Answer:
Seth would need 10 hours to paint the room.
Step-by-step explanation:
Let's define:
S = rate at which Seth works
T = rate at which Ted works
When they work together, the rate is S + T
And we know that when they work together they can pint one room in 5 hours, then we can write:
(S + T)*5 h = 1 room.
We also know that Ted alone would need one hour more than Seth alone.
Then if Seth can paint the room in a time t, we have:
S*t = 1room
and
T¨*(t + 1h) = 1room
Then we have 3 equations:
(S + T)*5 h = 1
S*t = 1
T¨*(t + 1h) = 1
(I removed the "room" part so it is easier to read)
We want to find the value of S.
First, let's isolate one variable (not S) in one of the equations.
We can isolate t in the second one, to get:
t = 1/S
Now we can replace it on the third equation:
T¨*(t + 1h) = 1
T¨*( 1/S + 1h) = 1
Now we need to isolate T in this equation, we will get:
T = 1/( 1/S + 1h)
Now we can replace this in the first equation:
(S + T)*5h = 1
(S + 1/( 1/S + 1h) )*5h = 1
Now we can solve this for S
(S + 1/( 1/S + 1h) )= 1/5h
S + 1/(1/S + 1h) = 1/5h
Now we can multiply both sides by (1/S + 1h)
(1/S + 1h)*S + 1 = (1/5h)*(1/S + 1h)
1 + S*1h + 1 = 1/(S*5h) + 1/5
S*1h + 2 = (1/5h*S) + (1/5)
Now we can multiply both sides by S, to get:
(1h)*S^2 + 2*S = (1/5h) + (1/5)*S
Now we have a quadratic equation:
(1h)*S^2 + 2*S - (1/5)*S - (1/5h) = 0
(1h)*S^2 + (9/5)*S - (1/5h) = 0
The solutions are given by the Bhaskara's formula:
[tex]S = \frac{-(9/5) \pm \sqrt{(9/5)^2 - 4*(1h)*(-1/5h)} }{2*1h} = \frac{-9/5 \pm 2}{2h}[/tex]
Then the solution (we only take te positive one) is:
S = (-9/5 + 2)/2h
S = (-9/5 + 10/5)/2h = (1/5)/2h = 1/10h
Then Seth needs a time t to paint one room:
(1/10h)*t = 1
t = 1/(1/10h) = 10h
So Seth would need 10 hours to paint the room.
The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss several different sampling methods that might be employed. (Select all that apply.) There are no potential problems with self reporting of distances.
Answer:
1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.
2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.
3)Certain problems arise with self reporting of distances, such as recording error or poor recall.
Step-by-step explanation:
1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.
2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.
3)Certain problems arise with self reporting of distances, such as recording error or poor recall.
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 82% confidence interval to 25 points, how many students should the administrator sample
Answer:
The appropriate solution is "259".
Step-by-step explanation:
According to the question,
[tex]\sigma = 300[/tex]
[tex]M.E=25[/tex]
At 82% CI,
[tex]\alpha = 0.18[/tex]
Critical value,
[tex]Z_c=1.341[/tex]
Now,
The sample size will be:
⇒ [tex]n=(Z_c\times \frac{\sigma}{E} )^2[/tex]
By substituting the values, we get
[tex]=(1.341\times \frac{300}{25} )^2[/tex]
[tex]=(1.341\times 12)^2[/tex]
[tex]=259[/tex]
Find z such that 4.8% of the standard normal curve lies to the left of z. (Round your answer to two decimal places)
Answer:
The correct answer will be "-1.66".
Step-by-step explanation:
Let z₀ be,
[tex]P(z<z_0)=4.8 \ percent[/tex]
[tex]=0.048[/tex]
⇒ [tex]\Phi (z_0)=0.048[/tex]
Now,
⇒ [tex]\Phi (-1.6646)=0.048[/tex]
[tex]z_0=-1.6646[/tex]
[tex]\simeq -1.66[/tex]
Thus the above is the right answer.
A university professor asked his class of 42 students when they had studied for his class the previous weekend. There responses were. please answer part a, b and c
ANSWERS:
a) 16 students
b) 25 students
c) 2 students
STEP BY STEP:
There are 42 students in total. This question can be solved by "Principal of Inclusion and Exclusion"
Question a)
The students that studied on Sunday in total with overlaps is 30. To figure out the students that ONLY studied on Sunday you need to first minus the overlaps in the combos:
the combos:
3, 10, 6, 2
Since the last combo included all of the other dates, we need to minus it:
1, 8, 4, 2
Now we can use the total of Sunday and minus the combos that includes Sunday:
30 - (4 + 2 + 8) = 16 students
Question b)
To figure out all the students that only studied on ONE day, not 2 not 3, just one day. We need to figure out the students that studied for Saturday and Friday using the same method before for figuring out Sunday:
Friday: 9 - 4 - 1 -2 = 2 students
Saturday: 18 - 1 - 2- 8 = 7 students
and now add them all together: 2 + 7 + 16 = 25 students
That is the total number of students that studied on one day.
Question c)
Now for the numbers of students that didn't study... We can just use the total to minus everything else!
42 - (25 + 1 + 4 + 8 + 2) = 2 students!!!
And thats all done! If you still don't get it, please ask!
what is proportion as applied in mathematics
Answer:
como se siente el actor al presentar la obra hola
A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as P=0.006A2−0.02A+120. Find the age of a man whose normal blood pressure measures 126 mmHg.
Round your answer to the nearest year.
Answer:
33 years
Step-by-step explanation:
Given the quadratic model :
P=0.006A2−0.02A+120
P = blood pressure ; A = Age
Given a blood pressure value of 126 mmHg ; the age, A will be ;
The equation becomes :
126 = 0.006A2−0.02A+120
0.006A² - 0.02A + 120 - 126 = 0
0.006A² - 0.02A - 6 = 0
Using the quadratic formula :
-b ± (√b²-4ac) / 2a
a = 0.006 ; b = - 0.02 ; c = - 6
Using calculator :
The roots are :
a = 33.333 or a = - 30
Age cannot be negative, hence, the age, A will be 33.333
Total the nearest year ; Age = 33 years
If x = y, then x – a = y – a represents the ________ property of equality.
Answer:
Subtractive Property of equality
Step-by-step explanation:
Since x = y, When you subtract anything from x, you must do the same to y for them to stay equal.
Answer:
Subtraction property of equality
a rectangle has an area of 186m2
one of the sides is 3m in length
work out the perimeter of the rectangle
seriously need help
Step-by-step explanation:
here is the ans
the perimeter= 130m
hope so this might help you
Paul baked 208 brown loaves. If the ratio of white loaves to brown loaves is 3:2, how many loaves did he bake in total?
Paul baked 520
loaves.
The owner of a restaurant is placing an order for bread.
On Friday there were 300 customers in the restaurant and 100 bread rolls were served.
On Saturday he is expecting 540 customers.
What would be a good estimate of how many bread rolls should he order? I
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Answer:
A. Total=520 loaves
B. Estimate= 180 rolls
Step-by-step explanation:
Can someone please help me with this.
Two long jumpers competed in a world-class track meet. The first athlete jumped a distance of 28.65 feet, and the second athlete reached a distance of 24.25 feet.
Answer:
Step-by-step explanation:
first athlete =28.65
second athlete=24.25
the first athlete jump - second athlete jump
28.65-24.25
= 4.40
the first athlete long jump then the second athlete
...............................................................
Determine the volume of a sphere with a diameter of 5 inches.Use 3.14 for Pi, and round your answer to the nearest inch.
Answer:
[tex]{ \bf{formular : \: { \tt{volume = \frac{4}{3} \pi {r}^{3} }}}} \\ { \tt{volume = \frac{4}{3} \times 3.14 \times {( \frac{5}{2}) }^{3} }} \\ { \tt{volume = 65.4 \: cubic \: inches}}[/tex]
Answer:
65
Step-by-step explanation:
formula = 4/3 * 3.14* r^3
= 4/3 * 3.14 * 2.5^3 (radius is half of the diameter)
= 65.44985
rounded to 65
21. Gabe Amodeo, a nuclear physicist, needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60%
solution. How many liters of each does he need make the needed 80 liters of 30% acid solution?
Gabe needs
liters of the 20% solution.
He also needs
liters of the 60% solution.
Let x be the amount (in liters) of 20% solution that Gabe uses, and y the amount (also in L) of the 60% solution.
He needs 80 L of 30% solution, so that
x + y = 80
0.20x + 0.60y = 0.30 (80) = 24
Solve for y in terms of x :
y = 80 - x
Substitute this into the second equation and solve for x :
0.20x + 0.60 (80 - x) = 24
0.20x + 48 - 0.60x = 24
24 = 0.40x
x = 60
Solve for y :
y = 80 - 60
y = 20
Surds see attached 20 points
Answer:
[tex]5\sqrt{2} \\45[/tex]
Step-by-step explanation:
just multiply
Answer:
a) 5√2
b) 135
Step-by-step explanation:
√5·√10 is equivalent to √50, which in turn is equivalent to √25·√2, or 5√2.
√27·√75 can be simplified by factoring:
√3·√9·√3√25, or (because √3·√3 = 3):
(3)(9)(5) = 135
write the equation of a line of a line passing through the points (3,1) and (6,3).
Answer:
i think its 2 1
Step-by-step explanation:
Answer:
y =2/3x-1
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( 3-1)/ (6-3)
= 2/3
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2/3x +b
Using a point
3 = 2/3(6)+b
3 = 4+b
3-4 =b
-1=b
y =2/3x-1
What is the constant of variation k of the direct variation y=KP through (-3, 2)
Answer:
isisis
Step-by-step explanation:
ISO’s
Answer:
-2/3
Answer: The constant of variation k for y = kx through (-3, 2) is k = -2/3.
What is y-3=3/4(x-5) in standard form?
Answer:
[tex]y-3=\frac{3}{4} (x-5)\\\\y-3=\frac{3}{4}x-\frac{3}{4}(5)\\\\y=\frac{3}{4} x+3-\frac{15}{4} \\\\y=\frac{3}{4} x+\frac{12}{4} -\frac{15}{4} \\\\y=\frac{3}{4} x-\frac{3}{4}[/tex]
Is this standard form? :\
Answer:
3x-4y=3
Step-by-step explanation:
Hi there!
We are given the equation y-3=[tex]\frac{3}{4}(x-5)[/tex], and we want to write it in standard form
Standard form is given as ax+by=c, where a, b, and c are integer coefficients, a CANNOT be 0 and CANNOT be negative, and b also CANNOT be 0
So let's expand the parentheses in the equation
Do the distributive property
y-3=[tex]\frac{3}{4}x-\frac{15}{4}[/tex]
Add 3 to both sides
y=[tex]\frac{3}{4}x-\frac{3}{4}[/tex]
We expanded the parentheses, but the equation is now in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)
Remember that we want it in standard form, which is ax+by=c
Subtract [tex]\frac{3}{4}x[/tex] from both sides
[tex]\frac{-3}{4}x+y=\frac{-3}{4}[/tex]
Remember that the coefficients of a, b, and c need to be integers, and also that a (the coefficient in front of x) CANNOT be negative
So multiply both sides by -4
[tex]-4(\frac{-3}{4}x+y)=-4(\frac{-3}{4})[/tex]
Distribute -4 to every number
[tex]-4(\frac{-3}{4}x)+-4(y)=-4(\frac{-3}{4})[/tex]
Multiply
[tex]\frac{12}{4}x-4y=\frac{12}{4}[/tex]
Simplify
3x-4y=3
There's the equation in standard form
Hope this helps!
Find the area of the triangle which the line 2x – 3y +6=0 forms with the coordinate axis.
2x-3y+6=0 has an x intercept of 2 and a y intercept of -3.
That means the 2 sides of the right triangle are 2 and -3
Area of triangle= 1/2×base×height
= 1/2×-3×2
=-3
∴ Area of the triangle=-3
The area of the asked triangle is 3 sq units.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a triangle is formed by the line 2x – 3y +6=0 and the coordinate axis.
When we plot the graph of the line, we get, y-intercept = 2 and x-intercept = -3
Hence, the height and base of the triangle will be 2 and 3 respectively.
Area of a triangle = 1/2 (base) (height)
Area = 1/2 (2)(3)
Area = 3
Hence, the area of the asked triangle is 3 sq units.
Learn more about areas, click;
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Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line.
Red car: y = 3 x + 5. Blue car: y = 4 x.
How many solutions should Sudhanshu find?
zero
one
two
infinite
Answer:
One
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptSolving systems of equations
Step-by-step explanation:
Step 1: Define
Identify systems
y = 3x + 5
y = 4x
Step 2: Solve
If we compare the 2 lines, we can see that they both have a different slope. If they had the same slope but different y-intercepts, then they would be parallel and have no solution. We can also see that the 2 lines aren't the same. If they were, then they would have infinite solutions.
∴ the systems should have only one solution.
Answer:
B
Step-by-step explanation:
Ms. Patel has 24 students in her class. When she collected yesterday's homework, Ms. Patel found that 16 students completed the homework in
pencil and 8 students used a pen.
What is the probability that the first two assignments Ms. Patel collected were completed in pencil?
Answer:
Maybe
1/8 is the probability that the first two assignments Ms.patel collected were completed in pencil
The angles in a triangle are represented by x, x+10, and x+50. What is the measure of the largest angle?
A.70 degrees
B.80 degrees
C.100 degrees
D.90 degrees
Given that,
The angles in a triangle are represented by x, x+10, and x+50.
We had to,
find the measure of the largest angle.
Let's start to solve,
→ x + (x+10) + (x+50) = 180°
→ x + x + x = 180° (-50 -10)
→ 3x = 180° -60
→ 3x = 120
→ x = 120/3
→ x = 40°
Then the value of x + 10,
→ x + 10
→ 40 + 10
→ 50°
Then the value of x + 50,
→ x + 50
→ 40 + 50
→ 90°
The measure of the largest angle is,
→ D. 90 degrees
Hence, option (D) is correct answer.
Step-by-step explanation:
good of you and good workings
What is the average
number of 4th graders per
class from the table above?
Answer:
29
Step-by-step explanation:
You need to find the average number of students
Add up all the students
27+31+28+33+26
145
Divide by the number of classes
145/5
29
The average is 29
32
Step-by-step explanation:
answer of number 30 is 32
If a concrete mix contains 1-1/2 cubic feet of gravel, 1/2 cubic foot of water,
1 cubic foot of cement, and 2 cubic feet of sand, what percentage of the mix is
sand?
Answer:
The correct answer is "50%".
Step-by-step explanation:
The given values are:
Gravel,
= [tex](1-\frac{1}{2} )[/tex]
Water,
= [tex]\frac{1}{2}[/tex]
Cement,
= 1
Sand,
= 2
Now,
The total mixture will be:
= [tex]Gravel+Water+Cement+Sand[/tex]
By substituting the values, we get
= [tex](1-\frac{1}{2} )+\frac{1}{2} +1+2[/tex]
= [tex]\frac{1}{2} +\frac{1}{2} +1+2[/tex]
= [tex]4 \ cubic \ feet[/tex]
hence,
The percentage of sand will be:
= [tex]\frac{Sand}{Total}\times 100[/tex]
= [tex]\frac{2}{4}\times 100[/tex]
= [tex]50[/tex]%
You have 8 quarts of milk. You need 1.25 cups to make one serving of deep fried chicken. How many servings can you make?
Answer: 25.6 servings (partial serving) / 25 servings (whole serving)
Step-by-step explanation:
Concepts:
As we can see from the question, there are two units applied. [Quarts] and [cups]; therefore, we need to do the unit conversion.
1 quart = 4 cups
Solve:
Step one: Convert quarts into cups
1 quart = 4 cups8 quarts = 4 × 8 = 32 cupsStep two: Divide the cups to find the number of servings
32 cups / 1.25 cups = 25.6 servings**Disclaimer** I am not sure about the rules that you apply in mathematics. Here, the answer is not an integer. I am concerned whether you would allow partial servings. In my understanding, the servings shall be a whole, thus should be rounded. However, if you are fine with decimals, then you have the choice.
Hope this helps!! :)
Please let me know if you have any questions
(9,2) and (5,-4) find the slope of the line containing the pair of points
Answer:
3/2
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= ( -4-2)/(5-9)
= -6/-4
=3/2
Certify Completion Icon Tries remaining:2 A town recently dismissed 10 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of age and 18 under 50. If the dismissed employees were selected at random, what is the probability that exactly 5 employees were over 50
Answer:
0.055 = 5.5% probability that exactly 5 employees were over 50.
Step-by-step explanation:
The employees are removed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
7 + 18 = 25 employees, which means that [tex]N = 25[/tex]
7 over 50, which means that [tex]k = 7[/tex]
10 dismissed, which means that [tex]n = 10[/tex]
What is the probability that exactly 5 employees were over 50?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]
0.055 = 5.5% probability that exactly 5 employees were over 50.
Please Help! What's the rule that represents the sequence 13, 27, 41, 55, ...?
Answer:
B
Step-by-step explanation:
an = a+(n-1)d
an=13+(n-1)14
d=14
7(x-9y) need an answer
Answer:
7x - 63y
Step-by-step explanation:
Given
7(x - 9y) ← multiply each term in the parenthesis by 7
= 7x - 63y
Given the functions below, find f(x) - g(x) f(x) = 3x^2 + 2x + 1 g(x) = x^2 - 6x + 3
Answer:
Here is your answer.....
Hope it helps....
The value of given function f(x) - g(x) is 2x² + 2x + 1.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.Given,
f(x) =3x² + 2x + 1
g(x) = x² - 6x + 3
f(x) - g(x) = ( 3x² + 2x + 1) - ( x²- 6x + 3)
= 3x² + 2x +1 - x² + 6x - 3
= 2x² +8x - 2
Therefore , the value of given function f(x) - g(x) is 2x² + 2x + 1.
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