what will be the 40th term in the sequence defined by an=-12+4(n-2)
Answer:
140
Explanation:
an=-12+4(n-2)
an=-12+4([40]-2)
an=-12+4(38)
an=-152-12
an=140
The 40th term in the sequence defined by aₙ= -12+4(n-2) is 140
using AP formula,
aₙ = a + (n - 1)d
where
a = first term
d = common difference
n = number of terms
Therefore,
aₙ = -12 + 4(n-2)
n = 40
a₄₀ = -12 + 4(40 - 2)
a₄₀ = -12 + 4(38)
a₄₀ = -12 + 152
a₄₀ = 140
The 40th term of the sequence is 140.
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What is 2052 divided by 76
Answer:
27
Step-by-step explanation:
Answer:
Yes, by 27 times
Step-by-step explanation:
I hope it helps you
Question 6 (1.25 points)
A researcher wants to test if the mean annual salary of all lawyers in a city is
different from $110,000. A random sample of 53 lawyers selected from the city
reveals a mean annual salary of $114,000. Assume that o = $17,000, and that the
test is to be made at the 1% significance level.
What is the value of the test statistic, z, rounded to three decimal places?
A
Answer:
Test statistic Z= 1.713
The calculated Z- value = 1.7130 < 2.576 at 0.01 level of significance
Null hypothesis is accepted
There is no difference between the mean annual salary of all lawyers in a city is different from $110,000
Step-by-step explanation:
Step(i):-
A researcher wants to test if the mean annual salary of all lawyers in a city is
different from $110,000
Mean of the Population μ = $110,000
Sample size 'n' = 53
Mean of the sample x⁻ = $114,000.
standard deviation of the Population = $17,000,
Level of significance = 0.01
Null hypothesis :
There is no difference between the mean annual salary of all lawyers in a city is different from $110,000
H₀: x⁻ = μ
Alternative Hypothesis : x⁻ ≠ μ
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{114000-110000}{\frac{17000}{\sqrt{53} } }[/tex]
Z = 1.7130
Tabulated value Z = 2.576 at 0.01 level of significance
The calculated Z- value = 1.7130 < 2.576 at 0.01 level of significance
Null hypothesis is accepted
There is no difference between the mean annual salary of all lawyers in a city is different from $110,000
Jim walks 6/7 of a mile every day. Russell walks 1/4 of a mile. How much farther does Jim work than Russell.
Answer:
Jim walked 17/28 for miles than Russel
Step-by-step explanation:
First you turn 6/7 and 1/4 to have the same denominators. In that case you find the least common multiple which is 28.
7: 7, 14, 21, 28
4: 4, 8, 12, 16, 20, 24, 28
Next you multiply the top and the bottom of your fraction my the factor you used to get 28 for your denominator
6/7 x 4/4 = 24/28
1/4 x 7/7 = 7/28
Lastly, you subtract the products you got.
24/28 - 7/28 = 17/28
Compare using <, > or = 7 2/5 _ 7 3/7
Answer:
<
Step-by-step explanation:
7 2/5 = 37/5
7 3/5 = 52/7
~~~~~~~~~~~
37/5 times 7 = 259/35
52/7 times 5 = 260/35
~~~~~~~~~~~~~~~~~
Subtract then you difference is one, therefor 7 3/5 is greater.
The graph represents f(x) = |x| + 3.
what is f(-2, 2)?
A) -2
B) 0
C) 1
D) 2
Write the hypothesis: If the pen is not blue then today is Friday.
a. The pen is not blue
b. If the pen is not blue
c. If today is Friday
d. today is not Friday
What is the sum of -6 and 12/6
Answer:
-4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
multiply -6 with 6 so we can have common denominator as 12/6
that's gives us -36/6+12/6
-36+12 is -24 so our answer up till now will be -24/6.... this can be simplified by 6 to get -4
pls mark this as brainliest!!!!
Mrs. Alonza ordered 4 x 10³ markers for her store. How many markers did she order?
Find the area of the trapezoid.
st
11 m
6 m
-
8 m
Answer:
the answer is 68
Joan planted 150 tulip bulbs, but only 20% of them bloomed. How many tulips
bloomed?
Amna wants to rent a boat and spend less than 51 . The boat costs 6 per hour, and Amna has a discount coupon for 3 off What are the possible numbers of hours Amna could rent the boat?
Answer:
9 hours or less. with a $3 off coupon she could spend up to $54. divide that by $6 per hour and that gives you a possibility of nine hours of boat rental.
PLEASE HELP FAST & CORrect 50 POINTS
Answer:
105
Step-by-step explanation:
A hot air balloon is descending at a rate of 6.75 feet per second.
What is the change in the balloon's height after 3 1/3 seconds?
The hot air balloon descends 22.498 feet after 3.333 seconds.
How much does a hot air balloon's height decreases?
The situation indicates that the height decrease is directly proportional to time. The distance is equal to the product of speed (v), in feet per second, and time (t), in seconds.
s ∝ t
s = v · t (1)
If we know that v= 6.75 ft / s and t = 3.333 ft, then the change in the height of the hot air balloon is:
s = (6.75 ft / s) · (3.333 s)
s = 22.498 ft
The hot air balloon descends 22.498 feet after 3.333 seconds.
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What function represents the amount of change given from a $10 bill, f(x), based on x, the number of bagels purchased? f(x) = 4x + O f(x) = -x + 10 Of(x) = x + 10 O f(x) = -x + 10
Answer:
the answer is c
Step-by-step explanation:hope this helps
Answer:
C or the third option, 3/4 x + 10
Step-by-step explanation:
100% correct please mark brainlist. HAVE A GREAT DAY
Estimate the squrae root to rhe nearest hundredth.
1. 138
2. 405
3. 800
4. 1150
5. 6500
6. 580
7. 300
8. 250
9. 284
10. 794
Salamt....
Answer:
1.11.83
2. 20.12
3. 28.28
4. 33.91
5.80.62
6.24.08
7.17.32
8. 15.81
9. 16.85
10. 28.18
Step-by-step explanation:
pls make me brainliest
Please give the correct answer and I will give a brainless
Answer:
It’s 40 I’m pretty sure because of the square. That’s how I was taught.
2 3/4 divided by 4 1/8 in fraction form
Answer:
Step-by-step explanation:
2 3/4 ÷ 4 1/8
23/4×8/41
23×8/4×41
46/41
=1.122
So the answer is 1.122
The solution after divide 2 3/4 by 4 1/8 in fraction form is,
⇒ 2/3
We have to given that,
To divide 2 3/4 by 4 1/8.
Simplify it as,
2 3/4 ÷ 4 1/8
11/4 ÷ 33/8
11/4 x 8/33
(11 x 8) / (4x33)
2/3
Therefore, The solution after divide 2 3/4 by 4 1/8 in fraction form is,
⇒ 2/3
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how do i solve this help
Answer is : A .. Hope it helped
*Find 6 5/8% of $1,480.90. Round to the nearest cent.
9514 1404 393
Answer:
$98.11
Step-by-step explanation:
If your calculator doesn't work with mixed numbers, you must first convert 6 5/8% to a decimal fraction.
6 5/8 = (6·8+5)/8 = 53/8 = 6.625
6 5/8% = 0.01×6.625 = 0.06625
Then the desired amount is ...
0.06625 × $1480.90 = $98.109625 ≈ $98.11
6 5/8% of $1,480.90 is $98.11.
Find an equation of the plane through the point (1, -4, 0) and perpendicular to the vector (5, 1, -4). Do this problem in the standard way or WebWork may not recognize a correct answer.
Answer:
x = = -5 ; y = -1 ; z = 4 [tex]\bigg | = 3 \bigg |[/tex]
Step-by-step explanation:
The equation of the plane through (1,-4,0) is,
a(x-1) + b(y+4) + c(z+0) = 0 ....... (1)
Again the plane is perpendicular to the vector (5,1,-4)
So, the direction ratios of the normal to the plane is proportional to the direction ratios of the vector (5,1,-4)
So, a/(5) = b/(1) = c/(-4 )
Let,a/(5) = b/(1) = c/(-4 ) = k
So, a = 5k, b = k and c = -4k
So, from (1) we have,
(5k)(x-1) + (k)(y+4) + (-4k)(z+0) = 0
Thus;
-5(x-1) -(y+4) +4(z+0) = 0
So,
-5x +1 -y-4+4z+0 =0
-5x - y +4z -3 = 0
-5x - y +4z = 3
x = = -5 ; y = -1 ; z = 4 [tex]\bigg | = 3 \bigg |[/tex]
Options:
-does
- does not
Answer:
It does!
Step-by-step explanation:
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
Source: Columbia.edu
(I'm greedy and want points )
In which pair do both decimals represent rational numbers?
O A. 0.296 and 0.9888...
B. 4.462837305718274... and 0.9888
O C. 6.32891237302554... and 0.9888...
D. 6.32891237302554... and 0.296
Answer:
Step-by-step explanation:
Option A. 0.296 and 0.9888 is correct because rational no are terminating and repeating ..
A librarian sorts 500 books at a constant rate. After 6 days, the librarian still has 200 books to sort. How much time does it take to sort the books from start to finish?
Answer: 10 days
Step-by-step explanation: So if the librarian sorted at a constant rate, then they sorted the same amount of books all 6 days. If they still have 200 books left to sort, then they sorted 300 books over 6 days. This means that they sorted 50 books per day. 200 divided by 50 is 4. So it will take 4 more days to finish sorting all the books. So altogether, it will take 10 days to sort all of the books.
The total number of required days is 10.
What is Unitary method ?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
The total number of books is 500.
The books left after 6 days is 200.
The number books read per day is given as,
(500 - 200)/6
= 300/6
= 50
Now, number of days the remaining number of books to be read is,
200/50 = 4
Thus, the total number of days is 6 + 4 = 10.
Hence, it will take 10 days from the start to finish all the books.
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Express into slope form
Answer: y= 3/2x+1
Step-by-step explanation:
What is 9x for x = 4
Answer:
36
Step-by-step explanation:
9x is equal to 9 multiplied by x.
x=4 so it is 9 x 4
9 x 4=36
Select the correct answer.
Brianna created a scatter plot and drew a line of best fit, as shown.
What is the equation of the line of best fit that Brianna drew?
The equation of the line of best fit that Brianna drew is: c. y = 2x + 5
Recall:
Line of best of fit of the line shown in the scatter plot can be found by finding the slope (m) and the y-intercept (b) of the line then substituting each value into y = mx + b.Thus:
Slope of a line (m) = change in y/change in x
From the scatter plot given,Change in y = 2 units
Change in x = 1 unit
Slope = 2/1 = 2
The y-intercept is the point where the line of best fit intercepts the y-axis which is at y = 5.
y-intercept (b) = 5
Substitute b = 5 and m = 2 into y = mx + b
y = 2x + 5
Therefore, the equation of the line of best fit that Brianna drew is: c. y = 2x + 5Learn more about line of best fit on:
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Answer:
c ..)
Step-by-step explanation:
Cathy's food usually costs $212.90 a week. One week, it cost $198.98. How
much less money did she spend that week?
Answer:
$13.92
Step-by-step explanation:
12. Sean lives 2.25 miles
from school. Write this
distance as a fraction in simplest form.
Assume the table gives data on field goal shooting for two members of the Benedict College 2014-2020 men's basketball team. Seth Fitzgerald Roberto Mantovani Made Missed Made Missed Two-pointers 123 118 87 84 Three-pointers 31 6 2 17 NOTE: The numerical values in this problem have been modified for testing purposes. (a) What percent of all field goal attempts did Seth Fiqzgerald make? (Enter your answers rounded to two decimal places.) Seth Fitzgerald's overall field goal percentage:_______ What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.) What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.) Roberto Mantovani's overall field goal percentage:______________. (b) Find the percent of all two-point field goals and all three-point field goals that both Seth and Roberto made. (Enter your answers rounded to two decimal places.) Seth Fitzgerald's two-pointers: ______________% Roberto Mantovani's two-pointers:___________ % Seth Fitzgerald's three-pointers:____________ Roberto Mantovani's three-pointers:__________ (c) Roberto had a lower percent than Seth for both types of field goals, but had a better overall percent. That sounds impossible, select the correct statement concerning the situation. i) This is an example of Simpson's paradox. The comparison that holds for both field goal groups is reversed when the groups are combined into one group. ii) The sample size is too small and this explains why the results seem contradictory. iii) You should never compare percentages for two different groups. iv) This is an example of correlation. The comparison that holds for both field goal groups is reversed when the groups are combined into one group.
Answer:
(a) What percent of all field goal attempts did Seth Fitzgerald make? (Enter your answers rounded to two decimal places.)
Seth Fitzgerald's overall field goal percentage:__59.69%_____
What percent of all field goal attempts did Roberto Mantovani make? (Enter your answers rounded to two decimal places.)
Roberto Mantovani's overall field goal percentage: ______40.31%________.
(b) Find the percent of all two-point field goals and all three-point field goals that both Seth and Roberto made. (Enter your answers rounded to two decimal places.)
Seth Fitzgerald's two-pointers: _____58.57%_________%
Roberto Mantovani's two-pointers:_____41.43%______ %
Seth Fitzgerald's three-pointers:_____64.58%_______
Roberto Mantovani's three-pointers:_____35.42%_____
(c) Roberto had a lower percent than Seth for both types of field goals, but had a better overall percent. That sounds impossible, select the correct statement concerning the situation.
i) This is an example of Simpson's paradox. The comparison that holds for both field goal groups is reversed when the groups are combined into one group
Step-by-step explanation:
a) Data and Calculations:
Benedict College 2014-2020 men's basketball team:
Seth Fitzgerald Roberto Mantovani Total
Made Missed Made Missed Made Missed
Two-pointers 123 118 87 84 210 205
Three-pointers 31 6 17 2 48 8
Total 154 124 104 86 258 210
a) All field goal attempts = 258 (154 + 104)
Field goal attempts by Seth Fitzgerald = 154/258 * 100 = 59.69%
Goal 154 - 124 = 30/258 * 100 = 11.63%
Roberto Mantovani = 104/258*100 = 40.31%
Goal 104 - 86 = 18/258 *100 = 6.98%
Percent of all two-point field goals and all three-point field goals that both Seth and Roberto made:
Goals by both = 48 (30 + 18) = 48/258*100 = 18.61 (11.63 + 6.98)
Seth Fitzgerald's two-pointers = 123/210*100 = 58.57%
Roberto Mantovani's two-pointers = 87/210*100 = 41.43%
Seth Fitzgerald's three-pointers = 31/48*100 = 64.58%
Roberto Mantovani's three-pointers = 17/48*100 = 35.42%
b) Simpson's paradox, also called Yule-Simpson effect, says that when we combine all of the groups together (e.g. two-pointer and three-pointer games played by Seth and Roberto respectively) and look at the data in total form, the correlation that we noticed before may reverse itself. The cause of this reversion is lurking variables or numerical values of the data.