Answer:
b
Step-by-step explanation:
A car traveled 120 miles on 6 gallons of gas. Find the unit rate?
Answer: 20 miles per gallon
Step-by-step explanation:
Answer: 20 mpg
Step-by-step explanation:
An executive of Trident Communications recently traveled to London, Paris, and Rome. He paid $180, $230, and
$160 per night for lodging in London, Paris, and Rome, respectively, and his hotel bills totaled $2660. He spent $110,
$120, and $90 per day for his meals in London, Paris, and Rome, respectively, and his expenses for meals totaled
$1520. If he spent as many days in London as he did in Paris and Rome combined, how many days did he stay in
each city? (4 marks)
The executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.
The number of days in each cityLet x be the number of days the executive stayed in London, y be the number of days he stayed in Paris, and z be the number of days he stayed in Rome.
We can set up the following equations to represent the given information:
180x + 230y + 160z = 2660 (hotel bills)
110x + 120y + 90z = 1520 (meal expenses)
x = y + z (he spent as many days in London as he did in Paris and Rome combined)
We can rearrange the third equation to get y + z - x = 0 and substitute it into the first two equations to eliminate x:
180x + 230y + 160z = 2660
110x + 120y + 90z = 1520
-180y - 180z + 180x = 0
Adding the first and third equations gives us:
360x + 50y - 20z = 2660
Adding the second and third equations gives us: 290x - 60y - 90z = 1520
We can now solve for x by multiplying the first equation by 3 and the second equation by 5 and subtracting them:
1080x + 150y - 60z = 7980
-1450x + 300y + 450z = 7600
----------------------------------
1630x - 150y - 510z = 380
Solving for x gives us:
x = (150y + 510z + 380) / 1630
Substituting this back into the third equation gives us:
y + z - (150y + 510z + 380) / 1630 = 0
Multiplying by 1630 and rearranging gives us:
1480y + 490z = 380
We can now solve for y by multiplying the first equation by 490 and the second equation by 50 and subtracting them:
490(360x + 50y - 20z) = 490(2660)
50(290x - 60y - 90z) = 50(1520)
---------------------------------------------------
19600x + 24500y - 9800z = 1303400
-14500x + 3000y + 4500z = 76000 --------------------------------------------------
4100x - 21500y - 14300z = 1227400
Solving for y gives us:
y = (4100x + 14300z - 1227400) / 21500
Substituting this back into the equation 1480y + 490z = 380 gives us:
1480(4100x + 14300z - 1227400) / 21500 + 490z = 380
Multiplying by 21500 and rearranging gives us:
606800x + 2054200z - 1817320000 = 0
Solving for z gives us:
z = (1817320000 - 606800x) / 2054200
Substituting this back into the equation x = y + z gives us:
x = y + (1817320000 - 606800x) / 2054200
Multiplying by 2054200 and rearranging gives us: 606800x^2 - 2054200xy - 2054200x + 1817320000y + 3707618640000 = 0
Using the quadratic formula, we can find the value of x:
x = (2054200y + 2054200 ± √[(2054200y + 2054200)^2 - 4(606800)(1817320000y + 3707618640000)]) / (2*606800)
Plugging in the value of y from earlier gives us:
x = (2054200(4100x + 14300z - 1227400) / 21500 + 2054200 ± √[(2054200(4100x + 14300z - 1227400) / 21500 + 2054200)^2 - 4(606800)(1817320000(4100x + 14300z - 1227400) / 21500 + 3707618640000)]) / (2*606800)
Simplifying and solving for x gives us:
x = 10
Substituting this back into the equation x = y + z gives us:
10 = y + z
Substituting this back into the equation 1480y + 490z = 380 gives us:
1480y + 490(10 - y) = 380
Solving for y gives us:
y = 6
Substituting this back into the equation 10 = y + z gives us: 10 = 6 + z
Solving for z gives us:
z = 4
Therefore, the executive stayed in London for 10 days, in Paris for 6 days, and in Rome for 4 days.
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4(2y + 7) - (y +13) = -20
Answer:
y=-5
Step-by-step explanation:
Y= -5
Step-by-step explanation:
Diego will ship 8 boxes in a large carton that is the shape of a right rectangular prism. Each box is 13 inches by 5 inches by 6 inches.
Diego determined the volume of one box by calculating (13 + 5 + 13 + 5) x 6.
Determine whether Diego is correct or incorrect.
If Diego is correct,
show or explain how you know he is correct
Include the volume in your work or explanation
If Diego is incorrect,
Find the correct answer
Show or explain the steps you used to find the correct answer. Include the correct answer in your work or explanation.
Enter your work and explanation in the space provided.
Answer:
46
Step-by-step explanation:
13 +5 +13+5 •6 witch is 46
does the point 2,4 lie on the line y=5x-6?
Answer:
substitute value of x and y as 2 and 4
y=5x-6
4= 5*2-6
4=4 so yes
Step-by-step explanation:
The point (2, 4) lie on the line y = 5x-6
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
For example, 3x + 5 = 15.
Given that, we need to check whether the point 2,4 lie on the line y=5x-6 or not,
So, the verification of the same, we will simply put the value of x (2) in the equation and see whether we are getting 4 or not, if not then points do not lie on the line, if yes, the point lies on the line.
So, the equation is
y = 5x-6
Put x = 2,
y = 5(2) - 6
y = 10-6
y = 4
Since, we get the value of y = 4, therefore, the point lies on the line.
Hence, the point (2, 4) lie on the line y = 5x-6
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Amazon Math Flow Questions • You have 30 associates who all work an 8 hour day, 5 days a week. 2 need to be indirect-they are not on the floor producing. Your direct rate is 150 units per hour but you have two 15 minute breaks during the day. How many units can your department produce in a 40 hour week? . If you need to produce an extra 10,000 units in a given week how many extra people will it require? Question: Each sandwich takes 10 minutes to make which means in the 10 hour shift there will be a... Each sandwich takes 10 minutes to make which means in the 10 hour shift there will be a total of 60 sandwiches. The deli wants an efficient way to increase the sandwich output using the same five workers and 10 hour shift (Don't Factor Break in) to produce 75 because of the 25% increase due to the expansion of the deli. What would you do to make the the process more efficient? Where each sandwich would take 8 minutes to make instead of 10 minutes. Please answer the question throughly.
Extra people required is 50.
Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Question 1 :
Number of associates = 30
Number of direct workers = 30 - 2 = 28
You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.
Direct rate = 150 units per hour
Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week
= 37.5 hours per week
Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units
28 people produce 5625 units in a week
Let x people produce 10,000 + 5625 = 15,625 units in a week
Using proportion,
28 : 5625 = x : 15,625
28 / 5625 = x / 15,625
x = (28 × 15,625) / 5625 = 77.78 ≈ 78
Extra people required = 78 - 28 = 50
Question 2 :
Number of sandwiches made in 10 minutes = 1
Number of sandwiches made in 10 hours = 60
5 workers are there. one worker makes 60/5 = 12 sandwiches
But Deli want number of sandwiches in 10 hours = 75
One worker should make 75/5 = 15 sandwiches instead of 12.
Number of sandwiches made in 8 minutes should be 1.
So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.
Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.
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What is the value of each angle and side of the triangle
x=13, no idea what y is.
a certain car travels at a constant speed of 40 miles per hour. how far does the car travel in 45 minutes
The car travels 30 miles in 45 minutes with the speed 40 miles/hour with the constant speed.
What is speed?Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. The distance traveled by a moving object in a specific amount of time is its speed. How quickly something is moving is determined by its speed. The distance traveled by an object in a given amount of time divided by the time gives the object's average speed.
Here,
45 minutes/60 minutes= .75 hours (this gives you the amount of time in hours)
time x speed = distance
.75 hours time x 40 mph speed = 30 miles distance
With a constant speed of 40 miles per hour, the car covers 30 miles in 45 minutes.
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Do the equations ;x + 2 = 6
and ;(*+ 2) = 6 represent the same situation?
Explain.
The given equations have in one, (1/5) is the coefficient of x, in the second equation, (1/5) is the coefficient of (x + 2), while both equations equals 6. Therefore, the value of x is different in both equations which do not represent the same situation.
How the given equations be evaluated?The given equations are presented as follows;
\(\frac{1}{5} \cdot x + 2 = 6...(1)\)
\( \frac{1}{5} \cdot (x + 2) = 6...(2)\)
Solving each equation for x gives;
For equation (1), x = 5×(6 - 2) = 20
x = 20
For equation (2), we have;
x = 6 × 5 - 2 = 28
x = 28
Given that the value of x in the given equations are different, the situations are different.
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What is the cardinality of the set W = {x | x is a day of the week} ?
Answer:
7
Explanation:
The cardinality of a set is the number of elements in the set
Given the set W = {x | x is a day of the week}
The days of the week are {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
Hence the set W will be;
W = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
n(W) = 7 (since there are 7 days in a week)
Hence the cardinality of the set W is 7
tammy rents a storage shed. the storage shed is in the shape of a rectangular prism with measurements as shown. a rectangular prism has a length of 10 feet, height of 9 feet and a width of 9 feet.
To find the volume of Tammy's storage shed, which is in the shape of a rectangular prism, we need to use the formula: Volume = Length × Width × Height.
Given the dimensions of the rectangular prism storage shed are:
Length = 10 feet
Width = 9 feet
Height = 9 feet
We can calculate the volume as follows:
Step 1: Multiply the length, width, and height.
Volume = 10 × 9 × 9
Step 2: Perform the multiplication.
Volume = 810 cubic feet
So, Tammy's storage shed has a volume of 810 cubic feet.
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A watercolor painting is 22 inches long by 9 inches wide. Ramon makes a border around the watercolor painting by making a mat that adds 3 inches to each side of the length and the width. What is the area of the mat?
The area of the mat is ____ square inches.
The value of area of mat is,
A = 222 in²
Since, We get;
the area of the mat = total area added - the original area of the water color painting.
Here, We have;
length of the mat is,
L = 22 in + 3 in + 3 in because 1 in is added to each side
L = 28 in
And, width of the mat is:
w = 9 in + 3 in + 3in
w = 15 in
Area of mat is,
= (28 in x 15 in) - ( 22 in x 9 in)
= 420 - 198
= 222 in²
Thus, The value of area of mat is,
A = 222 in²
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One surface of a cut gemstone is rectangular in shape. It is 0.0002 m wide and has an area of 0.000006 m2. How long is the surface? Do your work in scientific notation.
pls help me find the answer ik in scientific notation it is 12×10^-2 but is that right??
The length of the surface in scientific form is
\(3 \times {10}^{ - 2}\)
Given that :
Width = 0.0002 m
Width = 0.0002 mArea = 0.000006 m²
Length = l
Recall :
Area of rectangle = Length × width
Length = width / Area of rectangle
Length = 0.000006 / 0.0002
Length = 0.03 m
In scientific form ; 0.03 = 3 × 0.01 = 3 × 10^-2
=
\(3 \times {10}^{ - 2} \)
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how do i graph this in the image attached?
The value of the equation is P ( 4 , 4 ) , where P is the point of intersection of the equations
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
4x - 2y = 8
Adding 2y on both sides of the equation , we get
2y + 8 = 4x
Subtracting 8 on both sides of the equation , we get
2y = 4x - 8 be equation (1)
Now , let the second equation be represented as B
Now , the value of B is
y = ( 3/2 )x - 2
On simplifying the equation , we get
2y = 3x - 4 be equation (2)
Now , subtracting equation (2) from equation (1) , we get
4x - 8 - ( 3x - 4 ) = 0
4x - 8 - 3x + 4 = 0
x - 4 = 0
Adding 4 on both sides of the equation , we get
x = 4
Substitute the value of x = 4 in equation ( 1 ) , we get
2y = 8
y = 4
So , the value of x = 4 and y = 4
The equations are plotted on the graph and the point of intersection is the solution to the equation , P ( 4 , 4 )
Hence , the equations are solved
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Do not use decimals in your answer
60+15x=8
15x=8-60
15x=-52
x=-15/52
Answer:
60 + 15x = 8
Step-by-step explanation:
3 + \(\frac{3}{4}\) x = \(\frac{2}{5}\)
Multiply through by 20 ( the LCM of 4 and 5 ) to clear the fractions
60 + 15x = 8
- If x = 12, then 2x - 5 = 19.
Converse:
Is the converse true?
Biconditional:
Answer:
yes
Step-by-step explanation:
the converse is Right
what is the decimal equivalent of 0xc9?
The decimal equivalent of 0xc9 is 201.
Hexadecimals:
Hexadecimal is a number system with a base of 16, in which we use 16 distinct symbols to represent numbers. The symbols used in hexadecimal are the digits from 0 to 9 and the letters from A to F.
Hexadecimal notations are commonly used in computer programming and digital electronics because they can represent binary data more compactly than binary notation.
Here we have
0xc9
By converting each symbol as a number we can calculate as follows
Here 0x represents hexadecimal
And the value of c is 12
0xc9 = (12 × 16¹) + (9 × 16⁰)
= 192 + 9 = 201
Therefore,
The decimal equivalent of 0xc9 is 201.
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Maureen spends four times as long riding the train each day as riding the bus. If she spends 75 minutes on the bus and the train all together, how long did she spend riding the train
Answer:
60 minutes or 1 hour
Step-by-step explanation:
Set x as the amount of time she spends riding the bus
75 = time on bus + time on train
She spends 4 times as long on the train as on the bus so the time she spends on the train is 4x
75 = x + 4x
75 = 5x
x = 15 minutes on the bus
Since she spends 4 times as long on the train, we do 4 x 15 and we get 60 minutes which is 1 hour
(a) Jeffrey and Sara were building a sand castle. They decided to make it into a cone shape. After
some time, the diameter of the sand shaped cone was 10 in and the height was 10 in. What is the
exact volume of the sand cone? (Show your work. Remember you can draw a picture to help you solve the
problem
Pls I need this answer ASAP
Answer: 83.333333\(\pi\) (or 261.79939)
How?: volume = 1/3 x \(\pi\) x height
1/2 x \(\pi\) x \(5^2\) x 10
= 83.333333\(\pi\) (or 261.79939)
The figure below is dilated by a factor of 1/3 centered at the origin. Plot the resulting image. please helllpppp
The graph at the end of the response provides the dilated figure, which has the same format as the original figure but reduced side lengths as a result of the dilation with a scale factor of less than 1.
What is dilation?To make an opening or hollow structure wider or larger than usual, such as a blood vessel or the pupil of an eye.
The process of dilation entails growing an object's size without changing its shape.
The size of the object may rise or decrease depending on the scale factor.
Using dilation maths, a square with a side of 5 units can be made wider to have a side of 15 units, yet the square retains its original shape.
So, the coordinates of each vertex of the figure are multiplied by the scale factors to create a dilatation in the image.
The vertices for the original figure that was graphed are listed as follows:
I(0,6).
H(3,6).
G(9,0).
F(-6,-9).
E(-6,-6).
The coordinates of the resulting image are presented as follows since the dilation has a scale factor of 1/3, which means that the coordinates are multiplied by 1/3:
I'(0,2).
H'(1,2).
G'(3,0).
F'(-2,-3).
E'(-2,-2).
Therefore, the graph at the end of the response provides the dilated figure, which has the same format as the original figure but reduced side lengths as a result of the dilation with a scale factor of less than 1.
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Correct question:
The figure below is dilated by a factor of centered at the origin. Plot the resulting image. -109 -11 E Click twice to plot a segment. Click a segment to delete it. 4 -5 7 F A -9 10 9 B 4 I d 3 P BI 1 9 H 3 4 6 6 M
CAN SOMEONE HELP WITH THIS FOR BRAINLIEST
Answer:
12 inches
Step-by-step explanation:
A submarine dove from the surface at a rate of 50 meters per minute. It is now at a depth of 450 meters. Write a numeric equation using negatives to show the number of minutes it took to get to the current depth.
Explanation
Step1
let
\(\begin{gathered} \text{rate}=-50\frac{mt}{\text{sec}} \\ \text{rate}=\frac{dis\tan ce}{\text{time}} \end{gathered}\)\(\begin{gathered} y_1=initial\text{ position=0} \\ y_2=\text{ final positivion=-50} \\ \text{time}=\text{ 1 minute} \end{gathered}\)Step 2
equation
\(\begin{gathered} time=\text{ }\frac{\text{distance}}{-50}\text{ Equation(1)} \\ \\ \text{replacing} \\ \text{time}=\frac{-450\text{ mt}}{-50\text{ }\frac{mt}{\min}} \\ \text{time}=9\text{ minutes} \end{gathered}\)I hope this helps you
PLSS HELP ITS THE LAST QUESTION
Answer:
ABC=CDA
and #5 is CPCTC
Step-by-step explanation:
hope this helps
What is the solution of log2x + 6^8 = 3?
Group of answer choices
x = −2
x = 2
x = −3
x = 3
The value of x in the equation \(log_{2x + 6}8=3\) gives that x = -2.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
\(log_{2x + 6}8=3\\\\applying\ the\ logarithm\ rule:\\\\(2x+6)^3=8\\\\8x^3+72x^2+216+208=0\\\\x=-2\)
The value of x in the equation \(log_{2x + 6}8=3\) gives that x = -2.
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Can anyone pls help with this question?
Simplify the following algebraic fraction.
Answer:
work is pictured and shown
when Spencer was five years old he was 38 inches tall now he is 5 feet 3 inches what is the percentage increase in spencers height
The percentage increase in Spencer's height is 65.8%.
How to calculate the percentage increase?First and foremost, it's important to kite that 1 feet = 12 inches. Therefore, 5 feet 3 inches will be:
= (5 × 12) + 3
= 60 + 3
= 63 inches
In this case, when Spencer was five years old he was 38 inches tall now he is 5 feet 3 inches.
The percentage increase will be:
= Change in height / Previous height × 100
= (63 - 38) / 38 × 100
= 25/38 × 100
= 0.658 × 100
= 65.8%
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Select the FOUR equations that are equivalent to 2(x+3)−2=16. A x+3=9x plus 3 is equal to 9 B 2x=152 x is equal to 15 C 2(x+3)=182 times open paren x plus 3 close paren is equal to 18 D (x+3)−2=8open paren x plus 3 close paren minus 2 is equal to 8 E 2x=122 x is equal to 12 F (x+3)−1=8open paren x plus 3 close paren minus 1 is equal to 8
Sparky weighs 7 times as much as solo. How much does solo weight
Answer:
Divide sparkys weight by 7 and theres your answer for solo
Step-by-step explanation: not enough info to get the number
3
厂
= 2
Estimate root
divide 3.64 x 10(3) by 3.2 x 10 (4)
Step-by-step explanation:
3.64 x 10(3) by 3.2x 10(4)
v v
3.64 x 30 by 3.2 x 40
v v
109.2 divide 128= 0.85
(hope this was what you were looking for)