36 is a whole number.
Answer:
The number 3.6 is a rational number.
All numbers that can be represented as fractions made of two integers (whole numbers) are considered to be
In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of and a standard deviation of . Complete parts (a) through (d) below. (a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than . The probability of a student scoring less than is nothing. (Round to four decimal places as needed.) (b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between and . The probability of a student scoring between and is nothing. (Round to four decimal places as needed.) (c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than . The probability of a student scoring more than is nothing. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. A. than 0.05. B. than 0.05. C. The event in part is unusual because its probability is less than 0.05. D. The events in parts are unusual because its probabilities are less than 0.05.
The question is incomplete. Here is the complete question.
In a recent year, the socres for the reading portion of a test were normally distributed, with a mean of 23.3 and a standard deviation of 6.4. Complete parts (a) through (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 18. (Round to 4 decimal places as needed.)
(b) Find a probability that a random selected high school student who took the reading portion of the test has a score that is between 19.9 and 26.7.
(c) Find a probability that a random selected high school student who took the reading portion of the test ahs a score that is more than 36.4.
(d) Identify any unusual events. Explain your reasoning.
Answer: (a) P(X<18) = 0.2033
(b) P(19.9<X<26.7) = 0.4505
(c) P(X>36.4) = 0.0202
(d) Unusual event: P(X>36.4)
Step-by-step explanation: First, determine the z-score by calculating:
[tex]z = \frac{x-\mu}{\sigma}[/tex]
Then, use z-score table to determine the values.
(a) x = 18
[tex]z = \frac{18-23.3}{6.4}[/tex]
z = -0.83
P(X<18) = P(z< -0.83)
P(X<18) = 0.2033
(b) x=19.9 and x=26.7
[tex]z = \frac{19.9-23.3}{6.4}[/tex]
z = -0.67
[tex]z = \frac{26.7-23.3}{6.4}[/tex]
z = 0.53
P(19.9<X<26.7) = P(z<0.53) - P(z< -0.67)
P(19.9<X<26.7) = 0.7019 - 0.2514
P(19.9<X<26.7) = 0.4505
(c) x=36.4
[tex]z = \frac{36.4-23.3}{6.4}[/tex]
z = 2.05
P(X>36.4) = P(z>2.05) = 1 - P(z<2.05)
P(X>36.4) = 1 - 0.9798
P(X>36.4) = 0.0202
(d) Events are unusual if probability is less than 5% or 0.05. So, part (c) has an unusual event.
The probability will be:
(a) 0.2038
(b) 0.4046
(c) 0.0203
(d) Event in part (c) is unusual.
According to the question,
[tex]\mu = 23.2[/tex][tex]\sigma = 6.4[/tex]Let,
"X" shows the test scores.(a)
The z-score for X=18 will be:
→ [tex]z = \frac{X- \mu}{\sigma}[/tex]
[tex]= \frac{18-23.3}{6.4}[/tex]
[tex]= -0.828[/tex]
So,
The probability will be:
→ [tex]P(X<18) = P(z < -0.828)[/tex]
[tex]= 0.2038[/tex]
(b)
The z-score for X=19.9 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{19.9-23.3}{6.4}[/tex]
[tex]= -0.531[/tex]
The z-score for X=26.7 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{26.7-23.3}{6.4}[/tex]
[tex]= 0.531[/tex]
So,
The probability will be:
→ [tex]P(19.9 < X< 23.3) = P(-0.531 < z< 0.531)[/tex]
[tex]= 0.4046[/tex]
(c)
The z-score for X=36.4 will be:
→ [tex]z = \frac{X -\mu}{\sigma}[/tex]
[tex]= \frac{36.4-23.3}{6.4}[/tex]
[tex]= 2.047[/tex]
So,
The probability will be:
→ [tex]P(X > 36.4 )= P(z > 2.047)[/tex]
[tex]= 0.0203[/tex]
(d)
Just because it's probability value is less than 0.05, so that the events is "part c" is unusual.
Learn more about probability here:
https://brainly.com/question/23044118
please answer! I need these points for grade!
∡NMO = 59°
Step-by-step explanation:if MO bisect =>
=> ∡LMN = 2∡LMO =>
=> 5x - 22 = 2(x + 31)
5x - 22 = 2x + 62
5x - 2x = 62 + 22
3x = 84
x = 28°
∡LMO = ∡NMO => ∡NMO = x + 31
=> ∡NMO = 28 + 31 = 59°
Please
Help me asap!!
Answer:
z -2 = 10
Step-by-step explanation:
11z-9-10z+7 = 10
Combine like terms on the left side
11z -10z -9+7 =10
z -2 = 10
Answer: z=12
Step-by-step explanation:
[tex]11z-9-10z+7=10\\z-9+7=10\\z-2=10\\z=12[/tex]
Carlos is an administrative assistant at an insurance agency. He wants to gather feedback from customers on their service. He doesn't have a lot of time, and he wants to have some data to share with his supervisor. What is the best way for Carlos to gather feedback? O a) Individual interviews O b) Survey O c) Focus group d) Phone calls
When a person does not have enough time he must should take the faster and effective route in this case carlos does not have time for individual interviews or phone calls. Focus group will not work i guess because discussion takes time so i guess it should be survey. I am not sure but it should be Survey or Focus Group
Must click thanks and mark brainliest
Find the principal invested if $495 interest was earned in 3 years at an interest rate of 6%.
Answer: $2750
Step-by-step explanation:
Formula to calculate interest : I = Prt , where P = Principal amount , r = rate of interest ( in decimal) , t= time.
Given: I= $495
t= 3 years
r= 6% = 0.06
Then, according to the above formula:
[tex]495 = P (0.06\times3)\\\\\Rightarrow\ P=\dfrac{495}{0.18}\\\\\Rightarrow\ P=2750[/tex]
Hence, the principal invested = $2750
How much will $1000 deposited in an account earning 7% interest compounded annually be worth in 20 years? (which formula do I use? I am confused...txs)
Answer:
$3870
Step-by-step explanation:
Hello, the initial deposit is $1000.
After one year, we will get 1000 + 7%*1000= 1000 * ( 1+7%) = 1000 * (1+0.07)
= 1000 * 1.07
And we want to compound it so the second year we will get
[tex]1000 * 1.07 * 1.07 = 1000 * 1.07^2[/tex]
And after n years, we will get
[tex]1000 * 1.07^n[/tex]
In that example, we want to know how much we will get after 20 years, so this is:
[tex]1000 * 1.07^{20}=3869.684462...[/tex]
Thank you.
When interest is compounded, it means that both the interest and the amount deposited will earn interest.
We are to determine the future value of $1000 with annual compounding.
The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = amount deposited = $1000
R = interest rate = 7%
N = number of years = 20
$1000 x ( 1.07)^20 = $3,869.68
To learn more about compound interest, please check: https://brainly.com/question/14295570?referrer=searchResults
find three numbers in dip, such that their sum is 60 and the last one is three times the first
30,20 and 10
30 + 20 + 1/3×30 = 60
50 + 10 = 60
60 = 60
Must click thanks and mark brainliest
Ejercicio 2.-
Se dispone a almorzar en un restoran donde habitualmente deja como propina (tip) el
15% del total a pagar, o sea, del consumo más impuesto (tax).
El impuesto en ese condado es del 7% del consumo.
Se da cuenta de que no trajo sus tarjetas y solamente cuenta con $25
en efectivo (cash). Calcule el
valor máximo de los platos que va a ordenar en su almuerzo teniendo en cuenta tax y
tip.
Answer:
El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.
Step-by-step explanation:
Sea [tex]c[/tex] el coste máximo que puede asumir el comensal, medido en pesos, el cual es representada por la siguiente suma:
[tex]c = c_{o} + c_{i} + c_{ii}[/tex]
Donde:
[tex]c_{o}[/tex] - Coste del consumo, medido en pesos.
[tex]c_{i}[/tex] - Coste del impuesto en el condado, medido en pesos.
[tex]c_{ii}[/tex] - Coste de la propina, medido en pesos.
Ahora, los costes por impuesto y por propina se determinan en función del coste de consumo:
Coste del impuesto en el condado
[tex]c_{i} = r_{i}\cdot c_{o}[/tex]
Donde [tex]r_{i}[/tex] es la razón entre el coste del impuesto en el condado y el coste del consumo, adimensional.
Coste de la propina
[tex]c_{ii} = r_{ii}\cdot (c_{o}+c_{i})[/tex]
[tex]c_{ii} = r_{ii}\cdot (c_{o}+r_{i}\cdot c_{o})[/tex]
[tex]c_{ii} = r_{ii}\cdot (1 + r_{i})\cdot c_{o}[/tex]
Donde [tex]r_{ii}[/tex] es la razón entre el coste de la propina y la suma de los costes de consumo y del impuesto del condado, adimensional.
Entonces, la suma completa queda representada por:
[tex]c = c_{o} + r_{i}\cdot c_{o}+r_{ii}\cdot (1+r_{i})\cdot c_{o}[/tex]
[tex]c = [1+r_{i}+r_{ii}\cdot (1+r_{i})]\cdot c_{o}[/tex]
A continuación, se despeja el coste de consumo (valor máximo de los platos):
[tex]c_{o} = \frac{c}{1 +r_{i}+r_{ii}\cdot (1+r_{i})}[/tex]
Si [tex]c = \$\,25[/tex], [tex]r_{i} = 0.07[/tex] y [tex]r_{ii} = 0.15[/tex], entonces:
[tex]c_{o} = \frac{\$\,25}{1+0.07+0.15\cdot (1+0.07)}[/tex]
[tex]c_{o} = \$\,20.32[/tex]
El valor máximo de los platos a ordenar en el almuerzo es de $ 20.32.
Please help!
It took Suki 127 minutes from start to finish to carve her pumpkin. Carving the pumpkin took her 13 fewer minutes than 10 times as long as it took her to pick the pumpkin out at the pumpkin patch. Write and solve an equation to find how long it took Suki to pick out her pumpkin.
9514 1404 393
Answer:
14 minutes
Step-by-step explanation:
Let t represent the time it took Suki to pick out her pumpkin. The given relation is ...
10t -13 = 127 . . . . . equation for minutes to carve
10t = 140 . . . . . . . . add 13
t = 14 . . . . . . . . . . divide by 10
It took Suki 14 minutes to pick out her pumpkin.
pamela is 8 years older that jiri. the sum of their age is 102. What is jiris age?
There are two different ways we can solve this problem. We could use brute force, or we can use some equations to solve the problem. We can start by defining Pamela and Jiri's ages differently. If Jiri is j, and Pamela is p, we can say that p = j + 8, because Jiri + 8 years is Pamela's age.
Now, using our values for Pamela and Jiri, we can say that (j + 8) + j = 102. Now we just solve like a normal equation, so 2j = 94, and j = 47, so Jiri is 47 years old.
Answer:
J = 47
Step-by-step explanation:
P = Pamela
J = Jiris
P = 8 + J ;- Equation 1
P + J = 102 ;- Equation 2
Substitute equation 1 into 2 to get:
J + 8 + J =102
2J = 102 - 8
2J = 94
J = 47
So Jiris is 47 years old
Three friends say they are friends A,B and C and they want to buy a teacher a gift so they each put in $10($30 total) and a fourth friend say he is friend D and uses the money and buys a $25 gift and has $5 left and gives each of the three friends $1 back so they technically used $9 each but 9x3=27 and there is $2 left from the $5 but 27+2=29 so when is the last dollar like how does this work?
Answer:
Step-by-step explanation:
You are using the wrong accounting system
Forget the nine dollars.
If the thing bought was 25 dollars, then each one of A B and C put in 25/3 = 8.3333 dollars. If 1 dollar each was going back, then the sum became 9 1/3 dollars. 3 * 9 1/3 = 27 + 1 = 28. There is 2 dollars left. Everything is fine.
25 + 3 = 28
The three each got 1 dollar back. But the total accounted for is 25 + 3 = 28
There's 2 left over. That makes 30. Everything's fine. There is no missing dollar.
thank you for the help every one
Answer:
1. 1.66in
2. 6.66in
3. 3.33in
4. 1inch
Step-by-step explanation:
the area of a rectangle is found by multiplying the length times width or the two sides.
5 x 1/3 is about 1.66 inches
5 x 4/3 is about 6.66 inches
5/2 x 4/3 is about 3.33 inches
and 7/6 x 6/7 is 1 inch
additive inverse of 2/8
Answer:
-2/8is it's answer
Step-by-step explanation:
mark as Brainlist
-3x > 12
What is the value of x? Use substitution to support your answer.
Answer:
x < -4
Step-by-step explanation:
-3x > 12
----- ----
-3 -3
12 ÷ -3 = -4
Which means:
x < -4
(The sign changes because the equation is divided by a negative number)
Hope this helped.
Answer:
x <-4
Step-by-step explanation:
-3x > 12
Divide each side by -3. remembering to flip the inequality
-3x/-3 > 12/-3
x <-4
13,226 divided by 29
13226/29= 456.068965517
The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. Suppose there is not information about the proportion of students who might choose the option. What size sample should the department head take if he wants to be 95% confident that the estimate is within 0.10 of the true proportion
Answer:
96
Step-by-step explanation:
From the given information:
At 95% Confidence interval level,Level of significance [tex]\alpha[/tex] 0.05, the value of Z from the standard normal tables = 1.96
Margin of Error = 0.10
Let assume that the estimated proportion = 0.5
therefore; the sample size n can be determined by using the formula: [tex]n =(\dfrac{Z}{E})^2 \times p\times (1-p)[/tex]
[tex]n =(\dfrac{1.96}{0.1})^2 \times 0.5\times (1-0.5)[/tex]
[tex]n =(19.6)^2 \times 0.5\times (0.5)[/tex]
n = 96.04
n [tex]\approx[/tex] 96
What is the period of the function shown in the graph?
At origin, the value of the function is [tex]0[/tex]
and then it again becomes zero for the first time is at $2$
but the function isn't repeating itself (it's going downwards)
at $x=4$, it's exactly same, hence the period is $4$
Finding the sale price given the original price and percent...
The price of an item has been reduced by 10%. The original price was $99.
Use the ALEKS calculator to find the price of the item now.
W
x
3
?
At
Answer:
$89.1
Step-by-step explanation:
The original price is 99. The sale price is 99-99*(10/100)=89.1
How is the graph of y=4(2)^x-3 translated from the graph of y=4(2)^x
Subtracting 3 at the end of the equation shifts the graph down 3 units
Are the ratios 6:3 and 2:1 equivalent?
pls help! I need the answer fast
Answer:
D
Step-by-step explanation:
area of a rectangle : length × width = 6×3 = 18
area of a circle : pi×r² = pi × (1.5)² = pi × (3/2)² = pi×9/4
the area of the shaded region is simply the area of the rectangle minus the area of the circle.
and so it is
18 - 9×pi/4
Which phrase represents t times 33 he quotient of a number and 33 the product of a number and 33 the quotient of 33 and a number the difference of a number and 33
Answer:
the product of a number and 33
Step-by-step explanation:
The operation "times" is what is used to form the product of two operands.
"t times 33" is "the product of t and 33"
Solve the equation for y. Identify the slope and y-intercept then graph the equation.
Y=-3x+1
Y=
M=
B=
Please Include a picture of the graph and show your work if you can
Find s. Consider the set of differences between two dependent sets: 84, 85, 83, 63, 61, 100, 98. Round to the nearest tenth.
Answer:
s is [tex]s =15.3[/tex]
Step-by-step explanation:
From the question we are told that
The data is
Generally the mean is evaluated as
[tex]\= x = \frac{84+ 85+ 83+ 63+ 61+100+ 98}{7}[/tex]
[tex]\= x = 82[/tex]
The standard deviation is mathematically represented as
[tex]s = \frac{\sum (x- \= x)^2}{n-1}[/tex]
[tex]s =\sqrt{ \frac{ (84-82)^2+ (85-82)^2 +( 83-82 )^2 +(63-82) ^2 + ( 61-82)^2,+ (100-82)^2 + (98-82)^2}{7-1}}[/tex]
[tex]s =15.3[/tex]
Susan has an investment account which compounds interest annually at a rate of 3.2%. After 6 years, she has 86125 in the
account. How much money did she initially place in the account? Round your answer to the nearest whole number. Do not
include a s in your answer.
Provide your answer below:
Answer:
10610
Step-by-step explanation:
Given,
T=6years
R=3.2%
A=86125
Now,
CA=P[1+R/10]^T
or,P=86125/[1+3.2/10]^6
=86125/5.29
=10610
PLEASE SOLVE THE ABOVE PROBLEM you’ll get 43 POINTS
heya friend
0.2
0.2**10/10
=2/10
in 2/10 2 and 10 are integers
and 10 is not zero
so it is sacrificed
hope this helps u
Answer:
0.2
0.2**10/10
=2/10
in 2/10 2 and 10 are integers
10 is not 0
Step-by-step explanation:
You’ve been contracted to wallpaper a wall 10 feet wide and 12 feet high with a square window with 3 foot sides. How many square feet of wallpaper do you need to cover the wall if you were to exclude the opening for the window? _____ square feet
Answer:
111 ft²
Step-by-step explanation:
wall: 10 x 12 = 120
window: 3 x 3 = 9
wall - window = area to wallpaper
120 - 9 = 111
111 ft²
Answer:
111 sq ft
Step-by-step explanation:
wall: 10 x 12 = 120
window: 3 x 3 = 9
wall - window = area to wallpaper
120 - 9 = 111
111 ft²
Is the square root of 65 a rational number
Answer:
No
Step-by-step explanation:
The square root of 65 is irrational.
It is not a rational number because 65 is not a perfect square.
The square root of 65 is 8.06225775...
The square root of 65 is not a rational number.
65 is not a perfect square which means it's impossible to
find a whole number times itself to give us 65.
On a calculator if you type in the square root of 65,
you will get an infinite decimal number.
The decimal values never end and never have same repeated pattern.
A/An is a type of blood cell that's also called a red blood cell. a) Jeukocyte O b) thrombocyte c) plasma d) erythrocyte
Answer:
opt. (d)
Step-by-step explanation:
red blood cell, also called erythrocyte, cellular component of blood, millions of which in the circulation of vertebrates give the blood its characteristic colour and carry oxygen from the lungs to the tissues.
Fiona wrote the linear equation y = y equals StartFraction 2 over 5 EndFraction x minus 5.x – 5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s? x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 4 EndFraction.y = x – x minus StartFraction 5 over 4 EndFraction y equals StartFraction 25 over 2 EndFraction.y = x – x minus StartFraction 5 over 2 EndFraction y equals StartFraction 25 over 2 EndFraction.y =
Answer:
D. [tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Step-by-step explanation:
Given
[tex]y = \frac{2}{5}x - 5[/tex]
Required
Determine its equivalent
From the list of given options, the correct answer is
[tex]x - \frac{5}{2}y = \frac{25}{2}[/tex]
This is shown as follows;
[tex]y = \frac{2}{5}x - 5[/tex]
Multiply both sides by [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2} * y = \frac{5}{2} * (\frac{2}{5}x - 5)[/tex]
Open Bracket
[tex]\frac{5}{2} * y = \frac{5}{2} * \frac{2}{5}x - \frac{5}{2} *5[/tex]
[tex]\frac{5}{2}y = x - \frac{25}{2}[/tex]
Subtract x from both sides
[tex]\frac{5}{2}y - x = x -x - \frac{25}{2}[/tex]
[tex]\frac{5}{2}y - x = - \frac{25}{2}[/tex]
Multiply both sides by -1
[tex]-1 * \frac{5}{2}y - x * -1 = - \frac{25}{2} * -1[/tex]
[tex]-\frac{5}{2}y + x = \frac{25}{2}[/tex]
Reorder
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Hence, the correct option is D
[tex]x-\frac{5}{2}y = \frac{25}{2}[/tex]
Answer:
The 4th option
Step-by-step explanation: