The sum of three consecutive odd numbers is 177. Find the number. Step by step please
Answer:
57, 59 and 61
Step-by-step explanation:
Let the first odd number be n The next consecutive odd number is n + 2 and the next one after that is n + 4
(consecutive odd numbers have difference of 2 between them. For example if 7 is the first odd number next one is 9(7+2) and the next one is 11(7+4)
We are given that the sum of the numbers is 177. So we have the following equation:
n + (n + 2) + (n +4) = 177
Simplifying gives
n + n + 2 + n + 4 = 177
Collect like terms:
n + n + n + 2 + 4 = 177
3n + 6 = 177
Subtract 6 from both sides
==> 3n = 177 - 6
==> 3n = 171
Divide by 3 both sides
3n/3 = 171/3
n = 57 and this is the first of the odd numbers
The next odd number is 57+ 2 = 59
and the next one after that is 59 + 2 = 61 (same as 57 + 4)
Kristen goes on a cave tour with her family. They climb down to 8 meters below ground level.
Then they climb the opposite of -8 meters to return to ground level.
How many meters did they climb in all? Enter your answer in the box
Answer:
16 meters is the answer of this question
For the function
f(x) = x + 10/6x + 4, consider the following.
(a)Find the vertical and horizontal asymptotes for the graph of f.
Vertical:
Horizontal:
b)Find f^ −1.
f^ −1(x) =
c)Find the vertical and horizontal asymptotes for the graph of
f^ −1
Vertical:
Horizontal:
Show all steps.
Using the concepts of asymptotes and inverse function, we have that:
a) For f, the vertical asymptote is x = -2/3 and the horizontal asymptote is y = 1/6.
b) The inverse function is: [tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]
c) For the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.For this problem, the function is given by:
[tex]f(x) = \frac{x + 10}{6x + 4}[/tex]
The zero of the denominator is:
6x + 4 = 0
6x = -4
x = -4/6 = -2/3.
Hence the vertical asymptote is x = -2/3.
The horizontal asymptote is given as follows:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{x + 10}{6x + 4} = \lim_{x \rightarrow \infty} \frac{x}{6x} = \lim_{x \rightarrow \infty} \frac{1}{6} = \frac{1}{6}[/tex]
How to find the inverse function?To find the inverse function of a function y = f(x), we exchange x and y then isolate y.
Exchanging x and y, we have that:
[tex]x = \frac{y + 10}{6y + 4}[/tex]
Applying cross multiplication:
x(6y + 4) = y + 10
6xy - y = 10 - 4x
y - 6xy = 4x - 10
y(1 - 6x) = 4x - 10
[tex]y = f^{-1}(x) = \frac{4x - 10}{1 - 6x}[/tex]
Applying the same procedure, for the inverse function, the vertical asymptote is x = 1/6 and the horizontal asymptote is y = -2/3.
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Graph the line with a slope of 1/3 passing through point (-1, -1)
Considering the expression of a line, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.
Definition of lineA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing the value of slope m, substituting this value and the value of the point in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Line in this caseIn this case, you know:
The line has a slope of 1/3The line passes through point (x,y)=(-1, -1)Substituting the value of the slope m:
y= 1/3x +b
Substituting the point to calculate the value of b:
-1= 1/3×(-1) + b
-1= -1/3 + b
-1 + 1/3= b
-2/3= b
Finally, the line is y= 1/3x -2/3 and the graph of this line is shown in the attached image.
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determine smallest 3 digit number which is exactly divisible by 6, 8 and 12
Answer:
120
Step-by-step explanation:
Common Multiples of 6: 6,12,18,24,30,36,42Common Multiples of 8: 8,16,24,32,40,48,54Common Multiples of 12: 12,24,36,48,60,72We note that 2, 4 is the least common multiple of 6,8 and 12
We have to find the smallest 3 -digit multiple of 24.
Also 24 × 4 = 96 and 24 ×5 = 120.
The smallest 3-digit number which is exactly divisible by 6,8 and 12 is 120.
Answer:
120
Step-by-step explanation:
4. Airline fares can vary greatly, even from the same carrier within the same day. The following are fares from New York to Burbank, CA, over the past week. $430, $567, $334, $701, $424, $555, $890, $455, $450, $1,122 What is the standard deviation for this distribution? Round your answers to the nearest dollar.
Answer:
$235
Step-by-step explanation:
.....................
A car pulls forward 35 feet in 7 seconds, and then stops and sits still for 4 seconds, and then pulls backward 21 feet in 5 seconds. a) What is the distance that the car moved in the full 16 seconds? b) What is the total displacement of the car in the full 16 seconds? c) What are the average speeds in the first, second, and third parts of the car’s motion? d) What is the car’s average speed during the full 16 seconds? e) What is the car’s average velocity during the full 16 seconds?
a) The total distance covered is 56 feet
b) The total displacement is 14 feet
c) The average speed in the first, second, and third parts of the car’s motion are; 5 feet/sec, 0 feet/sec and 4.2 feet/sec
d) The average speed of the car is 3.5 feet/sec
e) The average velocity of the car is 0.875 feet/sec
What is the displacement?We must understand that the distance is the difference between two points but the displacement is the distance between two points in a definite direction. This implies that the distance is a scalar quantity while the distance is a vector quantity. Being a vector quantity means that when we are computing the displacement that we must take into account the direction of the motion and this also applies to the calculation of the velocity of the car.
Let us now carry pout the calculations;
a) Total distance = 35 feet + 21 feet = 56 feet
b) Total displacement = 35 feet - 21 feet = 14 feet
c) Average speed of the first, second, and third parts of the car’s motion;
i) 35 feet / 7 seconds = 5 feet/sec
ii) 0 feet/sec ( it sat still)
iii) 21 feet/5 seconds = 4.2 feet/sec
d) The cars average speed = 56 feet/16 seconds = 3.5 feet/sec
e) Average velocity = 14 feet/ 16 seconds = 0.875 feet/sec
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The vertices of a figure are given. What are the coordinates of the image after the given dilation? Identify the type of dilation?
Q (-3,0), R (-3,6), T (4,6), U (4,0)
k=1/3
The new images has vertices Q´(-1, 0), R´(-1, 2), T´(4/3, 2), U´(4/3, 0) and the type of dilation is contraction.
When we dilate the points of a given figure, we simply multiply each x-coordinate and y-coordinate by the scale factor.
Here the points are Q (-3,0), R (-3,6), T (4,6), U (4,0) and the scale factor is
k = 1/3
Therefore,
⇒ Q (-3,0) → Q´ (-3 × 1/3,0 × 1/3) = (-1, 0)
⇒ R (-3,6) → R´ (-3 × 1/3, 6 × 1/3) = (-1, 2)
⇒ T (4,6) → T´ (4 × 1/3, 6 × 1/3) = (4/3, 2)
⇒ U (4,0) → U´ (4 × 1/3, 0 × 1/3) = (4/3, 0)
Thus, the new images has vertices Q´(-1, 0), R´(-1, 2), T´(4/3, 2), U´(4/3, 0) and the type of dilation is contraction
What is dilation?
Dilation is the process of modifying the dimensions of an object or shape by varying some scale variables. For instance, a circle with a radius of 10 units gets shrunk to a circle with a radius of 5 units. This technique is applied in photography, fine art, logo design, and other fields.
Four fundamental categories of transformations exist in geometry.
These are:
RotationTranslationReflectionResizing or DilationLearn more about Dilation
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y=-x+4
x + 2y = -8
How many solutions does this linear system have?
a. one solution: (8,0)
b. one solution: (0,8)
c. no solution
d. infinite number of solutions
The linear system of equation has one solution as x = 16 and y = -12.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
The given system of equation are :
y=-x+4..........(1)
x + 2y = -8......(2)
Now, solving the above using substitution of y in equation (2) :
x + 2y = -8
x+2(-x+4) = -8
x-2x+8 = -8
-x = -16
x = 16
Now, substituting back x value in equation (1) we get :
y = -x+4
y = -16 +4
y = -12
Therefore, The linear system of equation has one solution as x = 16 and y = -12.
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Find the slope of the line graphed below.
PLEASE PLEASE PLEASE HELPP ME GUYS
Answer: m=2
Step-by-step explanation:
Highlighted points: (0, 4) and (-4, -4)
m=(y2-y1)/(x2-x1)
m=(-4-4))/(-4-0)
m=(-8)/(-4)
m=2
Mrs. Lin asked her students to
write a sequence with a common
ratio of 5 where a₁ is negative. Who
correctly completed the task?
KORY
-1, 5, -25, 125,
REID
-3, -15, -75,-375,..
KEISHA
-10,-5, 0, 5, 10,
ALLIE
2, 10, 50, 250,
Answer:
REID: -3, -15, -75,-375,..Step-by-step explanation:
If a GP has a positive common ratio and negative first term, it means all its terms are negative since formed by a product of positive and negative numbers.
We can only see one sequence with all negative terms and common ratio of 5, this is REID's.
help pls!!!!!!!!!!!!
Answer:
Step-by-step explanation:
E - 4,-2
F - 6, -3
G - 1, -4
Katherine buys eggs and apples at the store.
. She pays a total of $47.45.
. She pays a total of $6.77 for the eggs.
She buys 6 bags of apples that each cost the same amount.
Write and solve an equation which can be used to determine x, how much each bag
of apples costs.
Answer:
x = 5.94
Step-by-step explanation:
A rectangular room is 2 times as long as it is wide, and its perimeter is 32 meters. Find the
dimension of the room.
L=?
W=?
Answer: l=32/3 meters
w=16/3 meters
Step-by-step explanation:
P=perimeter, l=length, w=width
P=2l+2w
32=2(2w)+2w
32=4w+2w
6w=32
w=32/6
w=16/3 meters
32=2l+2(16/3)
32=2l+32/3
(32=2l+32/3)*3
96=6l+32
6l=64
l=64/6
l=32/3 meters
You can fill a 15-gallon tank of gas for $53.08 or buy gas for $3.60/gallon.
Answer: the better option would be to fill your tank up 15 gallons for $53.08
If you were to multiply 3.60 by 15, you would get 54.
53.08 < 54, therefore 53.08 is the better option.
Hope this helps!
Find the equation of the line perpendicular to the graph of x + 4y = 2 that contains the point (-1,3)
Answer:
y = 4x + 7
or y - 4x = 7
Step-by-step explanation:
x + 4y = 2
4y = -x + 2
y = -1/4x + 2
The slopes of two perpendicular lines are negative reciprocals of each other. So the slope of the perpendicular line should be negative reciprocal of -1/4, then it is 4
Given m = 4, y = 3, x = -1
y = mx + b
3 = 4(-1) + b
3 = -4 + b
b = 7
y = 4x + 7
The difference of range and equartile range of the data set present by is plit
The range measures the difference between the minimum value and the maximum value in a dataset. The interquartile range measures the difference between the first quartile (25th percentile) and third quartile (75th percentile) in a dataset. This represents the spread of the middle 50% of values
A dietitian at a hospital wants a patient to have a meal that has 53 grams of protein, 41 grams of carbohydrates, and
87.5 milligrams of vitamin A. The hospital food service tells the dietitian that the dinner for today is salmon steak,
baked eggs, and acorn squash. Each serving of salmon steak has 20 grams of protein, 30 grams of carbohydrates,
and 1 milligram of vitamin A. Each serving of baked eggs contains 20 grams of protein, 3 grams of carbohydrates, am
25 milligrams of vitamin A. Each serving of acorn squash contains 3 grams of protein, 20 grams of carbohydrates, an
37 milligrams of vitamin A. How many servings of each food should the dietitian provide for the patient?
How many servings of each food should the dietitian provide? Select the correct choice below and fill in any answe
boxes within your choice.
salmon steak (x),
baked eggs (y), and acorn squash (z).
OA. The dietitian should provide
(Simplify your answers.)
OB. There are an infinite number of combinations of servings of salmon steak (x), baked eggs (y), and acorn
squash (z) that the dietitian can provide. Using ordered triplets, the solution can be written as {(x,y,z) | x=
y=
z is any real number}
(Simplify your answers. Type expressions using z as the variable as needed.)
OC. There are no combinations of servings of each food that the dietitian can provide.
nwm życzę powodzenia kolego drogi
The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a "flipped" classroom. Complete parts (a) through (c) below.
Traditional
70.9
69.0
80.5
67.3
86.4
77.0
56.6
82.4
81.2
70.5
63.6
70.5
60.3
Flipped
76.5
71.0
64.4
72.8
79.0
91.8
78.3
76.0
81.4
69.4
92.6
77.8
76.9
Question content area bottom
Part 1
(a) Which course has more dispersion in exam scores using the range as the measure of dispersion?
The traditional course has a range of 29.829.8, while the "flipped" course has a range of 28.228.2. The
traditional
course has more dispersion.
(Type integers or decimals. Do not round.)
Part 2
(b) Which course has more dispersion in exam scores using the sample standard deviation as the measure of dispersion?
The traditional course has a standard deviation of 24.424.4, while the "flipped" course has a standard deviation of 29.129.1. The
flipped course has more dispersion.
For the given distributions, we have that:
a) The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.
b) The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.
What is the range of a distribution?
The range of a distribution is given by the difference between the greatest value and the smallest value.
Hence, for the Traditional classroom, the range is given by:
86.4 - 56.6 = 29.8.
For the Flipped classroom, the range is given by:
92.6 - 64.4 = 28.2.
Hence:
The traditional course has a range of 29.8, while the flipped course has a range of 28.2. Thus the traditional course is more dispersed using the range.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.Using a calculator, following the described procedure, the standard deviations are given as follows:
Traditional: 8.67.Flipped: 7.63.Hence:
The traditional course has a standard deviation of 8.67, while the flipped course has a standard deviation of 7.63. Thus the traditional course is also more dispersed using the standard deviation.
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Logan's bakeshop makes cupcakes that cost $.95 each. Logan knows that 20% of the cupcakes will spoil. Assume Logan wants a 35% markup on cost and produces 60 cupcakes. What should Logan charge for each cupcake?
The amount Logan should charge for each cupcake is $1.60 based on the markup of 35%
What is equivalent inputs for 60 cupcakes?
The equivalent inputs for 60 cupcakes, means the number of cupcakes that the materials used would have yielded in cupcakes if there was no wastage, hence, the cost per unit needs to be expressed to include 20% wastage
equivalent cost per unit=$0.95/(1-20%)=$1.1875
The 35% markup needs to be added to the equivalent cost per unit since markup is the profit as a percentage of cost
selling price=$1.1875*(1+35%)
selling price=$1.60
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change the subject. make x the subject
When the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))
How to change the subject and make x the subject?The equation is given as
x = 1 - 1/(1 - (1/(1 - y)^2)))
The question implies that we change the subject and make x the subject
However, in the equation;
The subject of the equation is x
This means that when the subject is changed for x, the equation is x = 1 - 1/(1 - (1/(1 - y)^2)))
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The store is selling lemons at $0.65 each. Each lemon yields about 2 tablespoons of juice. How much
will it cost to buy enough lemons to make two 9-inch lemon pies, each requiring half a cup of lemon
juice?
The cost of buying lemons to make two 9-inch lemon pies is $5.20.
What is the total cost?The first step is to convert cup to tablespoons
1 cup = 16 tablespoons
one 9-inch lemon pie would require 8 tablespoons (16 /2)
two 9-inch lemon pie would require 16 tablespoons (8 x 2)
The second step is to determine how much lemons would be needed.
Lemons needed = table spoons needed / table spoon one lemon would yield
16 / 2 = 8 lemons
The total cost of lemons needs to make the pies = cost of one lemon x number of lemons needed
8 x 0.65 = $5.20
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How can I solve for x
a) A software organisation employs 80,000 staff members. 16,000 employees are in the sales team, 24,000 are in the customer support team and 14,000 are in the software development and HR departments. What percentage of the organisation’s employees are a part of the finance team, if the size of the finance team makes up two-fifths of the remainder?
The organization’s employees are a part of the finance team, if the size of the finance team makes up two-fifths of the remainder is 13%
What is the number of employees who are regarded as remainder?
The number of employees out of the total workforce left after having deducted the number of employees making up the sales team, the customer support team the software development and HR departments is computed as shown below:
remainder of workforce=80,000-16,000-24,000-14,000
remainder of workforce=26,000
finance team=2/5*26000
finance team=10,400
finance team as % of total workforce=10,400/80,000
finance team as % of total workforce=13.00%
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6 3/7 + 7 5/7 as a mixed number in simplest form
Answer: 14 1/7
Step-by-step explanation:
An airplane takes 5 hours to travel a distance of 3900 miles with the wind. The return trip takes 6 hours against the wind. Find the speed of the plane in still air and the speed of the wind.
The speed of the plane in still air is ____ MPH and the speed of the wind is ____ MPH.
The speed of plane in still air is 715 MPH and the speed of the wind is 65 MPH
Distance travelled by airplane = 3900 miles
Time taken by the plane to travel the distance with the wind = 5 hours
Time taken by the plane to travel the distance against the wind = 6 hours
Let the speed of the plane in still air be x
Let the speed of the wind be y
Finding the speed of the air and airplane when distance is covered with the wind using the formula:
Speed of airplane + Speed of wind = Distance/Time
x + y= 3900/5
x + y = 780------(1)
Finding the speed of the air and airplane when distance is covered against the wind using the formula:
Speed of airplane - Speed of wind = Distance/Time
x - y = 3900/6
x - y = 650------(2)
Equating (1) and (2) we get:
2x = 1430
x = 715
Putting x = 715 in (1) we get:
y = 65
So, Speed of airplane in still air is 715 MPH and Speed of wind is 65 MPH
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Kenneth measured a hotel and made a scale drawing. The scale he used was 1 inch = 4 feet. The actual length of a room in the hotel is 20 feet. How long is the room in the drawing
Answer:
The room is 5 inches in the drawing.
Step-by-step explanation:
If the room is 20 feet and each inch in his drawing measures 4 feet what you need to do is see how many times 4 goes into 20.
4 times 5 = 20
So the answer would be 5
Hope it helps! =D
marco counts the sides on four quadrilaterals and three pentagons how sides does he count'
Answer: 31 sides
Step-by-step explanation: 4 sides per quadrilateral so 16 sides and 5 sides per pentagon so 15 sides. 16 + 15 = 31.
7(4x-5) - 4(6x+5) = -91
Answer:
x = -9Step-by-step explanation:
7(4x-5) - 4(6x+5) = -91
28x - 35 - 24x -20 = -91
28x - 24x = -91 + 35 + 20
4x = -36
x = -36 : 4
x = -9
---------------
Solve the system by back substitution.
-2x - 4y - z - 3w = -5
y + 6z + 2w = 8
4z + 4w = 8
-4w = -12
Solution should be set like {( _ , _ , _ , _ )}
Answer:
w = 3, x = -35/2, y = 8, z = -1
Step-by-step explanation:
Solve the following system:
{-3 w - 2 x - 4 y - z = -5
{2 w + y + 6 z = 8
{4 z + 4 w = 8
{-4 w = -12
In the fourth equation, look to solve for w:
{-3 w - 2 x - 4 y - z = -5
{2 w + y + 6 z = 8
{4 z + 4 w = 8
{-4 w = -12
Divide both sides by -4:
{-3 w - 2 x - 4 y - z = -5
{2 w + y + 6 z = 8
{4 z + 4 w = 8
{w = 3
Substitute w = 3 into the first, second, and third equations:
{-9 - 2 x - 4 y - z = -5
{6 z + y + 6 = 8
{4 z + 12 = 8
{w = 3
In the third equation, look to solve for z:
{-9 - 2 x - 4 y - z = -5
{6 z + y + 6 = 8
{4 z + 12 = 8
{w = 3
Subtract 12 from both sides:
{-9 - 2 x - 4 y - z = -5
{6 z + y + 6 = 8
{4 z = -4
{w = 3
Divide both sides by 4:
{-9 - 2 x - 4 y - z = -5
{6 z + y + 6 = 8
{z = -1
{w = 3
Substitute z = -1 into the first and second equations:
{-4 y - 2 x - 8 = -5
{y = 8
{z = -1
{w = 3
Substitute y = 8 into the first equation:
{-2 x - 40 = -5
{y = 8
{z = -1
{w = 3
In the first equation, look to solve for x:
{-2 x - 40 = -5
{y = 8
{z = -1
{w = 3
Add 40 to both sides:
{-2 x = 35
{y = 8
{z = -1
{w = 3
Divide both sides by -2:
{x = -35/2
{y = 8
{z = -1
{w = 3
Collect results in alphabetical order:
Answer: {w = 3, x = -35/2, y = 8, z = -1