Given that 58% of all gold dealers believe next year will be a good one to speculate
in South African gold coins, in a simple random sample of 150 dealers, what is the
probability that between 55% and 60% believe that it will be a good year to
speculate?
Answers
The normal distribution is a continuous probability distribution that is symmetrical around the mean. The mean in this case is 58%, and the standard deviation can be calculated using the formula:
standard deviation = sqrt( (p * (1 - p)) / n )
where p is the proportion of all gold dealers who believe that it will be a good year to speculate (58% in this case) and n is the sample size (150 in this case).
Plugging in the given values, we get:
standard deviation = sqrt( (0.58 * (1 - 0.58)) / 150 ) = 0.042
To find the probability that between 55% and 60% of the sample believe that it will be a good year to speculate, you can use a z-score table to find the z-score for 55% and 60%, and then use these z-scores to find the probability.
The z-score for 55% is (55 - 58) / 0.042 = -7.14, and the z-score for 60% is (60 - 58) / 0.042 = 2.38.
Using a z-score table, you can find that the probability of a z-score between -7.14 and 2.38 is approximately 0.45.
Therefore, the probability that between 55% and 60% of a sample of 150 gold dealers believe that it will be a good year to speculate in South African gold coins is approximately 0.45.
Related Questions
A pizza delivery company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1664 customers. The data is summarized in the table below.
Gender and Residence of Customers
Males Females
Apartment 206 149
Dorm 295 276
With Parent(s) 55 68
Sorority/Fraternity House 132 204
Other 180 99
What is the probability that a customer is female and lives in a dorm or is female and lives in 'Other'? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answers
Answer: 0.2254
Step-by-step explanation:
Let E= Event of getting of female lives in a dorm.
F = Event of getting of female lives in a 'Other'.
From the table , n(E) = 276 and n(F) = 99
and n(E∩F) = 0 [E and F are Mutually exclusive]
Now, n(E∪F)= n(E) + n(F) - n(E∩F)
= 276+99-0
= 375
also, n(S) =1664 (Sample size)
Required probability : \(P(E\cup F)=\dfrac{n(E\cup F)}{n(S)}\)
\(=\dfrac{375}{1664}\approx0.2254\)
Hence, the probability that a customer is female and lives in a dorm or is female and lives in 'Other' = 0.2254
What is 9.98- 2.53 and 7.68 + 13.07 and 100.03 - 16.28 show your work
Answers
Answer:
9.98- 2.53 = 7.45
7.68 + 13.07 = 20.75
100.03 - 16.28 = 83.75
Step-by-step explanation:
9.98
- 2.53
_____
7.45
1 1 - Process of carrying 10's
7.68
+ 13.07
_______
20.75
0000 13 ⇔ What the number becomes after carrying
↑↑↑↑↑
100.03
- 16.28
______
83.75
Happy New Year!
Which of the following sets of numbers could represent the three sides of a right triangle?
{40,41,58} , {16,30,34}, {16,30,34} , {14,84,85}, {14,84,85} , {39,52,66}, {39,52,66}
Answers
Answer:
16,30.34
Step-by-step explanation:
If x = 2 and y=-3, then xy^2 =
Answers
Step-by-step explanation:
Answer:
-18
Step-by-step explanation:
-xy^2 =
Let x=2 and y = -3
-(2) (-3)^2
-2 (9)
-18
Answer:
18.
Step-by-step explanation:
(2)(-3)^2
Parentheses first. There's nothing to do so, the exponent is next. -3^2 is 9. 9 * 2 = 18.
Hope this helps! :)
Trigonometry, Need Help please!!
Answers
The value of cos(2α + β) using trigonometric identities is; -1.0155
How to solve trigonometric Identities?We are given;
α = sin⁻¹(4/5)
β = tan⁻¹(12/5)
Thus;
sin α = 4/5
tan β = 12/5
From trigonometric ratios, we can say that;
cos α = 3/5
sin β = 12/13
cos β = 5/13
We know from trigonometric identities that cos (a + b) = cos a cos b - sin a sin b.
Thus;
cos(2α + β) = cos 2α cos β - sin 2α sin β
Thus;
cos(2α + β) = 2(3/5) * (5/13)) - ((2 * 4/5 * 12/13))
= 0.4615 - 1.477
= -1.0155
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DUE SOON!
PLEASE HELP EXPLAIN THIS IM SO CONFUSED!
Answers
Answer:
$20.44
Step-by-step explanation:
The average of a set of numbers is defined as:
\(\dfrac{\textrm{sum of values}}{\textrm{number of values}}\)
In this problem, we are shown a table where each row has a coupon value in the left column and the number of that coupon value in the right column (e.g., if we look at the top row, we can see there are 70 coupons each valued at $10).
So, the sum of values in this problem (i.e., the total number of dollars given out by the store in the form of coupons) is defined as the sum of the product of each row.
\(\textrm{sum of values} = (\$10 \times 70) + (\$20 \times 40) + (\$40 \times 20) + (\$60 \times 4) + (\$120 \times 2)\)
\(\textrm{sum of values} = \$700 + \$800 + \$800 + \$240 + \$240\)
\(\textrm{sum of values} = \$2780\)
The number of values in this problem is just the sum of the numbers in the right column (i.e., the number of coupons given out).
\(\textrm{number of values} = 70 + 40 + 20 + 4 + 2\)
\(\textrm{number of values} = 136\)
Finally, to answer the problem, we can plug the two numbers that we just solved for into the formula for the average of a set.
\(\textrm{average savings} = \dfrac{\textrm{value of all tickets}}{\textrm{number of tickets}}\)
\(\textrm{average savings} = \dfrac{\$2780}{136}\)
\(\textrm{average savings} \approx \$20.44\)
Solve the system of
equation graphically, by
substitution, and by
elimination.
2x-5y = 34
y=3x-25
Answers
2y = 4x - 12
Find the x and the y intercept of the line.
Answers
0 = 4x - 12
Adding 12 to both sides:
12 = 4x
Dividing both sides by 4:
3 = x
For Y:
2y = 4(0) - 12
2y = -12
Dividing both sides by 2:
y = -6
Therefore, the y-intercept of the line is y = -6.
what is the circumference of a circle with a radius of 6cm
Answers
The circumferance of a circle with radius of 6cm is 37.68cm
To find:
Circumferance of a circle
Given:
Radius of circle is 6cm
Solution:
Circumference is similar to perimeter as it is the total length required to draw a circle.
Let c be the perimeter.
c = 2πr
or
c = πd
This depends on knowing the radius (r) or diameter (d).
For example, let's calculate it manually.
If r = 6 cm, the circumference in π is c = 2π(6) = 12π cm.
When expressed numerically, it is 37.7 cm after the decimal point is rounded off.
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Can someone help me please?!?!
Answers
Your answer will be x= 3(c−k).
I hope this helps :)
In the following exercises, find the greatest common factor.
15y3, 21y2, 30y
Answers
Answer:
3yStep-by-step explanation:
each term has at least y^1
each term's coeficient is a factor of 3
3y(5y^2, 7y, 10)
3y is the GCF2. Determine the area of t he parallelogram. 3.7 m 12 m Formula: Plug in Values: Area:
Answers
The equivalent area of the parallelogram is 44.4m^2
The area of a parallelogramThe formula for finding the area of a parallelogram is expressed as:
Area = base * height
Given the following parameters
Base = 12m
Height = 3.7m
Substitute the given parameters into the formula to have:
Area = 12m * 3.7m
Area of the parallelogram = 44.4m^2
Hence the area of the parallelogram given is 44.4m^2
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Neil buys a refrigerator that costs him $995 plus a 9.3% sales tax rate. what is the sales tax of the retail purchase. round to two decimal place
Answers
Answer:
$92.54
Step-by-step explanation:
sales tax = cost * tax rate
= 995 * .093
= 92.535
please help ASAP ;)
Answers
Answer: use PEMDAS
Step-by-step explanation:
Pls help me it's urgent!
Answers
The formula that defines the sequence is f(n) = f(n-1) + 4
Recursive functionThe recursive function rule is expressed as;
f(n) = f(n-1) + d
where
d is the common difference
Given the following sequence
2, 6, 10, 14, 18..
Determine the common difference
d = 6-2 = 10-6
d = 4
Substitute to have
f(n) = f(n-1) + d
f(n) = f(n-1) + 4
Hence the formula that defines the sequence is f(n) = f(n-1) + 4
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In the diagram for this problem, lines BE and CF are congruent. Arc AB = 48 degrees. Arc BC = 42 degrees. Which measure is the greatest?
Answers
Answer:
arc AB
Step-by-step explanation:
uhhhh 48 is greater than 42
Find the value of y.
Answers
The value of y is 4√3
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.
Also , the ratio of corresponding sides of similar triangles are equal.
There are two triangles that are similar
Therefore;
y /16 = 4/y
y² = 48
y = √48
y = √16 × √ 3
y = 4√3
Therefore, the value of y is 4√3
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each function
f(x)=-4x-5;
ion for
Find ƒ(1)
for the given
Answers
When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.
The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.
Replacing x with 1, we have:
ƒ(1) = -4(1) - 5
Simplifying further:
ƒ(1) = -4 - 5
ƒ(1) = -9
Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.
Let's break down the steps taken to arrive at the solution:
1. Start with the function f(x) = -4x - 5.
2. Replace x with 1 in the function.
3. Evaluate the expression by performing the necessary operations.
4. Simplify the expression to obtain the final result.
In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.
It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.
Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.
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A subway system has six stations, A, B, C, D, E, and F, where trains only run from:
A to B B to A B to c
C to D D to B D to E F to A F to E F to C E to D
Passengers can transfer to different trains within a station.
Which station is unreachable by train from any other station?
Answers
A metro station, often referred to as a subway station, is a railway stop for a rapid transit system, also known as a "metro" or "subway" in its whole.
What is the Subway transfer stations ?Several different types of transfer stations can be found in the New York City Subway:
When two or more stations are linked by a corridor inside fare control, the area is referred to as a station complex. When counting every station individually, there are 472 in the New York City Subway. There are 424 total stations when station complexes are treated as one station each.Two or more lines are served by the station. The MTA classifies it as one station, regardless of whether it has many levels or platforms next to one another. A station typically has one line to which each track belongs.Two or more services are provided by the station. Tracks may be shared between different services. You can find a list of New York City subway stations instead of these stations in this article.The Complete Question is Subway transfer stations.
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work out the area of this circle take pi to be 3.142 and write down all the digits given by your calculator diameter 13cm
Answers
Area of circle of diameter with 13cm is 132.74
What is area of circle?
The space a circle takes up in a two-dimensional plane is known as the area of the circle.Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r², where r is the circle's radius, is the formula for calculating a circle's surface area. The square unit—for instance, m², cm², in², etc.—is the unit of area. In square units, the area of a circle is equal to r² or d²/4 where (Pi) = 22/7 or 3.14. The ratio of a circle's circumference to its diameter is known as pi (). This unique mathematical constant exists.Given :
Diameter of circle, d = 13cm
Radius of a circle, r = d/2
=13/2
=6.5
Area of circle = πr²
= 3.142 * 6.5 * 6.5
= 132.74
Hence, the Area of circle of diameter with 13cm is 132.74.
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Chris is selling chocolates
for a fundraiser. If he sells
over $115 worth of candy,
he'll win a prize. If chocolates
sell for $5.75 a box and Chris
has already sold $28.75
worth of candy, how many
more boxes does he have to
sell in order to win a prize?
Answers
Answer:
15
Step-by-step explanation:
28.75 ÷ 5.75= 5 so 5 boxes have been sold.
115÷ 5.75= 20- 5 = 15 boxes
Answer:
15
Step-by-step explanation:
Evaluate the expression.
-41-5(7–13)–19]
2(-1)
What is the value of the expression?
Answers
Answer:
-25
Step-by-step explanation:
k12
Answer:
-25
Step-by-step explanation:
ФωФPlease help asap! The question is below!
Answers
Based on the information, the hedgehogs have made the better offer
How to know who made the better offerThe Turkeys are offering a yearly salary of S(t) = 90000t over the course of eight years. To calculate the present value of each payment, an equation is used:
PV = S(t) * e^(-rt)
The variable "r" denotes a continuous interest rate of 0.03. "t" equals the years from t=0 to the time of payment. By this method, the current value of the Turkeys' offer can be assessed as follows:
PV(Turkeys) = ∫[0,8] 90000t * e^(-0.03t) dt
= 736,918.63
Comparatively, the Hedgehogs propose a yearly salary of S(t) = 80000t for nine years. Utilizing the formula employed in the previous scenario, the following result is derived:
PV(Hedgehogs) = ∫[0,9] 80000t * e^(-0.03t) dt
= 753,472.49
Given these calculations and the presumption that Rogelio may earn a continuous interest rate of 3% on his funds, it would best serve him to accept the Hedgehogs’ item offer since they have offered him a more favorable contract based on the accumulated present value of both contracts.
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What is the value of x in this proportion?
56=−4x+2
Responses
x=−2 4/5
x equals negative 2 and 4 over 5
x=−4 2/5
x equals negative 4 and 2 over 5
x=−5 1/5
x equals negative 5 and 1 over 5
x=−6 4/5
x equals negative 6 and 4 over 5
Answers
The value of x or the expression 56 = -4x + 2 is -27/2.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
56 = -4x + 2
Solve for x.
56 = -4x + 2
Subtract 2 on both sides.
56 - 2 = -4x
54 = -4x
Divide -4 into both sides.
-54/4 = x
x = -54/4
x = -27/2
x = -13(1/2)
Thus,
The value of x is -27/2.
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P, Q, R, S and T are different digits.
PQR x ST = 3864
find a solution
Answers
Note that the possible solutions where each letter must be represent a different digit are:
a) 168 x 23
b) 276 x 14
What is a Digit?
A digit is a symbol used to represent numbers in the decimal system. It can take on values from 0 to 9 and is used to construct larger numbers.
So, where in a)
1=P
6=Q
8=R
2=S; and
3 = T
168 x 23 = 3864
b)
2 = P
7 = Q
6 = R
1 = S
4 = T
a) 168 x 23 = 3864
b) 276 x 14 = 3864
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A farmer earns $___ for each orange she sells. She had to pay $___ for fertilizer. Part A: Rewrite the description by filling in the blanks with values of your choice to show the amount of money the farmer could earn selling any number of oranges, n. Make sure the values you choose make sense for this situation. (6 points) Part B: Write an algebraic expression from your written description used in Part A. Let n stand for the number of oranges. (6 points)
Answers
Part B: The algebraic expression for the amount of money the farmer could earn selling any number of oranges, n, is 0.20n - 25.
Fraction Multiplication and División:Question 4
Tina has $72 to spend on new t-shirts. If each t-shirt costs $12,
how many different t-shirts can Tina buy? Set up a fraction to
determine how many t-shirts Tina can buy. Then solve.
Answers
Answer: 6 T-shirts
Step-by-step explanation:72/12=6
What is the length of the midsegment of a trapezoid with bases of length 18 and 28?
The length of the midsegment of a trapezoid with the given bases is.
Answers
Answer:
midsegment = 23
Step-by-step explanation:
the midsegment is half the sum of the bases, that is
midsegment = \(\frac{18+28}{2}\) = \(\frac{46}{2}\) = 23
A factory manager wishes to install types of machines, small and large. A small machine needs 2 operators and occupies 4m² of floor space. A large machine needs 3 operators and accupies 8m³of floor space. There are up to 30 operators available and 72m² of floor space. At Least 4small machines and at least 5 large machines must be installed.
a) Taking X to be the number of small machine, and y as the number of large machine to be installed, write down. the four major inequalities required.
b) Draw a graph to show the region satisfying the inequalities
c) Determine the maximum number of machines he can install .
d) If the profit made by each small machine is 250,000 and by the large type is 300,000 per week, find the maximum profit the factory can make in one week and the number of machines of each type that should be installed.
Answers
a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72
b) We have drawn the graph.
c) The maximum number of machines that can be installed is 11.
d) The maximum profit is 2,500,000.
What is inequality?
An inequality is a mathematical statement that shows the relationship between two values where one value is either greater than or less than the other value. It is represented by symbols such as >, <, ≥, or ≤. For example, if x is a variable and we want to express that x is greater than 5, the inequality would be written as x > 5.
a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72
b) To graph the region, we can plot the lines that define the inequalities and shade the area that satisfies all of them.
c) Solving the system of inequalities graphically, we find the maximum number of machines that can be installed is 11 (6 small and 5 large).
d) To find the maximum profit, we need to substitute the number of machines into the profit equation. P = 250,000X + 300,000Y. Plugging in X = 6 and Y = 5, we find the maximum profit to be 2,500,000.
Hence,
a) X >= 4 and Y >= 5, 2X + 3Y <= 30 and 4X + 8Y <= 72
b) We have drawn the graph.
c) The maximum number of machines that can be installed is 11.
d) The maximum profit is 2,500,000.
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Which set of ordered pairs represents a function?
o {(1,3) (2,5) (4, 9) (4, 13)}
o {(1,3) (1,5) (4, 9) (6,3)}
o {(1,3) (2,5) (2,9) (6, 13)
o {(1,3) (2,5) (4,9) (6,5)}
pls help