Answer:
1/4
Step-by-step explanation:
-1 1/6 ÷ (-4 2/3)
Change to improper fractions
- ( 6*1 +1)/6 ÷ -(3*4 +2)/3
-7/6÷ -14/3
Copy dot flip
-7/6 * -3/14
Rewriting
-7/14 * -3/6
-1/2 * -1/2
1/4
Is the following relation a function?
Answer:
No, Given relation is not a function.Explanation:
We know that , if any vertical line cuts the given graph of relation at exactly one point, then the relation can be called as function.
From Given graph , we find that the vertical line through any point on x-axis greater than zero (ex : X = 5) cuts the graph at more than one point.
Hence, Given relation is not a function.
Hope this helps...
Good luck on your assignment...
If f(x) = x-5, ther match each of the following.
4
1 f(-1)
-6
2. f(0)
3. f(1)
-3
4. f(2)
3
5. f(5)
-5
6. f(8)
0
Answer:
1. f(-1) = -6
2. f(0) = -5
3. f(1) = -4
4. f(2) = -3
5. f(5) = 0
6. f(8) = 3
Step-by-step explanation:
1. f(-1)=-1-5=6
substitute the x value into the equation.
2. f(0)=0-5=-5
3. f(1)=1-5=-4
4.f(2)=2-5=-3
5. f(5)=5-5=0
6. f(8)=8-5=3
Approximate 0.007349 to 3 significant figure
Answer:
0.007349 to 3 significant figure=0.00735
Step-by-step explanation:
Approximate 0.007349 to 3 significant figure
Significant figure start from 1 to 9 with the exclusion of 0
From the question above, there are two zeros after the decimal point, so it will be ignored because it is not a significant figure.
0.007349
The first significant number is 7 after 0
The second significant number is 3
The next
The third significant number is 4
The fourth significant number is 9
We want to approximate to three significant figure, so, all figure after 4(third significant figure) will be rounded up or down.
If the numbers are below 5(0, 1,2,3,4) they will be rounded down to 0
If the numbers are above 4(5,6,7,8,9), they will be rounded up to 1
So the number after 4 is 9, therefore it will be rounded up to make 4=5
0.007349 to 3 significant figure=0.00735
Besides the proportion of the sides, what else
must always be true for the polygons to be
similar?
Answer:
For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.
Step-by-step explanation:
HOPE THIS HELPS AND PLSSS MARK AS BRAINLIEST]
THNXX :)
What must be true for two polygons to be similar?
Similar polygons: For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.
Pls help me with this question
Answer:
[tex]\sqrt[5]{x^7}[/tex]
or (x ^ 1/5) ^7
or ([tex]\sqrt[5]{x}[/tex])^7
Step-by-step explanation:
x ^ 1.4
Rewriting the decimal as an improper fraction
x ^ 14/10
x ^ 7/5
The top is the power and the bottom is the root
[tex]\sqrt[5]{x^7}[/tex]
or (x ^ 1/5) ^7
or ([tex]\sqrt[5]{x}[/tex])^7
Write an equation of a line with the given slope and y-intercept. m = 1, b = 4 a) y = x – 4 b) y = –1x + 4 c) y = x + 4 d) y = 4x + 1
Answer:
y = x+4
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 1x+4
y = x+4
Answer:
[tex]\boxed{y=x+4}[/tex]
Step-by-step explanation:
The slope-intercept form of a line:
[tex]y = mx+b[/tex]
m is the slope and b is the y-intercept
[tex]m=1\\b=4[/tex]
[tex]y = 1x+4[/tex]
The population of a city increase exponentially at a rate of x% every 5 years
In 1960 the population was 60100
In 2015 the population was 120150
Calculate the value of x
Answer:
1.1460277. Put in your decimal place given to you.
This is the percentage rate.
Step-by-step explanation:
f(x)=0=60100
55=120150
60100=a*b^0
120150/60100=60100/60100*b^5
b^5^(1/5)=5square root(120150/60100)=1.14860277
The Goodsmell perfume producing company has a new line of perfume and is designing a new bottle for it. Because of the expense of the glass required to make the bottle, the surface area must be less than 150 cm2. The company also wants the bottle to hold at least 100mL of perfume. The design under consideration is in the shape of a cylinder. Determine the maximum volume possible for a cylindrical bottle that has a total surface area of less than 150 cm2. Determine the volume to the nearest 10mL. Report the dimensions of the bottle and the corresponding surface area and volume. This cylindrical perfume bottle needs to be boxed in a prism for sale on store shelves. The Goodsmell perfume producing company would like a box with the smallest possible surface area which will hold your design for the perfume bottle. Report the dimensions of the box and the corresponding area and volume. The pretty perfume company, Goodsmell’s competition, has also designed a new perfume bottle. The bottle is to be a spherical shape with a diameter of 7cm. Determine the volume and surface area of this bottle. The spherical bottle has a conical shaped lid with a diameter of 5cm and a height of 4.5cm. Given this information, calculate the volume and surface area of the lid of the spherical shaped bottle. Determine the dimensions of the smallest possible box which could be used to package Pretty Perfume’s new bottle with its spherical bottle and conical-shaped lid. However, this box is not shaped like a rectangular prism. Pretty Perfume would like to have unique packaging and have chosen to have a box shaped like a pyramid. Calculate the volume and surface area of this pyramid shaped box. The Final Product: Prepare a written report that includes: A clear and concise explanation of the process that you used to solve the problem. The calculations that you made, presented in an organized fashion. A rationale (reason) for your selection of values.
Answer:
1. r = 2.82 cm
h = 5.6 cm
The maximum volume possible to the nearest 10 mL = 140 mL
2. Size side of square base of box is 5.64 cm
Height of box = 5.6 cm
The surface area of the box is 189.96 cm²
The volume of the box is 178.13 cm³
3. The procedure for solving the problem was through noting that the shape of the cross-section of the pyramid is an isosceles triangle ans also that smallest possible box for the pretty perfume is one which fits the angle of inclination of the lid. This was found out by initially using the combined height of the perfume and the lid (placed to fit the spherical outline of the bottle) to calculate the dimensions of the pyramid, from which it was observed that the angle of inclination of the lid is larger than that of the calculated dimension, such that the lid outline would be visible and could eventually tear the perfume box
With the inclination angle, β, which is the base angle of the isosceles triangle, the angle at the top of the pyramid cross-section is calculated and the following relations are used to calculate the triangular cross-section of the pyramid
h = a·cos(α/2)
b = 2·a·cos(β)
[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]
[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]
With the calculated dimensions, a, b, and h the area, A, of the square pyramid is calculated as 2×b×a + b² and the volume, V, as 1/3×b²×h
The attached diagram shows the the cross-section of the perfume in the pyramid box.
Step-by-step explanation:
1. The surface area of the cylinder = 2πr² + 2πrh = 150 cm².........(1)
The volume of the cylinder, V = πr²h = 100 mL = 100 cm³..............(2)
From equation (2), h = 100/(π·r²)
Substituting the value if h in equation (1), we have;
2πr² + 2πr100/(π·r²) = 150
2πr² + 200/r = 150
(2πr³ + 200)/r = 150
2πr³ + 200 = 150×r
2πr³ -150·r+ 200 = 0
150 = 2πr² + 2πrh
h = (150 - 2πr²)/(2πr)
h = (75- πr²)/(πr)
Substituting the value of h in the equation for the volume, we have;
V = πr²h = πr²(75- πr²)/(πr)
V = 75·r - π·r³
At maximum volume, dV/dr = 0, we have
d(75·r - π·r³)/dr = 75 - 3·π·r²= 0
3·π·r²= 75
π·r² = 25
r = 5√π/π
h = (75- πr²)/(πr) = (75- π(5√π/π)²)/(π(5√π/π)) = (75 -25)/(5·√π)
h = 50/(5·√π)= 10·√π/π
The maximum volume = πr²h = π×25/π×10·√π/π = 250·√π/π = 141.05 cm³
The maximum volume possible = 141.05 cm³ = 141.05 mL
The maximum volume possible to the nearest 10 mL = 140 mL
The dimensions of the bottle are;
r = 2.82 cm
h = 5.6 cm
The surface area of the bottle = 2π(2.82)² + 2π×2.82 ×5.6 = 149.2 cm
2
Given that the cylindrical bottle has r = 2.82 cm and h = 5.6 cm, we have;
Size side of square base of box = 2 × 2.82 = 5.64 cm
Height of box = 5.6 cm
The surface area of the box = 2 × Area of base + 4 × Area of side
The surface area of the box = 2 *5.64^2 + 4 * 5.6 * 5.64 = 189.96 cm²
The volume of the box = Area of base × Height = 5.64^2*5.6 = 178.13 cm³
3. Diameter of spherical bottle = 7 cm = 2×r
Volume of the sphere bottle = 4/3πr³ = 4/3*3.5^3*π = 343/6·π = 179.6 cm³
The surface area of the sphere bottle = 4πr² = 4*(7/2)^2*π = 49·π = 156.94 cm²
3 i. The volume of a cone = 1/3πr²h = 1/3*(5/2)^2*4.5 = 9.385·π = 29.45 cm³
The surface area of a cone = πrS
S = √(4.5^2 + (5/2)^2) = 5.15
The surface area of a cone = π*2.5*5.15 = 40.43 cm²
3 ii. The depth of fitness of the lid on the bottle = 7/2 - √(7/2)^2 - 2.5^2) = 1.05
The total height of the spherical bottle with the conical lid = 7 + 4.5 - 1.05 = 10.45 cm
3 iii. Given that the box is shaped like a pyramid we have;
Width of the box at middle of the height of the spherical bottle = 7 cm
Height of the box = 10.45 cm
[tex]r = \dfrac{b}{2}\sqrt{\dfrac{2a - b}{2a + b}}[/tex]
[tex]R = \dfrac{a^{2}}{\sqrt{4a^{2}-b^{2}}}[/tex]
With the aid of a graphing calculator, the width of the square pyramid is found to be 12.12 cm
The volume = 1/3*12.12^2*10.45 = 511.68 cm²
The surface area = 2*12.12*√(12.12/2)^2 + 10.45^2) +12.12²= 439.7 cm²
The angle of inclination of the lid = tan⁻¹ (4.5/2.5) = 60.95°
The angle of inclination of the calculated box is tan⁻¹ (10.45/6.06) = 59.88
Since the lid is steeper, we make use of the angle of the lid
The base angles are thus = 60.95°
The angle at the top is thus 180 - 60.95*2 = 58.11°
Therefore, by the formula, we find that
a = 12.25 cm
b = 11.897 cm
h = a·cos(α/2)
h = 10.707 cm
The volume = 1/3*11.897^2*10.707 = 505.15 cm³
The surface area = 2*11.897*√(11.897/2)^2 + 10.707^2) +11.897²= 432.98 cm²
The angle at the top of the box = 2
Given that:
r = 2.82 cmh = 5.6 cmThen the maximum volume possible to the nearest 10 mL =
140 mLGiven that:
The size side of square base of box is 5.64 cmHeight of box = 5.6 cmHence, the surface area of the box is
189.96 cm²The volume of the box is :
178.13 cm³What is Surface Area?This refers to the measure of the total area of an object.
The written report:The procedural method used to solve the problem was to identify the shape of the pyramid, then finding out the smallest possible box for the pretty perfume and then using the calculated dimensions, found the answers.
Read more about surface area here:
https://brainly.com/question/76387
Which set of ordered pairs does not represent a function?
A{(-8,0),(4,0),(5,-2), (7,-9)}
B{(-6,0), (-4,2), (4,0), (-1,-9)}
C{(6,-9),(-3,6),(-3,-7),(-9, -2)}
D{(5,-6), (0,5), (-4, -8), (1, -8)}
Answer:
C
Step-by-step explanation:
In a function, each domain has one range. But a range can have many domains.
Think about it like this:
Patty is eating dinner
Patty is swimming
Both can't happen at the same time.
But:
Patty is eating dinner
Leo is eating dinner
C has two domains of -3, each having different ranges.
Hope that helps, tell me if you need further info. =)
Answer:
C. C{(6,-9),(-3,6),(-3,-7),(-9, -2)}
Step-by-step explanation:
If you see the same x-coordinate used more than once, it is not a function.
Here, you only see this in choice C, where x = -3 for two points. That makes this relation not a function.
EF is a median of trapezoid ABCD. What is the value of x?
Answer:
x = 4
Step-by-step explanation:
The midsegment ( median is equal to half the sum of the parallel bases, that is
[tex]\frac{AB+CD}{2}[/tex] = EF, substitute values
[tex]\frac{4x-10+3x+8}{2}[/tex] = 13 ( multiply both sides by 2
7x - 2 = 26 ( add 2 to both sides )
7x = 28 ( divide both sides by 7 )
x = 4
Rewrite the equation y= 4/5.x + 3 in general form Ax + By + C = O
Work Shown:
y = (4/5)x + 3
5y = 4x + 15 ... multiply all terms by 5 to clear out the fraction
0 = 4x + 15 - 5y ... subtract 5y from both sides
4x-5y+15 = 0 .... rearrange terms
The equation is in standard form Ax+By+C = 0 where A = 4, B = -5, C = 15.
Some books use Ax+By = C to represent standard form. It's effectively the same thing just with C on the other side.
Romeo is using a common algorithm to find the product of 8,125 × 9. Drag the correct numbers to the problem to show the partial products and to complete the multiplication for Romeo.
Answer:
its harddd
Step-by-step explanation:
rightttttttt
What is the volume of a square pyramid with base side length of 22 cm and height of 8cm?
Answer:
Volume of a pyramid is
[tex] \frac{1}{3 } \times (area \: \: of \: base) \times height[/tex]
Since it's a square pyramid the base is a square
So we have
Area of a square = l²
where l is the length of one side
Area of square = 22²
= 484 cm²
So volume of the pyramid is
[tex] = \frac{1}{3} \times 484 \times 8 = 1290.7 {cm}^{3} [/tex]
Hope this helps you
Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation? because both triangles appear to be equilateral because∠MNL and ∠ONP are congruent angles because one pair of congruent corresponding angles is sufficient to determine similar triangles because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
Answer:
The correct option is;
Because ∠MNL and ∠ONP are congruent angles
Step-by-step explanation:
From the diagram shown in the question, ∠MNL and ∠ONP are vertically opposite angles as they are formed by crossing of the lines LP and MO making them congruent, that is ∠MNL ≅ ∠ONP
Given that two angle of triangle LMN are congruent to two angles of triangle PON , then by the Angle Angle (AA) rule of similarity, triangle LMN and PON are similar.
The information in the diagram enough to determine that △LMN ~ △PON because∠MNL and ∠ONP are congruent angles.
What are Congruent angles?These are referred to angles which have an equal measure. From the diagram ,vertically opposite angles are formed by crossing of the lines LP and MO thus,we can deduce that ∠MNL and ∠ONP are congruent angles.
This means that there is enough information to determine that △LMN ~ △PON using a rotation about point N and a dilation.
Read more about Congruent angles here https://brainly.com/question/1563325
#SPJ2
Our school's girls volleyball team has 14 players, including a set of 3 triplets: Alicia, Amanda, and Anna. In how many ways can we choose 6 starters if exactly two of the triplets are in the starting lineup?
Answer:
990 ways to choose 6 starters out of 14 with exactly two of the three triplets.
Step-by-step explanation:
Ways to choose 2 of the triplets
= C(3,2) = 3! / (2!1!) = 3
Ways to choose the remaining 4 starters out of 11 players left
= C(11,4) = 11! / (4!7!) = 330
Total number of ways to choose 6 starters
= 3*330 = 990
factor x^5y^2+x^2y^5
Answer:
x^2y^2(x+y)(x^2-xy+y^2)
Step-by-step explanation:
x^5y^2+x^2y^5
Factor out the greatest common factor
x^2y^2( x^3+y^3)
Apply the Sum of Cubes Formula x^3+y^3 =(x+y)(x^2-xy+y^2)
x^2y^2(x+y)(x^2-xy+y^2)
Answer:
The answer is
x²y²( x + y)(x² - xy + y²)Step-by-step explanation:
[tex] {x}^{5} {y}^{2} + {x}^{2} {y}^{5} [/tex]
To factorize the expression first factor
x²y² out
We have
x²y²( x³ + y³)
Using the expression
a³ + b³ = ( a + b)(a² - ab + b²)Factorize the terms in the bracket
So we have
x³ + y³ = ( x + y)(x² - xy + y²)
Combine the expressions
We have the final answer as
x²y²( x + y)(x² - xy + y²)Hope this helps you
In the xy-coordinate plane, a line has a slope of −5/3. If the line crosses the y-axis at (0, b), at what point does it cross the x-axis?
Answer:
([tex]\frac{3}{5}[/tex] b, 0 )
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Here m = - [tex]\frac{5}{3}[/tex] and b = b , thus
y= - [tex]\frac{5}{3}[/tex] x + b ← equation of line
The line crosses the x- axis when y = 0, substitute y = 0 into equation and solve for x, that is
- [tex]\frac{5}{3}[/tex] x + b = 0 ( multiply through by 3 to clear the fraction )
- 5x + 3b = 0 ( subtract 3b from both sides )
- 5x = - 3b ( divide both sides by - 5 )
x = [tex]\frac{3}{5}[/tex] b , thus
x- intercept = ( [tex]\frac{3}{5}[/tex] b, 0 )
Answer:
( b, 0 )
Step-by-step explanation:
On a multiple choice test with 13 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.
Select one:
A. 1.875.
B. 1.53.
C. 1.47.
D. 1.5.
E. 1.561.
Answer: E. 1.561.
Step-by-step explanation:
Given, Total choices for each question =4
Probability that a particular answer is correct : p = [tex]\dfrac{1}{4}=0.25[/tex]
Sample size : n= 13
Formula for standard deviation: [tex]\sigma=\sqrt{np(1-p)}[/tex]
Put all values, we get
[tex]\sigma=\sqrt{13(0.25)(1-0.25)}=\sqrt{13(0.25)(0.75)}[/tex]
[tex]\sigma=\sqrt{2.4375}\approx1.561[/tex]
Hence, the standard deviation is 1.561.
So, the correct option is E.
PLEASE HELP!!!!!!!
Find the Volume of the sphere rounded to the nearest hundredth
Answer:
14130 yd^3
Step-by-step explanation:
The volume of a sphere is
V = 4/3 pi r^3
The diameter is 30 so the radius is d/2 = 30/2 = 15
V = 4/3 pi (15)^3
V = 4500 pi
Letting pi = 3.14
V = 14130 yd^3
Answer:
Last one
Step-by-step explanation:
The volume of the sphere is given by the relation:
V = [tex]\frac{4}{3}[/tex]*π*r³ r is the radius wich is here 30/2 = 15V= [tex]\frac{4}{3}[/tex] *π* 15³
V= 14137.166 yd³
wich is approximatively 14130yd³
The function f(t) = -6r+ 11 has the range {- 37. - 25. - 13, -1). Select the domain values from the list
1. 2. 3. 4. 5. 6. 7. 8. Justify your choices by explaining how you determined the domain values.
answer
-6r+-11=-37
-6r=-37+11
-6r=-48
r=8
The distance from Parrot Point Airport to the Ivy Cliffs is 178 miles at and angle of 7.1 degrees northeast. There is a wind blowing southeast at 30 miles per hour. You want to make this trip in 2 hours by flying straight there. At what speed* and heading should you fly? * Round the speed to the nearest tenth of a mile per hour and angle to the nearest tenth of a degree. Where north is 0 degrees and positive is clockwise.
Answer:
The speed is 74.0 miles per hour and the angle is 65.1° north-east
Step-by-step explanation:
We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.
Since the wind is moving south east, it is at 45 south of east or a bearing of 135.
Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles
Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles
The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles
The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles
The total vertical displacement of the plane is 176.64 miles - 42.43 miles = 134.21 miles
The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles
The direction of this displacement is thus
Ф = tan⁻¹(total vertical displacement/total horizontal displacement)
= tan⁻¹(134.21/62.43)
= tan⁻¹(2.1498)
= 65.05°
= 65.1° to the nearest tenth degree.
The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.
So the speed is 74.0 miles per hour and the angle is 65.1° north-east
The table below shows some inputs and outputs of the invertible function f ff with domain all real numbers.
x: -14,-7,-12,9,10,-2
f(x):11,-12,5,1,-2,13
f^-1(1)+f(−14): ?
f^-1(−2): ?
PLEASE HELP!
Answer: [tex]f^{-1}(1)+f(-14)=20[/tex]
[tex]f^{-1}(-2)=10[/tex]
Step-by-step explanation:
The given table :
x: -14,-7,-12,9,10,-2
f(x):11,-12,5,1,-2,13
Since f is invertible ( given) , then [tex]f^{-1}(x)[/tex] exists.
Now , from table [tex]f^{-1}(1)=9[/tex] [ x= 9 corresponding to f(x) =1]
[tex]f(-14)=11[/tex] [ f(x) = 11 corresponding to x=-14]
then, [tex]f^{-1}(1)+f(-14)=9+11=20[/tex]
So, [tex]f^{-1}(1)+f(-14)=20[/tex]
Also, x= 10 corresponding to f(x) =-2, then
[tex]f^{-1}(-2)=10[/tex]
in the circle, m∠S=33°, mRS=120, and RU is a tangent. the diagram is not drawn to scale. what is m∠U? Please help!
Answer:
27°
Step-by-step explanation:
arc RT = 66
1/2(120 - 66) = 27
Answer:
∠ U = 27°
Step-by-step explanation:
The inscribed angle S is half the measure of its intercepted arc, thus
arc RT = 2 × ∠ U = 2 × 33³ = 66°
The secant- tangent angle U is half the measure of the difference of the measures of the intercepted arcs, that is
∠ U = 0.5( RS - RT) = 0.5(120 - 66)° = 0.5 ×54° = 27°
Show the pair of straight lines are perpendicular.
C number.
Answer:
not perpendicular
Step-by-step explanation:
perpendicular line has opposite reciprocal slope
√3x-2√3 y=13
-2√3y=13-√3x
y=-13/(2√3)+√3 x/2√3
y=1/2 x-13/2√3 ( slope is 1/2)
6x-3y+11=0
-3y=-11-6x
y=-11/-3+6x/3
y=2x+11/3 slope =2
Which circle has a center angle that measures 40 degrees
Answer: B
Step-by-step explanation:
A center angle is an angle that has rays that originate from the center.
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,600. A random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05. The confidence interval for this hypothesis test would be ________.
Answer:
A 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].
Step-by-step explanation:
We are given that a random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average debt load = $18,800
[tex]\sigma[/tex] = population standard deviation = $4,800
n = sample of students = 28
[tex]\mu[/tex] = population average debt load
Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 5% level of
significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]\$18,800-1.96 \times {\frac{\$4,800}{\sqrt{28} } }[/tex] , [tex]\$18,800+1.96 \times {\frac{\$4,800}{\sqrt{28} } }[/tex] ]
= [$17,022.05, $20,577.94]
Therefore, a 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].
A penny is dropped from a height of 144 feet. Calculate the time between when the rock was dropped and when it landed. If we choose
"down" as positive and ignore air friction, the function is h(t) 16t2 - 144.
Answer:
3 seconds
Step-by-step explanation:
Given the function :
h(t) = 16t2 - 144.
h = height = 144 and t = time after t seconds the ball penny was dropped.
When the penny lands, h = 0
Therefore, our function becomes ;
16t2 - 144 = 0
The we can solve for t
16t^2 - 144 = 0
16t^2 = 144
Divide both sides by 16
(16t^2 / 16) = 144 / 16
t^2 = 9
Take the square root of both sides
t = 3
Therefore, the time between when the rock was dropped and when it landed is 3seconds
Answer:
t = 3 seconds
Step-by-step explanation:
What did you multiply together to find the sales tax?
Answer:
Step-by-step explanation:
To find the sales tax on a purchased or sold item, first convert the sales tax percentage into the equivalent decimal fraction. If the sales tax rate is 5.5%, then the desired decimal fraction is 0.055. Next, multiply the selling price of the purchased or sold item by this decimal fraction. If, for example, the selling price is $100, the sales tax is 0.055($100) = $5.50
plz help, will give brainiest
(08.01, 08.02, 08.03 HC)
Create a factorable polynomial with a GCF of 3x. Rewrite that polynomial in two other equivalent forms. Explain how each form was created. (10 points)
Answer:
4x^2 + 8x + 4
4(x^2 + 2x + 1) - remove GCF of 4
4(x + 1)(x + 1) - factor
4(x + 1)^2 - collect like terms
Step-by-step explanation:
Then also expand it out by distributing:
21x^3 + 35x²
Form 1:
21x^3 + 35x² - unfactored
Form 2:
7x²(3x + 5) - factored with GCF of 7x² brought to the front
Update:
You could also multiply two binomials and make a quadratic.
Example:
(7x + 2)(3x + 5)
7x(3x + 5) + 2(3x + 5)
= 21x² + 35x + 6x + 10
= 21x² + 41x + 10
The favorable polynomial with a GCF of 3x will be 21x² + 41x + 10.
What is a polynomial?
A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
The polynomial will be solved as below:-
21x³ + 35x²
Form 1:
21x³ + 35x² - unfactored
Form 2:
7x²(3x + 5) - factored with GCF of 7x² brought to the front
You could also multiply two binomials and make a quadratic.
E = (7x + 2)(3x + 5)
E = 7x(3x + 5) + 2(3x + 5)
E = 21x² + 35x + 6x + 10
E = 21x² + 41x + 10
To know more about polynomials follow
brainly.com/question/2833285
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I have never understood these. Help.
Answer:
5 sqrt(5)
Step-by-step explanation:
sqrt(125)
sqrt( 25*5)
We know that sqrt(ab) = sqrt(a) sqrt(b)
sqrt(25) sqrt(5)
5 sqrt(5)
Answer:
5√(5)
Step-by-step explanation:
Notice that 125 is 25×5
If you couldn't do it use the prime factorization.
Prime numbers are 2,3,5.....
125 isn't divisible by 2 and 3 so we'll go with 5.
● 125 ÷ 5 = 25
Againg 25 is divisible by 5
● 25÷5 = 5
5 is divisible by 5
● 5÷5=1
So 125= 5×5×5 = 5^2 × 5
● √(125)= √(5^2×5) = 5√(5)