Answer:
5/2
Step-by-step explanation:
You change the signs to positive and then you put 15 as numerator and then 6 as denominator which gives you 15/6. But you can also simplify it which gives you 5/2. Hope this helps!
Let W be the solution set to the homogeneous system x + 2y + 3z = 0 2x + 4y + 6z = 0 Then W is a subspace of R3. Compute The Distance Between Y =[1 1 1] And W.
Answer:
Step-by-step explanation:
From the given information:
We can see that:
[tex]x + 2y + 3z = 0 --- (1) \\ \\ 2x + 4y + 6z = 0 --- (2)[/tex]
From equation (1), if we multiply it by 2, we will get what we have in equation (2).
It implies that,
x + 2y + 3z = 0 ⇔ 2x + 4y + 6z = 0
And, W satisfies the equation x + 2y + 3z = 0
i.e.
W = {(x,y,z) ∈ R³║x+2y+3z = 0}
Now, to determine the distance through the plane W and point is;
[tex]y = [1 \ 1 \ 1]^T[/tex]
Here, the normal vector [tex]n = [1\ 2\ 3]^T[/tex] is related to the plane x + 2y + 3z = 0
Suppose θ is the angle between the plane W and the point [tex]y = [1 \ 1 \ 1]^T[/tex], then the distance is can be expressed as:
[tex]||y|cos \theta| = \dfrac{n*y}{|n|}[/tex]
[tex]||y|cos \theta| = \dfrac{[1 \ 2\ 3 ]^T [1 \ 1 \ 1] ^T}{\sqrt{1^2+2^2+3^2}}[/tex]
[tex]||y|cos \theta| = \dfrac{[1+ 2+ 3 ]}{\sqrt{1+4+9}}[/tex]
[tex]||y|cos \theta| = \dfrac{6}{\sqrt{14}}[/tex]
[tex]||y|cos \theta| = 3\sqrt{\dfrac{2}{7}}[/tex]
A box of apples weighing 3 pounds was divided into 6 equal shares. What was the weight of each share in pounds?
Answer:
1/2 pounds or 0.5 pounds, 3/6 = 1/2 :)
hope i helped
Step-by-step explanation:
Answer:
0.5 pound/share
Step-by-step explanation:
Divide 3 pounds by 6 shares, obtaining 0.5 pound/share
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours.
Group of answer choices
A. 0.1946
B. 0.1285
C. 0.1469
D. 0.1346
Answer:
b. 01285 esa es, espero este buena y que te ayude
Assume that Publication is the root class of an inheritance tree. You want to form a linked list of different publications in the inheritance tree, including Book, Report, Newspaper, etc. What is the best way to create a linked list using PublListNode and Publication classes? a. The Publication class is derived from the PublListNode class. b. The PublListNode class is derived from the Publication class. c. The Publication class contains the PublListNode class. d. The PublListNode class contains the Publication class.
Answer:
The best way to create a linked list using PublListNode and Publication classes is ensuring that:
d. The PublListNode class contains the Publication class.
Step-by-step explanation:
A linked list contains a set of address-connected nodes (elements). The first node is called a header address, while the last node is called a null address. A linked list can be a single list (linear list), double list, multiple linked list, or circular linked list. The PublListNode is a type of multiple linked list. It forms a linked list of different publications using an inheritance tree.
. if f(x+3)=x+6 find inverse of function f(x)
Answer:
g(x)=x-3
Problem:
If f(x+3)=x+6 find inverse of function f(x).
Step-by-step explanation:
Let u=x+3, then x=u-3.
Make this substitution into our given:
f(u)=(u-3)+6
Simplify:
f(u)=u+(-3+6)
f(u)=u+3
Now let's find the inverse of f(u)...
Or if you prefer rename the variable...
f(x)=x+3
Now, we are going to solve y=x+3 for x.
Subtracting 3 on both sides gives: y-3=x.
Interchange x and y: x-3=y.
So the inverse of f(x)=x+3 is g(x)=x-3.
Answer:
The answer is g(x)=x-3
Step-by-step explanation:
If f(x+3)=x+6 find inverse of function f(x).
Let u=x+3, then x=u-3.
Make this substitution into our given:
f(u)=(u-3)+6
Simplify:
f(u)=u+(-3+6)
f(u)=u+3
Now let's find the inverse of f(u)...
Or if you prefer rename the variable...
f(x)=x+3
Now, we are going to solve y=x+3 for x.
Subtracting 3 on both sides gives: y-3=x.
Interchange x and y: x-3=y.
So the inverse of f(x)=x+3 is g(x)=x-3.
I need help with this
Answer:
Statement A is correct
Step-by-step explanation:
Statement A is correct: Model A1 (0.25) is more prefered than Model C3 (0.15)
Find the domain in the given ordered pairs.
{(2,8). (1,7), (2,9). (4, 6)}
Answer:
Domain: {1,2,4}
Step-by-step explanation:
The domain is the input values
We normally list the value in order from smallest to largest and only list the values one time if they appear more than once
Domain: {1,2,4}
Take the input values as domain.
→ 2,1,2,4
Now pick a number once if it is repeated and arrange in ascending order.
Then the domain will be,
→ 1,2,4
Hence, {1,2,4} is the domain of the pairs.
Solve similar triangles (advanced)
Solve for x
Answer:
4
Step-by-step explanation:
AD=4+8=12=DE thus angle EAD= angle AED=90÷2=45
angle ACB=90-45=45 thus CB=AB=4
Answer:
incorrect answer above
H(0)=_______________
Answer:
5
Step-by-step explanation:
the only point in the chart, which has x=0 as coordinate, is the point up there at y=5.
and that is automatically the result. there is not anything else to it.
Bobby opened a bag of candy and counted how many pieces were in the bag. There were 68 pieces of orange, lime, and cherry candies in total. He separated them by flavor and found that there were 2 more orange than lime and 4 more cherry than orange. How many cherry candies were in the bag?
Answer:
Number of limes are 20
Number of oranges are 22
Number of cherries are 26
Step-by-step explanation:
number of pieces of total candies = 68
Let the number of limes is y.
Number of orange = y + 2
Number of cherry = 4 + y + 2
So,
According to the question
y + y + 2 + 4 + 2 + y = 68
3 y + 8 = 68
3y = 60
y = 20
Number of limes are 20
Number of oranges are 22
Number of cherries are 26
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
UW = 6.3
Step-by-step explanation:
Given that,
VU = 7
∠U = 25°
We need to find the value of UW. It can be solved using trigonometry. So,
[tex]\cos\theta=\dfrac{B}{H}[/tex]
Where
B is base and H is hypotenuse
So,
[tex]\cos(25)=\dfrac{UW}{7}\\\\UW=7\times\cos(25)\\\\UW=6.3[/tex]
So, the value of UW is 6.3.
A tent maker wishes to support a 8-ft tent wall by attaching cable to the top of it, and then
anchoring the cable 7 feet from the base of the tent.
How long of a cable is needed?
Round your answer to the nearest tenth of a foot.
Answer with a numeric value only. That is, do not include "ft" or "feet" with your response.
Cable
Ground
Answer:
10.6
Step-by-step explanation:
A simple sketch of the question would give a right angled triangle. So that we can easily apply the Pythagoras theorem to determine the length of the cable required.
Let the length of the cable required be represented by x.
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]x^{2}[/tex] = [tex]8^{2}[/tex] + [tex]7^{2}[/tex]
= 64 + 49
[tex]x^{2}[/tex] = 113
x = [tex]\sqrt{113}[/tex]
= 10.63
x = 10.6
The length of the cable required is 10.6 in feet.
The length of the cable needed to support the tenth wall is approximately 10.6 ft.
The situation forms a right angle triangle.
Right angle triangle:Right angle triangle has one of it side as 90 degrees.
Therefore,
The tent wall is the opposite side of the triangle.
The table feet from the base of the tent is the adjacent side of the triangle.
Using Pythagoras's theorem the cable needed can be found.
Therefore,
c² = 8² + 7²c² = 64 + 49
c = √113
c = 10.6301458127
length of the cable ≈ 10.6 feet
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A 9.85 m ladder is placed against a wall. The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder. Find the height to the top and the distance between the wall and the foot of the ladder. find base and height
base...... m
height.....m
Given:
Length of the ladder = 9.85 m
The height to the top of the ladder is 5 m more than the distance between the wall and the foot of the ladder.
To find:
The height to the top and the distance between the wall and the foot of the ladder.
Solution:
let x be the distance between the wall and the foot of the ladder. Then the height to the top of the ladder is (x+5).
Pythagoras theorem: In a right angle triangle,
[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]
In the given situation, hypotenuse is the length of ladder, i.e., 9.85 m. The base is x m and the height is (x+5) m.
Using the Pythagoras theorem, we get
[tex](9.85)^2=x^2+(x+5)^2[/tex]
[tex]97.0225=x^2+x^2+10x+25[/tex]
[tex]0=2x^2+10x+25-97.0225[/tex]
[tex]0=2x^2+10x-72.0225[/tex]
Here, [tex]a=2, b=10,c=-72.0225[/tex]. Using the quadratic formula, we get
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-10\pm \sqrt{(10)^2-4(2)(-72.0225)}}{2(2)}[/tex]
[tex]x=\dfrac{-10\pm \sqrt{676.18}}{4}[/tex]
Approximating the value, we get
[tex]x=\dfrac{-10\pm 26}{4}[/tex]
[tex]x=\dfrac{-10+26}{4},\dfrac{-10-26}{4}[/tex]
[tex]x=\dfrac{16}{4},\dfrac{-36}{4}[/tex]
[tex]x=4,-9[/tex]
Distance cannot be negative so [tex]x\neq -9.[/tex]
Now we have [tex]x=4[/tex]
[tex]x+5=4+5[/tex]
[tex]x+5=9[/tex]
Therefore, the base is 4 m and the height is 9 m.
The base, height to the top of the ladder and height of the ladder when connected together we will get a triangle and then apply Pythagoras theorem we get base 4.0 m and height 9 m.
What is Pythagoras theorem?According to this theorem, the hypotenuse l, base b and opposite side a are connected by the equation written as follows:
hypotenuse² = base² + opposite side²
l² = a² + b².
Thus if we know either two sides or the triangle we can calculate the length of the unknown side of the triangle. It is given that the length of ladder is 9.85 m. It is placed against a wall and the base that is distance between foot and wall is 5 m less than the height to the top.
Assuming a triangle connecting these three points, the hypotenuse is the length of the ladder 9.85 m and let x be the base and opposite side that is the height to the top be x + 5. Now apply Pythagoras theorem.
9.85² = (x+5)² + x²
97.02 = 2 x² + 10x + 25
2 x² + 10x -72.02 = 0
Now solve for x using quadratic equation we get x = 4.00. The base of the triangle is 4 m and opposite side that is the height = x +5 = 4 +5 = 9m.
Therefore, base is 4 m and height to the top of the ladder is 9 m.
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A small liberal arts college in the Northeast has 300 freshmen. One hundred ten of the freshmen are education majors. Suppose sixty freshmen are randomly selected (without replacement). Find the standard deviation of the number of education majors in the sample.
Answer:
The standard deviation of the number of education majors in the sample is of 3.34.
Step-by-step explanation:
The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Standard deviation:
The standard deviation of the hypergeometric distribution is:
[tex]\sigma = \sqrt{\frac{nk}{N}(1 - \frac{k}{N})(\frac{N-n}{N-1})}[/tex]
In this question:
300 freshmen means that [tex]N = 300[/tex]
110 are education majors, which means that [tex]k = 110[/tex]
60 are chosen, which means that [tex]n = 60[/tex]
Find the standard deviation of the number of education majors in the sample.
[tex]\sigma = \sqrt{\frac{60*110}{300}(1 - \frac{110}{300})(\frac{240}{299})} = 3.34[/tex]
The standard deviation of the number of education majors in the sample is of 3.34.
Two different weight loss programs are being compared to determine their effectiveness. Ten men were assigned to each program (that is, a total of 20 men altogether). Their weight losses (in lbs), after a period of time, are recorded below. We are interested in determining which, if any, of the diets is more effective in terms of average weight loss. Assume weight loss for each diet to be normally distributed.
Diet 1 3.4 10.9 2.8 7.8 0.9 5.2 2.5 10.5 7.1 7.5
Diet 2 11.9 13.1 11.6 6.8 6.8 8.8 12.5 8.6 17.5 10.3
Carry out an appropriate test using a significance level of 0.10.
Answer:
WE reject the Null and conclude that one of the drug is more effective than the other.
Step-by-step explanation:
Given :
Diet 1 3.4 10.9 2.8 7.8 0.9 5.2 2.5 10.5 7.1 7.5
Diet 2 11.9 13.1 11.6 6.8 6.8 8.8 12.5 8.6 17.5 10.3
This is a matched pair sample :
The hypothesis :
H0 : μd = 0
H1 : μd ≠ 0
Hence, we intun the difference between the two groups of value :
Difference, d = -8.9,-2.2,-8.8,1,-5.9,-3.6,-10,1.9,-10.4,-2.8
The test statistic :
dbar ÷ (Sd/√n)
dbar = mean of difference = Σd / n = - 49.7 / 10 = - 4.97
Standard deviation of difference, Sd = 4.51
Test statistic :
-4.97 ÷ (4.51/√10)
Test statistic = - 3.485
The sample size, n = 10
df = n - 1 ; 10 - 1 = 9
Critical value (0.10, 9) = 1.833
If Test statistic > |Critical value |
Since 3.486 > 1.833 ; WE reject the Null and conclude that one of the drug is more effective than the other
If f(x) is an exponential function where f(-3.5) = 25 and
f(6)
= 33, then find the value of f (6.5), to the nearest hundredth.
Answer:
f(x)=27.63(1.03)^x
Step-by-step explanation:
Name different types of triangles. Illustrate how you can introduce each triangle to the foundation phase learner during the lesson presentation. Mention the resources that you will use.
Answer:
Following are the complete solution to the given question:
Step-by-step explanation:
The two main elements are geometry. One of them is analyzing the form of something. The second element is distance thinking. Four dominant sides are united into the triangle. Its sides can be of any height, however, the biggest side can be even more than and equal to a sum of the other two sides. Also, there are two concentric angles in a triangular, with the overall amount of three angles being 180 °.
Triangle Equilateral. It is a triangle with much the same length on all edges and 60 ° throughout all angles.Right triangle. Right pyramid. It is triangular with one correct angle and two acute angles, with only an oblique of less than 90º.Triangle of Isosceles It is a triangle with the same length along two sides.Acute triangle, three acute angles triangle.Triangle shabby. It is a three-way corner with three different elevations and a shallow angle, with a shallow angle which measures and over 90 °.Triangle scalene. The triangle has distinct lengths on any and all three sides.ajoke needs 400000 for her tuition. if her bank gives a 9% 180 day loan notes, with interest compounded daily, what would she owe at the end of 180 days? (assume 360days a year). what is the effective rate of interest?
Answer:
Very hard question i don't help you
What's -5√3(2+√5)?
h e l p .
Answer:
= -10√3 - √3 . 5^3/2
Step-by-step explanation:
Apply the distributive law: a(b + c) = ab + ac
a = -5 √3, b = 2, c = √5
-5 √3 . 2 + -(5√3) √5
Apply minus-plus rules: + (-a) = -a
= -5 . 2√3 - 5 √3 √5
Simplify
= -10√3 - √3 . 5^3/2
PLEASE HELP pleaseeeee
Answer:
C
Step-by-step explanation:
On a number cube from 1 to 6, there are only two numbers available that are equal to or greater than 5: 5 and 6. Out of the six possible options, only two options could meet these conditions. Therefore, the probability is 2/6. However, this can be further simplified as both 2 and 6 can be divided by two, which would equal 1/3.
What is the solution to 2x-8<12?
Answer:
X=10
Step-by-step explanation:
2x-,8<12
2x>12+ 8
2x>20
x>10
A medicine bottle contains 8 grams of medicine. One dose is 400 milligrams. How many doses does the bottle contain?
Answer:
20 doses
Step-by-step explanation:
400 milli. = 0.4 grams
8/0.4 = 20 doses
The sum of 2 times a number and 4 equals 9
Answer:
2x +4 = 9
x = 5/2
Step-by-step explanation:
Let x = number
2x +4 = 9
Subtract 4 from each side
2x+4-4 = 9-4
2x = 5
Divide by 2
2x/2 =5/2
x = 5/2
What is the answer to this question in the picture
9514 1404 393
Answer:
[tex]\displaystyle\sqrt{x+7}-\log{(x+2)}[/tex]
Step-by-step explanation:
It's pretty straightforward. You want ...
f(x) - g(x)
Substituting the given function definitions gives ...
[tex]\displaystyle\boxed{\sqrt{x+7}-\log{(x+2)}}[/tex]
(8 + 6)(-5+71) = help
Answer:
The answer is C. -82 + 26i
(8+6i)(-5+7i) = -82+26i
You have 42 oz of egg noodles. You need 5 oz to make one serving of chicken noodle soup. How many servings can you
Answer:
8 servings
Step-by-step explanation:
Take the total ounces and divide by the number of ounces per serving
42/5 =8.4
Round down since we don't want to short someone on their soup
8
Tony calculates that 3 cubic metres of concrete is enough for the path.
He decides to use a concrete mix which has:
• cement = 1 part
• sand = 2 parts
gravel = 3 parts
How many cubic metres of gravel does Tony need?
0.5
Answer:
1.5 cubic metres
Step-by-step explanation:
Given that in a concrete mix, cement makes up 1 part, sand makes up 2 parts and gravel makes up 3 parts.
The total number of parts = 1 + 2 + 3 = 6 parts.
The amount of marvel present the concrete mix = amount of marvel / total mix
= 3 parts / 6 parts = 1/2
Since 3 cubic metres of concrete is enough for the path, hence the amount of gravel needed is:
Amount of gravel = 1/2 * 3 cubic metres of concrete = 1.5 cubic metres
Tamanika got a raise in her hourly pay, from $14.00 to $17.95. Find the percent increase. Round to the nearest tenth of a percent.
Answer:
28.2 %
Step-by-step explanation:
Increase = 17.95 - 14 = $3.95
%age increase = 100 * 3.95 / 14
= 28.214
How long will it take for the money in an account that is compounded continuously at 4% interest to sextuple.
Answer:
t = 44.79 years
Step-by-step explanation:
6 = [tex]e^{.04t}[/tex]
ln(6) = .04t ln(e)
ln(6)/.04 =t
t = 44.79
The amount of time it required to sextuple is 27.5 years.
How to calculate time for sextuple?To find out how long it takes for the money in an account to sextuple (i.e., become six times its original value) with continuous compounding at an annual interest rate of 4%, we can use the formula for continuous compound interest:
A = Pe^(rt)
If we let P be the initial principal, then the final amount is 6P (since we want the account to sextuple), and the interest rate r is 0.04. So we can write:
6P = Pe^(0.04t)
Dividing both sides by P, we get:
6 = e^(0.04t)
Taking the natural logarithm of both sides, we get:
ln(6) = 0.04t
Dividing both sides by 0.04, we get:
t = ln(6)/0.04
Using a calculator, we can find that:
t ≈ 27.5 years
Therefore, it will take approximately 27.5 years for the money in the account to sextuple with continuous compounding at an annual interest rate of 4%.
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what is the root squar of 100
Answer: 10
Step-by-step explanation:
10
