By using the concept of linear equations, amount of driving when two of these plans cost the same will be at x = 100.
The cost when two plans cost the same is $67.
What is Linear Equation in one variable?The linear equation in one variable is written as ax + b = 0, where a and b are two integers and x is a variable. This equation has only one solution.
Given data:
First plan has it in initial fee of $55 and cost an additional $0.12 per mile.
Second plan has an initial fee of $50 in cost an additional $0.17 per mile.
Linear Equation for first plan: f(x) = 55+0.12x
Linear Equation for second plan: s(x) = 50+0.17x
Here, x is a variable.
To find out the distance when the two plans cost the same, we'll need to solve:
55 + 0.12x = 50 + 0.17x
55 - 50 = 0.17x- 0.12x
5 = 0.05x
x = 5/0.05
x = 100
The cost when the two plans cost the same :
f(100) = 55 + 0.12(100)
f(100) = $67
s(100) = 50 + 0.17(100)
s(100) = $67
Hence, two of the plans will cost the same at x=100 and cost will be $67.
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two cards are dealt at random from a standard deck of $52$ cards ($13$ hearts, $13$ clubs, $13$ spades, and $13$ diamonds). what is the probability that the first card is a $6$ and the second card is a queen?
The probability of getting a number 6 as the first card and a queen as the second card is 4/663.
Probability is mathematically defined as the ratio of the number of outcomes of a particular event or occurrence to the total number of outcomes.
For a standard deck, there are 52 total outcomes since there are 52 cards. A standard deck is divided into four suits - hearts, clubs, spades, and diamonds - with 13 cards each. Each suit has nine numbered cards from 2 to 10, three face cards (king, queen, and jack), and an ace.
The probability of having a numbered 6 card is 4/52. The probability is the same for getting a queen. Although, the probability of getting 6 as the first card and the queen as the second is different. This kind of probability requires the multiplication rule.
First card probability = 4/52
Second card probability = 4/51
The total number of outcomes for the second card is reduced since the first card is not replaced.
Probability (6 then queen) = (4/52)(4/51)
Probability (6 then queen) = 4/663
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The perimeter is 26. How much bigger is the longest side than the shortest side?
Answer:
8
Step-by-step explanation:
the perimeter is the sum of the 3 sides of the triangle.
Given perimeter = 26 , then
2a - 3 + 2a + 3a + 1 = 26 , that is
7a - 2 = 26 ( add 2 to both sides )
7a = 28 ( divide both sides by 7 )
a = 4
then
shortest side = 2a - 3 = 2(4) - 3 = 8 - 3 = 5
longest side = 3a + 1 = 3(4) + 1 = 12 + 1 = 13
the difference between the 2 sides is 13 - 5 = 8
the longer side is 8 units bigger than the shortest side
alexio has $100$ cards numbered $1$-$100$, inclusive, and places them in a box. alexio then chooses a card from the box at random. what is the probability that the number on the card he chooses is a multiple of $2$, $3$ or $5$? express your answer as a common fraction.
Answer:
37/50
Step-by-step explanation:
You want the fraction of integers in the range [1, 100] that are divisible by 2, 3, or 5.
DivisibilityAttached is a Venn diagram showing how the divisibility of numbers from 1 to 100 stacks up. Circle A includes all 50 numbers divisible by 2; Circle B counts all 33 numbers divisible by 3; and Circle C counts the 20 numbers divisible by 5.
Where the circles overlap, there are counts of the numbers divisible by the relevant combination of factors. For example, there are 3 numbers divisible by 2, 3, and 5. (They are 30, 60, 90.)
ProbabilityIn all, there are 74 numbers in the range 1–100 that are divisible by 2, 3, or 5.
The probability that a card chosen at random will have a number divisible by 2, 3, or 5 is 74/100 = 37/50.
P( 2, 3, or 5 divides N) = 37/50.
__
Additional comment
Roughly, the number of numbers in range [A, B] divisible by n is (B -A)/n. This is how we arrived at the counts shown in the attachment. For example, There are 100/(2·5) = 10 numbers divisible by both 2 and 5. Of those, there are 10/3 = 3 divisible also by 3. So, the number 3 is found in the area ABC, and the number 10-3=7 is found in the area AB'C.
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a sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order. what is the 2021st term of this sequence?
The 2021st term of the sequence is (- n - 2017).
Given,
A sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order.
We need to find out what is the 2021st term of this sequence.
What is an arithmetic sequence?An arithmetic sequence is a sequence where the difference between the consecutive terms is the same.
Example: 2, 4, 6, 8, 10
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
The nth term of an arithmetic sequence is given by:
= a + ( n - 1 ) d
Where a = the first term
d = common difference
Let the sequence that contains no digit less than 3 in ascending order be:
3 - n, 3 - (n + 1), 3 - (n+2), 3 - (n+3), 3 - (n+4),......
Where n = any real number from 1.
We see that the common difference is -1.
3 - (n+1) - (3 - n)
= 3 - n - 1 - 3 + n
= -1
3 - (n+2) - [3-(n+1)]
= 3 - n - 2 - 3 + n + 1
= -1
Find the 2021st term.
We have,
a = 3 - n
d = -1
n = 2021
= a + ( n - 1 ) d
= (3 - n) + ( 2021 - 1 ) (-1)
= 3 - n - 2020
= - n - 2017
Thus the 2021st term of the sequence is - n - 2017.
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Richard, Allan, and Fliss share some money in the ratio 4: 8: 5.
Allan gets £9 more than Fliss.
Work out the amount of money that Richard gets.
Step-by-step explanation:
the ratio is 4:8:5 for Richard, Allan and Fliss.
the sequence is important.
the money pool between them has 4+8+5 = 17 equal units.
Richard has 4 units of these 17, Allan has 8 units, and Fliss has the remaining 5 units.
we don't know the value of such a unit yet.
this we get from the second hint :
Allan gets £9 more than Fliss.
remember, Allan has 8 units, Fliss 5.
so, Allan has 3 units more than Fliss.
that means these 3 units are worth £9.
and that means each unit is worth 9/3 = £3.
Richard has 4 units, that means he has
4×3 = £12
At a football game, a vender sold a combined total of 144 sodas and hot dogs. The number of sodas sold was two times the numbers of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Identify an equation in point slope form for the perpindicular to y=-3x+5 that passes through (4,-1)
Answer:
[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]
Step-by-step explanation:
If we have a line y = mx + b where m is the slope and be is the y-intercept then a line perpendicular to this line will have slope -(1/m)
So the slope of the line perpendicular to y = -3x + 5 will be [tex]-\dfrac{1}{3}[/tex] = + 1/3 = 1/3
So the perpendicular line equation is
y = (1/3)x + b where b is the y intercept of this line
Since it passes through the point x = 4, y = -1 we plug in these values for x and y and solve for b
We get
[tex]-1=\dfrac{1}{3}\cdot \:4+b[/tex]
Switch sides
[tex]\dfrac{1}{3}\cdot \:4+b=-1[/tex]
[tex]\dfrac{4}{3}+b=-1[/tex]
Subtract [tex]\dfrac{4}{3}[/tex] from both sides
[tex]b = -1 - \dfrac{4}{3} = -\dfrac{3}{3} -\dfrac{4}{3} = -\dfrac{7}{3}[/tex]
So the equation of the perpendicular line is
[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]
Monica reads 7 ½ pages of a mystery book in 5 minutes. What is her average reading rate in pages per minute?
Answer:
1.5 or 1 ½ pages per min
Step-by-step explanation:
7.5/5=1.5
She reads 1 ½ pages per min
Answer: 1.5 pages per minute
Step-by-step explanation:
Divide the total number of pages she read by 5, the amount of time it took her. So it should look like this: 7.5/5
The answer is 1.5 pages per minute.
please help with this math! giving 40 points since both are different parts of 2 different hw pieces! :)
Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. what value of p makes the equation true? p =
When p = 0.125 the equation -3p + ( 1/8 ) = ( - 1/4 ) is true.
The given equation is:
-3p + ( 1/8 ) = ( - 1/4 )
On the left-hand side of the equation, the denominator of the two terms is not the same.
So, the LCM of 1 and 8 is 8.
Therefore,
- 3p × ( 8 / 8 ) + ( 1 / 8 ) × ( 1 / 1 ) = ( - 1 /4 )
- 24p / 8 + 1 / 8 = - 1 / 4
( - 24p + 1 ) / 8 = - 1 / 4
Now multiplying each side of the equation by 8.
We get,
[ ( - 24p + 1 ) / 8 ] × 8 = ( - 1 / 4 ) × 8
- 24p + 1 = - 8 / 4
- 24p + 1 = - 2
Subtracting 1 from each side of the equation,
- 24p + 1 - 1 = - 2 - 1
-24p = - 3
Now, divide each side of the equation by 24.
- 24p / 24 = - 3 / 24
- p = ( - 1 / 8 )
Multiplying by - 1 on each side of the equation,
( - p ) × ( - 1 ) = ( - 1 / 8 ) × ( - 1 )
p = 1 / 8
p = 0.125
The value of p = 0.125 will make the equation true.
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What is the slope of the line that passes through the points (6,10) and (6,−2)? Write your answer in simplest form.
The slope of the line passes through the points (6,10) and (6,−2) is undefined.
Here,
The points are (6,10) and (6,−2).
We have to find the slope of the line passes through the points (6,10) and (6,−2).
What is slope of line?
The slope of the line passes through the points (x₁, y₁) and (x₂, y₂) is;
[tex]m = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Now,
The points are (6,10) and (6,−2).
Hence, The slope of the line passes through the points (6,10) and (6,−2) is;
[tex]m = \frac{-2 -10 }{6-6 }= \frac{-12}{0}[/tex]
Which in undefined.
Therefore, The slope of the line passes through the points (6,10) and (6,−2) is undefined.
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the slope of the line that passes through the points (6,10) and (6,−2) is undefined.
Step-by-step explanation:
Find the values of x and z (please Help)
The value of x is 6° and value of z is 67°
We know that when two lines intersect then the vertically opposite angles are equal.
So according to the given figure
(11x + 47)° = (6x + 77)°
Solving the above equation for x we get
11x° + 47° = 6x° + 77°
5x° = 30°
x = 6°
Thus the value of x is 6°
Also note that the linear pair of angles make 180°. That is sum of the two angle is 180°. As we can see from the figure ∠z and (6x + 77)° make linear pair of angles, therefore there sum will be equal to 180°.
Thus, ∠z + (6x + 77)° = 180°
∠z + (6*6 + 77)° = 180°
∠z + 113° = 180°
∠z = 67°
Hence the value of z is 67°
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It takes 15 over 2 minutes to fill an empty aquarium to a depth of 3 over 5 meters. what is the unit rate in minutes per meter? write your answer as a fraction or a mixed number in simplest form.
The unit rate in minutes per meter is 25/2
We are given the time taken to fill an empty aquarium = 15/2 minutes
Also, the depth of aquarium = 3/5 meters
To find the unit rate in minutes per meter, we will simply keep the values in formula. We do not need to change the units, as they are already in required ones, which are minutes and meters.
Unit rate = minutes ÷ meter
Unit rate = 15/2 ÷ 3/5
Rewriting the fraction
Unit rate = 15×5 ÷ 3×2
Performing multiplication in both numerator and denominator
Unit rate = 75 ÷ 6
Performing division of both numerator and denominator by 3
Unit rate = 25/2
So, the unit rate in minutes per meter is 25/2.
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someone pls solve this for me w support work
Answer:
Slope = - 3
Step-by-step explanation:
The function of the line:
y = - 3x + 7
=> Slope = - 3
Write the rational numbers rounded to three decimal palaces.
19/6=
And
7/18=
30 points mathamatics
Answer:
1870
Step-by-step explanation:
Answer:
c) 1,870
Step-by-step explanation:
374 multiplied 5 times, or 374 in a group of 5, equals 1,870.
Have a good day <333
4. A right cone has a surface area of 258 cm² and a base radius of 4 cm. What is
the height of the cone to the nearest tenth of a centimetre?
Answer:
64.5cmStep-by-step explanation:
I hope this answer help you
Answer:
h = 16.0 cm
Step-by-step explanation:
Note: I am assuming that the surface area of 258 is the total surface area which includes the Lateral Area (L) and Base Area(B)
Total Surface Area of a right cone
= Lateral Area(L) + Base Area(B)
All numbers in intermediate calculations are rounded to tenth of centimeter i.e. 1 decimal point
Base Area is the area of the circle with radius 4 = [tex]\displaystyle \pi \cdot16 = 50.3[/tex] cm²
Total Area = 258 cm²
So Lateral Area = 258 - 50.3 = 207.7 cm²
Lateral Area is given by the formula
[tex]\displaystyle L = \pi r s \textrm{ where s is the slant height }[/tex]
So we get
[tex]\displaystyle \rm pi \cdot 4 \cdot s = 207.7\\\\\textrm {This gives } s = \dfrac{207.7}{4\pi} = 16.5\\\\[/tex] cm
Slant height is given by the formula:
[tex]s = \sqrt{r^2 + h^2} \textrm{ where r is the radius and h the height}[/tex]
Plugging in values we get
[tex]16.5 = \sqrt{4^2 + h^2} = \sqrt{16 + h^2}[/tex]
Square both sides
[tex]16.5^2 = 16 + h^2[/tex]
==> [tex]h^2 = 16.5^2 - 16 = 256.25\\\\h = \sqrt{256.25} = 16.003 = 16.0[/tex] rounded to 1 decimal place
So final answers is h = 16 cm
Three squares have been used to form a right triangle. What is the area of the third square if the area of the first two squares are 8 square units and 16 square units respectively?
The area of the third square is 24 units square.
How to find the area of a square?The squares forms a right angle triangle.
The side length of a square are equal.
Therefore, the side length of each square contribute to the three sides of the right triangle formed. The unknown length of the right triangle is the hypotenuse side of the triangle. That unknown length is the side length of the square.
area of a square = l²
where
l = side lengtharea of the first square = l²
√8 = l
l = 2√2 units
area of the second square = l²
√16 = l
l = 4 units
The length of the squares are the legs and hypotenuse of the right triangle formed.
using Pythagoras theorem,
a² + b² = c²Therefore,
a = 2√2 unitsb = 4 unitsc = ?(2√2)² + 4² = c²
16 + 8 = c²
c = √24
c = 2√6 units
area of the third square = (2√6)² = 24 unit²
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if 4x + 2y = 20 what is the value of 8x+4y/5
By using algebra properties and given that the linear equation 4 · x + 2 · y = 20, the value of (8 · x + 4 · y) / 5 is equal to 8.
How to determine the value associated to a linear equation
Herein we find a linear equation equal to a given number and we are asked to find a number associated with a modified form of the formula, this can be done by using algebra properties. The complete procedure is shown below:
4 · x + 2 · y = 20 Given
2 · (4 · x + 2 · y) = 20 · 2 Compatibility with multiplication
8 · x + 4 · y = 40 Associative and distributive properties
(1 / 5) · (8 · x + 4 · y) = (1 / 5) · 40 Compatibility with multiplication
(8 · x + 4 · y) / 5 = 8 Multiplication of fractions / Result
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define the points p(−4,−2) and q(3,−4). carry out the following calculation. find two vectors parallel to qp with length 4.
The vector is -2i+7j and the two parallel vectors with length 4 is u=-8/√53i+28/√53j and u=8/√53i-28/√53j respectively
The points are p(-4,-2) and q(3,-4)
The vector qp = vector p -vector q
qp= <-4+2,3+4>
qp=-2i+7j
|QP|=√(-2)^2+(7)^2
|QP|=√4+49
|QP|=√53
The unit vector in direction of QP is 1/√53(-2i+7j)
To get a unit vector parallel in direction of QP, multiply by 4
u=-8/√53i+28/√53j
Multiplying by -4 to get another parallel vector of length 4, we get
u=8/√53i-28/√53j
The term "parallel vectors" refers to 2 vectors which can be in the identical direction, have the equal attitude, but differ in magnitude.two vectors a and b are said to be parallel vectors if one is a scalar more than one of the opposite, the vectors could be parallel.Learn more about parallel vectors at:
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18=2(4+x) ughhhh? omg
Step-by-step explanation:
linear
8+2x=18
2x=10
x=5
Please answer I need help
Answer:
What's the wildflowers trails current length so I can help
Sam is driving a distance of 140 miles from his house to visit Melissa. Sam takes city roads, on which he can travel an average of 35 mph for a total of 1.5 hours. Sam also takes the highway, on which he travels an average of 65 mph for a total of x hours. Approximately how long does Sam travel on the highway, to the nearest tenth of an hour?
The hours travelled on the highway is 1.3 hours.
What is the time travelled?The first step is to determine the distance Sam travelled on the city road. The formula that would be used is the average speed formula. The average speed is the ratio of total distance travelled and the total time travelled.
Average speed = distance /time
average speed x time = distance
Distance = 35 x 1.5 = 52.50 miles
The second step is to determine the distance travelled on the highway.
Distance travelled on the high way = 140 - 52.50 = 87.50 miles
Now, determine the total hours travelled:
Hours travelled = distance / average speed
87.50 / 65 = 1.3 hours
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Answer: Sam traveled 1.3 hours.
Step-by-step explanation:
What will be the change in the temperature after 3 days?
Answer:21/2
Step-by-step explanation:
Answer:
-7/6
Step-by-step explanation:
If the temperature changes by -7/18 degrees, that shows us that it will continue to decrease, so we can assume the answer will be negative, which means we can get rid of the answers 21/6 and 7/6. If you add and multiply -7 by 3, you'll get -21, which would be -21/18. Then you would simply the answer, giving you -7/6.
Hope this helps!!! :)
what are the terms and coeffients 3m - 2n
Answer:
your question is did you mean why 2n is 2n 2 serve that this queston with not involved
6.018 to 1 decimal place
Answer:
6.0
Step-by-step explanation:
Answer:
Step-by-step explanation:
1.00
in rhombus $abcd$, points $e,f,g,$ and $h$ are the midpoints of $\overline{ab},\overline{bc},\overline{cd},$ and $\overline{da},$ respectively. quadrilateral $efgh$ has area 14 and perimeter 16. find the side length for rhombus $abcd$.
Side length of Rhombus ABCD is 8+2√2 unit
EFGH is a rectangle :
We know that ,
E, F , G , H are midpoints of AB, BC, CD , DA respectively
Since ABCD is a rhombus
AB = BC = CD = DA
AB ll CD and BC ll DA
since, E, F , G , H are midpoints of AB, BC, CD , DA respectively
from the figure below we can say that ,
1) AB ll CD ll FH and AB= CD = FH
2) BC ll DA ll GE and BC = DA = GE
Using mid point theorem we can say that ,
GH = EF = 1/2 AC and FG= EH = 1/2 BD
Since for the figure EFGH opposite sides are equal and and parallel , and the diagonals are equal in length we can say that EFGH is a rectangle.
Perimeter of a rectangle = 2(a+b) = 2( GH + EH ) = 2 (EF + GF) = 2 ( 1/2 AC + 1/2 BD )
= 2 x 1/2 ( AC + BD ) = 16
⇒ AC + BD = 16 (1)
now area of a rectangle is given by
A = ab = GH x EH = EF x GF = 1/2 AC x 1/2 BD = 1/4 (AC x BD) = 14
⇒AC x BD = 14 x 4 = 56
from equation (1)
AC ( 16 - AC) = 56
= 16 AC - AC ^2 = 56
⇒ AC^2 - 16 AC + 56 = 0
AC = 8 +/- 2√2
BD = ( 16 - AC) = 8 +/- 2 √2 = side length of rhombus ABCD
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Is the following relation a function? x y 1 4 −1 −2 3 10 5 16 a Yes b No
The relation that is represented in the table is a function. YES.
How to Determine a Relation that is a Function?For every relation that represents a function, the each of the x-value (domain element/input) corresponds to exactly one y-value (range element/output).
In the table given showing a relation, every single x-value (input) has exactly only one possible y-value (output) that it is assigned to. The x-values, 1, -1, 3, and 5, each have a specific y-value they each correspond to.
Thus, based on the definition of a function, the relation that is represented in the table is a function. YES.
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Slopes of perpendicular lines are equal. true or false
False, parallel lines have not the same slope whereas perpendicular lines have because of this. Perpendicular lines have equal slopes.
What is a slope in mathematics?The steepness and direction of a line, read from left to right, is referred to as its slope. Finding the ratio of will allow you to determine the slope or gradient. Between two places on the line, either by using the rise (vertical change) to the run (horizontal change). a slope-intercept version of a linear equation (y = mx + b).
based on the facts provided;
Two parallel lines' slopes are always their negative reciprocal of one another. The other has a slope of -3/2 if one has a slope of 2/3.
Therefore, perpendicular lines do not have equal slopes.
The sentence is
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Order the following numbers from least to greatest. Put the least number on the left. -0.32 -3.2 2 3|2
The numbers from least to greatest are arranged as -
-3.2, -0.32, 3/2, 2
What is ascending and descending order of arrangement of numbers?Ascending order is the arrangement of numbers from the smallest to the largest. For example, the following numbers are in ascending order: 3, 15, 28, 49. Descending order is an arrangement of numbers from the largest to the smallest. For example, the numbers 45, 32, 26, 12 are arranged in descending order.Given is the sequence of numbers as -
-0.32, - 3.2, 2, 3/2
The given sequence of numbers is -
-0.32, -3.2, 2, 3/2
The numbers from least to greatest are -
-3.2, -0.32, 3/2, 2
Therefore, the numbers from least to greatest are arranged as -
-3.2, -0.32, 3/2, 2.
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