Answer:
a) 22.4 pounds.
b) 0.17 pounds.
c) 0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d) c = 22.62
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Average 22.4 pounds with a standard deviation of 1.36 pounds.
This means that [tex]\mu = 22.4, \sigma = 1.36[/tex]
Consider the sample mean weight of 64 watermelons of this variety.
This means that [tex]n = 64, s = \frac{1.36}{\sqrt{64}} = 0.17[/tex]
a. What is the expected value of the sample mean weight?
By the Central Limit Theorem, 22.4 pounds.
b. What is the standard deviation of the sample mean weight?
By the Central Limit Theorem, 0.17 pounds.
c. What is the approximate probability the sample mean weight will be less than 22.02?
This is the p-value of Z when X = 22.02. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{22.02 - 22.4}{0.17}[/tex]
[tex]Z = -2.235[/tex]
[tex]Z = -2.235[/tex] has a p-value of 0.0127.
0.0127 = 1.27% approximate probability the sample mean weight will be less than 22.02.
d. What is the value c such that the approximate probability the sample mean will be less than c is 0.9?
This is the 90th percentile, that is, [tex]X = c[/tex] when z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.28 = \frac{c - 22.4}{0.17}[/tex]
[tex]c - 22.4 = 1.28*0.17[/tex]
[tex]c = 22.62[/tex]
The school band is selling items to raise $9,500 for a trip. For each item sold, the band's profit is a percent of the selling price, as shown in the table. The flutists' goal is to raise 18% of the total amount needed. The trumpeters' goal is 85% of the flutists' goal. If both of these groups meet their goals, which group raised more money? What was the difference in the amounts the students raised?
The goal amount of the student groups are given in percentages, which are fractions based on one hundred.
The flutist raised more money than the trumpetersThe difference in the amounts the student raised is $256.5Reasons:
The amount the school band is raising for the trip = $9,500
Goal of the flutist = To raise 18% of the total amount
Goal of the trumpeters = 85% of the flutist's goal
Required:
The group that raise more money, given that their goals are met
Solution:
Given that the goal of the trumpeters trumpeters is 85% of the goal of the flutist, the flutist raised more money.
Required:
The difference in the amount raised by the students
Solution:
The amount raised by the flutist = 18% of $9,500 = 0.18 × $9,500 = $1,710
Amount the trumpeters raised = 85% of $1,710 = 0.85 × $1,710 = $1,453.5
The difference in the amount raised = $1,710 - $1,453.5 = $256.5
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If a recipe uses 5 cups of flour for every 2 cups of sugar, how much sugar is used for every 1 cup of flour?
2/5 cup of sugar
you divide 5 by 5 to get 1 cup of flour, and you divide 2 by 5 to get 2/5 cup of sugar
A television is advertised as having a 65-inch measurement. Brenan measures the width of the television while at the store and finds that it is 57 inches wide.
If the space where Brenan plans to hang the television is 32 inches high, will he have enough vertical space to hang the 65-inch television?
Answer: the answer would be C
Yes, the television is approximately 8 inches shorter than the space.
Step-by-step explanation: My name is Ebenezer Haile
Each of the 14 students in the art club needs 4 1/4 ounces of paint for a project. The art store sells paint only in 8 ounce bottles. How many bottles of paint does the art club president need to buy for the project?
A - 3
B - 4
C - 7
D - 8
Answer:
C-7
Step-by-step explanation:
Answer: The art club president need to buy 14 bottles of paint for the project.
Step-by-step explanation: Given that each of the 14 students in the art club needs 4 ounces of paint for a project. The art store sells paint only in 8-ounce bottles.
We are to find the number of bottles of paint that the art club president need to buy for the project.
We will be using the unitary method to solve the given problem.
Number of bottles filled by 8 ounces of paint = 1.
So, the number of bottles filled by 1 ounce of paint is
So, the number of bottles filled by 4 ounces of paint will be
Now, number of bottles of paint needed by 1 student
Therefore, the number of bottles of paint needed by 14 students will be
Thus, the art club president need to buy 14 bottles of paint for the project.
An object starts from rest with a constant acceleration of 2m/s^2 along a straight line. Find the distance travelled for the interval of 10 s.
Answer:
Distance is 100 m
Step-by-step explanation:
From second equation of motion;
[tex]{ \rm{s = ut + \frac{1}{2} {at}^{2} }} \\ [/tex]
s is displacementu is initial velocity, u = 0 [ from rest ]a is acceleration, a = 2 m/s²t is time, t = 10s[tex]{ \rm{s = (0 \times 10) + ( \frac{1}{2} \times 2 \times {10}^{2}) }} \\ \\ { \rm{s = {10}^{2} }} \\ \\ { \rm{s = 100 \: {m} }}[/tex]
The distance covered is 200m
Data;
acceleration = 2m/s^2time = 10sdistance = ?Distance CoveredTo find the distance covered by the object, we have to use the formula
of velocity. But we are not given the velocity or speed of the object here.
[tex]v = s/t[/tex]
where s and t are the distance and time respectively.
But from acceleration,
[tex]a = v/t\\v = a*t\\v = 2 * 10 \\v = 20m/s[/tex]
The velocity of the object is 20m/s
let's use this to find the distance covered.
[tex]v = s/t\\20 = s/10\\s = 20*10\\s= 200m\\[/tex]
The distance covered is 200m
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Todd drinks 4 liters of water every day. There are approximately 29.6 Milliliters in 1 fluid ounce. Which measurement is closest of to the number of fluid ounces in 4 liters/
A.7 fl oz
B. 34 fl oz
C. 118 fl oz
D. 135 fl oz
Answer:
D is the closest. The exact is 135.256
If you borrow $2,000 at 5 percent simple interest, how much will you owe
after one year?
O A. You will owe the principal of $2,000 only.
O B. You will owe the principal of $2,000 minus 5 percent of the
principal
O c. You will owe the principal of $2,000 plus 5 percent of the principal.
Answer:
it is c I think that it is c good luck
Pls help pls Pls pls pls thanks
Factor of 20 but not 10
2. Neither factors of 10 and 20?
Answer:
Step-by-step explanation:
Help help math please I’m stuck help help help
Answer:
12x
Step-by-step explanation:
I am not really sure how to explain it I just looked it up
A line segment has endpoints at (3, 5) and (6, 1)
What is the x-coordinate of the midpoint?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{6+3}{2}~~,~~\cfrac{1+5}{2} \right)\implies \left( \cfrac{9}{2}~~,~~\cfrac{6}{2} \right)\implies \left(4\frac{1}{2}~~,~~3 \right)[/tex]
WILL MARK BRAINIEST!! 50 POINTS.
Part A: Describe two types of transformations that can be used to transform f(x) to g(x).
Part B: Solve for k in each type of transformation.
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x).
Answer:
Part A: The two types of types of transformation are
1) Rotation of 11.3° about (1, 2)
2) By algebraic transformation
Part B:
Rotation by 11.3° and T(2 - y)×1/2 + x, 0)
Part C: The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)
Step-by-step explanation:
The coordinates through which the linear function f(x) passes = (1. 3) and (3, 13)
The coordinates through which the linear function g(x) passes = (1, 3) and (1, 13)
The equation for f(x) in slope and intercept form. y = m·x + c is given as follows;
The slope, m = (13 - 3)/(3 - 1) = 5
The equation in point and slope form is y - 3 = 5×(x -1)
y = 5·x - 5 + 3 = 5·x - 3
y = 5·x - 3
The equation for g(x) in slope and intercept form. y = m·x + c is given as follows;
The slope, m = (13 - 3)/(1 - 1) = ∞
∴ The equation in point and slope form is x = 1
Therefore, the two equations meet at the point (1, 2)
The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)
2) Another transformation that can be used is to rotate f(x) by the vertex angle as follows
Vertex angle is 90° - tan⁻¹(m) = 90° - tan⁻¹(5) ≈ 11.3°
Rotation of f(x) by 11.3° about (1, 2) gives g(x)
Hope this helped!
1. What is the definition of function?
answer choices (select all that apply)
a) Has inputs and outputs
b) Every input has only ONE output
c) X-values can repeat
d) x-values and y-values
Please help me understand how I would pick the correct formula for step 1 for the question in the image? I am really confused.
Answer:
The first option
Step-by-step explanation:
We are doing height above shadow height. Since the telephone poll is 40 feet high with a 32 feet shadow, it is 40/32. We know the sign casts a 12 1/2 shadow, so this will be our denominator. h is our unknown, so we will have h / 12 and a half as our second fraction for our ratio.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Help help help math math
A man earns $9.99 for each of the first 36 hours he works in one week and $14.99 in overtime pay for each
additional hour he works in the same week. How much money will he make if he works 46 hours in one week?
Answer:
459.54
Step-by-step explanation:
46(9.99)
=459.54
Answer:
$159.89
Step-by-step explanation:
36 hours + 10 hours = 46
14.99 * 10 = 149.9
(36 hours) $9.99 + (overtime pay) $149.9 = (Total money) $159.89
$9.99 + $149.9 = $159.89
$159.89
The length of the diagonal of quadrilateral is 48m. The lengths of the Perpendiculars drawn on it from the opposite corners are 15m and 19m.Find its area.
Consider the functions f(x) = 12^x and g(x)= -2(12)^x. Which transformations must be applied to function F to produce the graph of function g?
SELECT ALL CORRECT ANSWERS
Vertical stretch
Vertical Shift
Vertical Compression
Reflection over the x-axis
Horizontal Shift
Answer:
Step-by-step explanation:
g(x) = -2f(x)
Vertical stretch by virtue of the factor 2
Reflection over the x-axis by virtue of the factor -1
The transformations which must be applied to function F to produce the graph of function g are vertical stretch and reflection over the x-axis.
To transform the function f(x)=12ˣ into the function g(x)=−2(12)ˣ
Since g(x) is multiplied by -2 compared to f(x), this represents a vertical compression.
The absolute value of the multiplier indicates the degree of compression/stretch.
The negative sign in front of 2(12)ˣ in g(x) reflects the graph over the x-axis. This means that the graph of g(x) is reflected below the x-axis compared to f(x).
Hence, vertical stretch and reflection over the x-axis are the transformations which must be applied to function F to produce the graph of function g.
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A particle moves along the x-axis so that at time t ≥ 0 its position is given by x(t) = 2t3 - 21t2 + 72t - 53. At what time t is the particle at rest?
Step-by-step explanation:
The particle is at rest when the derivative of x(t), which is its velocity, is zero, i.e.,
[tex]\dfrac{d}{dt}[x(t)] = \dot{x}(t) = 0[/tex]
Since [tex]x(t) = 2t^3 - 21t^2 + 72t - 53,[/tex] its derivative is
[tex]\dot{x}(t) = 6t^2 - 42t + 72[/tex]
Equating this to zero, we get
[tex]6t^2 - 42t + 72 = 0 \Rightarrow t^2 - 7t + 12 = 0[/tex]
This is a familiar quadratic equation whose roots are
[tex]t = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]\;\;\;= \dfrac{7 \pm \sqrt{(7)^2 - 4(1)(12)}}{2}[/tex]
[tex]\;\;\;= \dfrac{7 \pm 1}{2}[/tex]
[tex]\;\;\;= 3\;\text{and}\;4[/tex]
This means that the particle will be at rest at t = 3 and t= 4.
HELP PLEASE I REALLY NEED IT
Answer:
18
Step-by-step explanation:
1/2 bh
1/2 (6)(6) multiply
1/2 (36) divide
18
Salt water gargle can temporarily relieve a sore throat. One recipe calls for 3/4 teaspoon of salt in 1 cup of water. A second recipe calls for 1 teaspoon of salt in 2 cups of water. Which recipe will taste saltier?
Answer:
The first recipe - 3/4 tsp of salt in 1 cup of water
Step-by-step explanation:
1st recipe Salt per cup = 3/4 tsp / 1 cup = 3/4 tsp salt
2nd recipe Salt per cup = 1 tsp / 2 cups = 1/2 tsp salt
3/4 tsp > 1/2 tsp, hence the first recipe is saltier
can you guys help me plz
Answer:
1) x>1
2) x<6
3) x>34
4) x>-4
5) x<2
6) x>-36
7) x<=4
8) x>-2
9) x>=2
10) x>14
help me please I'm stuck on this question!!!!
Answer:
1: 2.8
Step-by-step explanation:
15:42
Divide each side by 15
15/15 : 42/15
1: 2.8
Differentiate y = sin^2x - cos^2x
Using the power and chain rules, the derivative of
y = sin²(x) - cos²(x)
is
dy/dx = 2 sin(x) cos(x) - 2 cos(x) (-sin(x))
dy/dx = 2 sin(x) cos(x) + 2 sin(x) cos(x)
dy/dx = 4 sin(x) cos(x)
and using the double angle identity for sine, this is equivalent to
dy/dx = 2 sin(2x)
Alternatively, we can first simplify y using the double angle identity for cosine:
cos(2x)= cos²(x) - sin²(x)
so that
y = -cos(2x)
and the derivative is
dy/dx = sin(2x) • 2
dy/dx = 2 sin(2x)
calculation of
24 – 16 ÷ 4 x 2 + 3
Answer:
19
Step-by-step explanation:
BODMAS
Brackets.
Of
Division
Multiplication
Addition and
Subtraction
go according to the BODMAS rule and solve the division first
24-(16÷4)×2+3
Then solve the multiplication part
24-(4×2)+3
Now solve like a regular sum
24-8+3
16+3
19
find the slope of a line that contains the points (0,1) and (1,3)
Answer:
the slope of the line is 2
Step-by-step explanation:
3-1
1-0
=
2
1
=
2
Find the slope of the line through (1, 2) and (- 9,7).
Step-by-step explanation:
formula y2-y1 / x2-x1
m = 5 / -10 = 1 / -2 = -0.5
Please help with algebra class I’m struggling
Answer:
Step-by-step explanation:
For what mileages will company A (which has a flat rate of $111) be less than the cost for company B
Company A < Company B
111 < 75 + 0.80m
solving
111 - 75 < 75 - 75 + 0.80m
36 < 0.80m
36/0.80 < 0.80m/0.80
as we are dividing by a positive number, we don't have to change the direction of the < sign.
45 < m
or m > 45
so if Ali intends to drive more than 45 miles, Company A's vehicle will be less expensive to rent
Please help!! Thank you!!!!
Answer:
total cost = 10 • months + 100
Step-by-step explanation:
The $100 application fee is extra, only needed to pay once. The $10 per month is multiplication. $10 • the number of months.
The sum of the first 15 terms of a geometric sequence with 7 as the first term and a common ratio of -3 is __________.
Step-by-step explanation:
the formula for the sum of the first n terms of a geometric sequence is
Sn = s1(1 - r^n)/(1 - r)
with r being the common ratio and s1 is the first term.
so,
S15 = 7×(1 - (-3)¹⁵)/(1 - -3) = 7×(1 - -14,348,907)/4 =
= 7×14,348,908/4 = 7×3,587,227 = 25,110,589
4,6,9,...
Find the 8th term.
Find the 8th term.
Answer:
4, 6, 9, 12, 15, 18, 21, 24.
Step-by-step explanation:
The 8th term is 24.
just +2 (add 2) every time.
