78 meals are eaten in a restaurant, 58 meals are eaten in a car, 33 meals are eaten at home and the question is solved by using linear equations.
What is the linear equation?
A linear equation is an algebraic equation of the form y =mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given that the total number of meals is 169.
Assume that,
a = number of meals eaten in a restaurant
b = number of meals eaten in a car
c = number of meals eaten at home
a + b + c = 169 .....(i)
Since the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13.
Thus b + c = a + 13 .....(ii)
Again twenty more restaurant-purchased meals will be eaten in a restaurant than at home.
a = 20 + c .....(iii)
Subtract equation (ii) from (i)
a + b + c - b - c = 169 - a - 13
2a = 156
Divide both sides by 2
a = 78
Substitute a = 78 in equation (iii)
78 = 20 +c
c = 58
Putting c =58 and a =78 in equation (ii)
b + 58 = 78 + 13
b = 33
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Question:
The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 169. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.
Find the volume of the rectangular prism.
8 m
8 m
8 m
Answer:
Step-by-step explanation:
I believe that the volume of the rectangular prism is 512.
Explanation: V = whl = 8 · 8 · 8 = 512
V=Volume
W= Width
H= Height
L= Length
It is expected that 750 people will attend
the concert. In fact, 600 people attended.
600 is what percent of the expected
number?
600 is the 80% of the the expected number
Number of people that expected to attend the concert = 750 people
Number of people that attended the concert = 600 people
600 is what percent of the expected number = ( Number of people that attended the concert ÷ Number of people that expected to attend the concert ) × 100
Substitute the values in the equation
600 is what percent of the expected number = (600 / 750) × 100
Divide the terms in bracket first
= 0.8 × 100
Multiply the given terms
= 80%
Hence, 600 is the 80% of the the expected number
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A house was valued at $321,000. Over several years, the value decreased by 9%, giving the house a new value.
Answer:
The new value is $292,110
Step-by-step explanation:
321,000 - (1 - 0.09) = 292,110
When you add an integer to +3, a negative sum or postive sum is possible. Use an example to show each possibilty.
It is true that when you add an integer to +3, a negative sum or postive sum is possible. An example is 2 + 3 = 5 and -4 + 3 = -1
How to calculate the value?It should be noted that from the information,we want to prove that addition of +3 to an integer can either be negative or positive.
This will be:
= 2 + 3
= +5
In this case, it gives a positive number.
Also, -4 + 3
= -1
This gives a negative number.
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(b) A local store is keeping track of service times. The table below
shows the number of customers served and the time it took.
Number of customers 2-6-7
Time (in minutes) 8-24-28
_It does not always take the same amount of time to serve each customer.
_It appears to take the same amount of time to serve each customer
Histogram for the following intervals will be,
5-9 (4)
10-14 (3)
15-19 (5)
20-24 (3)
What are histograms?The data are numerical.When establishing whether the output of a process is distributed roughly regularly, you want to see how the data are dispersed.determining whether a method can satisfy the needs of the customerexamining the appearance of the product of a supplier's procedureDetermining whether the outputs of two or more processes are different and determining whether a process has changed from one time period to another.You want to let others know about the rapid and simple sharing of data.Acc to our question-
On your y-axis, you would draw a frequency that goes up to 5. Because the data is sequential, make sure the bars are touching (in order).Name the customers on your x-axis.Label the frequency y-axis.hence, histogram will show the values.
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System of Equations Question:
John is in charge of feeding the pigs and cows on the farm. The cow's food costs twice as much as the pig's food. There are 46 cows and 22 pigs on the farm. John has an $860 budget for food a month. How much can John spend on food for each cow per month?
The amount John will spend on food for each cow per month is approximately 15.08 dollars
How to find the how much each cow feed per month?John is in charge of feeding the pigs and cows on the farm.
The cow's food costs twice as much as the pig's food.
Let
x = cost of pigs food
y = cost cow's food
Hence,
y = 2x
There are 46 cows and 22 pigs on the farm. John has an $860 budget for food a month.
46y + 22x = 860
Therefore, let's combine the system of equation.
y = 2x
46y + 22x = 860
46(2x) + 22x = 860
92x + 22x = 860
114x = 860
x = 860 / 114
x = 7.5 dollars
y = 2(7.54) = 15.08 dollars
Therefore, the cost of food for each cow is 15.08 dollars
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find the percentage increase if a number 3/8 increase to 3/4
Answer:
37,
Step-by-step explanation:
Write an exponential function represented by the graph
y= ?
Answer:
y = 8 [tex](\frac{1}{2}) ^{x}[/tex]
Step-by-step explanation:
an exponential function can be expressed in the form
y = a [tex]b^{x}[/tex]
to find a and b use points that lie on the graph
using (0, 8 ) , then
8 = a[tex]b^{0}[/tex] [ [tex]b^{0}[/tex] = 1 ] , then a = 8
y = 8[tex]b^{x}[/tex]
using (1, 4 ) , then
4 = 8[tex]b^{1}[/tex] = 8b ( divide both sides by 8 )
[tex]\frac{4}{8}[/tex] = b , that is b = [tex]\frac{1}{2}[/tex]
y = 8 [tex](\frac{1}{2}) ^{x}[/tex] is the exponential function
A circular plot with 1000 ft diameter is watered by a spray irrigation system. To the
nearest square foot, find the area that is watered as the sprinkler rotates 90°.
The area that is watered as the sprinkler rotates 90° is 196,250.
What is the area of the circular plot?
The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = πr², where r is the circle's radius, is the formula for calculating a circle's surface area.
Here, we have
Diameter = 1000ft
Radius = 500
Then, we apply the area of a circle and get
= (90/360)× π×(500)²
= 62,500 × π
= 196,250
Hence, the area that is watered as the sprinkler rotates 90° is 196,250.
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I don’t know it and I need help. question is in picture
If its 50 degrees outside and it drops 70 degrees, how cold will it get?. (Please give steps also..)
Answer:
Step-by-step explanation:
50
Find the values of x and y.
Answer:
y=60°, x=60°
Step-by-step explanation:
X=60° Angles in a Equaliteral triangles are all 60°
Alternate angle to get the base angle close to y
Y=60° because of Isoceless angles
A couple bought a rental house for $195,000 it’s assessed value was $180,000 if the tax rate is $1.50 per $100 of assessed value what is the monthly contribution the lender will require for taxes round to the nearest cent
Step-by-step explanation:
there is no interest and such involved. it is a straight forward calculation to allow the lender to accumulate enough funds (= the ESCROW account as part of the mortgage account structure) to be able to pay the taxes once a year on behalf of the owners.
so, the tax is $1.50 for every $100 of the assessed value of the house.
how many $100 units are in that value ?
180,000 / 100 = 1,800 units.
that means the tax for that house is
1800 × 1.5 = $2,700
in order for the lender to accumulate $2,700 in the ESCROW account in a year (= 12 months), the monthly contribution has to be
2700 / 12 = $225.00
Add.
−1 4/5 + (−1/4) + (−1/5)
The required simplified value of the given expression is given as -13/20.
Given that,
An expression is given, −1 4/5 + (−1/4) + (−1/5) we have to determine the sum of the expression.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
= -1 4/5 + (-1/4) + (-1/5)
= -1/5 -1/4 -1/5
= -2/5 -1/4
= -13/20
Thus, the required simplified value of the given expression is given as -13/20.
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Evaluate y(x ÷ 2) if x is 20 and y is 10
Answer:
100
Step-by-step explanation:
x = 20
x ÷ 2
= 20 ÷ 2
= 10
y = 10
y ( x ÷ 2 )
= 10 x 10
= 100
It takes 36 pounds of seed to completely plant a 6 acre field. How many acres can be planted per pound of seed?
Answer: 6 lbs per acre
Step-by-step explanation: just divide 36 by 6 and you get 6. To check your answer multiply 6 and 6. Then you get 36 and know your answer is right.
lee has seven 5-dollar bills and 6 quarters
in his pocket. How much money would he have
left in his pocket if he buys a leather jacket
worth $35.20.
Answer:
Lee would have $1.30 left.
Step-by-step explanation:
7 x 5 = $35
6 x .25 = $1.50
Altogether, Lee has $36.50 before buying the jacket
$36.50 - 35.20 = $1.30
Samuel is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 5 points. What would be Samuel's test score (out of 100) if he got 9 questions wrong? What would be his score if he got xx questions wrong?
If Samuel answers 9 questions wrong, his score will be 55 points, and if he answers x questions wrong his score is:
f(x) = 100 - x*5
What will be Samuel's score if he got 9 questions wrong?
We know that there are 100 points available, and each question gives 5 points, then the number of questions is given by the quotient:
100/5 = 20
There are 20 questions.
So, if you answer 9 wrong, then you answer:
20 - 9 = 11 correctly
Then your score is:
11*5 = 55
Your score will be 55 points.
And again, each answer gives 5 points, so if you answer x questions wrong your score will be the linear equation:
f(x) = (20 - x)*5
f(x) = 100 - x*5
Where x is an integer between 0 and 20.
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7
7
^
Why is randomization important?
Select the statement that best answers the question.
to ensure all treatment groups receive experimental units
to ensure all treatment groups are roughly equivalent regarding the experimental units
to ensure that all treatment groups are roughly equivalent regarding the variability within the experimental units
4) Intro
English
The correct answer is Option A.
Randomization important because it is used to ensure all treatment groups receive experimental units .
What is randomization ?Randomization is mostly used in experiments to establish a cause and effect link and regulate the underlying variable. Also, the evidence is strengthened by randomizing an experiment. Good. To ensure that the outcomes are accurate, randomization is mostly used in experiments.Every experimental unit has the same chance of receiving any therapy, and treatments are distributed to them entirely at random. -A random number table, computer, program, etc. are used to perform randomization.Fixed allocation randomization and adaptive randomization are the two main categories of randomization techniques. The majority of trials employ fixed randomization, in which subjects are assigned to the intervention or comparator with a probability that remains constant over the course of the investigation.
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Answer:
the answer is c. to ensure that all treatment groups are roughly equivalent regarding the variability within the experimental units
Step-by-step explanation:
Determine the slope-intercept form of the equation of the line parallel to y = -4/3x + 11 that passes through the point (–6, 2). y = x +
The equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
According to the question,
We have the following information:
The line is parallel to y = -4/3x + 11 and passes through the point (–6, 2).
Now, we know that the following formula is used to find the equation of the line:
y-y' = m(x-x')
In this case, m is the slope of the line.
m = -4/3
We have the following values:
x' = -6 and y' = 2
Now, we have the following expression:
(y-2) = -4/3(x+6)
y-2 = -4x/3-8
Adding 2 to both sides of the equation:
y = -4x/3-8+2
y = -4x/3-6
Hence, the equation of the line in slope-intercept form is y = -4x/3-6 when the line is parallel to y = -4x/3+11.
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find the volume, of the box that is 3ft, 4ft, 6ft
Find the intercepts of the line
Answer:
x-int=-40
y-int=15
Step-by-step explanation:
we have points 0,15 and -40,0 on the line.
It is as easy as the y-int being 15 and the x-int being -40!
the y-int will always be= (0,#)
the x-int will always be (#,0)
Mia tasted ocean water and found it very salty which statement best explains the salty nature of ocean water?
I think the answer is C. Because the energy from the sun does break Down rocks and release salt
How do I solve the following equation?
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{1}{3}}x+7\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is -1/3 and that it passes through (-2 , 5.5)
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5.5})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{1}{3} \\\\\\ \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}{5.5}=\stackrel{m}{- \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -5.5= -\cfrac{1}{3} (x +2)[/tex]
[tex]y-5.5=-\cfrac{1}{3}x-\cfrac{2}{3}\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+5.5\implies y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{55}{10} \\\\\\ y=-\cfrac{1}{3}x-\cfrac{2}{3}+\cfrac{11}{2}\implies {\Large \begin{array}{llll} y=-\cfrac{1}{3}x+\cfrac{29}{6} \end{array}}[/tex]
The animals at a safari park include camels,
kangaroos and meerkats.
There are 12 more kangaroos than there are
camels.
There are 3 times as many meerkats as there
are camels.
There are the same number of kangaroos as
there are meerkats.
How many camels are there at the safari park?
Who wants brainliest? First come first serve
The time is takes an object to move a certain distance is inversely propotional to the speed that it's travelling at.
it takes a car 12 minutes to travel the length of a road if it goes at an average speed of 60mph
a) How long would it take the car to travel down the same road if it travelled at an average speed of 30mph
Answer:
Hope the picture will help you
What miles per gallon did the car get after 280 miles using 8 gallons of gas?
Answer: 35 miles
Step-by-step explanation:
First we divide 280 by 8 to get the answer per gallon. 280 / 8 = 35, therefore each gallon equals 35 miles.
What is the equation of this graphed line?
Answer:
y = 2x +2
Step-by-step explanation:
You want the equation of the line through points (-4, -6) and (2, 6).
SlopeThe slope of the line is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (6 -(-6))/(2 -(-4)) = 12/6 = 2
Point-slope equationThe point-slope equation of a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Using the point (2, 6) and the found value of slope, an equation for the line can be written:
y -6 = 2(x -2) . . . . point-slope equation for the line
Slope-intercept equationSolving this equation for y and simplifying, we get the slope-intercept equation of the line.
y = 2x -4 +6 . . . . . eliminate parentheses, add 6
y = 2x +2 . . . . . . . . simplify; slope-intercept equation
2.) lee has seven 5-dollar bills and le quarters
in his pocket. How much money would he have
left in his pocket if he buyes a leather jacket
worth $35.20.
Amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
As given in the question,
Conversion of quarter into dollars is :
1 quarter = 0.25 dollars
Amount of money with Lee in his pocket is equal to :
= ( 7 × 5) dollars + ( 6 × 0.25) dollars
= (35 +1.5) dollars
=$ 36.5
Cost of leather jacket buy by Lee = $35.20
Amount of money left in lee's pockets after purchasing jacket
= $( 36.5 - 35.20)
= $ 1.3
Therefore, amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
The complete question is :
Lee has seven 5-dollar bills and 6 quarters in his pocket. How much money would he have left in his pocket if he buys a leather jacket
worth $35.20?
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