Given: The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.9 grams with a standard deviation of 0.2 grams.
a) The probability that a randomly chosen mouse has a mass of less than 20.74 grams is 0.2119.
b) The probability that a randomly chosen mouse has a mass of more than 21.14 grams is 0.1151.
c) The proportion of mice have a mass between 20.8 and 21.04 grams is 0.4495.
d) 10% of all mice have a mass of less than 21.15632 grams.
(a) The probability that a randomly chosen mouse has a mass of less than 20.74 grams.
Z = (X - μ)/σ, where X = 20.74, μ = 20.9, σ = 0.2.
Z = (20.74 - 20.9)/0.2Z
= -0.8P(X < 20.74)
= P(Z < -0.8)
Using standard normal distribution table, P(Z < -0.8) = 0.2119.
Thus, the required probability is 0.2119.
(b) The probability that a randomly chosen mouse has a mass of more than 21.14 grams.
Z = (X - μ)/σ, where X = 21.14, μ = 20.9, σ = 0.2.
Z = (21.14 - 20.9)/0.2
Z= 1.2
P(X > 21.14) = P(Z > 1.2)
Using standard normal distribution table, P(Z > 1.2) = 0.1151.
Thus, the required probability is 0.1151.
(c) To find the proportion of mice have a mass between 20.8 and 21.04 grams.
Z_1 = (X1 - μ)/σ
= (20.8 - 20.9)/0.2
= -0.5
Z_2 = (X2 - μ)/σ
= (21.04 - 20.9)/0.2
= 0.7
P(20.8 < X < 21.04) = P(-0.5 < Z < 0.7)
= P(Z < 0.7) - P(Z < -0.5)
Using standard normal distribution table,
P(Z < 0.7) = 0.7580
P(Z < -0.5) = 0.3085
Therefore, P(-0.5 < Z < 0.7) = P(Z < 0.7) - P(Z < -0.5)
= 0.7580 - 0.3085
= 0.4495
Thus, the required probability is 0.4495.
(d) 10% of all mice have a mass of less than grams.
Let the mass be X.
We have to find X such that P(X < k) = 0.1
Z = (X - μ)/σ, where μ = 20.9, σ = 0.2.
P(X < k) = P(Z < (k - μ)/σ)
0.1 = P(Z < (k - 20.9)/0.2)
0.1 = P(Z < 5k - 104.5)
Using standard normal distribution table, we get
5k - 104.5 = -1.2816k
k= 21.15632
Thus, 10% of all mice have a mass of less than 21.15632 grams.
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what are remainder theorem
Answer:
Step-by-step explanation:
When doing synthetic division, if the remainder is zero, we know that the divisor is a root of the polynomial. If the remainder is not zero, the remainder is the function vaue for that divisor.
Please help me with the questions please ASAP ASAP please please ASAP please please help please I’m begging please please
Answer:
3/2
Step-by-step explanation:
The ratio of perimeters of similar polygons is the same as the ratio of the lengths of corresponding sides.
WX/AB = 12/8 = 3/2
50 POINTS! Name a pair of whole numbers that have a geometric mean of 4.
How many pairs of rational numbers have a geometric mean of 4?
please help and don't say something random just for the points :)
Answer:
0, 16
1, 15
2, 14
3, 13
4, 12
5, 11
6, 10
7, 9
8, 8
Step-by-step explanation:
Any two numbers that have the product of positive 16 have a geometric mean of 4.
Please help will give brainliest
What are they coordinates
Answer:
let ABC be a right-angled triangle, where A is the right angle (left to right)
the original coordinates:
A (-8, 8)
B (-1, 8)
C (-8, 5)
by changing the coordinates from (x, y) to (-y, x)
A (-8, -8)
B (-8, -1)
C (-5, -8)
look attachment
what is x over 3 less than or equal to 7
Answer:
x≤21
Step-by-step explanation:
x/3≤7
Multiply both sides by 3
3x/3≤7×3
Simplify
x≤21
Hope this helped!!!
Can you explain why the bottom angle always has to be 90 degrees?
somebody help I don't understand this stuff.
Answer:
Dena's answer
14ft^2
Step-by-step explanation:
Her answer is correct because area of triangle is base times height divided by two. Base is 7 and height is 4
From there, you can find the area which is 14.
hope this is correct
At the 90% Confidence Interval, what are the (lower bound; upper bound)?
The lower bound of the interval is given as follows:
28.1.
The upper bound of the interval is given as follows:
29.9.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are listed as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 30 - 1 = 29 df, is t = 1.6991.
The lower bound of the interval is given as follows:
[tex]39 - 1.6991 \times \frac{3}{\sqrt{30}} = 38.1[/tex]
The upper bound is given as follows:
[tex]39 + 1.6991 \times \frac{3}{\sqrt{30}} = 39.9[/tex]
Missing InformationThe complete problem is:
"If n=30, (x-bar)=39, and s=3, at the 90% Confidence Interval, what are the (lower bound; upper bound)".
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Consider the following scenario. Suppose that
1000 people are involved in a conspiracy.
Suppose that every single individual involved in
the conspiracy can be trusted 99.9%, that is,
there is a 0.01% probability they reveal the
secrets of the conspiracy to the media within 50
years. This probability is the same for everyone
involved, and never changes over the course of
the 50 years. Moreover, suppose that the event
where anyone goes to the media (or not) is
independent if anyone else has (or hasn't)
already.
What is the probability that at least one
person involved in the conspiracy reveals their
involvement to the media within 50 years?
The probability that at least one person involved in the conspiracy reveals their involvement to the media within 50 years is approximately 0.994.
Consider the following scenario: There are 1000 individuals involved in a conspiracy.
Every person involved in the conspiracy can be trusted 99.9%, which means that there is a 0.01% probability that they will reveal the secrets of the conspiracy to the media within 50 years.
The probability of revealing the conspiracy is the same for everyone involved and remains constant throughout the 50 years.
Additionally, the probability of someone revealing the conspiracy is independent of whether anyone else has already done so or not.
What is the likelihood that at least one person will reveal their involvement to the media within 50 years? We can use the binomial distribution to determine the probability that at least one person in the conspiracy will reveal their involvement in the media in 50 years.
We'll use the following formula for the binomial distribution: P(X ≥ 1) = 1 - P(X = 0) where X is the number of individuals that reveal the secrets of the conspiracy.
In this situation, we know that there are 1000 people in the conspiracy, and the probability that each person will reveal the conspiracy is 0.01%.
We can therefore use the formula for the binomial distribution to solve for the probability of at least one person revealing the conspiracy:
P(X ≥ 1) = 1 - P(X = 0) P(X ≥ 1) = 1 - [tex](0.999)^{1000}[/tex] P(X ≥ 1) ≈ 0.994
Therefore, The probability that at least one person involved in the conspiracy reveals their involvement to the media within 50 years is approximately 0.994.
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What is the length of the terrace?
Answer:
A) 12 feet or d) 10 feet..
a) Work out the size of angle x.
100
B
b) Give reasons for your answer.
co-exterior angle
to
F
Н
G
Answer:
100°= angle b(VERTICAL OPPOSITE ANGLE)
100°+x°=180°[co interior angle]
x=180°-100°
x=80°
The Measure for angle x is 80 degree.
What is Vertical Angle?When two straight lines cross, they generate a pair of non-adjacent angles known as vertical angles. In the corners of the "X" created by two straight lines, or to put it another way, vertical angles are situated opposite one another. Due to their position opposite one another, they are also known as vertically opposite angles.
Given:
<CBD = 100 degree.
So, <ABF = <CBD (Vertical Opposite Angle)
<CBD = 100 degree.
Now, <ABF + <BFE = 180 (Angle on same side of Transversal)
<ABF + 100 = 180
<ABF = 180-100
x= 80 degree.
Hence, the measure for x is 80 degree.
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Define a relation R on N by (a,b) ∈ R if and only if a/b ∈ N. Which properties does R satisfy?
The relation R on the set of natural numbers (N) is defined as (a, b) ∈ R if and only if a/b is a natural number. This relation exhibits the properties of reflexivity, symmetry, and transitivity.
Reflexivity: For any natural number a, a/a = 1, which is a natural number. Therefore, (a, a) ∈ R for all a ∈ N. Hence, R is reflexive.Symmetry: If (a, b) ∈ R, then a/b is a natural number. This implies b/a is also a natural number since the division is commutative. Thus, (b, a) ∈ R. Therefore, R is symmetric.
Transitivity: Let (a, b), (b, c) ∈ R, which means a/b and b/c are natural numbers. As the division operation is closed under natural numbers, a/c = (a/b) * (b/c) is also a natural number. Therefore, (a, c) ∈ R, and R is transitive. In summary, the relation R on the set of natural numbers is reflexive, symmetric, and transitive, making it an equivalence relation.
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Question is in picture
Let x, y, and z be measured in meters, and suppose that F(x, y, z) = −yi+zj+3xk is the velocity vector (in m/s) of a fluid particle at the point (x, y, z) in a steady-state in- compressible fluid flow. (a) Find the net volume of fluid that passes in the upward direction through the hemisphere z = √(9-x² — y²) in 1 s. (b) Assuming that the fluid has a mass density of 1060 kg/m³, find the net mass of fluid that passes in the up- ward direction through the surface in part (a) in 1 s.
The fluid has a mass density of 1060 kg/m³, we can multiply the net volume by 1060 to obtain the net mass of fluid passing through the hemisphere in 1 second.
To find the net volume of fluid passing through the hemisphere, we need to calculate the flux of the velocity vector across the surface. The flux is given by the surface integral of the dot product of the velocity vector and the outward unit normal vector. Since the velocity vector is F(x, y, z) = -yi + zj + 3xk, we can calculate the dot product as -y(-y) + z(0) + 3x(√(9 - x² - y²)). Simplifying, we have F · dS = y² + 3x√(9 - x² - y²).
To evaluate the flux over the surface, we need to parameterize the hemisphere. Let's use spherical coordinates: x = r sinθ cosϕ, y = r sinθ sinϕ, and z = r cosθ, where 0 ≤ r ≤ 3, 0 ≤ θ ≤ π/2, and 0 ≤ ϕ ≤ 2π. The outward unit normal vector is given by n = (sinθ cosϕ)i + (sinθ sinϕ)j + (cosθ)k. Now, we can evaluate the flux by taking the surface integral: ∫∫(F · dS) = ∫∫(y² + 3x√(9 - x² - y²)) dA, where dA is the differential area element in spherical coordinates. Integrating over the appropriate limits, we can find the net volume of fluid passing through the hemisphere in 1 second.
To determine the net mass of fluid passing through the surface, we need to multiply the net volume by the fluid's mass density. Given that the fluid has a mass density of 1060 kg/m³, we can multiply the net volume by 1060 to obtain the net mass of fluid passing through the hemisphere in 1 second.
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convert the hexadecimal expansion (A95E)16 to a decimal expansion.
The hexadecimal expansion [tex](A95E)_{16}[/tex] is equal to the decimal expansion 43358. This conversion is achieved by assigning the positional values of each digit in the hexadecimal number and evaluating the corresponding decimal values.
To convert a hexadecimal number to decimal, we multiply each digit by the corresponding power of 16 and sum up the results. Starting from the rightmost digit, the value of A in hexadecimal is equivalent to 10 in decimal. The next digit 9 represents the value of 9 in decimal. Continuing in the same manner, the digit 5 represents 5 in decimal, and the final digit E is equal to 14 in decimal.
Now, we calculate the decimal equivalent using the formula:
[tex](10 * 16^3) + (9 * 16^2) + (5 * 16^1) + (14 * 16^0) = 43486[/tex]
Therefore, the hexadecimal expansion [tex](A95E)_{16}[/tex] is equal to 43486 in decimal.
In conclusion, the decimal equivalent of the given hexadecimal expansion is 43486.
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6) What is the equation of a line that passes
through (-1, -3) and has a slope of 2?
Answer:
y+3=2*(x+1)
Step-by-step explanation:
In the high-school courtyard, a memorial garden will be planted to commemorate those students who graduated and served in the military. A local nursery donated 2 cartons of plants. One carton contains 4 palms, 4 birds of paradise, and 2 plumbagos. The other box contains 5 palms and 3 birds of paradise. If Jasmine chooses one plant from each box at random, what is the probability that both plants will be birds of paradise? Express your answer as a fraction in lowest terms.
Answer:
:c
Step-by-step explanation:
F(-3)=11 and f(4)=55 find value of f(-1)
11(4)=55
44=55
f=55÷44
f=1.25(-3)
-3.75
Streaming movies from Company A costs $3 per month per movie plus a monthly fee of $9. Streaming movies from Company Bcost $4 per movie with no monthly fee. The monthly cost to stream depends on the number of movies, m streamed. Which inequality represents the situation when the montly cost at Company A is less than the montly cost at Company B.
Please help with numbers 7 and 8.
Answer:
Below
Step-by-step explanation:
Every triangle should add up to 180 degrees,
This is a right triangle because it has the square in the corner meaning it is 90 degrees.
39 + 90 = 129
180 - 129 = 51 degrees
A: 51 degrees
C: 90 degrees
Answer:
a. 51 degrees
c. 90 degrees
I think
I'm timed. Factor the Expression 4x - 30y
Answer:
23
Step-by-step explanation:
GCF of 4 is 2 and GCF of 30 is 6.
2(2*x)-6(5*y)
---
hope it helps
Solve the word problem using the plotted points on the graph.
Answer:
In the graph, we can see that the relation between length and weight is given by the adjusted line, which passes through the points (24, 16) and (28, 25)
Remember that a linear relation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If this line passes through the points (x₁, y₁) and (x₂, y₂) the slope can be calculated as:
a = (y₂ - y₁)/(x₂ - x₁)
Then in our case, the slope will be:
a = (25 - 16)/(28 - 24) = 9/4
y = (9/4)*x + b
Knowing that this line passes through (24, 16), we know that when x = 24, y must be equal to 16.
If we replace these in the equation, we can find the value of b.
16 = (9/4)*24 + b
16 = 54 + b
16 - 54 = b - 38
Then the equation is:
y = (9/4)*x - 38
Now that we know the equation, we can simply replace y by 34 pounds to find the value of x.
34 = (9/4)*x - 38
34 + 38 = (9/4)*x
72*(4/9) = x = 32
So we can estimate that the length of a fish that weighs 34 pounds is 32 (I do not know the unit of length, I can't see the horizontal axis on the image)
Eu tenho um ovo de páscoa que custa 24,99 e tem 185 gramas, tbm tenho uma barra de chocolate q custa 5,10 e tem 90 gramad. Qual da mais vantagem para mim?
Answer:
A maior vantagem para mim é a barra de chocolate.
Step-by-step explanation:
Temos que encontrar o custo de 1 grama de ovo de Páscoa e barra de chocolate
Para o ovo de páscoa
Tenho um ovo de Páscoa que custa 24,99 e tem 185 gramas.
185 gramas = 24,99
1 grama = x
Multiplicação cruzada
185 gramas × x = 1 grama × 24,99
x = 1 grama × 24,99 / 185 gramas
x = 0,1612258065
Aproximadamente = 0,16
O custo de 1 grama de ovo de Páscoa = 0,15
Para a barra de chocolate
Também tenho uma barra de chocolate que custa 5,10 e tem 90 gramas.
90 gramas = 5,10
1 grama = x
Multiplicação cruzada
90 gramas × x = 1 grama × 5,10
x = 1 grama × 5,10 / 90 gramas
x = 0,0566666667
Aproximadamente = 0,06
O custo de 1 grama de barra de chocolate = 0,06
A maior vantagem para mim é a barra de chocolate.
Laney bought a cup of coffee and two cookies at her
local coffee shop. The coffee cost $1.89. She got
$1.23 back as change from the $5.00 bill she gave the
cashier. How much did each cookie cost?
Page
Answer:
each cookie was $0.94
Step-by-step explanation:
5.00 - 1.89 = 3.11
3.11 - 1.23 = 1.88
1.88 divided by 2 = 0.94
can you help me with this due today
please help me thanks!
Answer:
2^9 (2 to the 9th power) = 512
Step-by-step explanation:
Since 2 is multiplied by itself 9 times, it can be represented as 2^9, which evaluates to 512.
Hopefully this helps - let me know if you have any questions!
A smartphone regularly sells for $125. It is on sale this week for $85. The sale
price is what percent of the regular price?
Answer:
68%
Step-by-step explanation:
85 divided by 125 = .68 * 100 = 68
Answer: The sale price is 40 percent of the regular price
Step-by-step explanation:
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If cost of 15 eggs is ? 75, then find out the cost of 4 dozens eggs
A. ? 185
B. ? 150
C. ? 300
D. ? 240
Answer:
D 240
Step-by-step explanation:
75÷15 to get the cost of each egg 5
5x12 to get 60
60x4 to get d 240
Answer:
D. 240 unitsStep-by-step explanation:
15 eggs ⇒ 75 units → divide by 151 egg ⇒ 75/15 = 5 units → multiply by 484 dozen = 4*12= 48 eggs ⇒ 48*5 = 240 unitsCorrect choice is D
A diver begins rising toward the surface from 180 feet below sea level. A few
minutes later, the diver is 40 feet below sea level. How many feet did the diver rise in
those few minutes?
Answer:
140
Explanation: cause -180 + 40 = -140 (but absolute value is 140)