Mathematically verify the outlier(s) in the data set using the 1.5 rule.
7, 8, 11, 13, 14, 14, 14, 15, 16, 16, 18, 19
1. 7 & 19 are outliers.
2. 7 & 8 are outliers.
3. 7, 8, & 19 are outliers.
4. There are no outliers.
Given:
The data values are:
7, 8, 11, 13, 14, 14, 14, 15, 16, 16, 18, 19
To find:
The outliers of the given data set.
Solution:
We have,
7, 8, 11, 13, 14, 14, 14, 15, 16, 16, 18, 19
Divide the data set in two equal parts.
(7, 8, 11, 13, 14, 14), (14, 15, 16, 16, 18, 19)
Divide each parenthesis in two equal parts.
(7, 8, 11), (13, 14, 14), (14, 15, 16), (16, 18, 19)
Now,
[tex]Q_1=\dfrac{11+13}{2}[/tex]
[tex]Q_1=\dfrac{24}{2}[/tex]
[tex]Q_1=12[/tex]
And
[tex]Q_3=\dfrac{16+16}{2}[/tex]
[tex]Q_3=\dfrac{32}{2}[/tex]
[tex]Q_3=16[/tex]
The interquartile range is:
[tex]IQR=Q_3-Q_1[/tex]
[tex]IQR=16-12[/tex]
[tex]IQR=4[/tex]
The data values lies outside the interval [tex][Q_1-1.5IQR,Q_3+1.5IQR][/tex] are known as outliers.
[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[12-1.5(4),16+1.5(4)][/tex]
[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[12-6,16+6][/tex]
[tex][Q_1-1.5IQR,Q_3+1.5IQR]=[6,22][/tex]
All the data values lie in the interval [6,22]. So, there are no outliers.
Hence, the correct option is 4.
15,000 ones 1,500 tens 15 thousands 15,000 15 ten thousands which is odd one out explain how you now
Answer:
15 ten thousands
Step-by-step explanation:
15,000 ones is 15,000 * 1 = 15,000
1,500 tens is 1,500 * 10 = 15,000
15 thousands is 15 * 1000 = 15,000
15,000 is 15,000 '-'
15 TEN thousands is 15 * 10,000 = 150,000
It could be 1.5 ten thousands. 1.5 ten thousands is 15,000.
Latoya created a factor tree and wrote the prime factorization of 90 shown below.
A factor tree of 90. 90 branches to 9 and 10. 9 branches to 3 and 3. 10 branches to 2 and 5. The equation is 90 = 2 times 3 times 5.
What is Latoya’s error?
She should not have found the factors of 9.
She should have included an exponent of 2 on the 3.
She should have included 9 and 10 in the prime factorization.
She should have started the tree with 2 times 45.
Answer:
She should have included an exponent of 2 on the 3
Step-by-step explanation:
The factor tree can be presented as follows;
[tex]{}[/tex] 90
[tex]{}[/tex] ↓
[tex]{}[/tex] 9 ↔ 10
[tex]{}[/tex] ↓ ↓
[tex]{}[/tex] 3 ↔ 3 2 ↔ 5
Therefore, the prime factorization of 90 is equal to 90 = 3 × 3 × 2 × 5
She should have wrote, 90 = 3² × 2 × 5
Therefore, the error is that she should have included an exponent of 2 on the 3.
Answer:
B
✔ She should have included an exponent of 2 on the 3.
Step-by-step explanation:
E2021
Which expression is equivalent to (9⋅5)2/3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\dfrac{(9 \times5) 2}{3}}[/tex]
[tex]\huge\boxed{9 \times 5 = \bf 45}[/tex]
[tex]\huge\boxed{ = \dfrac{45(2)}{3}}[/tex]
[tex]\huge\boxed{45(2) = \bf 90}[/tex]
[tex]\huge\boxed{= \dfrac{90}{3}} \\\\\huge\boxed{= \dfrac{90\div3}{3\div3}}\\\\\huge\boxed{= \dfrac{30}{1}}[/tex]
[tex]\huge\boxed{= \bf 30}[/tex]
[tex]\huge\boxed{\rm{Answer: 30}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
Answer:
30
Step-by-step explanation:
[tex] \small \sf = \frac{( 9 × 5 ) 2 }{3} \\ [/tex]Multiply 9 and 5 to get 45.
[tex] \small \sf = \frac{ 45 × 2 }{3} \\ [/tex]Multiply 45 and 2 to get 90.
[tex] \small \sf = \frac{ 90 }{3} \\ [/tex]Divide 90 by 3 to get 30.
= 30What is the value of tan 0 in the unit circle below?
Answer:
1 / sqrt(3)
Step-by-step explanation:
tan(o) = sin(o) / cos(o)
sin(o) is the vertical distance from the x-axis. and that is in this basic circle the y-coordinate of the point.
cos(o) is the horizontal distance from the y-axis. that is the x-coordinate of the point.
so,
tan(o) = (1/2) / (sqrt(3)/2) = (2×1) / (2×sqrt(3)) = 1/sqrt(3)
Which of the following is equivalent to the expression below?
2(-3x+1) – 4x
- -2x+2
- -10x+1
- 2x+1
- -10x+2
Answer:
[tex]\underline{\underline{ -10x +2}}[/tex]
Step-by-step explanation:
A expression is given to us and we need to simplify out the expression . The given expression is ,
[tex]\implies 2(-3x +1)-4x [/tex]
Open the brackets .
[tex]\implies -6x +2-4x [/tex]
Simplify the like terms .
[tex]\underline{\underline{ -10x +2}}[/tex]
Hence the correct option is (4) .
1) Enlun mixes 8 cups of pineapple juice and 14 cups of cranberry juice to make a fruit punch. Assuming he always mixes in the same ratio, write an equation that describes the proportional relationship between cups of pineapple juice (p) and cups of cranberry juice (c).
a) How many cups of pineapple juice are needed for 63 cups of cranberry juice?
Answer:
p = 4/7c
p = 36 cups when c = 63 cups
Step-by-step explanation:
Cups of pineapple juice, p = 8
Cups of cranberry juice, c = 14
equation that describes the proportional relationship between cups of pineapple juice (p) and cups of cranberry juice (c)
p = k * c
Where,
k = constant of proportionality
p = k * c
8 = k * 14
8 = 14k
k = 8/14
k = 4/7
Therefore,
p = 4/7c
How many cups of pineapple juice are needed for 63 cups of cranberry juice?
p = 4/7c
p = 4/7 * 63
= (4 * 63) / 7
= 252/7
= 36
p = 36
p = 36 cups when c = 63 cups
For a project in his Geometry class, Tyler uses a mirror on the ground to measure the height of his school building. He walks a distance of 14.65 meters from his school, then places a mirror on flat on the ground, marked with an X at the center. He then steps 0.8 meters to the other side of the mirror, until he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.15 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
Answer:
The height of the school building is approximately 21.06 meters
Step-by-step explanation:
The method of Geometry Tyler is using to determine the height of his school building is through the property that similar triangles have a common ratio of corresponding their sides
The given parameters for the triangle formed by Tyler and the mirror are;
The distance from Tyler's eyes to the ground = 1.15 meters
The horizontal distance between Tyler and the mirror at X = 0.8 m
The parameters of the triangle formed by the height, h, of the school building and the mirror at X are;
The horizontal distance between the school building and the mirror = 14.65 m
The height of the school building = h
Therefore, we have;
[tex]\dfrac{The \ distance \ from \ Tyler's \ eyes \ to \ the \ ground}{The \ height \ of the \ school \ building} =\dfrac{Tyler's \ horizontal \ distance \ from \ mirror }{The \ building \ to \ mirror \ horizontal \ distance }[/tex]Therefore;
[tex]\dfrac{1.15 \, m}{h} = \dfrac{0.8 \ m}{14.65 \ m}[/tex]
[tex]h = \dfrac{1.15 \, m \times 14.65 \, m }{0.8 \, m} = 21.059375 \ m[/tex]
The height of the school building h to the nearest hundredth meter ≈ 21.06 m.
Check the box labeled Show Altitude of Triangle ABC. The altitude divides into and through the point you determined in question 2. Measure and record the side lengths of and . Then measure and record the side lengths of and .
Answer:
Step-by-step explanation:
Step-by-step explanation:
.hhx cvs Gunther b but kcm
Based on the table below, what is the relationship between cups and tablespoons?
Answer:
the answer is A
Step-by-step explanation:
Solve for X (line a and b parallel)
Answer:
x=29°
Step-by-step explanation:
as lines are parallel.
external alternate angles are equal.
7x-86=4x+1
7x-4x=1+86
3x=87
x=87/3=29
The formula for the volume of a cylinder is V = srh.
Solve v = rn for h, the height of the cylinder.
Answer:
A
Step-by-step explanation:
Have a great summer :)
Anna is following this recipe to make biscuits.
Anna uses 750 g of margarine.
How many grams of sugar will she need?
Recipe: Makes 24 biscuits
60 g sugar
100 mL syrup
250 g oats
125 g margarine
60 g chocolate
Answer:
130
Step-by-step explanation:
Factor 6x ^ 2 - 3x - 45; 3(2x - 5) * (x + 3); 3(2x - 3) * (x - 5); 3(2x + 5) * (x - 3); 3(2x + 3) * (x - 5)
Answer:
[tex]3(2x+5)(x-3)[/tex]
Step-by-step explanation:
The given equation is:
[tex]6x^{2}-3x-45[/tex]
It can be solved by using middle term splitting.
So,
[tex]6x^{2}-3x-45=6x^2+15x-18x-45\\\\=3(2x+5)(x-3)[/tex]
So, the factors of [tex]6x^{2}-3x-45[/tex] are [tex]3(2x+5)(x-3)[/tex]
Look at the graph below. What type of function is represented by this graph?
Someone come through with the answers pls
calcula el área lateral de un prisma cuya base es un pentagono de 10cm de arista, 16.88 cm de apotema y 15 cm de altura
Answer:
Lateral surface area of pentagonal prism = 750 cm²
Step-by-step explanation:
Given information:
Height of pentagonal prism = 15 cm
Length of edge = 10 cm
Length of apothem = 16.8 cm
Find:
Lateral surface area of pentagonal prism
Computation:
Lateral surface area of pentagonal prism = 5(a)(h)
Lateral surface area of pentagonal prism = 5(10)(15)
Lateral surface area of pentagonal prism = 750 cm²
convert decimal number system into binary number system:216
Answer:
11011000
Step-by-step explanation:
the binary equivalent of decimal number 216 is 11011000
[tex]\huge\sf\red{Answer}[/tex]
11011000
__________
Hopefully it helps
Find the equation of the line.
Use exact numbers.
Answer:
Y = 2x + 5
Step-by-step explanation:
2x is your slope and 5 is your y intercept.
The formula for this is: y = mx + b
BRAINLEST IF CORRECT
Answer:
first option
Step-by-step explanation:
the graph has a point of (8,2)
so see which option proves this point
2=0.25(8)
2=2
so first option is correct
is my answers correct?
Answer:
Saleh is x years old. And 10 years ago he was 100 years old.
Suha is x years old. Saleh is 10 years younger than Suha. Saleh is 100 years old.
pls help im begging u..
HELP ME ASAP I need help with this problem
B.
the solution is in the picture
can anyone please explain this?
Find the equation of locus of a point A(-3,2) and B(0,4).....
what is locus actually?
Answer:
Solution given:
Let there be a point P(x, y) equidistant from
A(-3, 2) and B(0,4),
so PA = PB,
[tex]\sqrt{(x+3)²+(y-2)²}=\sqrt{(x-0)²+(y-4)²}[/tex]
squaring both side
[tex](\sqrt{(x+3)²+(y-2)²})^{2}=(\sqrt{(x-0)²+(y-4)²})²[/tex]
x²+6x+9+y²-4y+4=x²+y²-8y+16
x²+6x+y²-4y-x²-y²+8y=16-4-9
6x-4y+8y=3
6x-4y=3 is a required locus
Actually:
A locus is a curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.
If you answer this correctly you get a cookie
Answer:
3/9
Step-by-step explanation:
P(G,G) = 1/3 × 1/3 = 1/9
P(B,B) = 1/9
P(Y,Y) = 1/9
P(same colour) 1/9 + 1/9 + 1/9 = 3/9
Question 23 (5 points)
If a leg of a right triangle is 7 units and the hypotenuse is 25 units, what's the length
of the other leg?
1024 units
25.96 units
24 units
324 units
the answer is 1024 because 7²+25²=b²
factor out the square which gives you
(7+25)²=b²
32²=b²
squaring 32 gives 1024
Answer:
24 units
Step-by-step explanation:
i just took the quiz
which one ?
it says i need 20 characters so i’m just typing this
Someone please help me with this math problem? !!
Answer:
x = -1
Step-by-step explanation:
If you input -1 to both functions, you get 3.
Someone please tell me what the cube root of x to the power of 3 is?
Answer:
x
Step-by-step explanation:
The cube root of x to the power of 3 is
( [tex]\sqrt[3]{x}[/tex] )³ = ( [tex]x^{\frac{1}{3} }[/tex] )³ = x
or
[tex]\sqrt[3]{x^3}[/tex] = x
if 2/a=1/b-1/d find an expression for d in terms of a and b
Answer:
Step-by-step explanation:
2/a = 1/b - 1/d
2d/a = d/b - 1
2d/a - d/b = -1
d(2/a - 1/b) = -1
d(2b-a)/(ab) = -1
d(a-2b)/(ab) = 1
d = ab/(a-2b)
Find the values of x and y.
Answer:
since y is across from 60 so
y=60
and on the bottom it is 15 so
x+3=15
x=12
Hope This Helps!!!
