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:
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Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time.
a. True
b. False
Answer:
True
Step-by-step explanation:
A certain animal's body temperature has a mean of F and a standard deviation of F. Convert the given temperatures to z scores.
A certain animal's body temperature has a mean of 94.72° F and a standard deviation of 0.57°F. Convert the given temperatures to z scores.
a. 93.52 °F b. 95.22 °F c. 94.72 °F
Answer:
a. z = - 2.1053
b. z = 0.87719
c. z = 0
Step-by-step explanation:
Given that :
The population mean μ = 94.72
The standard deviation σ = 0.57
the formula for calculating the standard normal z score, which can be represented as:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
For a.
The sample mean [tex]\bar x[/tex] = 93.52
The z score can be computed as follows:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{93.52 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{-1.2}{0.57}[/tex]
z = - 2.1053
For b.
The sample mean [tex]\bar x[/tex] = 95.22
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{95.22 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0.5}{0.57}[/tex]
z = 0.87719
For c.
The sample mean [tex]\bar x[/tex] = 94.72
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{94.72 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0}{0.57}[/tex]
z = 0
Match each function name with its equation.
Answer:
a. Quadratic--[tex]y=x^{2}[/tex]
b. Absolute Value--[tex]y=|x|[/tex]
c. Linear--[tex]y=x[/tex]
d. Reciprocal Squared--[tex]y=\frac{1}{x^{2} }[/tex]
e. Cubic--[tex]y=x^{3}[/tex]
f. Square Root--[tex]y=\sqrt{x}[/tex]
g. Reciprocal--[tex]y=\frac{1}{x}[/tex]
h. Cube root--[tex]y=\sqrt[3]{x}[/tex]
Answer:
Step-by-step explanation:
y=[tex]x^{2}[/tex] is quadratic
y=x is an absolute value
y= |x| os linear
y= [tex]\frac{1}{x}[/tex] is reciprocal
y= [tex]x^{3}[/tex] is cubic
y= [tex]\sqrt{x}[/tex] is square root
y= [tex]\frac{1}{x^{2} }[/tex] is reciprocal squared
y= [tex]\sqrt[3]{x}[/tex] is cube root
Help please I need help as soon as possible!all answers are appreciated! Keisha tried to evaluate an expression step by step. 3+(−4)−7
Answer:
D no mistakes
Step-by-step explanation:
3+(-4)-7 is equal to 3-4-7=-8
Answer:0
Step-by-step explanation:
3+(-4)-7 when there are parenthesis around a negative number you flip it to positive and then 4+3-7=0
Show all work to solve 3x2 − x − 2 = 0.
Answer:
x=-2/3 and 1
Step-by-step explanation:
3x^2-x-2=0
(3x+2)(x-1)
3x=-2
x=-2/3
x=1
A buoy floating in the sea is bobbing in simple harmonic motion with amplitude 13 in and period 0.25 seconds. Its displacement d from sea level at time t=0 seconds is 0in, and initially it moves downward. (Note that downward is the negative direction.)Required:Give the equation modeling the displacement d as a function of time t.
Answer:
The equation is [tex]x(t) = -13 cos (8 \pi t )[/tex]
Step-by-step explanation:
From the question we are told that
The amplitude is [tex]A = 13 \ in[/tex]
The period is [tex]T = 0.25[/tex]
Generally the displacement function for a simple harmonic motion is mathematically represented as
[tex]x(t) = A cos (wt )[/tex]
Here [tex]w[/tex] is the angular frequency which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 \pi }{ 0.25}[/tex]
[tex]w = 8\pi[/tex]
Given that at t = 0 the displacement is equal to 0 it means that there is no phase shift and also we are told that it is initially moving downward which implies that its Amplitude is [tex]A = -13\ in[/tex]
So the equation modeling the displacement d as a function of time t is mathematically represented as
[tex]x(t) = -13 cos (8 \pi t )[/tex]
The energy E (in ergs) released by an earthquake is approximated by log E= 11.8 + 1.5M. Where M is the magnitude of the earthquake. What is the energy released by the 1906 San Francisco quake, which measured 8.3 on the Richter scale? This energy, it is estimated, would be sufficient to provide the entire world's food requirements for a day. Answer in ergs.
Answer:
[tex]\large \boxed{3.4 \times 10^{10}\text{ ergs }}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}\log E & = & 11.8 + 1.5M\\& = & 11.8 + 1.5 \times 8.3\\& = & 11.8 + 12.45\\& = & 24.25\\E & = & e^{24.25}\\& = & \mathbf{3.4 \times 10^{10}} \textbf{ ergs}\\\end{array}\\\text{ The energy released was $\large \boxed{\mathbf{3.4 \times 10^{10}}\textbf{ ergs }}$}[/tex]
Name one real-world object that suggests A. Points B. Lines and C. Planes
There are many examples to pick from, one is
point = location on map
line = straight road between two locations (aka two points)
plane = flat ground (the ground cannot have any hills or valleys)
First, let's write some useful definitions:
Point: it is an entity that has a location in a given space or plane, and do not have any surface nor measure.
Line: if we have two points, we can define a line as a straight, infinite ray that connects them. Still does not have a surface
Plane: We can define a plane as a line and a point outside of it, here appears the concept of the surface.
So, the easier one is a plane, a sheet of paper could be a good representation of a plane. And in the same way that a sheet of paper can bend in different ways, also do the planes.
For the line, we could use a really straight wire.
Finally, the point, which is the hardest one to describe (notice that we used points to describe the other two, lines, and planes) so here we could choose something small, that has near to no surface and that also has a location in the space. An example of this could be an electron or any other elemental particle.
If you want to learn more, you can read:
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WILL GIVE BRAINILY 5 STARS AND THANKS FOR CORRECT ANSWERLenora wants to buy granola bars for her hiking trip. Eight bars cost $2.40. She wants to buy 12 bars. How much will 12 bars cost?
Answer:
$3.60
Step-by-step explanation:
2.40/8=.30
$.30 per bar
.3 x 12= $3.60
Answer:
$3.60
Step-by-step explanation:
Proportions
8 bars ⇔ $2.4
12 bars ⇔ $W
W = 12*2.4/8
W = $3.6
A hunter shot 7 ducks. The hunter's dog recovered 5/7 of the ducks. How many ducks were recover
Answer:
5
Step-by-step explanation:
Just multiply 5/7 by 7 since his dog retrieved 5/7 out of the 7 ducks he shot.
Answer:
5
Step-by-step explanation:
7*5/7
7 represents the # of ducks
5/7 represents the # of ducks that were recovered
The question asks the number of ducks that were recovered so you should multiply the total # of ducks there are by the fraction that were recovered.
How much would you need to deposit in an account now in order to have $6,000 in the account in 8 years? Assume the account earns 6% interest compounded monthly. (could anyone do this whole problem out?
Answer:
$3,717
Step-by-step explanation:
Hello, in 1 year there are 12 months.
Let's note I the Initial amount.
So, after 1 month we will get the following, because we compute the interest amount for one month only.
I * ( 1 + 6% * (1/12) )
And the next month, we will have interest of the amount available from previous month so it gives
[tex]I * ( 1+6\% * \dfrac{1}{12} ) * ( 1+6\% * \dfrac{1}{12} ) \\\\=I*(1+\dfrac{6}{12*100})^2\\\\=I*(1+\dfrac{1}{200})^2\\\\=I*(1.005)^2[/tex]
... and after n months ...
[tex]I*(1.005)^n[/tex]
8 years is 8*12 = 96 months. so we are looking for I such that
[tex]I*(1.005)^{96}=6000\\\\<=> I =\dfrac{6000}{1.005^{96}}\\\\=\boxed{3717.14345....}[/tex]
Thank you.
Yiadom is y
years now.
What would be
his age in the next ten
years.
Answer:
(y+10 ) years
Step-by-step explanation:
If Yiadom is y years now.
Then after 10 years, his anew age will be = (y+10) yrs
Perimeter =68 Length (L) is 4 less than twice the width (W)
Answer:
Length = 21.3333333333; Width: 12.6666666667
Step-by-step explanation:
Perimeter = 68
Perimeter of a rectangle:
2 (L +W)
Length (L) = 2W - 4
Width = W
2 ( 2W -4 +W) = 68
=> 2 (3W - 4) = 68
=> 6w -8 = 68
=> 6w = 76
=> w = 12.6666666667
Length = (12.6666666667 X 2) - 4
=> 21.3333333333
simplify the expression 10 divided by 5 times 3
Answer:
= 2/3
Step-by-step explanation:
10 / (5*3)
= 10/15
= 2/3
The equation of a circle centered at the origin with a radius of unit length is x2 + y2 = 1. This equation changes if the center of the circle is not located at the origin or the radius is not of unit length.
Answer:
The equation for a unit radius circle, centered at the origin is:
x^2 + y^2 = 1
Now, if we want to move it horizontally, you can recall to the horizontal translations:
f(x) -----> f(x - a)
Moves the graph to the right by "a" units.
A vertical translation is similar.
Then, if we want a circle centered in the point (a, b) we have:
(x - a)^2 + (y - b)^2 = 1.
Now, if you want to change the radius, we can actually write the unit circle as:
x^2 + y^2 = 1^2
Where if we set x = 0, 1 = y, this is our radius
So if we have:
x^2 + y^2 = R^2
And we set the value of x = 0, then R = y.
So our radius is R.
Then:
"A circle of radius R, centered in the point (a, b) is written as:
(x - a)^2 + (y - b)^2 = R^2
What faction of a day is 5hrs 20 mine
Answer:
16/3 hours 5 1/3
Step-by-step explanation:
Answer: 5 1/3
Step-by-step explanation:
What are the solutions to the system of equations? {y=2x2−8x+5y=x−2 (3.5, 0.5) and (1, −1) (7, 5) and (0.5, −1.5) (3.5, 1.5) and (1, −1) (3.5, 1.5) and (−1, −3)
Answer:
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
Step-by-step explanation:
Given
[tex]y = 2x^2 - 8x+5[/tex]
[tex]y = x - 2[/tex]
Required
Determine the solution
Substitute x - 2 for y in [tex]y = 2x^2 - 8x+5[/tex]
[tex]x - 2 = 2x^2 - 8x+5[/tex]
Collect like terms
[tex]0 = 2x^2 - 8x - x + 5 + 2[/tex]
[tex]0 = 2x^2 - 9x + 7[/tex]
Expand the expression
[tex]0 = 2x^2 - 7x - 2x+ 7[/tex]
Factorize
[tex]0 = x(2x - 7) -1(2x - 7)[/tex]
[tex]0 = (x-1)(2x - 7)[/tex]
Split the expression
[tex]x - 1 = 0[/tex] or [tex]2x - 7 = 0[/tex]
Solve for x in both cases
[tex]x = 1[/tex] or [tex]2x = 7[/tex]
[tex]x = 1[/tex] or [tex]2x/2 = 7/2[/tex]
[tex]x = 1[/tex] or [tex]x = 3.5[/tex]
Recall that
[tex]y = x - 2[/tex]
When [tex]x = 1[/tex]
[tex]y = 1 -2[/tex]
[tex]y = -1[/tex]
When [tex]x = 3.5[/tex]
[tex]y = 3.5 - 2[/tex]
[tex]y = 1.5[/tex]
Hence, the solution is;
[tex](1,-1)[/tex] and [tex](3.5,1.5)[/tex]
The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x+12=48,where x represents the cost of a. Ticket.how much is one ticket
Answer:
x=9; one ticket is $9
Step-by-step explanation:
4x+12=48
4x=48-12
4x=36
x=36/4
x=9
What is numbers 1-30 added all together
Answer:
465
Step-by-step explanation:
The sum of consecutive numbers has a formula, and it's
[tex]\frac{n(n+1)}{2}[/tex].
Where n is the amount of numbers.
From 1-30, it's 30 numbers, so:
[tex]\frac{30(30+1)}{2} \\\\\frac{30(31)}{2} \\\\\frac{930)}{2} \\\\\\465[/tex]
Hope this helped!
use the product of powers property to simplify the numeric expression.
4 1/3 • 4 1/5 = _____
Answer:
The value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
Step-by-step explanation:
We need to simplify the numeric expression using property. The expression is as follows :
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]
The property to be used is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]
This property is valid if the base is same. Here, base is x.
In this given problem, x = 4, a = 1/3 and b = 1/5
So,
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}[/tex]
So, the value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
write 32 1/2 in radical form
Answer:
Nothing further, the simplest answer is 32 1/2
Step-by-step explanation:
If the average fixed cost (AFC) of producing 5 bags of rice is $20.00, the average fixed cost of producing 10 bags will be
Answer:$40.00
Step-by-step explanation:first divide 20 by 5 and the answer will be 4. now multiply 10 into 4 and you'll get the answer $40.00
Stepwise regression is a variable screening method, not a model building method.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
Stepwise regression is a variable-selection method for independent variables.
Stepwise regression helps us to recognize and choose the most handy descriptive variables from a list of several reasonable independent variables.
It entails a series of steps that is drafted to locate the most handy X-variable to incorporate in a regression model. During each step of the course of action or method, each X - variable is estimated by applying a set criterion to determine if it is meant to exist in the model.
The basis for selection can be choosing a variable which satisfies the stipulated criterion or removing a variable that least satisfies the criterion. A typical illustration of such criterion is the t value.
The upper-left coordinates on a rectangle are (-1,4), and the upper-right coordinates are (3,4). The rectangle
has a perimeter of 24 units.
Draw the rectangle on the coordinate plane below.
Answer:
Step-by-step explanation:
Note that the perimeter of a rectangle P = 2(Length + Breadth)
The distance between the upper-left coordinates on a rectangle and the upper-right coordinates is the breadth of the rectangle. To get the breadth of the rectangle, we will use tgw formula for calculating the distance between two points as shown.
D = √(y2-y1)²+(x2-x1)²
Given the coordinates (-1,4) and (3,4), the distance between the coordinates where x1 = -1, y1 = 4, x2 = 3 and y2 = 4 will be expressed as.
B = √(4-4)²+(3-(-1))²
B = √0+4²
B = √16
B = 4
Hence the breadth of the rectangle is 4 units.
Substituting the breadth into the formula for calculating the perimeter will give;
P = 2(L+B)
24 = 2(L+4)
L+4 = 24/2
L+4 =12
L = 12-4
L = 8
Hence the length of the rectangle is 8 units.
The diagram of the rectangle on a coordinate is as given in the attachment below.
what are the next terms in the number pattern -11, -8, -5, -2, 1
Answer:
4, 7, 10, 13
Step-by-step explanation:
Hey there!
Well in the given pattern,
-11, -8, -5, -2, 1
we can conclude that the pattern is +3 every time.
-11 + 3 = -8
-8 + 3 = -5
-5 + 3 = -2
-2 + 3 = 1
And so on
4, 7, 10, 13Hope this helps :)
Excel:In cell B13, create a formula using the VLOOKUP function that looks up the value from cell A11 in the range A5:B7, returns the value in column 2, and specifies an exact match.
Answer:
=Vlookup'B13' A11' 7'false
Press enter.
Step-by-step explanation:
Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:
=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.
where true is approximate match and false is exact match.
Answer:=VLOOKUP(J2,A2:G23,2,FALSE)
Step-by-step explanation:
a. In cell J3, begin to enter a formula using the VLOOKUP function.
b. Use the Project ID (cell J2) as the lookup value.
c. Use the Projects table (range A2:G23) as the table_array.
d. Use the Project Name column (column 2) as the col_index_num.
e. Specify an exact match (FALSE) for the range_lookup.
WHY CAN'T ANYONE HELP ME PLEASE?A 40% solution of fertilizer is to be mixed with a 80% solution of fertilizer in order to get 80 gallons of a 70% solution. How many gallons of the 40% solution and 80% solution should be mixed? 40% solution =? gallons, 80% solution =? gallons
Answer:
40% solution = 20 gallons
80% solution = 60 gallons
Step-by-step explanation:
x = gallons of 40% solution
y = gallons of 80% solution
Total volume is:
x + y = 80
Total amount of fertilizer is:
0.40 x + 0.80 y = 0.70 (80)
Solve by substitution.
0.40 x + 0.80 (80 − x) = 0.70 (80)
0.40 x + 64 − 0.80 x = 56
0.40 x = 8
x = 20
y = 60
Emily thinks the perfect tomato sauce has 8 cloves of garlic in every 500 mL, of sauce. Raphael's tomato sauce has 121 cloves of garlic in every 900 mL of sauce. What will Emily think of Raphael's tomato sauce? Choose 1 answer: Choose 1 answer: (Choice A) A It is too garlicky. (Choice B) B It is not garlicky enough. (Choice C) C It is perfect.
Answer:
A
Step-by-step explanation:
Let's find the ml per garlic for each sauce. Emily's has 1 clove of garlic for 62.5 ml. Raphael's has 1 clove of garlic for 7.438... ml. So, A, it will be too garlicky.
slope of -4/3x with point (7,20) find equation
Answer:
y= -4/3x+10 2/3
Step-by-step explanation:
To do this, just put the equation in point slope form and then rearrange it to y=mx+b, or slope intercept form. Slope point form is arranged like this, y-y1=m(x-x1). Now, just insert in the variables (x1=x coordinate of point, y1= y coordinate of point, m=slope). So your equation is now y-20=-4/3(x-7), which simplifies to y-20=-4/3x-9 1/3. Now rearrange it so that y in by itself, and all like terms are combined, making it look like this: y=-4/3x+10 2/3. Now its in slope intercept form and you've got your answer.
I hope my explanation wasn't confusing and that my answer helped.
4x + 1 -5x =2x +4(x-5)
Answer:
x = 3
Step-by-step explanation:
To answer for x first distribute the 4 in the parenthesis
4x + 1 - 5x = 2x +4x - 20
Next add or subtract the x's
-x + 1 = 6x - 20
Now subtract 6x and 1 on both sides to get x on the left and the rest on the right
-7x = -21
Lastly, divide -7 on both sides
x = 3
