Answer:
True
Step-by-step explanation:
First statement
[a b c | d][x]
[a b c]x=d
ax+bx+cx=d
Second statement
Ax=d
Given that A = [a b c]
[a b c]x=d
ax+bx+cx=d
ax+bx+cx=d
Then, they are going to have the same solutions
The statement is false. The solution sets for the augmented matrix [a, b, c, d] and the matrix equation Ax = d (where A = [a, b, c]) are not the same unless 'd' is consistently a column vector with 'a', 'b', 'c'.
Explanation:The statement presented in the question is false. When we talk about a linear system, an augmented matrix generally pairs a coefficient matrix with an answer matrix. This would look like [A|d], where 'A' would be a matrix, and 'd' is the constants column vector.
Conversely, Ax = d is a matrix equation where 'A' is again the coefficient matrix, 'x' is the variable matrix, and 'd' is the constants column vector.
In your provided augmented matrix, [a b c d], unless 'd' is a consistent column vector with the other column vectors, it can't be virtually the same as the matrix system Ax = d where A = [a b c] because the augmented matrix [a b c d] would mean that A = [a b c] and d = [d].
Unless 'd' is mathematically consistent with the column vectors 'a', 'b', and 'c', the solution sets would not be the same.
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Trish made a few pans of brownies to sell. Rachel also contributed 5 pans. Each pan of brownies was cut into 12 squares. If there were a total of 84 brownie squares, how many pans of brownies did Trish make ? Answer must be a two-step equation!!
Answer:
Trisha made 2 pans of brownies.
Step-by-step explanation:
Let the number of pans of brownies made by Trisha be 'x'.
Given:
Number of pans contributed by Rachel = 5
Number of squares in each pan = 12
Total number of squares (S) = 84
Total number of pans (N) = Number of pans by Trisha (x) + Number of pans by Rachel
So, [tex]N=x+5[/tex] -------- (1)
Total number of squares (S) = Number of squares in each pan × Number of pans (N).
[tex]S = 12N\\84=12N---- (2)[/tex]
Plug in the value of 'N' from equation (1) in equation (2). This gives,
[tex]84=12(x+5)[/tex]
Solve for 'x'.
[tex]12(x+5)=84\\\\x+5=\frac{84}{12}\\\\x+5=7\\\\x=7-5=2[/tex]
Therefore, Trisha made 2 pans of brownies.
The measures of the angles of XYZ are in the ratio 1:4:10. What are the measures of the angles?
(SHOW YOUR WORK)
Answer:the angles are 12 degrees, 48 degrees and 120 degrees.
Step-by-step explanation:
The sum of the angles in a triangle is 180 degrees.
The measures of the angles of XYZ are in the ratio 1:4:10. The total ratio is the sum of the proportion of each angle. It becomes
1 + 4 + 10 = 15
Therefore, the measure of the first angle would be
1/15 × 180 = 12 degrees
Therefore, the measure of the second angle would be
4/15 × 180 = 48 degrees
Therefore, the measure of the third angle would be
10/15 × 180 = 120 degrees
An urn contains n white and m black balls, where n and m are positive numbers.
(a) If two balls are randomly withdrawn, what is the probability that they are the same color?
(b) If a ball is randomly withdrawn and then replaced before the second one is drawn, what is the probability that the withdrawn balls are the same color?
(c) Show that the probability in part (b) is always larger than the one in part (a).
Answer:
a) (n²-n+m²-m)÷((n+m)×(n+m-1))
b)(n²+m²)÷(n+m)
c) part b is larger ,check below.
Step-by-step explanation:
a)If there are n white and m black balls ,total will be n+m balls. Let's find the probability of choosing two balls white.
First ball as white n÷(n+m) second ball to be white again is n-1÷(n+m-1) the reason why we take away 1 is because we already chose one white ball in the beginning .So the probability will be product of these to get the both balls white.
Let's find the the probability of choosing both black.Same strategy ,first ball black is m÷(n+m),second ball black is m-1÷(n+m-1).So the probability will be product of these to get the both balls black. We should add the final products and simplify
b)Because this time they are replacing the ball ,we will not take away 1.So to get both white probability is n÷(n+m) times n÷(n+m) .The probability of both black is m÷(n+m) times m÷(n+m).Add the products .
c) b will be always larger,We should compare the final products.
In b (n²+m²) is divided by (n+m)
In a (n²-n+m²-m)÷((n+m)×(n+m-1)) less amount divided by a bigger value ,so it will result always with a smaller quotient
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
A. The volume of the cylinder with height 10 is 60π60π cubic inches greater than the volume of the cylinder with height 6.
B. The volume of the cylinder with height 6 is 60π60π cubic inches greater than the volume of the cylinder with height 10.
C. The volume of the cylinder with height 10 is 60π60π cubic inches greater than the volume of the cylinder with height 6.
D. The volume of the cylinder with height 6 is 60π60π cubic inches greater than the volume of the cylinder with height 10.
E. The volume of the cylinder with height 6 is 240π240π cubic inches greater than the volume of the cylinder with height 10.
Answer:
the cylinder with height 6 has a volume of 60/π in³ greater than the volume of the cylinder with height 10 (option B , if 60π is changed for 60/π)
Step-by-step explanation:
The volume of a cylinder is
V= π*R²*H (H=height)
since the length L of the piece of paper is L=2*π*R →R=L/(2*π) (since is rolled to form the cylinder), then:
V= π*R²*H = π*L²/(2*π)²*H = L²*H/(4*π)
with L=10 in and H= 6 in we have
V₂= L²*H/(4*π)
the other way around is changing H for L
V₁= H²*L/(4*π)
the difference between the volumes will be
V₂- V₁ = L²*H/(4*π) - H²*L/(4*π) = L*H *(L-H)/(4*π)
replacing values
V₂- V₁ = L*H *(L-H)/(4*π) = 10*6*(10-6)/(4*π) = 60/π in³
then the cylinder with height 6 has a volume of 60/π in³ greater than the volume of the cylinder with height 10
Paul travel to the lake and back. The trip took 3 hours and the trip back took 4 hours He averaged 10 mph faster on the trip there than on the return trip. What was Paul's average speed on the outbound trip
Answer:
40 mph
Step-by-step explanation:
We assume "outbound" refers to the trip to the lake. The ratio of speeds is inversely proportional to the ratio of times, so ...
outbound speed : inbound speed = 4 : 3
These differ by one ratio unit, so that one ratio unit corresponds to the speed difference of 10 mph. Then the 4 ratio units of outbound speed will correspond to ...
4×10 mph = 40 mph
Paul's average speed on the outbound trip was 40 mph.
___
The distance to the lake was 120 mi.
Answer:Paul's average speed on the outbound trip is 40mph
Step-by-step explanation:
Let x represent Paul's outbound trip which is the trip to the lake.
The trip to the lake took 3 hours.
Distance travelled = speed × time
It means that
Distance covered on the trip to the lake would be
3 × x = 3x
the trip back took 4 hours. He averaged 10 mph faster on the trip there than on the return trip. It means that his speed would be
x - 10
Therefore, distance travelled on return trip would be
4(x - 10) = 4x - 40
Since the distance travelled is the same, it means that
3x = 4x - 40
4x - 3x = 40
x = 40
Amy drives her car until the gas gauge is down to 1/8 full, then she fills the tank to capacity by adding 14 gallons. What is the capacity of the gas tank?
Answer:
Amy's car tank capacity is 16 gallons.
Step-by-step explanation:
Let the capacity of the tank be 'x'
Given:
Amount of gas in the car till it is refilled = [tex]\frac{1}{8}\times x = \frac{1}{8}x \ gallons[/tex]
Amount of gas added = 14 gallons.
We need to find the capacity of the tank.
Solution:
Now we can say that
Total Capacity of the tank is equal to sum of Amount of gas in the car till it is refilled and Amount of gas added.
framing in equation form we get;
[tex]x=\frac{x}{8}+14[/tex]
Combining the like terms we get;
[tex]x-\frac{x}{8}=14[/tex]
Now making the denominators common we will use L.C.M.
[tex]\frac{8x}{8}-\frac{x\times1}{8\times1}=14\\\\\frac{8x}{8}-\frac{x}{8}=14\\\\\frac{8x-x}{8}=14\\\\\frac{7x}{8}=14[/tex]
Now multiplying both side by 8 we get;
[tex]\frac{7x}{8}\times 8=14\times8\\\\7x = 112[/tex]
Now dividing both side by 7 we get;
[tex]\frac{7x}{7}=\frac{112}{7}\\\\x=16\ gallons[/tex]
Hence Amy's car tank capacity is 16 gallons.
The number of bacteria in a certain culture doubled every hour. If there were 30 bacteria present in the culture initially, how many bacteria will be present at the end of the 8th hour?
Answer:
The number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]
Step-by-step explanation:
Given the initially 30 bacteria present in the culture.
Also, the number of bacteria got doubled every hour.
So, using the equation
[tex]A=A_0r^{n-1}[/tex]
Where [tex]A[/tex] is number of bacteria after [tex]n[/tex] hours.
[tex]A_0[/tex] is bacteria present initially.
[tex]r[/tex] is the common ration, in our problem it is given that bacteria doubles every hour. So, [tex]r=2[/tex]
And [tex]n[/tex] is the number of hours. In our problem we need amount of bacteria at the end of [tex]8th[/tex] hours. So, [tex]n=8[/tex]
Plugging values in the formula we get,
[tex]A=30(2)^{8-1}\\A=30\times 2^7\\A=30\times 128\\A=3840[/tex]
So, number of bacteria after [tex]8th[/tex] will be [tex]3840[/tex]
QUESTION 1
Which of the following statements are mathematical statements?
A: All the ladies love me.
B: 5 = 7
C: Contemporary Math is the best class ever.
D: Bye, Felicia!
E: The square root of 64 is 8 something, right?
F: If the storm is coming, then the sky is blue.
A. B, F
B. B, E
C. A, C
D. E, F
E. A, B, C
F. B, D, F
Answer: B
Step-by-step explanation:
Mathematical statements are those that can be objectively proven true or false. Among the options provided, statements B and F qualify as mathematical statements. Therefore, the correct answer choice is A.
The student asks which of the following statements are mathematical statements:
A: All the ladies love me.
B: 5 = 7
C: Contemporary Math is the best class ever.
D: Bye, Felicia!
E: The square root of 64 is 8 something, right?
F: If the storm is coming, then the sky is blue.
Mathematical statements are statements that can be objectively proven true or false.
B: 5 = 7 - This is a mathematical statement because it can be proven false.F: If the storm is coming, then the sky is blue - This is a conditional statement that can be tested and verified within the realm of logic and mathematics.Thus, the correct answer is A. B, F
The graph below shows f(x) and its transformation g(x). Enter the equation for g(x) as your answer. G(x) =
Answer:
[tex]\displaystyle g(x) = 2^{x - 3}[/tex]
Explanation:
See above graph
The exponent gives you the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL.
I am joyous to assist you anytime.
Is my answer correct???
Answer:
Line segment is part of a line bounded by two endpoints
Step-by-step explanation:
Line segment is part of a line bounded by two endpoints
You're selling snacks at a basketball game you're offering up hotdogs and fries. Each hot dog costs 1.50 and each order of fries costs 0.50. At the end of the night you made a whopping $78.50! You sold a total of 87 hotdogs and orders of fried combined. How many hotdogs were sold and how many orders of fries? (Let x=number of hotdogs and y=number of orders of fries
Answer: the number of hotdogs that were sold is 35
the number of orders of fries is 52
Step-by-step explanation:
Let x represent the number of hotdogs that were sold.
Let y represent the number of orders of fries.
You sold a total of 87 hotdogs and orders of fried combined. This means that
x + y = 87
Each hot dog costs 1.50 and each order of fries costs 0.50. At the end of the night you made a whopping $78.50! This means that
1.5x + 0.5y = 78.5 - - - - - - - - - - -1
Substituting x = 87 - y into equation 1, it becomes
1.5(87 - y) + 0.5y = 78.5
130.5 - 1.5y + 0.5y = 78.5
- 1.5y + 0.5y = 78.5 - 130.5
- y = - 52
y = 52
Substituting y = 52 into x = 87 - y, it becomes
x = 87 - 52
x = 35
The heights in feet of people who work in an office are as follows. Use the range rule of thumb to find the standard deviation. Round results to the nearest tenth.
5.9 5.7 5.5 5.4 5.7 5.5 5.6 6.2 6.1 5.5
Question 4 answers
a.1.2
b.0.1
c.0.2
d.0.5
Answer:
Step-by-step explanation:
mean=(5.9+5.7+5.5+5.4+5.7+5.5+5.6+6.2+6.1+5.5)/10=57.1/10=5.71
we assume mean=5.7
x mean |x-mean| (x-mean)^2
5.9 5.7 0.2 0.04
5.7 5.7 0 0
5.5 5.7 0.2 0.04
5.4 5.7 0.3 0.09
5.7 5.7 0 0
5.5 5.7 0.2 0.04
5.6 5.7 0.1 0.01
6.2 5.7 0.5 0.25
6.1 5.7 0.4 0.16
5.5 5.7 0.2 0.04
--------
0.63
standard deviation=√((0.63)/10)=√(0.063)≈0.251
so c
Final answer:
By finding the range of the office workers' heights and applying the range rule of thumb (estimating the standard deviation as approximately one-fourth the range), the calculated standard deviation is rounded to 0.2 feet, matching answer choice (c).
Explanation:
To estimate the standard deviation of the office workers' heights using the range rule of thumb, we first find the range, which is the difference between the maximum and minimum values in the data set. The maximum height is 6.2 feet and the minimum is 5.4 feet, so the range is 6.2 - 5.4 = 0.8 feet.
The range rule of thumb states that the standard deviation can be estimated as approximately one-fourth of the range. Therefore, the estimated standard deviation is 0.8 / 4 = 0.2 feet. When rounded to the nearest tenth, the standard deviation is 0.2 feet, which corresponds to answer choice (c).
Which calculation will ALWAYS give a result greater than 1? A.5 × a number less than 1 B.4/9+ a fraction less than 12 C. 1 3/4 - a fraction less than 3/4 D.7/8 × a number less than 1
Answer:
C. 1 3/4 - (a fraction less than 3/4)
Step-by-step explanation:
Your number sense should be able to help you with this one.
A. 5 × 1/10 = 1/2, not a number greater than 1
B. 4/9 + 1/3 = 7/9, not a number greater than 1
C. 1 3/4 -1/2 = 1 1/4, a number greater than 1 (see below for more explanation)
D. 7/8 × 1/2 = 7/16, not a number greater than 1.
__
More explanation
Let x represent a number less than 3/4. Then we want to make sure that ...
y = 1 3/4 - x
will be greater than 1.
Solving for x, we get ...
x = 1 3/4 - y
Applying the requirement that x < 3/4, we have ...
x < 3/4
(1 3/4 -y) < 3/4
1 3/4 < y + 3/4 . . . . . . add y
1 < y . . . . . . . . . . . . . . .subtract 3/4
We see that the condition on x makes sure that y is always greater than 1.
Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?A. 25%B. 3313%C. 50%D. 6623%E. 75%
Answer:
[tex]66\dfrac{2}{3}\%[/tex]
Step-by-step explanation:
Given,
The number of cartons = k,
Time taken by machine a = 8 hours,
So, the number of cartons made by machine a in one hour
= [tex]\frac{\text{Cartons in 8 hours}}{8}[/tex]
= [tex]\frac{k}{8}[/tex]
Time taken by machine b = 4 hours ,
So, the number of cartons made by machine b in one hour
= [tex]\frac{k}{4}[/tex]
Total cartons made in 1 hour = [tex]\frac{k}{8}+\frac{k}{4}[/tex]
[tex]=\frac{k+2k}{8}[/tex]
[tex]=\frac{3k}{8}[/tex]
∵ for the whole number value of k,
[tex]\frac{k}{4}>\frac{k}{8}[/tex]
i.e. machine b is faster,
Also, the percent of the cartons were sealed by the machine b
[tex]=\frac{\text{Cartons made in 1 hour by machine b}}{\text{Total cartons}}\times 100[/tex]
[tex]=\frac{\frac{k}{4}}{\frac{3k}{8}}\times 100[/tex]
[tex]=\frac{2}{3}\times 100[/tex]
[tex]=\frac{200}{3}[/tex]
[tex]=66\dfrac{2}{3}\%[/tex]
Hence, OPTION D is correct.
simplify
i3
a. -I
b. -1
c. I
d. 1
Answer:
a. -i.
Step-by-step explanation:
i^2 = -1 so
i^3 = i^2 * i
= -1 * i
= -i.
First, the population is subdivided by metropolitan area. Then a crime researcher uses a random number generator to select twenty-five members from each metropolitan area to study.A. CensusB. Simple Random SamplingC. Stratified SamplingD. Cluster SamplingE. Systematic SamplingF. Convenience Sampling
Answer:
C. Stratified Sampling
Step-by-step explanation:
Stratified sampling is a sampling method in which the overall population is divided into a number of smaller sub groups.
These smaller sub-groups are called as strata.
These sub-groups are formed on the basis of similar characteristics and attributes shared by the population.
It is also known as proportional random sampling.
A restaurant has fixed costs of $147.50 per day and an average unit cost of $5.75 for each meal served. If a typical meal costs $7, how many customers must eat at the restaurant each day for the owner to break even?
Answer:
The answer is 118.
Step-by-step explanation:
First we need to subtract the meal cost from average unit cost for each meal:
[tex]7-5.75=1.25[/tex]
A restaurant profits 1.25$ for each meal. If we divide fixed cost to profit for each meal:
[tex]147.5/1.25=118[/tex]
The restaurant have to sell 118 meals at least each day for the owner to break even
A mechanic sells a brand of automobile tire that has a life expectancy that is normally distributed, with a mean life of 29,000 miles and a standard deviation od 2400 miles. He wants to give a guarantee for free replacement of tires that don't wear weel. How should he work his guarantee if he is willing to replace approximately 10% of the tires?
Tires that wear out by _____ miles will be replaces free of charge. Round to the nearest mile as needed.
Answer:
[tex]a=29000 -1.28*2400=25928[/tex]
Tires that wear out by 25928 miles will be replaces free of charge
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(29000,2400)[/tex]
Where [tex]\mu=29000[/tex] and [tex]\sigma=2400[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
He wants to give a guarantee for free replacement of tires that don't wear weel so then we need to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.90[/tex] (a)
[tex]P(X<a)=0.10[/tex] (b)
Because we are interested in the lower tail.
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.10 and P(z>-1.28)=0.90
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.1[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.1[/tex]
But we know which value of z satisfy the previous equation so then we can do this:
[tex]z=-1.28=<\frac{a-29000}{2400}[/tex]
And if we solve for a we got
[tex]a=29000 -1.28*2400=25928[/tex]
So the value of height that separates the bottom 10% of data from the top 90% is 25928 mi.
Tires that wear out by 25928 miles will be replaces free of charge
Dave bought a box of fruit that weighed 8 to 2/9 kilograms if he brought a second box that weighed 3 to 2/10 kilograms, what is the combined weight of two boxes
The combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]
Step-by-step explanation:
We have to add the fractional weight of both boxes to find the combined weight of both boxes.
Given
Weight of Box 1: [tex]8\frac{2}{9}[/tex] kilograms
Weight of Box 2: [tex]3\frac{2}{10}[/tex] kilograms
So the total weight will be:
[tex]= 8\frac{2}{9} + 3\frac{2}{10}[/tex]
Simplifying the fractions
[tex]=\frac{74}{9} + \frac{32}{10}\\\\= \frac{74(10)+32(9)}{90}\\\\=\frac{740+288}{90}\\\\=\frac{1028}{90}\\\\=11\frac{38}{90}\\\\=11\frac{19}{45}\\[/tex]
Hence,
The combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]
Keywords: Fractions, addition
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The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.
If the relationship between cost and the number of chairs produced is linear, how do I write an equation that expresses this relationship?
Answer:
Step-by-step explanation:
If the relationship between cost and the number of chairs produced is linear, we would write an equation that expresses this relationship in the slope intercept form. It is expressed as
y = mx + c
Where
m represents the slope
c = intercept.
Slope = (y2 - y1)/(x2 - 1)
y2 = final value of y = 4800
y1 = initial value of y = 2200
x2 = final value of x = 300
x1 = initial value of x = 100
Slope, m = (4800 - 2200)/(300 - 100) = 2600/200 = $13 per chair.
To determine the intercept, we will substitute y = 4800, x = 300 and m = 13 into y = mx + c. It becomes
4800 = 13×300 + c = 3900
c = 4800 - 3900 = 900
The equation becomes
y = 13x + 900
To write an equation that expresses the relationship between cost and the number of chairs produced, we need to find the slope and y-intercept of the linear equation. The equation that expresses this relationship is Cost = $26(Number of Chairs) - $400.
Explanation:We must determine the slope and y-intercept of the linear equation in order to build an equation that describes the link between the price and the quantity of chairs produced.
Slope = Change in Cost / Change in Number of Chairs
Using the given values, the slope is (4800 - 2200) / (300 - 100) = $26 per chair.
Now, let's find the y-intercept. We can use either of the given data points. Substituting the values of one data point, we have:
$2200 = $26(100) + b
b = $2200 - $2600 = -$400.
Therefore, the equation that expresses this relationship is:
Cost = $26(Number of Chairs) - $400.
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"When servicing a drive shaft, technician A says that its a good idea to tape the U-joint caps to prevent them from coming off. Technician B says that needle bearings are used with these type U-joints. Which technician is correct?
Answer: Both Technicians
Step-by-step explanation: A drive shaft which is also called the propeller shaft,is a major part of a the drive train/ unit of a vehicle with the role of Transmitting TORQUE POWER TO THE WHEELS,it is usually made up of STEEL.
Drive shaft is elongated,it is round and it requires needle bearing for friction reduction and taping to prevent it from falling off when the shafts are removed during servicing. Both Technicians are correct as both options are needed.
Both technicians are correct. Technician A's suggestion to tape the U-joint caps is a preventative measure to prevent loss of needle bearings. Technician B is correct that needle bearings are used with U-joints.
Explanation:Both Technician A and Technician B are correct in their assertions. Technician A's suggestion to tape the U-joint caps when servicing a drive shaft is a basic preventative measure to ensure they do not come loose and cause a problem. This is because losing a cap can lead to a loss of the needle bearings, which are crucial to U-joint function.
Technician B's statement is also correct that needle bearings are indeed used with these type of U-joints. Needle bearings allow the U-joints to rotate smoothly under the high pressure of the drive shaft. If the needle bearings were to fail or come out, it can cause the U-joint to fail.
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Which linear inequality is represented by the graph?
y > 2/3x – 1/5
y ≥ 3/2x + 1/5
y ≤ 2/3x + 1/5
y < 3/2x – 1/5
Answer:
[tex]y\leq \frac{2}{3}x+\frac{1}{5}[/tex]
Step-by-step explanation:
step 1
Find the equation of the solid line
Find the slope
we have
(0,0.2) and (3,2.2)
[tex]m=(2.2-0.2)/(3-0)=\frac{2}{3}[/tex]
The y intercept b is equal to
[tex]b=0.2=\frac{2}{10}=\frac{1}{5}[/tex]
so
the equation of the solid line in slope intercept form is equal to
[tex]y=\frac{2}{3}x+\frac{1}{5}[/tex]
step 2
Find the equation of the inequality
we know that
The solution of the inequality is the shaded area below the solid line
therefore
[tex]y\leq \frac{2}{3}x+\frac{1}{5}[/tex]
Answer:
c,y>2/3x-1/5
Step-by-step explanation:
Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2 Monday Tuesday Wednesday Thursday
Answer:
Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2
(i) Monday
(ii) Tuesday
(iii) Wednesday
(iv) Thursday
Ans
(iv)Thursday
Step-by-step explanation:
Forecast for
Monday +4 Abs |+4| = 4
Tuesday –6 Abs |-6| = 6
Wednesday +7 Abs |+7| = 7
Thursday –2 Abs |-2| = 2
The most accurate is the day closest the temperature forecast is closest to observed temperature, which is
Thursday (-2)
Answer:
it is thursday
Step-by-step explanation:
hope it helps
A tank with 5 mg/L of phenol is mixed with a 55 gallon drum of phenol with 1536 mg/L. Mixing the two together results in a total mass of phenol in the new container that is less than that in the original two containers.
1)True
2)False
3)Not Enough Information
4)Sometimes
Answer: False
Step-by-step explanation:
The phenol would not evaporate or boil and would not reduce in quantity as it has a higher boiling point. So mixing it in different containers would not change the mass of phenol.
The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours spent exercising. The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the number of hours spent exercising. What is (f + g)(1)? Explain.
339 calories burned while dieting for 1 hour.
339 calories burned while combining diet with 1 hour of exercise.
212 calorie calories burned when combining diet with 1 hour of exercise.
212 calories burned while exercising for 1 hour.
This means 339 calories burned while combining diet with 1 hour of exercise
Step-by-step explanation:
Given the functions as:
f(x)=2x+210
g(x)=2x+125 then
(f+g)(x) = 2x+210 +2x+125 = 4x +335
(f+g)(1) = 4(1)+335
=339
This means 339 calories burned while combining diet with 1 hour of exercise
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Step-by-step explanation:
f(1) = 2+210 = 212
g(1) = 2+125 = 127
127+212= 339
The function f(x) = 2x + 210 represents the number of calories burned when exercising, where x is the number of hours spent exercising.
The function g(x) = 2x + 125 represents the calorie deficit that occurs when following a particular diet, where x is the number of hours spent exercising.
Answer:
meaning it is 339 calories burned while combining diet with 1 hour of exercise.
Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their pricing, Greyhound Lines randomly selects 120 busses during a certain week and surveys all passengers on the busses.
Answer: Cluster Sampling
Step-by-step explanation:
In cluster sampling, researcher divides the population into groups ,which are called clusters. Then random sample of clusters are chosen ,and researcher conduct study to collect data about the population.
Here each bus is considered a cluster ,because busses are selected at random ,this sampling would be an example of cluster type of sampling.
The equation of line LM is 5x − y = −4. What is the equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2)?
a) y = 5x + 13
b) y = negative one fifthx + seven fifths
c) y = negative one fifthx − seven fifths
d) y = 5x − 17
Answer: b) y = negative one fifthx + seven fifths
Step-by-step explanation:
Equation of a line in Slope intercept form : [tex]y=mx+c[/tex] (1)
, where m is slope and c is constant.
Given : The equation of line LM is [tex]5x - y = -4.[/tex]
Convert it into slope- intercept form, we get
[tex]y=5x+4[/tex]
Comparing it to (1) , we get
[tex]m= 5[/tex]
Let [tex]m_1[/tex] be the slope pf the line perpendicular to LM.
Since the product of slopes of two perpendicular lines is -1.
Therefore , [tex]m_1\cdot m=-1\Rightarrow m_1=\dfrac{-1}{m}=\dfrac{-1}{5}[/tex]
Equation of line passing through (-3,2) and having slope [tex]m_1=\dfrac{-1}{5}[/tex] will be :-
[tex](y-2)=\dfrac{-1}{5}(x-(-3))\\\\ y-2=(-\dfrac{1}{5})(x+3)=\dfrac{-1}{5}x-\dfrac{3}{5}\\\\\ y=\dfrac{-1}{5}x-\dfrac{3}{5}+2=\dfrac{-1}{5}x-\dfrac{10-3}{5}\\\\\Rightarrow\ y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex]
Hence, the equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2) is [tex]y=\dfrac{-1}{5}x+\dfrac{7}{5}[/tex].
Hence, the correct answer is b) y = negative one fifthx + seven fifths.
We want to find a line perpendicular to 5x - y = -4 that passes through the point (-3, 2). We will find that the line is: y = (-1/5)*x + 7/5
Perpendicular lines.A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Such that a line is perpendicular to the above one if and only the slope of this other line is the inverse of the opposite of the above slope, so the perpendicular line will be something like:
y = (-1/a)*x + c
Now we start with the line that we know, we need to find its slope:
5x - y = -4
We need to isolate y
y = 5x + 4
Then the slope of this line is a = 5, so the perpendicular line will be:
y = (-1/5)*x + c
Now we need to find the value of c such that the line passes through (-3, 2), this means that x = -3 and y = 2, then we have:
2 = (-1/5)*-3 + c
2 = (3/5) + c
2 - 3/5 = c
10/5 - 3/5 = c
7/5 = c
Then the equation is:
y = (-1/5)*x + 7/5
So the correct option is b.
If you want to learn more about linear equations, you can read:
https://brainly.com/question/4074386
Kadi is starting a kayak rental company. She is going to charge $20 to rent the kayak plus $5 per hour of rental. What is the slope and what does it represent?
Answer:
slope is 5
Step-by-step explanation:
the slope represents the cost of the kayak for as many hours as the person rents it for. the y intersect is 20 because that is the cost just to rent the boat before using it.
Please help me with this problem!!!!!!
Answer:
[tex]\sqrt{29}[/tex]
Step-by-step explanation:
The complex number x + yi can be expressed in coordinate form as
x + yi → (x, y ), thus
4 + 3i → (4, 3 )
6 - 2i → (6, - 2 )
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (6, - 2)
d = [tex]\sqrt{(6-4)^2+(-2-3)^2}[/tex]
= [tex]\sqrt{2^2+(-5)^2}[/tex]
= [tex]\sqrt{4+25}[/tex]
= [tex]\sqrt{29}[/tex]
Elainas old bicycle had tires with a 12-inch diameter her new bicycle had tires with a 16-inch diameter what is the difference in the circumference of the tires use 3.14 for pie
Answer:
The difference between the circumference of the tires is 12.56 inches.
Step-by-step explanation:
Given:
Diameter of old bicycle tires = 12 inch
Diameter of new bicycle tires = 16 inch
We need to find the difference in circumference of the tires.
Solution:
First we will find the circumference of Old bicycle tires.
Circumference can be calculated by π times diameter.
Circumference of Old bicycle tire = [tex]\pi \times 12 = 37.68\ in[/tex]
Now we will find the circumference of new bicycle tire.
Circumference of New bicycle tire = [tex]\pi \times 16 = 50.24\ in[/tex]
Now to find the difference between the circumference of the tires we will subtract Circumference of New bicycle tire from Circumference of Old bicycle tire we get;
framing in equation form we get;
difference between the circumference of the tires = [tex]50.24-37.68 =12.56\ in[/tex]
Hence The difference between the circumference of the tires is 12.56 inches.