Answer:
In the first 3.5 hours, the family travelled 175 miles.
Step-by-step explanation:
We have the table:
time (hours) distance ( miles)
0 0
1 50
2 100
3 150
4 200
5 250
6 300
7 350
8 400
9 450
This seems like a linear relationship, let's write the general line:
y = a*x + b
That represents this situation, y is the distance in miles and x is the time in hours.
In the line equation, a represents the slope and b the y-intercept.
And if the line passes through the points (x₁, y₁) and (x₂, y₂), then the slope of the line is:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we have a lot of points for the line, we can use any pair we want (we actually should use a few different pairs to see that the slope is always the same)
So if we use the first two (0, 0) and (1, 50)
the slope is:
a = (50 - 0)/(1 - 0) = 50
Now, if we use the third and fifth points (4, 200) and (5, 250) now the slope is:
a = (250 - 200)/(5 - 4) = 50/1 = 50
So we can conclude that the slope of the equation is a = 50
Then the equation is something like:
y = 50*x + b
To find the value of b, we can use any of the points of the line, for example (0, 0)
This means that when x = 0, y also must be 0, then:
0 = 50*0 + b
0 = b
Then the equation is:
y = 50*x
Now, to answer how many miles the family travelled in the first 3.5 hours, we just need to replace x by 3.5 in the equation:
y = 50*3.5 = 175
In the first 3.5 hours, the family travelled 175 miles.
simplify 5t + 8t - 12t (with explaining the steps)
Answer:
Hello There!!
Step-by-step explanation:
Combine like terms:
•5t+8t-12t
•5t+8t=13t
•13t-12t=1t
•1t=t
hope this helps,have a great day!!
~Pinky~
Answer:
T
Step-by-step explanation:
See the steps below:)
What is the approximate area of a circle with a diameter of 10 in?
A. 314 in2
B. 78.5 in2
C. 31.4 in2
D. 15.7 in2
Answer:
Hello! answer: 78.5 in2
Step-by-step explanation:
IMPORTANT ATTENTION: Im using 3.14 for pi so answers might vary if you are using say 22/7 for pi so please know that since this problem doesn't tell to use a certain method I will use 3.14
area can be found by doing radius × radius × 3.14 so... diameter is just twice the radius so... 10 ÷ 2 = 5 5 × 5 = 25
25 × 3.14 = 78.5 therefore 78.5 is the answer HOPE THAT HELPS!
The approximate area of a circle with a diameter of 10 in is,
⇒ Area of circle = 78.5 in²
Given that;
Diameter of circle = 10 in.
Now, We know that;
⇒ Area of circle = πr²
Where, 'r' is radius of circle.
Here, Diameter of circle = 10 in.
Hence, Radius = 10 / 2 = 5 in
Thus, We get;
⇒ Area of circle = πr²
⇒ Area of circle = 3.14 x (5)²
⇒ Area of circle = 78.5 in²
Thus, The approximate area of a circle with a diameter of 10 in is,
⇒ Area of circle = 78.5 in²
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What is the 46th term of the arithmetic sequence shown below? -1,-5,-9,-13,-17,-21,...
Answer:
-181
Step-by-step explanation:
According to the arithmetic calculator, it should be this.
a person jogs 1/6 mile in 1/42 hour. what is the person's speed in miles per hour
PLEASE HELP ME!! I APPRECIATE IT
Answer:
C
Step-by-step explanation:
Find the roots of the Equation 16+x^2=0
Answer:
x = 0 or x = - 16
Step-by-step explanation:
16+x^2=0
x ( x + 16 ) = 0
using the algebra rule a . b = a = 0 and b = 0
x = 0 or x = - 16
so the answer is x = 0 and x = -1 6
Mark brainliest plsssssssssss
(NR) Natural Resources:Question 10
Which statement best describes why large aquifers of groundwater are distributed unevenly
around the earth?
Answer: D) Groundwater collects only where the soil and geological features allow water to seep down into underground chambers.
In other words, as long as there are gaps to allow water through, then that would lead to underground aquifers. Another important component is the amount of rain water that happens. Sources such as rivers, lakes and streams are also a contributing factor.
Stuff like earthquakes, volcanic activity, and continental movement doesn't really have much an effect on where or how aquifers form. It's really all about the soil type and how the landscape is formed, and of course the other factors mentioned in the previous paragraph.
graph (-5,0) (9,0) (8,-39)
Answer:
just plot the coordinates down on graph and then u'll have them graphed
Step-by-step explanation:
I don't know I'm too lazy 2 put an explanation
Find the value of y when x=3.
y=10-3x
y=
Answer:
10
Step-by-step explanation:
A shopkeeper earns a profit of Rs. 1 by selling a pencil and a loss of 20 paisa by selling an eraser. In a given day he had a loss of Rs. 10. On this day, he sold 35 pencils. How many erasers were sold on this day
Given :
A shopkeeper earns a profit of Rs. 1 by selling a pencil and a loss of 20 paisa by selling an eraser.
To Find :
In a given day he had a loss of Rs. 10. On this day, he sold 35 pencils. How many erasers were sold on this day.
Solution :
Money earned by selling 35 pencils.
P = 35 × 1 = Rs 35 .
Now, it is given that he had a loss of Rs 10 .
Therefore, amount of loss done by money is :
E = 35 + 10
E = Rs 45
Now, number of erase sold :
[tex]n = \dfrac{E}{0.2}\\\\n = \dfrac{45}{0.2}\\\\n = 225\ erasers[/tex]
Hence, this is the required solution.
out of 2 billion person trips, 75 percent were leisure travel. what was the number of person trips for leisure travel?
The number of personal trips for leisure travel will be equal to 1.5 billion.
What is the percentage?The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that out of 2 billion person trips, 75 per cent were leisure travel.
The number of the person trips will be calculated as,
N = ( 2 x 75 ) / 100
N = 150 / 100
N = 1.5 Billion
Therefore, the number of personal trips for leisure travel will be equal to 1.5 billion.
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For a going-out-of-business sale, a jewelry shop owner
marks all of the store's merchandise 50% off. The price
tag on a necklace indicates that it is an additional 20%
off the sale price. If the original price of the necklace was
$600, what will it cost after the discounts?
Answer:420
Step-by-step explanation:
600 x 0.70 is 420. so 600 minus 420 is 180
HELPPPPPPPPPPPPPPPPPPP I’LL MARK YOU BRAINLIST SHOW WORK
Answer:
(-1,-1)
Step-by-step explanation:
From the diagram you can see that the two equation crossed each other at this point
A game company gave each customer one game to test and asked whether he or she would recommend the game. What is the probability that a customer who would recommend his or her game tested Game A?
Answer:
1/2 = 0.5
Step-by-step explanation:
Given that the game company gave each customer a single game for testing
There is definitely just two outcomes, i.e. the customer will either recommend the game or Not recommend the game.
since we do not have additional information regarding what might influence the decision of the customer, hence the probability of either recommending the tested game or not recommending the game will be equal
∴P ( recommending tested game ) = 1 - 0.5 = 0.5
Please help out I can’t really love this
========================================================
Explanation:
When we divide two fractions like this, we flip the second fraction and multiply like so...
[tex]\frac{5}{7} \div \frac{8}{9}\\\\\frac{5}{7} \times \frac{9}{8}\\\\\frac{5 \times 9}{7 \times 8}\\\\\frac{45}{56}\\\\[/tex]
which points us to choice B as the answer.
The fraction 45/56 cannot be reduced further because 45 and 56 do not have any factors in common other than 1.
Answer:
45/56
Step-by-step explanation:
5/7 ÷ 8/9
Copy dot flip
5/7 * 9/8
5*9 =45
7*8 = 56
45/56
The perimeter of a regular pentagon is 60 meters. How long is each side of the
pentagon?
Answer and Step-by-step explanation:
To find out how long each side is, divide 60 by 5 (since there are 5 sides in a pentagon).
60 divided by 5 = 12.
Each side is 12 meters long.
#teamtrees #PAW (Plant And Water)
Amy is packing up 434 books to ship a customer. She can fit 8 books in each box. How manky boxes will Amy need to use to ship the the entire order
Answer:
55
Step-by-step explanation:
the real answer would be 54.25 but you have to round
Step-by-step explanation:
434/8= 54.25
We can't have a decimal of a box, so,
55 boxes
The diagonal of a rectangle is 25 in. The width is 15 in. What is the area of the rectangle
Match each series with the equivalent series written in sigma notation
Answer:
[tex]3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n[/tex]
[tex]4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n[/tex]
[tex]2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n[/tex]
[tex]3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n[/tex]
Step-by-step explanation:
Given
See attachment for complete question
Required
Match equivalent expressions
Solving (a):
[tex]3 + 12 + 48 + 192 + 768[/tex]
The expression can be written as:
[tex]3 \to 3*4^{0[/tex] --- 0
[tex]12 \to 3 * 4^{1[/tex] ---- 1
[tex]48 \to 3 * 4^{2[/tex] --- 2
[tex]192 \to 3 * 4^{3[/tex] ---- 3
[tex]768 \to 3 * 4^{4[/tex] ---- 4
For the nth term, the expression is:
[tex]Term = 3 * 4^{n[/tex] ---- n
So, the summation is:
[tex]3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n[/tex]
Solving (b):
[tex]4 + 32 + 256 + 2048 + 16384[/tex]
The expression can be written as:
[tex]4 \to 4 * 8^0[/tex] --- 0
[tex]32 \to 4 * 8^1[/tex] ---- 1
[tex]256 \to 4 * 8^2[/tex] --- 2
[tex]2048 \to 4 * 8^3[/tex] ---- 3
[tex]16384 \to 4 * 8^4[/tex] ---- 4
For the nth term, the expression is:
[tex]Term \to 4 * 8^n[/tex] ---- n
So, the summation is:
[tex]4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n[/tex]
Solving (c):
[tex]2 + 6 + 18 + 54 + 162[/tex]
The expression can be written as:
[tex]2 \to 2 * 3^0[/tex] --- 0
[tex]6 \to 2 * 3^1[/tex] ---- 1
[tex]18 \to 2 * 3^2[/tex] --- 2
[tex]54 \to 2 * 3^3[/tex] ---- 3
[tex]162 \to 2 * 3^4[/tex] ---- 4
For the nth term, the expression is:
[tex]Term \to 2 * 3^n[/tex] ---- n
So, the summation is:
[tex]2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n[/tex]
Solving (d):
[tex]3 + 15 + 75 + 375 + 1875[/tex]
The expression can be written as:
[tex]3 \to 3 * 5^0[/tex] --- 0
[tex]15 \to 3 * 5^1[/tex] ---- 1
[tex]75 \to 3 * 5^2[/tex] --- 2
[tex]375 \to 3 * 5^3[/tex] ---- 3
[tex]1875 \to 3 * 5^4[/tex] ---- 4
For the nth term, the expression is:
[tex]Term \to 3 * 5^n[/tex] ---- n
So, the summation is:
[tex]3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n[/tex]
If you live in a rectangular city that is 1 mile along the southern border and contains 1000 people, what is the density of people in the city?
Group of answer choices
A. We cannot calculate this value.
B. 1000 people per square mile
C. 1 person per square mile
D. 100 people per square mile
Answer:
A. We cannot calculate this value.
Step-by-step explanation:
Had it on my test c:
We cannot calculate this value because the width is not given so we cannot find the area of the region option (A) is correct.
What is population density?It is defined as the ratio of the population to the total area. The population density represents the average number of people living on each square unit.
We have:
If you live in a rectangular city that is 1 mile along the southern border and contains 1000 people,
As we know,
population density = number of people/area of the region
As we have a rectangular city,
The area of the city = length×width
Width is not given so we cannot find the area of the region.
Thus, we cannot calculate this value because the width is not given so we cannot find the area of the region option (A) is correct.
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Which question is a statistical question? A Which U.S. States have mountains?Which U.S. States have mountains? B Which mountain range do U.S. Citizens most enjoy visiting?Which mountain range do U.S. Citizens most enjoy visiting? C How many mountain ranges are in the U.S.?How many mountain ranges are in the U.S.? D How tall is the tallest mountain in the U.S.?
Answer: C. How many mountain ranges are in the U.S.
Step-by-step explanation:
A statistical question first of all has to have a quantitative response i.e., answers should be in numbers.
The only two questions here that would yield a numeric answer are options C and D.
Furthermore, a statistical question has variability in it which means that the answer is based on multiple observations not just one. The observations in option C are mountain ranges and as the question requires finding out details about multiple mountain ranges, this is a statistical question.
This is opposed to option D which addresses issues surrounding just one mountain.
Austin’s monthly gross pay is $4,200. Federal withholding is 16.05% of his pay. His other deductions total $321.30. What is his net pay.
Answer:
[tex]gross \ pay = 4200\\\\federal \ deduction = \frac{16.05}{100} \times 4200 = 674.10\\\\Net \ pay = 4200 - 674.10 -321.30= 3204.60[/tex]
if x+y=12 and xy=27 . find x^3+y^3
pls help with steps
Answer:
Step-by-step explanation:
use formula
x^3+y^3=(x+y)^3-3*x*y(x+y)
=12^3-3*27(12)
=1728-972
=756
Answer:
x^3 + y^3 = 756
Step-by-step explanation:
Given that, x+y=12 and xy=27
We know that,
[tex]( x + y )^3 = x^3 + y^3 + 3xy(x + y)[/tex]
∴ [tex]12^3 = x^3 + y^3 + 3 * 27 * 12[/tex]
[tex]=> 1728 = x^3 + y^3 + 972[/tex]
[tex]x^3 + y^3 = 1728 - 972[/tex]
[tex]==> x^3 + y^3 = 756[/tex]
Amelia needs to buy some dog food. At the nearest store, 2 bags of dog food cost $7.50. How much would Amelia spend on 5 bags of dog food?
Answer: $18.75
Step-by-step explanation: Each bag cost $3.75 individually.
Find the surface area. 10 ft 3 ft 5ft
Answer:
5.7 feet i think
Step-by-step explanation:
can I have help, please
A line, line segment, or ray that intersects a line segment at its midpoint is a segment bisector. True or fals?
Answer:
true.
Step-by-step explanation:
hope this helps, i looked it up :)
Determine whether each expression is equivalent to 10^t^2+2t-3
All answer choices are equivalent
All the expressions given in option is equivalent to the expression
([tex]10^{t^{2}+2t-3 }[/tex])
What is an expression?An expression in maths, a sentence with a minimum of two numbers or variables and at least one maths operation. This maths operation can be addition, subtraction, multiplication, or division.
Given is an expression, ([tex]10^{t^{2}+2t-3 }[/tex])
We know, when equal base get multiplied with different powers, the power get added and in case of division they get subtracted,
([tex]10^{t^{2}+2t-3 }[/tex]) = [tex]10^{t^{2} }[/tex]x[tex]10^{2t}[/tex]x[tex]10^{-3}[/tex]
[tex]10^{t^{2} }[/tex]x[tex]10^{2t}[/tex]x[tex]10^{-3}[/tex] = [tex]\frac{10^{t^{2} +2t } }{1000}[/tex]
When we factorize, t²+2t-3, we get,
t²+2t-3 = (t+3)(t-1)
Therefore, ([tex]10^{t^{2}+2t-3 }[/tex]) = [tex]10^{t^{2} }[/tex]x[tex]10^{2t}[/tex]x[tex]10^{-3}[/tex] = [tex]\frac{10^{t^{2} +2t } }{1000}[/tex] = [tex]10^{(t+3)(t-1)}[/tex]
Hence, we can say that, All the expressions given in option is equivalent to the expression ([tex]10^{t^{2}+2t-3 }[/tex])
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If Uber charges a $4.15 pickup fee plus $1.12 per mile, which equation can be used to calculate the cost of a ride of
x
x miles?
Answer:
4.15+1.12x
Step-by-step explanation:
So lets go over what we know.
The cost of a pickup is 4.15 dollars.
The cost of the pickup fee increases by 1.12 dollars per mile.
So when we start off, it will orginate as 4.15 dollars.
We know that this price is going to be increased by the other value, so we can write it as:
4.15+
We know that for each mile, this price goes up by 1.12.
If we went 10 miles, for instance, it would be 1.12 10 times, or 11.2 dollars.
So we know that thr 4.15 will be increased by 1.12 times the amount of miles.
Or:
4.15+1.12*m
=
4.15+1.12m.
Hope this helps!
What number makes the expressions equivalent?
12(−1.4+0.4)=?+0.2
1
2
(
-
1
.
4
m
+
0
.
4
)
=
?
m
+
0
.
2
–1.4
1.4
–0.7
0.7
Answer:
-11,8 or 11,8........both are correct