a) The standard error of the mean is 0.90
b) The marginal error is 1.76
Given,
Number of samples in the population, n = 60
Sample mean of the population, μ = 25
Standard deviation of the population, σ = 7
We have to find the standard error of the mean and the margin of error at 95% confidence.
Here,
a) The standard error of the mean = Standard deviation / root of sample
= σ / √n
= 7/√60
= 0.90
b) The margin error;
Zₐ/₂ × σ / √n
= Zₐ/₂ × 7/√60
= 1.96 × 0.90
= 1.76
Therefore,
a) The standard error of the mean is 0.90
b) The marginal error is 1.76
Learn more about standard error and marginal error here;
https://brainly.com/question/17014419
#SPJ1
I need help please!!!
the slope of the given point is m=−3/4
Answer:-3/4
Step-by-step explanation:
to find slope using 2 points the equation is ...
y2-y1
x2-x1
What is an equation of the line that passes through the points (2, 2) and (1, -2)
Answer:
[tex]y=4x-6[/tex]
Step-by-step explanation:
The slope is [tex]\frac{-2-2}{1-2}=4[/tex].
[tex]y-2=4(x-2) \\ \\ y-2=4x-8 \\ \\ y=4x-6[/tex]
Which equation is true for the value b=10
Answer:
3(b-2)=24
Step-by-step explanation:
3b - 6 = 24
3b = 30
b= 10
f – 354 = 1,221 help pls
Answer: F = 1575
Step-by-step explanation: 1221 + 354 = 1575. So 1575 - 354 = 1221
How does "If the measure of an angle is not 180, then it is not a straight angle" relate to the conditional statement "If an angle is a straight angle, then its measure is 180."
Counterexample
Converse
Inverse
Contrapositive
Given statement " If the measure of an angle is not 180, then it is not a straight angle" when related to conditional statement "If an angle is a straight angle, then its measure is 180." then it represents the example of contrapositive.
As given in the question,
Given statement is equal to:
" If the measure of an angle is not 180, then it is not a straight angle"
And its conditional statement is given by:
"If an angle is a straight angle, then its measure is 180."
Explanation of the given options:
a. Counterexample : Concluding statement is against the given statement .
Here it is false.
b. Converse: If it is not a straight angle then the measure of an angle is not 180.
Here it is false.
c. Inverse : If the measure of an angle is 180, then it is a straight angle.
False.
d. Contrapositive : "If an angle is a straight angle, then its measure is 180."
Here it is true.
Therefore, for the given statement " If the measure of an angle is not 180, then it is not a straight angle" when related to conditional statement "If an angle is a straight angle, then its measure is 180." then it represents the example of contrapositive.
Learn more about statement here
brainly.com/question/28672510
#SPJ1
How far away from zero on the y-axis is the point (2, 5)?
A
2
B
0
C
5
D
1
Answer:a
Step-by-step explanation:
match each trigonometric function with its right triangle definition. (a) sine hypotenuse adjacent adjacent opposite hypotenuse opposite adjacent hypotenuse opposite hypotenuse opposite adjacent (b) cosine hypotenuse adjacent adjacent opposite hypotenuse opposite adjacent hypotenuse opposite hypotenuse opposite adjacent (c) tangent hypotenuse adjacent adjacent opposite hypotenuse opposite adjacent hypotenuse opposite hypotenuse opposite adjacent (d) cosecant hypotenuse adjacent adjacent opposite hypotenuse opposite adjacent hypotenuse opposite hypotenuse opposite adjacent (e) secant hypotenuse adjacent adjacent opposite hypotenuse opposite adjacent hypotenuse opposite hypotenuse opposite adjacent (f) cotangent hypotenuse adjacent adjacent opposite hypotenuse opposite adjacent hypotenuse opposite hypotenuse opposite adjacent
The trigonometric function with its right triangle definition is matched as below:
(a) sine
opposite/hypotenuse
(b) cosine
adjacent/hypotenuse
(c) tangent
opposite/adjacent
(d) cosecant
hypotenuse/opposite
(e) secant
hypotenuse/adjacent
(f) cotangent
adjacent/opposite
We Know That,
i) sine =opposite side of the triangle /hypotenuse side of the triangle
ii) cosine=adjacent side of the triangle/hypotenuse side of the triangle
iii) tangent=opposite side of the triangle/adjacent side of the triangle
iv) cosecant=hypotenuse side of the triangle/opposite side of the triangle
v) secant=hypotenuse side of the triangle/adjacent side of the triangle
vi) cotangent=adjacent side of the triangle/opposite side of the triangle.
Therefore, each trigonometric function is matched with its right triangle definition
Learn more about trigonometric function here:
brainly.com/question/6904750
#SPJ4
the following information will be used for parts 1 and 2 of this assignment. in 1978 congress established a gas guzzler tax to discourage the production and purchase of fuel-inefficient vehicles. every vehicle currently produced is labeled as a guzzler if its fuel efficiency in mpg is below a certain amount. trucks, suvs and minivans were uncommon in 1978 so are exempt from the tax. if interested, read more: https://www.epa.gov/fueleconomy/gas-guzzler-tax each vehicle in the data set epafe2021data.csv has a projected annual fuel cost that estimates how much the vehicle will cost over a year in fuel. for example, the volkswagen passat has an estimated annual fuel cost of $1450. use the epafe2021data.csv dataset and the comparingtwomeans da6.r script to compare the average annual fuel cost in dollars between guzzlers and non-guzzlers from 2021 vehicles. part 1. (6 points) exploring the data. a. (2 points) visualize the data with a side by side boxplot. i. (1 point) paste the side-by-side box plot of the data. ii. (1 point) add a title and axis labels. iii. optional to change the color of the plot. b. (2 points) describe the distribution in context. is there visual evidence the average annual fuel cost is different between the guzzler and non-guzzler vehicles? explain. c. (2 points) provide an organized table of the summary statistics. include the sample means, standard deviations and sample sizes for each group. round to nearest whole number. mean standard deviation sample size guzzler non-guzzler
This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.
A) 1: proportion of gas-guzzlers manufactured by American firms.
p2: proportion of gas-guzzlers manufactured by international firms.
In this way, the boundary of interest is p1 - p2.
B) H_0: p_1-p_2=0
H_1: p_1-p_2\neq0
C) The following requirements must be satisfied: n (1 p) 10 and np 10.
American Guzzlers do not meet this requirement because np = 7.
D) If H0 is true, the test statistics are as follows: frac(hat p_1-hat p_2)-(p_1-p_2)surfactant p_1(1-hat p_1)n_1+frachat p_2(1-hat p_2)n_2sim N(0,1)
E) The p-value is calculated by multiplying p-value by P(z-3.75) = 0.
F) The 95% confidence interval is calculated as follows: p_1-p_2=hat p_1-hat p_2pm z_0.975sqrtfrachat p_1(1-hat p_1) n_1+frachat p_2(1-hat p_2) n_2 -0.0859 p_1-p_2 -0.0269
g. H0 should be rejected because the p-value is less than the 0.05 significance level.
There is enough evidence for us to reject H0. There is sufficient evidence to draw the conclusion that the proportion of Guzzlers in 2017 automobile models produced by American and international automakers differs.
Additionally, the 95% CI does not contain zero, does it?This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.
Learn more about American here:
https://brainly.com/question/2600449
#SPJ4
OMG PLS HELP I SWEAR ITS NOT THAT HARD please yall?
Proving angles are congruent; write a two column proof
Using the Side Angle Side Theorem, ∆KWL ≅ ∆ALW.
In the given question we have to
Prove: ∆KWL ≅ ∆ALW
Given: ∠KWL ≅ ∠WLK, ∠AWL ≅ ∠WLK
As given that
∠KWL ≅ ∠WLK
∠AWL ≅ ∠WLK
WL = WL (Diagonal)
Equal Parallel Sides
WK = AL
WA = KL
From Corresponding Angle Theorem
∠KWL=∠WLK and ∠AWL = ∠WLK
So ∠W=∠L
So from the Side Angle Side(SAS) Theorem
∆KWL ≅ ∆ALW.
To learn more about Side Angle Side Theorem link is here
brainly.com/question/1411515
#SPJ1
3 resistance 5Ω , 7Ω , 9Ω are connected in parallel with a power supply of 9 volt. Calculate its equivalent resistance current passing through each resistance and total current passing through the circuit.
The equivalent resistance currents passing through each resistance are: 1.8 A , 1.29A , 1A.
The total current passing through the circuit is 19.83 A.
How can the current be calculated?The resistance 5Ω , 7Ω , 9Ω which are are connected in parallel, then,
R1 =5Ω,
R 2=7Ω,
R3 =9Ω; supply voltage V=9 volt.
Effective resistance of parallel combination can be calculated as :
1/RP = 1/R1 + 1/R2 + 1/R3
1/RP= 1/5 + 1/7 +1/9
Rp = 0.45397Ω
Then the Current through resistors
are R1, I1 = V/R1 = 9/5 = 1.8A
R2, I2 = V/R2 = 9/7 = 1.29A
R3, I3 = V/R3 = 9/9 = 1A
Then Total current I = V/Rp = 9/ 0.45397 = 19.83 A
Read more about resistance at:
https://brainly.com/question/25478115
#SPJ1
a small dataset contains 5 numbers: 21, 32, x, 99, 40 (where x is unknown). if the average is known to be 50, what is the median?
The median of the given data set is, 40.
What is median?
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.
Let, a data set contains 5 numbers: 21, 32, x, 99, 40.
x is the unknown number.
The average is to be 50.
Since,
Average = Sum of numbers / total numbers
50 = (21 + 32 + x + 99 + 40) / 5
50 x 5 = 192 + x
250 = 192 + x
x = 250 - 192
x = 58
Hence, the unknown number is 58.
Now to find the median,
Since median is the middle number of a data set.
So, write the numbers in ascending order.
21, 32, 40, 58, 99.
In this data set the middle number is, 40.
Therefore, the median is 40.
To know more about the median, click on the link
https://brainly.com/question/14532771
#SPJ4
how many solutions does 12 + 2x - x = 9x + 6 have?? giving brain and max points
Step-by-step explanation:
Enter a problem...
Pre-Algebra Examples
Popular Problems Pre-Algebra Solve for x 12+2x-x=9x+6
12
+2
x−x=
9x
+6Subtract
x from
2x
12+x
=9x+6
Move all terms containing
x
to the left side of the equation.
Tap for more steps...
12−8x=6
to the right side of the equation.
-8x=−6
Divide each term in
−8x=−6 by −8
and simplify.
The result can be shown in multiple forms.
Exact Form:
x=3/4
Decimal Form:0.75
A line has a slope of – 1 and includes the points (j, – 5) and (1,3). What is the value of j?
Answer: j = 9
Step-by-step explanation:
Slope = (y2-y1)/(x2-x1)
-1 = (3-(-5)) / (1-j)
-1 = (3+5) / (1-j)
-1 = 8 / (1-j)
Multiply both sides by 1 -j
= (1-j) = 8
= 1 - j = -8
= -j = -8 -1
j = 9
QUESTION 2/10 HELP ASAPP
The slope of the line is -32, and the y-intercept is 480 if the equation of the line is y = -32x + 480.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The equation of the line uses two points:
(0, 480) and (15, 0)
y = (-480/15)[x - 15]
y = -32(x - 15)
y = -32x + 480
y = mx + c
m = -32
c = 480
Thus, the slope of the line is -32, and the y-intercept is 480 if the equation of the line is y = -32x + 480.
Learn more about the straight line here:
brainly.com/question/3493733
#SPJ1
A quadratic function is defined by g(x) = 2x² + 12x + 1. Write this in the completed-square (vertex) form
and show all the steps.
The completed-square (vertex) form 2x² + 12x + 1 is 2(x+3)^2−17. Completing the Square is a technique to find maximum or minimum values of quadratic functions.
How to find completed-square ?Completing the square is a highly helpful technique or way to change a quadratic equation from also known as the "standard form," to its "vertex form,".
For some combinations of h and k, completing the square is a method for transforming a quadratic polynomial. In other words, the quadratic expression is completed by inserting a perfect square trinomial.
Finding the maximum or lowest values of quadratic functions can be done using the square method, sometimes known as "completing the square."
Use the form ax^2 + bx + c, to find the values of a, b, and c.
Consider the vertex form of a parabola.
a(x+d)^2+e
Find the value of d using the formula
d = b/2a.
d = 3
Find the value of e using the formula
e = c− b^2 / 4a.
e = −17
Substitute the values of a, d, and e into the vertex form 2(x+3)^2−17.
2(x+3)^2−17
To learn more about completed-square refer :
https://brainly.com/question/2044593
#SPJ1
Which congruence theorem, if any, can be used to prove that the triangles are congruent?
a) SAS
b) SSS
c) HL
d) ASA
e) AAS
f) Not enough information is given to prove that the triangles are congruent.
The congruence theorem that can be used to prove that the triangles are congruent is F. Not enough information is given to prove that the triangles are congruent
How to explain the congruence?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.
According to the Angle-Side-Angle Theorem (ASA), if two angles and their included side are congruent to two angles and their included side, then these two triangles are congruent.
The hypotenuse is always the opposite side of the right angle. The legs of the triangle are the other two sides of a right triangle. Because a right triangle has two legs and a hypotenuse, it is also known as a hypotenuse-leg (or HL) triangle.
In this situation, enough information aren't given about the triangles. Therefore, the correct option is F.
Learn more about triangles on:
https://brainly.com/question/2938476
#SPJ1
What do you have to remember about the signs of the numbers in factored form of a quadratic compared to the signs of the actual x-intercepts on the graph?
In contrast to the signs of the real x-intercepts on the graph, we must remember the signs of the values in a quadratic's factored form. because the cartesian coordinate points are shifted.
What is a quadratic function?Any function of the form [tex]\rm f(x) =ax^2+bx+c[/tex].where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.
When factoring by grouping is used, the replacement terms will both share the same middle-term sign. The factor signs will have one of each sign with the "stronger" number (the larger absolute value) matching the middle term if the last term is negative.
We can locate the function's x-intercepts or zeros with the aid of factored form.
Thus, in contrast to the signs of the real x-intercepts on the graph, we must remember the signs of the values in a quadratic's factored form. because the cartesian coordinate points are shifted.
Learn more about quadratic function here:
brainly.com/question/17177510
#SPJ1
how to use the clausius clapeyron equation to answer the following questions. derive the relationship of pressure and temperature for a system consists of vapor and condensed
The relationship between pressure and temperature for a consisting of vapour and condensed phases is [tex]l_{n}(p_{2}/p_{1}) = [ 1/T_{1}-1/T_{2}][(h_{g}-h_{f})/R][/tex].
The Clausius-Clapeyron equation is a differential equation which specifies the temperature dependence of pressure and vapour pressure. The Clausis-Clapeyron equation is named after Rudolf Clausius and Benoit Paul Emile Clapeyron.
The Clausius-Clapeyron equation at saturation temperature and pressure is
[tex]dP/dT[/tex]= [tex]h_{g} - h_{f}/T(v_{g}-v_{f} )[/tex] → 1
Assuming that [tex]v_{g} > > > v_{f}[/tex] , we write
[tex]v _{g}[/tex] = RT/P → 2 ( for both liquid and solid phases)
⇒ dP/dT = P([tex]h_{g} - h_{f}[/tex])/R[tex]T^{2}[/tex]
⇒ dP/P = dT/[tex]T^{2}[/tex]([tex]h_{g} - h_{f}[/tex]/R) → 2
By integrating 2 , we get
[tex]l_{n}(p_{2}/p_{1}) = [ 1/T_{1}-1/T_{2}][(h_{g}-h_{f})/R][/tex] → 3
Therefore, the equation to represent the relationship between pressure and temperature for a system consisting of vapour and condensed phases is equation 3 i.e. [tex]l_{n}(p_{2}/p_{1}) = [ 1/T_{1}-1/T_{2}][(h_{g}-h_{f})/R][/tex]
To know more about the Clausius-Clapeyron equation refer to:
https://brainly.com/question/21504082
#SPJ4
Evaluate c−a+bd if a=7/8 , b=−7/16 , c=0.8 , and d=1/4
Answer
-117/640
Step-by-step explanation:
ba + cd
b= -7/16
a= 7/8
c= 08.(4/5)
d= 1/4
Hence it can be calculated as follows
-7/16×7/8 + 4/5×1/4
-49/128 + 1/5
-246+128/640
= -117/640
The sum of the measures of angle P and angle S is 140⁰.
• The measure in degrees of angle P is represented by the expression (5x + 30)º.
●
• The measure of angle S is 80°.
What is the value of x?
A 38
B 6
C 10
D 22
Answer: Value of x is B equals 6
Step-by-step explanation:
(8th Grade Honors Geometry)
Triangle Congruence; Two Column Proofs
The triangles ΔABC and ΔCDE are congruent to each other using the SSS rule.
We are given two triangles. The vertices of the first triangle are A, B, and C. The vertices of the second triangle are C, D, and E. We need to prove that the triangles are congruent to each other.
The length of side AB is equal to that of side CD. The length of side BC is equal to that of side DE. We know that C is the midpoint of line segment AE. This means that the length of AC is equal to the length of CE.
All three corresponding sides of the two triangles are equal. Hence, the triangles are congruent to each other using the SSS rule for congruency.
To learn more about triangles, visit :
https://brainly.com/question/2773823
#SPJ1
How to find the x and
Check the picture below.
[tex]\stackrel{\measuredangle MNQ}{4x+16}\implies 4(14)+16\implies \stackrel{\measuredangle MNQ}{\text{\LARGE 72}}[/tex]
22. Which of the following equations is
NOT true?
A
B
225 X 4 = 9,000
225 X 0.04 = 9
22.5 X 4 = 90
D 225 X 0.4 = 90
Given f(x) = 4x+2 find f(x+3) find terms of x
The function f(x+3) in terms of x is 4x+14.
It is given that -
f(x) = 4x + 2
We have to find out f(x+3) in terms of x.
Now, f(x) = 4x + 2
=> f(x+3) = 4(x+3) + 2 [Substituting (x+3) in place of x]
=> f(x+3) = 4x + 12 + 2
=> f(x+3) = 4x + 14
Thus, the function f(x+3) in terms of x is 4x+14.
To learn more about function visit
https://brainly.com/question/21145944
#SPJ1
MULTIPLE CHOICE If you switch the input and the output values of the data in the table, is it a function? A Yes B No Practice Attempt 1 of 2 Submit
Answer:
yes
Step-by-step explanation:
as long as one input does not have two different outputs it is a function
Logan is selling dog tags to raise money for the dog rescue organization. Th e company that makes the tags charges a fl at fee of $348 plus $2 per tag. Logan plans to sell the tags for $5 each. a) Write an equation to show the total cost for the dog tags. b) Write an equation to show the revenue. c) How many dog tags must Logan sell in order to break even?
The equation for the total cost of the dog tags will be 348 + 2t.
The equation to show the revenue would be Revenue = 5t
The number of dog tags that Logan needs to sell to break even is 116 dog tags.
How to find the break even quantity?Assuming that the number of dog tags sold by Logan to raise money is represented by t, the total cost would be:
= Flat fee charge + Cost per tag x Number of tags
= 348 + 2t
The total revenue would be:
= Number of dog tags x Selling price per dog tag
= 5t
The breakeven point would be the point where total profit would be zero and so can be shown as:
0 = Sales - total cost
0 = 5t - (348 + 2t)
0 = 5t - 348 - 2t
3t = 348
t = 348 / 3
t = 116 tags
Find out more on total cost at https://brainly.com/question/25429775
#SPJ1
marcus wants to include the month of the year in the analysis as categories. how many dummy variables will be needed?
11 dummy variables will be needed.
A dummy variable is a numerical variable used in regression analysis to represent subgroups of the sample in your study. In research design, a dummy variable is often used to distinguish different treatment groups.
we know that,
dummy variable formula = K- 1,
here, K = 12 (months in a year)
this implies, K - 1 = 12 - 1 = 11
Therefore, no. of dummy variables needed = 11.
know more about variables here: https://brainly.com/question/20711705
#SPJ4
can someone help please!
Answer:
Step-by-step explanation:
The equations of four lines are given. Identify which lines are parallel. Line 1: y=1/2x -6 (Line 2: x-2y=-1 (Line 3: y=4x+6 (Line 4: y+3=1/4 (x-6)
In this question, line1 and line2 are parallel to each other by finding the slope.
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
Given four lines are
Line 1: y=1/2x -6
(Line 2: x-2y=-1
(Line 3: y=4x+6
(Line 4: y+3=1/4 (x-6)
We have to find out the slope of the corresponding lines such that
the slope of line 1 = 1/2
the slope of line 2 = 1/2
the slope of line 3 = 4
the slope of line 4 = 14
So the line has the same slope they are parallel to each other.
Hence in this question, line1 and line2 are parallel to each other.
Learn more about Slope, by the following link
https://brainly.com/question/3493733
#SPJ1
the equation for the var
3n+ 8 = 5n - 4
n = [?]
Answer:
Step-by-step explanation:
this is all about your algebra skillz, learn it , know it , live it :P
anyway
I'll make this very detailed , so you see the process. but lean it
3n+8 = 5n-4
begin using reverse operation order, note you need to know P.E.M.D.A.S , Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. starting from the "Parenthesis, and the working down thur each operation is forward operation order. I bet nobody has told you this before, huh. So to do the algebra on the equation above use reverse operation order.
so, I'm going to move the -4 , first
3n+8+4 = 5n-4+4 ( do the same thing on both sides of the equal sign)
3n+12 = 5n
now I'm going to move the 3n
3n+12 -3n = 5n -3n ( do the same on both sides again)
12 = 2n
now i'm moving up to Division, b/c it's next on our order of operations, i'll divide the 2 away from the n
12/2 = 2n / 2 ( same on both side again)
6 = n
now we have our answer for n, nice :P try this at home, school, or at your local coffee shop :P