The interval of the cost of the car is [5600, ∞).
Here we have to find the cost of the car.
Let x be the cost of the car.
So from the question, we have that the cost of the repair is 25% or more of the car's value.
So we have to find the interval notation of the cost of the car.
x ×25% ≥ 1400
x × 25/100 ≥ 1400
x ≥ 1400× 100/25
x≥ 5600
So we get that the cost of the car is greater than $5600.
Therefore the cost of the car in an interval is [5600, ∞)
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One leg of a right triangle is 8 units long, and its hypotenuse is 14 units long. What is the length of the other leg? Round to the nearest whole number.
The other leg has its length to be 11.49 units
How to determine the length of the other leg distance?To calculate the length of the other leg distance, we make use of the Pythagoras theorem
Mathematically, this theorem is represented by:
w² = y² + z²
Such that x = hypotenuse, y = leg and z = other leg
From the question, we have the following parameters
w = 14, y = 8 and z = the other leg
Substituting these values in w² = y² + z²
14² = 8² + y²
Evaluate the exponents
196 = 64 + y²
Evaluate the like terms
y² = 132
Take the square roots of both sides
y = 11.49
Hence, the length of the other leg is 11.49 units
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Answer: 11 units
Step-by-step explanation: i took the test and got it right
Solve the inequality -y +3 ≤ 8 and y + 2> 9.
Answer:
y ≥ -5 and y > 7
Step-by-step explanation:
Collect like terms
-y ≤ 8 - 3
-y ≤ 5
Divide both sides by -1
-1y/-1 ≤ 5/-1
y ≥ -5
And
y > 9 - 2
y > 7
use mental math to subtract. 8,329-7,218=
Answer:
1111
Step-by-step explanation:
Solve the inequality statement:
-5ω < 15
---
w >3
wς 3
w< -10
The simplified form of the given inequality is w > -3.
What is inequality?
When two values are compared, an inequality reveals whether one is bigger than, less than, or simply not equal to the other. The term "inequality" in mathematics refers to a relationship between two expressions or values that is not equal to one another. The occurrence of an unfair distribution of opportunities and resources among individuals of a certain society is referred to as inequality. To different people and in various contexts, the term "inequality" may mean different things.
Here the given inequality is ,
=> -5w<15
=> -5 *w < 15
=> w>15/-5
=> w > -3.
Hence the correct simplified form of the inequality is w >-3.
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Factor −4x2 + 12x. PLease help
Answer:
-4x(x-3)
Step-by-step explanation:
-4x^2+12x
divide by -4x
-4x(x-3)
The equation of the trend line is y = -0.36x + 12.6. Use the equation of the trend line to predict the wind chill for a wind speed of 58 mi/h. Round your answer to the nearest degree. The wind chill at 58 mi/h is °F.
Answer: -8
Step-by-step explanation:
Assuming that [tex]x[/tex] is the wind speed and [tex]y[/tex] is the wind chill, we can set [tex]x=58[/tex].
[tex]y=-0.36(58)+12.6 \approx -8[/tex]
if y varies inversely as x and y=3 when x=21, find y when x=9
After simplification, the value of y is 7 when x=9.
In the given question, if y varies inversely as x and y=3 when x=21, find y when x=9.
From the given question y varies inversely as x i.e.
y ∝ 1/x
When we remove the inversly sign then their is one variable should be added. Let the variable should be k.
Now the expression is
y = k/x
As we know that y=3 when x=21.
Now putting the value.
3 = k/21
Multiply by 21 on both side, we get
k = 3*21
k = 63
Now the value of k is 63.
Now finding the value of y when x=9
y = 63/9
y = 7
Hence, the value of y is 7 when x=9.
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The table shows the numbers of snare drum backbeats and bass guitar
notes in a disco song. Are the two quantities proportional? Explain.
Snare Drum Backbeats:
3
90
120
Bass Guitar Notes:
2
60
80
Yes, the two quantities have a proportional relationship because the variables x and y all have the same constant of proportionality.
What is a proportional relationship?Mathematically, a proportional relationship can be represented or modeled with the following mathematical expression:
y = kx
Where:
y represents the numbers of bass guitar notes.x represents the numbers of snare drum backbeats.k represents the constant of proportionality.In order for the two quantities to have a proportional relationship, the variables x and y must remain in a constant ratio.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 2/3
When x = 90 and y = 60, we have:
Constant of proportionality (k) = 60/90
Constant of proportionality (k) = 2/3
When x = 120 and y = 80, we have:
Constant of proportionality (k) = 80/120
Constant of proportionality (k) = 2/3
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Can anyone write the equation of the graph?
The equation of the absolute value graph is f(x) = |x - 3| + 5
How to determine the equation of the graph?The graph represents the given parameter
From the graph, we can see that the graph is an absolute value graph
An absolute value graph is represented as
f(x) = a|x - h| + k
Where h and k are the vertex of the graph
In this case, they are
h = 3 and k = 5
This is because the minimum point of the graph is (3, 5)
Substitute values for h and k in the form of the equation
So, we have the following representation
f(x) = a|x - 3| + 5
A point on the graph is (2, 6)
This gives
a|2 - 3| + 5 = 6
When the value of variable a is solved, we have
a = 1
So, the equation becomes
f(x) = 1 * |x - 3| + 5
Evaluate the products
f(x) = |x - 3| + 5
Hence, the equation of the graph is f(x) = |x - 3| + 5
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Which expression is equivalent to -51 - (-60)−51−(−60)minus, 51, minus, left parenthesis, minus, 60, right parenthesis?
The required expression which is equivalent to -51 -(-60) is -51 + 60.
Given that,
Which expression is equivalent to -51 - (-60) is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression = -51 - (-60)
Simplify by applying the property of distribution under the parenthesis,
= -51 + 60
Thus, The required expression which is equivalent to -51 -(-60) is -51 + 60.
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PLEASEE HELPPP GIVING ALL MY POINTS
Answer: 2
Step-by-step explanation:
This is because it is a scaled copy which means that the smaller has to multiply either by a whole or a fraction and the bigger can be divided by a whole or a fraction in order to be the smaller triangle if that makes sense. so 5*2=10, 12*2=24 thus if you were to divide 10/2=5, 24/2=12.
Answer:
The answer is 2:1
Step-by-step explanation:
This is because it is a 2/1 ratio
PLS HELP!!! I WILL GIVE BRAINLIEST TO CORRECT ANSWER!
What is the slope?
What is the y-intercept?
What does the slope of the line shown by the points mean in the situation?
What does the y-intercept mean in the situation?
Answer:
The slope is 20 or 20/1The y-intercept is at (0,60)The slope of the line shows for every class, the cost of fees increases by $20 at the gymThe y-intercept means that before a member can sign up for a class, they must pay a flat, one-time fee of $60Step-by-step explanation:
the slope-intercept formula is y = mx + bm = slope which is rise/runFinding Slope:
the two coordinates that I will be choosing is (0,60) and (1,80)using the slope formula stated above, I will plug in my coordinates. It does not matter which coordinate you choose as #1 and which one as #2, you just need to make sure that you keep it consistent80-60/1-0 = 20/1 = 20 is the slopeFinding Y-Intercept:
If you look at the graph, there is a point that is on the y-axis which is at (0,60). This means that the y-intercept is at (0,60)Answer:
1. Slope = 20
2. y-intercept = 60
Step-by-step explanation:
The slope of the line is found by dividing the change in y by the change in x or "rise over run":
[tex]\implies \textsf{slope}\:(m)=\dfrac{\textsf{change in $y$}}{\textsf{change in $x$}}=\dfrac{80-60}{2-1}=\dfrac{20}{1}=20[/tex]
The slope of the line for the given situation is the fee per class. Therefore, there is a $20 fee for each class a customer at the gym attends.
-----------------------------------------------------------------------------------------------
The y-intercept is the y-value at the point at which the line intercepts the y-axis, so when x = 0.
From inspection of the given graph, y = 60 when x = 0.
[tex]\implies \textsf{$y$-intercept}=60[/tex]
The y-intercept of the line for the given situation is the membership fee for the gym. Therefore, the membership fee for the gym is $60.
The function f(x) is given in the graph below. Find its average rate of change between the followin
points. Show the calculations that lead to your answer.
(a) x=-6 to x = 4
(b) x=-2 to x=2.
a) x = -6 to x =4
[tex](x_{1} , y_{1} ) (x_{2} , y_{2} ) = (-6,1) (4,3)[/tex]
Slope(m)[tex]= \frac{Y_{2}-Y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{1-3}{-6-4-}[/tex]
[tex]= \frac{-2}{-10}[/tex]
[tex]m = \frac{1}{5}[/tex]
Slope (m) of the function is 1/5.
b) x = -2 to x = 2
[tex](x_{1} , y_{1} ) (x_{2} , y_{2} ) = (-2,-1) (2,-3)[/tex]
slope (m)[tex]= \frac{Y_{2}-Y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{-3-(-1)}{-2-2}[/tex]
[tex]= \frac{-2}{-4}[/tex]
slope(m) [tex]= \frac{1}{2}[/tex]
Slope(m) of the given function is 1/2.
What is fraction ?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
In a simple fraction, both are integers.
A complex fraction has a fraction in the numerator or denominator.
In a proper fraction, the numerator is less than the denominator.
Define slope(m)?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
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1. The distance between the points (5, 7) and (8,-5) is
a) √153
b) √154
c) √13
d) √53
The distance between the points (5, 7) and (8,-5) is √13.
Define distance between points.The length of the path joining two points determines their distance from one another. It's crucial to know how to calculate the distance between two points when working with graphs. This makes it possible for a learner to estimate how long the line is, which is useful in a variety of circumstances. Using the distance formula is the most typical method of determining the distance.
Points (5, 7) and (8,-5)
Formula:
AB² = (x₂ - x₁)² + (y₂ + y₁)²
AB² = (8 - 5)² + (-5+7)²
AB² = (3)² +(2)²
AB² = 9 + 4
AB² = 13
AB = √13
The distance between the points (5, 7) and (8,-5) is √13.
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Simplify the expression:
2(2f+5) =
Answer:
4f+10
Step-by-step explanation:
multiply the 2 to both the numbers in the parenthesis. 2 times 2f is 4f and 2 times 5 is 10
Hey, guys! How is your day? (°ω°)
Wilson paints 40% of a bookcase in 20 minutes.
Write an equation using equal fractions to represent this situation. Use a box to represent the time it takes to paint the whole bookcase.
The time taken for Wilson to paint the bookcase is 50 minutes.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, Wilson paints 40% of a bookcase in 20 minutes. It should be noted that 40% = 0.4
Therefore, the time taken to paint the whole bookcase will be:
= Number of minutes / Percentage painted
= 20 / 0.4
= 50
He'll use 50 minutes.
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Solve the inequality 4x-7<5
Answer:
x<3
Step-by-step explanation:
4x<5+7
4x < 12
4/4 x < 12/4
x < 3
how many license plate combinations are there with either three letters then three numbers or three numbers then three letters
The license plate combinations with either three letters then three numbers or three numbers then three letters are 35152000.
The license plate combinations to be made are either three number followed by three letter or three letter followed by three number. we are here assuming that the repetition of the number and letter are allowed.
The number can be any three from 0-9. So, the total choices of number are 10.
The letter can be from A-Z. So, the total choices for letter are 26.
The total choices of the numbers possible are,
ΟΟΟ ΟΟΟ
1 2 3 4 5 6
The first three are the choices of letter and the last three are the choice of number. Two combinations are also possible by interchanging the position of the set of numbers and letters.
So, the possible combinations are,
2 x [26x26x26x10x10x10]
Hence,
The possible combinations for the license plate number are 35152000.
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a hamburger regularly cost $6.00 each additional topping cost $0.59. on Monday the cost of hamburger only is half off
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A burger consistently cost $6.00 each extra fixing cost $0.59.
Let 'c' be the cost and 't' be the cost of topping. Then the equation is given as,
c = 0.59t + 6
On Monday the expense of the burger just is half off. Then the equation is given as,
c = 0.50(0.59t + 6)
c = 0.295t + 3
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
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whats the product of 23 and 39
Answer:
Step-by-step explanation:
1. Product means multiplying sign in math
23*39=897
2. Answer: 897
0.00097 in standard form
Answer:
9.7x10^-4
Step-by-step explanation:
correct answer gets brainliest!
Answer:
arc RP = 136°
Step-by-step explanation:
the inscribed angle PQR is half the measure of its intercepted arc, then
arc PR = 2 × ∠ PQR = 2 × 68° = 136°
Determine which set of side measurements could be used to form a right triangle.
square root of 19 comma square root of 35 comma 54
square root of 15 comma 6 comma square root of 51
5, 8, 30
5, 6, 7
Answer:
Square root 19 comma, 5,8,30
Answer:5,8,30
Step-by-step explanation: i took a test
the numbers 33, 55, 77, aa and bb have an average (arithmetic mean) of 1515. what is the average of aa and bb?
The average of aa and bb is 740.
Define arithmetic mean.The result of adding together and dividing by the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value. In statistics, the arithmetic mean is significant. Central tendency is measured using the arithmetic mean. By giving each observation the same amount of weight, it enables us to determine the frequency distribution's center for a quantitative variable (in contrast to the weighted arithmetic mean).
Given,
Arithmetic mean = 1515
Total number of values = 5
Formula:
Sum/Total = Arithmetic mean
33 + 55 + 77 + aa + bb/ 5 = 1515
165 + aa + bb = 7575
aa + bb = 7575 - 165
aa + bb= 7410
The average of aa and bb is 740.
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calculate a 95% confidence interval for the effect of a one unit increase in exercise on resting heart rate for a non-smoker
A level of confidence of 95% was used in the case above. A table at the back of a statistics textbook can be used to get the value of z* for a certain confidence level. For a 95% confidence level, the value of z* is 1.96.
An error margin of 3.92 is discovered when the value of z*, the demographic standard error, and the sample size are entered into the equation.
Statistical Estimation's Justification
Where does the confidence interval calculation formula come from?
The population mean's true value is never known; it can only ever be estimated or approximated. The easiest way of doing this is to choose many identical-sized random samples from the population.
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Joseph, a programmer needs to write a program using subordinate functions. what function should joseph use in a program to call subordinate functions?
Use parentheses that may or may not contain parameters directly after the function name to invoke the function.
What do you mean by subordinate roles?As part of GAIA, the AI created for Project Zero Dawn in reaction to the Faro Plague, the subordinate functions are a part. The Faro Swarm's deactivation and the planet's terraforming are all objectives of Project Zero Dawn, and they are all accomplished through their extensive suite of subfunctions, each of which is dedicated to a particular purpose.
What is the total number of subordinate functions?There are nine supporting roles.
A top engineer on the Zero Dawn project known as an Alpha created each of the nine subordinate functions. They were supported by a project development team made up of professionals in their industry who were well-known throughout the world.
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In a certain skyscraper, the elevators whisk you to a restaurant in the skyscraper at a speed of 800 feet
in 10 seconds. If the restaurant is 300 feet up, how long will it take you to reach the restaurant by
elevator?
Answer:
[tex]3\frac{3}{4}[/tex] seconds
Step-by-step explanation:
So you travel 800 feet in 10 seconds. If you divide that by 2, then you travel 400 feet in 5 seconds, or 100 feet in 5/4 seconds. Multiply by 3 to get 300 feet in 15/4 seconds, or 15 feet in [tex]3\frac{3}{4}[/tex] seconds.
Drag the red and blue dots along the x-axis and y-axis to graph x - y = 6
The graph of x - y = 6 that shows the x and y-intercepts is in the attachment below.
What is the X and Y-intercepts of a Graph?For a linear graph, the x-intercept is point where the line intercepts the x-axis of a graph, of which the value of y is zero at this point. On the other hand, the y-intercept is the point where the line intercepts the y-axis and the value of x at this point is zero.
Given the equation x - y = 6, determine the x and y-intercepts.
To find the x-intercept, substitute y = 0 into the equation x - y = 6:
x - 0 = 6
x = 6
The x-intercept is (6, 0).
To find the y-intercept, substitute x = 0 into the equation x - y = 6:
0 - y = 6
-y = 6
y = -6
The y-intercept is (0, -6).
This means the line will cut the x-axis at 6, and also cut the y-axis at -6. The graph of the equation x - y = 6 is shown below.
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Hello, I am finding inverse functions and ran into this fraction. How would I simplify from here to find Y by itself?
The inverse function for the function f(x) = (1 -2x) / 3x is 1/3x+2.
Inverse function:
Inverse function means a function that serves to “undo” another function.
For example,
if f(x) produces y, then putting y into the inverse of f produces the output x.
Given,
Here we have the function f(x) = (1 -2x) / 3x.
Now, we need to find the inverse function f⁻¹.
To find the inverse function, swap x and y, and solve the resulting equation for x.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables by interchange the value of x by y and the value of y as x.
Then we get,
x = (1 - 2y)/3y
Now, solve the equation
x = (1 - 2y)/2y
for y, then we get,
y = 1/(3x + 2)
Therefore, the inverse function is 1/3x+2.
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what is 5 divided by 1 over 3
Answer: 15 !
Step-by-step explanation:
Change the division sign to a multiplication sign and reverse the fraction.
5 x 3/1 = 15