Answer:
f(x)= 2x-9
f(-2)= 2(-2)-9
f(-2)= -4-9
=-13
What are the more appropriate measures of center and spread for this data
set?
Except Option - A all satisfy the more appropriate measures of center and spread for the data that is median and IQR.
Given that,
We have to find what are the more appropriate measures of center and spread for data.
We know that,
Mean, median, and mode are the three central tendencies, and median is the more accurate indicator.
This is because
i) Extreme values affect the mean.
ii) If there are more outliers, the mean is in error.
iii) Means that are biassed to the right or left may not accurately reflect the nature of the data.
However, median is preferable to mean because it represents the center entry and is unaffected by extreme items or outliers.
Since extreme items will show higher standard deviation and some outliers may be misleading, IQR is a superior spread measurement tool. However, IQR provides an excellent idea.
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Write an equation of the line that passes through (-3,3) and is perpendicular to the line 2y = 8x - 6
The equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6 is y = (-1/4)x + 9/4.
What is the equation of line that passes through (-3,3) and is perpendicular to 2y = 8x - 6?The slope-intercept form is expressed as;
y = mx + b
Where m is slope and b is the y-intercept.
Given the equation of the original line.
Write in slope intercept form
2y = 8x - 6
y = 8x/2 - 6/2
y = 4x - 3
Using the slope intercept, slope m is 3.
The equation of a perpendicular line to 2y = 8x - 6 must have a slope that is the negative reciprocal of the original slope.
Slope of perpendicular line = -1 / ( 4 )
Slope of perpendicular line = -1/4
Plug the slope m = -1/4 and point (-3,3) into point-slope formula and simplify.
( y - y₁ ) = m( x - x₁ )
( y - 3 ) = (-1/4)( x - (-3) )
( y - 3 ) = (-1/4)( x + 3 )
y - 3 = (-1/4)x - 3/4
y = (-1/4)x - 3/4 + 3
y = (-1/4)x + 9/4
Therefore, the equation of the perpendicular line is y = (-1/4)x + 9/4.
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Given that cot 0 =
5
-, find csc 0.
√11
According to the given cosecant function the value of csc 0 is equal to 6/5.
What is the cosecant function?The sine function has a reciprocal called the cosecant function. The cosecant function is the hypotenuse divided by the opposite side, just like the sine function is the opposite side divided by the hypotenuse. The hypotenuse and legs are terms for the two sides that are not at the right angle.
It is given that:
[tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
According to trigonometric identity,
[tex]csc^2\ alpha - cot^2\alpha = 1\\csc^2\ 0 -\frac{11}{25} =1\\csc^2\ 0 = \frac{36}{25} \\csc\ 0= \frac{6}{5}[/tex]
Therefore the value of csc 0 is equal to 6/5.
Complete question;
Given that [tex]cot\ 0=\sqrt{\frac{11}{5} }[/tex]
find csc 0.
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factor each square root
0.7 times square root of 300
-0.125 times square root of 192
Answer:
To factor the first expression, "0.7 times square root of 300", we can rewrite it as:
0.7 * sqrt(300)
The prime factorization of 300 is 2 * 2 * 3 * 5 * 5, so we can rewrite the expression as:
0.7 * sqrt(2 * 2 * 3 * 5 * 5)
Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:
0.7 * sqrt(2) * sqrt(2) * sqrt(3) * sqrt(5) * sqrt(5)
Combining like terms, we get:
0.7 * 2 * sqrt(2) * sqrt(3) * sqrt(5)
= 1.4 * sqrt(2) * sqrt(3) * sqrt(5)
This is the fully factored form of the expression "0.7 times square root of 300".
To factor the second expression, "-0.125 times square root of 192", we can rewrite it as:
-0.125 * sqrt(192)
The prime factorization of 192 is 2 * 2 * 2 * 2 * 2 * 2, so we can rewrite the expression as:
-0.125 * sqrt(2 * 2 * 2 * 2 * 2 * 2)
Since the square root of a number is the same as the square root of that number's prime factorization, we can rewrite the expression as:
-0.125 * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2) * sqrt(2)
Combining like terms, we get:
-0.125 * 6 * sqrt(2)
= -0.75 * sqrt(2)
This is the fully factored form of the expression "-0.125 times square root of 192".
Answer:
for the second one the answer is - square root of 3
Step-by-step explanation:
i could only solve the second one sorry
PLEASE HELP!
An architect is designing a circular window to be installed in the
gable of a house. The metal window frame will be 1 foot wide and will be bordered by
the roof above and a wood beam below. The distance from the center of the window to the roof is 3 feet. What will be the circumference of the circular glass pane that will be
needed?
Exact Circumference = 4pi feet
Approximate Circumference = 12.56 feet (when using pi = 3.14)
======================================================
Explanation:
The larger circle has a 3 foot radius.
The inner circle has a 3-1 = 2 foot radius.
Let's find the circumference of the smaller inner circle, which represents the glass window and ignores the metal frame surrounding it.
C = 2pi*r
C = 2pi*2
C = 4pi
The exact circumference is 4pi feet. This is the perimeter around the circle.
If you wanted, you can use an approximation like pi = 3.14 to find that 4pi = 4*3.14 = 12.56 feet is the approximate circumference.
Find the length of side xx in simplest radical form with a rational denominator. 3
The length of x is 6 in simplest radical form.
What is a right-angled triangle?'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'
According to the given ,
Perpendicular = 3
Hypotenuse = x
We know,
sin∅ = 3/x
∅ = 30°
⇒ sin30 = 3/x
⇒ 1/2 = 3/x [ sin30 = /2 ]
⇒ x = 3 * 2
⇒ x= 6
Hypotenuse = 6
Applying Pythagoras theorem:
Hypotenuse² = Perpendicular² + Base²
6² = 3² + Base²
6² - 3² = Base²
Base² = 25
Base = √25
Base = 5
We can conclude the value of x to be 6.
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A bag contains 9 tiles, each with a different number from 1 - 9. You chose a tile without looking, put it aside, choose a second tile without looking, put it aside, then choose a third tile without looking. What is the probability that you choose tiles with the numbers 1, 2, and 3 in that order?
Someone pls explain this. I know the answer is 1/504 but how do you get there?
The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation and is equal to 1/504.
What are permutations?Permutations refer to the arrangements of objects in certain order or way.
The number of alternative arrangements in a set can be calculated mathematically using a permutation where the order of the configurations is important.
The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation.
The probability is obtained as 1 / ₉P₃
where;
₉P₃ = 9! / (9 - 3)!
₉P₃ = 9! / 6!
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1
₉P₃ = 504
Hence, the probability = 1/504
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I need the answer to this question
Answer:
it is not factorable
Step-by-step explanation:
There are no factors of 24 that will make -4, so it is not factorable
 A jar filled with maple syrup weighs 1.5 pounds. Two jars filled with honey weigh 3 pounds. What is the weight of the jar?
The weight of the jar after solving equation simultaneously is w=0.
Define system of linear equation.A set of two or more first-degree equations with two or more connected unknowns is known as a system of linear equations.
How to solve system of linear equation.A system of equations is solved by determining the value of each unknown until the system's equations are all satisfied. That is, it is necessary to find the values of the unknowns so that, when substituted, they will produce the suggested solution in both equations.
j+w=1.5
2j+w=3
Simultaneously solving gives
w=0
the weight of jar is 0.
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What’s the answer pls?
Therefore ,option 3 is hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.
Triangle definitionAny three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.
Here,
From the provided figure, it is clear that there are two triangles.
ABC and EFG are the triangles.
AB = EF
AC = FG
BC = EG
As a result, the triangles ABC and EFG are congruent according to the triangle's SSS theorem, and angle A is equal to angle D.
Therefore ,D and E are hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.
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What is the range of f(x) = 3* + 9?
O {yly<9}
O {yly>9}
O {yly> 3}
O {yly<3}
On solving the provided question, we can say that - the range [tex]|x + 1| = 0[/tex] [tex]x + 1 = 0 = > x = -1[/tex] and [tex]y = 3[/tex]
What is range?Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.
The regions where the absolute values are zero are known as the vertex points of an absolute value function.
[tex]|x + 1| = 0\\x + 1 = 0\\x = -1[/tex]
[tex]y = |-1 + 1| + 3\\y= 0 + 3\\y = 3[/tex]
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Evaluate x−25 when x=35.
Answer: 5
Step-by-step explanation:
1. Since you are told x=35. Plug it into x.
35-25
2. Simplify
35-25=5
Answer: 10
Step-by-step explanation:
x-25
substitute 35 for x
35-25 = 10
Question 2(Multiple Choice Worth 2 points)
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the length and g the line segment shown
!!!!please help me!!!!
The measurement of the hypotenuse is obtained as 9 units using the Pythagoras theorem.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
According to the graph -
The perpendicular measures 4 units.
The base measures 3 units.
To find the hypotenuse g apply the Pythagoras theorem -
(hypotenuse)^2=(base)^2+(perpendicular)^2
(g)^2=(3)^2+(4)^2
(g)^2=9+16
(g)^2=25
g=[tex]\sqrt{25}[/tex]
g=5
Therefore, line segment g measures 5 units.
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Select the correct answer. Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equation. g ( x ) = − 18 ( 1 3 ) x + 2 Which statement correctly compares the two functions on the interval [-1, 2]? A. Only function f is increasing, but both functions are negative. B. Both functions are increasing, but function g increases at a faster average rate. C. Both functions are increasing, but function f increases at a faster average rate. D. Only function f is increasing, and only function f is negative.
The correct comparison between two function is
Both functions are increasing, but function g increases at a faster average rate.
The Correct option is (B).
What is an increasing function?If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.
Let us assume
f(x) = [tex]ab^x[/tex]+ c
so, at x=0, f(0)=-10
a +c = -10
Similarly, by satisfying the above table in the f(x)
f(x) = -33/5 [tex](1/11)^x[/tex] - 17/5
and, f'(x) > 0
Thus, f(x) is an increasing function.
Now, g(x) = -18 [tex](1/3)^x[/tex] +2
g'(x) = -18 [tex](1/3)^x[/tex] log(1/3)
as log 1/3 <0
So, g'(x) > 0
Thus, g(x) is an increasing function.
For any x ∈ f(x) and x ∈ g(x), g'(x) > f'(x).
Hence, Both functions are increasing, but function g increases at a faster average rate.
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? Question
Drag the tiles to the correct boxes to complete the pairs.
Solve each equation using the square root property. Then, match the solutions to the equatio
Tiles
Help please
The solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,
x = [tex]\sqrt{13}[/tex] , - [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .
Given equations ,
[tex]x^{2}[/tex] + 81 = 0 ,[tex]x^{2}[/tex]-22 = -26 , 3[tex]x^{2}[/tex]-18=21 ,2[tex]x^{2}[/tex] +15 = -13
What is Quadratic equation ?
quadratic equation can be defined as the equation which is in the form of a[tex]x^{2}[/tex]+bx + c = 0 .
where a,b,c are constants .
By solving we get ,
[tex]x^{2}[/tex] +81 = 0
[tex]x^{2}[/tex] = -81
x = 9i , -9i
[tex]x^{2}[/tex] - 22 = -26
[tex]x^{2}[/tex] = -26 + 22
[tex]x^{2}[/tex] = -4
x = 2i,-2i
3[tex]x^{2}[/tex] - 18 = 21
3[tex]x^{2}[/tex] = 18+21
3[tex]x^{2}[/tex] = 39
[tex]x^{2}[/tex] = 13
x = [tex]\sqrt{13}[/tex] , - [tex]\sqrt{13}[/tex]
2[tex]x^{2}[/tex] +15 = -13
2[tex]x^{2}[/tex] = -13-15
2[tex]x^{2}[/tex] = -28
[tex]x^{2}[/tex] = -14
x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i
Hence the solutions for the given equations are x = 9i , -9i , x = 2i,-2i ,
x = [tex]\sqrt{13}[/tex] , - [tex]\sqrt{13}[/tex] , x = [tex]\sqrt{14}[/tex]i , - [tex]\sqrt{14}[/tex]i .
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x^2-2x+10=0
is the vertex of this parabola a maximum value or minimum value?
Step-by-step explanation:
minimum.
since the term with x² has a positive factor, this will grow exponentially in the positive direction compared to the other terms, so y (the functional value) will grow and grow with growing distance of x to the vertex.
and that makes the vertex the minimum of the parabola (which opens upwards).
if the factor would be negative (like -x² - 2x + 10), the vertex would be a maximum, and the parabola would open downwards.
Determine how many tablets, capsules, or ml to give to the patient. Answers should be either expressed as 1/2 tablets or rounded to the nearest whole tablet.
Ordered: Voltaren 450 mg
Label reads: Voltaren 150 mg tablets
How many tablet(s) should you give?
Answer: We know that the order from the doctor is 450mg
The stock available has a value of 150mg
Order/Available stock=450mg/150mg=3 tablets
Step-by-step explanation:
Which phrase should be inserted on the line correctly compare the two fractions? Use the models to help.
Answer:
is greater than
Step-by-step explanation:
7/8 is bigger than 2/4
Find the value of g(f(-1))
Answer: I say 13
Step-by-step explanation:
A band expects to put 15 songs on their next CD. The band wriand records 60% more songs than they expect to put on the CD. During the editing process, 50% of the songs are removed. How many songs will there be on the final CD
Answer:
18 songs
Step-by-step explanation:
15 x 1.6 = 24
24 x 0.75 - 18
1.1.2 Quiz: What Is Health?
Question 2 of 10
In order to maintain wellness, the parts of the health triangle always need to
be
Select two responses.
and
A. working together
B. apart from one another
C. independent of one another
D. in balance
Answer:
The World Health Organization (WHO) defines health as 'a state of complete physical, mental and social wellbeing and not merely the absence of disease or infirmity'
the width of a rectangle is 6n - 3.5 feet and the length is 3.5n + 7 feet
The perimeter of the rectangle is 19n + 7.
How to find the perimeter of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.
The perimeter of a rectangle is the sum of the whole sides of the rectangle.
Therefore, let's find the perimeter of the rectangle with width of 6n - 3.5 ft and length of 3.5n + 7 ft. Hence,
perimeter of a rectangle = 2(l + w)
where
l = lengthw = widthTherefore,
w = 6n - 3.5
l = 3.5n + 7
Hence,
perimeter of a rectangle = 2(6n - 3.5 + 3.5n + 7)
perimeter of a rectangle = 2(6n + 3.5n - 3.5 + 7)
perimeter of a rectangle = 2(9.5n + 3.5)
perimeter of a rectangle = 19n + 7
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Identify the slope and y-intercept of the line given by the equation: y = 1/3x - 2
Answer:
this is in the form of slope intercept. y = mx + b
m is the slope
and b is the y intercept
meaning that -2 is the y intercept
and 1/3 is the slope
(meaning on a graph you go up one, and over 3)
Step-by-step explanation:
Let a = (2, 1, 0), b = (3, -1, 2), c = (4, 0, 3)
Find the volume of the parallelopiped with sides a, b and c.
The volume of the parallelopiped is 14 cubic units
What is the volume of a parallelopiped?The volume of a parallelopiped with vector sides a, b and c is given by
V = (a × b).c
Given that the parallelopiped has sides
a = (2, 1, 0)b = (3, - 1, 2) and c = (4, 0, 3)So, we have that
(a × b) = (2, 1, 0) × (3, -1, 2) = (2 × 3)i × i + (2 × -1)i × j + (2 × 2)i × k + (1 × 3)j × i + (1 × -1)j × j + (1 × 2)j × k + (0 × 3)k × i + (0 × -1)k × j + (0 × 2)k × k
Since
i × i = 0, j × j = 0, k × k = 0, i × j = k, j × i = -k, j × k = i, k × j = -i, k × i = j, i × k = -j,So,
(a × b) = (2, 1, 0) × (3, -1, 2) = (6) × 0 + (-2)k + -(4)j + 3i + (-1) × 0 + (2)i + -(3)j + -(0)i + (0) × 0
= 0 -2k - 4j + 3i + 2i - 3j - 0 + 0
= 5i -7j - 2k
= (5, -7, -2).
Since (a × b) = (5, -7, -2)
So, the volume of the parallelopiped is
V = (a × b).c
= (5, -7, -2).(4, 0, 3)
= 5 × 4 + (-7 × 0) + (-2 × 3)
= 20 - 0 - 6
= 14.
So, the volume is 14 cubic units.
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Water flows at 2 feet per second through a pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.
a. What is the exact volume, in cubic inches, of water flowing out of the pipe every second? Leave your answer in terms of π.
The volume is
cubic inches.
Question 2
b. What is the height, in inches, of the water in the tank after 5 minutes?
The height in the tank is about
inches.
Question 3
c. How many minutes will it take to fill 75% of the tank?
It will take about
minutes.
a. The exact volume, in cubic inches, of water flowing out of the pipe every second is 32π cubic inches.
b. The height, in inches, of the water in the tank after 5 minutes is 600 feet.
c. It will take 0.132 minutes to fill 75% of the tank
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, Water flows at 2 feet per second through a pipe with a diameter of 8 inches so it is a cylindrical shape.
Therefore, The exact volume, in cubic inches, of water flowing out of the pipe every second is,
= π(4)²×2.
= 32π cubic inches.
The volume of the cylindrical tank is,
= π(7.5)²×6.
= 337.5π cubic inches.
The height, in inches, of the water in the tank after 5 minutes would be
= (32π×300)/π×16).
= 600 feet.
Now, 75% of 337.5π cubic inches is (0.75×337.5π) = 253.125π cubic inches.
Therefore the time required to fill 75% of the tank is,
= [(253.125π/32π)]/60 minutes.
= 7.91/60 minutes.
= 0.132 minutes.
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PLEASE HELP ME ASAP DUE TODAY NOW
Answer:
y = [tex]\frac{3}{4}[/tex]x + 3
Step-by-step explanation:
find the slope m
m = [tex]\frac{y2 - y1}{x2 - 21}[/tex]
m = [tex]\frac{3 - 0}{0 - - 4}[/tex]
m = [tex]\frac{3}{4}[/tex]
y = mx + b
find b
insert y1 and x1 into the equation
0 = [tex]\frac{3}{4}[/tex](-4) + b
0 = -3 + b
b = 3
y = [tex]\frac{3}{4}[/tex]x + 3
PLEASE ANSWER
Write an equation in point-slope form passing through the given point and parallel to the given line:
(- 4, 4)
y = - 7/4x + 2
Answer:
y-4=-7/4(x+4)
Step-by-step explanation:
Point Slope Form: y-y*sub*1=m(x-x*sub*1)
Parallel lines have the same slope as the line to which they are parallel.
y-4=-7/4(x+4)
Hope this helps :)
How do you do numb 3. please help
Step-by-step explanation:
first we need to identify the lines themselves.
the line from bottom left to top right is simply
y = x
the line is solid, so the points on the line are included.
the dotted line (the points on the line itself are not included) goes through
(0, 2) and (3, 0)
the y-intercept is therefore 2 (the y value when x = 0).
and for the slope
x changes by +3 (from 0 to 3).
y changes by -2 (from 2 to 0).
the slope is -2/+3 = -2/3
and the line is
y = (-2/3)x + 2
we see that the desired gray area is above both lines (">"), and we need to consider, whether the points in the lines are included or not.
so, the system of inequalities is
y >= x
y > (-2/3)x + 2
Three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally, how much of the candy bar will each person get?
The candy bar will each person get will be 4 / 15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that three friends went to the movies. They shared 4/5 of a candy bar. If they share the bar equally.
The amount of candy shared by each person will be,
Amount = ( 4 / 5 ) ÷ 3
Amount = 4 / 15
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Cones A and B both have volume 48pi cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B.
The possible radius and height for Cone B are 3 units and 16 units respectively
How to determine the radius and height of the cone
The formula for calculating the volume of a cone is expressed mathematically;
Volume = 1/3 πr²h
Given that;
π takes the value 3.1 4r is the radius of the coneh is the height of the coneFrom the information given, we have that;
Both cone A and B have volume of 48πCone A has 6 units and height of 4 unitsNow, let the height of cone B be 16 units
Substitute the value into the formula, we have;
48π = 1/ 3 × π × r² × 16
multiply the values, we have
48 = 16r²/3
cross multiply
16r² = 144
Divide both sides by 16
r² = 144/16
r² =9
Find the square root of both sides
r = 3units
Hence, the values are 3 units and 16 units
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