Eight trials are simulated. The results are shown in the table.
Simulation
105 104 110 112
114 106 108 109
What is the estimated margin of error, using standard deviation?
Enter your answer, rounded to two decimal places, in the box.
±
Answers
Answer:
2.897
Step-by-step explanation:
Let us find the mean and variance for the sample first.
105 104 110 112
114 106 108 109
Mean = sum/8 = 108.5
Variance = 12
Std dev = sq rt of variance = 3.464
Std error = std dev/ sq rt n
since n =8, we get std error = 1.225
Since sample size is small, df =8-1 =7
For 95% confidence intervals, t critical value for two tailed=2.365
Margin of error = std error x t critical = 1.225(2.365)
=2.897
Related Questions
Isaiah puts a kilogram weight on a pan balance, how many
100 gram weights does he need to balance the scale
Answers
Isaiah would have to put 10 one-hundred gram weights to balance it out because there are 1000 grams in a kilogram.
Given: △DMN, DM=10 3 m∠M=75°, m∠N=45° Find: Perimeter of △DMN
Answers
Answer:
The perimeter of [tex]\triangle DMN[/tex] will be 62.1939...
Step-by-step explanation:
In [tex]\triangle DMN[/tex], the length of side [tex]DM = 10\sqrt{3}[/tex] and the measures of [tex]\angle M[/tex] and [tex]\angle N[/tex] are 75° and 45° respectively.
As the sum of all angles in a triangle is always 180°, so the measure of [tex]\angle D[/tex] will be: 180°- (75°+45°) = 180°- 120° = 60°
Now using Sine rule, we will get......
[tex]\frac{MN}{Sin(D)}=\frac{DN}{Sin(M)}=\frac{DM}{Sin(N)}\\ \\ \frac{MN}{Sin(60)}=\frac{DN}{Sin(75)}=\frac{10\sqrt{3}}{Sin(45)}\\ \\ MN= \frac{10\sqrt{3}}{Sin(45)}*Sin(60)=21.2132...\\ \\ DN=\frac{10\sqrt{3}}{Sin(45)}*Sin(75)=23.6602...[/tex]
So, the perimeter of [tex]\triangle DMN[/tex] will be: [tex]DM+MN+DN = 10\sqrt{3}+21.2132...+23.6602... =62.1939...[/tex]
A 4-digit pin number is to be created using the digits 0 through 9. The first digit must be a 5 or an 8, and the last digit cannot be 0. How many pin numbers can be created?
A.
5,040
B.
6,561
C.
1,458
D.
1,800
Answers
Second:Any of 0 to 9 so 10 possible numbers
Third:Any of 0 to 9 so 10 possible numbers
Last:Any of 1 to 9 so 9 possible numbers
So Answer is,
2*10*10*9=1800
what is x and y math help
Answers
x and y are whatever you want them to be.
It can be convenient for solving a problem like this to use x and y to represent what the problem is asking for: the number of cans of cola and the number of cans of root beer. It is also convenient (less confusing) to use those variable names in the same order that the nouns of the problem are named:
... x = # of cans of cola
... y = # of cans of root beer
Then the problem statement tells you ...
... x + y = 30 . . . . . . . 30 cans total were bought
... x = 2y . . . . . . . . . . the number of cans of cola is twice the number of cans of root beer
_____
This set of equations is nicely solved by substitution: use the second equation to substitute for x in the first.
... (2y) +y = 30 . . . . . put 2y where x was
... 3y = 30 . . . . . . . . collect terms
... y = 10 . . . . . . . . . divide by 3
... 2y = x = 20
You're not done yet. You need to answer the question the problem asks.
Jared bought 20 cans of cola and 10 cans of root beer.
_____
Comment on x and y
You customarily see x and y as the variables of a problem. Personally, I like to use variables that remind me what they stand for. In this problem, I might use "c" for cans of cola and "r" for cans of root beer. Then when I've found the solution, I know exactly how it relates to what the question is asking.
Always start by writing down what the variables stand for (as we did here). Sometimes, this is called writing a Let statement: Let x = number of colas; let y = number of root beers.
Comment on problems of this type
When a proportional relationship is given between the items in a sum (2 cola cans for every root beer can), it is often convenient to work the problem in terms of groups of items. Here, a group of 3 items can consist of 2 cola cans and 1 root beer can. Then 30 items will be 10 groups, so 10 root beers and 20 colas. The problem is solved even before you can name the variables.
Even when the relationship isn't exactly proportional, you can add or subtract the extras and still work the problem this way. Had we said colas numbered 3 more than twice as many root beers, we could have our groups of 3 total 27 (30 less the 3 extra), giving 9 root beers and 21 colas (3 + 2·9).
What is the value of x? x+4/5=11 Enter your answer in the box in simplest form. Please explain how you got your answer.
Answers
x = [tex]\frac{51}{5}[/tex]
subtract [tex]\frac{4}{5}[/tex] from both sides of the equation
x = 11 - [tex]\frac{4}{5}[/tex] = [tex]\frac{55}{5}[/tex] - [tex]\frac{4}{5}[/tex] = [tex]\frac{51}{5}[/tex]
Answer:
10.92 or 10 23/25
Step-by-step explanation:
What you do is you try to get X by itself so put the fraction 4/5 on the other side so that is turns out to be 11-4/5. Now you can turn 4/5 into a decimal which would be .8 and subtract that by 11which gives you 10.92 or if you want to keep it as a fraction .92 as a fraction is 23/25 so you get 10 23/25
What is the area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) ?
Enter your answer in the box.
Answers
Given
A triangle.
with vertices at (−2, 1) , (2, 1) , and (3, 4)
Find out the area of a triangle.
To proof
Formula
[tex]Area\ of\ triangle = \frac{1}{2}[ x_{1} (y_{2} -y_{3} ) + x_{2} (y_{3} - y_{1})+x_{3}(y_{1}-y_{2})[/tex]
As given the vertices at (−2, 1) , (2, 1) , and (3, 4)
put in the above equation
we get
[tex]= \frac{1}{2} [-2(1-4)+ 2 (4-1) + 3 ( 1-1) ][/tex]
solving
[tex]= \frac{1}{2} [6 + 6][/tex]
thus
[tex]=\frac{1}{2} [12][/tex]
area of the triangle is 6 units².
Hence proved
The area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) is; Area = 6 units²
The formula for the area of a triangle when given the 3 vertices is;
Area = ½[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]
In this question, the vertices coordinates are; A(−2, 1), B(2, 1), and C(3, 4)
Thus;
Ax = -2
Bx = 2
Cx = 3
Ay = 1
By = 1
Cy = 4
Plugging in the relevant values into the area equation gives;
Area = ½[-2(1 - 4) + 2(4 - 1) + 3(1 - 1)]
Area = ½(6 + 6 + 0)
Area = ½ × 12
Area = 6 units²
Read more at; https://brainly.com/question/19044159
Calculate the variance for the data set. Round your answer to the nearest hundredth. Show all of your steps. { 10 , 19 , 21 , 28 , 12 , 20 , 16 }
Answers
Answer:
Variance of the given data = 31.143
Explanation:
Variance, [tex]\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2[/tex], where n is the number of observations, μ is the mean and [tex]x_i[/tex] is the observations made.
Number of observations, n = 7
Mean, μ = [tex]\frac{10+19+21+28+12+20+16}{7} = 18[/tex]
[tex]\sum_{i=1}^{n}(x_i-\mu)^2=(10-18)^2+(19-18)^2+(21-18)^2+(28-18)^2+(12-18)^2+(20-18)^2+(16-18)^2\\ \\ \sum_{i=1}^{n}(x_i-\mu)^2=64+1+9+100+36+4+4=218[/tex]
[tex]\sigma^2=\frac{1}{n} \sum_{i=1}^{n}(x_i-\mu)^2=\frac{218}{7} =31.143[/tex]
So variance of the given data = 31.143
Final answer:
The variance of the given data set {10, 19, 21, 28, 12, 20, 16} is calculated by finding the mean, squaring the deviations from the mean, summing these squares, and dividing by the number of data points minus one, resulting in a variance of approximately 36.33.
Explanation:
Calculating Variance of a Data Set
To calculate the variance, we first need to find the mean (average) of the data set. Then, we subtract the mean from each data point (deviation), square each deviation, sum them all up, and finally, divide by the total number of data points minus one to account for sample variance.
The given data set is {10, 19, 21, 28, 12, 20, 16}. Let's calculate the mean:
Mean = (10 + 19 + 21 + 28 + 12 + 20 + 16) / 7 = 126 / 7 = 18
Next, calculate each deviation from the mean, square it, and sum these squared deviations:
(10 - 18)² = 64
(19 - 18)² = 1
(21 - 18)² = 9
(28 - 18)² = 100
(12 - 18)² = 36
(20 - 18)² = 4
(16 - 18)² = 4
Sum of squared deviations = 64 + 1 + 9 + 100 + 36 + 4 + 4 = 218
The variance is then the sum of the squared deviations divided by n - 1 (where n is the number of data points in our sample):
Variance = 218 / (7 - 1) = 218 / 6 ≈ 36.33
what is the length of chord CD in O below?
A. 4.01 units
B. 16.04 units
C. 8.02 units
D. 8.31 units
Answers
why hello there
Your answer is C 8.02
If u can please mark me as brainliest i really want genius!
Answer:
The correct option is C.
Step-by-step explanation:
Given information: In circle O, AB=8.02, the distance of cord AB from the center is 8.31, the distance of cord CD from the center is 8.31.
According to the chords equidistant from the center theorem, if two cords are equidistant form the center, the length of both cords are equal.
Since the cords AB and CD are equidistant form the center O, therefore
[tex]AB=CD[/tex]
[tex]8.02=CD[/tex]
The length of cord CD is 8.02 units.
Therefore correct option is C.
Tatum wants to use partial products to find 14x39 how do I do this?
Answers
Answer: 546
Step-by-step explanation:
14 ⇒ 10 + 4
x 39 ⇒ 30 + 9
36 | ← 9 x 4
90 | ← 9 x 10
120 | ← 30 x 4
300 | ← 30 x 10
546
A die was rolled 6 times and the results are displayed in matrix A. If the die rolls were repeated with the same results, which formula shows how to find the matrix that would display these results?
Answers
Answer:
None of the above. (Ask your teacher to show you how to work this problem.)
Step-by-step explanation:
Since the results are identical, the matrix of the next three rolls will look exactly like this matrix. (A)
The matrix of all 6 rolls will look like a 6-row matrix with the bottom 3 rows identical to the top 3 rows.
Adding or multiplying A by a constant will not produce these results.
_____
You can replicate columns using matrix multiplication, so you can transpose A, multiply it by a suitable version of an identity matrix, then transpose the result:
((A^T)·[I | I ])^T will turn the 3-row matrix to a 6-row matrix where I is a 3x3 identity matrix. I've used [I | I] here to mean the 3x3 identity matrix is itself replicated horizontally to make a 6-column matrix. ^T indicates transpose.
To represent the results of repeating die rolls in a matrix, each entry in the initial results matrix A is multiplied by the scalar value of the experiment repetition. If matrix A reflects 6 die rolls, the matrix for repeating these results would be 2A.
The student's question pertains to outcomes from rolling a six-sided die and recording the results in a matrix. To find the matrix representation of repeating the same die rolls, we would need to multiply the matrix A by the scalar value that represents the number of times the experiment is repeated. For example, if we denote matrix A as the initial 6 results and they repeated the experiment for the same number of times, then we would just need to multiply each entry in matrix A by 2 (since the results were repeated once more).
If matrix A is represented as:
A = [a b cd e f]
Then the new matrix, after repeating the rolls, would be:2A = [2a 2b 2c
2d 2e 2f]
This process does not change the probability of each result but simply scales the frequency of each outcome according to how many times the experiment is replicated.
Help with algebra please
Answers
Range- [-3,1] - What y values there are
If it is like in the picture, then:
Domain = [-3, 3] (we read from the x axis)
Range = [-3, 1] (we read from the y axis)
If there are no points at the ends of the segments, then:
Domain = all real numbers
Range = (-∞ , 1]
What number rounds to 168,356 when rounding to the nearest ten thousand
Answers
so the answer is 170,000
98 POINTS
Alice, Deepak, and Ivan each measure the length of a 6.5-inch pencil five times. They record their measurements as shown below. Who took the most ACCURATE measurements? Who took the most PRECISE measurements?
Alice: 6.25 in., 6.83 in., 6.11 in., 6.94 in., 6.19 in.
Deepak: 7 in., 7 in., 6 in., 7 in., 6 in.
Ivan: 6.5 in., 6.4 in., 6.5 in., 6.5 in., 6.4 in.
Answers
precise and accurate are two different things in measurements:
most precise means the most detailed. here Alice has 2 decimals so her measurements are the most precise.
but her measurements are very different so they are not accurate.
most accurate measurements are Ivan's as they are very close to each other.
Answer:
✔ Ivan
took the most accurate measurements.
✔ Alice
took the most precise measurements.
Step-by-step explanation:
got it right:)
HEEEEEEEEEEEEELP WILL GIVE TEN POINTS
Question:
Evaluate. Show all work for full credit.
If c = 30 and d = 8, then 2c + 4d = ?
Answers
2c + 4d = 92
substitute the given values into the expression and evaluate
2c + 4d = (2 × 30) + (4 × 8) = 60 + 32 = 92
The answer is 92. First substitute in 30 for c and multiply it by 2, and you get 60. Then, substitute in 8 for d and multiply it by 4 to get 32. Add 60 + 32 and it equals 92.
Let C ( t ) be the number of US cell phone subscribers in millions in t years since 1995. A linear model for the data is F ( t ) = 18.997 t + 17.711 .
Use the model to predict the year in which the number of subscribers will 324 million
Answers
ANSWER
In 16 years time.
EXPLANATION.
If the number of subscribers is 324 million, then it means
[tex]f(t)=324[/tex]
But we were given that,
[tex]f(t)=18.997t+16.711[/tex]
This implies that,
[tex]324=18.997t+16.711[/tex]
We now solve for t,
[tex]324-16.711=18.997t[/tex]
[tex]307.289=18.997t[/tex]
[tex]\frac{307.289}{18.997}=t[/tex]
[tex]16.17566=t[/tex]
That will be approximately in the 16th year.
In order to calculate the year where the number of US cell phone subscribers matches a certain number using the given linear model equation, you solve for the time variable. With the specified 324 million subscribers, the corresponding year would be approximately 2011.
Explanation:To use the provided linear model F(t) = 18.997t + 17.711 to predict the year where the number of subscribers will be 324 million, we need to solve the equation for t with C(t) set to 324:
324 = 18.997t + 17.711
To do so, subtract 17.711 from both sides to isolate the term with t:
324 - 17.711 = 18.997t
Then, divide both sides by 18.997 to solve for t:
(324 - 17.711) / 18.997 = t
After calculating, you will get approximately t = 16.123. Remember, t is the number of years after 1995, so you would add 16 (rounded from 16.123) to 1995. Thus, the model predicts that the number of US cell phone subscribers will reach 324 million in 2011.
Learn more about Linear Model here:https://brainly.com/question/29122305
#SPJ3
If b is the midpoint of ac, ac=cd, ab=3x+4, ac=11x-17, and ce=49, find de
Answers
Answer:
de=11
Step-by-step explanation:
We are given that b is the midpoint of ac
ac=cd, ab=3x+4,ac=11x-17 and ce=49
We have to find the value of de
b is the midpoint of ac therefore we have
ab=bc
ac=ab+bc=ab+ab=2ab
[tex]11x-17=2(3x+4)[/tex]
[tex]11x-17=6x+8[/tex]
[tex]11x-6x=8+17=25[/tex]
[tex]5x=25[/tex]
[tex]x=\frac{25}{5}=5[/tex]
Then , substitute the value of x
[tex]ab=3(5)+4=19[/tex]
ac=[tex]11(5)-17=55-17=38=cd[/tex]
ce=cd+de
49=38+de
[tex]de=49-38[/tex]
de=11
The measure of segment DE is 11.
Given:
[tex]AB = 3x+4\\AC = 11x-17\\CE=49[/tex]
See image in the attachment below showing the information given in the question.
Since B is the midpoint of AC, therefore:
[tex]AB = AC[/tex]
[tex]2(AB) = AC[/tex]
Substitute
[tex]2(3x+4)=11x-17[/tex]
Solve for x
[tex]6x +8=11x-17\\17 + 8 = 11x-6x\\25 = 5x\\[/tex]
Divide both sides by 5
[tex]5 = x\\x=5[/tex]
Find DE:
[tex]DE = CE - CD[/tex] (Segment Addition Postulate)
[tex]AC = CD = 11x-17[/tex]
Plug in the value of x
[tex]CD = 11(5) -17 = 38[/tex]
[tex]CE = 49 (given)[/tex]
Substitute
[tex]DE = 49 - 38\\DE = 11[/tex]
Therefore the length of DE = 11.
Learn more about segments here:
https://brainly.com/question/16553579
Write four decimals with the digit 4 in a different place in each ones, thenths,hundredths, and thousandths.Then write a statement that compares the value of the digit 4 in the different decimals.
Answers
The number 87.65487.65487, point, 654 can be placed on a place value chart as follows:
Tens Ones . Tenths Hundredths Thousandths
888 777 ..point 666 555 444
Decimal place value
The first digit after the decimal represents the tenths place. The next digit after the decimal represents the hundredths place. The remaining digits continue to fill in the place values until there are no digits left.
Example: 0.810.810, point, 81
The number 0.\blueD8\greenD10.810, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD is made up of \blueD88start color blueD, 8, end color blueD tenths and \greenD11start color greenD, 1, end color greenD hundredth.
We can also write this as:
0.\blueD8\greenD1=\blueD{0.8}+\greenD{0.01}0.81=0.8+0.010, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD, equals, start color blueD, 0, point, 8, end color blueD, plus, start color greenD, 0, point, 01, end color greenD
or
0.\blueD8\greenD1=\blueD{\dfrac8{10}}+\greenD{\dfrac1{100}}0.81=
10
8
+
100
1
0, point, start color blueD, 8, end color blueD, start color greenD, 1, end color greenD, equals, start color blueD, start fraction, 8, divided by, 10, end fraction, end color blueD, plus, start color greenD, start fraction, 1, divided by, 100, end fraction, end color greenD
Or we can use a place value chart:
Ones . Tenths Hundredths
000 ..point \blueD88start color blueD, 8, end color blueD \greenD11start color greenD, 1, end color greenD
Want to learn more about decimal place value? Check out this video.
Want to review whole number place value? Check out this article.
Practice
3,8,13,18, and 23 are the actual _____ of this sequence
Answers
Answer: The 3,8,13,18 and 23 the actual common difference of this sequence.
Explanation:
The given terms of the sequence are 3,8,13,18 and 23.
Where first term is 3, second is 8, thirst term is 18, fourth term is 18 and fifth term is 23.
The difference between second and third term is 5.
[tex]8-3=5[/tex]
The difference between third and fourth term is 5.
[tex]13-8=5[/tex]
So, the common difference of the sequence is 5. Since the difference between terms are same, therefore it is an arithmetic progression.
The formula to find the nth term is ,
[tex]a_n=a+(n-1)d[/tex]
Where a is the first term and d is the common difference.
How you could use a number line to show that -4 plus 3 and 3 plus (-4) have the same value. Which property of addition states that these sums are equivalent
Answers
Using a number line to show what -4 + 3 equals:
Start at the -4. Move three spaces to the right (+3). You land on -1.
Using a number line to show what 3 + (-4) equals:
Start at the 3. Move four spaces to the left (-4). You land on -1.
The commutative property of addition states that a + b = b + a.
Select the multiplication sentence that applies the associative property of multiplication to the example. Example: 1 × (9 × 5) = 45 A. 1 × (9 + 5) = 14 B. (8 × 5) + 5 = 45 C. (1 + 9) × 5 = 50 D. (1 × 9) × 5 = 45
Answers
The example is 1 x (9 x 5) = 45
Using the associative property of multiplication, we basically rearrange the parenthesis to group the first two terms like so: (1 x 9) x 5
So this is why choice D (1 x 9) x 5 = 45 is the answer
This means that 1 x (9x 5) = (1 x 9) x 5 is a true equation
Please help me
10 points
Answers
and on number 3 u can put that you need to subtract the 7 from both sides so thats where you get -3 on the left side and on number 4 you can put that you need to divide by negative 3 to get the answer which is 7
In step 2 multiply what is inside the parenthesis by 7 (distributive property):
7 * x = 7x
7 * 3 = 21
In step 3 subtract -7x on both sides of the equation. (Property of subtraction of equality)
Then -7x + 4x = -3x
7x-7x + 21 = 21
In step 4, both sides of the equation are divided by -3. (owned by the equality division)
So:
-3x / -3 = x
-21 / -3 = 7
Recall that the division of equal signs results in a positive number.
What is the value of the number 3 in the the number 12,532.628
Answers
What is the value of the number 3 in the the number 12,532.628
Solution
Here we need to use the place chart. I have attached the place value chart.
According to the place chart 3 is in tens place.
Therefore, the value of the number 3 in the number 12,532.628 is 3 x 10 = 30.
The answer is 30.
In the number 12,532.628, the digit 3 is located in the hundreds place, which means its value is 300.
The value of the number 3 in the number 12,532.628 is located in the hundreds place. To determine the place value of this digit, we start from the rightmost digit after the decimal point and move towards the left before the decimal point, labeling each position as follows: tenths, hundredths, thousandths, then units, tens, hundreds, thousands, and so on.
In 12,532.628, there are 2 units, 5 tens, 3 hundreds, 2 thousands, and 1 ten-thousands. Hence, the value of the number 3 here is 300. The digit 3 represents three hundred because it is in the hundreds place value.
A large group can weigh 1/3 ton.How much does a large grouper weigh to the nearest pound. I don’t understand this question it’s my homework but i really don’t understand it
Answers
667 pounds is the answer. There are 2000 pounds in a ton. 1/3 of a ton is 666.666667 pounds. I think this question is a conversion from tons to pounds?
I NEED HELP!!!!!!!!!!!! FAST!!!!!
On a piece of paper, graph this system of inequalities. Then determine which region contains the solution to the system.
y ≥ 3x + 2
A. Region B
B. Region C
C. Region A
D. Region D
Answers
From the graph, we know the y-intercepts (look at the picture).
y = 2 → y = 3x + 2
y = 3 → y = -1/3x + 3
We have
y ≥ 3x + 2 (shadow up of a line)
y ≤ -1/3x + 3 (shadows down of a line)
the common region is D.
Answer: D. Region D.Answer:
Option (a) and (d) are correct.
region A and region D satisfies the given inequality y ≥ 3x + 2.
Step-by-step explanation:
Given : The graph of the system of inequalities y ≥ 3x + 2.
We have to determine which region contains the solution to the system.
We will chose a test point in each region and see which point satisfies the given inequality.
For region A)
(0,6) is in region A
Put x = 0 and y = 6 in given inequality
We get,
6 ≥ 3(0) + 2.
6 ≥ 2 (True)
For region B)
(4,6) is in region B
Put x = 4 and y = 6 in given inequality
We get,
6 ≥ 3(4) + 2.
6 ≥ 12 + 2 = 14 (False)
For region C)
(0,0) is in region C
Put x = 0 and y = 0 in given inequality
We get,
0 ≥ 3(0) + 2.
0 ≥ 2 (False)
For region D)
(-2,2) is in region A
Put x = -2 and y = 2 in given inequality
We get,
2 ≥ -3(2) + 2.
2 ≥ -6+ 2 = -4 (True)
Thus, region A and region D satisfies the given inequality
Thus, Option (a) and (d) are correct.
Which of the following is graphed below?
Answers
Answer:
[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]
C is correct
Step-by-step explanation:
In the given graph function break at point x=2.
Left side about point x=2 is parabolic and right side straight line.
So, it would be piece wise function.
For parabola:
vertex: (0,4) and passing point (2,8)
[tex]y=a(x-h)^2+k[/tex]
[tex]y=ax^2+4[/tex]
[tex]a=1[/tex]
[tex]y=x^2+4[/tex] For x<2
For straight line:
Twp points (4,0) and (2,2)
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-2=\dfrac{0-2}{4-2}(x-2)[/tex]
[tex]y-2=-1(x-2)[/tex]
[tex]y=-x+4[/tex] For x≥2
Hence, The piece wise function will be
[tex]f(x)=\left \{ {{x^2+4}\ \ \ \ \ x<2 \atop {-x+4}\ \ \ x\geq 2}\right[/tex]
Need help evaluate the expression 5x - 7 for x =9? What is the answer?
Answers
An expression involving a variable is a way to express an idea, rather than a specific number. So, writing [tex] 5x-7 [/tex] means that there is a certain quantity, x, and you want to multiply it by 5, and then subtract 7.
Note that we don't want to know the value of x, we're only saying that we will multiply it by 5 and then subtract 7.
So, if we know that x=9, we will multiply it by 5 and then subtract 7:
[tex] 5x-7 = 5\cdot 9 - 7 = 45-7 = 38 [/tex]
Plot the data points on the graph below. Make sure you use the corresponding color dot for the point according to the following: 1st point - yellow dot, 2nd point - blue dot, 3rd point - green dot, 4th point - red dot, 5th point - pink dot, 6th point - purple dot. x values y values 1 18 2 9 3 6 6 3 9 2 18 1 (Inverse relationship, k = 18)
Answers
Hello,
Please, see the attached graph.
Thanks.
Answer: :)
Step by Step: :)
A family's lunch bill is $10.19 before tax and tip. Using the percents shown for sales tax and gratuity, how much money should the family pay if the gratuity is calculated after tax?
Answers
Answer:
12.36
Step-by-step explanation:
Answer:
Its: 12.36
Step-by-step explanation:
Given one factor of the polynomial, factor the polynomial completely.
16. f(x)=x^3-4x^2-7x+10;x-5
17. g(x)=2x^3+3x^2-23x-12;2x+1
Answers
Use synthetic division to solve these problems
5 | 1 -4 -7 10
| v 5 5 -10
1 1 -2 0
This leads to x^2+x-2
Next we find what adds to 1 and multiplies to -2
The factors of f(x) are 2 and -1, written out as (x+2) and (x-1)
-1/2 | 2 3 -23 -12
| v -1 -1 12
2 2 -24 0
This leads to 2x^2+2x-24
Next, multiply the 2 from the a value (since a is the value with x^2 and c is the value without any x) with -24, which is -48
Now find what adds to 2 and multiplies to -48
The values for this are 8 and -6, but keep in mind, when multiplying the value of a by c, you now have to add the values in place of what you tried adding it to, this time in the problem we found using synthetic division, in this case the 2 in the b value (the middle of the equation, or the value with only one x)
2x^2+8x-6x-24
When group factoring, you'd get 2x(x+4) -6 (x+4)
So, the factors of g(x) are (x+4) and (2x-6)
A running coach checks on his team's best recorded sprinting times during practice. Drag the runners in order from the greatest to the least unit rate in meters per second.
Answers
Carla
Amir
Carlo
Esther
From greatest to least!
Answer:
1. Carla
2. Amir
3. Carlo
4. Esther