A circle's arc length can be determined from its radius and central angle using the formula Length of an Arc = r, where is in radians.
How to Find Arc Length With the Radius and Central Angle?Length of an Arc = r, where is in radians, is a formula that may be used to calculate the arc length of a circle given its radius and central angle. A circle's length is equal to (r/180)r, where r is the radius and is the angle. The length of the arc on a circle of radius r intercepted by a central angle is S = r.
Multiply the radius (6 in) by the central angle's measurement in radians to determine the length of the arc. Remember that the angle must be expressed in radians in order to employ the calculation s = r.
Assuming that is measured in radians, the formula for the length s of the arc that is intercepted on a circle with radius r by a central angle is: s = r.
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An isosceles triangle has base angles that each measure x degrees. The measure of the third angle is 72 degrees. Write an equation that can be used to determine x, the measure of each base angle of the isosceles triangle.
Answer:
lol i don't know this
Step-by-step explanation:
lol= laugh out loud
For what value of k does the system of equations kx 2y 5 and 3x 4y 10 have no solution?.
Hence value of k does the system of equations k x +2y= 5 and 3x - 4y =10 have no solution[tex]\frac{-3}{2}[/tex]
The given system of equations:
k x + 2y = 5
⇒ k x + 2y - 5 = 0 ….( i)
3x - 4y = 10
⇒3x - 4y - 10 = 0 …(ii)
These equations are of the forms:
a1x + b1y + c1 = 0
a2x + b2y + c2 =0
where, a1 = k
b1 = 2
c1 = -5
a2= 3
b2 =-4
c2 = -10
[tex]\frac{a1}{a2} \neq \frac{b1}{b2}[/tex]
[tex]\frac{k}{3} \neq \frac{2}{-4}[/tex]
[tex]k\neq \frac{-3}{2}[/tex]
Thus for all real values of k other than −3/2 ,
the given system of equations will have a unique solution.
(ii) For the given system of equations to have no solutions, we must have:
[tex]\frac{a1}{a2} = \frac{b1}{b2}\neq \frac{c1}{c2} \\\\ \frac{k}{3} = \frac{2}{-4}\neq \frac{-5}{-10} \\ \\ \frac{k}{3} = \frac{2}{-4}\\ \\ \frac{k}{3} \neq \frac{1}{2} \\ \\ \\k \neq \frac{3}{2} \\\\k =\frac{-3}{2} \\[/tex]
Hence value of k does the system of equations k x +2y= 5 and 3x - 4y =10 have no solution[tex]\frac{-3}{2}[/tex]
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How do you find the inverse of a function in vertex form?.
The inverse of a function in vertex form can be determined by substituting the function in the standard form of a quadratic function
The various steps to find the inverse of a function in vertex form can be noted as -
First, it is required to write the equation in the quadratic function's usual form: y = a(x - h)² + k, where (h, k) is the vertex.The following formula should be changed: x = a(y - k)² + h.Now, by putting y on one side of the equation, solve for y: y = (x - h)/a² + kThe equation can be made simpler by adding -1/a² to the numerator and denominator to get the following result: y = -(x-h)²/a + kThe function will now be in vertex form, with the leading coefficient -1/a, and the vertex (h, k).Read more about vertex form on:
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What is the formula of median for class 7?.
The formula of median is Med(x) = X [n=1/2].
The median of the data is the value of the middle observation found after sorting the data in ascending order. In many cases, it is challenging to consider the entire data set as a representation; in these cases, median is helpful. The median is a simple metric to calculate among statistical summary metrics. Since the data that is in the center of a sequence is used as the median, the median is also known as the Place Average.
Median Formula When n is Odd
Median = [(n + 1)/2] th term
Median Formula When n is Even
Median = [(n/2) th term + ((n/2) + 1) th term]/2
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On parallelogram ABCD below, if A(1, 1), B(8, 5), C(5,-5) and D(-2,-9), what are the coordinates of point E?
The coordinates of point E on the parallelogram are given as follows:
(3, -2).
How to obtain the coordinates of point E?The coordinates of point E are obtained considering that the point E is the midpoint of segment AC, hence it's coordinates are the mean of the coordinates of A and C.
Then the x-coordinate of point E is obtained as follows:
x = (1 + 5)/2 = 3.
The y-coordinate of point E is obtained as follows:
y = (1 - 5)/2 = -4.
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Consider the rectangle with a width of 6 cm and a length of 9 cm. Write a ratio of the length to the width and simplify.
Answer:
Step-by-step explanation:
ttt
(05.05 MC)
Using the two-way table, what percentage of the students that do not like to travel out of state like camping? Round to the nearest whole percent.
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals
Likes Camping 52 38 90
Does Not Like Camping 36 74 110
Column totals 88 112 200
a
32%
b
34%
c
38%
d
42%
AND
(05.05 LC)
Dean collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected:
Favorite Sport
Swimming Running Volleyball Row totals
Grade 8 0.17 0.24 0.05 0.46
Grade 9 0.14 0.18 0.22 0.54
Column totals 0.31 0.42 0.27 1
Based on the data, which statement is most likely correct?
a
In Grade 8, 17 students liked swimming.
b
In Grade 9, 27% of students liked volleyball.
c
In Grade 9, 14 students liked running.
d
In Grade 9, 18% of students liked running.
The percentage of the students that do not like camping like travelling out of state is 33% and this can be determined by using the given data.
what is meant by camping?
The statement is most likely In Grade 9, 18% of students liked running is a correct answer.Based on the data, in grade9, 27 of student liked volleyball most likelyed.Using the two-way table, what percentage of the students that do not like to travel out of state like camping near whole percent is 42%.Camping is an outdoor activity that involves spending the night somewhere other than your house, either without shelter or with just a tent or other form of portable shelter.Usually, people travel from more urbanized regions to spend time outside in more rural ones in search of enjoyable or educational activities.Camping is distinguished from day trips, picnics, and other equally brief recreational activities by the night (or more) spent outside.To the complete questions is;
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals Likes Camping 52 38 90
Does Not Like Camping 36 74 110
Column totals 88 112 200
a)32% b)34% c)38% d)42%
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Use point-slope form to write the equation of a line that passes through the point (-14,6) with slope -7/4
By using the point-slope form, the equation of a line that passes through the point (-14, 6) with slope -7/4 is equal to y = -7x/4 + 30.5.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided above, we have the following slope and data points on the line:
Points = (-14, 6).Slope, m = -7/4At data point (-14, 6), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 6 = -7/4(x - (-14))
y - 6 = -7/4(x + 14)
y = -7x/4 + 24.5 + 6
y = -7x/4 + 30.5
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The ratio to the total number of tudent in cla i 4 to 7. How many tudent are girl if the cla ha 21 tudent in all
There are total of 12 girls in the class.
what is ratio?A mathematical comparison of two or more values or quantities is called a ratio. It can be used to compare the relative sizes or amounts of various items since it expresses the relationship between the values in terms of a proportion or a fraction.
Let the number of girls in the class be x and the number of boys in the class be y
so total number of students in the class is x+y
ration of number of girls to the total number of students is x/(x+y)
given that total number of student is x+y which is 21
so x/21 = 4/7
=> x= (21*4)/7
=> x= 3*4
=> x=12
so the total number of girls in the class is 12.
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Complete question:
The ratio of girls to the total number of students in class is 4 to 7. How many students are girls if class has 21 students in all?
help me with my ALEKS topics pls, i have 5 left and i need to finish them quick
Answer:
V ≈ 13036 ft³
Step-by-step explanation:
the volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height )
here diameter = 19, then r = 19 ÷ 2 = 9.5 and h = 46 , then
V = 3.14 × 9.5² × 46
= 3.14 × 90.25 × 46
≈ 13036 ft³ ( to the nearest whole number )
Suppose that the functions u and w are defined as follows.
u(x) = -x +3
w (x) = 5x+2
Find the following.
(w-u) (-5) = [
(uw) (-5) =
0⁰ 0/6
X
The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
What is composite function?Function composition is an operation о used in mathematics that takes two functions, f and g, and creates a function, h = g о f, such that h(x) = g. The function g is applied in this operation to the outcome of applying the function f to x.
Given:
u(x) = x^2 + 3
w(x) = √x+2
We have to find (w о u)(2) and (u о w)(2).
First to find (w о u)(x)
(w о u) = w(u(x))
= w(x^2 + 3)
(w о u) = √(x^2 + 3) + 2
(w о u)(2) = √(2^2 + 3) + 2
(w о u)(2) = √7 + 2
Now to find (u о w).
(u о w)(x) = u(w(x))
= u(√x+2)
= (√x+2)^2 + 3
= x + 4√x + 4 + 3
(u о w)(x) = x + 4√x + 7
(u о w)(2) = 2 + 4√2 + 7
(u о w)(2) = 9 + 4√2
Hence,
The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
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¿Cuáles son las medidas de un cono (radio, altura) si su volumen es 500 cm3?
The dimensions of the cylinder are -
{r} = √500/πh
{h} = (500/r²)
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the volume of the cylinder as -
V = 500 cm³
We can write -
V = 500
So, we can write -
πr²h = 500
So, we can write -
{r} = √500/πh
{h} = (500/r²)
Therefore, the dimensions of the cylinder are -
{r} = √500/πh
{h} = (500/r²)
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{Question in english -
What are the measurements of a cylinder (height, radius) if its volume is 500 cm3}
Nelly works at an hourly rate of $11. 28 per hour and worked 45 hours last week. She earns overtime for hours exceeding 40 hours. She is paid overtime at a rate of time and a half. What was her gross pay last week?.
Nelly's gross pay is $451.20 + $84.60 = $535.80.
Gross pay refers to the total amount of money an employee earns before any deductions or taxes are taken out. It is the total amount of money earned by an employee for the hours worked, including any overtime or bonuses.
First, we calculate her regular pay.
She worked 45 hours last week, and her regular hourly rate is $11.28 per hour. Therefore, her regular pay for the week is 40*$11.28 = $451.20. This is the pay she receives for the hours she worked up to 40 hours, which is considered the standard workweek.
Next, we calculate her overtime pay. Nelly worked 45 hours last week, and she is entitled to overtime pay for hours exceeding 40 hours. Therefore, she worked 45-40 = 5 hours of overtime.
Since she is paid time and a half for overtime, her overtime pay is calculated by multiplying her regular hourly rate by 1.5. Therefore, her overtime pay is 5*$11.28*1.5 = $84.60.
Finally, we add her regular pay and her overtime pay to get her gross pay. Her gross pay is the total amount she earns for the week, including both her regular pay and her overtime pay.
Therefore, her gross pay is $451.20 + $84.60 = $535.80.
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How do you find the range of Class 6?.
The range is calculated as follows by combining the lowest and highest values. Organize the information in ascending or descending order first, then calculate the maximum and minimum values.
The range of a particular data set is the distinction between those maximum and minimum values. Range = Maximum Value–Minimum Value
The range of a set of data is the differential between the collective's maximum and minimum values.
Domain and range are keywords in relations and functions. The range is the set of all potential dependent values produced by a relation from a domain value.
To identify the range, first, arrange the data in ascending or descending order to gain a clear picture of the data's Maximum and Minimum terms.
Then, to get the data range, subtract the lowest value from the largest value in the collection.
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Complete each congruency statement, and name the rule used.
If you cannot show the triangles are congruent from the given information, leave
the triangle's name blank and write CNBD for "CanNot Be Determined" in place
of the rule.
Answer: [tex]\triangle LAW \cong \triangle WKL[/tex] by ASA
Step-by-step explanation:
[tex]\angle AWL \cong \angle WLK[/tex] (right angles)[tex]\angle ALW \cong \angle LWK[/tex] (given)[tex]\overline{WL} \cong \overline{WL}[/tex] (reflexive)Therefore, [tex]\triangle LAW \cong \triangle WKL[/tex] by ASA.
Simplify the following polynomial expression.
(5x^4 - 9x^3 + 7x -1) + (-8^4 - 3x + 2) - (-4x^3 + 5x - 1) (2x - 7)
Answer:
[tex]\boxed{\mathrm{Option \;D: 5x^4-37x^3-6x^2+41x-6}}[/tex]
Step-by-step explanation:
You can solve such multiple choice questions using a trick. This especially is useful in a time constrained question
Consider only the coefficients of the terms relating to x⁴ and the constant
If you expand (-4x³ + 5x - 1)(2x - 7) this will work out to
(--4x³) (2x) +..... + (-1)(-7)
This will result in (- 8x⁴ +..... + 7)
Since there is a negative sign before this last term, expanding will change the signs of the terms
-(-8x⁴ + ..... + 7) = 8x⁴ -7
Add the coefficients of the x⁴ terms to get
(5 - 8 + 8)x⁴ = 5x⁴
Add the constants of the individual terms
--1 + 2 - 7 which is -6
So the simplified polynomial is of the form
5x⁴ +....... - 6
Only option D fits these values, so the correct choice is Option D:
[tex]\mathrm{5x^4-37x^3-6x^2+41x-6}[/tex]
ANSWER
--------------------------------------------------------------------------------------------------
If you want to do it the hard way,
First evaluate the last product using FOIL:
[tex]\left(-4x^3+5x-1\right)\left(2x-7\right)\\\\= \left(-4x^3\cdot \:2x-4x^3\left(-7\right)+5x\cdot \:2x+5x\left(-7\right)-1\cdot \:2x-1\cdot \left(-7\right)\right)\\\\= \left(-8x^4+28x^3+10x^2-37x+7\right)\\\\[/tex]
With the negative sign in front of this expression this becomes:
[tex]-\left(-8x^4+28x^3+10x^2-37x+7\right)\\\\= 8x^4-28x^3-10x^2+37x-7\\\\[/tex]
From the original polynomial expression, group like terms:
[tex]\left(5x^4-9x^3+7x-1\right)+\left(-8x^4+4x^2-3x+2\right)-\left(-4x^3+5x\:-1\right)\left(2x-7\right)\\\\[/tex]
[tex]=\left(5x^4-9x^3+7x-1\right)+\left(-8x^4+4x^2-3x+2\right) + (8x^4-28x^3-10x^2+37x-7)\\\\[/tex]
helphelp plsssssssss
-8 hshdjdbdkdndidjdndjdodjfodjdjd
Step-by-step explanation:
2*(-2)-4=
-4-4=
-8
How do you simplify 9x?.
To simplify 9x, you need to use the distributive property.
The distributive property states that when you multiply a number by a group of numbers or variables, you can separate the group into individual components, multiply each component by the number, and then add the products together.
For example, 9x can be simplified as follows:
9x = 9x(1)
Using the distributive property, you can separate the 1 into individual components:
9x = 9x(1) = 9x(1 + 0)
Then, you multiply each component by the number:
9x = 9x(1) = 9x(1 + 0) = 9x(1) + 9x(0)
And finally, you add the products together:
9x = 9x(1) + 9x(0) = 9x + 0
Therefore, 9x can be simplified to 9x.
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There are 5280 feet in a mile and about 3.28 feet in a meter. Given that sound travels about 343 meters per second what’s is the distance in miles from alyssa to the lighting bolt
Answer: We know that sound travels about 343 meters per second. To convert the distance in meters to miles, we need to use the conversion factor that there are 3.28 feet in a meter and 5280 feet in a mile.
1 mile = 5280 feet = 5280/3.28 meters = 1600 meters
Therefore, the distance in miles from Alyssa to the lightning bolt can be calculated by dividing the distance in meters by the number of meters per mile:
distance in miles = distance in meters/1600
So, the distance in miles from Alyssa to the lightning bolt is 343 meters/1600 miles = 0.215 miles (approx)
Note that this calculation is based on the assumption that sound travels 343 meters per second and it's an approximation.
Step-by-step explanation:
Kevin had to measure the diameter of a hair strand and the diameter of a grain of sand for his science experiment. He found the diameter of the hair strand to be 0.00006 inches and the diameter of a gain of sand to be 1.3 x 10^-3 inches.
The diameter of the grain of sand is _____ x 10^-3 inches more than the diameter of the hair strand.
M,
Lauren has watermelons and oranges in a ratio of 88:14. How many watermelons
does she have if she has 7 oranges?
Answer:
Lauren has 44 watermelons
Step-by-step explanation:
Let us use W to denote the number of watermelons and O to denote the number of oranges
We have
W:O = 88:14
This can be represented as a fraction:
[tex]\dfrac{W}{O} = \dfrac{88}{14}[/tex]
Divide numerator and denominator of [tex]\dfrac{88}{14}[/tex] by 2
[tex]\dfrac{88 \div 2}{14 \div 2} = \dfrac{44}{7}\\\\\\\\\mathrm{So\; \dfrac{W}{O} = \dfrac{44}{7}}\\\\[/tex]
This means for every 7 oranges there are 44 times that number of watermelons
Since we are given that there are 7 oranges she should have 44 watermelons
Another way of looking at this is from the relation
[tex]\dfrac{W}{O} = \dfrac{44}{7}}\\\\[/tex]
Putting in O = 7 we get
[tex]\dfrac{W}{7} = \dfrac{44}{7}\\\\[/tex]
Since the denominators are the same the numerators must be the same i.e. W = 44
Lauren has 44 watermelons
Re-write the quadratic function below in Standard Form
y= 4(x-7)(x-1)
Standard form of the quadratic function is,
⇒ y = 4x² - 32x + 28
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 quadratic equation is,
⇒ y = 4 (x - 7) (x - 1)
Now, We can simplify the equation in standard from as;
⇒ y = 4 (x - 7) (x - 1)
⇒ y = 4 (x² - x - 7x + 7)
⇒ y = 4 (x² - 8x + 7)
⇒ y = 4x² - 32x + 28
Thus, The standard form is,
⇒ y = 4x² - 32x + 28
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PLS HELP ASAP - algebra 2
India is studying microbiology and is doing an experiment with bacteria. She notices that one of her colonies is dying at a rate of 5% per day. if the original number of colonies was 2757, answer the following:
a. write the equation to model the data that India is witnessing
b. sketch a graph of your equation from part a.
An equation to model the data that India is witnessing is f(x) = 2757(0.95)^x.
A graph of this exponential equation is shown in the image attached below.
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical expression:
f(x) = ab^x
Where:
a represents the initial value or y-intercept.x represents time.b represents the rate of change.Since her colonies is dying at a rate of 5% per day, this ultimately implies that the relationship is geometric and the rate of change (decay rate) is given by:
Rate of change (decay rate) = 100 - 5 = 95% = 0.95.
Substituting the parameters into the exponential equation, we have the following;
f(x) = 2757(0.95)^x
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What is 1 4 of a circle in degrees?.
1 in 4 angle of slope in degree is 90°.
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located.
The inverse tangent function is called arctangent, often known as arctan or tan-1. Tangent only has a limited domain for its inverse function.
So to find the 1 in 3 angle we have to put the value 1/3 in arctan function
which is tan inverse function.
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
The probability that a student studied for exactly 1 hour is 0.23 Or 23%. The correct option is A.
What is probability?
Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
A table is given where the first column represents the number of hours a student studied math and the second column represents the number of students.
The sum of the second column is 30. So it is the total number of students. And only 7 of them studied mathematics for 5 hours.
Therefore, The probability that a student studied for 5 hours is,
= 7/30.
= 0.23 or 23%.
Therefore, the correct option is A. 23.0.
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The question is incomplete. Your most probably complete question is given below:
23.0
0.70
0.23
0.16
How do you know if its inverse?.
The process to identify if the function is inverse is identified through the horizontal line test.
Function in math is known as a correspondence from one value x of the first set A to another value y of the second set B.
Here we need to identify the way to know that whether the given unction is inverse function or not.
By using the horizontal line test that is If any horizontal line intersects the graph of f more than once then the function f does not have an inverse.
Where as If no horizontal line intersects the graph of f more than once, then the function f does have an inverse.
Here we have also have the property of having an inverse is very important in mathematics, and it has a name.
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What is the definition of the sine ratio in a right triangle?.
The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine.
If you know at least one side of the triangle and one of the acute angles, you can use this function to calculate the length of the side.The trigonometric ratio sine compares the lengths of the right triangle's two sides. Sin, though commonly abbreviated to sin, is actually pronounced sine. If you know at least one side of the triangle and one of the acute angles, you can use this function to calculate the length of the side. In a nutshell, the sine, cosine, and tangent ratios are the three basic trig ratios.To learn more about the sine triangle here
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What is the nature of roots of the quadratic equation 5x² 2x 3 0?.
The roots are hypothetical, meaning that they have two false roots. As a result, a quadratic equation has real, unequal, and irrational roots.
What is the roots equation's nature?The quadratic equation with roots ax2 + bx + c = 0 has real and unequal roots when a, b, and c are real numbers, a 0, and the discriminant is positive.
5x 2 2x+3=0 a=5, b=2, c=3, D=b 2 4ac D=56 0
What kind of roots are they?The equation's nature of roots indicates whether it contains rational, irrational, or fictitious roots. Imaginary roots and unreal roots are synonyms.
What makes a quadratic equation what it is?A degree two equation of the form ax2+bx+c = 0—where an is not equal to 0—is a quadratic equation. The quadratic equation's roots are the value of x in this equation. The only roots of a quadratic equation are two. These roots can have both real and made-up characteristics.
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Full Question = Write the nature of roots of the quadratic equation 5x2 - 2x + 3 = 0.
Cahew and peanut are combined to make a nut mixture. At leat 1/4 of the mixture, by weight, i cahew, and the total weight of the mixture cannot exceed 48 ounce. Which ytem of inequalitie model thi ituation
The weight of the cashews plus the weight of the peanuts cannot be more than 192 ounces and the weight of the cashews must be at least one-fourth of the total weight of the mixture.
Step 1: Let c = weight of cashews
Step 2: Let p = weight of peanuts
Step 3: 0.25c + p ≤ 48
Step 4: Multiply both sides by 4
Step 5: 4(0.25c + p) ≤ 4(48)
Step 6: c + p ≤ 192
This system of inequalities models the situation of combining cashews and peanuts to make a nut mixture. The first inequality states that the weight of the cashews plus the weight of the peanuts cannot exceed 48 ounces, and the second inequality states that the weight of the cashews must be at least one-fourth of the total weight of the mixture. To model this situation, we let c equal the weight of the cashews and p equal the weight of the peanuts. We then multiplied both sides of the first inequality by four to get the second inequality, which states that the weight of the cashews plus the weight of the peanuts cannot exceed 192 ounces. This system of inequalities accurately models the situation of combining cashews and peanuts to make a nut mixture, and it ensures that the weight of the cashews is at least one-fourth of the total weight of the mixture.
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the table below shows imformation about the distance walked by some hikers work out the minimum number of hikers who could have walked between 8 miles and 19 miles work out the maximum number of hikers who could have walked between 8 and 19 miles
PLEASE HELP!
The minimum number of hikers that could have walked between 8 miles and 19 miles is given as follows:
7.
The maximum number of hikers that could have walked between 8 miles and 19 miles is given as follows:
17.
How to obtain the amounts?The frequency table gives the number of observations on each interval.
Then the minimum number of hikers that could have walked between 8 miles and 19 miles is obtained when:
All the 4 observations in the interval 5 <= x < 10 are less than 8.All the 6 observations in the interval 15 <= x < 20 are more than 19.Hence the minimum amount is of 7.
The maximum number of hikers that could have walked between 8 miles and 19 miles is obtained when:
All the 4 observations in the interval 5 <= x < 10 are more than 8.All the 6 observations in the interval 15 <= x < 20 are less than 19.Hence the maximum amount is of 4 + 7 + 6 = 17.
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