Using the normal distribution, it is found that:
a) 4.75% of drivers have a reaction time greater than 1.8 seconds.
b) The reaction time is of at least 1.73 seconds.
Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.In this problem, the mean and the standard deviation are given by, respectively:
[tex]\mu = 1.5, \sigma = 0.18[/tex]
Item a:
The proportion is one subtracted by the p-value of Z when X = 1.8, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1.8 - 1.5}{0.18}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
1 - 0.9525 = 0.0475 = 4.75%.
4.75% of drivers have a reaction time greater than 1.8 seconds.
Item b:
The reaction time is of at least X seconds, in which X is the 90th percentile, that is, X when Z = 1.28, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 1.5}{0.18}[/tex]
[tex]X - 1.5 = 1.28(0.18)[/tex]
[tex]X = 1.73[/tex]
The reaction time is of at least 1.73 seconds.
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A package of 24 Oreo cookies cost $3.89. How much would 3 cookies cost? 5 cookies?
Answer:
3 equals 49 cents 5 equals 81 cents
Ms. James bought 3 world maps for her classroom. The total cost of the 3 maps was $73.77. The clerk told Ms. James that each map cost $2.45. Do you agree with the clerks calculations? Explain your reasoning.
please help ASAP please will give branlyist if i can figure it out
Answer:
The clerk is wrong because the total cost per map is $24.59
Step-by-step explanation:
since you know that you spent $73.77 for 3 maps you can set up the equation 73.77 = 3X (where x = cost per map)
once you divide 73.77 by 3 you get 24.59 and that equals the price per map
if it was like the clerk said and each map was 2.45 then the total cost shoud have been 7.35.
All equilateral triangles are ____
triangles
A. Right
B. Acute
C. Scalene
D. Obtuse
Answer:
Acute
Explanation:
Due to the fact that all the angles of an equilateral triangle have a measure of 60 degrees, the triangle must be acute as the measure of all acute angles are less than 180 degrees.
Answer:
Option B
Step-by-step explanation:
All equilateral triangles are "acute triangles" or option B. Acute triangles have degrees that are less than the degree of a right triangle which is 90 degrees. In this case all equilateral triangles have the sum of 60 degrees, which is less than the degree of a right triangle which means it is indeed a acute angle. It's not option D because obtuse triangles are triangles with angles that are more than 90 degrees, it's also not option C because each side of a scalene triangle is of different length in terms of degrees.
Hope this helps.
Solve the following system of equations two ways:
First solve using elementary row operations (you may use back-substitution if you like). Make sure you annotate your work clearly.
Second solve by expressing the system as a matrix equation of the form Ax=b (make sure you provide some explanation of where this matrix comes from.), find A^-1, and then multiply both sides of the equation with A^-1.
Here is your system of equations:
x + y - 2 = 4
2x – y + z = 2
-3x + y + 5z = 2
Answer:
im sorry this is not an answer, im just doing this to complete my profile sorry
Choose the expression that is equal to 28.3
There are no other expressions intered. Please write them too.
Answer:
It CAN be 28.30
52. What are the given facts?plssss?help this is
I will give brainlisted for correct answer!
Look at the function below.
f(x) = 5.25
Which of the choices correctly describe x?
I. an element of the domain
II. an element of the range
ill. an input value
IV. an output value
A.) I and IV
B.) only |
C.) I and III
D.) only III
Answer:
C
Step-by-step explanation:
x is an input value and an element of the domain. f(x), the range, is 5.25.
What is the vertex of this
quadratic function?
y = 4(x-3)2 – 8
Answer:
The vertex of [tex]y = 4\, (x - 3)^{2} - 8[/tex] is at [tex](3,\, -8)[/tex].
Step-by-step explanation:
Consider a quadratic function with the point [tex](h,\, k)[/tex] as the vertex (for some constants [tex]h[/tex] and [tex]k[/tex].) It would then be possible to express this function in the vertex form [tex]y = a\, (x - h)^{2} + k[/tex] for some constant [tex]a[/tex] where [tex]a \ne 0[/tex]. (Note the minus sign in front of [tex]h[/tex].)
For example, the quadratic function [tex]y = 4\, (x - 3)^{2} - 8[/tex] in this question is expressed in this vertex form:
[tex]y = 4\, (x - 3)^{2} + (-8)[/tex].
The values of [tex]h[/tex] and [tex]k[/tex] are [tex]h = 3[/tex] and [tex]k = (-8)[/tex], respectively. Thus, the vertex of this parabola would be at the point [tex](3,\, -8)[/tex].
Answer:
[tex]\displaystyle [3, -8][/tex]
Explanation:
First off, this equation came from the quadratic equation [tex]\displaystyle [y = Ax^2 + Bx + C],[/tex]in which it was [tex]\displaystyle y = 4x^2 - 24x + 28.[/tex]In the vertex equation [tex]\displaystyle [y = A(x - h)^2 + k],[/tex]the vertex is represented by [tex]\displaystyle [h, k],[/tex]in which −h gives you OPPOCITE TERMS OF WHAT THEY REALLY ARE, so be careful there.
I am joyous to assist you at any time.
PLEASE HELP WILL GIVE BRAINLIEST!!!!
Answer:
C E A F B D
Step-by-step explanation:
A function is translated to the right by h units when x is replaced by (x-h) in the function. So, the larger h is, the farther right the vertex of the quadratic is.
The vertices will be arranged left to right by the ordering ...
[tex]\boxed{y=f(x+3)}\rightarrow\boxed{y=f(x+2)}\rightarrow\boxed{y=f(x)}\rightarrow\boxed{y=f\left(x-\dfrac{1}{2}\right)}\\\\\rightarrow\boxed{y=f(x-4)}\rightarrow\boxed{y=f(x-7)}[/tex]
NEED HELP ASAP
BEST ANSWER WILL BE MARKED AS BRAINLEST
Answer:20x2
Step-by-step explanation:
I love my chocolate company makes dark chocolate and light chocolate
Answer:
this is great to hear I personally like light
The cost of manufacturing a single DVD is represented by: C(x) = 0.35x+ 1.75. What is the cost of manufacturing 12 DVDs?
Answer:
£5.95
Step-by-step explanation:
To find the cost of 12 DVDs, let x = 12
C(12) = 0.35 x 12 + 1.75
C(12) = 4.2 + 1.75
C(12) = 5.95
The cost of manufacturing 12 DVDs is $5.95.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Given that, the cost of manufacturing a single DVD is represented by C(x) = 0.35x+ 1.75.
When, x=12
C(12)=0.35×12+1.75
C(12)=5.95
Therefore, the cost of manufacturing 12 DVDs is $5.95.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each circle equation to its corresponding center and radius.
center = (3,-5)
radius = 2 units
center = (-3,-5)
radius = 4 units
center = (3,5)
radius = 2 units
center = (-3,5)
radius = 2 units
center = (3,-5)
radius = 4 units
center = (3,5)
radius = 4 units
(x + 3)2 + (1 + 5)2
= 16
(x + 3)2 + (1 – 5)2 = 4
+
=
(x – 3)2 + (x – 5)2
= 4
|(1 – 3)2 + (1 + 5)2 = 16
-
=
By using the general equation for a circle, we will see that the correct options are:
1) This is a circle centered at (-3, - 5) with a radius of 4 units.2) The center is (-3, 5) and the radius is 2 units.3) The center is (3, 5) and the radius is 2 units.4) This is a circle centered at (3, - 5) with a radius of 4 units.How to write a circle equation?
For a circle of radius R and center (a, b), the equation is given by:
(x - a)^2 + (y - b)^2 = R^2
With that in mind, if we look at the first equation:
(x + 3)^2 + (y + 5)^2 = 16 = 4^2
This is a circle centered at (-3, - 5) with a radius of 4 units.
For the second equation:
(x + 3)^2 + (y - 5)^2 = 4 = 2^2
The center is (-3, 5) and the radius is 2 units.
The third equation is:
(x - 3)^2 + (y - 5)^2 = 4 = 2^2
The center is (3, 5) and the radius is 2 units.
The fourth equation is:
(x - 3)^2 + (y + 5)^2 = 16 = 4^2
This is a circle centered at (3, - 5) with a radius of 4 units.
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I need serious help with this.
Think About the Process, In Triangle ABC, m
A=?
B=?
C=?
when you write its thi t would be an acute triangle. Basically, the one you think of when you think triangle.
but when its multi step its c
Step-by-step explanation:
Sum exterior measure = ( n-2)*180
( n-2 ) *180
(3-2)*180
180
x+4x-2+5x = 180
10x-2 = 180
10x = 180+2
10x = 182
x = 18.2
A = x
A = 18.2°
B=5x
B = 5(18.2)
B = 91°
C = 4x-2
C = 4(18.2)-2
C = 72.8-2
C = 70.8°
electrician cuts a 21 ft piece of wire into two pieces. One piece is 4 ft longer than the other. How long are the pieces?
21=a+(a+4)
one piece is 8.5 ft
the other is 12.5 ft
for each ordered pair determine whether it is a solution to 2x+7y=-5
(-6, 1)
(9, 2)
(8, -3)
(-5, -4)
Hey there!
In order to determine whether an ordered pair is a solution, all we have to do is plug in the values of x and y and see if we end up with a true statement.
The first pair is (-6, 1)
plug in 1 for y and -6 for x:
2(-6)+7(1)=-5
-12+7=-5
-5=-5
Yep! Here we have a true statement.
Therefore, this ordered pair is a solution.
2(9)+7(2)=-5
18+14=-5
Well, we can see that we have a false statement, because
32≠-5
and ≠ means "not equal to"
Let's try the third ordered pair.
2(8)+7(-3)=-5
16-21=-5
-5=-5
Great! We have another true statement :)
Let's try the last option.
2(-5)+7(-4)=-5
-10-28=-5
-38=-5
As we can see, we ended up with a false statement.
-38≠-5
Hence,
[tex]\boxed{\boxed{\bold{options~A~and~C~are~correct.}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#LearningDoesn'tEnd
:-)
There are 230 cal in a 48G packet of Eminem how many calories are in a 33.60 g bag?
The answer will be 160.99 or 161????
Mill river middle school has 320 families with students at the school. For the open house, 240 families were present. What percentage of families came to open house?
Answer:
75%
Step-by-step explanation:
in order to find the percentage of something like this, all you need to do is divide the part by the whole, thus 240/320 to make 75%
Please answer these two questions!
Answer:
the answer is B. this is because since they are on the same horizontal line, the distance is the value of the 3 plus the value of 6. so 6+3=9.
If you think about it in positives like 5 and 2, you'd subtract to get that the distance is 3. It's the same for -6 and 3.
Let's find
(-6,4)(3,4)y=4
Distance of x axis we need
|-6|+36+39unitsThe least common denominator for 3/9 and 3/6
Answer:
The least common denominator is 18:)
Refer to the following information on full-term births in the United States over a given period of time.Type of Birth Number of BirthsSingle birth 47,200,000Twins 600,000Triplets 3000Quadruplets 200Use this information to estimate the probabilities of the following events.(a) A randomly selected pregnant woman who reaches full term delivers twins. (Give the answer to three significant figures.)(b) A randomly selected pregnant woman who reaches full term delivers quadruplets. (Give the answer to three significant figures.)(c) A randomly selected pregnant woman who reaches full term gives birth to more than a single child. (Give the answer to three significant figures.)
Answer:
Refer to the following information on full-term births in the United States over a given period of time.
Type of Birth Number of Births
Single birth 47,200,000
Twins 600,000
Triplets 3000
Quadruplets 200
Use this information to estimate the probabilities of the following events.
(a) A randomly selected pregnant woman who reaches full term delivers twins. (Give the answer to three significant figures.)
(b) A randomly selected pregnant woman who reaches full term delivers quadruplets. (Give the answer to three significant figures.)
(c) A randomly selected pregnant woman who reaches full term gives birth to more than a single child. (Give the answer to three significant figures
A researcher collected data from car shoppers about their favorite car color. He asked 250 people about their favorite vehicle color. How many more people said their favorite color is white compared to those who said black. Your answer should be written as a number not a percentage. And then the percents for the circle graph are 20% red 24% white 32% blue 18% black 4% silver and 2% other
Answer:
35 more preferred white
Step-by-step explanation:
Black 18% * 250 = 18/100 * 250 = 45
White 32%*250 = 32/100 * 250 = 80
The difference is 80 - 45 = 35
Angelo’s score in a video game was changed by -75 points because he missed some targets. He got -15 points for each missed target. How many targets did he miss?
Answer:
the answer is 5 targets
1/2 × 1/2
Solve pls i need help on thus
Answer:
=> 1/2 × 1/2
=> 2/2
=> 1
--------------------------
Nonsense will be reported!!
Answer:
Step-by-step explanation:
[tex]\bf \left( \dfrac{-11}{2} * +3 \right) -2*\left(\dfrac{11}{4}x-\dfrac{5}{2} \right) =\left( \dfrac{-33}{2} \right) - 2*\dfrac{11}{4}x - (-2) * \dfrac{5}{2}\\\\\\[/tex]
[tex]\bf = \dfrac{-33}{2}-\dfrac{11}{2}x + \dfrac{10}{2}\\\\\\ = \dfrac{-33-11x+10}{2}\\\\\\ = \dfrac{-23-11x}{2}[/tex]
What is the y-intercept for the equation y=-4(x – 3)2 +1?
Answer:
(0,25)
Step-by-step explanation:
Answer:
I believe the y intercept is (0,25)
7500 in account paying 1.5 compound interest, how much after 8 years
Answer:
The amount of money after 8 years is $8448.69
Step-by-step explanation:
The rule of the compound interest is
[tex]A=p(1+r)^{t}[/tex] , where
A is the new valueP is the original valuer is the rate in decimalt is the time in years∵ There is $7500 in an account
∴ P = 7500
∵ The account paying 1.5% compound interest
∴ r = 1.5% = 1.5/100 = 0.015
∵ The money will invest for 8 years
∴ t = 8
→ Substitute all of these values in the rule above to find A
∵ [tex]A=7500(1+0.015)^{8}[/tex]
→ Use your calculator to find the answer
∴ A = 8448.69
∴ The amount of money after 8 years is $8448.69
An art teacher had 2/3 gallon of paint to pour into containers. If he poured 1/8 gallon of paint into each container untill he ran out of paint. How many containers had paint in them including the one that was partially filled
Answer:
Ok 2/3 / 1/8 = 2/3 *8 = 16/3. 16/3 is 5.33 which is 5 and a third of a container which is counted in this so 6 is the answer
Step-by-step explanation:
the midpoint of (1,4) and (-7,10)
Answer:
i’m pretty sure the answer is y=3/4x-13/4
Step-by-step explanation:
A clock shows time as 1:10pm is 20 minutes fast what is the correct time
Answer:
12:50
Step-by-step explanation:
in time after 60 minutes it goes to the next hour
so since is 20 minutes faster we are going to take it back 20 minutes backward
--› 1:10{when going backwards after 1:00 is 12:59}
--› 1:10 - 20
--› 12:50
The correct time on the clock is given by the equation A = 12 : 50 PM
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the correct time on the clock be represented as A
Now , the equation will be
The present time on the clock P = 1 : 10 PM
And , the time on the clock is 20 minutes faster than the actual time
So , substituting the values in the equation , we get
The correct time on the clock is given by A = present time on the clock P - 20 minutes
On simplifying the equation , we get
The correct time on the clock is given by A = 12 : 50 PM
Therefore , the value of A is 12 : 50 PM
Hence , the equation is solved
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