Answer:
1. vertical line. slope is undefined.
2. horizontal line. slope of 0
3. vertical line. slope is undefined.
4. horizontal line. slope of 0
Step-by-step explanation:
Soe found a sweatshirt that she wanted at JC Penny when she went shopping the other day it was on sale for 30% off. What was the original cost of the sweat shirt if the sale price was $21
Answer:
$30
Step-by-step explanation:
x*0.70=21
21/0.70= 30
Answer this question please! 25 points and brainliest!
Answer: c
Step-by-step explanation:
the number with one dot < on the left side means its the smaller number
Answer:
c x< 9
Step-by-step explanation:
A number less than 9
x must be less than 9
No equals sign because it is less than
The inequality faces the larger number
x < 9
If f(x) varies directly with x^2, and f(x) = 75 when x = 5, find the value of f(8).
192
256
25
40
Answer:
The correct answer option is 192.
Step-by-step explanation:
We know that f(x) varies directly with [tex]x^{2}[/tex] so we can write it as:
[tex]f(x)[/tex] ∝ [tex]x^{2}[/tex]
Changing it to an equality by the addition of a constant [tex]k[/tex]:
[tex]f(x) = k.x^{2}[/tex]
If f(x) = 75 when x = 5, then we can find the value of k:
[tex]75=k(5)^2[/tex]
[tex]k=\frac{75}{25} =3[/tex]
If k = 3, we can find the value of f(8):
[tex]f(8)=3(8)^2[/tex]
[tex]f(8)=3*64[/tex]
[tex]f(8)=[/tex]192
Erin has a balance of $1,150.34 in her check register. On her statement, the balance of her account is $844.93. Not reported on the bank statement are deposits of $125.56, $50, and $212.34. There are outstanding checks in the amount of $15 and $78.25 and an ATM withdrawal of $40. After Erin reconciles her check register with her statement, what entry does she need to make in her register?
Erin needs to make a -$50.76 entry in her register to reconcile her check register with her bank statement. This takes into account deposits not reported on her bank statement, along with outstanding checks and an ATM withdrawal.
Explanation:To reconcile Erin's check register, we need to account for all transactions not yet reported on the bank statement. First, add the value of the deposits not reported ($125.56 + $50 + $212.34 = $387.90) to the balance of the bank statement ($844.93 + $387.90 = $1232.83). Then, subtract the amount of the outstanding checks and ATM withdrawal ($15 + $78.25 + $40 = $133.25) from this sum ($1232.83 - $133.25 = $1099.58).
The reconciled balance in Erin's check register should be $1099.58. Consequently, Erin needs to adjust her register to reflect the correct balance. Given that Erin’s original balance was $1150.34 and the reconciled balance is $1099.58, Erin needs to subtract $50.76 from her register.
Learn more about Bank Reconciliation here:https://brainly.com/question/29097188
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Candy buys 20 ounces of mixed nuts. She puts an equal amount of ounces in each of 3 bags. How many ounces of mixed nuts will be in each bag? Write the answer as a whole number and a fraction.
Answer:
[tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.
Step-by-step explanation:
unit rate is defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.
Given the statement: Candy buys 20 ounces of mixed nuts. She puts an equal amount of ounces in each of 3 bags.
Total number of mixed nuts Candy buys = 20 ounces.
As she puts an equal amount of ounces in each of the 3 bags.
Unit rate per bag = [tex]\frac{20}{3} = 6\frac{2}{3}[/tex] ounces.
therefore, [tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.
Omar is an avid video game player and movie watcher. He has a choice of belonging to a video club with a monthly fee of $12 and $1-a-day rental fee for any movie or game, or he can be a nonmemeber and pay $2.50-a-day rental fee for any movie or game. Find the number of movies or video games Omar must rent for one day for the cost to be equal between membership and nonmembership.
Answer:
8 movies or video games.
Step-by-step explanation:
Let x be the number of movies or video games on rent.
We have been given that Omar has a choice of belonging to a video club with a monthly fee of $12 and $1-a-day rental fee for any movie or game. We can represent the charges for x movies or video games for a member of club as: [tex]x+12[/tex].
Omar can be a non-member and pay $2.50-a-day rental fee for any movie or game. We can represent the charges of a non-member for x movies or video games as: [tex]2.5x[/tex].
To find the number of movies for one day for the cost to be equal we will equate our both expressions.
[tex]x+12=2.5x[/tex]
[tex]x+12-x=2.5x-x[/tex]
[tex]12=1.5x[/tex]
[tex]x=\frac{12}{1.5}[/tex]
[tex]x=8[/tex]
Therefore, Omar must rent 8 movies or video games for one day for the cost to be equal between membership and non-membership.
By renting 8 movies or video games charges for membership will be: 8+12=20.
By renting 8 movies or video games charges for a non-membership be: 2.5*8=20.
Hence charges of renting 8 movies or video games are same for both membership or non-membership.
Omar needs to rent 8 movies or video games in one month for the costs of a membership and nonmembership to be the same. The membership includes a monthly fee of $12, and rentals cost $1 per day. Non-membership rentals cost $2.50 per day.
Omar wants to determine how many movies or video games he must rent for the cost of membership and non-membership to be equal. To find this, we will set up an equation comparing the two costs.
Membership Plan:
Monthly fee: $12Rental fee: $1 per movie/game per dayNon-membership Plan:
Rental fee: $2.50 per movie/game per day
Let's denote the number of movies or games rented by x.
For the membership plan, the total cost is: $12 + $1x
For the non-membership plan, the total cost is:$2.50x
We set the two costs equal to find x: $12 + $1x = $2.50x
Subtract $1x from both sides: $12 = $1.50x
Divide both sides by $1.50: x = 8
Omar must rent 8 movies or video games in one month for the costs of membership and non-membership to be equal.
If the ratio of two complementary angles is 4 to 5, explain how you would set up an equation to solve for the angle measures.
"A ratio of 4 to 5" means that dividing the two angles (whatever they may be) simplifies to 4/5. One example is 40 degrees and 50 degrees so 40/50 = 4/5. Another example is the pair of angles 20 and 25, so 20/25 = 4/5
For now, we don't know the angles. Let's call them x and y. Based on the info above, we can say
x/y = 4/5
also we know that x and y add to 90 degrees because the angles are complementary. So x+y = 90 which solves to y = 90-x if you isolate y.
Let's cross multiply on the first equation to get...
x/y = 4/5
5*x = 4*y
Now replace y with 90-x. Solve for x
5x = 4(90-x)
5x = 360 - 4x
5x+4x = 360
9x = 360
x = 360/9
x = 40
Use this to find y
y = 90 - x = 90 - 40 = 50
So the two angles are 40 degrees and 50 degrees.
To find two complementary angles with a ratio of 4 to 5, set up the equation 4x + 5x = 90, where x is the common multiplier. Solve for x to find each angle's measure. Check that the sum equals 90 degrees to confirm the solution.
Explanation:To determine the measures of two complementary angles with a ratio of 4 to 5, you first need to understand that complementary angles add up to 90 degrees. Let's call the angles A and B, with A being the smaller angle. Since they are in a ratio of 4 to 5, we can represent them as 4x and 5x, respectively, where x is a common multiplier. The equation to solve for x is set up based on the definition of complementary angles:
4x + 5x = 90
Combine like terms to simplify:
9x = 90
Now, divide both sides by 9 to solve for x:
x = 90 ÷ 9
x = 10
Once you have the value of x, you can find the measures of the angles:
A = 4x = 4(10) = 40 degrees
B = 5x = 5(10) = 50 degrees
Always check your answer to confirm it makes sense. In this case, A + B should equal 90 degrees, which it does (40 + 50 = 90).
Sean places 28 tomato plants in rows. All rows contain the same number of plants. There are netween 5 and 12 plants in each row. How many plants are in each row?
Answer:
4 rows of 7 plants each
Step-by-step explanation:
To find the number of plants in each row between 5 and 12 requires us to find the factors of the total 28.
28 has factors 1,28 and 2,14 and 4,7. Only 4,7 has a number between 5 and 12. There are 4 rows of 7 plants.
Use the substitution method to solve the system of equations
Answer:
We put the value of "y" into the second equation:
x * 5 = -15
x = -15 / 5
x = -3
Step-by-step explanation:
What is the interquartile range of this data set 2,5,9,11,18,30,42,48,71,73,81
First, find the median: 30
Then, find the median of the 2 sides from 30 (Q1 and Q3)
The middle value between 2 and 18 is 9. The middle value between 42 and 81 is 71. Now, just subtract 71-9.
The IQR is 62 :)
Final answer:
The interquartile range, or IQR, is the range of the middle 50 percent of the data values, found by subtracting the first quartile from the third quartile. For the given data set, the IQR is determined to be 61.
Explanation:
The interquartile range, represented as IQR, is found by subtracting the first quartile (Q1) from the third quartile (Q3). To find the interquartile range for the data set 2, 5, 9, 11, 18, 30, 42, 48, 71, 73, 81:
Sort the data in ascending order: 2, 5, 9, 11, 18, 30, 42, 48, 71, 73, 81
Calculate Q1 and Q3: Q1 = 10, Q3 = 71
Find IQR: IQR = Q3 - Q1 = 71 - 10 = 61
A line has slope 5/6 and y-intercept −3.
Which answer is the equation of the line?
A.y=5/6x−3
B.y=3x+5/6
C.y=−3x+5/6
D.y=5/6x+3
Answer: A. y=5/6x-3
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
I'm almost 100% sure this is right.
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have
[tex]m=\dfrac{5}{6},\ b=-3[/tex]
Substitute:
[tex]\boxed{y=\dfrac{5}{6}x-3}[/tex]
A study found that out of 300 people 60% of them prefer to eat hamburgers rather than hot dogs. Find the 95% confidence interval for the true proportion of people who prefer to eat hamburgers rather than hot dogs in the entire population.
Answer:
(0.5446, 0.6554)
Step-by-step explanation:
As the sample is sufficiently large, the formula is used to estimate the proportion shown in the attached image.
Where:
P: sample proportion = 0.6
n: Sample size = 300
[tex]1-\alpha[/tex]: Confidence level = 0.95
α: Significance = 0.05
[tex]Z_{\alpha / 2} = 1.96[/tex] *
* Obtained from the normal standard table.
When introducing these values in the formula shown in the image we obtain:
[tex]0.6 + 1.96 *\sqrt {\frac{0.6*0.4}{300}}[/tex]
[tex]0.6 - 1.96 *\sqrt{\frac{0.6*0.4}{300}}[/tex]
Finally, the confidence interval is:
(0.5446, 0.6554)
Which calculation should be used to calculate s9 for the arithmetic sequence an=3n-1
Answer: Choice A
S9 = (9/2)*(2+26)
===============================================
The formula is
Sn = (n/2)*(a1+an)
where
Sn = sum of the first n terms (nth partial sum)
n = number of terms
a1 = first term
an = nth term
In this case,
n = 9
a1 = 2 (plug in n = 1 into the formula an = 3n-1 and simplify)
an = a9 = 26 (plug n = 9 into the formula an = 3n-1 and simplify)
So,
Sn = (n/2)*(a1+an)
S9 = (9/2)*(2+26)
will help us find the sum of the first 9 terms of this arithmetic sequence
Answer:
A. S9 = (9/2)*(2+26)
Jasmine works at the public library after school. she makes $7.00 per hour. she cannot work more than 15 hours per week. if y = 7x represents jasmine's earning, what are the values in the domain?
a.x ≤ 15
b.0 ≤ x ≤ 15
c.1 ≤ x ≤ 15
d.all real numbers
Answer: ITS B
Step-by-step explanation:
Which property explains why these two expressions are equal?
a(b + c) = a(c + b)
A) identity property
B) symmetric property
C) associative property
D) commutative property what the answer
Answer:
Commutative property.
Step-by-step explanation:
Commutitive property suggests that, for example; b + c = c + b
'a' is used as a constant here.
Which assignment for the events in the sample space will work?
C
Step-by-step explanation:You want to choose an assignment of numbers that makes the number of numbers that represent each color be the same.
Numbers 0–33 include 34 numbers. Numbers 0–99 include 100 numbers, so blue blocks are over-represented by scenario A.
Scenario B suffers the same problem as scenario A in that 0–3 includes 4 numbers and 0–9 includes 10 numbers.
Scenario D has the opposite problem: 1–31 is 31 numbers, but 32–63 is 32 numbers. Blue blocks are under-represented in this scenario.
___
Scenario C has 3 of 9 numbers representing each color—just what you want.
If a normal distribution has a mean of 132 and a standard deviation of 20 what is the value that has a z score of 2.4?
Answer:
The value is 180
Step-by-step explanation:
The formula for z score is given by
x - mean
z= -------------
standard deviation
We know z= 2.4
We know the standard deviation =20
and we know the mean = 132
We can find x
x - 132
2.4 = ----------------
20
Multiply each side by 20
2.4 *20 = x-132
48 = x-132
Add 132 to each side
48+132 = x -132+132
180 = x
Answer:
The value that has a z score of 2.4 is 180.
Step-by-step explanation:
Given : If a normal distribution has a mean of 132 and a standard deviation of 20.
To find : What is the value that has a z score of 2.4?
Solution :
The formula of z-score is given by
[tex]z=\frac{x-\mu}{\sigma}[/tex]
where, z=2.4 is z score value
[tex]\mu=132[/tex] is the mean of the normal distribution
[tex]\sigma=20[/tex] is the standard deviation
x is the value of z score.
Substituting all the values in the formula,
[tex]2.4=\frac{x-132}{20}[/tex]
[tex]2.4\times 20=x-132[/tex]
[tex]48=x-132[/tex]
[tex]x=180[/tex]
Therefore, The value that has a z score of 2.4 is 180.
Fatema bought 35 feet of window trim at a hardware store. The trim cost $1.75 per foot, including sales tax. If Fatema paid with a $100.00 bill, how much change should she have received?
Answer:$38.75
Step-by-step explanation:
35(number of feet) * $1.75(cost per foot) = $61.25(total cost)
$100(bill used) - $61.25(total cost) = $38.75(amount given in change)
Answer:
$38.75
Step-by-step explanation:
We have given that : The trim cost per foot =$1.75
for 35 feet of window trim cost = 35×1.75 = $61.25
Now, Fatima paid $100.00 bill
Amount she received = Amount she pay - cost of trim she buy
= $100 - $61.25
=$38.75
Uncle Drew scored 2828 points in 5 5/6 ? minutes during a game of basketball. How many points did he average per minute during that 5\dfrac565 6 5 ? minutes?
Answer:
4.8 points per minute
Step-by-step explanation:
Uncle Drew scored 28 points in [tex]5 \frac{5}{6}[/tex] minutes. We have to convert the mixed fraction first:
[tex]t = 5 \frac{5}{6}=\frac{5\cdot 6+5}{6}=\frac{35}{6}[/tex]
So, the time is 35/6 minutes.
In order to find the number of points he scored in a minute, we have to divide the total number of points by the number of minutes, so:
[tex]mean = \frac{28}{35/6}=28 \cdot \frac{6}{35}=4.8[/tex]
So, he scored 4.8 points per minute.
Answer:
4.8
Step-by-step explanation:
Please help ASAP! Algebra 2!
The choice options for both are negative or positive
In quadrant III, cosine is negative
In quadrant III, sine is negative
x^2+y^2 = 1 represents the unit circle. This is a circle centered at the origin with radius 1. The point (x,y) is on the unit circle where x = cos(theta) and y = sin(theta)
If theta is between 180 and 270 degrees, then
x = cos(theta) leads to -1 < x < 0, ie x is some negative number between -1 and 0
y = sin(theta) leads to -1 < y < 0, so y has similar properties to x above.
Because we don't know what value theta is exactly, we can only comment on the fact that each result is positive or negative.
The four quadrants are set up where quadrant 1 is in the upper right corner. Then you move counter-clockwise to sweep through the other quadrants 2 through 4.
Cynthia wants to take out a $8500 loan with a 4.75% APR. She can afford to pay $245 per month for loan payments. How long should he borrow the money so that she can afford the monthly payment?
Answer:
She should borrow the money for 3.1161... years so that she can afford the monthly payment.
Step-by-step explanation:
Monthly payment formula is: [tex]M=P*\frac{r(1+r)^n}{(1+r)^n -1}[/tex] , where
M = Monthly payment amount, P = Loan amount, r = rate of interest per month and n = total number of months.
Given that, Cynthia wants to take out a $8500 loan with a 4.75% APR and she can afford to pay $245 per month.
That means, [tex]P= 8500, M= 245[/tex] and [tex]r= \frac{0.0475}{12}= 0.0039583[/tex]
Plugging these values into the above formula, we will get........
[tex]245=8500*\frac{0.0039583(1+0.0039583)^n}{(1+0.0039583)^n-1} \\ \\ 245=\frac{33.64555(1.0039583)^n}{(1.0039583)^n -1}\\ \\ 245(1.0039583)^n -245=33.64555(1.0039583)^n\\ \\ 211.35445(1.0039583)^n=245\\ \\ (1.0039583)^n=\frac{245}{211.35445}=1.15919\\ \\ n= log_{1.0039583}(1.15919)=37.39327[/tex]
So, [tex]n= 37.39327 months =\frac{37.39327}{12} years = 3.1161... years[/tex]
That means, she should borrow the money for 3.1161... years so that she can afford the monthly payment.
The area of a rectangle is 180 squared in2. The ratio of the length to the width is 5 : 4Find the length and the width. The length of the rectangle is nothing in.
Answer:
length = 100 squared Width = 80 squared
Step-by-step explanation:
You add the to ratio number ( 4+5 ). You take that number (9) and divide with 180. You receive the answer 20. Then you multiply 20 by 5 to get the length and multiply 20 by 4 to width. Then you just add back the square operation.
Final answer:
The length and width of the rectangle are found by setting up equations using the given ratio and area. By solving the equations, the length is determined to be 15 inches and the width 12 inches.
Explanation:
To find the length and width of the rectangle with an area of 180 square inches and a ratio of length to width of 5:4, we can set up equations using the ratio and area information. Since the area of a rectangle is equal to the length times the width, we can express the length (L) and width (W) in terms of the ratio:
L = 5x
W = 4x
We know that the area (A) is 180 square inches, so:
A = L × W
180 = (5x) × (4x)
180 = 20x₂
Therefore:
x₂ = 180 / 20
x₂ = 9
x = 3
Now we can find L and W by substituting x back into L = 5x and W = 4x:
L = 5 × 3 = 15 inches
W = 4 × 3 = 12 inches
Hence, the length of the rectangle is 15 inches, and the width is 12 inches.
What is the value of x?
13.6
68
84
9.09
Answer:
x=13.6
Step-by-step explanation:
These are vertical angles, so they are equal
8x+16 = 3x+84
Subtract 3x from each side
8x-3x+16 = 3x-3x+84
5x+16 = 84
Subtract 16 from each side
5x+16-16 = 84-16
5x = 68
Divide by 5
5x/5 =68/5
x = 13.6
Given that line segments are taken to line segments of the same length during rigid transformations, which transformation maps the line segment AB onto itself?
A) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → x-axis reflection
B) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection
C) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
D) rotation counterclockwise of 180° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
Answer:
Correct choice is C
Step-by-step explanation:
Points A and B have coordinates (1,-2) and (4,3), respectively.
1. Rotation counterclockwise of 90° about the origin has a rule:
(x,y)→(-y,x).
Then the image of point A is point A'(2,1) and the image of point B is point B'(-3,4).
2. Refection about the x-axis has a rule:
(x,y)→(x,-y).
Then the image of point A' is point A''(2,-1) and the image of point B' is point B''(-3,-4).
3. Rotation counterclockwise of 270° about the origin has a rule:
(x,y)→(y,-x).
Then the image of point A'' is point A'''(-1,-2) and the image of point B'' is point B'''(-4,3).
4. Refection about the y-axis has a rule:
(x,y)→(-x,y).
Then the image of point A''' is point A(1,-2) and the image of point B''' is point B(4,3).
HELP BECAUSE IM STUPID!
What is the explicit rule for the sequence?
13, 10.5, 8, 5.5, 3, 0.5, ...
an=15+2.5n
an=15.5+2.5n
an=15−2.5n
an=15.5−2.5n
The explicit rule for the decreasing arithmetic sequence 13, 10.5, 8, 5.5, 3, 0.5, ... is 'aₙ = 15.5 - 2.5n'. This rule reflects the initial term and the common difference between terms.
The sequence provided is 13, 10.5, 8, 5.5, 3, 0.5, and we are finding the explicit rule for this sequence. To find the explicit rule, we will look at the differences between the terms. The differences are consistently -2.5, thus the sequence decreases by 2.5 each time. Assume the first term corresponds to n=1, the next step is to find the initial value at n=1.
Starting with the first term, when n=1, the value is 13. Keeping in mind the sequence decreases by 2.5 with each step, if we reverse one step back (which would be 0 steps), we would be at the initial value, which is 13 + 2.5 = 15.5. Therefore, the explicit rule can be written in the form aₙ = initial value - difference times (n-1), which simplifies to aₙ = 15.5 - 2.5n.
So, given the options provided, the explicit rule for the given sequence is aₙ = 15.5 - 2.5n.
3 log 2x=4 Please solve
[tex]3 log 2x=4\ /:3\\log2x=\frac{4}{3}\\10^{\frac{4}{3}}=2x\ /:2\\x=\frac{10\sqrt[3]{10} }{2}\\x=5\sqrt[3]{10}[/tex]
given parallelogram abcd, find the value of y.
a) 64
b) 26
c) 82
d) 180
Answer:
c) 82
Step-by-step explanation:
<ABE and <BEC are supplementary because they form a line.
<ABE + <BEC = 180
116+ x = 180
Subtract 116 from each side.
116-116+x = 180 -116
x = 64
The angles in triangle ECB add to 180 because it is a triangle
<BEC + <ECB + <CBE = 180
x + 34+y = 180
64 + 34+ y = 180
98 + y = 180
Subtract 98 from each side.
98-98+y = 180-98
y = 82
Subtract 7a^4-4a^2b^2+67a 4 −4a 2 b 2 +6 from 3a^4+2ab^2+113a 4 +2ab 2 +11.
Final answer:
To subtract the polynomials, we subtract the coefficients of like terms: the a⁴ terms give -4a⁴, there are no changes to the ab² term since it's not present in both polynomials, and for the a terms, we get 46a. So, the result is -4a⁴ + 2ab² + 46a.
Explanation:
The question asks us to perform polynomial subtraction. Specifically, the question requires subtracting 7a⁴ - 4a²b² + 67a from 3a⁴ + 2ab² + 113a. To do this, we subtract the coefficients of like terms, which are terms with the same variable raised to the same power.
Let's subtract step-by-step:
Subtract the a⁴ terms: 3a⁴ - 7a⁴ = -4a⁴Subtract the ab² terms: We do not have a term with ab² in the second polynomial, so we simply bring down the 2ab² term.Subtract the a terms: 113a - 67a = 46aPutting it all together, the result of our subtraction is -4a⁴ + 2ab² + 46a.
A study is conducted to determine if a newly designed text book is more helpful to learning the material than the old edition. The mean score on the final exam for a course using the old edition is 75. Ten randomly selected people who used the new text take the final exam. Their scores are shown in the table below. Person A B C D E F G H I J Test Score 92 83 93 74 85 97 88 70 69 79 Use a 0.010.01 significance level to test the claim that people do better with the new edition. Assume the standard deviation is 10.5. (Note: You may wish to use statistical software.)
The claim that people do better with the new edition regarding the given situation is false at 0.01 level of significance.
How to form the hypotheses?There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.
Null hypothesis is the one which researchers try to disprove.
For this case, the hypothesis we'll lay down are:
Null hypothesis: People are performing less than or equal(compared with old performance) with the new edition
Alternate hypothesis: People are doing better with the new edition
This can be symbolically written as:
Null hypothesis: [tex]H_0: \mu_2 \leq 75\\[/tex]
Alternate hypothesis: [tex]H_1: \mu_2 > 75[/tex]
(where [tex]\mu_1[/tex] = 75 is mean test score with old edition, and [tex]\mu_2[/tex] is mean test score with new edition(of the population) )
Mean score with old edition is given to be [tex]\mu_1= 75[/tex]
Mean score with new edition(of the sample) is ratio of sum of scores to total count of scores = [tex]\overline{x} = \dfrac{830}{10} = 83[/tex] ([tex]\overline{x}[/tex] is representative of the population mean with new edition)
The standard deviation for both cases is: [tex]\sigma = 10.5[/tex]
Since sample size = 10 < 30, thus, we'll perform t-test for single mean (as first mean is mean of population and not of any sample).
Degree of freedom = sample size - 1 = 9
Level of significance = 0.01
t test statistic's value for given case = [tex]\dfrac{\overline{x} - \mu_1}{s / \sqrt{n}} = \dfrac{ 83-75 }{9.82/\sqrt{10}} \approx 2.57[/tex]
(where s is sample standard deviation)
From the p-value calculator, we get the p-value for t = 2.57 at 0.01 level of significance with d.f.= 9 as : p = .015 > level of significance = 0.01
Thus, as p value is bigger than the level of significance, we fail to reject the null hypothesis, and thus, conclude that there is no significant improvement because of the new edition.
Thus, The claim that people do better with the new edition regarding the given situation is false at 0.01 level of significance.
Learn more about hypothesis testing here:
https://brainly.com/question/18831983
A one-sample t-test is used to determine if there's a significant difference in mean scores between the old and new textbook. The null hypothesis is not rejected because the t-score is lesser than the critical value, implying that there is not sufficient evidence that the new textbook is more helpful at the 0.01 significance level.
Explanation:To determine if the newly designed textbook is more helpful for learning material than the old edition, we can use a one-sample t-test. The null hypothesis (H0) is that there is no difference in mean scores between the old and the new textbooks, meaning the mean score with the new textbook is 75. The alternative hypothesis (Ha) is that the mean score with the new textbook is greater than 75.
We're given that the standard deviation (σ) is 10.5, the sample size (n) is 10, and the sample mean (μ) is calculated from the provided scores. To perform the t-test, we first calculate the sample mean (μ) = (92 + 83 + 93 + 74 + 85 + 97 + 88 + 70 + 69 + 79) / 10 = 830 / 10 = 83.
Next, we calculate the t-score using the formula: t = (sample mean - population mean) / (standard deviation / sqrt(n)).
t = (83 - 75) / (10.5 / sqrt(10)) = 8 / (10.5 / 3.162) = 8 / 3.316 = 2.412.
With a significance level of 0.01 and 9 degrees of freedom (n-1), we look up the critical t-value from the t-distribution table or use a statistical software to find that the critical value for a one-tailed test is approximately 2.821. Since our t-score of 2.412 is lesser than the critical value, we do not reject the null hypothesis, suggesting that there is not enough evidence to support that the new textbook is more helpful at the 0.01 significance level.
B is the midpoint of AC and D is the midpoint of CE solve for X given BD equals 3X +5 and ae equals 4X +20?
Answer:
x = 5
Step-by-step explanation:
Refer the attached image.
B is midpoint of AC
D is midpoint of CE
So,
[tex]AB=BC=CD=DE[/tex]
[tex]BD=BC+CD= AB+DE=\frac{1}{2}(AE)[/tex]
[tex](3x+5)=\frac{1}{2} (4x+20)[/tex]
Solving for 'x' we get,
[tex]3x+5=2x+10[/tex]
[tex]3x-2x=10-5[/tex]
[tex]x=5[/tex]
So the value of 'x' is 5.