Answers
Answer:
dependent systemx = 2 -ay = 1 +az = aStep-by-step explanation:
Let's solve this by eliminating z, then we'll go from there.
Add 6 times the second equation to the first.
(3x -3y +6z) +6(x +2y -z) = (3) +6(4)
9x +9y = 27 . . . simplify
x + y = 3 . . . . . . divide by 9 [eq4]
Add 13 times the second equation to the third.
(5x -8y +13z) +13(x +2y -z) = (2) +13(4)
18x +18y = 54
x + y = 3 . . . . . . divide by 18 [eq5]
Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:
y = 3 -x . . . . solve eq5 for y
x +2(3 -x) -z = 4 . . . . substitute into the second equation
-x +6 -z = 4
x = 2 - z . . . . . . add x-4
y = 3 -(2 -z)
y = z +1
So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...
x = 2 -a
y = 1 +a
z = a
_____
Check
First equation:
3(2-a) -3(a+1) +6a = 3
6 -3a -3a -3 +6a = 3 . . . true
Second equation:
(2-a) +2(a+1) -a = 4
2 -a +2a +2 -a = 4 . . . true
Third equation:
5(2-a) -8(a+1) +13a = 2
10 -5a -8a -8 +13a = 2 . . . true
Our solution checks algebraically.
Related Questions
The probability that Hugo is on time for a given class is 71 percent. If there are 57 classes during the semester, what is the best estimate of the number of times out of 57 that Hugo is on time to class? Round your answer to the nearest integer.
Answers
Answer:
40
Step-by-step explanation:
P(Hugo is on time for a given class)=71%=0.71
If there are 57 classes during the semester
The number of times Hugo is on time to class during the semester will
=0.71 X 57
=40.47
[tex]\approx 40 $ (correct to the nearest integer.)[/tex]
Hugo is on time to class approximately 40 out of 57 times.
I NEED HELP PLEASE, THANKS! :)
Find the angle θ between u = <7, –2> and v = <–1, 2>.
47.5°
42.5°
132.5°
137.5°
Answers
Answer:
Step-by-step explanation:
Cos θ = u*v
IuI *IvI
u * v = 7*(-1) + (-2)*2
= -7 - 4
= -11
IuI = [tex]\sqrt{7^{2}+(-2)^{2}}\\[/tex]
= [tex]\sqrt{49+4}\\\\[/tex]
= [tex]\sqrt{53}[/tex]
I vI = [tex]\sqrt{(-1)^{2}+2^{2}}\\[/tex]
= [tex]\sqrt{1+4}\\\\[/tex]
= [tex]\sqrt{5}\\[/tex]
Cos θ = [tex]\frac{-11}{\sqrt{53}*\sqrt{5} } \\\\[/tex]
= [tex]\frac{-11}{16.28}\\\\[/tex]
Cos θ = -0.68
θ = 132.5°
11.Which word or words best complete the sentence? Two lines that lie in parallel planes _____ intersect. Sometimes Always Never
Answers
Answer:
never intersect
Step-by-step explanation
parallel lines do not intersect and neither do parallel planes
If f(7) = 8 find
f-1(8)
Answers
Answer:
34293
Step-by-step explanation:
because it 36 and 45. it is right
In a random sample of high school seniors, the proportion who used text messaging was 0.88. In a random sample of high school freshmen, this proportion was 0.68. Researchers found the difference in proportions to be statistically significant and obtained one of the following numbers for the p-value. Which is it?
a. 1.5
b. 0.02
c. 0.78
d. 0.30
Answers
Answer:
Option B - 0.02
Step-by-step explanation:
In this question, the p-value is used to tell us the probability that a difference of (0.88 – 0.68) which is 0.2 or greater would occur in the distribution of simulated differences. This is created done with the assumption that there is no true difference in the two populations.
Due to the fact that the researchers found the difference in proportions to be statistically significant, hence these results would rarely occur due to just the sampling variability and thus the p-value must be small.
Looking at the options, the p-value in Option (B) will be the correct response,l as it indicates that a difference of 0.2 or more would only occur about 2% of the time by chance alone provided the proportion who text were the same in the population of seniors and the population of freshmen. This resonates well with the claim that the difference in proportions is statistically significant.
Thus, Option B is the correct answer.
A normally distributed data set with a mean of 35 and a standard deviation of 5 is represented by the normal curve. What is the z–score corresponding to 45?
Answers
Answer:
The z–score corresponding to 45 is z=2.
Step-by-step explanation:
We have a random variable X represented by a normal distribution, with mean 35 and standard deviation 5.
The z-score represents the value X relative to the standard normal distribution. This allows us to calculate probabilities for any given normal distribution with the same table.
The z-score for X=45 can be calculated as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{45-35}{5}=\dfrac{10}{5}=2[/tex]
The z–score corresponding to 45 is z=2.
How much dirt is in a hole that is 3 in by 3 in by 1 ft? Please give a detailed explanation for Brainliest.
Answers
Answer:
Well the best answer would be 1 0.75 cubic feet bag of dirt
Step-by-step explanation:
Misty surgery lasted 2 1/4 hours. Convert the time to seconds
Answers
======================================================
Work Shown:
1 hour = 60 minutes
2 hours = 120 minutes (multiply both sides by 2)
1/4 hour = 15 minutes (divide both sides of the first equation by 4)
2 & 1/4 hours = 2 hours + 1/4 hour
2 & 1/4 hours = 120 minutes + 15 minutes
2 & 1/4 hours = 135 minutes
---------------------
1 minute = 60 seconds
135 minutes = 8100 seconds (multiply both sides by 135)
2 & 1/4 hours = 8100 seconds
We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measured in feet, after t seconds is h ( t ) = − 16 t 2 + 128 t + 320 . What is the highest altitude that the object reaches?
Answers
Answer:
The highest altitude that the object reaches is 576 feet.
Step-by-step explanation:
The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be [tex]h(t) = -16\cdot t^{2} + 128\cdot t + 320[/tex], the first and second derivatives are, respectively:
First Derivative
[tex]h'(t) = -32\cdot t +128[/tex]
Second Derivative
[tex]h''(t) = -32[/tex]
Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:
[tex]-32\cdot t +128 = 0[/tex]
[tex]t = \frac{128}{32}\,s[/tex]
[tex]t = 4\,s[/tex] (Critical value)
The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:
[tex]h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320[/tex]
[tex]h(4\,s) = 576\,ft[/tex]
The highest altitude that the object reaches is 576 feet.
(06.01 MC) What is the value of the expression shown below? 8 + (7 + 1) 2 ÷ 4 ⋅ (5 points) Select one: a. 7 b. 9 c. 21
Answers
Answer:
b. 9
Just use PEMDAS
Dividends Per Share Seventy-Two Inc., a developer of radiology equipment, has stock outstanding as follows: 60,000 shares of cumulative preferred 3% stock, $20 par and 410,000 shares of $25 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $34,000; second year, $76,000; third year, $80,000; fourth year, $100,000. Determine the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "0.00". 1st Year 2nd Year 3rd Year 4th Year Preferred stock (dividends per share) $ 0.57 $ 0.63 $ 0.6 $ 0.6 Common stock (dividends per share) 0.00 0.09
Answers
Answer and Step-by-step explanation:
The computation of dividends per share on each class of stock for each of the four years is shown below:-
Particulars 1st year 2nd-year 3rd-year 4th year
Preferred dividend
paid a $34,000 $38,000 $36,000 $36,000
Number of preferred
stock b 60,000 60,000 60,000 60,000
Dividend per share
(a ÷ b) $0.57 $0.63 $0.60 $0.60
Dividend paid to common
stockholders c $0 $38,000 $44,000 $64,000
Number of common stock
shares d 410,000 410,000 410,000 410,000
Dividend per share
on common stock $0 $0.093 $0.11 $0.16
(c ÷ d)
Working note:
Preferred dividend = Number of preferred stock shares × Par value per share × Percentage of dividend
= 60,000 × $20 × 3%
= $36,000
Preferred stock
For 1st year
= $34,000
For 2nd-year
Dividend in year 2+ Dividend balance in year 1
= $36,000 + ($36,000 - $34,000)
= $38,000
For 3rd-year
= $36,000
For 4th year
= $36,000
Common stock dividend
Particulars 1 year 2 year 3 year 4 year
Total dividend paid $34,000 $76,000 $80,000 $100,000
Less:
Preferred stock
dividend $34,000 $38,000 $36,000 $36,000
Dividend paid to common
stockholders $0 $38,000 $44,000 $64,000
SNOG PLEASE HELP! (x-1)(y+8)
Answers
Answer:
xy + 8x - y - 8
Step-by-step explanation:
We can use the FOIL method to expand these two binomials. FOIL stands for First, Outer, Inner, Last.
F: The First means that we multiply the first terms of each binomial together. In this case, that would be x · y = xy.
O: The Outer means that we multiply the outer terms, or the first term of the first binomial and the second term of the last binomial, together. In this case, that would be x · 8 = 8x.
I: The Inner means that we multiply the inner terms, or the second term of the first binomial and the first term of the second binomial, together. In this case, that would be (-1) · y = -y.
L: The Last means that we multiply the last terms of each binomial together. In this case, that would be (-1) · 8 = -8.
Adding all of these together, we get xy + 8x - y - 8 as our final answer.
Hope this helps!
Answer:
[tex]xy+8x-y-8[/tex]
Step-by-step explanation:
=> (x-1)(y+8)
Using FOIL
=> [tex]xy+8x-y-8[/tex]
The expression 3 × 7 – 4 × 8 + 2 is equivalent to which of the following?
Answers
Answer:
-9
Step-by-step explanation:
3 time 7
minus
4 times 8
21 - 32
-11+2= -9
If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion? When a number is divisible by 9, the number is divisible by 3.
Answers
Answer:
when a number is divisible by 9, then the number is divisible by 3.
Step-by-step explanation:
They tell us "When a number is divisible by 9, the number is divisible by 3" we could change it by:
when a number is divisible by 9, then the number is divisible by 3.
Which makes sense because the number 9 is a multiple of the number 3, which means that the 9 can be divided by 3, therefore, if the number can be divided by 9, in the same way it can be divided by 3 .
Answer:
a
Step-by-step explanation:
A 12 sided die is rolled the set of equally likely outcomes is 123 456-789-10 11 and 12 find the probability of rolling a number greater than three
Answers
Answer:
6
Step-by-step explanation:
nerd physics
QUICK HELP HURRY! Simplify the expression. [tex]10^{-2} +10^{-1}[/tex]
Answers
Answer:
11/100 or 0.11
Step-by-step explanation:
10^-2 is also equal to 1/100
10^-1 is also equal to 1/10
Simply add them now:
1/100+1/10
= 1/100+ 10/100
= 11/100=0.11
Hope this helped!
if 2 X degree is the exterior angle of triangle and x degree and 45 degree are opposite interior angle find the value of x degree
Answers
Answer:
x = 45 degrees
Step-by-step explanation:
The measure of exterior angles is equal to the sum of non-adjacent interior angles
=> 2x = x+45
=> 2x-x = 45
=> x = 45 degrees
Answer:
45 degrees.
Step-by-step explanation:
The exterior angle = sum of the 2 opposite interior angles.
2x = x + 45
2x - x = 45
x = 45.
What is the range of the graph of the equation y= k/x?
Answers
Answer:
all real number except 0
Step-by-step explanation:
Tony used a photocopier to dilate the design for a monorail track system. The figure below shows the design and its photocopy
A
10 m
B
F
E
8 m
D
D
С
G
Design
Photocopy
The ratio of CD:GH is 2:3. What is the length, in meters, of side EH on the photocopied image? (5 points)
Answers
Answer:
12 m
Step-by-step explanation:
Given that the design, ABCD, was dilated to get a photocopy, EFGH, a scale factor or ratio was multiplied by the original lengths of the design to get the new measurement of the photocopy.
Thus, we are given the ratio, CD:GH = 2:3.
This means, any of the corresponding lengths of both figures would be in that same ratio.
Using the ratio of the design to the photocopy, 2:3, we can find the length of side EH of the photocopy.
The corresponding side of EH in the design is AD = 8m. Thus, AD to EH = ⅔
[tex] \frac{AD}{EH} = \frac{2}{3} [/tex]
[tex] \frac{8}{EH} = \frac{2}{3} [/tex]
Cross multiply
[tex] 3*8 = 2*EH [/tex]
[tex] 24 = 2*EH [/tex]
Divide both sides by 2 to make EH the subject of formula
[tex] \frac{24}{2} = \frac{2*EH}{2} [/tex]
[tex] 12 = EH [/tex]
The length of side EH = 12 m
Which is the best description for the graph?
The graph is increasing everywhere
The graph is decreasing everywhere
The graph is increasing then decreasing
The graph is decreasing then increasing
Answers
Answer:
D
Step-by-step explanation:
It's decreasing then once it hits the origin, it starts to increase again. I hope this helps you:)
Answer:
D
Step-by-step explanation:
Please answer this correctly
Answers
Answer:
3/20s
Step-by-step explanation:
Factor: 3d + 6d + 3.
Answers
Hey there! :)
Answer:
3(d + 1)²
Step-by-step explanation:
Given 3d² + 6d + 3:
Begin by factoring out '3' from each term:
3(d² + 2d + 1)
Factor terms inside of the parenthesis:
3(d + 1)(d + 1) or 3(d + 1)².
Answer quick! EASY! WILL GIVE YALL BRAINLIESTTT
Answers
Answer:
7
Step-by-step explanation:
:)
of the following fractions which is 50% greater than 3/7
Answers
Answer:
9/14
Step-by-step explanation:
3/7 + 50%×3/7 =
= 3/7 + 1/2×3/7
= 3/7 + 3/14
= 6/14 + 3/14
= 9/14
The required fraction which 50% grater than 3/7 is 9/14.
Fraction to determine that 50% grater than 3/7.
Fraction of the values is number represent in form of Numerator and denominator.
Here, fraction = 50% grater than 3/7
= 1.5 x 3/7
= 4.5/7
= 45/70
= 9/14
Thus, The required fraction which 50% grater than 3/7 is 9/14.
Learn more about fraction here:
https://brainly.com/question/10354322
#SPJ5
What is the volume of this aquarium?
Answers
Answer:
9,000 inches^3
Step-by-step explanation:
The first part is 20 x 20 x 20, which equals 8,000
The second part is 10 x 10 x 10, which is 1,000
1,000 + 8,000 = 9,000
A certain shampoo is available in two sizes. A 13.5 ounces bottle cost $2.98. A 29.2 ounce bottle cost $6.12. Find the Unit price for each size. Then state which size is the better buy based on the unit price. Round your answer to the nearest cent
Answers
Answer:
9.2 ounce bottle cost $6.12 is better buy with unit price of $0.22
Step-by-step explanation:
Unit price of any product is given by
unit price = weight of product/ price of product
Given sizes
A
13.5 ounces bottle cost $2.98
cost of 1 ounce of shampoo for this size = cost price/weight of shampoo
cost of 1 ounce of shampoo for this size =2.98/13.5 = $0.22
Unit price for this size is $.022
B
9.2 ounce bottle cost $6.12
cost of 1 ounce of shampoo for this size = cost price/weight of shampoo
cost of 1 ounce of shampoo for this size =6.12/9.2 = 0.66
Unit price for this size is $0.66
As $0.22 is less than $0.66 thus,
9.2 ounce bottle cost $6.12 is better buy.
College students spend $183 more each year on textbooks and course materials than on computer equipment. They spend a total of $819 on textbook and course materials and equipment each year. How much is spent each year on textbooks and course materials and computer equipment?
Answers
Answer:
Textbooks: $506Course Materials and Electronics: $323Step-by-step explanation:
First, we need to divide the amount into 2 equal parts:
$819/2 = $414.50
Now, because they spent $183 more on textbooks, we add half of that to $414.50.
$414.50 + $91.50 = $506
$414.50 - $91.50 = $323
To make sure that the amount spent on textbooks is $183 more than the amount spent on course materials and computers, we need to add $183 to $323. If we get $506, our answer is correct.
$323 + $183 = $506 ✅
Textbooks: $506Course Materials and Electronics: $323I'm always happy to helpA man bought a pair of jeans for $23.00 a shirt for $14.00 and two ties for $7.98 each. What was the total cost of his clothing ?
Answers
Answer:
$52.96
Step-by-step explanation:
To find the total cost of his clothing, add up the prices of everything he bought.
Jeans: $23.00
Shirt: $14
Ties: 2 ties for $7.98 each.
Each tie costs $7.98, and the man bought two ties. Therefore, multiply 2 and $7.98
2*$7.98 = $15.96
Add all the prices together.
jeans + shirt + ties
$23 + $14 + $15.96
$37 + $15.96
$52.96
The total cost of his clothing is $52.96
Answer:
total cost=52.96
Step-by-step explanation:
Things he bought:
jeans for $23.00
a shirt for $14.00
two ties for $7.98 each
the total const would be the sum of all his clothes
which is
jeans for $23.00
+shirt for $14.00
+one tie for $7.98
+one tie for $7.98
_______________
total cost=52.96
HOPE IT HELPS :0
PLEASE MARK IT THE BRAINLIEST!
Helppp Please!!!!!!!!!
Answers
Answer:
B. 17°.
Step-by-step explanation:
To solve the problem, we can use SOH CAH TOA.
SOH = Sine, Opposite divided by Hypotenuse
CAH = Cosine, Adjacent divided by Hypotenuse
TOA = Tangent, Opposite divided by Hypotenuse
In this case, we are given both the opposite and the hypotenuse, so we will use sine to solve it.
sine(N) = 4 / 14
sine(N) = 2 / 7
N = sec(2/7)
N = 16.6015496, which is about B. 17°.
Hope this helps!
Multiply: –c2(3c – 2)
Answers
Answer:
3c^3+2c^2
Step-by-step explanation:
Answer:
3c^3 +2c^2
Step-by-step explanation:
–c^2(3c – 2)
Distribute
=c^2 * 3c - c^2 * -2
3c^3 +2c^2