Answer:
the number of days when instructor do the work alone is 8 days
Step-by-step explanation:
Given that
The apprentice can do the work in 24 days
And, the apprentice and instructor together can do it in 6 days
We need to find out the number of days when instructor do the work alone
So,
[tex]= \frac{1}{6} - \frac{1}{24} \\\\= \frac{4 - 1}{24} \\\\= \frac{3}{24} \\\\= \frac{1}{8} \\\\= 8[/tex]
hence, the number of days when instructor do the work alone is 8 days
the product of nine, y and x not simplified.
Answer:
9yx
Step-by-step explanation:
product means multiply.
nine, y and x
9yx
The length of a rectangle is 5 cm longer than its width.
If the perimeter of the rectangle is 42 cm, find its area.
Answer:
The area is 104
Step-by-step explanation:
Length: 5 + x
width: x
(5+x)*2=10+2x
x*2=2x
2x+10+2x=42
10+4x=42
-10 -10
4x=32
/4. /4
x=32
5+8=13
13*8=104
A large tank is filled to capacity with 700 gallons of pure water. Brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 7 gal/min. The well-mixed solution is pumped out at a rate of 14 gallons/min. Find the number A(t) of pounds of salt in the tank at time t.
Answer:
[tex]A(t) = 1400(1 - e^{\frac{-t}{50}})[/tex]
Step-by-step explanation:
The net mass flow rate dA/dt = mass flow rate in - mass flow rate out
mass flow rate in = concentration of brine in × brine flow rate in = 4 lb/gal × 7 gal/min = 28 lb/min
Let A(t) be the amount of salt at time t. The concentration of salt in the tank at time, thus C = amount of salt/volume of tank = A(t)/700 lb/gal.
Since the well mixed solution is pumped out at a rate of 14 gal/min, the mass flow rate out = concentration of salt in tank × volume flow rate out = A(t)/700 lb/gal × 14 gal/min = m(t)/50 lb/min
So, dA/dt = mass flow rate in - mass flow rate out
dA/dt = 28 lb/min - A(t)/50 lb/min
dA/dt = 28 - A(t)/50
dA/dt = [1400 - A(t)]/50
separating the variables, we have
dA/[1400 - A(t)] = dt/50
integrating both sides, we have
∫dA/[1400 - A(t)] = ∫dt/50
-1/-1 × ∫dA/[1400 - A(t)] = ∫dt/50
1/-1 × ∫-dA/[1400 - A(t)] = ∫dt/50
-1 × ㏑[1400 - A(t)] = t/50 + C
-㏑[1400 - A(t)] = t/50 + C
㏑[1400 - A(t)] = -t/50 - C
taking exponents of both sides, we have
[tex]1400 - A(t) = e^{\frac{-t}{50} - C} \\1400 - A(t) = e^{\frac{-t}{50}}e^{-C}\\1400 - A(t) = Be^{\frac{-t}{50}} ( B = e^{-C}) \\A(t) = 1400 - Be^{\frac{-t}{50}}[/tex]
when t = 0, A(0) = 0. So,
[tex]A(t) = 1400 - Be^{\frac{-t}{50}}\\A(0) = 1400 - Be^{\frac{-0}{50}}\\0 = 1400 - Be^{0}\\0 = 1400 - B\\B = 1400[/tex]
So,
[tex]A(t) = 1400 - 1400e^{\frac{-t}{50}}\\A(t) = 1400(1 - e^{\frac{-t}{50}})[/tex]
Graph the image of this triangle after a dilation with a scale factor 1/2 centered origin
i dont know this questions
How many sides do 2 octagons, 4 pentagons, and 5 triangles have in all?
Answer: 51
Step-by-step explanation:
2 octagons have 16 sides because an octagon has eight sides. So, 8x2=16.
4 pentagons have 20 sides because a pentagon has 5 sides. So, 4x5=20.
5 triangles have 15 sides because a triangle has 3 sides. So, 5x3=15.
In all, 16+20+15= 51
A swimming pool is open for 7 1/2hours during a day. The pool keeps one lifeguard on
duty at a time, and each lifeguard's shift is 2 1/2hours long. How many shifts are there
per day?
7 shifts
5 shifts
3 shifts
4 shifts
Answer:
3 shifts a day
Step-by-step explanation:
7 1/2 hours = 7.5 2 1/2 hours = 2.5
7.5 divided by 2.5 = 3
Answer:
3 shift
Step-by-step explanation:
7 1/2 / 2 1/2
(15/2) / (5/2)
keep, change, flip
(15/2) x (2/5)
30/10 = 3 shifts
An accessories store sells $8 custom socks and $11 custom hats. If 11 items were sold on Monday, and the
total sales were $100, how many socks were sold?
Answer:
7 socks were sold
Step-by-step explanation:
7*8=56
11-7=4
4×11=44
56+44=100
This proves the answer of 7 to be correct
Two boats started to move towards each other from two docks, located 30 miles apart. One boat moved at a speed of 3 miles per hour, the other moved twice as fast. How soon will the boats meet?
Answer:
3.333 hours
Step-by-step explanation:
Given the total distance is 30 miles, and boat 1 travels at 3 mph and boat 2 travels at 6 mph, and the time for both is the same. Distance is speed S times time T so
30 = D(boat 1) + D(boat 2)
30 = (S1 * T) + (S2 * T)
30 = 3T + 6T
30 = 9T
3.333 = T
The window has the shape of a kite. How many square meters of glass were used to make the window?
Answer:
1568cm²
Step-by-step explanation:
28cm + 28cm = 56cm
35cm + 21cm = 56cm
56 × 56 = 3136cm²
3136cm² ÷ 2 = 1568cm²
Write the quadratic equation in standard form:
8x2=8x + 13 + 4x2
what is the constant rate change shown in the graph below?
Answer:
the two points be
(0,0) and (1,-3)
slope [m]=[-3-0]/[1-0]=-3
constant rate is-3.
PLS HELP!! need the answer asap
Answer:
8
Step-by-step explanation:
[tex]\angle RPS = 3x + 12,\ \angle QPR = 7x + 88\ =>\ \angle QPS = 3x + 12 + 7x + 88 = 180[/tex]
[tex]3x + 12 + 7x + 88 = 180[/tex]
[tex]10x + 100 = 180[/tex]
[tex]10x = 80[/tex]
[tex]x = 8[/tex]
Which of these lines is perpendicular to the line 5y = -6x + 2?
Answer:6y= -5x + 3
Step-by-step explanation:
The product of the slope of the perpendicular lines is equal to a negative one. Then the equation of the perpendicular line is 6y = 5x.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equation of the line is given below.
5y = -6x + 2
The slope of the equation is -6/5.
Then the equation of the line which is perpendicular to 5y = -6x + 2 is given as
y = mx + c
The product of the slope of the perpendicular lines is equal to a negative one.
The slope of the perpendicular line will be
(-6/5) m = -1
m = 5/6
Then the equation will be
y = (5/6)x + c
Let the equation is passing through the origin, then we have
6y = 5x
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ2
3. Find mZS.
Q= 5x + 2)
P= 10x - 3)
(7x - 11)=ºR
(13x - 31)º=S
(8x - 19)=T
Answer:
∠S = 151
Step-by-step explanation:
The figure shown is a pentagon
The angles in a pentagon add up to equal 540
Thus, ∠Q + ∠P + ∠T + ∠S + ∠R = 540
Or 10x - 3 + 5x + 2 + 7x - 11 + 13x - 31 + 8x - 19 = 540
This is the equation we will use to solve for x
Step 1 combine like terms
10x = 5x + 7x + 13x + 8x = 43x
-3 + 2 - 11 - 31 - 19 = -62
We now have 540 = 43x - 62
Step 2 add 62 to each side
-62 + 62 cancels out
540 + 62 = 602
we now have 602 = 43x
Step 3 divide each side by 43
43x / 43 = x
602 / 43 = 14
we're left with x = 14
Finally we plug in 14 for x in the given expression for ∠S
∠S = 13x - 31
* substitute 14 for x *
∠S = 13 ( 14 ) - 31
∠S = 13 * 14 = 182
182 - 21 = 151
Thus, ∠S = 151
The measure of ∠S is equal to 151°.
What is a shape?In mathematics, shapes define the perimeters or contours of an object. The forms can be categorized into numerous groups according to their individual traits. A border or outline made up of points, lines, curves, etc. frequently surrounds the forms.
As per the given data:
We are given the diagram of a shape and all its internal angles.
As the given shape is having 5 sides, it will be a pentagon.
The sum of all internal angles in a pentagon is equal to 540°.
∴ ∠P + ∠Q + ∠R + ∠S + ∠T = 540°
⇒ 10x - 3 + 5x + 2 + 7x - 11 + 13x - 31 + 8x - 19 = 540
= 43x - 62 = 540
= 43x = 602
x = 14
To find the measure of ∠S.
∠S = 13x - 31
∠S = 13(14) - 31
∠S = 151°
The measure of ∠S is equal to 151°.
To learn more about shape, click:
brainly.com/question/28978432
#SPJ2
PLEASE HELP!! Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the trigonometric ratios with their values based on the triangle shown in the diagram
this is the answer on edmentum
The matching will be given below.
12/25 = sin D × cos D3/5 = sin D16/15 = cos C × tan D4/5 = sin CWhat is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The value of sin C will be
sin C = 3 / 5
The value of sin D will be
sin D = 4 / 5
The value of cos C will be
cos C = 4 / 5
The value of cos D will be
cos D = 3 / 5
The value of tan C will be
tan C = 3 / 4
The value of tan D will be
tan D = 4 / 3
The product of sin D and cos D will be
sin D × cos D = (4 / 5) × (3 / 5)
sin D × cos D = 12 / 25
The product of tan C and tan D will be
tan C × tan D = (3 / 4) × (4 / 3)
tan C × tan D = 1
The product of cos C and tan D will be
cos C × tan D = (4 / 5) × (4 / 3)
cos C × tan D = 16 / 15
Then the matching will be given below.
12/25 = sin D × cos D3/5 = sin D16/15 = cos C × tan D4/5 = sin CMore about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ5
Find the Experimental Probability of Spinning a 4
Answer:
....................................,..............................,................................,...................................,...........................,..................,......,,,.,.................................
Step-by-step explanation:
Help plz:)))I’ll mark u Brainliest
Answer:
2,144.66 miles³
Step-by-step explanation:
v = (4/3)πr³
v = (4/3)π(8³)
v = 2,144.6605848506
Rounded
2,144.66 miles³
The diameter is 24 cm. Find the
length of arc CD
Answer:
s = 4π Exact answer
s = 12.56 Decimal approximation
Step-by-step explanation:
cicrumference = πd
s = (∅/360)(πd)
s = (60/360)(π * 24)
s = 4π Exact answer
s = 4 * 3.14
s = 12.56 Decimal approximation
Find the height of a rectangular pyramid with a length of 15.8 meters, a width of 9.2 meters, and a volume of 1235.56 cubic meters
FINDING PERIMETER need help right now
Answer:
if you want to find perimeter you must do addition for the corners. For example on long side in the regtangle the number is 4. And the short side is 6. The one thing we must do is addition. Than the answer will be 10. You're welcome.
Wavelength and Frequency
A chord consists of notes that sound good together. the C major chord, starting at middle C, has the following frequencies:
C - 262 Hz
E - 330 Hz
G - 392 Hz
Determine the ratio of the frequency of G to C. Express the answer in a simple integer ratio. (Due to rounding the ratio will be approximate. )
a. 5 to 4
b. 3 to 2
c. 6 to 5
d. 9 to 8
Please select the best answer from choices provided
Answer:
B. 3 to 2
Step-by-step explanation:
I calculated it logically
The ratio of the frequency of G to C is 1.5. So, option b is correct.
What is meant by frequency ?Frequency of a wave is defined as the number of oscillations completed by the wave in one second.
Here,
The frequency of note G, f(G) = 392 Hz
The frequency of note C, f(C) = 262 Hz
The ratio of the frequency of G to C, r = frequency of G/frequency of C
r = f(G)/f(C)
r = 392/262
r = 1.496 approximately r = 1.5
Hence,
The ratio of the frequency of G to C is 1.5
To learn more about frequency, click:
https://brainly.com/question/30333783
#SPJ7
Solve the system of equations -x-y=-4−x−y=−4 and -2x+4y=4−2x+4y=4 by combining the equations.
9514 1404 393
Answer:
(x, y) = (2, 2)
Step-by-step explanation:
We can put the second equation into standard form by dividing by -2.
x -2y = -2
Adding this to the first equation eliminates x
(x -2y) +(-x -y) = (-2) +(-4)
-3y = -6
y = 2 . . . . . divide by -3
-x -(2) = -4 . . . . substitute for x in the first equation
2 = x . . . . . . . . add 4+x
The solution is (x, y) = (2, 2).
There were 35 children and 10 adults at a cookout. What is the ratio of adults to children at the cookout?
Answer:
2:7
Step-by-step explanation:
10:35 can also be written as 2:7
Thenks and mark me brainliest :))
suzanne babysits to earn extra money. she charges $15 for each hour that she babysits. What represents the independent variable in this situation?
A. The total amount charged for babysitting
B. The rate she us paid per hour
C. The number of hours she babysits
D. The number of children she babysits
Answer:
C. The number of hours she babysits
Step-by-step explanation:
In this situation, the number of hours she babysits is the independent variable.
This is because it will directly influence the amount of money that she earns, which is the dependent variable.
For example, working for 1 hour will earn her $15.
So, the correct answer is C. The number of hours she babysits
which of the following represents the equality for the sum of 11 and Y is greater than -33
Answer:
11+y > -33
Step-by-step explanation:
Answer:
You wrote
"Which of the following" Meaning there's should be options present.
But Going with the statement...
The sum of 11 and y is greater than -33
I'd say
11 + y > -33.
The equation below represents the trend line of a scatter plot showing the hours spent studying versus science test scores. y = 6.5 x + 42.4
The equation below represents the trend line of a scatter plot showing the hours spent studying versus math test scores. y = 7.2 x + 34.7
If a student does not study for either test, on which test should the student expect the higher score?
A) on the science test because the rate of change is greater
B) on the math test because the rate of change is greater
C) on the science test because the y-intercept is greater
D) on the math test because the y-intercept is greater
Answer: C: on the science test because the y-intercept is greater
Step-by-step explanation: I got the question right on edge.
Answer:
C
Step-by-step explanation:
ind g(x), where g(x) is the translation 5 units right of f(x) = x.
Write your answer in the form mx + b, where m and b are integers.
A. g(x)= x + 5
B. g(x)= x - 5
C. g(x)= x(5)
D. none of the above
GIVING BRAINLY FOR WHOEVER ANSWERS THIS
Answer:
20%
Step-by-step explanation:
Probability is always expressed as a part of a whole, thereby in fractions or percentages. From the statistics gathered, it said that 80% of the time, the plane arrives right on schedule in El Centro. That means that the probability of NOT arriving on time is the other portion, which is 20%. The answer is 20%.
Type the correct answer in each box.
Consider the table modeling function f.
-2
-1
0
1
2
-28
-9
-2
-1
0
Complete the table modeling the inverse of function f.
-1
0
4–1()
-2
0
The screenshot is the correct answers
The table modeling the inverse of function f is,
[tex]x[/tex] [tex]f^{-1}(x)[/tex]
-28 -2
-9 -1
-2 0
-1 1
0 2
What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."What is inverse function?"A function g is the inverse of a function f if whenever y = f(x) then x = g(y)"
For given question,
We have been given a table modeling function f.
x f(x)
-2 -28
-1 -9
0 -2
1 -1
2 0
We need to complete the table modeling the inverse of function f.
We know that the inverse of function y = f(x) is [tex]x=f^{-1}(y)[/tex]
For given function f(x), we find inverse of f(x)
[tex]x[/tex] [tex]f^{-1}(x)[/tex]
-28 -2
-9 -1
-2 0
-1 1
0 2
Learn more about the inverse of function here:
https://brainly.com/question/20663378
#SPJ2
Trey invested $15,000 into a savings account for five years at 7% interest. How much is in the account if the interest is compounded monthly?
Multipuly po ba (15;000 7%)