9.A standard IQ test produces normally distributed results with a mean of 100 and a standard deviation of 15. A class of high school science students is grouped homogeneously by excluding students with IQ scores in either the top 15% or the bottom 15%. Find the lowest and highest possible IQ scores of students remaining in the class.(7)
Answer:
The lowest possible IQ scores of students remaining in the class is 84.46.
The highest possible IQ scores of students remaining in the class is 115.54.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
Find the lowest and highest possible IQ scores of students remaining in the class.
Lowest:
The 15th percentile, which is X when Z has a pvalue of 0.15, so X when Z = -1.036.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.036 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = -1.036*15[/tex]
[tex]X = 84.46[/tex]
Highest:
The 100 - 15 = 85th percentile, which is X when Z has a pvalue of 0.85, so X when Z = 1.036.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.036 = \frac{X - 100}{15}[/tex]
[tex]X - 100 = 1.036*15[/tex]
[tex]X = 115.54[/tex]
The lowest possible IQ scores of students remaining in the class is 84.46.
The highest possible IQ scores of students remaining in the class is 115.54.
A ______________ consists of an a sample space and a list of events with their probabilities.
probability model
sample space
likelihood
outcome
Sample space َََ َ َ َ َ َ َ َ َ َ
I need help
Please ?!!!!!!
Answer:
High blood pressure
Step-by-step explanation:
Possible DEATH
Answer:
High blood pressure
Step-by-step explanation:
High blood pressure is dangerous
Samantha, a business development representative at Apricot Inc., took her client out for a dinner that cost $180.75 before taxes. If she paid taxes of $18.08 on the meal, calculate the tax rate.
Answer:
10%
Step-by-step explanation:
Samantha is a business development representative
She took her client out for a dinner that costs $180.75 before taxes
She paid tax of $18.08 on the meal
The tax rate can be calculated as follows
= 18.08/180.75
= 0.1 ×100
= 10%
Hence the tax rate is 10%
6
YA
Triangle ABC has vertices A(-4,-1), B(-3,-5), C(-1, -1). Graph and label the vertices of ABC
and its image A'B'C' after translating it to 4 units right and 3 units up. Choose the correct
ordered pairs of the image A'B'C'.
(2 Points)
O A'(4.1), B (3,5), C' (1.1)
O A'(0,2), B(1, -2). C'(3.2)
O A'(0.2), B (1,2), C'(-3,-2)
Answer:
A'(0,2), B(1, -2). C'(3,2)
Step-by-step explanation:
Given
[tex]A = (-4,-1)[/tex]
[tex]B = (-3,-5)[/tex]
[tex]C =(-1,-1)[/tex]
Solving (a); Graph and Label ABC
See attachment for graph
Solving (b): Graph and Label A'B'C'
Translation:
4 units right
3 units up
4 units right
The rule is:
[tex](x,y) \to (x + 4,y)[/tex]
So, we have:
[tex]A = (-4,-1)[/tex] ==> [tex](-4+4,-1) =(0,-1)[/tex]
[tex]B = (-3,-5)[/tex] ==> [tex](-3+4,-5) =(1,-5)[/tex]
[tex]C =(-1,-1)[/tex] ==> [tex](-1+4,-1) =(3,-1)[/tex]
3 units up
The rule is:
[tex](x,y) \to (x,y+3)[/tex]
So, we have:
[tex](0,-1)[/tex] ==> [tex]A' =(0,-1+3) = (0,2)[/tex]
[tex](1,-5)[/tex] ==> [tex]B' =(1,-5+3) = (1,-2)[/tex]
[tex](3,-1)[/tex] ==> [tex]C' =(3,-1+3) = (3,2)[/tex]
The coordinates of A' B' and C' are:
A'(0,2), B(1, -2). C'(3,2)
See attachment for graph
HELP PLSSSSSSSSSSSSSSSSSSSSSSS
Answer:
3) not equivalent
4) equivalent multiply by 2
5) equivalent multiply by 2
What is the length of arc S shown below?
S
2
7 cm
The angle in the figure is a central angle in radians.
Answer: S= 14 cm
Step-by-step explanation:
Answer: 14
Step-by-step explanation: Khan Academy
Mr Baxter deposits 2,000 in an account that earns %5 simple interest how much is mr Baxter investment after 8 years?
Answer:
$2,800
Step-by-step explanation:
The formula for simple interest is I = PRT, where I is the interest (earned or paid), P is the principal amount invested/borrowed, R is the rate in decimal form, and T is the time in years.
I = (2000)(0.05)(8)
I = $800
Then we add that to the principal to get $2,800
---------------------------------
Joey made a deposit into an account that earns 6% simple interest. After 3 years, Joey earned $400. How much was Joey's initial deposit?
I = PRT
400 = P(0.06)(3)
400 = 0.18P
P = $2,222. 22
----------------------------------------
Peter is calculating the interest earned on a deposit of $275 in an account that earns 8% simple interest after 12 years. What is the ??? guessing interest earned?
I = PRT
I = (275)(0.08)(12)
I = $264
------------------------------------
Neil's grandmother has left him a small inheritance of $6,000. Neil would like to invest it at a rate of 5% interest. What is the simple???
I = PRT
I = (6000)(0.05)(T)
Please let me know if you have questions, or want to fill in the missing information on questions 3 & 4.
Consider the line plot below.
What is the median of the data?
What is the mean?
Shannon is creating a scale drawing of her classroom. If she is using the scale 1/2 inch = 1 foot and the room model is 10 inches by 15 inches, what are the dimensions of the actual room. Please help me!
Answer:
30 foot by 20 foot
Step-by-step explanation:
1 inch = 10 inch
2 foot = d foot
Cross products: 1xd=2x10
d=20foot
1 inch = 15 inch
2 foot = d foot
Cross products: 1xd=2x15
d=30foot
Which of the following scatterplots would have a trend line with a negative slope?
Answer:
Step-by-step explanation:
If we let the points in the first graph define the position and slope of a line through the points, this line would have a negative slope and a negative trend line. As x increases, y decreases.
Answer: it’s A. I took the test.
Step-by-step explanation:
the Beatles are better than the stones and that is a fact
Alma is estimating the proportion of students in her school district who, in the past month, read at least 1 book. From a random sample of 50 students, she found that 32 students read at least 1 book last month. Assuming all conditions for inference are met, which of the following defines a 90 percent confidence interval for the proportion of all students in her district who read at least 1 book last month?
a. 32 + or - 1.645 underroot(32)(18)/50.
b. 32 + or - + 1.96 underroot(32)(18)/50.
c. 0.64 + or - 1.282 underroot(0.64)(0.36)/50.
d. 0.64 + or - 1.645 underroot(0.64)(0.36)/50.
e. 0.64 + or - 1.96 underroot(0.64)(0.36)/50.
Answer:
[tex]0.64 \pm 1.645\sqrt{\frac{0.64*0.36}{50}}[/tex], option D
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
From a random sample of 50 students, she found that 32 students read at least 1 book last month.
This means that [tex]n = 50, \pi = \frac{32}{50} = 0.64[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
Confidence interval:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.64 \pm 1.645\sqrt{\frac{0.64*0.36}{50}}[/tex]
So the correct answer is given by option D.
Johnny wants to invest $10,000 at 4.5% interest rate compounded quarterly, How much will he have after 38 years?
Answer:
a= $54764.26
Step-by-step explanation:
r=R/100
r=4.5/100
r=0.045 rate per year
A = P(1 + r/n)nt
A = 10,000.00(1 + 0.045/4)(4)(38)
A = 10,000.00(1 + 0.01125)(152)
A = $54,764.26
Find the length of chord AD
9514 1404 393
Answer:
AD = 15
Step-by-step explanation:
The products of the segment lengths are the same.
(x -2)(x +7) = 4(2x -1)
x^2 +5x -14 = 8x -4
x^2 -3x -10 = 0
(x -5)(x +2) = 0
The positive solution is x=5.
Chord AD is ...
(x -2) +(x +7) = 2x +5 = 2(5) +5 = 15
Chord AD is 15 units long.
the solution of the equation x2-6x=0 is ?
Help!!! Quick answer please!
Answer:
18 sq ft
Step-by-step explanation: all you have to do is add the sides. 5+5=10
4+4= 8
10+8=18
This makes the most sense with the answers givin
Mrs. Torchia picked 54 flowers, which represents 60% of all the flowers in her garden.How many flowers are left in Mrs. Torchia’s garden?
g A report on the nightly news broadcast stated that 10 out of 108 households with pet dogs were burglarized and 20 out of 208 without pet dogs were burglarized. Suppose that this data is used to test the claim that the proportion of households with dogs that are burglarized is the same as the proportion of households without dogs that are burglarized. What would be the test statistic for this test
Answer:
Test statistic |Z| = 0.1040 < 1.96 at 0.05 level of significance
Step-by-step explanation:
Step(i):-
Given that a report on the nightly news broadcast stated that 10 out of 108 households with pet dogs were burglarized
First proportion
[tex]p_{1} = \frac{x_{1} }{n_{1} } = \frac{10}{108} = 0.0925[/tex]
Given that a report on the nightly news broadcast stated that 20 out of 208 households without pet dogs were burglarized
Second proportion
[tex]p_{2} = \frac{x_{2} }{n_{2} } = \frac{20}{208} = 0.0961[/tex]
where
[tex]P = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1} +n_{2} }[/tex]
P = 0.09486
Q = 1 - P = 1 - 0.09486 = 0.90514
Step(ii):-
Test statistic
[tex]Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }[/tex]
[tex]Z = \frac{0.0925-0.0961 }{\sqrt{0.09486 X 0.90514(\frac{1}{108 } +\frac{1}{208 } )} }[/tex]
Z = -0.1040
|Z| = |-0.1040|
|Z| = 0.1040
Critical value Z = 1.96 at 0.05 level of significance
Solve the equation for the value of x
-15x=45
Show your work please, thank you.
Answer:
x=-3
Step-by-step explanation:
-15x=45
x=-45/15
x=-3
Answer:
okay x=-3
Step-by-step explanation:
-15x=45
-15/-15=45/15
x=-3
a. In the diagram above, angles ABCABC and CBDCBD are
, and their measures sum to
degrees.
b. The measure of \angle ABC∠ABC is
degrees.
Show your work in the box below.
Answer:
Step-by-step explanation:
..
Determine whether the triangle is a right triangle 12, 10, 11...
Answer:
no it's not right angled
Step-by-step explanation:
thats because the left hand side is not equal to the right hand side
Answer:
You were on the right track: basically if a²+b²=c² is true , it's a right triangle...
a²+b²=c²
11²+10²=12²?
121+100=144?
221=144?
221≠144
Since they're not equal, the triangle isn't a right triangle.
Find the missing angle
90 minus 63 equals 37
Answer:
27 degrees
Step-by-step explanation:
x together with 63deg form a right angle (90deg)
x + 63 = 90
x = 90 - 63
x = 27

HELP ASAP! I will mark Brainlist! Thanks (:
Answer:
Corresponding angles postulate
Answer:
definition of parrallel lines
Step-by-step explanation:
oh sorry. I understood it as parrallel
3(x+2)=15
I just need help with this problem please.
Answer:
x=3
Step-by-step explanation:
Divide both sides by 3
3(x+2)/3 = 15/3
You get x+2=5, subtract 2 from each side
x+2(-2)=5(-2)
x=3
of 20 possible books you plan to take 5 with you on vacation. how many different collections of 5 books can you take?
PLEASE HELPPP
what is the volume of this rectangular prism. ??
Brainlist + Five starts
Answer:
The answer is a
Step-by-step explanation:
it’s a because each dude is 1/2 and you add another one half that’s one and you keep on doing until the last one.
brainliest pls
I hope this helped and was right.
Step-by-step explanation:
Length: 6
width: 4
height:3
Formula :
Volume= l x w x h
6x4x3 =72
72 x 1/2= 36in3/A
find the value of x. Pregunta matemática
Answer:
Ejercicios Resueltos
ANGULOS
1. Si el complemento de ángulo x es 2x, ¿Cuál es el valor de x en
grados?
Solución:
2x x 90 += °
3x 90
x 90 / 3
x 30
= °
= °
= °
2. Si el suplemento del ángulo x es 5x, ¿Cuál es el valor de x?
Solución:
5x+x=180
6x=180
x=180 /6
x=30
°
°
°
°
3- Determínese los dos ángulos x e y, cuya suma es 90 y cuya
diferencia es 10 .
°
°
Solución:
-Planteamos el sistema de ecuaciones:
x y 90
x y 10
+= °
−= °
-Resolvemos el sistema. Mediante el método de suma y resta
obtenemos:
2x 100
x 100 / 2
x 50
= °
= °
= °
-Hacemos la sustitución del valor encontrado de x en la primera
ecuación: 50 y 90
y 90 50
y 40
°+ = °
= °−
= °
°
∴La solución al problema es x 50 , y 40 =°= °
°
4. Hállense dos ángulos complementarios tales que su diferencia sea
30° .
Solución:
-Planteamos el sistema de ecuaciones:
x y 90
x y 30
+= °
−= °
-Resolvemos el sistema. Mediante el método de suma y resta
obtenemos:
2x 120
x 120 / 2
x 60
= °
= °
= °
-Hacemos la sustitución del valor encontrado de x en la primera
ecuación:
60 y 90
y 90 60
y 30
°+ = °
= °−
= °
∴La solución al problema es x 60 , y 30 = °= °
°
5. Hállense dos ángulos suplementarios tales que el uno sea 20 mayor
que el otro.
°
Solución:
-Planteamos el sistema de ecuaciones:
x y 180
x y 20
+= °
=+ °
-Resolvemos el sistema:
(y 20 ) y 180
2y 180 20
2y 160
y 80
+ °+ =
= °− °
= °
= °
-Hacemos la sustitución del valor encontrado de y en la primera
ecuación: x 80 180
x 180 80
x 100
+ °=
= °−
= °
°
°
∴La solución al problema es:
x = °= ° 100 , y 180
TRIANGULOS
1.- ¿Cuánto miden cada uno de los ángulos interiores del siguiente
triángulo?
Solución:
Nota: La suma de los ángulos interiores de los triángulos es
180° .
((( A B C 180 ++= °
3x 5x 4x 180 ++ = °
12x 180 = °∴( ( (( A 22.5 , B 52.5 , C 30 , CBR 127.5 = ° = ° =° = °
x 15 = °
∴( ( A 45 , B 75 ,C 60 =° =°= °
°
°
°
°
°
°
2.- ¿Cuánto miden cada uno de los ángulos del siguiente triángulo?
Solución
a) Ángulo extendido
( ( B CBR 180 + = Esto debido a que son ángulos suplementarios
(B 15x 60 180 + − °=
(B 180 60 15x = °+ °−
(B 240 15x = °−
b) Suma de los ángulos interiores del triángulo
((( A B C 180 ++=
3x (240 15x) 4x 180 + °− + =
7x (240 15x) 180 + °− =
− + °= 8x 240 180− =− 8x 160°
x 7.5 =
∴( ( (( A 22.5 , B 52.5 , C 30 , CBR 127.5 = ° = ° =° = °
3.- Escribe la definición de bisectriz del triángulo.
Es la semirrecta que biseca el ángulo, es decir, divide el ángulo
en dos ángulos congruentes.
4.- ¿Qué es la mediatriz de un triángulo?
La mediatriz de un lado de un triángulo (y en general de un
segmento de recta), es la recta perpendicular a ese lado en su
punto medio.
5.- ¿Que es la mediana de un triángulo?
La mediana de un triángulo, es el segmento de la recta que une
un vértice con el punto medio del lado opuesto.
CUADRILATEROS
1.- ¿Qué cuadrilátero tiene las dos diagonales iguales y sus lados son
iguales dos a dos?
Rectángulo
2.- Si los ángulos de un cuadrilátero miden, respectivamente, 80º, 110º
y 70º, ¿Cuánto medirá el ángulo que falta?
100º
3.- ¿Cuál es el paralelogramo que tiene las diagonales perpendiculares?
Rombo
4.- ¿Cómo se llama el cuadrilátero que tiene dos lados paralelos?
Trapecio
5.- Encuentra el área del paralelogramo que tiene 5cm de base y 3 de
altura
A b*a
A 5*3
A 15
=
=
=
POLÍGONOS 1.- Cuatro ángulos interiores de un pentágono valen respectivamente
110°, 90°, 85° y 125°. ¿Cuánto vale el quinto ángulo?
Solución:
Si la suma de los ángulos interiores de un polígono es:
180°*(n-2)=180°*(5-2) = 540°, a lo que le se le resta los
valores de los ángulos que se dieron, consecuentemente, el
quinto ángulo vale 130°.
2.- ¿Cuántos lados tiene, en cada caso, el polígono cuyos ángulos
interiores suman respectivamente 1080°, 900°, 1260°?
Solución:
Despejando de la fórmula el valor de n, tenemos que:
. 2
180
suma angulos n = ° + , y esto aplicado a cada valor de la suma de los
ángulos internos, obtenemos que los valores de n son 8, 7 y 9
respectivamente.
3.- ¿Cuánto vale cada ángulo exterior de un octágono regular?
Solución:
Aplicando el teorema de que la suma de los ángulos exteriores
de un polígono es 360°, entonces cada ángulo exterior vale
360°/8 = 45°
4.- Calcular los ángulos exteriores de un triángulo rectángulo que tiene
un ángulo agudo doble del otro.
Solución:
Se tiene que la suma de los ángulos interiores es
180°*(n-2)= 180° y éste a su vez es igual a 90° + x + 2x,
despejando x de 3x = 90°, x= 30°, entonces los ángulos
interiores son 30°, 60° y 90°, teniendo como ángulos exteriores
150°, 120° y 90°.
Step-by-step explanation:
- 5 (-2x+10) = 10
equation with parentheses
Answer: x=6
Step-by-step explanation:
−
5
(
−
2
+
1
0
)
=
1
0
−
5
(
−
2
x
+
10
)
=
10
−5(−2x+10)=10
Solve
1
Distribute
−
5
(
−
2
+
1
0
)
=
1
0
−
5
(
−
2
x
+
10
)
=
10
−5(−2x+10)=10
1
0
−
5
0
=
1
0
10
x
−
50
=
10
10x−50=10
2
Add
5
0
50
50
to both sides of the equation
3
Simplify
A worker at a snack stand opened a new box of cups. The first day, the worker used
30 cups from the box. The second day, the worker used 15% of the remaining cups in the
box. A total of 90 cups were used on the second day. What was the original number
of cups in the box before any cups were used?
A
400
B
570
с
630
D
800
Find the missing angles
Answer:
See explanation:
Step-by-step explanation:
1: 180-50=130
3: vertical angles are the same, therefore 50
4: 180-50=130
5: angle 1 equals angle 5, therefore 130
6: 50
7: 50, angles 6 and 7 are vertical therefore equal
8: 180-50=130