Using it's concepts, the domain of the composite functions are given as follows:
Domain of f(g(x)): x > 0.Domain of g(f(x)): x > 0 and x ≠ 1.What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input of the function.The range of a function is the set that contains all the values of the output of the function.In a graph, the domain and the range are found as follows:
The domain is given by the values of x, present in the horizontal axis of the graph.The range is given by the values of y, present in the vertical axis of the graph.For the composite functions in this graph, we have that:
g(x) is defined only for x > 0, due to the asymptote, hence f(g(x)) will also be defined only for x > 0, meaning that the domain of f(g(x)) is x > 0.f(x) is defined for all real values, assuming all real values expect y = 1 as range. g(x) is defined for all values of x > 0, hence, considering the two restrictions, the domain of g(f(x)) is x > 0 and x ≠ 1.More can be learned about the domain of a relation at https://brainly.com/question/10197594
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The 53 term of the arithmetic sequence-12, -1, 10
Answer: 560
Step-by-step explanation: i had this exact question on OW
Answer:
a₅₃ = 560
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 12 and d = a₂ - a₁ = - 1 - (- 12) = - 1 + 12 = 11 , then
a₅₃ = - 12 + (52 × 11) = - 12 + 572 = 560
a mechanic charges $150 per hour,plus the cost of parts to fix your car if the parts cost $257 write an equation to model the total cost use h as the variable for the number of hours in rakes the mechanic to fix your car and c as the cost
The Equation representing the charge to be to paid to mechanic is -
c = 150h + 257.
What is Equation modelling?Equation modelling is defined as a method for deriving a mathematical relation from a mathematical statement taking into consideration the variables defined and the relations between them.
Given is a mechanic who charges $150 per hour. He also charge the cost of parts to fix the car.
Assume that the mechanic worked for 'h' hours and 'c' represents the total cost of repair. Extra cost of parts is $257.
If the mechanic works for 'h' hours, then the money received by the mechanic will be → $150 x h.
The equation representing the above situation can be written as -
c = $150 x h + Extra parts charge.
c = 150h + 257
Therefore, equation representing the charge to be to paid to mechanic is - c = 150h + 257.
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noel runs a shop that sells christmas trees. her supplier connie furr charges$80 forfor each real tree
The cost of 32 Christmas trees when Noel orders the trees is $2560.
How to calculate the cost?Based on the information, it should be noted that
Noel runs a shop that sells christmas trees and that her supplier Connie for charges $80 for each Christmas tree.
Therefore, the cost of 32 Christmas trees will be:
= Price of one Christmas tree × Number ordered
= $80 × 32.
= $2560
Therefore, the cost of 32 Christmas trees when Noel orders the trees is $2560.
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Noel runs a shop that sells christmas trees. Her supplier Connie for charges $80 for each Christmas tree. What is the cost of 32 Christmas trees?
Rearrange the formula, V =
2
лr²h
3
ندا
to solve for r.
Answer:
[tex] \sf \: r = \sqrt{V/2πh³} [/tex]
Step-by-step explanation:
V=2πr²h³
Divide both sides by 2πh³
V/2πh³= 2πr²h³/2πh³
V/2πh³ = r²
Flip equation
r² = V/2πh³
Take square root of both sides
√r² = √V/2πh³
∴ r = √V/2πh³
I will give brainlist
Divide 4 and 5 over 6 ÷ negative 2 and 1 over 7.
negative 10 and 15 over 42
negative 8 and 5 over 42
negative 2 and 23 over 90
negative 2 and 1 over 2
The value of the expression given as [tex]4 \frac{5}{6} \div - 2\frac 17[/tex] is [tex]-2\frac{23}{90}[/tex]
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the solution to the expression?The expression is given as
Divide 4 and 5 over 6 ÷ negative 2 and 1 over 7.
Rewrite the above expression properly as follows:
Divide 4 5/6 ÷ -2 1/7
Using LaTeX, the above expression can be further represented as
[tex]4 \frac{5}{6} \div - 2\frac 17[/tex]
Rewrite the above fractions and express it as improper fractions
[tex]\frac{29}6 \div -\frac{15}7[/tex]
Rewrite the above fractions and express it as products
[tex]\frac{29}6 \times -\frac7{15}[/tex]
Evaluate the product in the above expression
[tex]-\frac{203}{90}[/tex]
Rewrite the above expression as a mixed fraction
[tex]-2\frac{23}{90}[/tex]
Hence, the value of the expression given as [tex]4 \frac{5}{6} \div - 2\frac 17[/tex] is [tex]-2\frac{23}{90}[/tex]
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H(x)=-3/5x-3 find the inverse
Answer:
y
=
x
−
3
5
Explanation:
Replace
f
(
x
)
with
y
.
y
=
5
x
+
3
Swap
x
and
y
.
x
=
5
y
+
3
Solve for
y
.
x
−
3
=
5
y
x
−
3
5
=
y
Step-by-step explanation:
In the figure below, k | l and m | n. Find the values of y and z.
m
yo
5z 82
#
68°
N
=
11
Answer:
y = 112 and z = 30
Step-by-step explanation:
Since the y angle and the 68 angle are same side exterior angles, they add up to 180
68+y = 180
y = 112
If we take (5z -82) angle's alternate interior angle, we get:
5z-82+112 = 180
5z = 150
z = 30
Match the vocab word with the definition:
Question 3 options:
Least Common Denominator
Greatest Common Factor
Integer
Simplifying Fractions
Dimensional Analysis
Factor
1.
It is the largest number that divides exactly into two or more numbers.
2.
Also called reducing means to make the fraction as simple as possible.
3.
The LCM of two or more denominators.
4.
A number that is multiplied by another number.
5.
A procedure of multiplying be conversion factors to divide out common units and convert between different measurements.
6.
All the numbers within the whole number set {0,1,2,3,…} as well as all of the opposites.
1. Least Common Denominator ⇒ The LCM of two or more denominators.
2.Greatest Common Factor ⇒ It is the largest number that divides
exactly into two or more numbers.
3. Integer ⇒ All the numbers within the whole number set {0,1,2,3,…} as
well as all of the opposites.
4. Simplifying Fractions ⇒ Also called reducing means to make the
fraction as simple as possible.
5. Dimensional Analysis ⇒ A procedure of multiplying be conversion factors to divide out common units and convert between different measurements.
6. Factor ⇒ A number that is multiplied by another number.
What is Greatest Common Factor ?
The highest number that divide exactly into two or more numbers is called Greatest Common Factor.
Now, We can match each by the definitions as;
Since, Least Common Denominator is the LCM of two or more denominators.
1. Hence, Least Common Denominator ⇒ The LCM of two or more denominators.
Since, Greatest Common Factor is the largest number that divides exactly into two or more numbers.
Hence, Greatest Common Factor ⇒ It is the largest number that divides exactly into two or more numbers.
Since, All the numbers within the whole number set {0,1,2,3,…} as well as all of the opposites.
Hence, Integer ⇒ All the numbers within the whole number set {0,1,2,3,…} as well as all of the opposites.
Since, Simplifying Fractions also called reducing means to make the fraction as simple as possible.
Hence, Simplifying Fractions ⇒ Also called reducing means to make the fraction as simple as possible.
Since, A procedure of multiplying be conversion factors to divide out common units and convert between different measurements is called
Dimensional Analysis.
Hence, Dimensional Analysis ⇒ A procedure of multiplying be conversion factors to divide out common units and convert between different measurements.
Since, When a number is multiplied by another number then it is called a factors of that number.
So, Factor ⇒ A number that is multiplied by another number.
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Priya and Elena are members of the Science Club. Last week, they observed two families of birds nesting in the woods. The members were divided into two equal groups; each group studied one family. Every day after school for 5 days, each group hiked to visit their bird family. Priya’s group hiked 2.5 fewer kilometers each day than Elena’s group. If Priya’s group hiked a total of 19 kilometers last week, how far did Elena’s group hike each day?
Define a variable to represent the unknown
Use your variable to write an equation that represents the scenario.
Using proportions, it is found that Elena's group hiked 6.3 km each day.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the measures using a rule of three, that can be either direct or inverse, deriving from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
For this problem, we have that Priya's group hiked 19 kilometers in 5 days, hence the daily amount is found applying the proportion as follows:
19/5 = 3.8 km a day.
Elena's group hiked 2.5 km a day more, hence:
3.8 + 2.5 = 6.3 km a day.
Elena's group hiked 6.3 km each day.
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Which of the following lines is not parallel to the graph of y = 3x+9?
a.
3x-y = 10
C.
3y-x-10
b. y-3x = 11
d. 6x-2y=10
Please select the best answer from the choices provided
OA
OB
C
OD
someone i beg u pls help me FAAAST..
Answer: C - 290 kg
700-410=290
the weight of the moose is 290kg greater than the weight of a polar bear
HELP NOW ASAP RN RN FAST
Simplify the following expression: (-5)(-3)(4) (1 point)
-65
-60
60
65
Answer: The following expression: (-5)(-3)(4) = 60
Step-by-step explanation:
Given that,
The following expression is : (-5)(-3)(4)
Let us assume,
These values represented by X1, X2, X3
Let us assume, X1 = -5
X2 = -3
X3 = 4
So, the following expression is: (X1)(X2)(X3)
(-5)(-3)(4)
This values using by multiplication,
So, we can write,
= (X1)(X2)
= (-5)(-3) [sign (-) (-) = (+)]
= 15
Therefore, X1X2 values = 15
We can solve X3 value,
= (X1)(X2)(X3)
= 15 (X3)
Replace X3 value,
= 15(X3)
= 15 (4)
= 60
Therefore, (X1)(X2)(X3) = 60
The following expression: (-5)(-3)(4) = 60
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not tile A 10 x 12 plane
Answer:120
Step-by-step explanation:
so if its a 10x12 plane that would be 10 12 times so 10+10+10+10+10+10+10+10+10+10+10+10
or 12+12+12+12+12+12+12+12+12+12
Question 3
What is WX? Explain your reasoning.
W
30°
BIUX² X₁
Z
10
60 45%
Y
15px
45%
X
AVA
E
Check the picture below.
A father is three times as old as his son. After 4 years, his age will be 4 times his son's age 2 years ago. Find their present age.
The present age of the father is 36 and the present age of the son is 12 years.
What is an expression?The mathematical expression is the combination of 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 be used to denote the logical syntax's operation order and other properties.
Given that a father is three times as old as his son. After 4 years, his age will be 4 times his son's age 2 years ago.
Let the present age will be "F" and "S". The equations will be solved as:-
F = 3S
F + 4 = 4 ( S - 2 )
F + 4 = 4S - 8
3S + 4 = 4S - 8
S = 12 years
F = 3S
F = 3 x 12 = 36 years
Therefore, the present age of the father is 36 and the present age of the son is 12 years.
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Hayley and Maxwell are jogging on a track. Hayley jogs 3/4 mile in 1/6 hour. Maxwell jogs 2/3 mile in 2/15 hour. Who is faster? How much faster? Show your work.
Maxwell is faster than Hayley by 0.5 miles per hour
How to calculate the average speed of both Hayley and Maxwell ?
The first step is to calculate the average speed of Hayley
Average= distance/time
3/4÷1/6
= 3/4 × 6/1
= 9/2
= 4.5
The next step is to calculate the average speed of Maxwell
= 2/3 ÷ 2/15
= 2/3 × 15/2
= 5
The difference between the average speed of both individuals
= 5-4.5
= 0.5
Hence Maxwell is faster than Hayley by 0.5 miles per hour
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In Exercises 6-8, poing M is between L and N on line LN. Write an eqeustion in tems fo x. LM=x squared, MN = x squared + 9x LN =56
The equation expressed in terms of x is x = √47/ 2
What is a line segment?A line segment can be defined as the part of a line that connects two points which are considered to be its endpoints.
From the information given, we have that LN is a line with segments LM, MN and LN and M is the midpoint between L and N
Now, the equation is expressed as;
LM + MN = LN
Where;
LM = x²MN = x² + 9LN = 56Substitute the values
x² + x² + 9x = 56
collect like terms
2x² = 56 - 9
2x² = 47
To make 'x' the subject of formula
x² = 47/ 2
Find the square root of both sides
x = √47/ 2
Thus, the equation expressed in terms of x is x = √47/ 2
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Fill in table y=10x-1
The complete table is
x y
-5 49
-1 9
0 -1
1 -11
From the question, we are to fill in the table for the given values of x
Using the given equation,
y = -10x - 1
Determine the value of y when x = -5
y = -10x - 1
y = -10(-5) - 1
y = 50 - 1
y = 49
Determine the value of y when x = -1
y = -10x - 1
y = -10(-1) - 1
y = 10 - 1
y = 9
Determine the value of y when x = 0
y = -10x - 1
y = -10(0) - 1
y = 0 - 1
y = -1
Determine the value of y when x = 1
y = -10x - 1
y = -10(1) - 1
y = -10 - 1
y = -11
Hence, the complete table is
x y
-5 49
-1 9
0 -1
1 -11
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The scale on a map uses 1 cm to represent 10 km which proportion could be used to determine the number of kilometers represented by 8
The number of kilometers represented by 8cm is 80km.
According tot he question we have been the proportion of scaling on the map which is as follows:
1 cm : 10 km or it is also written as 1cm/10km
We need to find the number of kilometers represented by 8 cm
Let the number of kilometers that we need to find be x km. Mathematically the proportion can be written as
8 cm : x km or it is written as 8cm / x km
Also both the proportion will be equivalent. Therefore, the proportion is equal to
1/10 = 8/x
we will solve this for x, we get
x = 8*10
x = 80 km
Hence the number of kilometers represented by 8cm is 80 km
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In the college there are 1400 male students and 1050 female students.
Select one:
O a. Absolute difference: 350
Relative difference: 3.3%
O b. Absolute difference: 350
Relative difference: 33.3%
O c. Absolute difference: -350
Relative difference: -25%
O d. Absolute difference: 350
Relative difference: 25%
Answer:
B.
Give me brainliest answer
I hope I could help
ILL GIVE BRAINLY PLEASE HELP
Answer:
B
Step-by-step explanation:
a c and d are unessecary answers
There are 3 triangles and 15 circles. What is the simplest ratio of triangles to total shapes?
3:15=3/15
The numerator and the denominator can both be divided by 3.
so, it is 1/5 which is equal to 1:5.
The simplest ratio of triangles to total shapes is 1 : 6.
Given that, there are 3 triangles and 15 circles.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, total number of shapes
= 3+15
= 18
Now, ratio of triangles to total shapes is 3 : 18
So, the simplest form = 1 : 6
Hence, the simplest ratio of triangles to total shapes is 1 : 6.
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Convert each equation into slope intercept form. 2x+2y=10
Answer:
Y = -X + 5
Step-by-step explanation:
I want this equation in the form
y = mx = b
2x + 2y = 10 Subtract 2x from both sides of the equations
2y = -2x + 10 Now divide everything by 2
y = -1x + 5
or
y = -x + 5
help help help help help help help
Answer:5
Step-by-step explanation:look on my page
Work out the equation of the line which has a gradient of ½ and passes through the point (4,2).
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\hspace{10em} \underset{gradient}{\stackrel{slope}{m}} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y - 2 = \cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x[/tex]
Robel is unsure of how many nights he will stay in Los Angeles.
a) Write an equation that will allow Robel to calculate what his total cost will be if he is charged $52 as a one-time fee and the cost per night is $94.
b) What will be Robel’s total cost if he decides to stay 3 nights. Show all your work to justify your answer.
We need to know about
linear equation
to solve this problem. (a) The equation that will allow Robel to calculate what his total cost will be is 52+94n (b) Robal's total cost if he decides to stay 3 nights is $334
A
linear equation
is one that has
one or two variables
in it, the variables in a linear equation are linearly related to each other which means that the graph of such an equation is a straight line.
In part (a) it is said that Robel is charged $52 as a one time fee and the
cost per night
is $94, let us consider the
total cost to be t
and the
number of nights he stays be n,
then the equation for the total cost will be
t=52+94n
In part (b) we have to find out the total cost if he stays 3 nights, which means n=3,
substituting the value of n
in the equation for total cost
t=52+94x3=334
Therefore we found out that the
equation for Robel's total cost
is 52+94n and the total cost if he stays for 3 nights is $334.
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Directions: Combine the following units of measurement. Be sure to convert unlike units to like units before combining. Use an online calculator if needed.
1. 40mm + 50mm =
2. 68mg + 57g =
3. 45L + 34mL =
4. 78km + 33m =
5. 67cg + 23g =
6. 34km + 89m =
7. 72cm + 88mm =
8. 121L + 42cL =
9. 156cg + 38mg =
10. 56kg + 333mg =
11. 31km 1/3m + 82km 1/6m =
12. 48m 50cm + 17m 281 1/2cm =
13. 97L 3/4mL + 44L 2/3mL =
14. 26km 5/9mm + 64km 1/5mm =
15. 27Kg 1/4g + 67Kg 1/3g =
16. 30kL 1/3mL + 3kL 1mL =
17. 87kg 1024mg + 23kg 237mg =
18. 83L 1/3 cL + 22L 1/6cL =
19. 93kg 1/5g + 29kg 1/3g =
20. 32m 572mm + 78m 2/7mm =
The values of the given summation of units are;
90 mm57.068 g45.034 L78.033 km23.67 g34.089 km80.8 cm121.042L158.8 cg56.333 kg113 km 1/2 m65 m 331 m 1/2 cm141 L 17/12 m/L90 km 34/45 mm94 kg 7/12 g33 kL 4/3 mL110 kg 1261 mg105 L 1/2 cL122 kg 8/15 g110 m 572 2/7 mmWhat are the values of the unit of measurement expressions?The values of the given expressions are;
1. 40 mm + 50 mm = 90 mm
2. 68 mg + 57 g is found as follows;
1000 mg = 1 g
68 mg = 0.068 g
Therefore;
68 mg + 57 g = 0.068 g + 57 g = 57.068 g
3. 45 L + 34 mL is found as follows;
1,000 mL = 1 L
Therefore;
34 mL = 0.034 L
45 L + 34 mL = 45 L + 0.034 L = 45.034 L
4. 78 km + 33 m is found as follows;
1000 m = 1 km
Therefore;
33 m = 0.033 km
78 km + 33 m = 78 km + 0.033 km = 78.033 km
5. 67 cg + 23 g is found as follows;
100 cg = 1g
Therefore;
67 cg = 0.67 g
67 cg + 23 g = 0.67 g + 23 g = 23.67 g
6. 34 km + 89 m
34 km + 89 m = 34 km + 0.089 km = 34.089 km
7. 72 cm + 88 mm
10 mm = 1 cm
88 mm = 8.8 cm
72 cm + 88 mm = 72 cm + 8.8 cm = 80.8 cm
8. 121 L + 42 cL
100 cL = 1 L
Therefore;
121 L + 42 cL = 121 L + 0.042 L = 121.042L
9. 156 cg + 38 mg
10 mg = 1 cg
156 cg + 38 mg = 156 cg + 3.8 cg = 158.8 cg
10. 56 kg + 333 mg
56 kg + 333 mg = 56 kg + 0.333 kg = 56.333 kg
11. 31 km 1/3 m + 82 km 1/6 m = 113 km 1/2 m
12. 48 m 50 cm + 17 m 281 1/2 cm = 65 m 331 m 1/2 cm
13. 97 L 3/4 m/L + 44 L 2/3 m/L = 141 L 17/12 m/L
14. 26 km 5/9 mm + 64 km 1/5 mm = 90 km 34/45 mm
15. 27 kg 1/4 g + 67 kg 1/3 g = 94 kg 7/12 g
16. 30 kL 1/3 mL + 3 kL 1 mL = 33 kL 4/3 mL
17. 87 kg 1024 mg + 23 kg 237 mg = 110 kg 1261 mg
18. 83 L 1/3 cL + 22 L 1/6 cL = 105 L 1/2 cL
19. 93 kg 1/5 g + 29 kg 1/3 g = 122 kg 8/15 g
20. 32 m 572 mm + 78 m 2/7 mm = 110 m 572 2/7 mm
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Question 1(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $190, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
50x + 35 = 190; x = 3.1 hours
50x − 35 = 190; x = 4.5 hours
35x + 50 = 190; x = 4 hours
35x − 50 = 190; x = 6.9 hours
Question 2(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
Write and solve an equation that represents the following math sentence.
Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5.
24 = 10.5 + 4.5m; m = 60.75
24 = 10.5 + 4.5m; m = 3
24 equals 10.5 plus m over 4.5; m = 3
24 equals 10.5 plus m over 4.5; m = 60.75
Question 3(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
Write 'five more than three times a number equals 21' as an equation.
3x + 5 = 21
5x + 3 = 21
3x(5) = 21
5x(3) = 21
Question 4(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
Three friends ate at a restaurant. They ordered nachos for $19.95 and jalapeno poppers. Each friend paid $9.73, not including sales tax or tip, which was one third of the total. Determine the cost of the jalapeno poppers.
$6.65
$9.24
$18.48
$29.19
Question 5(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
Write an equation for the following math sentence.
One third times the difference of thirty and a variable is three fourths.
one third times the quantity 30 minus y equals three fourths
one third times the quantity y minus 30 equals three fourths
one third times 30 minus y equals three fourths
one third times y minus 30 equals three fourths
Question 6 (Essay Worth 4 points)
(Writing Two-Step Equations HC)
Warren is building shelves for his 3-D printed model collection. He has a piece of wood that is 4.5 feet long. After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over.
Part A: Write an equation that could be used to determine the length of each of the five pieces of wood he cut. (1 point)
Part B: Explain how you know the equation from Part A is correct. (1 point)
Part C: Solve the equation from Part A. Show every step of your work. (2 points)
1) The equation that determines the number of hours worked by the plumber at Jerald's house is A. 50x + 35 = 190; x = 3.1 hours.
2) The equation that represents, "twenty-four equals the sum of 10.5 and the quotient of a number and 4.5" is B. 24 = 10.5 + 4.5m; m = 3.
3) An equation representing 'five more than three times a number equals 21' is A. 3x + 5 = 21.
4) The cost of the jalapeno is B. $9.24.
5) The equations for the mathematics statements are:
a) 1/3(30 - y) = 3/4
b) 30(1/3) - y = 3/4
c) 1/3y - 30 = 3/4
d) 30(1/3) - y = 3/4
6A) The equation to determine the length (x) of each of the five pieces is x = (4.5 - 0.7) ÷ 5.
6B) The above equation is correct because it can be solved to get the length of each of the five pieces.
6C) The solution and steps of the equation in Part A are as follows:
x = (4.5 - 0.7) ÷ 5
x = 3.8 ÷ 5
x = 0.76 feet
Data and Calculations:1) Jerald:
Plumber's fixed charge = $35
Plumber's variable charge per hour = $50
Total charges by plumber = $190
The number of hours worked = 3.1 hours ($190 - $35)/$50
2) 24 = 10.5 + 4.5m; m = 3
24 = 10.5 + 4.5 x 3
24 = 10.5 + 13.5
24 = 24
3) 3x + 5 = 21
3x = 21 - 5
3x = 16
x = 5.333
4) The total amount paid by the three friends = $29.19 ($9.73)
The cost of nachos, including tax and tip = $19.95
The cost of jalapeno, including tax and tip = $9.24 ($29.19 - $19.95)
5) Equations:a) 1/3(30 - y) = 3/4
b) 30(1/3) - y = 3/4
c) 1/3y - 30 = 3/4
d) 30(1/3) - y = 3/4
6) Length of wood = 4.5 feet
The number of equal pieces = 5
Remainder = 0.7 feet
The cut length of the wood = 3.8 feet (4.5 - 0.7)
Length of each cut piece = 0.76 feet
The equation and its solution to determine the length of each of the five pieces are:
x = (4.5 - 0.7) ÷ 5
x = 3.8 ÷ 5
x = 0.76 feet
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In a game experience, the level of monsters, L, is measured by the formula L= 250M E, where M=number of monsters and E=experience of monsters. Solve the formula for E
The formula for E is given as E = L/250M
According to the question we have been given that the level of monsters is measured by as follows
L = 250M E (1)
where , M = number of monsters
E = experience of monsters.
Now we need to find the formula for E. For that we will solve equation (1) for E .
L = 250M E
Dividing both the sides by 250M we get
L/250M = E
or, E = L/250M
Thus above is the equation or the formula for E.
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The length of students' college careers at Anytown University is known to be normally distributed with a mean length of 5.5 years and a standard deviation of 1.75 years. What percent of students have college careers lasting between 2 and 9 years?
The per cent of students who have college careers lasting between 2 and 9 years is 95%.
Given that, the normally distributed with a mean length of 5.5 years and a standard deviation of 1.75 years.
What is a normal distribution?The normal distribution is a continuous probability distribution that is symmetrical around its mean with most values near the central peak.
Let x be the length of student's college careers.
\mu = 5.5 years
\sigma = 1.75 years
A percentage of students have college careers lasting between 2 and 9 years.
P(2<=x<=9)=P (2-5.5<=x-5.5<=9-5.5)
P(2<=x<=9)=P (-3.5<=x-5.5<=3.5)
=P (-3.5/1.75<=(x-5.5)/1.75<=3.5/1.75)
We know if x =-=N (4.6^2)
Then x-\mu/\sigma =-= Z (0.1)
=P(-2<=Z<=2)
=0.95
Percentage = P(-2<=Z<=2)*100
=95%
Therefore, the per cent of students who have college careers lasting between 2 and 9 years is 95%.
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