Answer:
The system is dependent:
x=-3t-7
y=-5t-15
z=t
Step-by-step explanation:
I chose to use a matrix to solve this system of equations. Once put into matrix form, you need to row reduce the system into its simplest form (Row Reduced Echelon form). Doing this, we find that the system is dependent on the z variable. And following usual procedures, we let z equal some other letter; which is t in this case. Then we isolate each variable to get the answer.
Check the attachment for the work.
[The arrows indicate a row swap and the parenthesis indicates addition if a constant multiple of one row to another]
If x represents the rate that Joy traveled at for the first half of the trip, write an
expression that represents the amount of time it takes Joy to complete the second half of the
trip at the slower rate.
Answer:
time taken for trip 2nd half > time taken for trip 1st half
Step-by-step explanation:
Let the total distance of Joy's trip be = D
Then, the first half distance travelled = D/2
The rate (speed) at which Joy travels during first half = x
So, time taken to travel first half = Distance / Speed
= (D/2) / x = D / 2x
Second half of trip distance travelled = remaining D/2Let the rate (speed) at which Joy travels during second half = x'
As given, x' (second half speed) < x (first half speed)
So, time taken to travel first half = Distance / Speed
(D/2) / x' = D / 2x'
As x' < x : D / 2x' > D / 2x .
Trip 1st half Time taken trip < 2nd half ; or trip 2nd half time taken > 1st half
The time required for workers to produce each unit of a product decreases as the workers become more familiar with the production procedure. It is determined that the function for the learning process is T(x) = 2 + 0.3 1 x , where T(x) is the time, in hours, required to produce the xth unit. Find the time required for a new worker to produce units 10 through 19.
Answer: 2.79 hours.
Step-by-step explanation:
Given that the function for the learning process is T(x) = 2 + 0.3 1 x , where T(x) is the time, in hours, required to produce the xth unit
To calculate the time for the new worker to produce 10 units, substitute 10 for x in the equation above.
T(x) = 2 + 0.31 (10)
T(x) = 2 + 3.1
T(x) = 5.1 hours
To calculate the time for the new worker to produce 19 units, substitute 19 for x in the equation above.
T(x) = 2 + 0.31(19)
T(x) = 2 + 5.89
T(x) = 7.89 hours
The time required for a new worker to produce units 10 through 19 will be
7.89 - 5.1 = 2.79 hours
Mark each of the following as true or false and explain how you know.
true false false true...is the quick answer
Remember that negatives are always less than positive numbers.
please help me to answer this question
Answer:
I can not see any questions
Jamar rolls a 6-sided number cube with the numbers 1 through 6 on it. What is the
probability that he does not roll a prime number?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
In a 6 sided die, the numbers that are possible to be rolled are
1, 2, 3, 4, 5, and 6.
We know that the numbers 2, 3, and 5 are prime, while 1, 4, and 6 are not.
3 out of the 6 numbers are prime, therefore 3 out of the 6 numbers are not prime.
So the fraction is [tex]\frac{3}{6}[/tex]
This simplifies to [tex]\frac{1}{2}[/tex].
Hope this helped!
Answer:
1/2
Step-by-step explanation:
the prime numbers between 1 and 6 inclusive are: 2, 3, 5 (i.e 3 possible outcomes)
the non prime numbers are : 1, 4 and 6 (i.e 3 possible outcomes)
for each roll, the total number of possible outcomes is 6 (because its a 6-sided die)
P(does not roll a prime number) = P (rolls 1, 4 or 6)
= number of possible non-prime outcomes / total number of outcomes
= 3/6
= 1/2
determine x in the following equation 2x - 4 = 10
Answer:
7
Step-by-step explanation:
10+4 = 14
14/2 = 7
x = 7
The mean area of 7 halls is 55m².If the mean of 6 of them be 58m², find the area of the seventh all.
Answer:
Area of 7th hall = 37 m^2
Step-by-step explanation:
Total area of 7 halls = 7*55 = 385
Total area of 6 halls = 6*58 = 348
Area of 7th hall = 385-348 = 37 m^2
Answer:
The area of the seventh hall = 37m²
Step-by-step explanation:
for 6 halls
Mean area of 6 halls = 58m²
[tex]Mean\ area = \frac{sum\ of\ areas}{Number\ of\ halls} \\58\ =\ \frac{sum\ of\ areas}{6} \\sum\ of\ areas\ of\ 6\ halls\ = 58\ \times\ 6 = 348\\sum\ of\ areas\ of\ 6\ halls\ = 348[/tex]
Let the area of the 7th hall be x
The sum of the areas of 7 halls = 348 + x - - - - - - (1)
[tex]Mean = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\55 = \frac{sum\ of\ the\ areas\ of\ 7\ halls}{7} \\sum\ of\ the\ areas\ of\ 7\ halls\ = 55\ \times\ 7\ = 385\\sum\ of\ the\ areas\ of\ 7\ halls\ =\ 385 - - - - (2)[/tex]
notice that equation (1) = equation (2)
348 + x = 385
x = 385 - 348 = 37m²
Therefore, the area of the seventh hall = 37m²
If 2y = 6 - 3x, find y when x = 0
Answer:
2y= 6-3x when x=0
2y= 6-3(0)
2y= 6-0
2y= 6
y= 6/2
y= 3
#i'm indonesian
#hope it helps.
Answer:
[tex] \boxed{y = 3}[/tex]
Step-by-step explanation:
Given, x = 0
[tex] \mathsf{2y = 6 - 3x}[/tex]
plug the value of x
⇒[tex] \mathsf{2y = 6 - 3 \times 0}[/tex]
Multiply the numbers
⇒[tex] \mathsf{2y = 6 - 0}[/tex]
Calculate the difference
⇒[tex] \mathsf{2y = 6}[/tex]
Divide both sides of the equation by 2
⇒[tex] \mathsf{ \frac{2y}{2} = \frac{6}{2} }[/tex]
Calculate
⇒[tex] \mathsf{y = 3}[/tex]
Hope I helped!
Best regards!
Emily made a pot cream of pumpkin soup for thanksgiving dinner she put 5 cups of cream in the soup she poured the soup into 24 small bowl show much cream measured in oz is used for each small bowl of soup?
Answer:
each bowl can contain 5/3 oz. of soup.
Step-by-step explanation:
1 cup = 8 oz.
8 oz.
5 cups x -------------- = 40 oz.
1 cup
to get the measurement of each bowl,
40 oz. divided into 24 bowls.
therefore, each bowl can contain 5/3 oz. of soup.
“Type ‘equal, supplementary, complementary, or vertical in the space provided’”
Answer:
Supplementary
Step-by-step explanation:
When the sum of 2 angles equal 180°, they are called supplementary angles. And they also form a straight line together.
<AOB (40°) and <BOC (140°) are not equal angles.
<AOB (40°) and <BOC (140°) are not complementary angles. Complementary angles add up to equal 90°.
<AOB (40°) and <BOC (140°) are not vertical angles. Vertical angles are opposite angles formed when two lines intersect.
<AOB (40°) and <BOC (140°) are supplementary angles. They add up to equal 180°.
In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?
Answer:the mean is greater than the median
Step-by-step explanation:
The mean is less than the median. Then the correct option is A.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
Half the students scored 87.
The next highest score is 71.
Then the median will be
(71+ 87) / 2 = 79
A few students scored 52, so the mean is slightly lower than the mean of 71 and 87.
Thus, the mean is less than the median.
Then the correct option is A.
The missing options are given below.
A. The mean is less than the median.
B. The mean and the median is the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
More about the statistics link is given below.
https://brainly.com/question/10951564
#SPJ2
Write a variable expression for a number w increased by 4 (A) 4 ÷ w (B) w + 5 (C) w + 4
Answer:
C) w+4
Step-by-step explanation:
w=the variable
+4= increased by 4
HOPE THIS HELPS!!!!!! :)
<33333333333
The data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of and use a class width of . Does the frequency distribution appear to be roughly a normal distribution?
Answer:
The frequency distribution does not appear to be normal.
Step-by-step explanation:
The data provided is as follows:
S = {0.38 , 0 , 0.22 , 0.06 , 0 , 0 , 0.21 , 0 , 0.53 , 0.18 , 0 , 0 , 0.02 , 0 , 0 , 0.24 , 0 , 0 , 0.01 , 0 , 0 , 1.28 , 0.24 , 0 , 0.19 , 0.53 , 0 , 0, 0.24 , 0}
It is provided that the first lower class limit should be 0.00 and the class width should be 0.20.
The frequency distribution table is as follows:
Class Interval Count
0.00 - 0.19 21
0.20 - 0.39 6
0.40 - 0.59 2
0.60 - 0.79 0
0.80 - 0.99 0
1.00 - 1 . 19 0
1.20 - 1. 39 1
The frequency distribution does not appear to be normal. This is because the frequencies does not start and end at almost equivalent points and the mid-distribution does not consist of the highest frequency.
Thus, the frequency distribution does not appear to be normal.
Help!!!!!!! Thank you!!!!!!!
Answer:
D
Step-by-step explanation:
The ratio of yellow paint to blue paint is 4:3. We can make the largest amount of green paint by using all of the 20 quarts of yellow paint so we have to solve for x in 4:3 = 20:x, since 4 * 5 = 20, 3 * 5 = x so we use 15 qts of blue paint, therefore we will have 20 + 15 = 35 qts of green paint.
Answer:
D
Step-by-step explanation:
Joy is preparing 20 liters of a 25% saline solution. She has only a 40% solution and a 10% solution in her lab. How many liters of the 40% solution and how many liters of the 10% solution should she mix to make the 25% solution?
Answer:
10 Liters of 40% solution
Step-by-step explanation:
Answer:
10 liters of the 40% solution, and 10 liters of the 10% solution
Step-by-step explanation:
Let us say that x = the liters of the 40% solution, and y = liters of the 10% solution in her lab. We know that Joy is preparing a solution containing a total 20 liters, so x + y = 20. We can respectively create the following system of equations,
x + y = 20,
0.40x + 0.10y = 0.25 ( 20 )
And now we have to solve this system of equations for x and y, the liters of the 40% solution and the liters of the 10% solution,
[tex]\begin{bmatrix}x+y=20\\ 0.4x+0.1y=0.25\left(20\right)\end{bmatrix}[/tex] ( Substitute x as 20 - y )
[tex]0.4\left(20-y\right)+0.1y=0.25\cdot \:20\end{bmatrix}[/tex] ( Isolate y )
[tex]8-0.3y=5[/tex] ⇒ [tex]80-3y=50[/tex] ⇒ [tex]-3y=-30[/tex] ⇒ y = 10
[tex]x=20-10 = 10[/tex] ⇒ x = 10
Therefore, there are 10 liters of both the 40% and 10% solution.
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped10 times and the man is asked to predict the outcome in advance. He gets 7 out of10 correct. What is the probability that he would have done at least this well if hehad no ESP?
Answer:
I would say 70%
Step-by-step explanation:
He got 7 of of 10 (7/10 = 70%) right so I would say he would do just as well without ESP since it doesn't exist.
A middle school has 470 students. Regina surveys a random sample of 40 students and finds that 28 have cell phones. How many students at the school are likely to have cell phones? A. 132 students B. 188 students C. 329 students D. 338 students Please include ALL work! <3
Answer:
C. 329
Step-by-step explanation:
So 28 is 70% of 40
so we know that 70% percent of students have phones
70% of 470
329
Thats how I solved it have a great day :)
Can somebody please solve this problem for me!
Answer:
x = 200.674
Step-by-step explanation:
tan∅ = opposite/adjacent
Step 1: Find length of z
tan70° = 119/z
ztan70° = 119
z = 119/tan70°
z = 43.3125
Step 2: Find length z + x (denoted as y)
tan26° = 119/y
ytan26° = 119
y = 119/tan26°
y = 243.986
Step 3: Find x
y - z = x
243.986 - 43.3125 = x
x = 200.674
I need help on this question
Answer:
Figure G.
Step-by-step explanation:
Let's check through the values and calculate the radius and area for all the circle.
For circle R
Diameter = 2 feet
Radius= 1 feet
Area= πr²
Area= 3.14*1
Area= 3.14 feet²
CircleS
Diameter= 4 feet
Radius= 2 feet
Area= πr²
Area= 3.14*2²
Area= 12.56 feet²
Circle T
Diameter= 8 feet
Radius= 4 feet
Area = π r²
area= 3.14*4²
Area=50.24 feet²
Circle U
Diameter= 12 feet
Radius= 6 feet
Area = π r²
area= 3.14*6²
Area=113.04 feet²
The values of the radius and Area all match the graph in figure G
A die is rolled five times and the number of fours that come up is tallied. Find the probability of getting the given result. Exactly 3 fours.
A. 0.161
B. 0.002
C. 0.116
D. 0.216
Answer:
0.0321
Step-by-step explanation:
This can be found by binomial probability distribution as the probability of success is constant. There are a given number of trials. the successive tosses are independent.
Here n= 5
The probability of getting a four in a roll of a die = 1/6
The probability of not getting a four in a roll of a die = 5/6
The probability of getting exactly three 4s in five throws is given by
5C3 (1/6)³ (5/6)² = 10 (0.0046) (0.694)= 0.0321
Help someone please!!
Answer:
A. 5:4
Step-by-step explanation:
Since the question mentions twelfths of a pie, it is easier to say each pie has 12 pieces or 36 total pieces ordered from the 3 pies. Ty ate 5 and Rob ate 15 which is 3 times more than Ty. A total of 20 pieces have been eaten from the 36 you started with. Eaten = 20 and Remaining = 16. So the ratio is 20:16 which is simplified to 5:4.
Help plz! Jim is climbing a mountain that has a base 150 feet above sea level. If he climbs 233 feet then descends into a cave 64 feet, how far above sea level is Jim
Answer:
150+233-64=319
Jim is 319 ft above sea level.
Step-by-step explanation:
-50 POINTS- please help
Answer:
-13
-10
Step-by-step explanation:
A x = B
To find X
A ^ -1 A x = A ^ -1 B
x = A^ -1 B
x = -3/2 -5/2 2
-1 -2 4
Across times down
-3/2 * 2 + -5/2 *4 = -13
-1 *2 -2 * 4 = -10
The matrix is
-13
-10
Answer:
[tex]\Large \boxed{\bold{D.} \ \left[\begin{array}{ccc}-13\\ -10\end{array}\right]}[/tex]
Step-by-step explanation:
[tex]AX=B[/tex]
To find [tex]X[/tex]
[tex]X=A^{-1} \cdot B[/tex]
[tex]\displaystyle \left[\begin{array}{ccc}-\frac{3}{2} \cdot 2 + - \frac{5}{2} \cdot 4\\ -1 \cdot 2 + -2 \cdot 4\end{array}\right][/tex]
[tex]\displaystyle \left[\begin{array}{ccc}-3 + - 10\\ -2 + -8\end{array}\right][/tex]
[tex]\displaystyle \left[\begin{array}{ccc}-13\\ -10\end{array}\right][/tex]
Please answer this correctly without making mistakes
Answer:
2 13/15 miles
Step-by-step explanation:
Hey there!
Well first we need to find the distance between Lancaster and Hillsdale and Lancaster to Silvergrove.
9 + 7 13/15
= 16 13/15
LS is just 14 miles.
Now we can do,
16 13/15 - 14
= 2 13/15 miles
Hope this helps :)
Determine whether Rolle's Theorem can be applied to f on the closed interval
[a, b].
f(x) = −x2 + 3x, [0, 3]
Yes, Rolle's Theorem can be applied.No, because f is not continuous on the closed interval [a, b].No, because f is not differentiable in the open interval (a, b).No, because f(a) ≠ f(b).
If Rolle's Theorem can be applied, find all values of c in the open interval
(a, b)
such that
f '(c) = 0.
(Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)
c =
Answer:
Yes, Rolle's theorem can be applied
There is only one value of c such that f'(c) = 0, and this is c = 1.5 (or 3/2 in fraction form)
Step-by-step explanation:
Yes, Rolle's theorem can be applied on this function because the function is continuous in the closed interval (it is a polynomial function) and differentiable in the open interval, and f(a) = f(b) given that:
[tex]f(0)=-0^2+3\,(0)=0\\f(3)=-3^2+3\,(3)=-9+9=0[/tex]
Then there must be a c in the open interval for which f'(c) =0
In order to find "c", we derive the function and evaluate it at "c", making the derivative equal zero, to solve for c:
[tex]f(x)=-x^2+3\,x\\f'(x)=-2\,x+3\\f'(c)=-2\,c+3\\0=-2\,c+3\\2\,c=3\\c=\frac{3}{2} =1.5[/tex]
There is a unique answer for c, and that is c = 1.5
Rolle's theorem is applicable if [tex]f(a)=f(b)[/tex] and $f$ is differentiable in $(a,b)$
since it's polynomial function, it's always continuous and differentiable..
and you can easily check that $f(0)=f(-3)=0$
so it is applicable.
now, $f'(x)=-2x+3=0 \implies x=\frac32$
there is only once value (as you can imagine, the graph will be downward parabola)
Solve for x: x/25 > 5
Answer:
x>125
Step-by-step explanation:
Answer:
x > 125
Step-by-step explanation:
Multiply each side by 25, so it now looks like this: x > 125I hope this helps!
The fastest fish in the world is the sailfish. If a
sailfish could maintain its speed, as shown in the
table, how many miles could the sailfish travel in 6
hours?
p.s the top is hour traveled and the bottom is miles traveled
Answer:
(C) 408 miles
Step-by-step explanation:
Looking at this table, we can see that the beginning point is (0,0) so this is a linear slope, meaning we won’t have to add anything.
This means that for every time we rise in x, y will rise by the same amount.
When x is 1, y is 68 - so the constant of proportionality here is 68.
So, to find how much 6 hours would be we just multiply.
[tex]6\cdot68=408[/tex]
Hope this helped!
800,000+700 standard form
Answer:
800700
Step-by-step explanation:
800000 + 00000 + 0000 + 000 + 00 + 0
000000 + 00000 + 0000 + 700 + 00 + 0
------------------------------------------------------------
= 800700
Answer:
Hey there!
800000+700=800700
Hope this helps :)
Write a differential equation that fits the physical description. The at time t is proportional to the power of its .
Complete Question
The complete question is shown on the first uploaded image
Answer:
The differential equation that fits the physical description is [tex]\frac{d (v(t))}{dt} = z [v(t)]^2[/tex]
Step-by-step explanation:
From the question we are told that
The acceleration due to air resistance of a particle moving along a straight line at time t is proportional to the second power of its velocity v, this can be mathematically represented as
[tex]a(t) \ \ \alpha \ \ \ [v(t)]^2[/tex]
Where [tex]a(t)[/tex] is the acceleration at time t
and [tex]v(t)[/tex] is the velocity at time t
So
=> [tex]a(t)= z [v(t)]^2[/tex]
Where z is a constant
Generally acceleration is mathematically represented as
[tex]a(t) = \frac{d (v(t))}{dt}[/tex]
So
[tex]\frac{d (v(t))}{dt} = z [v(t)]^2[/tex]
Gavin goes to the market and buys one rectangle shaped board. The length of the board is 16 cm and width of board is 10 cm. If he wants to add a 2 cm wooden border around the board, what will be the area of the rectangle board?
Answer:
The answer is 216
Step-by-step explanation:
if there is a 2 cm border, that means that the sides will both become 2 centimeters longer. so (16+2)*(10*2) = 18*12 = 216.