Hamish and Harry work as plumbers. harry earns a dollar more than 5/4 the amount Hamish earns per hour. the amount Harry earns per hour is 2$ less than 7/5 the amount Hamish earns per hour. how much to both of them earn per hour?
Answer:
Hamish earns $20 per hour, and Harry earns $26 per hour.
Step-by-step explanation:
Harry earns
$1+(5/4)•x and also (7/5)•x-$2
$1+(5/4)•x = (7/5)•x-$2
$1+$2= (7/5)•x-(5/4)•x
3=(7•4•x-5•5•x)/20
3=3x/20
3•20=3x
X=20, Hamish earns $20
Substitute x in one of the expressions
1+(5/4)•20=1+25=26, Harry earns $26
Which of the following statements is true?
Answer:
B
Step-by-step explanation:
1/9 can be simplified to 1/3 as 1/3 x 1/3 = 1/9 and 49/25 can be simplified to 7/5 as 7/5 x 7/5 = 49/25.
Now looking at both the fraction 1/3 and 7/5
1/3 simplifies to 0.34
It is an irrational value as the 3 keeps repeating.
7/5 simplifies to 1.4
It is a rational value as the decimal value is not repeating.
Thus making the second option the answer.
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Step-by-step explanation:
[tex] \frac{5 {}^{ - 4x + 7} }{125 {}^{x} } [/tex]
[tex] \frac{5 {}^{ - 4x + 7} }{5 {}^{3x} } [/tex]
[tex]5 {}^{ - 4x + 7 - 3x} [/tex]
[tex]5 {}^{ - 7x + 7} [/tex]
in need of assistance
Answer:
60
Step-by-step explanation:
_---&$'_-4$':/-&$$--(:'##4--&&4___&$$_666&4&&&&&
Dr. Hick writes an order for Amoxicillian 300 mg by mouth daily. Pharmacy dispenses 200 mg/2 mL. How many mL per dose?
a. 4
b. 3
c. 2
d. 1
Answer:
b
Step-by-step explanation:
2 ml/200 mg so divide and you get 1 ml per 100 mg then multiply that my 3 to get 3ml/300 mg therefore the answer is b
Answer:
b. 3 ml
Step-by-step explanation:
300 mg / 200 mg/ 2 ml = 300 * 2 / 200 ml = 3 ml
Given a function described by the table below, what is y when x is 5?
XY
26
48
59
612
Answer:
y = x + 4
when x is 5, y is 9
Step-by-step explanation:
the pattern from the table is that the y value is 4 more than the x value, so the equation would be y = x + 4.
if you plug in x = 5, then this would be y = 5 + 4 = 9
Raul's pet store has a play area that can fit up to 30 cats and dogs. His son is allergic to cats so the pet store never has more than 8 cats in the play areas.
How many of each type of pet can they have at the
pet store?
Write a system of inequalities.
Answer:
Step-by-step explanation:
Let :
C = number of cats
D = number of dogs
Raul's pet store has a play area that can fit up to 30 cats and dogs.
C + D = 30
The pet store never has more than 8 cats in the play areas.
C < 9(there can never be 9 or more cats)
As or the number of dogs :
C + D = 30
C = 30 - D
Since we know that C < 9. To get the number of dogs allowed, we just plug in 30 - D for C.
30 - D < 9
30 - 9 < D
or
D > 21
(dogs have to be 22 or more)
Expert Mathematicians, please help!
Answer:
Two functions which satisfies the H(x) are f(x) = 2x - 4, (x) = x⁵ and
f(x) = 2x, g(x) = x⁵ - 2
Step-by-step explanation:
The given question is based on the decomposition of a given function into two functions
Decomposition of a function :- functional decomposition is the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed from those parts by function composition
so the function given in the question is H(x) = 2x⁵ - 4
now by using the concept of decomposition of a function we can find two functions f and g
therefore,
f(x) = 2x - 4
and g(x) = x⁵
similarly we can find another pair which satisfies the function H(x)
f(x) = 2x
and g(x) = x⁵ - 2
more about decomposition of functions at :
https://brainly.com/question/14310025
#SPJ10
Integration by Parts Evaluate e-2x cos(2x) dx.
Let
[tex]I = \displaystyle \int e^{-2x} \cos(2x) \, dx[/]tex
Integrate by parts:
[tex]\displaystyle \int u \, dv = uv - \int v \, du[/tex]
with
[tex]u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \cos(2x) \, dx \implies v = \dfrac12 \sin(2x)[/tex]
Then
[tex]\displaystyle I = \frac12 e^{-2x} \sin(2x) + \int e^{-2x} \sin(2x) \, dx + C[/tex]
Integrate by parts again, this time with
[tex]u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \sin(2x) \, dx \implies v = -\dfrac12 \cos(2x)[/tex]
so that
[tex]\displaystyle I = \frac12 e^{-2x} \sin(2x) - \frac12 e^{-2x} \cos(2x) - \int e^{-2x} \cos(2x) \, dx + C\\\\ \implies I = \frac{\sin(2x)-\cos(2x)}{2e^{2x}} - I + C \\\\ \implies 2I = \frac{\sin(2x) - \cos(2x)}{2e^{2x}} + C \\\\ \implies I = \boxed{\frac{\sin(2x) - \cos(2x)}{4e^{2x}} + C}[/tex]
PLEASE HELP!!!!!!!!!
Answer:
correct answer is B.
Step-by-step explanation:
for more information see the attachment.
Answer:
no 2/B is the correct answer
need help with this please
The values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
Given the equation of x as the function of t is
x= 5 cos t
similarly, the equation of y as the function of t is
y= 3 sin t
At t=3 the value of x will be
x (at t=3) = 5 cos 3= 5(-0.989)= -4.95
At t=3 the value of y will be
y (at t=3) = 3 sin 3= 3(0.141)= 0.423
The derivative of the function of x with respect to t will be
dx/dt= d(5 cos t)/dt= 5d(cos t)/dt= -5 sin t
at t=3 the value of dx/dt will be
dx/dt (at t=3) = -5 sin 3= -5(0.141)= 0.71
The derivative of the function of y with respect to t will be
dy/dt= d(3 sin t)/dt= 3d(sin t)/dt= 3 cos t
at t=3 the value of dy/dt will be
dy/dt (at t=3) = 3 cos t= 3(-0.989)= -2.97
The tangent slope is dy/dx which can be calculated by
dy/dx= (dy/dt)(dt/dx)= (dy/dt)/(dx/dt)= 3 cos t/ -5 sin t= (-3/5) cot t
at t=3 the value of tangent slope will be
dy/dx (at t=3) = (-3/5) cot 3= 4.21
The speed at t=3 will be
speed v= [tex]\sqrt{v_{x} ^{2} + v_{y} ^{2} }[/tex]
= √(dx/dt)²+(dy/dt)²
at t=3
= √(0.71)²+(-2.97)²
= √9.325
= 3.05 unit/sec
Therefore the values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
Learn more about the function
here: https://brainly.com/question/12047216
#SPJ10
Use a calculator to graph the functions y=-3x-21 and y=x³-3x-3. How many points of intersection do the
functions share?
0
1
2
3
Answer:
1
Step-by-step explanation:
When you graph the functions they intersect at one point
(-3.368119, -31.10436)
Question 6 of 15
Gloria invested $1200 in an account that earns 2.5% interest, compounded
annually. The formula for compound interest is A(t) = P(1 + i)t. How
much did Gloria have in the account after 5 years?
O A. $3662.11
OB. $6150.00
OC. $1470.00
OD. $1357.69
Answer:
D
Step-by-step explanation:
[tex]1200( {1.025}^{5} ) = 1357.69[/tex]
Superman needs to save lois from the clutches of lex luthor. It take superman 5 seconds to get to Lois who is 210 feet away. What is supermans rate?
Answer:
42 ft/s
Step-by-step explanation:
if superman travels 210 feet in 5 seconds, he will travel a fifth of 210 ft in 1 second
a fifth of 210ft is 210/5=42
hence 42ft/s is his rate.
The equation for the pH of a substance is pH = -log[H*], where H+ is the concentration of hydrogen ions. A basic
solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentratic
of hydrogen ions between the two solutions?
1.6x10-9
O4.0x10-3
O 6.7x10-1
O 1.6x10¹11
The approximate difference in the concentration of hydrogen ions between the two solutions is 4.0×10⁻³
What is pH value?The pH of a solution is a measurement of the concentration of hydrogen ions in the solution, as well as its acidity or alkalinity. Normally, the pH scale ranges from 0 to 14.
pH value for basic solution = 11.2
pH value for acidic solution = 2.4
Concentration for a basic solution:
[tex]\rm = 10^{-11.2}[/tex]
[tex]= 6.309\times10^{-12}[/tex]
Concentration for an acidic solution:
[tex]\rm = 10^{-2.4}[/tex]
[tex]= 3.981\times10^{-3}[/tex]
Difference between the concentration:
[tex]= 3.981\times10^{-3}- 6.309\times10^{-12}[/tex]
[tex]= 3.98\times10^{-3}[/tex]
[tex]= 4\times10^{-3}[/tex]
Thus, the approximate difference in the concentration of hydrogen ions between the two solutions is 4.0×10⁻³
Learn more about the pH value here:
brainly.com/question/1503669
#SPJ1
Rewrite exponential expressions
This is from Khan academy I have to attach a PNG if you can help me solve it! Thank you!
Answer:
Step-by-step explanation:
The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
The true statement is:
"The range of the function is all real numbers less than or equal to 9."
Which statements are true?
Here we have the quadratic function:
[tex]f(x) = -x^2 - 4x + 5[/tex]
And we want to see which of the given statements are true.
The first one is:
"The domain is al real numbers less than or equal to -2"
This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).
The second statement is:
" The domain of the function is all real numbers less than or equal to 9."
Also false
Third one:
" The range of the function is all real numbers less than or equal to −2"
The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.
In this case, the quadratic function is:
[tex]f(x) = -x^2 - 4x + 5[/tex]
So the vertex is at:
[tex]x = 4/(2*-1) = -2\\[/tex]
Then the y-value of the vertex is:
[tex]f(-2) = -(-2)^2 - 4*(-2) + 5 = -4 + 8 + 5 = 9[/tex]
So the range is the set of all real numbers less than or equal to 9.
So the above statement is false, and the final one:
"The range of the function is all real numbers less than or equal to 9."
Is the true statement.
If you want to learn more about quadratic functions:
https://brainly.com/question/1214333
#SPJ1
How many yards are in 1 mile 60 feet?
Answer:
1780
Step-by-step explanation:
multiply the length value by 1760
and then divide the length value by 3
work hours
frequency
0 - <10
45
10 - <20
33
20 - <30
20
30 - <40
7
40 - <50
8
Use your calculator to find the mean and standard deviation
The mean and the standard deviation are 16.15 and 12.03, respectively
How to determine the mean and the standard deviation?The table of values is given as:
Work hours Frequency
0 - <10 45
10 - <20 33
20 - <30 20
30 - <40 7
40 - <50 8
Start by rewriting the table using the midpoint of each class
x f
5 45
15 33
25 20
35 7
45 8
The mean is then calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
This gives
[tex]\bar x = \frac{5 * 45 + 15 * 33 + 25 * 20 35 * 7 + 45 * 8}{45 + 33 + 20 + 7 + 8}[/tex]
Evaluate the sum and the products
[tex]\bar x = \frac{1825}{113}[/tex]
Divide
[tex]\bar x = 16.15[/tex]
The standard deviation is:
[tex]\sigma =\sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
This gives
[tex]\sigma= \sqrt{\frac{45 * (5 - 16.15)^2 + 33 * (15 - 16.15)^2 + 20 * (25 - 16.15)^2 + 7 * (35 - 16.15)^2 + 8 * (45 - 16.15)^2 }{45 + 33 + 20 + 7 + 8}}[/tex]
Evaluate the sum and the products
[tex]\sigma= \sqrt{\frac{16350.4425}{113}}[/tex]
Divide
[tex]\sigma= \sqrt{144.694181416}[/tex]
Take the square root
[tex]\sigma= 12.03[/tex]
Hence, the mean and the standard deviation are 16.15 and 12.03, respectively
Read more about mean and standard deviation at:
https://brainly.com/question/14650840
#SPJ1
Need number 7 the answer please.
Answer:
h(x) = -2|x+2| + 2
Step-by-step explanation:
let me know if you want an explanation :))
what is −4/5+40/75+100%=
-0.8+1.875+100%
1.05+100%
0.1
what is ⅛ in a percentage form
Answer:
12.5%
Step-by-step explanation:
1/8 × 100% = 12.5%
So 9f you multiply an eighth by one hundred percent and simplify accurately you'll get 12.5%
what is the first shape
Answer:
The first type of solid shapes to be discovered are known as Platonic solids, which include the cube, the tetrahedron, the octahedron, the dodecahedron, and the icosahedron
I WILL GIVE BRAINLIEST
Which is true of dependent events?
ANSWER CHOICES:
The probability of all dependent events can be calculated using the OR formula P(A+B) =P(A) +P(B)-P(A and B) .
You can use a two-way frequency table to calculate the conditional probability of events that are dependent.
You can find the AND probability of dependent events using the formula P(A or B)= P(A) times P(B) .
The outcome of one event has no effect on the outcome of a second event.
Probability helps us to know the chances of an event occurring. The correct option is A.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Dependent events are those events in which the outcome of the first event affects the outcome of the second event. The statement that is correct about the dependent event is that the probability of all dependent events can be calculated using the "OR" formula P(A+B) =P(A) +P(B)-P(A and B).
Hence, the correct option is A.
Learn more about Probability:
https://brainly.com/question/795909
#SPJ1
If y = 2x-3, then which of the following ordered pairs lies on the graph?
O (-3,0)
O (1,-1)
O (5,4)
Plug in the points and see if they satisfy the equation.
y = 2x - 3
(1, -1)
-1 = 2(1) - 3
-1 = 2 - 3
-1 = -1
So (1, -1) satisfies the equation.
(-3, 0)
0 = 2(-3) - 3
0 = -6 - 3
0 = -9
So (-3, 0) does not satisfy the equation.
(5, 4)
4 = 2(5) - 3
4 = 10 - 3
4 = 7
So (5, 4) does not satisfy the equation.
Therefore your answer is (1, -1).
Answer:
the answer is 5,4
What is the perimeter in units ?
Answer:
12 + [tex]4\sqrt{5}[/tex] approximates to 20.944
Step-by-step explanation:
VU - 8 units
UW - 4 units
VW - [tex]\sqrt{64+16} = \sqrt{80} =4\sqrt{5}[/tex]
12 + 4sqrt(5)
Answer:
6 (2 + √5) units
Step-by-step explanation:
Finding the length of the 3rd side :
*Applying Pythagorean Theorem*
VW² = 4² + 8²VW² = 16 + 64VW = √80VW = 6√5The perimeter :
4 + 8 + 6√512 + 6√56 (2 + √5) units
1.9^4 × 10 × 2.9 x 10^1
3779.309 is the answer....
Determine the equation of the tangent line in both cases
1. x^2/x+2 at (2,1)
2. x^3+2y^2=10y at (2,1)
Differentiate the function/equation with respect to x and solve for the derivative, dy/dx. The value of dy/dx at the given point is the slope of the tangent line to the curve at that point. Then use the point-slope formula to get the equation of the tangent.
1.
[tex]y = \dfrac{x^2}{x+2} \implies \dfrac{dy}{dx} = \dfrac{2x\times(x+2) - x\times1}{(x+2)^2} = \dfrac{x(x+4)}{(x+2)^2}[/tex]
When x = 2, the derivative is
[tex]\dfrac{dy}{dx}\bigg|_{x=2} = \dfrac{2(2+4)}{(2+2)^2} = \dfrac34[/tex]
Then the equation of the tangent line at (2, 1) is
[tex]y - 1 = \dfrac34 (x - 2) \implies \boxed{y = \dfrac{3x}4 - \dfrac12}[/tex]
2.
[tex]x^3 + 2y^2 = 10y \implies 3x^2 + 4y \dfrac{dy}{dx} = 10 \dfrac{dy}{dx} \implies \dfrac{dy}{dx} = \dfrac{3x^2}{10-4y}[/tex]
When x = 2 and y = 1, the derivative is
[tex]\dfrac{dy}{dx}\bigg|_{(x,y)=(2,1)} = \dfrac{3\times2^2}{10-4\times1} = 2[/tex]
Then the tangent at (2, 1) has equation
[tex]y - 1 = 2 (x - 2) \implies \boxed{y = 2x - 3}[/tex]
find the indicated side of the right triangle
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 3\sqrt3 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: \tan(60) = \cfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: \sqrt{3} = \dfrac{x}{3} [/tex]
[tex]\qquad \tt \rightarrow \: x = 3 \sqrt{3} [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
the data below shows the number of workers employed in the various section s of each a construction company in the Lagos
Carpenter 24
plumber 12
labourers 27
plasterers 15
painters 9
Messengers 3
bricklayers 18
if the Worker is retrenched, what is the probability that he is a plumber or a plasterer?
If the Worker is retrenched, the probability that he is a plumber or a plasterer will be 0.0152.
What is probability?The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,
The probability that the employee is a plumber;
[tex]\rm P(plumber)= \frac{No \ of \ plumber}{Total \ number \ of \ employ} \\\\ P(plumber)=\frac{12}{108} \\\\\ P(plumber)= 0.11[/tex]
The probability that the employee is a plasterer;
[tex]\rm P(plasterers )= \frac{No \ of \ plasterers }{Total \ number \ of \ employ} \\\\ P(plasterers )=\frac{15}{108} \\\\\ P(plasterers )= 0.13[/tex]
The probability that he is a plumber or a plasterer:
P = 0.13 × 0.11
P= 0.0152
Hence, if the worker is retrenched, the probability that he is a plumber or a plasterer will be 0.0152.
To learn more about the probability, refer to the link;
https://brainly.com/question/11234923
#SPJ1
