Answer: A.
The system is consistent because the rightmost column of the augmented matrix is not a pivot column.
Explanation: a system is consistent if and only if the rightmost column of the augmented matrix is not a pivot column. Since every column of the coefficient matrix is a pivot column, none of the leading coefficients are in the rightmost column of the augmented matrix. Therefore the rightmost column of the augmented matrix cannot be a pivot column and the system must be consistent.
Consider the function.
f(x) = -x-24
Which conclusions can be drawn about f'(x)? Select two options.
F1(x) has a slope of -
f'(x) has a restricted domain.
f(x) has a y-intercept of (0, -36).
F'(x) has an x-intercept of (-36,0).
f'(x) has a range of all real numbers.
Answer:
f(x) has a slope of -1 and has a range of all real numbers.
Step-by-step explanation:
A linear function is a continuous function, so that exist a range value for all value of the domain, which corresponds to all real numbers. Regarding the function described above, the y- and x-intercepts are, respectively:
x-Intercept
[tex]0 = - x-24[/tex]
[tex]x = -24[/tex]
f(x) has a x-intercept of (-24,0).
y-Intercept
[tex]f(x) = 0 - 24[/tex]
[tex]f(x) = -24[/tex]
f(x) has a y-intercept of (0, -24).
Lastly, the linear function has a slope of -1.
Answer:
D AND E
Step-by-step explanation:
edu I took it
(-3)^(-2) please help
Can someone please help me :)
Answer:
90 degree
Step-by-step explanation:
Three points A, B, and C are added and shown in attached picture.
As the property of inscribed angle in circle:
angle BAC = (1/2) x 88 = 44 deg
As the property of complement angle:
angle ABC = 180 - 89 = 91 deg
As the property of sum of three angles in a triangle:
angle ACB + angle ABC + angle BAC = 180 deg
=> angle ACB = 180 - angle ABC - angle BAC = 180 - 44 - 91 = 45 deg
One more time, we use the property of inscribed angle in circle:
x = 2 x angle ACB = 2 x 45 = 90 deg
Hope this helps!
A new car is purchased for 15100 dollars. The value of the car depreciates at 12.25% per year. To the nearest year, how long will it be until the value of the car is 2300 dollars?
Answer: 14
Step-by-step explanation:
What is the value of x in the equation
5x - y = 30, when y = 157
Answer:
x = 37.4
Step-by-step explanation:
Answer:
37.4
Step-by-step explanation:
If you plug in 157, we get 5x-157=30. Then we will add 157 to both sides to get 5x=187 and then divide by 5 on both sides leaving x on one side and the answer on the other so, 187/5=37.4.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Measurements of the sodium content in samples of two brands of chocolate bar yield the following results (in grams):Brand A: 34.36 31.26 37.36 28.52 33.14 32.74 34.34 34.33 34.95Brand B: 41.08 38.22 39.59 38.82 36.24 37.73 35.03 39.22 34.13 34.33 34.98 29.64 40.60 Let formula415.mml represent the population mean for Brand B and let formula417.mml represent the population mean for Brand A.Find a 98% confidence interval for the difference formula419.mml. Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.
Answer:
Step-by-step explanation:
For brand A,
Mean, x1 = (34.36 + 31.26 + 37.36 + 28.52 + 33.14 + 32.74 + 34.34 + 34.33 + 34.95)/9 = 33.44
standard deviation, s1 = √(summation(x - mean)²/n
Summation(x - mean)² = (34.36 - 33.44)^2 + (31.26 - 33.44)^2 + (37.36 - 33.44)^2 + (28.52 - 33.44)^2 + (33.14 - 33.44)^2 + (32.74 - 33.44)^2 + (34.34 - 33.44)^2 + (34.33 - 33.44)^2 + (34.95 - 33.44)^2 = 49.6338
Standard deviation = √(49.6338/9
s1 = 2.35
For brand B,
Mean, x2 = (41.08 + 38.22 + 39.59 + 38.82 + 36.24 + 37.73 + 35.03 + 39.22 + 34.13 + 34.33 + 34.98 + 29.64 + 40.60 )/13 = 36.89
Summation(x - mean)² = (41.08 - 36.89)^2 + (38.22 - 36.89)^2 + (39.59 - 36.89)^2 + (38.82 - 36.89)^2 + (36.24 - 36.89)^2 + (37.73 - 36.89)^2 + (35.03 - 36.89)^2 + (39.22 - 36.89)^2 + (34.13 - 36.89)^2 + (34.33 - 36.89)^2 + (34.98 - 36.89)^2 + (29.64 - 36.89)^2 + (40.60 - 36.89)^2 = 124.5024
Standard deviation = √(124.5024/13
s2 = 3.09
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 98% confidence interval, we would determine the z score from the t distribution table because the number of samples are small.
Degree of freedom =
(n1 - 1) + (n2 - 1) = (9 - 1) + (13 - 1) = 20
z = 2.528
x1 - x2 = 33.44 - 36.89 = - 3.45
Margin of error = z√(s1²/n1 + s2²/n2) = 2.528√(2.35²/9 + 3.09²/13) = 2.935
The 98% confidence interval is
- 3.45 ± 2.935
A car is traveling at a speed of 63 kilometers per hour. What is the car's speed in kilometers per minute? How many kilometers will travel in 5 minutes?
Answer:
5.25 kilometers
Step-by-step explanation:
63k/60 = 1.05k
1.05k x 5 = 5.25k
Twice a number is decreased by 7, and this quantity is multiplied by 3. the result is 9 less than 10 times the number. What is the number?
Answer:
(7-2x)3 =9-10x
x= -3
Step-by-step explanation:
we let the number to be x.
twice a number=2x is decreased by 7 that is to say 7-2x, is multiplied by 3, we have (7-2x)3.
the result is 9 less than 10times the number which is =9-10x.
so bringing all these together we have;
(7-2x)3=9-10x.
what is the number?
solving, we have:
(7-2x)3=9-10x
21-6x=9-10x
21-9= -10x+6x
12= -4x
dividing both sides by -4 we have our number
x= -3.
for proof we can substitute x=-3 into the equation.
21-6(-3) =9-10(-3)
21+18=9+30
39=39
Ana purchased a gallon of milk for $2.22, bagels for $2.97, and a box of
cereal for $2.42. How much money did Ana spend in all? Do not include s in
your answer.
Answer:
7.61
Step-by-step explanation:
Sum all of the values
2.22+2.97+2.42=7.61
Answer:
761
Step-by-step explanation:
What is the number of possible permutations of 6 objects taken 3 at a time?
Answer:
120
Step-by-step explanation:
Find the least common denominator for these fractions. 5/7 and 4/6
Answer: 21 is the least common denominator
Step-by-step explanation:
The least common denominator of 7 and 6 is 42, but will be simplified.
The fractions would turn into 30/42 and 28/42.
Now simplify.
15/21 and 14/21
This cannot be simplified any further without losing the common denominator
Answer:
The least common denominator is 21.
Step-by-step explanation:
Put the fractions out of a denominator of 42
5/7 = 30/42 4/6 = 28/42
Divide both fractions by 2
35/42 = 15/21 4/6 = 14/21
Statistical Process Control (SPC) is often described as an applied side of the Binomial, Poisson, and Normal distributions. Many have said that an X-bar control chart is simply a Normal distribution turned on its side. Some argue that our statistics course shouldn't try to cover these applications because they represent an analytical skill rather thana statistical technique. Discuss, first whether or not you agree with the notion that SPC is an application of what we're learning in this class, and second, whether coverage of the topic is helpful in this class. How might your outcomes after this class be affected - positively or negatively - by whether or not we cover Chapter 16 in the text?
Answer: The answer is provided below
Step-by-step explanation:
Statistical Process Control (SPC) is described as the applied side of binomial, poisson, and the normal distributions. It has been often said that an X-bar control chart is a normal distribution that is turned on its side. Some people argue that statistics shouldn’t cover these applications because it represent an analytical skill rather than statistical technique. It's an application of what is learnt on statistics.
Statistical Process Control(SPC) is very useful in our lives. As a statistics student, one should be thorough with every mathematical concepts and its applications.
Factor 4x^2+20x-24 into bionomials
Answer:
4( x+6) (x-1)
Step-by-step explanation:
4x^2+20x-24
Factor out the greatest common factor
4(x^2 +5x-6)
What 2 numbers multiply to -6 and add to 5
6*-1 = -6
6+-1 = 5
4( x+6) (x-1)
Answer:
[tex]4(x-1)(x+6)[/tex]
Step-by-step explanation:
→Take out the GCF (Greatest Common Factor), which is 4:
[tex]4x^2+20x-24[/tex]
[tex]4(x^2+5x-6)[/tex]
→Split the middle term into two numbers that can be added to get 5 and multiplied to get 6:
[tex]4(x-1)(x+6)[/tex]
The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 One-fourth(4x – 8y = 12) → x – 2y = 3 2x = 18 What is the solution of the system of equations? a(1,2) b(3,9) c(5,5) d(9,3)
Answer:
D
Step-by-step explanation:
because i took the test
Answer:
Option D: (9,3)
Step-by-step explanation:
Fernando bought a jacket for 185 and sold it for 1 1/2 what he paid. Marisol spent 1/5 as much as Fernando on the same jacket but sold it for 1/2 as much as Fernando. How much money did Marisol make?
Answer:
Marisol made $138.75 on the sale of the jacket
Step-by-step explanation:
First we are told that Fernando bought a jacket for $185, and sold it for 1 1/12 what he paid.
Therefore, 1 1/2 of 185;
= 1.5 × 185 = $277.5
Therefore, Fernando sold the Jacket for $277.5
Next, we are told that:
Marisol spent 1/5 as much as Fernando on the same jacket
This means that Marisol spent 1/5 of $185 on the jacket
= 1/5 × 185 = 0.2 × 185 = $37
Therefore, Marisol spent $37 to buy the same jacket
Next, Marisol sold the jacket for 1/2 as much as Fernando. Since Fernando sold the Jacket for $277.5, Marisol sold the jacket for 1/2 of 277.5, and this is calculated as:
1/2 of 277.5 = 0.5 × 277.5 = 138.75
Therefore, Marisol made $138.75 on the sale of the jacket.
Evaluate the expression y-x+ z for x = 4.6, y=6, and z=0.59
y - X+2=
(Type an integer or a decimal.)
Answer:
1.99Solution,
y-x+z
=6-4.6+0.59
=6+0.59-4.6
=6.59-4.6
=1.99
Hope this helps...
good luck on your assignment
What is the product?
2x(x-4)
2x2-4
O 2x2-8
2x2 - 4x
B
2x2-8x
Answer:
2x^2 -8x
Step-by-step explanation:
2x(x-4)
Distribute
2x*x -2x*4
2x^2 -8x
The right answer is 2x^2-8x
please see the attached picture for full solution
Hope it helps
good luck on your assignment
f(x) = x2 - x - 1
What is the average rate of change of f over the interval -1 < x < 1?
Answer:
-1
Step-by-step explanation:
The average rate of change is the ratio of the difference in y-values to the difference in x-values of corresponding points.
At x=-1, f(x) = (-1)^2 -(-1) -1 = 1
At x=1, f(x) = (1)^2 -(1) -1 = -1
So, points on the graph are (-1, 1) and (1, -1).
Then the change in y over that interval is -1 -1 = -2.
The change in x over that interval is 1 -(-1) = 2.
The average rate of change is ...
∆y/∆x = -2/2 = -1 . . . . average rate of change on (-1, 1)
When a group of five hundred exchange students were questioned over a decade after their study abroad experience, over 90 percent said that the experience was a key influence on the direction of their lives. Which reason should Mariah include to support to her claim that study abroad programs should be instituted in high schools across the country?
Answer:
over 90 percent said that the experience was a key influence on the direction of their lives.
Step-by-step explanation:
This is the most helpful reason to implement study abroad programs in high schools.
Answer:
C
Step-by-step explanation:
i took the test
Brady and JaQuan were selling cupcakes together at a bake sale. They hope to make $100 so they can both go on the band field trip to New York City. In the first hour Brady sold 1/3 of the cupcakes and Jaquan sold 3/8...
Answer:
The initial amount of cupcakes = 48
If they sold each cupcake for $2.75, they would make $132 which is more than the required $100 to go on band field trip to New York.
The excess money available for spending is thus $32
Step-by-step explanation:
The complete question is presented in the attached image to this answer.
They need to make $100
Let x be the initial amount of cupcakes
During the first hour, Brady sold (1/3) of the cupcakes and Jaquan sold (3/8)
Total amount of cupcakes sold in the first hour = [(1/3) × x] + [(3/8) × x] = (17x/24)
Amount of cupcakes remaining after the first hour = x - (17x/24) = (7x/24)
After the first hour, they sold 2 cupcakes
Amount of cupcakes left after the first hour = (7x/24) - 2 = (0.292x - 2)
During the second hour, they sold 75% of the remaining cupcakes, meaning they had 25% of the remaining cupcakes left.
Amount of cupcakes left = 25% × (0.292x - 2)
= (0.07292x - 0.5)
During the third hour, they sold the remaining 3 cupcakes
Meaning that the amount of cupcakes left from the second hour = 3
(0.07292x - 0.5) = 3
0.07292x = 3.5
x = (3.5/0.07292) = 47.998 = 48 cupcakes.
Hence, the initial amount of cupcakes = 48.
If they sold each cupcake for $2.75, they would make 2.75 × 48 = $132
Which is more than the required $100 to go on band field trip to New York.
The excess money available for spending is thus $132 - $100 = $32.
Hope this Helps!!!
The distribution of the amount of change in UF student's pockets has an average of 2.02 dollars and a standard deviation of 3.00 dollars. Suppose that a random sample of 45 UF students was taken and each was asked to count the change in their pocket. The sampling distribution of the sample mean amount of change in students pockets is
Answer:
[tex] \bar X \sim N (\mu ,\frac{\sigma}{\sqrt{n}})[/tex]
Then the mean would be:
[tex] \mu_{\bar X}= 2.02[/tex]
And the deviation:
[tex] \sigma_{\bar X}= \frac{3.00}{\sqrt{45}}= 0.447[/tex]
And the distribution would be given by:
[tex] \bar X \sim N(2.02, 0.447)[/tex]
Step-by-step explanation:
For this case we can define the variable of interest X as the amount of change in UF student's pockets and we know the following parameters:
[tex] \mu = 2.02, \sigma =3.00[/tex]
And we select a sample of n=45. Since this sample size is higher than 30 we can apply the central limit theorem and the distirbution for the sample size would be given by:
[tex] \bar X \sim N (\mu ,\frac{\sigma}{\sqrt{n}})[/tex]
Then the mean would be:
[tex] \mu_{\bar X}= 2.02[/tex]
And the deviation:
[tex] \sigma_{\bar X}= \frac{3.00}{\sqrt{45}}= 0.447[/tex]
And the distribution would be given by:
[tex] \bar X \sim N(2.02, 0.447)[/tex]
Find the arc length AB
Answer :
34.56
I hope it helps
Given: WXYZ is a parallelogram.
ZX WY
Prove: WXYZ is a rectangle
Answer:
Step-by-step explanation:
A quadrilaterals are plane figures bounded by four sides. Examples are; square, rectangle, parallelogram, kite, trapezium etc.
Given: parallelogram WXYZ
ZX ≅ WY
Prove: WXYZ is a rectangle
WZ ≅ XY (opposite sides property)
YZ ≅ WX (opposite sides property)
<WZY ≅ <ZWX ≅ <WXY ≅ <XYZ = [tex]90^{0}[/tex] (angle property of a rectangle)
<YZW ≅ <WXY (opposite angles are congruent)
ΔZYW ≅ ΔXTW (Side-Angle-Side property)
ZX ≅ WY
Therefore, the parallelogram is a rectangle.
Answer: This is the right answer
Step-by-step explanation:
Below
Simplify the radical expression √100/2
Answer: 5
Step-by-step explanation:
sqrt of 100 = 10
10/2 = 5
What is the slope of the line described by the equation below?
y= 10x + 2
A. -10
B. 10
C. 2
O D. -2
Answer:
B because when you compare y= mx+ c where M is the slope or gradient
What is the area of this polygon?
coordinates are -5,2(-2,3)(3,3)(3,-3)(-2,-3)
Enter your answer in the box.
Answer:
30
Step-by-step explanation:
In a study, 43% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 13 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 13 adults are randomly selected, at most 3 are in excellent health.
Answer:
13.44% probabilith that at most 3 are in excellent health.
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they are in excellent health, or they are not. The probability of an adult being in excellent health is independent of other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
43% of adults questioned reported that their health was excellent.
This means that [tex]p = 0.43[/tex]
13 adults randomly selected
This means that [tex]n = 13[/tex]
Find the probability that when 13 adults are randomly selected, at most 3 are in excellent health.
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{13,0}.(0.42)^{0}.(0.58)^{13} = 0.0008[/tex]
[tex]P(X = 1) = C_{13,1}.(0.42)^{1}.(0.58)^{12} = 0.0079[/tex]
[tex]P(X = 2) = C_{13,2}.(0.42)^{2}.(0.58)^{11} = 0.0344[/tex]
[tex]P(X = 3) = C_{13,3}.(0.42)^{3}.(0.58)^{10} = 0.0913[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0008 + 0.0079 + 0.0344 + 0.0913 = 0.1344[/tex]
13.44% probabilith that at most 3 are in excellent health.
If f (x )equals left brace Start 2 By 1 Matrix 1st Row 1st Column 2 x minus 3 if minus 2 less than or equals x less than or equals 5 2nd Row 1st Column x cubed minus 5 if 5 less than x less than or equals 6 EndMatrixf(x)= 2x−3 if −2≤x≤5 x3−5 if 5
Answer:
(a)f(0)=-3
(b)f(1)=-1
(c)f(5)=7
(d)f(6)=211
Step-by-step explanation:
[tex]f(x)=\left\{\begin{array}{ccc}2x-3, &-2\leq x \leq 5 \\x^3-5, &5<x\leq6 \end{array}\right[/tex]
(a) f(0)
For x such that , [tex]-2\leq x \leq 5, f(x)=2x-3[/tex]
Since [tex]-2\leq 0\leq 5[/tex]
[tex]f(0)=2(0)-3=0-3\\f(0)=-3[/tex]
(b)f(1)
For x such that , [tex]-2\leq x \leq 5, f(x)=2x-3[/tex]
Since [tex]-2\leq 1\leq 5[/tex]
[tex]f(1)=2(1)-3=2-3\\f(1)=-1[/tex]
(c)f(5)
For x such that , [tex]-2\leq x \leq 5, f(x)=2x-3[/tex]
Since [tex]-2\leq 5\leq 5[/tex]
[tex]f(5)=2(5)-3=10-3\\f(5)=7[/tex]
(d)f(6)
For x such that [tex]5<x\leq6, f(x)=x^3-5[/tex]
[tex]f(6)=6^3-5\\f(6)=211[/tex]
Find the surface area of the triangular prism shown below .
Answer:
the surface area should be 544 (whatever the unit is)
Step-by-step explanation:
You start by taking the rectangles on the side and finding their area.
1. (10×14)×2 ←Because there are two rectanglular sides.
2. find the area of the triangles on the side. 1/2bh = area of triangle.
(.5×8×6)×4 ← in order to find the area for all of the triangles.
3. lastly take the base of the prism and find the area then add the previously found values together.
(12×14)+(.5×8×6)×4+ (10×14)×2 = 544
Answer:
544
Step-by-step explanation:
It is right on Khan academy so I hope this helps!!!
What is the value of x in the equation- x - y = 30, when y= 15?
4
8
80
200
Answer:
x - 15 = 30
x = 45
Step-by-step explanation:
Answer:
D: 200
Step-by-step explanation:
1/5x-2/3 times 15=30
Simplify each term
x/5 -10=30
Move all terms not containing x to the right side of the equation
x/5=40
Multiply both sides of the equation by 5
5 times x/5=5 times 40
Simplify both sides of the equation
x=200
Hope this helped!
