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]
Sasha spent $7.00 of the $20.00 in her wallet. Which decimal represents the fraction of the $20.00 Sasha spent?
Answer:
0.7
Step-by-step explanation:
Answer:
0.35
Step-by-step explanation:
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.
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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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.
Joan planted 150 tulip bulbs, but only 20% of them bloomed. How many tulips
bloomed?
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 )
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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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:
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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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
*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.
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
how do i solve this help
Answer is : A .. Hope it helped
Mrs. Alonza ordered 4 x 10³ markers for her store. How many markers did she order?
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
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
Find the area of the trapezoid.
st
11 m
6 m
-
8 m
Answer:
the answer is 68
PLEASE HELP FAST & CORrect 50 POINTS
Answer:
105
Step-by-step explanation:
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 ..
c) If the speed of the car is tripled, what will happen to the time taken?
Answer:
I think the time taken will be 1/3 of what the time is now since the time of the car is tripled.
Step-by-step explanation:
Answer:
divide time by 3 since time&speed are directly proprtional
Step-by-step explanation:
so there.
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.
How do I solve this problem?
Answer:
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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
Una parte de 25 000 dólares se invierte al 10% de interés, otra parte al 12 % y el resto al 16%. El ingreso anual total de las tres inversiones es de 3200 dólares. Además, el ingreso de la inversión al 16% es igual al ingreso de las otras dos inversiones combinadas. ¿Cuánto se invirtió a cada tasa de interés?
Answer:
$5000 at 10%, $10000 at 12% and 10000 at 16%Step-by-step explanation:
One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?==================
Let the parts be x, y and z
As per given we get below system of equations:
x + y + z = 250000.1x + 0.12y + 0.16z = 32000.1x + 0.2y = 0.16zSubstitute 0.1x + 0.2y in the second equation:
0.16z + 0.16z = 32000.32z = 3200z = 3200/0.32z = 10000Now we have:
x + y + 10000 = 25000 ⇒ x + y = 15000and
0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600Multiply the second equation and then subtract the first one:
10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000x + 1.2y - (x + y) = 16000 - 150000.2y = 1000y = 10000Then
x = 15000 - 10000 = 5000So the parts are:
$5000 at 10%, $10000 at 12% and 10000 at 16%Need help with statistics question please.
25. Filling Bottles A certain brand of apple juice is supposed to have 64 ounces of juice. Because the punishment for under filling bottles is severe, the target mean amount of juice is 64.05 ounces. However, the filling machine is not precise, and the exact amount of juice varies from bottle to bottle. The quality-control manager wishes to verify that the mean amount of juice in each bottle is 64.05 ounces so that she can be sure that the machine is not over- or under filling. She randomly samples 22 bottles of juice and measures the content and obtains the following data:
64.05 64.05 64.03 63.97 63.95 64.02 64.01 63.99 64.00 64.01 64.06 63.94 63.98 64.05 63.95 64.01 64.08 64.01 63.9 63.97 64.10 63.98
(a) Because the sample size is small, she must verify that the amount of juice is normally distributed and the sample does not contain any outliers. The normal probability plot and box plot are shown. Are the conditions for testing the hypothesis satisfied?
(b) Should the assembly line be shut down so that the machine can be re calibrated? Assume =0.06 ounces and use a 0.01 level of significance.
(c) Explain why a level of significance = 0.01 of might be more reasonable than 0.1 [Hint: Consider the consequences of incorrectly rejecting the null hypothesis.]
Answer: Hmm this question was very hard.
Step-by-step explanation:
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.
Anna worked worked 37 hours this week at £8.97 hour. she then worked nine hours overtime at time and a half. how much does she get paid in total? round your answer to the nearest pound.
417
Step-by-step explanation:
I hope this helps :)
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:
5. My red or blue shirt club has 32 members. If the number of people wearing read shirts
is 4 less than triple the number of people wearing blue shirts, how many people are
wearing red shirts?
Answer:
(red shirt people) r - 4[tex]\sqrt[3]{b}[/tex] (blue shirt people)
Step-by-step explanation:
I don't know if you want an equation or an exact answer. I have an equation though.
I got this answer like this:
4 less is minus 4
triple is multiplication and/or times