Answer:
The percentage is [tex]P(x_1 < X < x_2) = 47.7 \%[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 150000[/tex]
The standard deviation is [tex]\sigma = \$ 1200[/tex]
The prices we are considering is [tex]x_1 = \$150000 \to \ x_2 = \$ 152400[/tex]
Given that the price is normally distributed , the percentage the percentage of buyers who paid between $150,000 and $152,400 is mathematically represented as
[tex]P(x_1 < X < x_2) = P(\frac{x_1 - \mu}{\sigma } < \frac{X - \mu}{\sigma } < \frac{x_2 - \mu}{\sigma })[/tex]
So [tex]\frac{X - \mu}{\sigma }[/tex] is equal to z (the standardized value of X )
So
[tex]P(x_1 < X < x_2) = P(\frac{x_1 - \mu}{\sigma } <Z < \frac{x_2 - \mu}{\sigma })[/tex]
substituting values
[tex]P(x_1 < X < x_2) = P(\frac{150000 - 150000}{1200 } <Z < \frac{152400 - 150000}{1200 })[/tex]
[tex]P(x_1 < X < x_2) = P(0<Z < 2)[/tex]
[tex]P(x_1 < X < x_2) = P( Z < 2) - P( Z < 0 )[/tex]
From the standardized normal distribution table [tex]P(Z < 2 ) = 0.97725[/tex] and
[tex]P(Z < 0) = 0.5[/tex]
So
[tex]P(x_1 < X < x_2) = 0.97725 - 0.5[/tex]
[tex]P(x_1 < X < x_2) = 0.47725[/tex]
The percentage is [tex]P(x_1 < X < x_2) = 47.7 \%[/tex]
an auto dealer offers a compact car, a midsize, a sport utility vehicle, and a light truck, each either in standard, custom, or sport styling, a choice of manual or automatic transmission, and a selection from 7 colors. How many ways of buying a vehicle from this dealer are there?
Answer: 168
Step-by-step explanation:
First, let's count the types of selection:
We can select:
Type of car: a compact car, a midsize, a sport utility vehicle, and a light truck (4 options)
Pack: standard, custom, or sport styling, (3 options)
type of transmission: Manual or automatic (2 options)
Color: (7 options)
The total number of combinations is equal to the product of the number of options in each selection:
C = 4*3*2*7 = 168
A machine fills containers with 35 ounces of raisins
The correct graph will be the first one (A)
The alpha level that a researcher sets at the beginning of the experiment is the level to which he wishes to limit the probability of making the error of____________
Answer:
not rejecting the null hypothesis when it is false.
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis.
For making the error, it should not reject the null hypothesis at the time when it should be false.
What is alpha level?It is the level where the probability of rejecting the null hypothesis at the time when the null hypothesis should be true. It is relevant for making the incorrect decision. Also, it is the statistical test that measured the probability of type 1 error.
Therefore, For making the error, it should not reject the null hypothesis at the time when it should be false.
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Given: ∠N ≅ ∠S, line ℓ bisects at Q. Prove: ∆NQT ≅ ∆SQR Which reason justifies Step 2 in the proof? If two lines are parallel, then the corresponding angles formed are congruent. If two lines are parallel, then the alternate interior angles formed are congruent. Vertical angles are congruent. If two lines are parallel, then the same-side interior angles formed are congruent.
Answer:
Vertical angles are congruent.
Step-by-step explanation:
Vertical angles are opposite angles formed by intersecting lines, and are always congruent.
can someone EXPLAIN this to me? you don't have to answer the questions. They are for my college class. Last assignment! thank you..
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (f o g)(-5)
In randomized, double-blind clinical trials of Prevnar, infants were randomly divided into two groups. Subjects in group 1 received Prevnar, while subjects in group 2 received a control vaccine. Aft er the second dose, 137 of 452 subjects in the experimental group (group 1) experienced drowsiness as a side effect. After the second dose, 31 of 99 subjects in the control group (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the αα=0.05 level of significance?
Answer:
Step-by-step explanation:
From the summary of the given data;
After the second dose, 137 of 452 subjects in the experimental group (group 1) experienced drowsiness as a side effect.
Let consider [tex]p_1[/tex] to be the probability of those that experience the drowsiness in group 1
[tex]p_1[/tex] = [tex]\dfrac{137}{452}[/tex]
[tex]p_1[/tex] = 0.3031
After the second dose, 31 of 99 subjects in the control group (group 2) experienced drowsiness as a side effect.
Let consider [tex]p_2[/tex] to be the probability of those that experience the drowsiness in group 1
[tex]p_2[/tex] = [tex]\dfrac{31}{99}[/tex]
[tex]p_2[/tex] = 0.3131
The objective is to be able to determine if the evidence suggest that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.05 level of significance.
In order to do that; we have to state the null and alternative hypothesis; carry out our test statistics and make conclusion based on it.
So; the null and the alternative hypothesis can be computed as:
[tex]H_o :p_1 =p_2[/tex]
[tex]H_a= p_1<p_2[/tex]
The test statistics is computed as follows:
[tex]Z = \dfrac{p_1-p_2}{\sqrt{p_1 *\dfrac{1-p_1}{n_1} +p_2 *\dfrac{1-p_2}{n_2}} }[/tex]
[tex]Z = \dfrac{0.3031-0.3131}{\sqrt{0.3031 *\dfrac{1-0.3031}{452} +0.3131 *\dfrac{1-0.3131}{99}} }[/tex]
[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *\dfrac{0.6969}{452} +0.3131 *\dfrac{0.6869}{99}} }[/tex]
[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *0.0015418 +0.3131 *0.0069384} }[/tex]
[tex]Z = \dfrac{-0.01}{\sqrt{4.6731958*10^{-4}+0.00217241304} }[/tex]
[tex]Z = \dfrac{-0.01}{0.051378 }[/tex]
Z = - 0.1946
At the level of significance ∝ = 0.05
From the standard normal table;
the critical value for Z(0.05) = -1.645
Decision Rule: Reject the null hypothesis if Z-value is lesser than the critical value.
Conclusion: We do not reject the null hypothesis because the Z value is greater than the critical value. Therefore, we cannot conclude that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2
Two similar data sets are being compared. The standard deviation of Set A is 4.8. The standard deviation of Set B is 6.5.
Answer:
The spread of the data in Set B is greater than the spread of the data in Set A.
Step-by-step explanation:
Just took the test :3
show all work!! Plus this is the same question as my last one so you get a total of 25 points if you answer both! Just copy the answer you got from this one and paste it in the other question (the same question)
Answer:
increase of 30
Step-by-step explanation:
1255- 1075 = 180
This is an increase of 180
Divide by the number of numbers which is 6
180 /6 = 30
The mean will increase by 30
Answer:
+30
Step-by-step explanation:
1255- 1075 = 180
180 /6 = 30
(I NEED HELP) The data below shows the scores of some students on a test: 23, 27, 21, 20, 25, 31, 22 Which box-and-whisker plot represents the data?
Answer:
B
Step-by-step explanation:
Answer:
the 2nd one
Step-by-step explanation:
because the Minimum is 20
the Maximum is 31
the median is 23
20, 21, 22, 23, 25, 27, 31,
21, 22, 23, 25, 27
22, 23, 25,
23
For each of the following research scenarios, decide whether the design uses a related sample. If the design uses a related sample, identify whether it uses matched subjects or repeated measures. (Note: Researchers can match subjects by matching particular characteristics, or, in some cases, matched subjects are naturally paired, such as siblings or married couples.)
You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores.
The design described ___________a, b, or c_________________________.
a. uses a related sample - repeated measures
b. uses a related sample - matched subjects
c. does not use a related sample
John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample to lonely people to the sleep quality of a random sample of nonlonely people.
The design described ______a, b, or c_________________________.
a. does not use a related sample
b. uses a related sample (repeated measures)
c. uses a related sample (matched subjects)
Answer:
a. uses a related sample - repeated measures
c. uses a related sample (matched subjects)
Step-by-step explanation:
A) You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores.
The design described uses a related sample - repeated measures because the scores were compared on the Hoarding Severity scale before and after the treatment.
B) John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample of lonely people to the sleep quality of a random sample of nonlonely people.
The design described uses a related sample (matched subjects)
Degree Of Length Degree Of Width Degree Of Height Degree Of Volume
Answer: length = 1, width = 1, height = 3, volume = 5
Step-by-step explanation:
Degree is the biggest exponent for the variables in the expression
Length = 4x - 1. The exponent for x is 1 --> degree = 1
Width = x The exponent for x is 1 --> degree = 1
Height = x³ The exponent for x³ is 3 --> degree = 3
Volume = 4x⁵ - x⁴. The biggest exponent for x is 5 --> degree = 5
Answer:
- First answer: 1
- Second answer: 1
- Third answer: 3
- Last answer: 5
Step-by-step explanation:
Correct on E2020
which quadratic function in standard form has the value a= -3.5, b=2.7, and c= -8.2?
Answer:
y = -3.5x² + 2.7x -8.2
Step-by-step explanation:
the quadratic equation is set up as a² + bx + c, so just plug in the values
Answer:
[tex]-3.5x^2 + 2.7x -8.2[/tex]
Step-by-step explanation:
Quadratic functions are always formatted in the form [tex]ax^2+bx+c[/tex].
So, we can use your values of a, b, and c, and plug them into the equation.
A is -3.5, so the first term becomes [tex]-3.5x^2[/tex].
B is 2.7, so the second term is [tex]2.7x[/tex]
And -8.2 is the C, so the third term is [tex]-8.2[/tex]
So we have [tex]-3.5x^2+2.7x-8.2[/tex]
Hope this helped!
The area of an Equilateral triangle is given by the formula A= 3pi squared/4(s)Squared. Which formula represents the length of equilateral triangle’s side S?
Answer:
The formula that represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A) is [tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex] .
Step-by-step explanation:
We are given the area of an Equilateral triangle which is A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex] . And we have to represent the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).
So, the area of an equilateral triangle = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]
where, s = side of an equilateral triangle
A = [tex]\frac{\sqrt{3} }{4} \times \text{s}^{2}[/tex]
Cross multiplying the fractions we get;
[tex]4 \times A = \sqrt{3} \times \text{s}^{2}[/tex]
[tex]\sqrt{3} \times \text{s}^{2}= 4\text{A}[/tex]
Now. moving [tex]\sqrt{3}[/tex] to the right side of the equation;
[tex]\text{s}^{2}= \frac{4 \text{A}}{\sqrt{3} }[/tex]
Taking square root both sides we get;
[tex]\sqrt{\text{s}^{2}} = \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]
[tex]\text{s}= \sqrt{ \frac{4 \text{A}}{\sqrt{3} }}[/tex]
Hence, this formula represents the length of an equilateral triangle’s side (s) in terms of the triangle's area (A).
Verify the Cauchy-Schwarz Inequality and the triangle inequality for the given vectors and inner product.
p(x)=5x , q(x)= -2x^2+1, (p,q)= aobo+ a1b1+ a2b2
Required:
a. Compute (p,q)
b. Compute ||p|| and ||q||
Answer:
To verify the Cauchy-Bunyakovsky-Schwarz Inequality, (p,q) must be less than (or equal to) ||p|| • ||q||
(1,1,1) is not equal to (-10,5)
Step-by-step explanation:
a°b° + a^1b^1 + a^2b^2 < 5x (-2x^2 + 1)
Any algebra raised to the power of zero is equal to 1.
a°b° = 1 × 1 = 1
1 + ab + a^2b^2 < -10x^3 + 5x
The vectors:
(1,1,1) < (-10,5)
This verifies the Cauchy-Schwarz Inequality
Triangle Inequality states that for any triangle, the sum of the lengths of two sides must be greater than or equal to the length of the third side.
given sin theta=3/5 and 180°<theta<270°, find the following: a. cos(2theta) b. sin(2theta) c. tan(2theta)
I hope this will help uh.....
Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 64 + x2 − y2 R = {(x, y): x2 + y2 ≤ 64}
The area of the surface above the region R is 4096π square units.
Given that:
The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]
The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].
To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.
The integral for the area is given by:
[tex]Area = \int\int_R f(x, y) dA[/tex]
To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.
Using polar coordinates, we can parameterize the region R as follows:
x = rcos(θ)
y = rsin(θ)
where r goes from 0 to 8, and θ goes from 0 to 2π.
Now, rewrite the integral in polar coordinates:
[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]
Now, we can integrate with respect to r first and then with respect to θ:
[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]
Integrate with respect to r:
[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]
Now, we can integrate with respect to θ:
[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]
Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))
Area = 4096π + 128(0) - 0
Area = 4096π square units
So, the area of the surface above the region R is 4096π square units.
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Which set of integers does NOT represent the lengths of the sides of a triangle? A. {6,6,11} B. {9,10,11} C. {4,8,12} D. {4,7,9}
Answer:
C
Step-by-step explanation:
I suppose you have learned that for the sides of a triangle to work, it has to be a + b > c, the 4 is the a, the 8 is the b, the 12 is the c.
So: 4 + 8 > 12; however this is not true, they are equal so the triangle wont be a triangle, it would be lines that never connect.
plzzz help 6≥ -6(a+2)
Answer:
a[tex]\geq[/tex]-3
Step-by-step explanation:
Answer:
-3 ≤ a
Step-by-step explanation:
6≥ -6(a+2)
Divide each side by -6, remembering to flip the inequality
6/-6 ≤ -6/-6(a+2)
-1 ≤ (a+2)
Subtract 2 from each side
-1 -2 ≤ a+2-2
-3 ≤ a
3 sides of the triangle are distinct perfect squares. What is the smallest possible perimeter of the triangle?
Answer:
77
Step-by-step explanation:
At first, you would probably think that the side lengths are 1², 2², 3² = 1, 4 and 9 but these side lengths don't form a triangle. The Triangle Inequality states that the sum of the two shortest side lengths must be greater than the largest side length, and since 1 + 4 > 9 is a false statement, it's not a triangle. Let's try 2², 3², 4² = 4, 9, 16. 4 + 9 > 16 is also false so that doesn't work. 3², 4², 5² = 9, 16, 25 but since 9 + 16 > 25 is false (25 isn't greater than 25), that doesn't work either. 4², 5², 6² = 16, 25, 36 and since 16 + 25 > 36 is true, this is our triangle which means that the perimeter is 16 + 25 + 36 = 77.
Answer:
e
Step-by-step explanation:
e
Linda, Reuben, and Manuel have a total of $70 in their wallets. Reuben has $10 more than Linda. Manuel has 2 times what Linda has. How much does each have? Amount in Linda's wallet: $ Amount in Reuben's wallet: $ Amount in Manuel's wallet:
Answer:
Linda has $15Reuben has $25Manuel has $30Step-by-step explanation:
Together, they have 4 times what Linda has, plus $10. So, Linda has 1/4 of $60 = $15.
Linda has $15
Reuben has $25 . . . . . . $10 more than Linda
Manuel has $30 . . . . . . twice what Linda has
f(x)=x^2+12x+7 f(x)=(x+_)^2+_ Rewrite the function by completing the square
Answer:
f(x) = (x + 6)² - 29
Step-by-step explanation:
Given
f(x) = x² + 12x + 7
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² + 12x
x² + 2(6)x + 36 - 36 + 7
= (x + 6)² - 29, thus
f(x) = (x + 6)² - 29
answers are 6, and -29
Which of the following ordered pairs satisfied the inequality 5x-2y<8
A) (-1,1)
B) (-3,4)
C) (4,0)
D) (-2,3)
Answer: A, B, and D
Step-by-step explanation:
Input the coordinates into the inequality to see which makes a true statement:
5x - 2y < 8
A) x = -1, y = 1 5(-1) - 2(1) < 8
-5 - 2 < 8
-7 < 8 TRUE!
B) x = -3, y = 4 5(-3) - 2(4) < 8
-15 - 8 < 8
-23 < 8 TRUE!
C) x = 4, y = 0 5(4) - 2(0) < 8
20 - 0 < 8
20 < 8 False
D) x = -2, y = 3 5(-2) - 2(3) < 8
-10 - 6 < 8
-16 < 8 TRUE!
(very urgent) will gave 20 pts
Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that
a) the bit string has exactly two 1s;
b) the bit string begins and ends with 0;
c) the bit string has the sum of its digits equal to seven;
d) the bit string has more 0s than 1s;
e) the bit string has exactly two 1s, given that the string begins with a 1.
Answer:
a. 45/1024
b. 1/4
c. 15/128
d. 193/512
e. 9/256
Step-by-step explanation:
Here, each position can be either a 0 or a 1.
So, total number of strings possible = 2^10 = 1024
a) For strings that have exactly two 1's,
it means there must also be exactly eight 0's.
Thus, total number of such strings possible
10!/2!8!=45
Thus, probability is
45/1024
b) Here, we have fixed the 1st and the last positions, and eight positions are available.
Each of these 8 positions can take either a 0 or a 1.
Thus, total number of such strings possible
=2^8=256
Thus, probability is
256/1024 = 1/4
c) For sum of bits to be equal to seven, we must have exactly seven 1's in the string.
Also, it means there must also be exactly three 0's
Thus, total number of such strings possible
10!/7!3!=120
Thus, probability
120/1024 = 15/128
d) Following are the possibilities :
There are six 0's, four 1's :
So, number of strings
10!/6!4!=210
There are seven 0's, three 1's :
So, number of strings
10!/7!3!=120
There are eight 0's, two 1's :
So, number of strings
10!/8!2!=45
There are nine 0's, one 1's :
So, number of strings
10!/9!1!=10
There are ten 0's, zero 1's :
So, number of strings
10!/10!0!=1
Thus, total number of string possible
= 210 + 120 + 45 + 10 + 1
= 386
Thus, probability is
386/1024 = 193/512
e) Here, we have fixed the starting position, so 9 positions remain.
In these 9 positions, there must be exactly two 1's, which means there must also be exactly seven 0's.
Thus, total number of such strings possible
9!/2!7!=36
Thus, probability is
36/1024 = 9/256
12. What is m∠GEA?
Answer:
90°
Step-by-step explanation:
Circumcenter of a triangle is obtained by drawing perpendicular bisectors of the sides of a triangle. Hence GE is perpendicular to AC.
Therefore, m∠GEA = 90°
If a pair of dice are rolled,
what is the probability that at least
one die shows a 5?
Answer:
11/36
Step-by-step explanation:
Find the probability that neither dice shows a 5 (also means the dice can show any number except 5- where there are 5 possible choices out of 6):
= 5/6 x 5/6
=25/36
If we subtract the probability that neither dice shows a 5, we can obtain the probability that at least 1 dice shows a 5- (either one of them is 5, or both of them is 5)
1- 25/36
=11/36
You are selling your product at a three-day event. Each day, there is a 60% chance that you will make money. What is the probability that you will make money on the first two days and lose money on the third day
Answer:
The required probability = 0.144
Step-by-step explanation:
Since the probability of making money is 60%, then the probability of losing money will be 100-60% = 40%
Now the probability we want to calculate is the probability of making money in the first two days and losing money on the third day.
That would be;
P(making money) * P(making money) * P(losing money)
Kindly recollect;
P(making money) = 60% = 60/100 = 0.6
P(losing money) = 40% = 40/100 = 0.4
The probability we want to calculate is thus;
0.6 * 0.6 * 0.4 = 0.144
Refer to the following wage breakdown for a garment factory:
Hourly Wages Number of employees
$4 up to $7 18
7 up to 10 36
10 up to 13 20
13 up to 16 6
What is the class interval for the preceding table of wages?
A. $4
B. $2
C. $5
D. $3
Answer:
The class interval is $3Step-by-step explanation:
The class interval is simply the difference between the lower or upper class boundary or limit of a class and the lower or upper class boundary or limit of the next class.
In this case for the class
$4 up to $7 18 and
$7 up to $10 36
The lower class boundary of the first class is $4 and the lower class boundary of the second class is $7
Hence the class interval = $7-$4= $3If Juan drives 50 mph for 1/2 hour then 60 mph for 1 1/2 an hour, how far does he drive?
Answer:
115 miles
Step-by-step explanation:
First find the distance at 50 mph
d = 50 mph * .5 hours
= 25 miles
Then find the distance at 60 mph
d = 60 mph * 1.5 hours
= 90 miles
Add the distances together
25+90
115 miles
Answer:
he drives a 115 miles
Step-by-step explanation:
if he drives 50 mph for half an hour he drove 25 miles then if he drives 60 mph for 1 hour and 30 minutes he would of drove 90 miles. 60 + 30=90
90+25=115 so he drove 115 miles.
What is the horizontal distance from the end of the ramp to the back of the truck?
Answer:
134.4 centimetersStep-by-step explanation:
Given,
Hypotenuse ( h ) = 158 cm
Perpendicular ( p ) = 83
Base ( b ) = ?
Now, Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]
Plug the values
[tex] {b}^{2} = {158}^{2} - {83}^{2} [/tex]
Evaluate the power
[tex] {b}^{2} = 24964 - 6889[/tex]
Calculate the difference
[tex] {b}^{2} = 18075[/tex]
[tex]b = \sqrt{18075} [/tex]
Calculate
[tex]b = 134.4 \: cm[/tex]
Hope this helps..
Best regards!!