Answer: Tom is 46 years old and Jerry is 34 years old.
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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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
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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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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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
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:
.....................
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!
how many cubic feet water will aquarium A hold 16ft and 8ft
Answer:
128 feet
Step-by-step explanation:
8*16 is 128 feet
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
6 3/7 + 7 5/7 as a mixed number in simplest form
Answer: 14 1/7
Step-by-step explanation:
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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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
help pls!!!!!!!!!!!!
Answer:
Step-by-step explanation:
E - 4,-2
F - 6, -3
G - 1, -4
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.
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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XZ is the perpendicular bisector of segment WY. Solve for k. Enter a NUMBER only.
=====================================================
Explanation:
"bisect" means to "divide in half"
So segment WY is split into two smaller equal pieces.
Segments WX and XY are the same length
WX = XY
6k+8 = 11k-12
6k-11k = -12-8
-5k = -20
k = -20/(-5)
k = 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 loptop and 3 tablets cost $810. A laptop and 1 tablet cost $630. How much does one laptop cost? How much does one tablet cost?
Answer: Tablet costs $225
Laptop costs $135
Step-by-step explanation:
Laptop is = x
Tablet = T
x + 3t = 810
x + t = 360
x = 360 - t
360 - t + 3t =810
2t = 450
t = 225
x + 225 = 360
x = 135
Distributive property 3(2x+7)
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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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
How can I solve for x
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
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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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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An object is moving at a speed of 360 kilometers per hour. Express this speed in miles per day. Round your answer to the nearest whole number.
We get the speed of the object as 5365 miles / day after rounding off.
We are given that an object is moving at a speed of 360 kilometers per hour.
We know that:
1 km = 0.621 miles.
So, 360 km will be:
360 km = 223.56 miles.
Also, we know that:
we have 24 hours in 1 day.
1 day = 24 hours.
1 hour = 1 / 24 day.
Re-writing the speed of the object, we get that:
223.56 miles in 1 / 24 day
That is:
5365.44 miles / day.
Rounding off:
= 5365 miles / day.
Therefore, we get the speed of the object as 5365 miles / day after rounding off.
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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:
Use the phrase below to answer the following questions.
The sum of -15y and 16y is −4.
Translate the phrase into an algebraic equation.
Now, use your equation to solve for y.
y =
The translation of the phrase The sum of -15y and 16y is −4 is
-15y + 16y = -4 and the value of y is -4.
What is an algebraic equation?An algebraic equation is written in the form of variables and constants and we combine these variables and constants with arithmetic operations.
In the given question there is a statement The sum of -15y and 16y is −4 and we have to express it in form of numerical and solve for y or find the value of y.
∴ The sum of -15y and 16y is −4 can be expressed numerically as,
-15y + 16y = -4.
y = -4.
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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.