The slope shows a change in the amount of fuel left in each mile. Since the slope is -0.04, the amount of fuel left drops by 0.04 gallons each mile
what is slope ?The slope of a line governs its steepness. Using mathematics, the gradient is expressed as "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical (rise) to the horizontal (run) change in distance between any two sites. Every time the equation for a straight line is written as y = mx + b, the slope-intercept representation of the equation is utilized. At the location of the y-intercept, the line has a slope of m, b, and c. (0, b). As an example, the y-intercept of the equation y = 3x - 7 has a value of 3. (0, 7).
given
It is evident that with each additional row, the distance is increased by one mile and the fuel level is altered.
From one row to the next in the table, the amount of fuel left changes by -0.04 gallons.
The distance in the table that changes from one row to the next is 1 mile.
The slope is the pace at which the amount of fuel left changes in relation to the change in distance.
The line that passes through the places listed in the table has a slope of -0.04 degrees.
The slope shows a change in the amount of fuel left in each mile. Since the slope is -0.04, the amount of fuel left drops by 0.04 gallons each mile.
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Identify the range of the function shown in the graph.
the range of the function shown in the graph -1 [tex]\leq[/tex] y[tex]\leq[/tex] 1.
What is the sine and cosine graph's range?All real numbers fall within the domain of the sine and cosine functions. Both the sine and cosine functions have a range of [1,1]. An angle's sine and cosine have the same absolute value as their respective reference angles.
What is a cosine graph's range?An illustration of the function's range in the graphs of cos and sine
The cosine function's graph appears as follows: The range of the function y=cos(x) is 1y1, and the domain is all real numbers (cosine is defined for any angle measure).
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Is maths hard or easy?
Maths can be hard or easy, depending on the level of difficulty and the individual's experience and understanding numbers.
Maths is a subject that can range in difficulty depending on the level of complexity and the individual's experience and knowledge. Some people may find it easy, while others may find it difficult. In the end, it all depends on the level of understanding and the amount of effort put into learning and practicing.
Maths can be hard or easy, depending on the level of difficulty and the individual's experience and understanding numbers
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Answer:
BOTH!
Step-by-step explanation:
See math can be easy or hard. It all depends on YOU. The equation itself isn't hard at all. Mybe a little more work to put in. but its your brain that tells you comething is too challenging or too hard. Now if you are a straight A students and you love math then ofcource your going to be like this is easy!
For a loan of. 8,75,000 how much interet will be charged by the bank for 2
month if the rate i 4. 75% per year?
Total interest charged by bank in 2 months is 6793.83.
What is compound interest ?Compound interest is the interest paid on both principal and interest, compounded at regular intervals. At regular intervals, the interest so far accumulated is clubbed with the existing principal amount and then the interest is calculated for the new principal. The new principal is equal to the sum of the Initial principal, and the interest accumulated so far.
The interest that is obtained through the reinvestment of money is known as compound interest. The original principal investment grows substantially more quickly (sometimes referred to as exponentially) when interest is reinvested and allowed to compound over time.
Total loan amount = 875000
total time = 2 months
Rate = 4.75%
Total interest = 875000(1 + [tex]\frac{4.75}{100}[/tex])[tex]\)^{\frac{1}{6} }[/tex] - 875000 = 6793.83
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Stefanie has 18 grams of 20% sugar syrup and john 30 of 25% what is the concentration in the new mixture
The concentration in the new mixture will be 11.1 grams.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Stefanie has 18 grams of 20% sugar syrup.
And, john has 30 grams of 25%.
Here,
Stefanie has 18 grams of 20% sugar syrup.
Hence, The amount of sugar = 18 × 0.2
= 3.6 grams
And, john has 30 grams of 25%.
Hence, The amount of sugar = 30 × 0.25
= 7.5 grams
Thus, The concentration in the new mixture = 3.6 + 7.5 grams
= 11.1 grams
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what is the answer for -40= -50 + x ?
Answer:10
Step-by-step explanation: Because negative 40 equals -50 + x equals 10
Trapezoid LMNO with bases LM and ON , and Median PQ
If PQ = t +6, LM = t +3 and ON = 3t – 7, find ON
The length of base ON of trapezoid LMNO is 17 units
We know that the median theorem of trapezoid, which states that the median of a trapezoid is parallel to each base. Also, the length of the median equals one-half the sum of the lengths of the two bases.
Consider the following diagram of trapezoid LMNO with bases LM and ON , and Median PQ.
Given that the equations for the bases and median of trapezoid LMNO .
PQ = t +6, LM = t +3 and ON = 3t – 7
From above theorem,
PQ = 1/2 (LM + ON)
t + 6 = 1/2 ( t + 3 + 3t - 7)
2(t + 6) = 4t + 3 - 7
2t + 12 = 4t - 4
4t - 2t = 12 + 4
2t = 16
t = 8 units
So, ON = 3t - 7
ON = 3(8) - 7
ON = 24 - 7
ON = 17 units
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How do you tell if a set of ordered pairs satisfies an exponential function?
The following presumption has to be verified in order to establish whether the collection of ordered pairs fulfills an exponential function: The x-coordinates must have the same increment or a consistent difference.
What is an exponential function?A mathematical function of form f (x) = aˣ is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's basis and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the foundation for exponential functions that are most frequently utilized.
Characteristics are:
The fact that a⁰ = 1 causes them all to include the point (0, 1). Always an asymptote, the x-axis. If (0 < a < 1) or (1 < a), they are decreasing and growing, respectively.To know more about exponential function refer to:
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Identify the independent variable and the dependent variable. A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
The independent variable is the brand of algaecide. The dependent variable is the treatment of pool water with algae.
What is the independent and dependent variable?
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.
Here, we have
Given
A pool store owner wants to determine the effect of algaecide brands on the treatment of pool water with algae. He contacts customers who have purchased the brands of algaecide and asks their opinion of the algaecide.
We have to determine the independent variable and the dependent variable.
We concluded that the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
Hence, the independent variable is the brand of algaecide and the dependent variable is the treatment of pool water with algae.
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Can you help me with this
Find the values of x and y.
-2x+y=-35
L
to
||
2x°
(y + 10)°
yᵒ
Answer:
x = 60 , y = 85
Step-by-step explanation:
assuming the figure is a trapezoid
• each lower base angle is supplementary to the upper base angle on the same side.
x + 2x = 180
3x = 180 ( divide both sides by 3 )
x = 60
and
y + y + 10 = 180
2y + 10 = 180 ( subtract 10 from both sides )
2y = 170 ( divide both sides by 2 )
y = 85
I would like help with this, please. Someone give me an answer in the next day or two.
Answer:
one solution
Step-by-step explanation:
The two lines cross at exactly one point. That means there is one solution.
N plus 75 used in a real world sentence.
Answer:
Laura has "n" amount of nickels. She receives 75 more from her grandmother.
Explanation:
(If this is not what the question meant, please let me know!)
Because the question is asking us to write a sentence for an addition problem, we need to write a sentence that involves two amounts of one thing being combined, in this case nickels.
- 6 <1/3(6y + 12) < 14
Answer:
1 - 5 < y < 5
I hope you pass your assignment
The range of solutions for the given inequality is -5<y<5.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is -6<1/3(6y + 12)<14.
Here, -6<(2y + 4)<14
-6<(2y + 4)
Subtract 4 on both the sides of an inequality, we get
-10<2y
Divide 2 on both the sides of an inequality, we get
-5<y
(2y + 4)<14
Subtract 4 on both the sides of an inequality, we get
2y<10
Divide 2 on both the sides of an inequality, we get
y<5
So, -5<y<5
Therefore, the range of solutions for the given inequality is -5<y<5.
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(25 points for the answer)
If John save 1/5 of his paycheck how much money would it take him to get to 14,500$ for his holiday trip? He earns $9062.5 each paycheck. (Unrealistic question unless you are under paid severely)
Use multiplication or division ONLY!
The amount of john would save 2900 rs
14500*1/5=2900
How much he earns on paycheck?A paycheck, also spelled paycheque, pay check or pay cheque, is traditionally a paper document issued by an employer to pay an employee for services rendered.a check used to pay an employee the amount of money the employee has earned.A paycheck can be an actual piece of paper (a check) that a person can take to the bank to deposit to their account or exchange for cash. Alternatively, a paycheck can be money a company electronically deposits directly into the employee's bank account.Take a look at how each common payroll interval works: Weekly: Once a week (52 paychecks per year) Biweekly: Once every other week (26 paychecks per year) Semimonthly: Twice per month (24 paychecks per yearTo learn more about paycheck refers to:
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convert y=2(x-5)(x+2) into standard form
Answer:
Step-by-step explanation:
y=2x-5+2
then you do minus 2 on both sides
Hope this helped!
A cookery course is divided into two groups. In group X, the average score in the test was 76. In group Y, the average score in the test was 70. If the average score of all 30 trainees in the course was 74, how many trainees are in group X
On solving the provided question, we can say that by equation 8 trainees are in group X
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Let a be the number of trainees in group X
76*a + 70 (30 - a) = 30*74
76a + 2,100 - 70a = 2,220
6a = 120
a = 20
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How do you solve for asymptotes?
There are three types of asymptotes solved in the following way:
1. Horizontal asymptotes is y = k for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.
2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.
3. Slant asymptotes is y = mx + c.
Asymptote is the representation of the line which approaches to the given curve but never touch or meet with the curve.Three types of asymptotes : Horizontal asymptote, vertical asymptote, and the slant asymptote.1. Horizontal asymptotes is y = k for x→∞ and x→ -∞ , when degree of denominator > degree of numerator. 2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator. 3. Slant asymptotes is y = mx + c.Horizontal asymptote rarely cross the given curve but vertical asymptote never.Slant asymptote represents the slope of the function.Therefore, the three types of asymptotes solved in the following way:
1. Horizontal asymptotes is y = k for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.
2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.
3. Slant asymptotes is y = mx + c.
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B is the circumcenter of △ADG. find AE and DG
When B is the circumcenter of triangle ADG the lengths of AE and DG are 4 and 12 respectively
What is circumcenter in a triangle?The intersection of the perpendicular bisectors of a triangle's sides is known as the circumcenter of that particular triangle.
In other terms, the circumcenter is the point at which the bisector of a triangle's sides coincides.
The perpendicular lines radiating from the sides of the triangle are the bisectors hence the line it radiates from shares the is shared into two halves at that point
Having this in mind
AE = DE = 4
and
DF = GF = 6
Also, DF + GF = DG
DG = DF + DF
DG = 6 + 6
DG = 12
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The temperature of the water in a hot water tank is recorded at 15 minute intervals after the heater is switched on. \begin{matrix} \text{Time (x minutes)} & \text{15} & \text{30} & \text{45} & \text{60} & \text{75} & \text{90}\\ \text{Temperature} (y ^\circ C) & \text{20} & \text{30} & \text{40} & \text{50} & \text{60} & \text{70}\\ \end{matrix} Time (x minutes) Temperature(y ∘ C) 15 20 30 30 45 40 60 50 75 60 90 70 a. Plot a graph of these data on your GDC. b. Find the linear model, T(x), for the temperature of the liquid with respect to time. c. Find the temperature of the water after 85 minutes.
Answer: a. Plotting a graph of the data on a graph paper, you can represent the time on the x-axis and the temperature on the y-axis. And plot the given points (15,20), (30,30), (45,40), (60,50), (75,60), (90,70) as ordered pairs on the graph. This will give you a line graph, showing the temperature increasing over time.
b. To find the linear model, T(x), for the temperature of the liquid with respect to time, you can use the slope-intercept form, y = mx + b, where y is the temperature, x is the time, m is the slope and b is the y-intercept. Using two of the given points, you can find the slope of the line by calculating the change in y over the change in x,
m = (y2 - y1) / (x2 - x1).
where x1,y1 and x2,y2 are two distinct points on the graph.
Once you have the slope, you can use one of the points to find the y-intercept, by substituting the point's coordinates into the slope-intercept form equation and solving for b.
Once you have the slope and y-intercept, you can write the linear model as T(x) = mx + b
c. To find the temperature of the water after 85 minutes, you can substitute the value of x = 85 into the linear model equation that you found in the previous step to get the corresponding value of y (temperature).
Please keep in mind that the temperature and time value here are random and are not based on any real-life scenario, and they were provided to show you the concept of linear model.
Step-by-step explanation:
4. The table gives the height and shoe sizes of six randomly selected men.
Height 67 70 73. 5 75 78 66
Shoe size 8. 5 9. 5 11 12 13 8 CO
a. What is the equation of line of best fit: 4= 42x-19. 81
b. What is the slope, and what does it mean in this problem?
C. What is the y intercept? What does it mean in this problem?
d. Using the equation of the line of best fit, if a man has a shoe size of 10. 5, what would be his predicted height?
The predicted height if the man with shoe-size 10 is 427.09 cm.
We get the answers using the following steps.
a. The equation of the line of best fit is: y = 42x - 19.81
b. The slope, 42, represents the rate of change of the height variable with respect to the shoe size variable. It means that for every 1-unit increase in shoe size, we can expect a 42-unit increase in height.
c. The y-intercept, -19.81, is the point where the line of best fit crosses the y-axis. It represents the height when the shoe size is 0. It means that if a man has 0 shoe size, his height would be -19.81, both of which is impossible.
d. To predict the height of a man with a shoe size of 10.5, we substitute x = 10.5 into the equation of the line of best fit:
y = 42x - 19.81
y = 42(10.5) - 19.81
y = 447.9 - 19.81
y = 427.09
So, a man with a shoe size of 10.5 would have a predicted height of 427.09 cm
It's worth noting that this is just a predicted value and it might not be accurate. The line of best fit is calculated based on the given data set, it might not be accurate for other data points.
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How do you find the value of 3 7?
What is 2 step used for?
The two step equations are used to represent the equations and solve real life problems .
What is Two Step Equations ?
The Equations that can be solved in exactly two steps are called as Two Step Equations .
We can use the two-step equations to represent and solve real-world problems by translating the problem into an algebraic equation, and solving equation, and then interpreting the solution of equation.
An example of the two step equation is : If a rental car costs $40 plus extra 10 cents for every mile driven, then how many miles can be driven for $50 ?
Translating The problem into equation we get [tex]40 + 0.1m = 50[/tex] where m is number of miles driven.
Step(i) we Subtract 20 from both sides
we get , [tex]0.1m = 10[/tex].
Step(ii) We Divide both sides by 0.1 ;
we get , [tex]m = 100[/tex].
Therefore , the problem to find the number of miles is solved in exactly two steps .
The given question is incomplete , the complete question is
What is the two step equation used for ?
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y=5/4x-2 y=5/4x-1 !HELP ME GRAPH AND ANSWER THE QUESTION!!
Answer:
Y=54x−2y=54x−1
I hope this helps you!
400 people are asked if they drink tea. [tex]\frac{7}{10}[/tex] say Yes and 20% of the people who say Yes drink at least 3 cups each day.
I really need help on a) Complete the frequency tree, I don't know how to work that one out.
The missed value in the frequency tree is 224.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that 400 people are asked if they drink tea.
7/10 say Yes and 20% of the people who say Yes drink at least 3 cups each day
7/10 of 400 is 280
Which means 280 people drink tea.
The remaining people does not drink tea.
Remaining =400-280=120.
Now let us find 20% of 280
20/100×280
0.2×280=56
So 56 drink at least 3 cups each day.
280-56=224
So 224 people drink tea but not three cups.
Hence, the missed value in the frequency tree is 224.
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Given:
sin (C) 4/9
Find tan (C)
[tex]sin(C)=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{9}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{9^2 - 4^2}=a\implies \sqrt{65}=a \\\\[-0.35em] ~\dotfill[/tex]
[tex]tan(C)=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{\sqrt{65}}}\implies tan(C)=\cfrac{4}{\sqrt{65}}\cdot \cfrac{\sqrt{65}}{\sqrt{65}}\implies tan(C)=\cfrac{4\sqrt{65}}{65}[/tex]
-50 POINTS- (Curtisqn don’t even try you’re slow.)
SSS
SAS
ASA
SAA
HL
A cooker is priced at £80 after a 20% reduction from the original price.
Answer: original price: £400
Step-by-step explanation:
20/100 × original price = £80
Original price = £80 ÷ 20/100
= £400
PLEASE HELP ME I DONT UNDERSTAND :(( GIVIN 100 POINTS
Question 1: The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average of 3/4 foot per year
) Some students misunderstood question #1 and wrote the following equations in point-slope form:
a) y − 3 = 3/4(x-0)
b) y - 6 = 3/4(x-4)
c) y - 4.5 = 3/4(x-2)
d) y - 12 = 3/4(x-12)
(e) y - 15= 3/4(x-15)
Is this equation okay to use for the height of the trees in this problem?
There is one equation that is incorrect.... determine which one? why is it incorrectly?
Creat two new equations written in point slope form
The equation in option e) is not correct because it would not give correct height of the trees in this problem
How to write equation in slope-point form?Since the Magnolia trees are 3 feet tall and grow at an average of 3/4 foot per year.
If x is the number of years and y is the height. we can write:
y = 3/4(x) + 3
The slope-point equation of a line is given as:
y-y1 = m(x−x1)
y = 3/4(x) + 3 in slope-point form is:
y = 3/4(x) + 3
y-3 = 3/4(x-0)
This means option a) is correct
Yes, this equation is okay to use for the height of the trees in this problem
b) y - 6 = 3/4(x-4)
y - 6 = 3/4(x-4)
y - 6 = 3/4(x)- 3
y - 6 + 3 = 3/4(x)
y - 3 = 3/4(x)
This is correct
c) y - 4.5 = 3/4(x-2)
y - 4.5 = 3/4(x-2)
y - 4.5 = 3/4(x)- 1.5
y - 4.5 + 1.5 = 3/4(x)
y - 3 = 3/4(x)
This is correct
d) y - 12 = 3/4(x-12)
y - 12 = 3/4(x-12)
y - 12 = 3/4(x) - 9
y - 12 + 9 = 3/4(x)
y - 3 = 3/4(x)
This is correct
(e) y - 15= 3/4(x-15)
y - 15= 3/4(x-15)
y - 15= 3/4(x)-11.25
y - 15 + 11.25= 3/4(x)
y - 3.75 = 3/4(x)
This is not correct because it does not reflect the given information
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A "Pick 2" lottery game involves drawing 2 numbered balls from separate bins each containing balls labeled from 0 to 9. So there are 100 possible selections in total: 00, 01, 02, ..., 98, 99. Players can choose to play a "straight" bet, where the player wins if they choose both digits in the correct order. Since there are 100 possible selections, the probability a player wins a straight bet is 1/100. The lottery pays $50 on a successful $1 straight bet, so a player's net gain if they win this bet is $49. Let X represent a player's net gain on a $1 straight bet. Calculate the expected net gain E(X). Hint: The expected net gain can be negative. E(X) = dollars
The expected net gain E(X) in the context of this problem is given as follows:
E(X) = -$0.5.
How to obtain the expected net gain?The net gain for this problem is modeled for a discrete distribution, as there are only two possible outcomes, given as follows:
Winning $49.Losing $1.The probability of winning is of 1% = 0.01, while the probability of losing is of 99% = 0.99, hence the distribution of gains for this problem is given as follows:
P(X = -1) = 0.99.P(X = 49) = 0.01.The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.
Hence the expected net gain for this game is calculated as follows:
E(X) = -1 x 0.99 + 49 x 0.01.
E(X) = -$0.5.
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What is the area when the diameter is 16?
201.06 square units (rounded to 2 decimal places) is the area of the given circle.
The formula for the area A of a circle is A = πr², where r is the radius of the circle and π is the famous, well-known irrational number pi equal to 3.14159 (rounded to 5 decimal places).
Given that the circle's diameter is 16, and that a circle's radius is equal to half its diameter, the following conclusions can be drawn:
r = d/2
= 16/2
= 8
A=πr2
AND HALF THE DIAMETER IS THE RADIUS (r)
r=8
A= πr2 = π (8) squared = 64 * π = 200.96
or,
Now, substituting the values of r and π into the formula for the area of a circle, we get
A = πr²
= (3.14159)(8²)
= (3.14159)(64)
= 201.06 square units (rounded to 2 decimal places) is the area of the given circle.
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