Answer:
y= -17/18x-1/3
Step-by-step explanation:
The slope-intercept form of the equation is y = (-17/18)x -1/3.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
A linear equation 17x + 18y = -6.
To find the slope-intercept form:
Simplifying,
17x + 18y = -6
18y = -6 -17x
y = -17/18x -1/3
Therefore, y = (-17/18)x -1/3 is the slope-intercept form.
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The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.
a) Is f'(t) positive or negative? Why?
b) What are the units of f'(35)?
c) Suppose that |f'(35)| = 1.5 and f(35) = 68. Fill in the blanks (including units where needed) and select the appropriate terms to complete the following statement about the temperature of the coffee in this case.
At ____ minutes after the coffee was put on the counter, its temperature is ____ and will ____ by about ____ in the next 30 seconds.
Answer:
a
f'(t) is negative
b
The unit is degC/min
c
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
Step-by-step explanation:
From the question we are told we are told that
The equation for the temperature of a cup of coffee place on a counter is
[tex]H= f(t)[/tex]
Here t is the time in minutes the coffee was put on the counter
Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time
Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative
Generally the unit of the temperature is in degrees Celsius while that of time is in minutes
So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)
From the question we are told that
[tex]|f(35)'| = 1.5[/tex]
i.e the rate of change of temperature after 35 minutes is 1.5
and
[tex]|f(35)| = 68[/tex]
i.e the temperature of the cup of coffee after 35 minutes is 67 degC
Now after another t= 30 seconds = [tex]\frac{30}{60}= 0.5 \ minutes[/tex] the rate of change of the temperature of the cup of coffee is
[tex]R = |f(35)'| * t[/tex]
=> [tex]R = 1.5 * 0.5 [/tex]
=> [tex]R = 0.75 [/tex]
So
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
The value of f'(t) is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.
The units of f'(35) = degC/min.
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
Given
The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.
1. The value of f'(t) is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.
2. What are the units of f'(35)?
The units of f'(35) = degC/min.
3. At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
At ║f'(35)║ = 1.5 and f'(35) = 68
|f'(35)| = 1.5 represents the rate of change of temperature every 35 minutes = 1.5.
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F(4) for the function f(x)=2x+5
Answer:
= 13
Step-by-step explanation:
Use direct substitution:
2(4)+5 = 13
The graph of a linear function is given below.
What is the zero of the function
A. -5
B.2/5
C.2
D.5/2
Answer:
A. - 5
Step-by-step explanation:
Since, line is intersecting x-axis at - 5, therefore zero of the function is - 5.
complete the pattern 444 4440 44,400 444,000 ______ _______ what goes on does 2 spots
Answer:
4440,000 and 44.400,000
Step-by-step explanation:
All you do is add another zero to the end
Is this relation a function? Justify your answer.
Please help me!! 5:45pm est! Answer as soon as you can!
Answer:
D
Step-by-step explanation:
Please help me fast.
Answer:
26
Step-by-step explanation:
all you have to do is count and add i took the test before
Homer sold cupcakes and cookies yesterday. Each cupcake sold for $2.25 and each cookie sold for $0.25. At the end of the day, Homer has sold $55.50 worth of cookies and cupcakes. If he sold 54 cupcakes and cookies combined, how many cupcakes were sold and how many cookies were sold
Answer: 21 cupcakes and 33 cookies were sold.
Step-by-step explanation:
Let x= Number of cupcakes
y = Number of cookies
As per given,
x+y= 54 (i)
Cost: 2.25x+0.25y=55.50 (ii)
Multiply 0.25 to (i0, we get
0.25x+0.25y = 0.25(54)
⇒0.25x+0.25y = 13.5 (iii)
subtract (iii) from (ii), we get
2x=42
Divide both sides by 2, we get x= 21
Put this in (i) , we get 21+y =54 ⇒ y= 54-21= 33
Hence, 21 cupcakes and 33 cookies were sold.
The college tutoring center staff are considering whether the center should increase the number of math workshops they offer to help students improve their performance in math classes. Faculty would like to know if requiring student attendance at these math workshops will improve overall passing rates for their students in their math classes. They plan to use the number of workshops attended to predict the final exam score and regression analysis to determine the effectiveness of the mandatory workshop attendance policy.
For each of the following classify the variable as explanatory, response, or neither.
a. Whether the student attended a workshop.
b. Number of workshops attended
c. Whether the student passes the course
Answer:
a. Whether the student attended a workshop. Neither
b. Number of workshops attended. Explanatory variable
c. Whether the student passes the course. Response variable
Step-by-step explanation:
In a given experiment, the response variable addresses the core of the question that was asked. In the experiment above, we are trying to determine the passing rate. That is the response variable. The explanatory variable provides an explanation for the response.
The number of workshops attended by the students would provide an explanation of their passing rates. Whether the student attended a workshop is not a consideration in the experiment, because it is believed that they would attend the workshop.
Help me ASAP please !!!! I attached a pic
Two side of a triangle have the following measures. Find the range of possible measures for the third side.
8, 9
_______ < x < _______
Answer:
8<x<9
Step-by-step explanation
4 divied by 217 long divisions
Answer:
Step-by-step explanation:
Answer: 0.018 or not simplified: 0.01843317972
0. 0 1 8
2 1 7 4. 0 0 0
− 0
4 0
− 0
4 0 0
− 2 1 7
1 8 3 0
− 1 7 3 6
9 4
Joe wants to divide 304 gumballs into boxes of 100. How many boxes of
100 gumballs will he fill completely?
Answer:
3
Step-by-step explanation:
since there are 304 goumballs and a box can only fit one hundred the question says how many boxes will be COMPLETELY full
Answer:
3 boxes
Step-by-step explanation:
304÷100=3.04
An insurance policy sells for $800. Based on past data, an average of 1 in 50
policyholders will file an $8,000 claim, an average of 1 in 100 policyholders will file
a $20,000 claim, and an average of 1 in 250 policyholders will file a $50,000 claim. Find
the expected value to the company per policy sold.
Answer: i needed this question too!
There are six wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use.
Required:
Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested.
Answer:
There are 720 possible sequences of assembly that must be tested.
Step-by-step explanation:
We are given that;
No. of wires needed to be attached to a circuit board = 6
We want to find the number of possible sequences of the assembly that must be tested.
From multiplication rule of counting;
Number of possible sequences of the assembly = 6!
1st selection of wire = 6 possible choices
2nd selection of wire = 5 possible choices
3rd selection of wire = 4 possible choices
4th selection of wire = 3 possible choices
5th selection of wire = 2 possible choices
6h selection of wire = 1 possible choice
Thus,
number of possible sequences = 6 × 5 × 4 × 3 × 2 × 1 = 720
Thus, there are 720 possible sequences of assembly that must be tested.
Help my daughter please k gtg
Answer:
5.7, 4.6, 5.6, 6.7
Step-by-step explanation:
Answer:
2.63+3.07= 5.7
9.4-4.8= 4.6
3.92+1.68= 5.6
8.5-1.8= 6.7
-1/2(-2x+4y) someone expand this pls
Answer:
-1/2(-2x+4y)=
x-2y
Multipy (2x + 4 (x - 4)
Zzz
Answer:
6x−16
Step-by-step explanation:
A $55 pair of shoes was discounted 15% making a sale price $46.79 the discounted price was sent us Canada game by 10% explain how you would find the final price of the shoes?
Answer:
A $55 pair of shoes was discounted 15% making a sale price $46.79 the discounted price was sent us Canada game by 10% explain how you would find the final price of the shoes?
hello please help will give brainliest!
Answer:
420
Step-by-step explanation:
Answer:
A. 420
Step-by-step explanation:
nice
what is 1555 times 67
Answer:
104185
Step-by-step explanation:
Answer:
104,185
Step-by-step explanation:
What is the probabiWhich value cannot represent the probability of an event occurring?
StartFraction 1 over 100 EndFraction
0.29
85%
Three-halflity of an event that is certain?
Given problem:
Which value cannot represent the probability of an event occurring?
Values:
[tex]\frac{1}{100}[/tex] 0.29 [tex]\frac{85}{100}[/tex] Three-halflity
Probability is the likelihood of an event to occur.
For an event that we are sure of occurring, the probability value is 1, and those that cannot occur have a probability value of 0.
The probability of any event is usually a fraction between 1 and 0.
So we can see that the odd one is the Three-halflity which is clearly greater than 1.
Answer:
D 3/2
Step-by-step explanation:
3.99 x 10^-2 - 1.5 10^-3
put it in scientific notation
Answer:
its 3.45 x 10^5
Step-by-step explanation:
The solution of the given expression will be 3.84 x 10⁻².
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 3.99 x 10⁻² - 1.5 x 10⁻³. The expression will be solved as below:-
E = 3.99 x 10⁻² - 1.5 x 10⁻³
E = ( 3.99 x 0.15 ) x 10⁻²
E = 3.85 x 10⁻²
Therefore, the solution of the expression is 10⁻².
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Calvin is starting a new job this summer. He has created a table to represent his earnings, which are dependent on the number of hours he works. Write an equation to represent y, Calvin’s total earnings based on x the number of hours he works. * PLEASE HELPPP!!!!!!
Answer:
I think its 232.5
Step-by-step explanation:
Divide 3 by one then multiply that by 15.
Answer:
how much does he make in a hour
Step-by-step explanation:
What is an advantage of using a check book
the heights of adult males are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches. an adult male is categorized as shirt if he is less than 64 inches tall and categorized as tall if he is in the top 2% of adult males in term of height. how tall does an adult make need to be to be assigned to the tall category.
Answer:
76.2
Step-by-step explanation:
Use a calculator or chart to find the z-score associated with the probability.
P(Z > z) = 0.02
P(Z < z) = 0.98
z = 2.054
Find the height.
z = (x − μ) / σ
2.054 = (x − 70) / 3
x = 76.2
The number of kilograms of water in a human body varies directly as the mass of the body. An 84-kg person contains 56 kg of water. How many kilograms of water are in a 63-kg person?
kg of water are in a 63-kg person.
Answer:
42
Step-by-step explanation:
To find the amount of water in a 63-kg person you must first find the unit rate in an 84-kg person.
84 ÷ 56 = 1.5
1.5 is how much human body weight there is as a unit rate over 1-kg of water.
1.5 x 56 = 84, so this shows we are correct.
84 ÷ 1.5 = 56, so that goes even further to prove you are correct.
Now, what's the amount of water in a 63-kg person?
1.5 is the unit rate we found out was used, so it should still be proportional.
63 ÷ 1.5 = 42.
Indeed, it is proportional. You are correct.
The answer is 42.
There is 42 kg of water in a 63 kg person.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
We have,
The number of kilograms of water in a human body varies directly with the mass of the body.
This means,
W ∝ M
Where W is the kg of water and M is the mass of the body.
Now,
W = KM
W = 56 kg
M = 84 kg
So,
56 = 84K
K = 56/84
Now,
For M = 63,
W = KM
W = 56/84 x 63
W = 42
Thus,
There is 42 kg of water.
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6 is added to three-fifths of p
Answer:
Is that the question? I don't think it is
solve for n: 10/60 =n/84
Answer:
n=14
Step-by-step explanation:
Heather wants to purchase an electric guitar the price of the guitar with tax is $2,240.if she can save $90 per month how linf will it take her to save up for the guitar
Answer:
25
Step-by-step explanation:
We would like to know the velocity of the block when it reaches some position x. Finding this requires an integration. However, acceleration is defined as a derivative with respect to time, which leads to integrals with respect to time, but the force is given as a function of position. To get around this, use the chain rule to find an alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx.
Answer:
An alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]
Step-by-step explanation:
We know that :
[tex]a_x=\frac{dv_x}{dt}[/tex]
Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex]
So, We will use chain rule over here :
[tex]a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}[/tex]
Hence an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]
The alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx is [tex]a_x = v_x \frac{dv_x}{dx}[/tex]
Chain rule:Here we used the chain rule:
It is the basic method for differentiating a composite function. Here the first factor on the right, Df(g(x)), represents that the derivative of f(x) is first found and then x, wherever it arises, is replaced by the function g(x).
So,
[tex]a_x = \frac{dv_x}{dt}\\\\ = \frac{dv_x}{dt} \times \frac{dx}{dx}\\\\= \frac{dv_x}{dx} \times \frac{dx}{dt}\\\\ = \frac{dv_x}{dx} \times \frac{dx}{dt} (\frac{dx}{dt} = v_x)\\\\ = \frac{dv_x}{dx} \times v_x\\\\= v_x\frac{dv_x}{dx}[/tex]
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