Answer: 3x + 4y - 3z - 3 = 0
Step-by-step explanation:
with the given point (3, 0, 2), the plane is orthogonal to this line so it
has directional ratios (3, 4, -3)
therefore the given equation can be written as;
(x+2)/3 = (y-2)/4 = (z+1)/-3
so equation of the plane passing through point x1, y1 and z1 in the one point form is given as;
a(x-x1) + b(y - y1) + c(z -z1) = 0
abc represent the direction ratio
so we substitute
3(x-3) + 4(y-0) + (-3(z-2)) = 0
3x - 9 + 4y - 0 - 3z + 6 = 0
3x + 4y - 3z - 3 = 0
therefore the equation of the plane through the point is 3x + 4y - 3z - 3 = 0
Solving and Simplifying Equations
5r = -3(r +3) +7
Answer:
-2/8
Step-by-step explanation:
-3r-9+7=5r
-2=5r+3r
r=-2/8
hope this helped you( ꈍᴗꈍ)
Answer:
r = -1/4
Step-by-step explanation:
5r = -3(r + 3) +7
multiplying -3 with r + 3
5r = -3r - 9 +7
taking -3r on the other side of equality sign
5r + 3r = -9 + 7
8r = -2
dividing 8 by -2
r = -2/8
simplifying -2/8
r = -1/4
Consider triangle GHJ. What is the length of line segment HJ.
Answer:
5 sqrt 3
Step-by-step explanation:
on edge 2020
Write an equation through: (-1, 2)and (0, -1)
Answer:
Step-by-step explanation:
(-1 - 2)/(0 + 1) = -3/1 = -3
y + 1 = -3(x - 0)
y + 1 = -3x + 0
y = -3x - 1
How do you answer this question?
Answer:
Step-by-step explanation:
You would have 58 hours per day of work. We need to divide 720 by 58 in order to get your answer. Because 720 is 30 days times 24 hours.
9. Margie and Glenn are trying to solve the following system of equations.
5x - 4y= 23
7x + 8y = 5
Glenn thinks that the elimination method will not work. Margie is not so sure about that.
With your team, decide whether Glenn is correct and write a few sentences justifying
your conclusion. If the elimination method will work, show how. If not, use another
method to solve the system.
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p: n = 195, x = 162; 95% confidence.a. 0.788 < p < 0.873.
b. 0.789 < p < 0.873.
c. 0.778 < p < 0.883.
d. 0.777 < p < 0.884.
Answer:
c. 0.778 < p < 0.883.
Step-by-step explanation:
The formula for confidence interval for proportion =
p ± z score × √p(1 - p)/n
p = x/n
n = 195, x = 162
z score for 95% confidence Interval = 1.96
p = 162/195
p = 0.8307692308
p ≈ approximately equal to = 0.8308
0.8308 ± 1.96 × √0.8308 × (1 - 0.8308)/195
0.8308 ± 1.96 ×√0.8308 × 0.1692/195
0.8308 ± 1.96 × √0.0007208788
0.8308 ± 1.96 × 0.0268491862
0.8308 ± 0.052624405
Confidence Interval
= 0.8308 - 0.052624405
= 0.778175595
Approximately = 0.778
= 0.8308 + 0.052624405
= 0.883424405
Approximately = p
0.883
Therefore, the confidence interval for this proportion = (0.778, 0.883) or option c. 0.778 < p < 0.883
If a car travels 10 ft due north and then 15 feet due west, how far is the car from it starting point?
Answer:
initial velocity = o
then , answer will be 0 because initial velocity.
displacement =o
Tasha finds the length of the sides of the quadrilateral
before finding the perimeter. Which statement is true
about the length of the sides of quadrilateral ABCD?
O Side DA has a length of 13 units.
O Side AB has a length of 5 units.
O Side BC has a length of 2/5 units.
O Side CD has a length of 2/10 units.
Answer:C.
Step-by-step explanation:just took on edge
what is 11.510510510 as a fraction
Answer:
1151051051/100000000
Step-by-step explanation:
11.510510510 as a fraction equals 1151051051/100000000
1000 coins are tossed find the probability of getting exactly 500 heads.
Answer:
probability of getting exactly 500 heads= 1
Step-by-step explanation:
If a coin is tossed, the probability of obtaining a head = 0.5
If a coin is tossed, the probability of obtaining a tail= 1- probability of obtaining a head
If a coin is tossed, the probability of obtaining a tail=1-0.5
If a coin is tossed, the probability of obtaining a tail=0.5
So if 1000 coin are tossed, the probability of getting exay 500 heads which is already the half of 1000 is 1
Combine these radicals.
– бу 100 +36
оооо
о – бу 136
0 – 616
What the answer!
Answer:
Answer. 5.0/5. 6.
Step-by-step explanation:
I am not doing step by step you should know this
A tree is 4 1/2 feet tall. It is expected to grow 1 3/4 feet per year. At this growth rate, how many years will it take for the tree to have a height greater then 40 feet?
Answer:
21 years
Step-by-step explanation:
Given
[tex]Initial\ Height = 4\frac{1}{2}[/tex]
[tex]Final\ Height = 40[/tex]
[tex]Difference = 1\frac{3}{4}[/tex]
Required
Determine the years it'll take to grow to the final height
This question depicts arithmetic progression and will be solved using
[tex]T_n = a + (n - 1)d[/tex]
Where
[tex]T_n = 40[/tex]
[tex]a = 4\frac{1}{2}[/tex]
[tex]d = 1\frac{3}{4}[/tex]
Substitute these values in the given formula;
[tex]40 = 4\frac{1}{2} + (n - 1)1\frac{3}{4}[/tex]
Convert all fractions to decimal
[tex]40 = 4.5 + (n - 1) * 1.75[/tex]
Open Brackets
[tex]40 = 4.5 + 1.75n - 1.75[/tex]
Collect Like Terms
[tex]1.75n = 40 - 4.5 + 1.75[/tex]
[tex]1.75n = 37.25[/tex]
Divide both sides by 1.75
[tex]n = \frac{37.25}{1.75}[/tex]
[tex]n = 21.2857142857[/tex]
[tex]n = 21[/tex] (Approximated)
The number of years it will take for the tree to have a height greater than 40 feet is 23 years
Given:
Height of the tree = 4 1/2 feet
Growth rate per year = 1 3/4 feet
Expected growth rate = 40 feet
Expected Number of years = y
The inequality:
4 1/2 + 1 3/4y > 40
Subtract 4 1/2 from both sides
1 3/4y > 40 - 4 1/2
7/4y > 40 - 9/2
7/4y > (80-9)/ 2
7/4y > 79/2
divide both sides by 7/4
y > 79/2 ÷ 7/4
y > 79/2 × 4/7
y > (79×4) ) (2×7)
y > (316) / 14
y > 22.57142857142857
Approximately,
y > 23 years
Therefore, number of years it will take for the tree to have a height greater than 40 feet is 23 years
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example of an irrational number between 5 and 6. thank you :)
Answer: 25 and 30 is an example... hope this helped. If you have any more question lmk
henry begins to drain a water tank by opening a valve. Then he opens another valve. Then he closes the first valve. He leaves the 2nd valve open until the tank is empty. Discrete or Continuous?
Answer:
Continuous
Step-by-step explanation:
There is never a period of time when the water's flowing halts because the opening and closing of the first and second pipe are overlapping. Hope this helps (:
The subjects of a study by Dugoff et al. (A-5) were 10 obstetrics and gynecology interns at the University of Colorado Health Sciences Center. The researchers wanted to assess competence in performing clinical breast examinations. One of the baseline measurements was the number of such examinations performed.
The following data give the number of breast examinations performed for this sample of 10 interns.
Intern Number No. of Breast Exams Performed
1 30
2 40
3 8
4 20
5 26
6 35
7 35
8 20
9 25
10 20
Source: Lorraine Dugoff, Mauritha R. Everett, Louis Vontver, and Gwyn E. Barley, "Evaluation of Pelvic and Breast Examination Skills of Interns in Obstetrics and Gynecology and Internal Medicine," American Journal of Obstetrics and Gynecology, 189 (2003), 655-658. 6.4 CONFIDENCE INTERVAL FOR THE DIFFERENCE BETWEEN TWO POPULATION MEANS 177 Construct a 95 percent confidence interval for the mean of the population from which the study subjects may be presumed to have been drawn.
Answer:
The 95 percent confidence interval for the mean of the population from which the study subjects may be presumed to have been drawn is (19.1269, 32.6730).
Step-by-step explanation:
Intern No. of Breast
Number Exams Performed X²
1 30 900
2 40 1600
3 8 64
4 20 400
5 26 676
6 35 1225
7 35 1225
8 20 400
9 25 625
10 20 400
∑ 259 ∑ 7515
Mean= X`= ∑x/n= 259/10= 25.9
Variance = s²= 1/n-1[∑X²- (∑x)²/n]
= 1/0[7515- (259)²/10]= 1/9[7515- 6708.1]
= 806.9/9=89.655= 89.66
Standard Deviation= √89.655= 9.4687
Hence
The value of t with significance level alpha= 0.05 and 9 degrees of freedom is t(0.025,9)= 2.262
The 95 % Confidence interval is given by
x`±t(∝,n-1) s/√n
So Putting the values
25.9± 2.262( 9.4687/√10)
= 25.9 ±2.262 (2.9943)
= 25.9 ± 6.7730
= 25.9 +6.7730=32.6730
25.9 -6.7730= 19.1269
= 19.1269, 32.6730
The 95 percent confidence interval for the mean of the population from which the study subjects may be presumed to have been drawn is (19.1269, 32.6730).
In order to find the zeros of f(x)=x2−8x+12, Jessica needs to first factor the quadratic function. Which of the following is the factored form of the function?
2) Paul has two and two-thirds pounds of peanuts and a quarter of a pound of cashews . How many more pounds of cashews does he have
Answer:
Step-by-step explanation:
2 2/3
Multiply (2x - 3) and (3x + 6)
Answer:
Step-by-step explanation:
(2x−3)(3x+6)
=(2x+−3)(3x+6)
=(2x)(3x)+(2x)(6)+(−3)(3x)+(−3)(6)
=6x2+12x−9x−18
=6x2+3x−18
a rectangular piece of paper 71 cm long and 10m wide . a cylinder is formed by rolling the paper along its length , find volume ??
Answer:
Volume=355 cm³
Step-by-step explanation:
I assume it should be 10 cm, not 10 m. If it is 10 m, everything will have to be adjusted.
Circumference = 2[tex]\pi[/tex]r
10=2[tex]\pi[/tex]r
10÷2[tex]\pi[/tex]=r
1.59=r
V=[tex]\pi[/tex]r²h
V=[tex]\pi[/tex](1.59)(71)
v=355
To qualify for the long jump competition in track, an athlete must jump a combined distance of more than 16 meters in 3 jumps. Juan jumped 4.76 meters, 5.428 meters, and 5.9 meters. Did Juan qualify for (meet) the competition
Answer:
Yes.(16.088m combined jump)
Step-by-step explanation:
Combining jumps=4.76+5.428+5.9=16.088
16.088>16
Therefore Juan qualified for the competition
which expresions are equivalent to 3 1/4 - _ 5/8 select all that apply
What is 5.75 divide by 0.08
Answer:
71.875
use long division so the 5.75 goes on top of the 0.08
Find FH
Need help ASAP !!
Answer:
FH=24
Step-by-step explanation:
37-13=24
A study was conducted on the relationship between speeds of cars and gas mileage. The correlation coefficient was 0.45. Later, the researchers found the speedometers read 5 mph too high. Researchers recomputed the coefficient. The new value will be:
Answer:
0.45
Step-by-step explanation:
The correlation coefficient is used to measure the relationship between how two variables change. In this question, the two variables are cars speed and gas mileage. Since the speedometers were wrong as they were 5 mph too high in a constant manner, then the correlation between how changes in speed affect gas mileage will not be changed.
For example, if we are measuring how an increase of 15 mph decreased gas mileage, we are looking at the change in speed and it is the same if we start with 75 mph and then increase speed to 90 mph, or if we start with 45 mph and then increase to 60 mph. The change in speed for both cases will remain unchanged at 10 mph.
Now, since we have seen that the change in speed remains unchanged and since correlation coefficient is a measure of the relationship between how two variables change, then the new value of the correlation coefficient will remain the same as 0.45.
What is the center of the circle that has a diameter whose endpoints are (9, 7) and (-3, -5)?
Answer:
(3, 1)
Step-by-step explanation:
Midpoint of the diameter is the center
Since endpoints are (9, 7) and (-3, -5)
Midpoint will be:
((9 - 3)/2, (7-5)/2) = (3, 1)So the center is (3, 1)
Answer:
(3, 1)
Step-by-step explanation:
Midpoint of the diameter is the center
Since endpoints are (9, 7) and (-3, -5)
Midpoint will be:
((9 - 3)/2, (7-5)/2) = (3, 1)
or 3/1, 2/2 = (3,1)
So the center is (3, 1)
If the patient is less than 70 years old, the loading dose is 80 Howell Units2 per kilogram of DM. One Howell Unit is equivalent to 0.0020 mg of pure heparin. 2. Calculate how many mg of pure heparin is in 80 Howell Units. Do not worry about the kilograms of DM yet. 00.1600mg The loading dose, in mg of heparin for a 5-year-old with a total body weight of 40 lbs., with 10% bodyfat (that is, 90% of that 40 lbs. is lean body mass). You may also be interested to know that 1 kg = 2.20 lbs. Think about the steps you need to go through to find the correct dose. Remember, first you need to find the dosing mass....
Answer:
1) 0.16 mg of pure heparin is in 80 Howell units
2) the loading dose, in mg of heparin for the 5-year-old boy is 2.618 mg
Step-by-step explanation:
Given that;
if a patient is less than 70 years of age then loading dose is 80 Howell units square per Kg of DM,
One Howell unit is equivalent to 0.0020 mg of pure heparin
1)
how many mg of pure heparin is in 80 Howell units.
that will be;
80 × 0.0020 = 0.16 mg
therefore 0.16 mg of pure heparin is in 80 Howell units
2)
First we find the dosing mass
so dosing mass = body weight of the 5year old boy × 90%
from the question his total body weight of 40 lbs and 1 kg = 2.20 lbs
so
dosing mass = 40lbs × 1kg/2.20lbs × 90/100
dosing mass(kg) = 16.37 kg
Now to calculate the Loading dose we say;
Loading dose = dosing mass × heparin required per kg
Loading dose = 16.36 kg × 0.16 mg heparin per 1kg
loading dose = 2.618 mg heparin
therefore the loading dose, in mg of heparin for the 5-year-old boy is 2.618 mg
Michael is using a number line to evaluate the expression –8 – 3.
A number line going from negative 12 to positive 12. A point is at negative 8.
After locating –8 on the number line, which step could Michael complete to evaluate the expression?
Michael could rewrite the expression as Negative 8 + 3 and move 3 spaces to the right.
Michael could rewrite the expression as Negative 8 + negative 3 and move 3 spaces to the right.
Michael could rewrite the expression as Negative 8 + 3 and move 3 spaces to the left.
Michael could rewrite the expression as Negative 8 + negative 3 and move 3 spaces to the left.
Answer:
Micheal could rewrite the equation as negative 8 + negative 3 and move 3 spaces to the left.
Step-by-step explanation:
-8 - 3 = -8 + (-3)
The step which complete evaluate Michael expression is "Michael could rewrite the expression as negative 8 + negative 3 and move 3 spaces to the left".
What is subtraction on number line?Subtraction on a number line helps to subtract smaller numbers very easily. While subtracting numbers on a number line, we need to jump (move) towards the left-hand side of a number line. We always start with the minuend and move towards the left according to the number given as the subtrahend. 'Minuend' is the number from which we subtract and 'subtrahend' is the number which is subtracted.
According to the given question.
We have an expression -8 -3
For evaluating the given expression on number line Michael have to follow some following steps:
Step1: Michael have to locate -8 on the number line.
Step2: Michael have to move towards the left hand side of the number line according to the number given in the subtrahend. In the given expression the subtrahend is 3, so we will move 3 units left. And at -11 he have to stop.
So, -11 will be the answer of the even expression.
Hence, the step which complete evaluate Michael expression is "Michael could rewrite the expression as negative 8 + negative 3 and move 3 spaces to the left".
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This graph contains a Hamilton circuit? (Picture provided)
True
False
Determine how many terms should be used to estimate the sum of the entire series with an error of less than 0.001.
Answer: 9
Step-by-step explanation:
Tₙ ₊ ₁ < 0.001
1 / ( (n+1) 3 +1 ) < 0.001
(n+1)3 + 1 > 1000
(n+1)3 > 999
n+1 > 9.9966
n = 8.9966 => n = 9
I should take n = 9 to be sure that the error is less than 0.001.
Find the difference of 3/4 and 1/28. 5/7,21/28,11/14,23/28
Answer:
5/7, pretty sure a 4th of 21
Step-by-step explanation:
Answer:
5/7
Step-by-step explanation: