On average, students using method 1 score between 6.46 and 11.94 points higher than students using method 2.
To find the critical value for constructing the 95% confidence interval, we need to use a t-distribution since the sample sizes are relatively small and the population standard deviations are not known.
The degrees of freedom for the t-distribution can be calculated using the following formula:
df = [(s1^2/n1 + s2^2/n2)^2] / [((s1^2/n1)^2)/(n1-1) + ((s2^2/n2)^2)/(n2-1)]
where s1 and s2 are the standard deviations for method 1 and method 2, n1 and n2 are the sample sizes for method 1 and method 2, and df represents the degrees of freedom.
Substituting the given values, we get:
df = [(5.87^2/169 + 17.66^2/128)^2] / [((5.87^2/169)^2)/(169-1) + ((17.66^2/128)^2)/(128-1)]
= 249.00
Using a t-table with 249 degrees of freedom and a 95% confidence level, we find the critical value to be 1.971.
Therefore, to construct the 95% confidence interval for the true difference between testing averages for students using method 1 and students using method 2, we can use the following formula:
CI = (x1 - x2) ± t*(sqrt(s1^2/n1 + s2^2/n2))
where x1 and x2 are the sample means for method 1 and method 2, s1 and s2 are the standard deviations for method 1 and method 2, n1 and n2 are the sample sizes for method 1 and method 2, and t is the critical value we just calculated.
Substituting the given values, we get:
CI = (81.7 - 72.5) ± 1.971*(sqrt(5.87^2/169 + 17.66^2/128))
= 9.2 ± 2.74
= (6.46, 11.94)
Therefore, we can be 95% confident that the true difference between the mean testing scores for method 1 and method 2 lies between 6.46 and 11.94.
Learn more about average at: brainly.com/question/24057012
#SPJ11
On purchasing a cell phone, Tia got an offer and got the cell phone for $35\%$ less than the tag price. If she saved $\$140$ on that cell phone. Then price on the tag must be $\$$
On purchasing a cell phone, Tia got an offer and got the cell phone for 35% less than the tag price. If she saved 140 on that cell phone. Then price on the tag is 400.
Since, the cell pone is sold with 35% discount on it.
Tia got that phone at selling price with 35% discount on tag price. Also, she saved around 140 on buying the cell phone.
Therefore, the discount on the cell phone on the tag price is her saving on buying the cell phone.
Hence,
35% discount on tag price=Saved amount
(35/100)×T=140
where T is the tag price.
T=(140×100)35
T=14000/34
T=400
Therefore, on buying the cell phone with 35% discount on tag price costs around 140. Then the tag price is 400.
Learn more about Discount on
https://brainly.com/question/188305
#SPJ1
A bag contains lettered tiles. the theoretical probability of choosing a vowel is 40%. the bag contains 78 consonants. how many tiles are in the bag?
The total number of ties present in the bag are 130.
What is probability?Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."
Formula for probability is -
Probability(Event) = Favourable Outcomes/Total Outcomes
It P(E) is the probability for occurring any event.
'x' be the favourable outcome.
'n' be the total outcome.
Then,
P(E) = x/n.
Calculation for the total tiles present the bag.
The probability of choosing a vowel is 40% = 0.4.
Then, the probability of choosing a consonants will be 1 - 0.4 = 0.6 or 60%.
Let P(E) be the probability of the occurrence of the consonants.
Then,
P(E) = total number of consonants/total tiles in the bag.
Let 'T' be the total tiles in the bag.
0.6 = 78/T
T = 78/0.6
T = 130
Therefore, the total tiles present in the bag are 130.
To know more about the probability, here
https://brainly.com/question/13604758
#SPJ4
16. c= vλ. If c = 2.998 x 10^8 m/s, v= 4.41 x 10¹4 s-¹; find a value for λ.
Answer:
6.80 x 10⁻⁷ m
Step-by-step explanation:
You can find the value of λ by inserting the given values into the equation and simplifying.
c = vλ <----- Given equation
2.998 x 10⁸ m/s = (4.41 x 10¹⁴ s⁻¹)λ <----- Insert values
6.80 x 10⁻⁷ m = λ <----- Divide both sides by 4.41 x 10¹⁴
check out the pic first
Answer: (0, 16)
Step-by-step explanation:
y = mx + c
c is the y intercept
from the equation, c = 16
(it's not exactly mx but you don't need to solve for x)
3\sqrt(6)*6\sqrt(6)
Please quick reply!
Answer: 3
Step-by-step explanation:
Multiply the numerator to get 3 x 6 is 18
Multiply the denominator to get √6 x √6 = 6
Divide 18 by 6 to get the answer is 3
The weights of certain machine components are normally distributed with a mean of 7.75 ounces and a standard deviation of 0.07 ounces. Find the two weights that separate the top 4% and the bottom 4%. These weights could serve as limits used to identify which components should be rejected. Round your answer to the nearest hundredth, if necessary.
The weight that separates the top 4% is x = 7.87 (round nearest hundredth) .
The weight that separates the bottom 4% is x = 7.63 (round nearest hundredth).
What is normal distribution?The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous distribution of probability that really is symmetrical around in its mean.
The probability for values that are farther from of the mean tapered down equally both in directions.
Now, use z-chart to find the z-value for that separates the top 4% and the bottom 4%.
The values of z = +1.75 and z = -1.75
Let the weight of the machines be 'x'.
Use the formula for z- value
z = (x - μ)/ σ
Where,
σ is standard deviation = 0.07 ounces.
μ is mean = 7.75 ounces.
Substitute all the values and calculate the weight.
case 1: when z = +1.75
1.75 = (x - 7.75)/0.07
x = (1.75×0.07) + 7.75
x = 7.872
x = 7.87 (round nearest hundredth)
case 2: when z = -1.75
-1.75 = (x - 7.75)/0.07
x = (-1.75×0.07) + 7.75
x = 7.6275
x = 7.63 (round nearest hundredth)
Therefore,
x = 7.87 (round nearest hundredth) is weight which separates top 4%.
x = 7.63 (round nearest hundredth) is weight which separates bottom 4%.
To know more about the characteristics of a normal distribution, here
https://brainly.com/question/23418254
#SPJ4
A movie ends at 7:45 P.M. The next movie begins 50 minutes later. What time does the next movie begin?
Answer:
8:35 PM
Step-by-step explanation:
First, subtract 15 from 50.
50-15=35
Add that 15 taken from 50 to 7:45.
7:45 + 0:15 = 8:00
Add 35 to 8:00
8:00 + 0:35 = 8:35
The next movie will start at 8:35 PM.
Hope this helps!
Find the area of the figure.
Answer:
60 ft^2
Step-by-step explanation:
1. Find the pattern in this sequence. Then write
the next three terms in the sequence.
5,2,1,...
Answer:
-1,-3,-4 it is just subtracting the same amount.
Step-by-step explanation:
Given the right triangle, use the pythagorean theorem to find "a" (one of the legs) when c=85 and b= 53. (round answer to nearest tenth).
Answer:
a= 100.2
Step-by-step explanation:
You solve it like you ate looking for the hypotenuse
A square pool is surrounded by a paved area that is 2 metres wide. If the area of the paving is 72m2, what is the length of the pool?
The length of the square pool is 8. 49cm
How to determine the areaNote that the formula for finding the area of a square is given as;
Area = length^2
We have
Area = 72 m²
Substitute into the formula
I^2 = 72
Find the square root of both sides
I= √72
I = 8. 49cm
The length of the square pool given as I is 8. 49cm
Thus, the length of the square pool is 8. 49cm
Learn more about area of a square here:
https://brainly.com/question/486778
#SPJ1
When solving an equation, Anne's first step is shown below. Which property justifies
Anne's first step?
The justification used is multiplicative property of equality because both sides are multiplied by the same value
Solving linear equationsGiven the expression below
-1/3(4x^2 - 3) - 3 = 5x^2 - 2
We are to determine the justification by Anne to get the step 2 as shown
(4x^2 - 3) - 3 = -3(5x^2 - 2)
Expand
(4x^2 - 3) - 3 = -15x^2 + 6
Hence the justification used is multiplicative property of equality because both sides are multiplied by the same value
Learn more on multiplicative property of equality here: https://brainly.com/question/1978763
#SPJ1
Solve:
2a + 6 = 12
a =
Answer:
8
Step-by-step explanation:
because hhhhhh
gghhhh
jkkkkk
lllll
vvvvv
dddfff
oooooo
eeeerer
kkkkkk
lllll.ssss
The probability is .80 that a standard normal random variable is between -z and +z. The value of z is approximately:________
The z value for the probability in the standard normal table is 1.29.
In this question,
Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution.
The value of probability is 0.80
A standard normal random variable is between -z and +z, So
P(-z < 0 < z) = 0.80
⇒ 2P(0 < z) = 0.80
⇒ P(0 < z) = [tex]\frac{0.80}{2}[/tex]
⇒ P(0 < z) = 0.40
From the standard normal table, z value for the probability 0.40 is
⇒ z = 1.29
Thus P(0 < 1.29) = 0.40
Hence we can conclude that the z value for the probability in the standard normal table is 1.29.
Learn more about Z-Score here
https://brainly.com/question/9399510
#SPJ4
(Refer to the attached image)
Answer:
D. 10
Step-by-step explanation:
To find the distance between two points, use the distance formula:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Define the two points:
[tex]\textsf{Let }(x_1,y_1)=(4,-3)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(-4,3)[/tex]
Substitute the two defined points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(-4-4)^2+(3-(-3))^2}[/tex]
[tex]\implies d=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\implies d=\sqrt{(-8)^2+6^2}[/tex]
[tex]\implies d=\sqrt{64+36}[/tex]
[tex]\implies d=\sqrt{100}[/tex]
[tex]\implies d=\sqrt{10^2}[/tex]
[tex]\implies d=10[/tex]
Therefore, the distance between the two given points is 10 units.
Formula given by
[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{8^2+6^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{10^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=10units[/tex]
Option D
A plane can cover 9904 km in 8 hours how mucb distance will it cover in 1 hour?
In one hour the plane will cover a distance of 1238 km.
What is a linear equation?
A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y is x is given.
calculation:-
today distance = 9904 km.
total time is taken = 8 hours.
∴total distance covered in one hour = 9904/8
= 1238 km.
Learn more about the equation here:- https://brainly.com/question/2972832
#SPJ2
A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.
A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°
The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, angle of depression from the helicopter can be found as follows:
tan x = opposite / adjacent
where
x = angle of depression
Hence,
tan x = 660 / 280
tan x = 2.35714285714
x = tan⁻¹ 2.35714285714
x = 67.1231281953
x = 67°
Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
learn more on right triangle here: https://brainly.com/question/26253402
#SPJ1
Answer:
D = 67
Step-by-step explanation:
Convenience sampling Multiple Choice is the same as simple random sampling. ensures that samples are representative of the population. is an unbiased sampling method. collects sample information from groups that are easy to obtain.
Option (d) is correct. Convenience sampling collects sample information from easy-to-collect groups.
Given convenient sampling.
Convenience sampling is defined as a method adopted by researchers in which they collect market research data from a pre-existing group of respondents. This is the most commonly used sampling technique because it is extremely fast, simple and economical. In many cases, members are easily accessible to be part of the template. It is non-probability sampling and therefore different from random sampling. Since the samples are taken for convenience, the samples are not always representative of the population and therefore have bias. In this case, people were sampled simply because they were convenient.
Thus, convenience sampling collects sample information from easy-to-collect groups.
Learn more about convenience sampling from here brainly.com/question/1282909
#SPJ4
What addition/subtraction equation should I put?
Answer:
7 - 10
Step-by-step explanation:
Because it is -3 and 7 - 10 = -3
The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. Group of answer choices mean: 1.39; standard deviation: 0.80 mean: 1.18; standard deviation: 0.64 mean: 1.39; standard deviation: 0.64 mean: 1.18; standard deviation: 1.30
The value of the Mean & Standard deviation is 1.30 and 1.18.
According to the statement
we have a given that the random variable x represents the number of computers that families have along with the corresponding probabilities.
And we have to find the mean and standard deviation from the given data which is related to the probabilities values
So, according to the given data
The formula to compute the mean is:
Mean = summation [x*p(x)]
Compute the mean as follows:
Mean = summation [x*p(x)]
Mean = summation [0*0.49 + 1* 0.05 + 2*0.32 + 3*0.07 + 4*0.07]
Mean = 0 +0.05 + 0.64 + 0.21 + 0.28
Mean = 1.18
The mean of the random variable x is 1.18.
And after calculating the variance from the formula get
The value of standard deviation is 1.30
So, The value of the Mean & Standard deviation is 1.30 and 1.18.
Learn more about mean and standard deviation here https://brainly.com/question/14650840
#SPJ4
10 points please help me!!!
Step-by-step explanation:
16-19 -> 3 (16, 17, 19)20-23 -> 1 (21)24-27 -> 3 (24, 26, 26)28-31 -> 4 (28, 29, 30, 31)32-35 -> 5 (32, 33, 34, 34, 35)Question 12
From the given graph, use two points to write an equation in point-
slope form and then change to slope-intercept form.
Step 1: Use the two points to find the slope.
Step 2: Use the slope and one point to complete point-slope form.
y-y₁ = m(x-x₁)
Step 3: Change point-slope form into slope intercept form by solving
for y. Show your work!
y=mx+b
At 3:20, what is the measure in degrees of the lesser angle formed by the hour hand and the minute hand
Answer: 30 degrees
Step-by-step explanation:
solve for x -
[tex] x^{2} + 5x + 6 = 0 \\ \\ [/tex]
ty! :)
Hello,
x² + 5x + 6 = 0
a = 1 ; b = 5 ; c = 6
∆ = b² - 4ac = 5² - 4 × 1 × 6 = 25 - 24 = 1 > 0
2 solutions :
[tex] x_{1} = \frac{ - b - \sqrt{\Delta} }{2a} = \frac{ - 5 - 1}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]
[tex]x_{2} = \frac{ - b + \sqrt{\Delta} }{2a} = \frac{ - 5 + 1}{2 \times 1} = \frac{ - 4}{2} = - 2[/tex]
S = { -3 ; -2}
Select the equivalent expression. 2^-4 = ?
Answer:
1/16
Step-by-step explanation:
This means 1/2x2x2x2 = 1/16
How would you describe the graph for the equation |x| <4?
a.) An open circle on 4 with a solid line drawn to an open circle on -4.
b.) A closed circle on 4 with a solid line drawn to a closed circle on -4.
c.) A closed circle on 4 with a solid line drawn to an open circle on -4.
d.) An open circle on 4 with a solid line drawn to a closed circle on -4.
Answer:
a.) An open circle on 4 with a solid line drawn to an open circle on -4.
Explanation:
Open circles are used for signs: < and >
Closed circles are used for signs: ≤ and ≥
Here in the given expression: |x| < 4
[<] sign is used so open circle is used
If |y| < a then -a < y < a
so here, -4 < x < 4
Both circles should be opened, drawn with a solid line from -4 to 4.
find the value of x from the figure
Answer:
x = 30
Step-by-step explanation:
110 and 3x - 20 are supplementary angles, sum to 180° , then
110 + 3x - 20 = 180
90 + 3x = 180 ( subtract 90 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Answer:
x = 30
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
For this question, you must be clear of the angle properties.
z + 110 = 180 (Sum of Angles on a straight line)
z = 180 - 110 = 70
z = 3x - 20 (Corresponding Angles)
3x - 20 = z
3x - 20 = 70
3x = 70 + 20
3x = 90
x = 90 / 3 = 30
Read the following description of a relationship:
Ron is making a banner by stringing letters on a cord. The cord weighs 8
ounces, and each letter weighs 10 ounces.
Let n represent the number of letters and w represent the weight of the banner.
This relationship can also be shown in a table. Complete the equation that represents the
relationship between n and w
The equation that represents the relationship between n and w is w = 10n + 8.
How to illustrate the expression?From the information, Ron is making a banner by stringing letters on a cord and the cord weighs 8
ounces and each letter weighs 10 ounces.
Let represent the number of letters
Let w represent the weight of the banner.
In this case, when n = 6, w = 68 and when n = 7, w = 78.
Therefore, the relationship will be:
w = 10n + 8
To confirm let's use n = 6
10n + 8
10(6) + 8
= 68
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Answer:
Step-by-step explanation:
w=10n+8
Nina thought of a number. she added 24 , tripled the result, subtracted 18 , multiplied the result by 2 and got 120 . what was nina's number?
Answer:
Step-by-step explanation:
If we subtract 3 from the unknown number, we get just as much as if we subtracted 7 from the unknown number and we multiplied the result by 2
mel cuts a slice of cake if her slice is 4/15 of the cake, what is the central angle of her slice, please give answer in degrees
Answer:
Below in bold.
Step-by-step explanation:
That would be 4/15 * 360 as there are 360 degrees in a circle
= 96 degrees.