Answer:
9
Step-by-step explanation:
(-2+5)^2
3^2
9
Use the Empirical The mean speed of a sample of vehicles along a stretch of highway is 70 miles per hour, with a standard deviation of 5 miles per hourEstimate the percent of vehicles whose speeds are between 60 miles per hour and 80 miles per hour(Assume the data set has a bell-shaped distribution )
Using the empirical rule, 95% of vehicles travel between 60 miles per hour and 80 miles per hour.
What is the empirical rule?Generally, Given that
Mean = 66 and Standard deviation 4To find the percent of vehicles whose speeds are between 60 miles per hour and 80 miles per hour
60 = 70-(2*5) ,
this shows that the 58 value is 2 standard deviations below the mean
and
80 = 70 +( 2*5)
This shows that the 74 value is 2 standard deviations above the mean
Using the empirical rule, we know that 95% of data fall within 2 standard deviations from the mean.
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Find the point on the curve y = -x^2 - 2 that is closest to the point (0, 1)
Answer:
[tex](0,-2)[/tex]
Step-by-step explanation:
Let the coordinates of the desired point be [tex](a, -a^2-2)[/tex]. Let the distance of this point from [tex](0,1)[/tex] be [tex]f(a)[/tex].
By the distance formula, [tex]f(a)=\sqrt{a^2+(a^2+3)^2}[/tex].
Clearly, [tex]f(a)[/tex] is minimized when the radicand is minimized.
Clearly, the radicand is always increasing, so the minimum is achieved at the left endpoint of the maximal domain of [tex]f(a)[/tex], which is [tex]a=0[/tex].
So, the coordinates are [tex](0,-2)[/tex].
The point on the curve y = -x^2 - 2 that is closest to the point (0, 1) will be (0, -2)
How to calculate the value?From the information, we want to know the point on the curve y = -x^2 - 2 that is closest to the point (0, 1).
Let the coordinates of the desired point be illustrated as (a - a² - 2).
The distance of the point from (0, 1) is depicted as f(a).
When the radicand is minimized, f(a) is minimized.
In this case, the minimum will be achieved at the left endpoint of the maximal domain of f(a) which is a = 0.
Therefore, the coordinates will be (0, -2).
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Please help me and give me all 3 of the answers i dont need an expalanation or anything just the answers this is due in 25 minutes.
Simplify all:
a) 2/5 : 3/4 = 2/5 × 4/3 = 8/15b) 9/4 : (- 3/4) = - 9/4 × 4/3 = - 9/3 = - 3c) - 5/7 : (- 1/3) = 5/7 × 3 = 15/7 or 2 1/7d) - 5/3 : 1/6 = - 5/3 × 6 = - 10Solve for the value of n.
(6n+5)°
(4n-5)°
Step-by-step explanation:
(6n+5)°(4n-5)°
use the method of expand
6n(4n-5)+5(4n-5)
24n²-30n+20n-25
24n²- 10n -25
use middle term/ quadratic formula
n=5/4 (1.25) or n= -5/6 (-0.833333)
56 parts were lost. 3% of the total parts were lost. How many total parts were there?
Answer:
3% = 56
100% = ?
Rule of three:
56 x 100
—————
3
Answer = 1,866.667 ≈ 1.867
Step-by-step explanation:
dont mind the answer below have a great day ______
\|/
the late fee for library books is $2.00 plus 15 each day for a book that is late. If Maria's fee for a late book was $3.20, wrote and solve a linear equation to find how many days late the book was
Answer:
8 days
Step-by-step explanation:
I assume you meant $0.15/day late fee (15 cents per day)? If so, the answer is:
x = # of days late
$2.00 + ($0.15/day)x = $3.20
($0.15/day)x = $3.20 - $2.00 = $1.20
x = $1.20/ ($0.15/day) = 8 days
Sine/Cosine of Complementary Angles Solve for x
In a right triangle,sin (8x-9) = cos (x+6) Round to the nearest tenth if nessecary
The value of the variable , x is 10. 33
How to determine the value of the variable
It is important to note that in mathematics, complementary angles are defined as angles that sum up to 90 degrees.
Some properties of complementary angles are;
If the addition of two angles add up to 90 degrees in a right angle, they are called complementary anglesC represents complement and also for the corner of a right angleComplementary angles can be adjacent or non-adjacent anglesFrom the information given, we have the angles as;
8x - 9x + 6Equate the angles to 90 degrees
8x - 9 + x + 6 = 90
collect like terms
8x + x = 90 +3
add the like terms, we get;
9x = 93
Make 'x' the subject of formula by dividing both sides by 9
x = 93/9
x = 10. 33
Hence, the value is 10.33
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Select the equivalent expression to 4^-3/4^-1
The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The fundamentals of algebra taught us a way to express an unknown price using letters which includes x, y, z, and so on. these letters are referred to as here as variables. An algebraic expression can be a combination of both variables and constants. Any value this is located earlier than and accelerated with the aid of a variable is a coefficient.
Given
expression ,
4^-3 / 4^-1
= 4 ^ (-3-(-1))
= 4^ (-3+1)
= 4^(-2)
= 1/4^2
= 1/16 .
Therefore , The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .
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Find the missing parts of each quadrilateral and name the type of quadrilateral that best describes the figure.
I already know the missing angles, but I'm not sure how to classify these shapes.
The quadrilaterals in a and b have the missing values of x as 85° and 57° respectively and can be best described as a scalene quadrilateral.
What is a scalene quadrilateralA scalene quadrilateral is a four-sided polygon in which all four sides have different lengths and all four angles have different measures. This is also known as an asymmetric quadrilateral.
we shall evaluate for the missing values of x as follows:
x + 109° + 96° + 70° = 360° {sum of interior angles of a quadrilateral}
x + 275° = 360°
x = 360° - 275° {subtract 275° from both sides}
x = 85°
x + 85° + 94° + (180° - 58°) = 360° {sum of interior angles of a quadrilateral}
x + 301 = 360°
x = 360° - 303° {subtract 303° from both sides}
x = 57°
Therefore, the missing values of x for quadrilaterals in a and b are 85° and 57° respectively, and can be best described as a scalene quadrilateral.
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The notation "f(x)" (f of x) is another way of representing y-values in a function
It represents the output values, hence the claim that "The notation "f(x)" (f of x) is another means of encoding y-values in a function" is accurate.
What is meant by function?An expression that can be used to define and depict the relationship between two or more variables in a data collection is referred to as a function in mathematics.
In conclusion, this means that a function typically illustrates the link between a data set's input values (x-values or domain) and output values (y-values or range), as well as demonstrating how the components in a table are uniquely paired (mapped).
Generally speaking, the output values (y-values or range) of a data set (function) are displayed on the y-coordinate of a graph, and they are typically denoted by either the notation f(x) or y.
The complete question is:
The notation "f(x)" (f of x) is another way of representing y-values in a function. True or False?
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12.57 rounded to the nearest tenth of a centimeter
The length of a rectangle is seven more than triple the width.if the perimeter is 126 inches, find the dimension
Complete the following tables with values for the functions f _ and h given that: (a) f is an odd function: (b) g is an even function. (c) h = g(f(x)) h(x)
The result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.
f(x) | -2 | -1 | 0 | 1 | 2
-------|----|----|----|----|----
f(x) | 5 | -3 | 0 | -3 | 5
g(x) | -2 | -1 | 0 | 1 | 2
-------|----|----|----|----|----
g(x) | 6 | 0 | 0 | 0 | 6
h(x) | -2 | -1 | 0 | 1 | 2
-------|----|----|----|----|----
h(x) | 6 | 0 | 0 | 0 | 6
h(x) = g(f(x))
For x = -2, h(x) = g(f(-2)) = g(5) = 6
For x = -1, h(x) = g(f(-1)) = g(-3) = 0
For x = 0, h(x) = g(f(0)) = g(0) = 0
For x = 1, h(x) = g(f(1)) = g(-3) = 0
For x = 2, h(x) = g(f(2)) = g(5) = 6
Since f is an odd function and g is an even function, then h(x) = g(f(x)) will be an even function. This means that for any given x, h(x) will always equal 0 or a positive value. For the set of values provided above, the result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.
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Abdi and Bashir run in an ultra marathon. After 5 hours Abdi is 4 miles behind Bashir If at this point in the race, Abdi begins to run at a constant speed of 8 mph and Bashir runs at a speed of 6 mph. How long will it take for Adbi to catch up with Bashir?
Using the Time-Distance Formula, it will take Adbi 2 hours.
How to Use Time-Distance Formula to Calculate Time?We can use the time-distance formula to find how long it will take for Abdi to catch up with Bashir. The time-distance formula is distance = speed x time.
Let t be the time in hours that it takes for Abdi to catch up with Bashir.
We know that the distance Abdi has covered is 4 miles more than Bashir, and the relative speed between the two runners is 8mph - 6mph = 2mph.
So we can write the equation:
4 = (8 - 6) * t
Solving for t, we get t = 4/2 = 2 hours.
So it will take Abdi 2 hours to catch up with Bashir.
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The solutions of a quadratic equation are -4 and 9. What is the standard form of a related quadratic function?
The standard form of a related quadratic function is,
⇒ (x² - 5x - 36)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The solutions of a quadratic equation are -4 and 9.
Let the factors of the quadratic equation are,
⇒ (x - (-4)) (x - 9)
⇒ (x + 4) (x - 9)
⇒ (x² - 9x + 4x - 36)
⇒ (x² - 5x - 36)
Thus, The quadratic function is,
⇒ (x² - 5x - 36)
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Please answer this question for me
Hector has to put the fixed point of the compass on points A and C.
Option (C) is correct.
What is the angle bisector of an angle?
The angle bisector of an angle is a line, ray, or segment that divides an angle into two congruent angles. It is a line that bisects (divides into two equal parts) the angle.
For example, if you have a right angle of 90 degrees, the angle bisector would be a line that divides the angle into two 45-degree angles.
In the given figure, Hector is using a compass and straightedge to construct the bisector of angle CEB.
So he has to put the fixed point of the compass on points A and C.
Hence, Hector has to put the fixed point of the compass on points A and C.
Option (C) is correct.
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if 3100 people in population of 46785 complain of headaches - and 6.6% complain - how was this answer figured out?
The number of the people with headaches to the nearest whole number is 3100
What is percentage?Percentage can be defined as the number or ratio expressed as fraction of 100.
It is represented using the mathematically sign"%".
Due to this, percentage is a dimensionless number.
it is known to have no unit of measurement.
They are also seen as fractions with 100 as their denominators. It is the relative value of a quantity with 100.
From the information given, we have that;
The total number of people = 46785The percentage with headaches = 6.6%Then,
6.6/100 × 46785
Multiply the values, we get
3087. 81 people
Hence, the value is 3100 people in the nearest whole number.
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When building a house, the number of days required to build is inversely
proportional to with the number of workers. One house was built in 85 days by 5
workers. How many days would it take to build a similar house with 25 workers?
It would take 17 days to build a similar house with 25 workers.
What is Inverse Proportion?Inverse proportion is a type of proportionality relationship. If two quantities are inversely proportional then as one quantity increases, the other decreases. In inverse proportion, the product of the given two quantities is equal to a constant value
One house was built in 85 days by 5 workers;
The relationship will be;
d ∝ 1/n
where
n = number of workers
d = number of days
d = k/n
when d = 5
k = 85
k = 5 x 85
k = 425
when n = 25
d = 425/25
d = 17
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please help will mark BRAINLIEST
Answer:
110
Step-by-step explanation:
180-70 =110
A nurse prescribes a patient 73 mL of Tylenol3 every 6 hours. Tylenol3 has 17 milligrams of codeine for every 30 mL of Tylenol3. How much Codeine is Ken being prescribed per day?
The amount of codeine that Ken is being prescribed every day, given the Tyelenol 3 being prescribed is 165. 47 milligrams of Codeine
How to find the amount prescribed ?The amount of codeine in 30 ml of Tylenol 3 is:
= ( 17 x 73 ) / 30
= 41. 37 mL of Codeine
The number of 6 hour periods in a day is:
= 24 / 6
= 4
The amount of codeine that Ken is being prescribed a day is therefore:
= 4 x 41. 37
= 165. 47 milligrams of Codeine
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Today 5 friends went out for lunch. Their total bill was $35.20 including tax and gratitude. They decide to split the bill equally and each paid with a $10 bill how much money will each person get back
??
Answer: The total bill including tax and gratitude is $35.20
And each one of the 5 friends paid $10 for the bill.
So the total amount paid is $10*5 = $50
If each person paid $10 and the total bill was $35.20
then the change will be $50-$35.20 = $14.80
And since they split the bill equally then each one of them will get back $14.80/5 = $2.96
So each person will get back $2.96
Step-by-step explanation:
If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000 operating hours, what is the probability of unscheduled maintenance in exactly 5,000 hours?
If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000. The probability of unscheduled maintenance in exactly 5,000 hours is:.7135.
How to find the probability?Using this formula to the probability of unscheduled maintenance in exactly 5,000 hours
P ( X < 5000) = 1 - e^(-λx)
Where:
e = exponent
-λ = Operating hour
x = Number of hours
Let plug in the formula
P ( X < 5000) = 1 - e^(-(1/4000) × 5000)
P ( X < 5000) = 1- e^-1.25
P ( X < 5000) = 1 - .2865
P ( X < 5000) = .7135
Therefore the probability is .7135.
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How to solve -7=5x-2. 2 step equations using inverse operations
Answer:
-1
Step-by-step explanation:
Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x.
Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x.
So the solution to the equation is x = -1.
Alternatively, you can also use inverse operations to solve the equation by isolating x to one side.
Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x
Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x
So the solution to the equation is x = -1.
50% means___ parts of a total 200
Answer:
Step-by-step explanation:
50% of 200 is =100
let f be the continuous function defined on [-4, 3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. let g be the function given by
The value of g(2) = -1/4 and the value of g(-2) is π/2 - 3/2
Consider function g(x)
[tex]g(x) = \int\limits^x_1 {f(t)} dt[/tex]
Here, function f be the continuous function defined on interval [-4, 3]
The graph of function f is shown below.
It consists of three line segments and a semicircle centered at the origin, is given above.
For x = 2,
g(2)
[tex]=\int\limits^2_1 {f(t)} dt[/tex]
= -(1/2) × 1 × (1/2) .........(From the graph of function f)
= -1/4
For x = -2,
g(-2)
[tex]=\int\limits^{-2}_1 {f(t)} dt\\\\=-\int\limits^{1}_{-2} {f(t)} dt[/tex]
= -(3/2 - π/2) .........(From the graph of function f)
= π/2 - 3/2
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The complete question is:
Let f be the continuous function defined on [-4, 3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by [tex]g(x) = \int\limits^x_1 {f(t)} dt[/tex]
Frin dthe values of g(2) and g(-2)
suppose that a large influx of electric scooter rentals in a crowded downtown area results in a lot of new riders on the streets. for their safety, the mayor of the city decides to enact a law requiring helmets when renting scooters. these new helmets reportedly decrease the probability of injury by 29% in the event of a scooter crash. While the new helmets (increase/decrease) the probability of injury resulting from a scooter accident, they also incentivize individuals to ride (more/less) recklessly, which could (increase/decrease) the number of scooter collisions and therefore injuries to renters. Please choose one
While the new helmets decrease the probability of injury resulting from a scooter accident, but they also incentivize individuals to ride more recklessly, which could increase the number of scooter collisions and therefore injuries to renters.
The reason for the above statement is based on the concept of risk compensation. When the perceived risk of an activity is reduced, individuals may engage in more risky behavior. For example, if individuals believe that wearing a helmet makes them safer while riding a scooter, they may feel less concerned about the potential consequences of riding recklessly, leading to an increase in the number of accidents. On the other hand, the helmet does decrease the probability of injury in the event of a crash, but an increase in the number of crashes could lead to an overall increase in the number of injuries, offsetting the protective effect of the helmets. Therefore, the net impact of the new helmets on the number of scooter injuries is unclear, and further study is needed to determine their overall effect.
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Solve the system of equations: 3 � - � = 17 5 � + 3 � = 5
The solution to the system of equations 3x - y = 17 and 5x + 3y = 5 is (4, -5)
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Given the equations:
3x - y = 17 ; multiplying by 3:
9x - 3y = 51 (1)
5x + 3y = 5 (2)
To solve by elimination method, subtract add 2 to equation 1, hence:
14x = 56
Dividing by 14:
x = 4
Put x = 4 in equation 2:
5(4) + 3y = 5
20 + 3y = 5
3y = -15
y = -5
The solution is (4, -5)
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Elizabeth practices the piano 504 minutes in 2 weeks. Assuming she practices the
same amount every week, how many minutes would she practice in 1 weeks?
Elizabeth will practice piano for 252 minutes in one week by solving function f(x)=504x where x = time in multiple of 2years.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
As given
f(x)=504x where x = time in multiple of 2 years
For 1 year x=1/2
Hence,
y=504*1/2
y=252 minutes
Elizabeth will practice piano for 252 minutes in one week.
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Given the system of equations: 5x + 2y = 3 4x − 8y = 12 Solve for (x, y) using elimination.
To solve the system of equations using elimination, we can follow these steps:
Multiply the first equation by 4, and the second equation by 2:
20x + 8y = 12
8x - 16y = 24
Add the two equations together:
20x + 8y = 12
8x - 16y = 24
28x - 8y = 36
Solve for x by dividing both sides of the equation by 28:
x = 36/28 = 9/7
Substitute the value of x back into one of the original equations:
5x + 2y = 3
5(9/7) + 2y = 3
45/7 + 2y = 3
2y = -42/7
Solve for y by dividing both sides by 2:
y = -21/7
So the solution of the system of equations is (x,y) = (9/7, -21/7)
It is also worth noting that we could have also multiplied the first equation by -2 and the second equation by 5 and added them together, this will also lead us to the same solution.
On the coordinate plane, the segment B(1-4) toC(7,4) forms, one side of triangle BCD. The triangle has an area of 15 square units select all points where D you could be
A coordinate plane is a two-dimensional graph that is used to locate points in a plane using an x-axis and a y-axis.
Explain about coordinate plane:Each point on the plane is defined by an x-coordinate (horizontal position) and a y-coordinate (vertical position). It is used in various branches of mathematics and sciences, such as geometry, algebra, and physics. It is a fundamental tool for graphing and analyzing mathematical equations and functions.To find the possible coordinates of point D, we first need to find the equation of the line that passes through points B(1, -4) and C(7, 4). We can use the slope-intercept form (y = mx + b) to find the equation of the line. Each point on the plane can be identified by its x and y coordinates, which are the distances from the point to the y-axis and x-axis, respectively. The x-coordinates are measured to the right of the y-axis, and the y-coordinates are measured upward from the x-axis. The coordinate plane is used to graph equations and inequalities, plot points, and identify patterns in data. It is a fundamental tool for understanding and manipulating mathematical concepts.The slope of the line is (4-(-4))/(7-1) = 8/6 = 4/3.
The y-intercept is -4.
So the equation of the line is y = (4/3)x - 4.
We know that the area of triangle BCD is 15 square units. To find the possible coordinates of point D, we can use the formula for the area of a triangle (A = (1/2)bh). Since we know the area and the base, we can find the height of the triangle and use that to find the possible coordinates of point D.
The equation of the line is y = (4/3)x - 4. We can use this equation to find the y-coordinate of point D.
y = (4/3)x - 4
15 = (1/2)(x)((4/3)x - 4)
By solving the equation above, we can find the possible x coordinate of point D, which are (-2, -4/3) and (12, 4). Therefore, the possible coordinates of point D are (-2, -4/3) and (12, 4).
Note: you can use the same formula to find the y coordinate if you were given the x coordinate of D, but it gives the same solution.
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