The weights of laboratory cockroaches follow a normal distribution with mean 80 grams and standard deviation 2 grams. about what percent of the cockroaches have weights between 76 and 84 grams?
Answers
Answer:
95%
Step-by-step explanation:
0.68% per cent of the cockroaches have weights between 76 and 84 grams.
Given that, the weights of laboratory cockroaches follow a normal distribution with mean 80 grams and a standard deviation 2 grams.
We need to find out what per cent of the cockroaches have weights between 76 and 84 grams.
What is the standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
First of all let's find the z-score which is given by the formula;
z = (x' - μ)/σ
From the question, mean= μ = 80 g and standard deviation; σ = 2 g
Test score; x' = 85 g
Thus;
z = (83 - 80)/2
z = 3/2
z = 1.5
From the z-distribution table attached, at z = 1.5, the probability is:
P(z > 1.5) = 1 - 0.9932 = 0.0068 or 0.68%
Therefore, 0.68% per cent of the cockroaches have weights between 76 and 84 grams.
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Related Questions
The ratio of men to women working for a company is 5 to 8 . if there are 104 women working for the company, what is the total number of employees?
Answers
5:8
104:x
8x104=5x
832=5x
832/5=x
166.4 =x
However, you cannot have 0.4 of a person, so the number of men is 166.
Total number of employees are: 166+104=270
Hope I helped :)
Form the union for the following sets.
R = {10, 15, 20}
S = {20, 25}
R ∪ S =
A. { }
B. {20}
C. {10, 15, 25}
D. {10, 15, 20, 25}
Answers
In our case, the sets are:
R = {10, 15, 20}
S = {20, 25}
The union for the sets R and S are:
D. {10, 15, 20, 25}
Intersection on the other hand is the set that contains the elements that belong both in set R and set S.
What is the equations of the quadratic function with a vertex (4, -4) and a point at (3, -6)?
Answers
y-k = a(x-h).
The equivalent equation of a horiz. polynomial is x-h = a(y-k)^2.
Plot the given points and try to determine from your graph whether the parabola in question is vertical or horizontal.
You could, of course, just begin substituting the coordinates of the given points and determine whether doing so leads to a proper equation of a parabola.
Let's actually try this for the parabola with vertex (4,-4) that passes thru the point (3,-6):
y-[-4] = a(x-4)^2
Let's now substitute the coordinates of the point (3,-6):
-6+4 = a(3-4)^2
This becomes -2 = a. Thus, from the given two points, we end up with the equation of a vertical parabola
y+4 = -2(x-4)^2
Let's check our work here. First, focus on the vertex: It's (4,-4). Let's substitute these coordinates into y+4 = -2(x-4)^2. Is the equation then true?
-4+4= -2(4-4)^2 Is 0 = to 0? Yes. What does that tell us?
Q is the midpoint of PR R is the midpoint of QS Prove: PR = QS
Answers
2. PQ = QR 2. Definition of midpoint of a segment
3. R is the midpoint o QS 3. Given
4. QR = RS 4. Definition of midpoint of a segment
5. PQ + QR = QR + RS 5. Addition property of equality
6. PR = QS 6. Segment addition postulate
Proving that PR = QS
Given: Q is the midpoint of PRThe midpoint of a segment: PQ = QR
Given: R is the midpoint of QS
The midpoint of a segment: PQ = QR
The addition property of Equality : QR + RS = PQ + QR
Therefore, PR = QS
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Use the chart to multiply the binomial by the trinomial (y+3)(y^2-3y+9) What is the product? y3 + 27 y3 – 27 y3 – 6y2 + 27 y3 + 6y2 + 27
Answers
What is another way to express 64? A) 3 ^4 B) 6 ^4 C) 6.4 x 10^2 D) 8^2
Answers
Simplify 4a + 8b - 6b + 2a
Answers
Answer:
The answer is 6a+2b
Step-by-step explanation:
hope it's helpful :)
Garrick gets paid $4.70 an hour with time-and-a-half for overtime (over 40 hours) How much did he earn one week when he worked 48 hours?
A. $195.05
B. $220.90
C. $230.30
D. $188
pleeeaaase explain your process on how you got to that answer you picked
Answers
Which statement best describes the effect of replacing the function f(x) = 2x + 2 with the function g(x) = 2x - 3?
The graph shifts 1 unit left.
The graph shifts 5 units left.
The graph shifts 5 units right.
The graph shifts 1 unit right.
Answers
However, if you looked at g(x), you will find that g(x) has decreased from +2 to -3 with a decrease of 5 units.
This means that any value put in g(x) will be 5 units less than its correspondent in f(x).
Therefore, your graph will be shifted 5 units right
Order 0.40mm, 40mm , 0.4 mm, and 0.004mm from most to least precise
Answers
What is the expression for "the difference between five times a number and twice that number"? 5(2 - n) 5n - 2n 2n - 5n?
Answers
Because 5 times n is 5n and 2 times n is 2n
How to do this I don’t understand what I’m doing wrong
Answers
on 3), we don't know how long are the segments GA and AC, therefore, we can't quite say that A is right in the middle of GC.
however, notice on DH, the units are right there on the grid, and you can count them.
A fair coin is tossed 4 times. find the probability of obtaining exactly 2 heads
Answers
i think
tell me if i got it right...
Final answer:
The probability of obtaining exactly 2 heads when a fair coin is tossed 4 times is 3/8.
Explanation:
To find the probability of obtaining exactly 2 heads when a fair coin is tossed 4 times, we need to determine the number of ways to get 2 heads out of 4 tosses and divide it by the total number of possible outcomes.
Step 1: Determine the number of ways to get exactly 2 heads.
There are four coin tosses, and we want 2 of them to be heads. We can choose the positions for the 2 heads out of the 4 tosses in 4C2 = 6 ways.
Step 2: Determine the total number of possible outcomes.
Each coin toss has two possible outcomes: heads or tails. Since there are 4 tosses, the total number of outcomes is 24 = 16.
Step 3: Calculate the probability.
The probability of obtaining exactly 2 heads is 6/16 = 3/8.
Matter must have two physical properties: 1. have mass, and 2._____.
Answers
help with pythagorean theorem!! BRAINLIEST ANSWER
Answers
x^2 +x^2 = C^2
x^2 +x^2 = 15^2
x^2 + x^2 = 225
225/2 = 112.5 = x^2
sqrt(112.5) = 10.6066
round answer as needed
note the answer can also be written as 15sqrt(2)/2
A box of books has a mass of 4.10 kilograms for every meter of its Height . Convert this ratio into pounds per foot.
Answers
Answer:
0.498 on edg
Step-by-step explanation:
The gym trainer is purchasing some new weights and a new balance bar. The weights cost $4.50 each. The balance bar costs $78. The trainer has $156. What is the greatest number of weights the trainer can purchase?
Question 13 options:
17
18
20
24
Mr. Blair is taking his family to the Great Wolfe Lodge. There are 10 people going to the Great Wolfe Lodge, and they need 3 rooms. Mr. Blair pays $110 for each of the three rooms. He gives each person including himself an allowance of money to spend. Mr. Blair has budgeted $530 for the rooms and the spending money he gives each family member. How much money did he allow in the budget for each member to spend?
Question 14 options:
$15.00
$20.00
$43.00
$53.00
Answers
156 - 78 = 78 / 4.5 = 17
2. 110 x 3 = 330
530 - 330 = 200
200 / 10 = $20 each
The greatest number of weights the trainer can purchase is 17.
Explanation:To find the maximum number of weights the trainer can purchase, we need to divide the trainer's total budget by the cost of each weight.
Step 1: Find the cost of weights per trainer's budget: $156 - $78 = $78
Step 2: Divide the cost of weights by the cost of each weight: $78 / $4.50 = 17.33
Since you cannot purchase a fraction of a weight, the trainer can purchase a maximum of 17 weights.
a figure consisting of two points and all the points in between is a
Answers
Amy deposited dimes and quarters into the coinstar machine at her local grocery store. The total money she deposited was $11.35.
Answers
What are the center and radius of the circle with equation (x + 8)^2 + (y + 3)^2 = 121?
Answers
If the product of a number and negative −3 is subtracted from the number, the result is 11 more than the number. find the number.
Answers
This sentence as an expression would be n - (-3n) = n + 11.
Solve it and you'll get 2.2!
Which statement best explains whether △JKL is congruent to △MNP?
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a rotation of 180° about the origin followed by a translation 2 units up.
△JKL is not congruent to △MNP because there is no sequence of rigid motions that maps △JKL to △MNP.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the y-axis.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the x-axis followed by a rotation of 180° about the origin.
Two triangles are graphed on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. In triangle J K L, the vertex labeled as J lies on begin ordered pair negative 4 comma 2 end ordered pair. The vertex labeled as K lies on begin ordered pair negative 2 comma 3 end ordered pair. The vertex labeled as L lies on begin ordered pair negative 2 comma negative 1 end ordered pair. In triangle M N P, the vertex labeled as M lies on begin ordered pair 4 comma 0 end ordered pair. The vertex labeled as N lies on begin ordered pair 2 comma negative 1 end ordered pair. The vertex labeled as P lies on begin ordered pair 2 comma 3 end ordered pair.
Answers
Then translating the resulting triangle 2 units up will result in a triangle with corresponding vertices (4, -2), (2, -3) and (2, 1) which is the same triangle as the given triangle MNP.
Therefore, the statement that best explains whether △JKL is congruent to △MNP is △JKL is congruent to △MNP because △JKL can be mapped to △MNP by a rotation of 180° about the origin followed by a translation 2 units up.
△JKL is congruent to △MNP because it can be mapped to △MNP through a reflection across the y-axis and a translation 2 units up.
Explanation:To determine if △JKL is congruent to △MNP, we need to see if a series of rigid motions (rotations, reflections, translations) can map △JKL exactly onto △MNP. Looking at the positions of the vertices for both triangles, we can observe that if we carry out a reflection of △JKL across the y-axis (changing the sign of the x-coordinates) and then translate the reflected △JKL 2 units upward (+2 to the y-coordinates), we end up getting the vertices for △MNP. Therefore, △JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the y-axis and a translation 2 units up. This option is not given explicitly in the original options, but this explanation provides the correct transformational sequence.
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2. How are Angle 3 and Angle 7 related?
1 point
Corresponding angles
Vertical angles
Same Side Interior angles
Alternate exterior angles
Answers
When two lines are crossed by another line, the angles in matching corners are called corresponding angles.
What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve.
Answers
(x2 - 7) (x2 + 2) = 0
(x2 - 7) = 0 and (x2 + 2) = 0
x2 = 7 and x2 = - 2
√x2 = √7 and √x2 = √-2
x = √7 and x = √-2 --> it doesn't exist
Answer: The required solutions of the given equation are
[tex]x=\pm\sqrt7,~\pm\sqrt2i.[/tex]
Step-by-step explanation: We are given to find the solutions of the following bi-quadratic equation :
[tex]x^4-5x^2-14=0~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Let us consider that
[tex]x^2=y~~~~~\Rightarrow x^4=y^2.[/tex]
So, equation (i) becomes
[tex]y^2-5y-14=0,[/tex]
which is a quadratic equation in the variable y. The above equation in variable y can be solved using factorization as follows :
[tex]y^2-5y-14=0\\\\\Rightarrow y^2-7y+2y-14=0\\\\\Rightarrow y(y-7)+2(y-7)=0\\\\\Rightarrow (y-7)(y+2)=0\\\\\Rightarrow y-7=0,~~~y+2=0\\\\\Rightarrow y=7,-2.[/tex]
Therefore, we get
[tex]x^2=7\\\\\Rightarrow x=\pm\sqrt7[/tex]
and
[tex]x^2=-2\\\\\Rightarrow x=\pm\sqrt{-2}\\\\\Rightarrow x=\pm\sqrt2i,~~~~~~~~~~~~~[\textup{where }i=\sqrt{-1}][/tex]
Thus, the required solutions of the given equation are
[tex]x=\pm\sqrt7,~\pm\sqrt2i.[/tex]
One number is 3 more than twice another number. if the sum of two number is 39, find the two numbers
Answers
X+y=39
3+2y+y=39
3y=39-3=36
Y= 12,x= 3+2*12=27
(X+3)^2-x^2=39 x^2+6X+9-x^2=39 6x+9=39. 6x=30 x =5 x+3=8
The original price of the DVD is nine dollars the sale price is 80% of the price what is the sale price of the DVD?
Answers
DVD: $9.00 originally but on sale with an 80% discount.
80%=0.80
9.00(0.80) = $7.20
$9.00 - $7.20 = $1.80
Thus, the sales price is: $1.80
multiply $9 by 80%
80% = 0.80
9 * 0.8 = 7.20
subtract that from original price
9 - 7.20 = 1.80
Sale price is $1.80
HEEEEELP AGAIN LOL PLZ PLZ
Which fraction is between – 3/8 and – 9/16 on a number line?
the options are:
-15/ 32
-23/64
-5/16
-5/8
Answers
-5/16 cannot be the answer, because -3/8 is one slot to the left of it.
-5/8 cannot be the answer, because if you convert it to 16ths, its -10/16.
-23/64 cannot be the answer, because it could also be one slot to the RIGHT of -3/8.
Help please pre calculus
Answers
A typical running track is an oval with 74-m-diameter half circles at each end. a runner going once around the track covers a distance of 400 m . suppose a runner, moving at a constant speed, goes once around the track in 1 min 40 s. what is her centripetal acceleration during the turn at each end of the track?
Answers
Answer:
Her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]
Step-by-step explanation:
Total distance covered in one round , D= 400 m
Time taken to cover one round , T = 1 min 40 s = 100 sec
Speed of runner , [tex]V=\frac{D}{T}=\frac{400}{100}\, \frac{m}{s}= 4.0\, \frac{m}{s}[/tex]
Now centripetal acceleration is given by
[tex]a_c=\frac{V^{2}}{R}[/tex]
where [tex]V= 4.0\frac{m}{s}[/tex]
[tex]Radius, R= \frac{Diameter}{2}=\frac{74}{2}m=37\, m[/tex]
[tex]\therefore a_c=\frac{4^{2}}{37}\, \frac{m}{s^{2}}=0.432\, \frac{m}{s^{2}}[/tex]
Thus her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]
The centripetal acceleration of runner at each end of track is [tex]\boxed{0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .
Explanation:
It is given that the diameter of oval track that consists of two half circles at each end is [tex]74{\text{ m}}[/tex] .
The distance runner runs once around the track is [tex]400{\text{ m}}[/tex] . The runner covers one round of track in [tex]1{\text{ m}}[/tex] and [tex]40{\text{ s}}[/tex] .
Our aim is obtain the value of centripetal acceleration for runner at each track.
The expression for centripetal acceleration is shown below.
[tex]{a_c}=\frac{{{v^2}}}{R}[/tex] …… (1)
Here, [tex]v[/tex] is the speed of the runner and [tex]R[/tex] is the radius of track.
The speed of the runner is the ratio of distance she takes to cover the track to the time taken by her.
The time in seconds is calculated as,
[tex]\begin{aligned}t&=60{\text{ s}}+40{\text{ s}}\\&=100{\text{ s}}\\\end{aligned}[/tex]
The distance covered is [tex]400{\text{ m}}[/tex] , so the speed calculated is shown below.
[tex]\begin{aligned}{\text{speed}}&=\frac{{{\text{distance}}}}{{{\text{time}}}}\\&=\frac{{400{\text{ m}}}}{{100{\text{ s}}}}\\&=4{\text{ }}{{\text{m}}\mathord{\left/{\vphantom {{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{aligned}[/tex]
The radius of track calculated is shown below.
[tex]\begin{aligned}R&=\frac{d}{2}\\&=\frac{{74{\text{ m}}}}{2}\\&=37{\text{ m}}\\\end{aligned}[/tex]
Substitute [tex]4[/tex] for [tex]v[/tex] and [tex]37[/tex] for [tex]R[/tex] in equation (1) to obtain the centripetal acceleration [tex]{a_c}[/tex] .
[tex]\begin{aligned}a_{c}&=\frac{(4\text{ m/s})^{2}}{37\text{ m}}\\&=\frac{16}{37}\text{ m/s}^{2}\\&=0.432\text{ m/s}^{2}\end{aligned}[/tex]
Therefore, the centripetal acceleration [tex]{a_c}[/tex] is [tex]0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}[/tex] .
Thus, the centripetal acceleration of runner at each end of track is [tex]\boxed{0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .
Learn More:
1. Centripetal Force https://brainly.com/question/6372960
2. Velocity and Momentum https://brainly.com/question/11896510
3. Centripetal force on orbit https://brainly.com/question/7420923
Answer Details:
Grade: High School
Subject: Physics
Chapter: Circular Motion
Keywords:
Track, running, diameter, circle, runner, distance, moves, constant, speed, centripetal, acceleration, force, motion, uniform, radius, velocity and oval.
What is the slope of the line that passes through the points (-1, 2) and (-4, 3)?
Answers
Answer: -1/3
Step-by-step explanation:
Slope is the difference between the y coordinate points divided by the x coordinate points
We have (-1, 2) and (-4, 3)
Slope = 3 - 2/ -4 - (-1)
Slope = -1/3