a) If the tank is full, using mathematical operations based on the 2004 Toyota Corolla, you will run 422.4 miles before running out of gas, according to Toyota's advert.
b) Using AAA's estimate, one could drive 381.4 miles before running out of gas.
c) Based on the AAA estimate, on a single tank of gas, you can predict that you will get 40.9 miles less.
What are mathematical operations?The mathematical operations include subtraction, addition, division, and multiplication.
For our purpose, we have used the mathematical operations of multiplication and subtraction to determine the above values.
Claimed mileage per gallon, according to the Toyota advert = 32 miles
The number of gallons of gas in Toyota Corolla's full tank = 13.2 gallons.
AA fuel efficiency on 2004 Toyota Corolla = 28.9 mpg
a) Miles to run before running out of gas (Toyota advert) = 422.4 (32 x 13.2) miles
b) Miles to run before running out of gas (AAA rating) = 381.48 (28.9 x 13.2) miles
c) The difference in miles between (a) and (b) above = 40.92 (422.4 - 381.48) miles
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Which of the following proves these triangles are congruent?
A. neither
B. SAA
C. ASA
Answer:
Step-by-step explanation:
Neither, they are not congruent.
Please Help Please ASAP
The graph of the inequality y < 1 - 3x is in the attachment below.
How to Graph an Inequality?Given the inequality, y < 1 - 3x, we need to determine if the line of the inequality graph will be dashed or solid, the slope (m) of the line, and the y-intercept (b).
The slope (m) of the inequality y < 1 - 3x is -3. This means the line would be a declining line where the rise/run = -3.
The y-intercept (b) of the inequality y < 1 - 3x is 1. This means the line would intercept the y-axis at y = 1.
The boundary line of the inequality graph for y < 1 - 3x would be a dashed line because of the inequality sign "<". It also means the shaded part would be below the boundary line, because, the inequality sign, "<" means the the values are not included.
The graph that will represent the inequality given is the image attached below.
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Complete the equation
-67-?=0
Is it 67
yes or no and why?
no it is not 67 becuase if you subtract -67-67 it will equal -134
it is -67 bc -67- -67=0
Determine the range of the following graph: Please help!!!!! I need an answer asap
The range of the function shown on the graph above is: -10 ≤ y ≤ 3.
What is a range?A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values (real numbers), which are shown on the y-axis of a graph.
How to identify the range of this graph?The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown, the range of this graph in interval notation can be rewritten as follows:
Range = [-10, 3]
Range = -10 ≤ y ≤ 3.
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write 34,000 , 43,000,000 , 0.0000087 , 91,000,000 , 16.6 x 10^3 , and 0.00372 x 10^-3 in scientific notation
To write a number in scientific notation you must know:
1. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10
2. A number can be converted to scientific notation by increasing the power of 10 by one for each place the decimal point is shifted to the left.
Then so:
[tex]34000=3,4x10^3[/tex][tex]43000000=4.3x10^7[/tex][tex]0.0000087=8.7x10^{-6}[/tex][tex]91000000=9.1x10^7[/tex][tex]16.6x10^3=1.66x10^4[/tex][tex]0.00372x10^{-3}=3.72x10^{-6}[/tex]pick a game of chance using cards or dice and a certain outcome in that game, (such as a large straight in yahtzee, or a four of a kind in poker). explain how many ways the outcome could happen and the total number of different hands or rolls there are in that game, and show the probability of your chosen outcome.
Yahtzee is a game of chance like dice or poker. The numbers of ways the outcomes ( straight rolling ) is 240 .
Probability of hitting a large straight is 240 / 7776 = 1/32
Yahtzee is the one of dice game that uses five standard six-sided dice. After rolling each die, the player can decide which die to keep and which to reroll. Goals include many different types of combinations, many of which originate from poker.
The two types of combinations that players must roll are called roads: small roads and large roads. Similar to poker straights, these combinations consist of consecutive dice. A small straight uses 4 out of the 5 dice and a large straight uses all 5 dice. Since the dice rolls are random, we can use probability to analyze the likelihood of hitting large straight on a single roll. Assumes that the dice used are fair and independent of each other. Now, you need to know how many ways you can roll a big/ large straight. Here it is more difficult than calculating the sample size. Big straights are harder to roll than small straights, but it’s easier to count the number of times you’ve rolled a big straight than the number of times you’ve rolled a small straight.
Next, determine the number of ways to get a straight by rolling the given dice. To get a nice straight with dice {1, 2, 3, 4, 5}, you can arrange the dice in any order. It turns out that you just swap the five dice. There are 5! = 120 ways to do this. There are two dice combinations that form the large Straight, each with 120 ways to roll, so there are 2 x 120 = 240 ways to roll the large Straight.
Now the probability of hitting a big/ large straight can be calculated with simple division. Since there are 240 ways to get the big straight in one roll, and 7776 rolls 5 dice, the odds of getting the big straight are 240/7776, close to 1/32, and lie 3.1%.
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PLEASE HELP!! THANK YOU
is (3,1) a solution of the equation y= -x + 3
Answer:
Yes
Step-by-step explanation:
This is the correct answer good job!
3. Given the perimeter of the figure is 76 ft, Find
the dimensions of the shape.
R
(4x-5) ft
(25-x) ft
(13 + x) ft
S
T
(3x+1) ft
All the dimensions of the shape is found as 19 ft.
What is termed as the perimeter?The perimeter of any closed shape is the total length of its boundary. The total length around a shape is described as its perimeter. It is the length of any two-dimensional spatial shape's outline or boundary. Depending on the dimensions, the perimeters of irregular shapes can indeed be equal in size.For the given question, the dimensions of the shape is given as;
(4x-5) ft(25-x) ft(13 + x) ft(3x+1) ftThe perimeter of the shape = 76 ft.
The formula of the perimeter = sum of length of all sides.
Let 'P' be the perimeter.
P = (4x-5) + (25-x) + (13 + x) + (3x+1) ing
Simplifying
P = 4x - x + x + 3x - 5 + 25 + 13 + 1
76 = 7x + 34
7x = 76 - 34
7x = 42
x = 6
Thus, the dimensions of the shape is; Put x = 6
(4×6-5) ft = 19 ft(25-6) ft = 19 ft(13 + 6) ft = 19 ft(3×6+1) ft = 19 ftThus, all the dimensions of the shape is found as 19 ft.
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ind the intersection of the three sets: A = {–4, 3, 10}, B = {3, 6, 10, 15}, C = {–4, 10, 20}.
{–4, 10}
{–4, 3, 6, 10, 15, 20}
{10}
{–4, 3, 10}
The intersection of the A, B and C sets is { 10}
Which of the following numbers is NOT equivalent to 40%? A 0.04 B 0.40 c.? D *I • 10
The option that is not equivalent to the given percentage of 40% is; A:0.04.
What is the correct percentage?
We are given the percentage as 40%.
Now, this percentage can be rewritten as a proper fraction as;
40% = 40/100
In decimal form, this is expressed as 0.40
Now, the proper fraction 40/100 can be broken down into;
40/100 = 4/10
Further more when we divide both numerator and denominator by 2, we will get the fraction 2/5.
Thus, the only option that is not equivalent to the given percentage is option A which is 0.04.
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The correct options are;
A) 0.04
B) 0.40
C) 2/5
D) 4/10
the tuition at a certain college was $29,694 last year and increased 5.6% from last year to the current year. how much is this year's tuition?
the tuition at a certain college was $29,694 last year
Intial Tution fees of college = $29,694
increased 5.6% from last year to the current year
i.e. Increased fees amonut = 5.6% of intial fees
So, tution of college at present year is : Intial Tution fees of college+ 5.6% of intial fees
[tex]\begin{gathered} \text{Tution f}ees\text{ of college at present year = 29694+5.6\% of 29694} \\ \text{Tution f}ees\text{ of college at present year }=29694+\frac{5.6\times29694}{100} \\ \text{Tution f}ees\text{ of college at present year }=29694+1662.864 \\ \text{Tution f}ees\text{ of college at present year }=31356.864 \end{gathered}[/tex]So, This year tution fees is $31356.864
In the nearest dollars it will be: $31357
flagpole of height 5 meters is tied to the ground by a 7 meter cable. How far from the base of the flagpole is the cable tied
We know that
• The height is 5 meters.
,• The cable is 7 meters long.
Using the given information, we can represent the situation with a diagram.
In the diagram above you can observe that the x is a leg of the right triangle. So, we have to use Pythagorean's Theorem to find x.
[tex]7^2=5^2+x^2[/tex]Then, we solve for x.
[tex]\begin{gathered} 49=25+x^2 \\ x^2=49-25 \\ x^2=24 \\ x=\sqrt[]{24} \\ x\approx4.9 \end{gathered}[/tex]Hence, the base of the flagpole is 4.9 meters from the cable, approximately.(30 points) need answer asap
Answer:
x=38
Step-by-step explanation:
The are supplementary. This is because the 2 lines are parallel and the corresponding angle to 2x-15 is supplementary. And because corresponding angles are congruent 2x-15 and 3x+5 are supplementary.
2x-15+3x+5=180
5x-10=180
5x=190
x=38
One person paints 1/4, one 1/3 and one 1/5. When they’re done 15m is unpainted, what is the total length?
Show your calculation
The total length of the wall that the individuals have to paint is 69 3/13 m.
What is the total length?The first step is to add the fractions of the wall painted by the three people together. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
Sum of the fractions:
[tex]\frac{1}{4} + \frac{1}{3} + \frac{1}{5}[/tex]
[tex]\frac{15 + 20 + 12}{60}[/tex] = [tex]\frac{47}{60}[/tex]
The fraction of the wall that has not been painted = 1 - [tex]\frac{47}{60}[/tex] = [tex]\frac{13}{60}[/tex]
13/60 of the wall = 15m
13/60 x w = 15
w = 15 ÷ 13/60
w = 15 x 60 /13 = 69 3/13 m
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Pls help asap I’ll give brainliest
Firstly multiplication operation will be performed and the value on simplification will be -7.
The expression will be solved based on the sequence in order of operations. In the mentioned expression, parenthesis and exponents are not there. Thus, firstly we will multiply the values followed by division. Then we will perform addition and subtraction (PEMDAS).
Performing multiplication first -
Value = 27 ÷ 27 - 8
Performing division at second step -
Value = 1 - 8
We are left with subtraction, so performing it -
Value = -7
Therefore, firstly multiplication will be performed and the value is -7.
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Please help ASAP, will mark brainliest!
Type SSS, SAS, ASA, AAS, or HL to justify why triangle ABC is congruent to triangle FBD.
Answer:
ASA
Step-by-step explanation:
Answer:
ASA
Step-by-step explanation:
1. Few months ago, Frank purchase stock for
$6, 150. Last week he sold the stock for. $8,250.
what was his gross capital gain?
Frank's gross capital gain was $2,100.
What is gross capital gain?
the discrepancy between the overall cost base of your asset and your capital gains. Your share of the capital gain - If more than one person owns this asset, your share of the gain is equal to the percentage of the asset that you personally hold.
You want the gross capital gain resulting from selling a stock purchased for $6,150 and sold for $8,250.
Capital Gain
The capital gain resulting from the sale is the difference between the selling price and the purchase price:
gain = selling price - purchase price
gain = $8,250 -6,150
gain = $2,100
Frank's gross capital gain was $2,100.
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1. PET CARE You buy a 6.3-pound bag of dry cat food
for your cat. The function c = 6.3-0.25p represents
the amount of cat food c remaining in the bag when
the cat is fed the same amount each day for p days.
Find the zero of this function. Describe what this
value means in this context.
The zero of the function is 25.6 and it means that the total number of days is 25.6
How to find and interpret the zero of the function?From the question, the equation of the function is given as
c = 6.4 - 0.25p
The zero of this function is when the function equals 0
This is represented as
c = 0
Substitute c = 0 in c = 6.4 - 0.25p
So, we have
6.4 - 0.25p = 0
The above equation becomes
0.25p = 6.4
Divide both sides by 0.25
p = 25.6
So, the zero is 25.6 and it represents that the total number of days
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How much simple interest does $2,560 earn in 17 months at a rate of 1*1/8 Round to the nearest cent.
The simple interest of the $2,560 earned in 17 months at a rate of 1*1/8 will be; $185.90
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of the principal amount, rate, and period.
The formula for simple interest is:
Simple Interest = (Principal × Rate × Time) / 100
Where I am interested
P ⇒ amount deposited.
R ⇒ interest rate
T ⇒ period for investing
Given that the time is 17 months = 17/12 years
1 and 1/8 = 1.125
I = 2,560 ×17/12 × 1.125/100
= 2560 × 17/12 × 0.01125
= $185.86667
The simple interest of the $2,560 earned in 17 months at a rate of 1*1/8 will be; $185.90
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If the area of a triangle is 2x^2-2x-4 and it has a height of x-2, write the base of the triangle.base of the triangle:_________________
The base of the triangle = 4(x + 1)
Explanations:The Area of a triangle is given by the formula:
[tex]\text{Area = }\frac{1}{2}\times\text{ base }\times\text{ height}[/tex][tex]\begin{gathered} \text{Area = 2x}^2-2x-4 \\ \text{Height = x -2} \end{gathered}[/tex]Substituting these expressions into the formula for the area of a triangle:
[tex]\begin{gathered} 2x^2-2x-4\text{ = }\frac{1}{2}\times\text{ b }\times(x-2) \\ 2(2x^2-2x-4)\text{ = b (x - 2)} \\ 4x^2-4x-8\text{ = b (x-2)} \\ 4x^2-8x\text{ + 4x - 8 = b (x - 2)} \\ 4x(x\text{ - 2) + }4(x\text{ - 2) = b(x-2)} \\ (4x+4)(x-2)\text{ = b(x-2)} \\ b\text{ = }\frac{(4x+4)(x-2)}{(x-2)} \\ b\text{ = 4x + 4} \end{gathered}[/tex]b = 4 (x + 1)
The base of the triangle = 4(x + 1)
I WILL GIVE BRAINLEST 1+1
it is 2 becuase 1 plus 1 is two when you have an apple and a freind gives you an apple you have 2 appelapples
Answer:
1+1=2
Step-by-step explanation:
if you have one of me then you duplicate me or make a dopleganger than you now have 2
have a great day^^
(
5
h
3
−
8
h
)
+
(
−
2
h
3
−
h
2
−
2
h
)
Answer: -3h
Step-by-step explanation:
( 5h + 3 - 8h ) + ( -2h x 3 - h x 3 - 2h )
( 15h - 8h ) + ( -6h - 2h - 2h )
15h - 8h - 6h - 2h - 2h
-3h
Kelsey starts with $150 in her account and she adds $25 a month. Kyle starts with $200 in his account and adds $20 a month to his account. Write an equation/inequality to show when Kelsey will have more money than Kyle.
Let x represents the number of months it will take Kelsey to have more money than Kyle.
Given that Kelsey starts with $150 in her account and she adds $25 a month, it means that the amount that he would have saved after x months is
150 + 25 *x
= 150 + 25x
Given that Kyle starts with $200 in his account and adds $20 a month to his account, it means that the amount that he would have saved after x months is
200 + 20 *x
= 200 + 20x
For Kelsey to have more money than Kyle, the inequality would be
150 + 25x > 200 + 20x
25x - 20x > 200 - 150
5x > 50
a pyramid has an isosceles , triangle base with sides 25,25 and 48 units . the height of the pyramid is 30 units . calculate The volume of the pyramid
A pyramid has an isosceles triangle base with sides of 25,25 and 48 units.
The height of the pyramid is 30 units. The volume of the pyramid is 13What is the volume?We have a pyramid with four sides and a square base. Two-thirds of the pyramid's sides make up its height. The volume of a pyramid is 1, and we need to determine which of them matches our volume. Third, multiplying the length by the width gives us our base's area, which is s times s, or s square.This tells us that our base's height is equal to two-thirds of its side because it is a square base.
That makes it 2 to times s, or 2 s over 3. So we incorporate that into our equations next. We have a volume that is equal to 1/s squared / 2 / s spanning 3 points.Therefore, a pyramid has an isosceles triangle base with sides of 25,25, and 48 units.
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What is the
domain?
Ahh someone give me the answer plsss
Answer:
0≤x≤|R
Step-by-step explanation:
I'm not really sure but I think the domain is all positive real numbers including zero
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)
= 6; = 2
P(5 ≤ x ≤ 9) =
The probability P(5 ≤ x ≤ 9) is 0.6847
Assume that x has a normal distribution
We have been the mean and standard deviation μ = 6; σ = 2.
To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.
z = (5 - 6)/2
= -0.5
and z = (9 - 6)/2
= 1.5
Then the probability is calculated as:
P(x ≤ 5) = 0.3085
P(x ≤ 9) = 0.9932
P(5 ≤ x ≤ 9) = 0.9932 - 0.3085
P(5 ≤ x ≤ 9) = 0.6847
Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847
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the volumes of soda in quart soda bottles can be described by a normal distribution with a mean of 32.3 ounces and a standard deviation of 8.8 ounces. (a) what proportion of bottles will have a volume more than 32 ounces? 0.5136 correct: your answer is correct. (4 decimal places) (b) what is the 85th percentile for this distribution? 23.18 incorrect: your answer is incorrect. (2 decimal places)
a)The percentage of bottles expected to have a volume more than 32 oz is 33.60%
b) 85% of 0.3360 is 0.2856
a) The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz
b=8.8 oz
Let S be the volume of randomly selected soda bottles
Y-score: S-a/b
For S=32 oz
Substitute the values of S,a and b into the equation
Y=32-32.3/8.8
Y= - 0.0341
Probability of bottles that have a volume more than 32 oz is
P(S>32)=P(Y>-0.0341)= 0.3360
Percentage of bottles that have volume more than 32 oz will be
0.3360×100%=33.60%
b) 85% of 0.3360 is 0.2856
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give an example of a rational function that has a horizontal asymptote at y=3
An example of a rational function is y = (3x²+7x+4)/(x²+3x+2) which has a horizontal asymptote at y = 3.
To give it a horizontal asymptote of y = 3, we require the degrees in the numerator and denominator to be and the lead coefficient ratio to be 1.
Yet, in producing the hole, we need to have the rest of the function, disregarding the (x + 1)'s, = 1 when x = -1 to ensure the y-value of the hole is at + 1. When we add all of this together, we get.
y = (3(x+1)(x+k))/((x+1)(x+2)) and the last condition requires k = + 4/3, so
By distributing the 3 in the numerator to the 2nd linear component, we get.
y = (3(x+1)(x+4/3))/((x+1)(x+2))
y = ((x+1)(3x+4))/((x+1)(x+2))
y = (3x²+7x+4)/(x²+3x+2)
Thus, the example of a rational function is y = (3x²+7x+4)/(x²+3x+2) which has a horizontal asymptote at y = 3.
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if the total value of the coins is $5.50 and kayleigh has 17 quarters, how many nickels does she have?
Kayleigh have 25 nickels with her.
Given,
The total value of coins Kayleigh have = $5.50
Number of quarters with Kayleigh = 17 quarters
We have to find the number of nickels Kayleigh with her.
Lets see:
1 dollar = 4 quarters
1 dollar = 20 nickels
Here, we have a total of 5.50 dollar
In this, 17 quarters are there.
So,
17 / 4 = 4.25
That is, the value of coins as quarters is $4.25
Now,
5.50 - 4.25 = 1.25
That is,
$1.25 is in the form of nickels.
Number of nickels = 1.25 × 20
Number of nickels = 25
Therefore,
Kayleigh have 25 nickels with her.
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Let f(x)=2x²+x-11 and g(x)=x-1. Perform the function operation and then find the domain.
(f+g)(x)
(f+g)(x) = (Simplify your answer.)
Answers:
[tex](f+g)(\text{x}) = \boldsymbol{2\text{x}^2+2\text{x}-12}[/tex]
Domain = set of all real numbers
========================================================
Work Shown:
[tex](f+g)(\text{x}) = f(\text{x})+g(\text{x})\\\\(f+g)(\text{x}) = (2\text{x}^2+\text{x}-11)+(\text{x}-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+\text{x}-11+\text{x}-1\\\\(f+g)(\text{x}) = 2\text{x}^2+(\text{x}+\text{x})+(-11-1)\\\\(f+g)(\text{x}) = 2\text{x}^2+2\text{x}-12\\\\[/tex]
The domain of each f(x) and g(x) is "set of all real numbers" since we can replace x with any real number to get some output.
By extension, this means the domain of (f+g)(x) is also "set of all real numbers".
It turns out any polynomial will have this domain. We don't have to worry about things like applying square roots to negatives, or dividing by zero. This is why there isn't a restriction on x.
To write "set of all real numbers" in interval notation, we would say [tex](-\infty, \infty)[/tex] to indicate x is anything between negative infinity and positive infinity.