Answer:
The 95% confidence interval for the difference in population means is (−26.325175 , 36.325175)
Step-by-step explanation:
Given that :
sample size n₁ = 36
sample mean [tex]\over\ x[/tex]₁ = 83
standard deviation [tex]\sigma[/tex]₁ = 5
sample size n₂ = 49
sample mean [tex]\over\ x[/tex]₂= 78
standard deviation [tex]\sigma[/tex]₂ = 3
The objective is to construct a 95% confidence interval for the difference in the population means
Let the population means be [tex]\mu_1[/tex] and [tex]\mu_2[/tex]
The 95% confidence interval or the difference in population means can be calculated by using the formula;
[tex](\overline{x_1} - \overline{x_2}) \pm t_{\alpha /2} \ \times s_{p}[/tex]
where;
the pooled standard deviation [tex]s_{p} = \dfrac{(n_1-1)s_1^2+(n_2-1)s^2_2}{n_1+n_2-2}[/tex]
[tex]s_{p} = \dfrac{(36-1)5^2+(49-1)3^2}{36+49-2}[/tex]
[tex]s_{p} = \dfrac{(35)25+(48)9}{83}[/tex]
[tex]s_{p} = \dfrac{875+432}{83}[/tex]
[tex]s_{p} = \dfrac{1307}{83}[/tex]
[tex]s_p[/tex] = 15.75
degree of freedom = [tex]n_1 +n_2 -2[/tex]
degree of freedom = 36+49 -2
degree of freedom = 85 - 2
degree of freedom = 83
The Critical t- value 95% CI at df = 83 is
t critical = T.INV.2T(0.05, 83) = 1.9889
Therefore, for the population mean , we have:
= (83 - 78) ± (1.9889 × 15.75)
= 5 ± 31.325175
= 5 - 31.325175 , 5 + 31.325175
= (−26.325175 , 36.325175)
Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the form [a b c] , where at most one of a , b and c is non 0.
The set is a subspace.
The set is not a subspace.
If so, give a proof. If not, explain why not.
Answer:
Not a subspace
Step-by-step explanation:
(4,0,0) and (0,4,0) are vectors in R3 with zero or one entries being nonzero, but their sum, (4,4,0) has two nonzero entries.
Simplify i to the 31st power
Answer:
?
How did you simplify
What is the conjugate of 3 + 6i?
A -3 - 61
B 3 - 6i
C 3 + 6i
D 9i
Answer:
C.3-6
Step-by-step explanation:
Every complex number has a complex conjugate.
Examples is a+bi the conjugate is a-bi,if your adding the two conjugate its going to be 2a and if your subtracting the result is 2bi.And if multiplied it is seen as complex number which are a²+b²
It has been reported that 20.4% of incoming freshmen indicate that they will major in business or a related field. A random sample of 400 incoming college freshmen was asked their preference, and 95 replied that they were considering business as a major. Estimate the true proportion of freshman business majors with 98% confidence. Does your interval contain 20.4%?
Answer:
The 98% confidence interval
[tex]0.1884 < p < 0.2876[/tex]
The confidence interval contains 20.4%
Step-by-step explanation:
From the question we are told that
The sample size is n = 400
The number that replied that they were considering business as a major [tex]x = 95[/tex]
The sample proportion is mathematically evaluated as
[tex]\r p = \frac{95}{400}[/tex]
[tex]\r p = 0.238[/tex]
Given that the confidence level 98% then the level of significance is evaluated as
[tex]\alpha = 100 - 98[/tex]
[tex]\alpha = 2 \%[/tex]
[tex]\alpha = 0.02[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{ \alpha }{2} } = 2.33[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * \sqrt{ \frac{ p (1 - p )}{n} }[/tex]
[tex]E = 2.33 * \sqrt{ \frac{ 0.238 (1 - 0.238 )}{400} }[/tex]
[tex]E = 0.0496[/tex]
The 98% confidence interval is mathematically represented
[tex]\r p - E < p < \r p + E[/tex]
=> [tex]0.238 - 0.0496 < p <0.238 + 0.0496[/tex]
=> [tex]0.1884 < p < 0.2876[/tex]
The Junior class has raised
4/7
of the amount of money that is needed for the Junior-Senior
Prom, and the Senior class has raised 3/11 of the amount of money that is needed. Estimate
what portion of the money the two classes have already raised of the money
A.1/4 of the money
B.all of the money
C.1/2 of the money
D.3/4 of the money
Answer:
B. all of the money this is my answer
The joint density function for a pair of random variables X and Y is given. f(x, y) = Cx(1 + y) if 0 ≤ x ≤ 4, 0 ≤ y ≤ 4 0 otherwise f(x,y) = 0
A) Find the value of the constant C. I already have 1/24.
B) Find P(X < = 1, Y < = 1)
C) Find P(X + Y < = 1).
Answer:
A) C = 1/96
B) P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places
C) P(x+y<=1) = 5/2305, or 0.0021701 to 7 places
Step-by-step explanation:
f(x,y) = C x (1+y)
A)
To find C, we need to integrate the volume under region bound by
0 <= x <= 4, and
0 <= y <= 4
This volume equals 1.0.
Find integral,
int( int(f(x,y),x=0,4), y = 0,4) = 96C
therefore C = 1/96
or
F(x,y) = x (1+y) / 96 ............................(1)
B)
P(x<=1, y<=1)
Repeat the integral, substitute the appropriate limits,
P = int( int(F(x,y),x=0,1), y = 0,1)
= 1/128 or 0.0078125
P(x<=1, y<=1) = 1/128 or 0.0078125 to 7 places
C)
P(x+y<=1)
From the function, we know that this is going to be less than one half of the probability in (B), closer to 1/4 of the previous.
It will be again a double integral, as follows:
P = int( int(F(x,y),x=0,1-y), y = 0,1)
= 5/2304
= 0.0021701 (to 7 decimals)
P(x+y<=1) = 5/2305, or 0.0021701 to 7 places
It used to take 20 hours to get to Los Angeles, now it takes 12 hours, how much shorter was it?
Step-by-step explanation:
It takes 20 Hours to get to Los Angeles
Now it takes 12 hours....
Therefore we subtract 20 from 12
which becomes
20 - 12= 8.
So it's 8 hours shorter
In the xy-coordinate system above, line / (not shown) does not contain point in either quadrant II or
quadrant IV. Which of the following could be the equation of line /?
•x=3
•y=3x
•y=3x+3
•y=-3x-3
Answer:
y=3x
Step-by-step explanation:
If the line cannot be in quadrants II or IV, it must pass through the origin(0,0) and be in quadrants I and III.
Substitute (0,0) for y and x to find the answer.
1) x=3, 0=3 NO
2) y=3x, 0=3(0), 0=0 YES
3) y=3x+3, 0=3(0)+3, 0=3 NO
4) y=-3x-3, 0=-3(0)-3, 0=-3 NO
So the answer must be 2) y=3x
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs $3.25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most $30 before tax. The restaurant only sells pancakes in stacks of 44 pancakes for $5.50 . Let S represent the number of stacks of pancakes that Benjamin buys. 1) Which inequality describes this scenario?2) What is the largest number of pancakes that Benjamin can afford?
Answer:
3.25 + 5.50S ≤ 30
Step-by-step explanation:
Given:
Chocolate milk cost $3.25.
Maximum bill that Benjamin wants = $30
Cost of a stack pancake(44) = $5.50
Let number of stacks of pancakes bought = S
Benjamin will spend all the money available on 1 chocolate milk and S number of stacks of pancakes.
Cost of 1 pancake = $5.50
Cost of S number of stacks of pancakes = S*5.50
=5.50S
Total money spent =$3.25+5.50S
The total money spent should either be lesser than or equal to $30
The inequality is
3.25 + 5.50S ≤ 30
Largest number of pancakes Benjamin can afford
3.25 + 5.50S ≤ 30
5.50S ≤ 30-3.25
5.50S ≤ 26.75
Divide both sides by 5.50
S ≤ 4.86
1 stack=44 pancakes
4.86 stacks= 4.86 *44
=213.84 pancakes
Answer:
3.25+5.50S≤30
and 16 pancakes
Step-by-step explanation:
Find the product of the roots of the equation
xl-5x - 36 = 0
Answer:
Step-by-step explanation:
Hello, I assume that you mean
[tex]x^2-5x-36[/tex]
The product is -36.
[tex]x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]
So in this example, it means that the sum is 5 and the product is -36.
Thank you
What expression describes 2a in the expression 2a2+2a-11
Answer:
Step-by-step explanation:
2a is the middle term of a quadratic expression. 2 is the coefficient of a to the first power.
Not much more you can say about this.
Please, if the original question includes answer choices, share those choices. Thank you.
A plot of land has vertices as follows, where each coordinate is a measurement in feet. Find the perimeter of the plot of land. (1,7),(7,7),(7,1),(1,1) please help and explain how to do this type of thing because i am lost
Answer:
Perimeter of ABCD = 36 ft
Step-by-step explanation:
Given:
A (1,7)
B (7,7)
C (7,1)
D (1,1)
Find:
Perimeter of ABCD
Computation:
Distance between two point = √(x1-x2)² + (y1-y2)²
So,
AB = √(1-7)²+(7-7)²
AB = 6 ft
BC = √(7-7)²+(7-1)²
BC = 6 ft
CD = √(7-1)²+(1-1)²
CD = 6 ft
DA = √(1-1)²+(1-7)²
DA = 6 ft
Perimeter of ABCD = AB + BC + CD + DA
Perimeter of ABCD = 6 + 6 + 6 +6
Perimeter of ABCD = 36 ft
The perimeter of the plot is the sum of side length of the plot of land.
The perimeter of the plot is 24 feet.
Represent the vertices as follows:
[tex]W = (1,7)[/tex]
[tex]X = (7,7)[/tex]
[tex]Y = (7,1)[/tex]
[tex]Z = (1,1)[/tex]
First, we calculate the side length using the following distance formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]WX = \sqrt{(1- 7)^2 + (7- 7)^2} = \sqrt{36} = 6[/tex]
[tex]XY = \sqrt{(7- 7)^2 + (7- 1)^2} = \sqrt{36} = 6[/tex]
[tex]YZ = \sqrt{(7- 1)^2 + (1- 1)^2} = \sqrt{36} = 6[/tex]
[tex]ZW = \sqrt{(1- 1)^2 + (1- 7)^2} = \sqrt{36} = 6[/tex]
The perimeter (P) is then calculated as follows:
[tex]P = WX + XY + YZ + ZW[/tex]
So, we have:
[tex]P = 6 + 6 + 6 + 6[/tex]
[tex]P = 24[/tex]
Hence, the perimeter of the plot of land is 24 feet.
Read more about perimeters at:
https://brainly.com/question/394193
Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
a^2-2a-224=0
Answer:
{-14, 16}
Step-by-step explanation:
The coefficients of this quadratic are a = 1, b = -2 and c = -224.
Thus, the discriminant is b^2 - 4ac, or (-2)^2 - 4(1)(-224), or 900, whose square root is 30.
Thus, the roots (solutions) are
-(-2) ± 30
x = ----------------- = {-14, 16}
2
For an experiment with 3 groups of 10 participants in each group. Fcrit for alpha 0.05=_________
a. 3.35
b. 2.35
c. 5
d. 12
Answer:
a. 3.35
Step-by-step explanation:
Given that :
an experiment with 3 groups consist of 10 participant in each group.
This implies that:
number of group k = 3
number of participants n = 10
N = nk
N = 10 × 3 = 30
The degree of freedom within can be calculate as:
dfw = N - k
dfw = 30 - 3
dfw = 27
The degree of freedom for the critical value
dfc = n- 1
dfc = 3 - 1
dfc = 2
At the level of significance ∝ = 0.05
The F critical value from the standard normal F table
i.e
[tex]F_{critical { (2, 27)}=[/tex] 3.35
What is the inverse of the function a(x)=1/x-2
Answer:
x = 1/x - 2
Step-by-step explanation:
Which graph represents the function h(x) = |x – 3|?
On a coordinate plane, an absolute value graph has a vertex at (0, 3).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
On a coordinate plane, an absolute value graph has a vertex at (3, 0).
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
Answer:
option 3
Step-by-step explanation:
i know because i got it right.
1) Dada a função, em reais, definida por f(x)=3.x-5. calcule :
a) f(2)=
b) f(-1)=
Answer:
f(x)= 3x-5
f(2) = 3(2)-5 = 6-5= 1
f(-1)= 3(-1)-5= -3-5= -8
Hope this helps
if u have question let me know in comments ^°^
1
2
3
4
Which value of a in the exponential function below would cause the function
f(x)
=a
Tln wilt ml
4
o
Answer:
Step-by-step explanation: sajkdkdksskkcfd
A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At 95% confidence, test to determine if at least 22% of the population will like the new soft drink.
Required:
Determine the p-value.
Answer: p-value of the test = 0.167
Step-by-step explanation:
Given that,
sample size n = 400
sample success X = 80
confidence = 95%
significance level = 1 - (95/100) = 0.05
This is the left tailed test .
The null and alternative hypothesis is
H₀ : p = 0.22
Hₐ : p < 0.22
P = x/n = 80/400 = 0.2
Standard deviation of proportion α = √{ (p ( 1 - p ) / n }
α = √ { ( 0.22 ( 1 - 0.22 ) / 400 }
α = √ { 0.1716 / 400 }
α = √0.000429
α = 0.0207
Test statistic
z = (p - p₀) / α
z = ( 0.2 - 0.22 ) / 0.0207
z = - 0.02 / 0.0207
z = - 0.9661
fail to reject null hypothesis.
P-value Approach
P-value = 0.167
As P-value >= 0.05, fail to reject null hypothesis.
Since test is left tailed so p-value of the test is 0.167. Since p-value is greater than 0.05 so we fail to reject the null hypothesis.
Find a9 for the geometric sequence 5, –20, 80, ...
Answer:
327680
Step-by-step explanation:
The general formula of the formula for the sequence is 5*(-4)^(n-1). The 9th term will be 5*(-4)^8=327680
What is the oppisite of 0.7?
Answer: negative 0.7
Step-by-step explanation:because you are looking for the opposite if you make a number line
What is the area, in square meters, of the shaded part of the rectangle shown below?
Answer:
C) 100 cm²
Step-by-step explanation:
(14*6)/2*10
20/2*10
10*10
100
The area of the given shaded part of the rectangle is 100 square meters as shown.
What is the area of a triangle?The entire space filled by a triangle's three sides in a two-dimensional plane is defined as its area.
The fundamental formula for calculating the area of a triangle is A = 1/2 b h.
The area of the shaded part = area of the rectangle - area of the triangle
The area of the shaded part = 14 × 10 - (1/2) × 8 × 10
The area of the shaded part = 140 - 80/2
The area of the shaded part = 140 - 40
Apply the subtraction operation, and we get
The area of the shaded part = 100 meters²
Thus, the area of the given shaded part of the rectangle is 100 square meters.
Learn more about the triangles here:
https://brainly.com/question/17997149
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mortician math word problem
Answer:
wat do u want me to do
Step-by-step explanation:
What is 20×10 to the third power equal
Lauren is a college sophomore majoring in business. This semester Lauren is taking courses in accounting, economics, management information systems, public speaking, and statistics. The sizes of these classes are, respectively, 375, 35, 45, 25, and 60.Required:Find the mean and the median of the class sizes. What is a better measure of Lauren's "typical class size"—the mean or the median?
Answer:
Mean = 108
Median = 45
The better measure of Lauren's "typical class size" is the Mean
Step-by-step explanation:
1. Calculating mean and median.
The mean is an important measure of central tendency, and it is the average of the measurement of a given set of data. It is calculated as follows:
[tex]Mean\ (\overline {X}) &= \frac{\sum X}{N}[/tex]
where X = individual data sets
N = total number of data
[tex]Mean= \frac{375\; +\ 35\ +\ 45\ +\ 25\ +\ 60}{5} \\=\frac{540}{5} \\= 108[/tex]
The Median divides the measurements into two equal parts, and in order to calculate the median, the distribution has to first be arranged in ascending or descending order. Arranging this series in descending order:
375, 60, 45, 35, 25
The formula for calculating median is given by:
[tex]M_{d} = \frac{N\ +\ 1}{2} th\ data\\\\=\frac{5\ +\ 1}{2}th\ data\\\\=\frac{6}{2} th\ data\\= 3rd\ data\\M_{d} = 45[/tex]
from the list or arranged data in descending order (375, 60, 45, 35, 25), the third data is 45.
Therefore, Median = 45
2. The better measure of typical class size is Mean because the mean depends on all the values of the data sets, whereas the median does not. When there are extreme values (outliers) the effect on the median is very small, whereas it is effectively captured by the mean.
Natalie's team needs to make a decision on how to handle a big product recall. People on the team have a lot of strong opinions. Management wants everyone to come to a consensus and to find a solution that everyone can support. What's the best way to get to a consensus?
a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then votes. Oc) The team passes the decision-making responsibility to an outside person. O di The team leader makes a decision without input from the other members.
Answer:
a) Everyone on the team talks until the entire team agrees on one decision.
Step-by-step explanation:
Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense
Lydia drives from city a to city b to transport goods. her return speed is 3 times her departure speed and she takes 40 minutes less on her return trip. how long did her departure trip take?
Answer:
1 hour
Step-by-step explanation:
Hello, let's say that her departure trip takes t in minutes, as her return speed is 3 times her departure speed, she took t/3 for the return and we know that this 40 minutes less, so we can write.
t/3=t-40
We can multiply by 3
t = 3t -40*3 = 3t - 120
This is equivalent to
3t -120 = t
We subtract t
2t-120 = 0
2t = 120
We divide by 2
t = 120/2 = 60
So this is 60 minutes = 1 hour.
Thank you.
Describe the following sequence using an algebraic expression as a rule 0; 2,4; 6
Answer:
Step-by-step explanation:
I assume the sequence is 0, 2, 4, 6
nth term = 2(n-1)
Compare –3.5 and . Use <, >, or =.
–3.5 >
–3.5 <
–3.5 =
Answer:
-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5Step-by-step explanation:
Give any integer that suits the expression:-3.5 > -4.5-3.5 < -1.5-3.5 = -3.5• The farther a negative integer from 0, the smaller its value.[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
trigonometric identities
1/tan x = cot x
Cot x + tan x = 1/ sin x cos x
The answer is D.