Step-by-step explanation:
The question is wrong. The correct equation is :
[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex]
We know that the equation gives the relation between temperature readings in Celsius and Fahrenheit.
Therefore, giving that we know the value in Fahrenheit ''F'' we can find the reading in Celsius ''C''. This define a function C(F) that depends of the variable ''F''.
So for the incise (a) we answer Yes, C is a function of F.
For (b) we need to find the mathematical domain of this function. Giving that we haven't got any mathematical restriction, the mathematical domain of the function are all real numbers.
Dom (C) = ( - ∞ , + ∞)
For (c) we know that the water in liquid state and at normal atmospheric pressure exists between 0 and 100 Celsius.
Therefore the range will be
Rang (C) = (0,100)
Now, we need to find the domain for this range. We do this by equaliting and finding the value for the variable ''F'' :
For C = 0 :
[tex]0=\frac{5}{9}F-\frac{160}{9}[/tex] ⇒ [tex]F=32[/tex]
And for C = 100 :
[tex]100=\frac{5}{9}F-\frac{160}{9}[/tex] ⇒ [tex]F=212[/tex]
Therefore, the domain as relating temperatures of water in its liquid state is
Dom (C) = (32,212)
For (d) we only need to replace in the equation by [tex]F=71[/tex] and find the value of C ⇒
[tex]C=\frac{5}{9}F-\frac{160}{9}[/tex] ⇒
[tex]C=(\frac{5}{9})(71)-\frac{160}{9}[/tex]
[tex]C=\frac{65}{3}[/tex] ≅ 21.67
C(71) = 21.67 °C
a. Yes, C is a function of F.
b. Domain of the function is: ( - ∞ , + ∞)
c. Range of function C is: (0, 100)
the domain of function C is: (32, 212).
d. [tex]\mathbf{C(71) = 21.67^{\circ}C}[/tex]
Range and Domain of A FunctionThe domain of a function is the input value, while the range is the corresponding output value.
a. Given the equation of the function as, [tex]C = \frac{5}{9}(F) - \frac{160}{9}[/tex], this means that, the value of C is dependent on the value of F, therefore, the answer is, Yes, C is a function of F.
b. Since no mathematical restriction was stated, therefore:
Domain of the function is: ( - ∞ , + ∞)
c. Temperature of water in its liquid state ranges between 0 and 100°C, therefore:
Range of function C is: (0, 100)
To find the domain, substitute C = 0 and C = 100, respectively, into [tex]C = \frac{5}{9}(F) - \frac{160}{9}[/tex].
Thus:
[tex]0 = \frac{5}{9}(F) - \frac{160}{9}\\\\F = 32[/tex]
[tex]100 = \frac{5}{9}(F) - \frac{160}{9}\\\\F = 212[/tex]
Therefore, the domain of function C is: (32, 212).
d. To find C when F = 71°, substitute F = 71° into [tex]C = \frac{5}{9}(F) - \frac{160}{9}[/tex].
Thus:
[tex]C(71) = \frac{5}{9}(71) - \frac{160}{9}\\\\C(71) = \frac{65}{3} \\\\\mathbf{C(71) = 21.67^{\circ}C}[/tex]
Learn more about domain and range of function on:
https://brainly.com/question/10197594
What’s the slope intercept equation
Answer:
y=mx + b
Step-by-step explanation:
y= y intercept coordinate
m=slope=x coordinate
b = y intercept
(5.8 x 10^-6): (2 x 10^-3) =
Find the quotient .
write answer in Scientific notation
Which expression is modeled by this arrangement of tiles?
A. -40÷10
B. 40÷(-10)
C. 40÷10
D. 40÷40
Answer:
c
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
I NEED HELP WITH B AND E
Write the conclusion:
If Charlie goes to the store, then Harry loves school
A. Charlie doesn't go to the store
B. Harry does not love school
C. Charlie goes to the store
D. Harry loves school
a. then Harry loves school
b. Harry loves school
c. Charlie goes to the store,
d. Then Charlie goes to the store,
Question 5
Write the converse:
If the team does not play on Tuesday then the project is not due Friday.
a. If the project is not due Friday then the team does not play on Tuesday
b. If the team plays on Tuesday then the project is due FridayThis answer is incorrect.
c. If the project is due Friday then the team plays on Tuesday
d. The team plays on Tuesday if and only if the project is due Friday.
Question 7
Write the converse:
If Don goes to the store then George doesn't go to the store.
A. If George doesn't go to the store then Don goes to the store
B. Don doesn't go to the store if and only if George goes to the store.
C. If George goes to the store then Don doesn't go to the store
D. If Don doesn't go to the store then George goes to the store
a. If George doesn't go to the store then Don goes to the store
b. Don doesn't go to the store if and only if George goes to the store.
c. If George goes to the store then Don doesn't go to the store
d. If Don doesn't go to the store then George goes to the store
Question 9
Write a counterexample:
If the product of two numbers is 80, then one number must be 10.
a. x = 10 and y = 8
b. x = 1 and y = 8
c. x = 10 and y = 80
d. x = 1 and y = 80
Answer:
A
Step-by-step explanation:
beacause Harry loves school so he go to school
Please help me with this
Answer:
$62.50
Step-by-step explanation: 250 divided by 4 equals $62.10
the first six multiples of 6
A pair of shoes was $5 but is now on sale for
$4. What is the percent discount?
Answer:
20%
Step-by-step explanation:
i actually dont know sorry :(
Answer:
20% discount
Step-by-step explanation:
4/5 = 80%
5/5 - 4/5 = 1/5
1/5 = 20%
Explain to me in words how you would find the slope of this line and explain your answer
Answer:
5/3
Step-by-step explanation:
Looking at the two points, we count the rise (rise/run). It'd be 5 going up from the bottom point all the way to the same level as the top point. Then we count how many units over, which is 3. The slope of this would be 5/3. in slope form would be y=5/3x
Answer:
The slope is 6
Step-by-step explanation:
To find the slope you use the formula rise/run
The rise is the second y coordinate minus the first y coordinate
The run is the second x coordinate minus the first y coordinate
Step one:
Take any 2 points: I used (-1,2) and (-4,-3)
Step two:
Use the formula: rise/run
-4-2/-2-(-1)
-6/-1
6
I hope this helps :)
Use the normal distribution to compute probability with technology - Calculator Question Suppose that the annual household income in a region is normally distributed with mean $25,000 and standard deviation $6,000. If the poverty level for the region is at or below $12,000, what percentage of the population lives in poverty? • Round your answer to two decimal places.
Answer:
0.02
Step-by-step explanation:
Given a normal distribution :
Mean income (m) = 25000
Standard deviation of income (s) = 6000
X ≥ 12000
Using the relation to fund the standardized score :
Zscore =(x - m) / s
Zscore = ( 12000 - 25000) / 6000
Zscore = -13000 / 6000
Zscore = - 2.167
Using a z probability calculator :
P(Z ≤ - 2.167) = 0.015117
= 0.02
The triangles below are congruent and their corresponding parts are marked
∠A ≅ ∠Z
you can determine this by seeing that both angles have two curved lines, therefor showing they have the same measurement.
∠B ≅ ∠Y
you can also determine this by seeing that they both have one curved line showing that they share the same measurement.
∠C ≅ ∠X
once again, you can determine this by seeing that both angles are marked with three curved lines, meaning they share the same measurements.
line AB ≅ line ZY
just like before, you can determine that they are equivalent to each other by seeing that both lines have three dashes showing that they have the same measurement.
line AC ≅ line ZX
you can determine these lines are equivalent because they both have one dash showing they are the same length as each other.
line BC ≅ line YX
once again, both lines have two dashes, showing that they are equivalent in length.
ΔCAB ≅ XZY
you can determine this by seeing that all three angles and all three sides on both triangles share measurements with the other triangle
Jonathan pays $1.90 per pound for potatoes. He buys 8.3 pounds of potatoes. He determines that he will pay $15.77, before tax, for the potatoes. Which best describes the reasonableness of Jonathan’s solution?
Jonathan’s answer is reasonable because there are two decimal places in the factors and two in the product.
Jonathan’s answer is unreasonable because there are three decimal places in the factors and two in the product.
Jonathan’s answer is reasonable because 2 times 8 is 16, and 16 is close to 15.77.
Jonathan’s answer is unreasonable because 1 times 8 is 8, and 8 is not very close to 15.77.
Answer:here is the right answer took the test and got it right trust and believe Jonathan’s answer is reasonable because is 16, and 16 is close to 15.77.
Step-by-step explanation:
5.)
A ball is thrown into the air with an initial velocity of 96 feet per second. Given the formula below wheret,
represents time in seconds and s(t), the height of the ball, when will the ball hit the ground?
s(t) = -16t? + 960
Show full work
Answer: The ball will hit the ground 6 seconds after it has ben thrown, at t = 6s.
Step-by-step explanation:
The equation for the height of the ball should be:
s(t) = (-16ft/s^2)*t^2 + 96ft/s*t
When s(t) = 0ft, means that the ball is in the ground
This represents the height of the ball as a function of t, the time in seconds.
We can see that at t = 0s:
s(0s) = (-16ft/s^2)*(0s)^2 + 96ft/s*(0s) = 0ft
Then at the time 0 seconds, the ball is in the ground, so we must look at the other root of the equation
(-16ft/s^2)*t^2 + 96ft/s*t = 0ft
To find it, we can use the Bhaskara equation, in this case is:
[tex]t = \frac{-96ft/s +- \sqrt{(96ft/s)^2 - 4*(-16ft/s^2)*0} }{-2*16ft/s^2} = \frac{-96ft/s^2 +-96ft/s^2}{-32ft/s^2}[/tex]
Then we have the two solutions:
t = (-96ft/s + 96ft/s)/(-32 ft/s^2) = 0s (the one that we already found)
And the other one is:
t = (-96ft/s - 96ft/s)/(-32ft/s^2) = 6s
Then:
s(6s) = 0ft
This means that the ball will hit the ground at t = 6 seconds.
The time required to hit the ground is required.
The time taken by the ball to reach the ground is 2.45 seconds.
The equation is
[tex]s(t)=-16t^2+96[/tex]
At the ground [tex]t=0[/tex]
so,
[tex]0=-16t^2+96\\\Rightarrow 16t^2=96\\\Rightarrow t=\sqrt{\dfrac{96}{16}}\\\Rightarrow t=2.45\ \text{s}[/tex]
The time taken by the ball to reach the ground is 2.45 seconds.
Learn more:
https://brainly.com/question/18769085?referrer=searchResults
Complete the proof Prove: angle UWX = angle UWV
Answer:
Step-by-step explanation:
Statements Reasons
1). UW bisects ∠VUX 1). Given
2). UW bisects ∠VWX 2). Given
3). ∠VUW = ∠WUX 3). Definition of angle bisector
4). ∠UWV = ∠UWX 4). Definition of angle bisector
5). UW = UW 5). Reflexive property of congruence
6). ΔUWX ≅ ΔUWV 6). ASA postulate of congruence
Help plz I really need it
Answer:
here up I have upload photosHelp!! Please help with this question.
Answer:
The slope seems to be 4.
Step-by-step explanation:
The line seems to be starting at (3,0) and if you use the rule rise/run, it goes up (rises) 4 units and moves over (runs) 1 unit. You then rewrite this as 4/1 and you get 4 as the slope!
Answer:
The slope is 4
My logic:
Slope is delta y over delta x so if you take any 2 points on that graph and get the x and y of each point and find the change of the two x and the two y and put the change in y over the change in x. you get slope. like so= 16/4 or 4
In the figure, is a median. If = 6 + 10 and = 2 + 12, find the length of . Show your work.
Answer:
26.
Step-by-step explanation:
Given, BD is a median. As it divides the AC equally, that's why it will AD=CD. Given, AD= 6x+10 and CD= 2x+12
Now, AD= CD
or, 6x+10=2x+12
or, 6x-2x= 12-10
or, 4x= 2
or, x= 1/2
So the value of x is 1/2. As BD divided AC equally, both AD and CD will be equal and AD+CD= AC.
So, 6x+10+2x+12= AC
or, 8x+22= AC
or, 8 X (1/2) + 22= AC
or, 4+22 = AC
or, AC= 26.=
5 men build a wall in 10 days how long will it take one man
Answer:
50 days?
Step-by-step explanation:
Answer:
i think it is 2 because
10 divide by 5 = 2
1 x 2 = 2
2 days
Circle circumference
Will mark brainliest
what is the approximate area of the shaded sector in the circle shown below?
Answer:
The sector given in the figure is a semi-circle because the degree measure of the chord is 180 degrees.
Area of semicircle = 0.5π[tex]r^{2}[/tex] = 0.5π×4.5 = 6.75 sq. inches
I Need Helpp PLZZ i will mark as brainliest
Answer:
9x+18Reasoning:
You multiply x by 9 and 2 by 9 and it expands out from 9(x+2) to 9x+18
I hope this helps and good luck!
Answer:
9x + 18
Step-by-step explanation:
9 times x = 9x
9 x 2 = 18
Instead of handing out candy like a well-adjusted person on Halloween, grumpy, anti-social Professor Sosa decides to stand on top of a 400 ft building and toss candy treats onto the ground below. If he drops a bag of candy corn, how long will it take for it to land on the ground? What will the velocity of the bag be when it hits the ground?
Answer: The bag of candy corn will take 5 seconds to land on the floor and it will hit it with velocity of 49m/s.
Step-by-step explanation: A free falling object has only Gravitational Force acting on it, so acceleration will be due to gravity, which has magnitude
g = 9.8m/s².
As Professor Sosa drops the bag, its initial velocity and time are 0.
The building has a height of 400ft, so adjusting units: y = 121.92 m and [tex]y_{0}[/tex] = 0.
For this problem, going down will be the positive reference.
Then:
[tex]y=y_{0}+v_{0}t+\frac{g}{2}t^{2}[/tex]
[tex]\Delta y=v_{0}t+\frac{g}{2}t^{2}[/tex]
[tex]121.92=\frac{9.8}{2}t^{2}[/tex]
[tex]t=\sqrt{\frac{121.92*2}{9.8} }[/tex]
t ≈ 5
It will take 5s for the candy corn bag to land on the ground.
Acceleration is the change in velocity per change in time, so:
[tex]g=\frac{\Delta v}{\Delta t}[/tex]
As initial velocity and time are 0 and rearraging it:
v = g.t
v = 9.8*5
v = 49
The bag will hit the ground with velocity of magnitude 49 m/s.
Let's estimate 534–395.
(a) Round each number to the nearest hundred.
534 rounds to
395 rounds to
(b) Subtract the rounded numbers.
I
Answer:
A)
534 rounds to 500
395 rounds to 400
B) 100
Step-by-step explanation:
A)
534 rounds to 500 because the next digit 3 is less than 5 which means that you round down.
395 rounds to 400 because the next digit 9 is greater than 5 which means that you round up.
B)
500-400=100
Hope this helps! :)
Select the expression that is NOT equivalent to 2 × (3 + 6).
A. 6 + 12
B. (2 × 3) + (2 × 6)
C. (2 × 6) + (2 × 3)
D. (2 × 3) + (3 × 6)
Answer:
D
Step-by-step explanation:
in answer D, the values would equal "6" and "18" which is not equivalent to the given equation
Greta mails 4 postcards on Monday, Wednesday, and Friday. She mails 5 postcards on Tuesday and Thursday and no postcards Saturday or Sunday. She believes that she will mail over 200 postcards if she does this for the entire 12 weeks that she is studying abroad.
Which are reasonable estimates for the number of postcards that Greta mails? Check all that apply.
60
120
200
220
240
f (x) = x squared What is f(x) + f(x) + f(x)?
Answer:
Step-by-step explanation:
fx^3
What 90
4 l is
3
?
You have 41 students three are absent what percentage of students are absent?
Answer:
Step-by-step explanation:
If 41 students is in the roll (total), then
[tex]\frac{3}{41}[/tex] = [tex]\frac{x}{100}[/tex] ⇒ x = [tex]\frac{3*100}{41}[/tex] ≈ 7.3 %
Prove or give a counterexample: Every positive integer can be expressed as the sum of three or fewer perfect squares. (A perfect square is an integer n for which there is an integer k with the property: n
Answer:
Statement is incorrect
Step-by-step explanation:
Every positive integer cannot be expressed as the sum of three or fewer perfect squares.
Supposing the number 7 only squares less than are 0, 1 and 4
Clearly 7 can not be written using three or fewer of these numbers
It is proved
By taking Cube root of 7
[tex]\sqrt[3]{7}[/tex] = 1.912931183
Now By taking
[tex]\sqrt{7}[/tex] = 2.64575131
So both values 1.912931183 and 2.64575131 are not positive integers.
Hence the statement is incorrect.
PLS HELP MEEEEEE
Two babysitters have the following price schedules: Susan charges $5 per hour plus a $2 base fee. Sarah charges $7 per hour. Use graphing to find the point where the two
will charge the same amount.
Answer:
hhhhhhhhhhhhhhhhhhjhhhhhhhhh
Perform the indicated operation.
(4g²-9) ÷ (2g-3)
A. 2g-3
B. 2g+3
C. 2g+3 R 18
Answer:
Solving [tex](4g^2-9) \div (2g-3)[/tex] we get 2g+3
Option B is correct.
Step-by-step explanation:
We need to solve [tex](4g^2-9) \div (2g-3)[/tex]
We know that [tex]a^2-b^2=(a-b)(a+b)[/tex]
So, [tex]4g^2-9[/tex] can be written as [tex](2g)^2-(3)^2[/tex]
So, using above formula we will get:
[tex]4g^2-9\\=(2g^2)-(3)^2 \\Using \ formula a^2-b^2 = (a-b)(a+b)\\=(2g-3)(2g+3)[/tex]
So, numerator will become
[tex]\frac{(2g-3)(2g+3)}{(2g-3)} \\Simplifying:\\=2g+3[/tex]
So, solving [tex](4g^2-9) \div (2g-3)[/tex] we get 2g+3
Option B is correct.