at a large university, 68% of the students have a laptop, while only 43% of professors have one. let p hat subscript s and p hat subscript p be the sample proportions of students and professors, respectively, who have a laptop. suppose 56 students and 31 professors from this university are selected at random and asked if they have a laptop. which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of p hat subscript s baseline minus p hat subscript p ?
The correct calculation of the standard deviation of the sampling distribution of p_hat subscript s - p_hat subscript p is 0.0934.
What do you mean by standard deviation?
In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of population
N = number of observation of population
X = mean
μ = population mean
We are given that;
Percentage of students with laptop=68%
Percentage of professors with laptop=43%
p_s = 0.68 and p_p = 0.43.
Now,
The formula for the standard deviation of the sampling distribution of the difference between two sample proportions is:
sqrt[(p_s * (1 - p_s) / n_s) + (p_p * (1 - p_p) / n_p)]
where p_s and p_p are the population proportions of students and professors who have a laptop, respectively, n_s and n_p are the sample sizes of students and professors, respectively.
We are also given that 56 students and 31 professors were selected at random and asked if they have a laptop. Therefore, n_s = 56 and n_p = 31.
Substituting these values into the formula, we get:
sqrt[(0.68 * (1 - 0.68) / 56) + (0.43 * (1 - 0.43) / 31)]
sqrt[0.00367143 + 0.00505484]
= sqrt(0.00872627)
= 0.0934 (rounded to four decimal places)
Therefore, by standard deviation the answer will be 0.0934.
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Can someone plz help me on this
Answer:
i don't know but I hope you find out good lucky
16/x 45/3 find the value of x round to the nearest tenth
Answer:
x would be equal to 1.1
Step-by-step explanation:
Step 1: Determine the value of x
I assume that the equation looks like this: 16/x = 45/3
Therefore, using the cross multiply method we can do (16*3) = (x*45)
This will give us 48 = 45x
Then we divide both sides by 45 so we can isolate x by itself
45x/45 = 48/45
x = 1.0667
Then we round to the nearest tenth
x = 1.0667
x = 1.1
Answer: x would be equal to 1.1
Answer:
x = 16/15, or (to the nearest tenth) x = 1.1
Step-by-step explanation:
Note: there must be an " = " sign between the two fractions:
16 45
------- = -------
x 3
Also note that 45/3 reduces to 15: 16/x = 15
Multiplying both sides by x yields 16 = 15x, so that x must be x = 16/15 = 1.1
What is the solution to the system of equations?
5x – 4y = 6
-5x + 4y = -10
O (4,4)
0 (-2,-5)
O infinitely many solutions
O no solution
Hey there! I'm happy to help!
We have a 5x is one equation and a -5x in another equation. We can combine the two equations to cancel out the x and then solve! This is called solving by elimination.
5x-4y=6
+
-5x+4y=-10
0= -4
Since we lost our x and y while solving, there cannot be any solution.
Therefore, the answer is no solution.
Have a wonderful day!
the manager of a bank record of the amount of each Time customer spent waiting in the line during peak business hours on Monday the waiting times are shown below find the mean waiting time Roger answer to one Decimal place 6.8 min 7.5 min 7.2 min brainly
Answer:
To find the mean waiting time, you need to add up all the waiting times and divide by the number of customers. In this case, the total waiting time is 6.8 + 7.5 + 7.2 = 21.5 minutes. Since there are 3 customers, the mean waiting time is 21.5 / 3 = 7.17 minutes. Rounded to one decimal place, the mean waiting time is 7.2 minutes.
Step-by-step explanation:
Connor can travel 2 3/4 miles in 2 1/2 hours. What is his average speed in miles per hour?
Answer:
C 1.1 mph
Step-by-step explanation:
Divide 2 3/4 by 2 1/2 to get 1.1
A rectangle that is 9 meters long has an area of 36 square meters what is the perimeter
Answer:
the perimeter of the rectangle is 26 meters.
Step-by-step explanation:
To find the perimeter of the rectangle, we need to know its width. We can find the width by dividing the area by the length:
width = area / length = 36 / 9 = 4 meters
Now we can use the formula for the perimeter of a rectangle:
perimeter = 2(length + width)
Substituting the given values, we get:
perimeter = 2(9 + 4) = 2(13) = 26 meters
Therefore, the perimeter of the rectangle is 26 meters.
susie change 500 dollars to euros $1 = 1.0697 euros
Answer:
€ 534.35Step-by-step explanation:
Use the rate to change:
$1 = €1.0697$500 = xx = 500*1.0687 = 534.35\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
Here's the conversion :
$ 1 = € 1.0697$ 500 = € 1.0697 × 500$ 500 = € 534.85The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, . . . (where F0 0).
(a) Give the recursive definition for the sequence.
(b) Write out the first few terms of the sequence of partial sums: 0, 0 + 1, 0 + 1 + 1,. . .
(c) Give a closed formula for the sequence of partial sums in terms of Fn (for example, you might say F0 + F1 + · · · + Fn 3F 2 n−1 + n, although that is definitely not correct).
(Discrete Mathematics)
The Fibonacci sequence is the sequence in which the numbers are written such that each succeeding number is sum of two preceding numbers.
The Fibonacci sequence is defined recursively as follows:
F0 = 0
F1 = 1
For n > 1, Fn = Fn-1 + Fn-2
(b) The sequence of partial sums is:
S0 = 0
S1 = 0 + 1 = 1
S2 = 0 + 1 + 1 = 2
S3 = 0 + 1 + 1 + 2 = 4
S4 = 0 + 1 + 1 + 2 + 3 = 7
S5 = 0 + 1 + 1 + 2 + 3 + 5 = 12
(c) A closed formula for the sequence of partial sums in terms of Fn is not possible, since the sequence of partial sums depends on the values of all previous terms in the Fibonacci sequence. However, it is possible to express the nth term of the sequence of partial sums, Sn, in terms of the nth term of the Fibonacci sequence, Fn, using the following formula:
Sn = F0 + F1 + ... + Fn = (F0 + F1) + (F1 + F2) + ... + (Fn-1 + Fn) = F1 + F2 + ... + Fn + F0 + F1 + ... + Fn-1 = 2Sn-1 - Fn + F0
This formula can be derived by considering the previous term in the sequence of partial sums and adding the current term of the Fibonacci sequence to it.
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Write these fractions as whole nombers
8/4
21/3
56/8
48/8
Answer:2, 7, 7, 6
Step-by-step explanation:
Answer:
1) 8/4 = 2
2) 21/3 = 7
3) 56/8 = 7
4) 48/8 = 6
Step-by-step explanation:
To convert a fraction into a whole number: Divide the numerator by the denominator.
What's a numerator?:
A numerator is the part of a fraction above the line. So, 8 in 8/4 is the numerator.
What's a denominator?:
A denominator is the bottom number in a fraction. So, 4 in 8/4 is the denominator.
1) 8/4 = 8 divided by 4 = 2.
2) 21/3 = 21 divided by 3 = 7
3)56/ 8 = 56 divided by 8 = 7
4) 48 / 8 = 48 divided by 8 = 6
the prime factorization for 2020 is 2^2 x5^1 x 101^1. How many different whole numbers are factors of 2020?
There are three different whole numbers are factors of 2020.
What is Prime factorization ?
Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors. As we know, a composite number has more than two factors, therefore, this method is applicable only for composite numbers and not for prime numbers.
Prime factors of 2020 = 2,2,5,101
different whole numbers are = 2,5,101
As these three numbers are prime numbers, these are the different whole numbers for 2020.
Therefore, there are three different whole numbers are factors of 2020.
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What is the slope of the line represented by the equation y = -1/2 X + 1/4
Step-by-step explanation:
y = -1/2 X + 1/4
comparing with y = mx+c
m = -1/2 and m is slop
henve slope = -1/2
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The true statements are
The value of f(–10) = 82
The graph of the function is a parabola.
The graph contains the point (20, –8).
What is a Parabola:A parabola is a type of conic section that is formed when a plane intersects a cone in such a way that the angle between the plane and the vertical axis of the cone is equal to the angle between the plane and a generator (a straight line passing through the vertex and the base of the cone).
The resulting shape is a symmetrical, U-shaped curve. The standard form of the parabola is a quadratic function.
Here we have
The quadratic function f(x) = x²/5 – 5x + 12
Now check each option as follows
1. The value of f(–10) = 82
To check this find f(-10) as follows
f(-10) =1/5 (-10)²– 5(-10) + 12 = 20 + 50 + 12 = 82
Hence, The value of f(–10) is equal to 82
2. The graph of the function is a parabola.
As we know the standard equation of a parabola is a quadratic function that is in the form of ax² + bx + c
Hence, the quadratic function represents a parabola
3. The graph of the function opens down.
In the given function f(x) = x²– 5x + 12, the coefficient of the x² term is 1. Since the coefficient of x² is positive, the parabola opens upwards.
Hence, The graph of the function opens down is false
4. The graph contains the point (20, –8).
To check this substitute the point in f(x)
=> –8 = 1/5(20)²– 5(20) + 12
=> –8 = 80 – 100 + 12
=> –8 = –8 [ Which is true ]
Hence, The graph contains the point (20, –8).
5. The graph contains the point (0, 0).
=> 0 = (0)²– 5(0) + 12
=> 0 = 12 [ which is not true ]
Hence, The graph doesn't contain the point (0, 0).
Therefore,
The true statements are
The value of f(–10) = 82
The graph of the function is a parabola.
The graph contains the point (20, –8).
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Given 3 + 7 + 11 + 15 + ... find S20
someone down to help...............
PLEASE PLEASE PLEASE HELP
Answer:
the answer to your question is -8.5
Answer:
-3.4 × 2.5 = -8.5
Step-by-step explanation:
Since these are short decimals, you can probably convert these into fractions if you'd like.
So -3.4 = -17/5
And 2.5 = 5/2.
So just multiply this like you would multiply two fractions, just multiply across the numerator, and denominator, and then just simplify; numerator × numerator / denominator × denominator.
So
The trick when multiplying by 5 is to divide the number in half, and multiply by 10.
-17/5 × 5/2 = -17 × 5 / 5 × 2 = -17/2 × 10 / 10 = -8.5 × 10/10 = -8.5 × 1 = -8.5
(The tens just cancel and make 1 so you are just left with this answer)
You can also try splitting the decimals up into factors:
-3.4 × 2.5 = (-3 - 0.4)(2 + 0.5) = -6 + -0.8 + -1.5 + 0.2 = -6 + -1 + -1.5 = -7 + -1.5 = -8.5.
According to the chart below, what percentage of Ralph’s expenses are items other than taxes? A circle graph titled Ralph's Annual Expenses. Federal taxes, 29 percent; State/local taxes, 6 percent; Housing and household, 25 percent; Food, 8 percent; Medical care, 11 percent; Transportation, 7 percent; Recreation, 6 percent; Clothing, 5 percent; Other, 10 percent. a. 65% b. 71% c. 75% d. 94%
according to the chart below, what percentage of ralph’s expenses are items other than taxes?
a. 65%
b. 71%
c. 75%
d. 94%
the answer is A 65%
A) 65%
Step-by-step explanation:
4856
Find the value of x and y
Answer:
x = 70
y = 40
Step-by-step explanation:
First, we need to find the measure of x.
As x and the angle 110 share a line, they must add up to 180 degrees. This means that the measure of x is 70.
The two ticks on the sides of the triangle indicate that these sides are equal in length. This also means that the corresponding angles will also be equal. This means that both x and the other angle are 70.
This means that we have two of the three angles in the triangle, so we can easily find the third, which is y.
\(70+70+y=180\\\\y+140=180\\\\y=40\)
Answer:
x=70
y=20
Step-by-step explanation:
x=180-110 (because they lie on a straight line)
=70
90+70+y=180 (the interior angle of a triangle is 180)
160+y=180
y =180-160
y =20
Give a proof showing that the following formula is a theorem. Be sure to submit your answer by clicking the submit button. V.2 3 pts TE (A → (B − C)) → (B → (A → C)) 11
We can prove the formula given in the question as a theorem using the truth table method.
A Truth Table is referred to as a logic table that can be used to perform logic functions with some formulas. The logic functions that can be performed include Boolean algebra.
Let A, B, and C represent propositions. We construct a truth table as follows:
A B C (A → (B − C)) (B → (A → C))
T T T T T
T T F T F
T F T T T
T F F T T
F T T T T
F T F T T
F F T T T
F F F T T
From the truth table, we can see that the formula holds for all possible truth values of A, B, and C. Therefore, the formula is a theorem.
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The first term of a geometric sequence is 5 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?
Step-by-step explanation:
s1 = 5
s2 = s1 × -2 = 5×-2 = -10
s3 = s2 × -2 = -10 × -2 = 20
...
now, we could do all that manually.
but there is also a formula for geometric sequence.
in fact, there are 2 - one for finite and one for infinite sequences.
and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.
since we need the sum of the first 5 terms, which of the 2 do you think we need ?
of course, finite, because 5 is a normal number we can "touch". it is not infinity.
so, the formulas for finite sums of geometric sequences are :
if |r| < 1, Sn = a(1 - r^n)/(1 - r)
if |r| > 1, Sn = a(r^n - 1)/(r - 1)
if r = 1, Sn = na
if r = -1, then Sn = a or 0 depending on if n is odd or even.
the sequence is in general
s1 = a
sn = sn-1 × r
in our case a = 5, r = -2.
so, what form of the formula do we need ?
|-2| = 2, and 2 > 1, so ...
S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =
= 5 × 11 = 55
quick check, as the 5 terms are
5
-10
20
-40
80
and their sum is : 55
correct !
HELPPPPPP
Order the following numbers from least to greatest.
10 square number 5
10square number -99
10 square number -17
10 square number 14
10 square number -5
10 square number 30
Answer:
10^-99
10^-17
10^-5
10⁵
10¹⁴
10³⁰
need help calulating that
The distance that the thermometer should be standing from the lightbulb is 0.6 m.
How to calculate the distanceTo calculate this, we need to note that the expected figure we are to find is x. In this case, all we have to do is to divide both sides by 3.7. So,
3.7x/3.7 = 2.25/3.7
x = 0.6.
So, the true distance that the model thermometr should be standing from the lightbulb in order to simulate the warmth of the sun is 0.6 m
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The image of the point (-5, 4) under a translation is (-3,-1). Find the
coordinates of the image of the point (-2,9) under the same translation.
Help
Answer:
The coordinates of the image of the point (-2,9) under the same translation will be: (0, 4)
Step-by-step explanation:
Given that the image of the point (-5, 4) under a translation is (-3,-1).
It means the image (-3, -1) is obtained by moving the right side by 2 units and moving 5 units down.
In other words, the rule of translation is:
P(x, y) → (x+2, y-5)
(-5, 4) → (-5+2, 4-5) → (-3, -1)
now
TRANSLATING THE POINT (-2, 9)
We already know the translation rule
P(x, y) → (x+2, y-5)
so
(-2, 9) → (-2+2, 9-5) → (0, 4)
Therefore,
The coordinates of the image of the point (-2,9) under the same translation will be: (0, 4)
what is the value of the expression ?
Answer:
-5
Step-by-step explanation:
-x + y*z - y
Substitute using the given values: x = -3, y = - 2, z = 5
Pay attention to order of operation (meaning that multiplication is before addition)
-x = -(-3)
Two negatives = positive
3 + (-2*5) - (-2)
Open parenthesis
3 - 10 + 2 = -7 + 2 = -5
The answer is -5
Hope this helps :)
Have an awesome day!
Helpp please find the value of s! I will give brainlist
We have :
s - 39⁰+ s - 9⁰ = s + 29⁰
s + s - s = 29⁰ + 9⁰ + 39⁰
s = 77⁰
Answer: 77⁰
Ok done. Thank to me :>
Convert 14 feet per
minute to yards per
minute
Answer:
answr 5
Step-by-step explanation:
answer 5
At which values of x does the function Fx) have a vertical asymptote? Check
all that apply.
F(x) =
2/3x(x - 1)(x + 5)
I A. -1
B. 2
C. 1
D. -5
E. 0
F. 3
9514 1404 393
Answer:
C, D, E
Step-by-step explanation:
Vertical asymptotes are found where the denominator is zero. The denominator will be zero when any of its factors is zero. Then the vertical asymptotes are ...
x = 0 ⇒ x = 0 . . . . . . choice E
x -1 = 0 ⇒ x = 1 . . . . . choice C
x +5 = 0 ⇒ x = -5 . . . choice D
Sets of rational numbers integers and whole numbers
sets of rational numbers = Q
sets of rational numbers is represented by \( \mathbb{Q}\)
Sets of intigers is represented by Z
Sets of whole numbers is represented by W
You are playing a solitaire game in which you are dealt three cards without replacement from a simplified deck of 10 cards (marked 1 through 10). You win if one of your cards is a 10 or if all of your cards are odd. How many winning hands are there?
The total number of winning hands are 276.
What is the probability?Probability is defined as the ratio of favorable outcomes to all other possible outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The probability of an event can be calculated using the following formula.
Probability of an event = Number of favourable outcomes/Total number of outcomes = x/n.
In the given question,
If the first card drawn is a 10, then there are
\(P_9^2=\frac{9!}{(9-2)!} =9*8=72 hands\)
There are 9 possible numbers if the second card is a 10, and there are 8 possible numbers if the third card, giving us,
\(9*8= 72 hands\)
If the third card is 10 then there are 9 possible numbers for the first card and 8 possible numbers for
second card, it gives us
\(9*8= 72 hands\)
And there are 5 odd cards, and it gives us:
\(P_5^3=\frac{5!}{(5-3)!} =5*4*3=60 hands\)
So, we have that in total we have
72+72+72+60=276 winning hands.
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How would you create a statistical analysis based on the scenario below? What level of significance would you test at and why? A researcher is examining preferences among four new flavors of ice cream. A sample of n + 80 people is obtained. Each person tastes all four flavors then picks a favorite. The distribution preferences is as follow. Do these data indicate any significance preferences among the four flavors using the chi-square test? Ice Cream Flavor - A. 12 B. 18 C. 28 D. 22.
The statistical analysis is created using the chi-squared test. The significance level used is 5% because of the probability to reject the null hypothesis. The given data indicate that there are significant preferences among the four flavors of ice cream.
When the sample sizes are big, the statistical hypothesis test known as the chi-squared test is utilized in the study of contingency tables. This test is primarily used to determine whether two categorical factors have independent effects on the test statistic. We shall use a significance level of α=0.05 in this case.
First, determine the null and alternative hypotheses.
Null hypothesis H₀: There is no preference in choosing ice cream flavors.
Alternate hypothesis H₁: There is a preference in choosing ice cream flavors.
The probability of choosing a particular flavor of ice cream is 1/4. Then, the Ei= (1/4)×80= 20.
Now construct the chi-square table. And find the chi-square value,
\(\begin{aligned}\chi^2&=\sum\frac{(O_i-E_i)^2}{E_i}\\&=3.2+0.2+3.2+0.2\\&=6.8\end{aligned}\)
Find the degree of freedom (df).
df = n-1 = 4-1 = 3.
From the chi-square table, using the chi-square value and df, we get the p-value,
P(χ²>6.8)= 0.0786
Here, the p-value is greater than 0.05. As a result, the alternative hypothesis is accepted and the null hypothesis is rejected. From this, we can tell that there is a significant preference in choosing the flavors.
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