The solution of the equation 3g + 5 = 7g + 4 will be 1/4.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
3g + 5 = 7g + 4
Simplify the equation, then we have
3g + 5 = 7g + 4
- 7g + 3g = 4 - 5
- 4g = - 1
g = (-1) / (-4)
g = 1 / 4
The solution of the equation 3g + 5 = 7g + 4 will be 1/4.
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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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if side of the triangle in 8cm and side 2 is 5cm, then what is the possible range for the length of the third side of the triangle?
Answer:
7cm
Step-by-step explanation:
You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
x -3 0 3 6
f(x) -5 4 1 7
f'(x) -1 2 -2 4
The table above gives values of a twice-differentiable function f and its first derivative f' for selected values of x. Let g be the function defined by
g(x)= f(x^3-x )
Required:
What is the value of g (3)?
Answer:
17
Step-by-step explanation:
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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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
Calculate 3cm ,4cm, 10cm and 2cm
Answer:
19cm
Step-by-step explanation:
(chose one way)
1. way using commutativity
(3cm+4cm)+(10cm+2cm)=7cm+12cm=19cm
2. way just writing
3cm+4cm+10cm+2cm=19cm
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:
Help me ASAP please !!!! I attached a pic
-1/2(-2x+4y) someone expand this pls
Answer:
-1/2(-2x+4y)=
x-2y
A birthday celebration meal is $47.40 including tax, but not the tip. Find the total cost if a 15% tip is added to the cost of the meal.
th
The total cost is $
Answer:
$54.51
Step-by-step explanation:
In the figure shown, r l l s
Question 9 of 25
What is the measure of angle b
А
35
C
B
Answer: C
Triangular dimesion x missing number = 120
120 + 5 = 125
Anyone want to try this?
I’ll give the answer later.
If your try doing this then... good luck! :)
Answer:
D
Step-by-step explanation:
Volume of cylinder = Base x height
Base = πr^2 = 25π
Volume = 25π x 10 = 250π
Volume of cone = 1/3 Base x height
= 1/3 x 25π x 5 = 125π/3
Volume of silo = cylinder + cone + cone
= 250π + 125π/3 + 125π/3
= 785.4 + 130.9 + 130.9
= 1047.2
What is the value of the expression below.
||3-7| - |-6+3||
Answer:
1
Step-by-step explanation:
[tex]||3-7| - |-6+3||[/tex]
||-4|- |-3||
|4-3|
|1|
What do the factors in the factored form represent?
Answer:
The factored form tells you the times at which the object's height is zero (the roots). ... Write the equation for this parabola in vertex form, factored form, and general form. From the graph you can see that the x-intercepts are 3 and 5. So the factored form contains the binomial expressions (x 3) and (x 5).
Step-by-step explanation:
could u answer my newest question? ive been stuck on it for hours
plz help. its easy brainliest
Answer:
ur welcome brainliesit pls
Step-by-step explanation:
6. x=2
7. x=3
8.x=-7
What is 2. 1.
— • —?
3. 2
Simplify to the lowest terms.
PLEASE HELP ASAP!! 20 points!!!
A. 1
—
6
B. 1
—
4
C. 1
—
3
D. 1
—
2
Answer:
a is the answer
Step-by-step explanation:
What is an advantage of using a check book
Given:
p: student achieves 90 percent on the geometry final.
q: student will receive a passing grade in geometry class.
Which statement is logically equivalent to q - p?
If a student achieves 90 percent on the geometry final, then the student will pass geometry class.
If a student passes geometry class, then the student achieved 90 percent on the geometry final.
If a student did not achieve 90 percent on the geometry final, then the student did not pass geometry class.
Olfa student did not pass geometry class, then the student did not achieve 90 percent on the geometry final.
Answer:
c
Step-by-step explanation:
Mrs Buchanan is planning
Answer:
what?
Step-by-step explanation:
Answer:
Your question is not clear
If (6, -5) is reflected across the y = -x the new point would be:
A.
(-5, -6)
B.
(5, -6)
C.
(5, 6)
D.
(-5, 6)
Please help me fast.
Answer:
26
Step-by-step explanation:
all you have to do is count and add i took the test before
What is the slope of the line?
The graph shows the relationship between the volume
of a rectangular prism and the volume of a square
pyramid with an identical base and height.
0-
Prism vs. Pyramid
3
10
9
B
8
03
02
Prism Volume (cubic units)
2
1
23
5
6 7
8
9 10
Answer:
The slope of the line is 3.
Step-by-step explanation:
The slope of the line between the volume of a rectangular prism and the volume of a square pyramid is given by m = 3
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 1 , 3 )
Let the second point be Q ( 2 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 6 - 3 ) / ( 2 - 1 )
Slope m = 3 / 1
m = 3
Therefore , the value of m = 3
Hence , the slope of the line is m = 3
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Multipy (2x + 4 (x - 4)
Zzz
Answer:
6x−16
Step-by-step explanation:
What is 5 tens + 5 tens in standard form
Answer:
19531250
Step-by-step explanation:
I hope it helps
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
Is <1 and <7 supplementary
Stacey and her friend went to Outback Steakhouse and spent $45. They wanted to leave a 20% tip, because the service was terrific. What was the total cost of the bill with tip?
Answer:
$54
Step-by-step explanation:
20% of $45 is $9. (45 * 2/10)
Add 9 to 45 and you get 54
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A college Statistics class conducted a survey concerning community attitudes about the college's large homecoming celebration. That survey drew its sample in the following manner: Telephone numbers were generated at random by selecting one of the local telephone exchanges (first three digits) at random and then generating a random four-digit number to follow the exchange. If a person answered the phone and the call was to a residence, then that person was taken to be the subject for interview. (Undergraduate students and those under voting age were excluded, as was anyone who could not speak English.) Calls were placed until a sample of 200 eligible respondents had been reached.
Required:
a. Did every telephone number that could occur in that community have an equal chance of being generated?
b. Did this method of generating telephone numbers result in a simple random sample (SRS) of local residences? Explain.
c. Did this method generate an SRS of local voters? Explain.
d. Is this method unbiased in generating samples of households? Explain.
Answer:
A) Yes
B) No
C) No
D) No
Step-by-step explanation:
A) Yes, every telephone number that could occur in that community will have an equal chance of being generated because the telephone numbers were generated randomly.
B) No, this method of generating telephone numbers would not result in a simple random sample (SRS) of local residences because the first three digits were generated in a different random way than the last four digits.
C) No, this method would not generate an SRS of local voters because not everybody will be pick up when they call because they may not be at home or they may be too busy to pick up.
D) No, this method is not unbiased in generating samples of households because there will be nonresponse bias since not everyone will pick up the call
hello please help will give brainliest!
Answer:
420
Step-by-step explanation:
Answer:
A. 420
Step-by-step explanation:
nice