = LA/πr
⇒ r = LA/πs
Hence, s = LA/πr and r = LA/πs are two equivalent equations in the given options.
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The graphs below are both quadratic functions. The equation of the red graph is f(x)=x^2 . Which of these is the equation of the blue graph g(x)
Answer:
[tex]{ \bf{c). \: g(x) = {(x - 3)}^{2} }}[/tex]
Industrial Designs has been awarded a contract to design a label for a new wine produced by Lake View Winery. The company estimates that 150 hours will be required to complete the project. The firm’s three graphic designers available for assignment to this project are Lisa, a senior designer and team leader; David, a senior designer; and Sarah, a junior designer. Because Lisa has worked on several projects for Lake View Winery, management specified that Lisa must be assigned at least 40% of the total number of hours assigned to the two senior designers. To provide label designing experience for Sarah, the junior designer must be assigned at least 15% of the total project time. However, the number of hours assigned to Sarah must not exceed 25% of the total number of hours assigned to the two senior designers. Due to other project commitments, Lisa has a maximum of 50 hours available to work on this project. Hourly wage rates are $30 for Lisa, $15 for David, and $18 for Sarah.Formulate a linear program that can be used to determine the number of hours each graphic designer should be assigned to the project to minimize total cost (in dollars). (Assume L is the number of hours Lisa is assigned to the project, D is the number of hours David is assigned to the project, and S is the number of hours Sarah is assigned to the project.)
Answer:
a) Minimize Z =30 X1 +25 X2+18 X3
subject to following constraints
[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]
b) Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.
c) As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.
Step-by-step explanation:
Step 1:-
a)
Let's take
X1 to be the number of hours assigned to Lisa
X2 to be the number of hours assigned to David
X3 to be the number of hours assigned to Sarah.
The objective function is to attenuate the entire cost of the project by deciding an optimum number of hours for every person. the target function is given by -
Minimize Z =30 X1 +25 X2+18 X3
subject to following constraints
[tex]1.X1\geq 0.4\left ( X1+X2 \right )\\2.X3\geq 0.15\left ( X1+X2+X3 \right )\\3.X1+X2+X3\leq 150\\4.X3\geq 0.25\left ( X1+X2 \right )\\5.X1\leq 50\\6.X1,X2,X3\geq 0[/tex]
Constraints and explanation:
1. Lisa must be assigned a minimum of 40% of the entire number of hours assigned to the 2 senior designers.
2. Sarah must be assigned a minimum of 15% of the entire project time.
3. The corporate estimates that 150 hours are going to be required to finish the project.
4. The number of hours assigned to Sarah must not exceed 25% of the entire number of hours assigned to the 2 senior designers.
5. Lisa features a maximum of fifty hours available to figure on this project.
6. Non-negative condition.
Step 2:-
b)
From the above equations, we get
The number of hours assigned to Lisa is 48 hours
The number of hours assigned to David 72 hours
The number of hours assigned to Sarah 30 hours.
Total cost=[tex]30 \times 48+15\times72+18\times30[/tex] = $3180.
Step 3:-
c)
As the dual price for constraint five is zero hence additional work hours for Lisa won't change the optimum solution.
Help!!! ASAP Please and thank you!
Answer:
1. 6 (2a-3b)
6×2a - 3b
=12a-18b
2. a(2ab+3)
a×2ab+3
=2a²b + 3a
3. (x-4)(3x)
=3x² - 12x
just kembangkan... answer my question plss..help me.
a & gb & e(2)=6(2a-3b)= 12a-18b=a(2ab+3)=2a^b+3a= (x-4) (3x)= 3x^-12x
I am a 2 digit number ,my two digit and the sum of my digit are in sequence .what number I am?
Answer:
I don't understand the meaning of question
What do you add to 2 7/8 to make 5
Answer:
2 1/8
Step-by-step explanation:
7/8 is the same as 0.875 and therefore you need 0.125 also known as 1/8 to make it a whole number. When you add it to the already existing whole 2 you get three. Subtract three from five to make two which is what you need to add on top to finally get 5.
work out the area of this shape
Answer:
1000
Step-by-step explanation:
Someone please help thanks
Answer:
By similar triangles: BE/20 = 18/25 BE 14.4
Also, (ED + 26) / 26 = 18/14.4
ED = 6.5 and AD = 32.5
PLEASE HELP ME! I am so confused
Answer:
x = 5.5
Step-by-step explanation:
Based on the Mid-segment theorem of a triangle, we would have the following:
EF = 2(AB)
AB = 7
EF = 2x + 3
Plug in the values
2x + 3 = 2(7)
Solve for x
2x + 3 = 14
Subtract 3 from each side
2x + 3 - 3 = 14 - 3
2x = 11
2x/2 = 11/2
x = 5.5
PLESE HELP WITH ANSWER. rewrite the function in the given form
s hard and too long I'm only of class 13
Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.8. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2004?
Answer:
The people dies in 2004 by aids are 413042853.4
Step-by-step explanation:
growth factor = 1.8
People died in 1983 = 1800
Let the people dies in 2004 is P.
Time, t = 2004 - 1983 = 21
So,
[tex]P = 1800 \times (1.8)^{21}\\\\P = 413042853.4[/tex]