Answer:
2517 = 3*839
Step-by-step explanation:
Prime no. are those numbers which are multiple of 1 and the number itself.
example
2,3,5,7 ....
A composite number is one which is multiple of other numbers as well apart from 1 and the number itself
example 24
24 can be written as 2*2*3
It is expressed as product of prime numbers. these number 2 and 3 are called prime factors because they are prime number and cannot be further expressed as product of any other number.
_______________________________________
we have to Express 2517 as a product of prime factor
lets find the factor of 2517
2517= 3*839
839 is a prime number itself and cannot be expressed as product of any other number .
Hence, 2517 expressed as product of prime factors is 3*839.
listed below are costs in dollars of round trip flights between two cities. All flights involve one stop and a two week stay. Find a coefficient of variation for each of the two sets of data, then compare the variation.
30 days in advance: 250 286 305 256 288 282 254
1 day in advance: 454 619 557 912 619 1049 562
The coefficient of variation for the prices of tickets purchased 30 days in advance is ____% (round to the three decimal places as needed)
Answer:
coefficient of variation = 7.108%
Step-by-step explanation:
From the given information:
The objective is to determine the coefficient of variation for the prices of tickets purchased 30 days in advance is ____%
The mean [tex]\overline x[/tex] = [tex]\dfrac{250+286+305+256+288+282+254}{7}[/tex]
The mean [tex]\overline x[/tex] = [tex]\dfrac{1921}{7}[/tex]
The mean [tex]\overline x[/tex] = 274.4285714
The standard deviation also can be computed as follows:
[tex]\sigma =\sqrt{ \dfrac{\sum (x_i-\mu)^2}{N}}[/tex]
[tex]\sigma =\sqrt{ \dfrac{ (250-274.43)^2+(286-274.43)^2+(305-274.43)^2+...+(254-274.43)^2}{7}}[/tex][tex]\sigma =19.507[/tex]
Finally; the coefficient of variation can be calculated with the formula:
coefficient of variation = [tex]\dfrac{\sigma}{\overline x}[/tex]
coefficient of variation = [tex]\dfrac{19.507}{274.43}[/tex]
coefficient of variation = 0.07108
coefficient of variation = 7.108%
To decide whether two different types of steel have the same true average fracture toughness values, n specimens of each type are tested, yielding the following results.
Type Sample Average Sample SD
1 60.7 1.0
2 60.5 1.0
Required:
a. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 100. (Round your answer to four decimal places.)
b. Calculate the P-value for the appropriate two-sample z test, assuming that the data was based on n = 500. (Round your answer to four decimal places.)
c. Is the small P-value for n = 500 indicative of a difference that has practical significance
Answer:
a. P-value = 0.1589
b. P-value = 0.0016
Step-by-step explanation:
a. This is a hypothesis test for the difference between populations means.
The claim is that the two types of steel have different true average fracture toughness values.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is α=0.05.
The sample 1, of size n1=100 has a mean of 60.7 and a standard deviation of 1. The sample 2, of size n2=100 has a mean of 60.5 and a standard deviation of 1.
The difference between sample means is Md=0.2.
[tex]M_d=M_1-M_2=60.7-60.5=0.2[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{100}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{100}}=\sqrt{0.02}=0.1414[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.1414}=\dfrac{0.2}{0.1414}=1.4142[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=100+100-2=198[/tex]
This test is a two-tailed test, with 198 degrees of freedom and t=1.4142, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t>1.4142)=0.1589[/tex]
As the P-value (0.1589) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the two types of steel have different true average fracture toughness values.
b. As the sample size changes, the standard error and the degress of freedom change.
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{1^2+1^2}{500}}\\\\\\s_{M_d}=\sqrt{\dfrac{2}{500}}=\sqrt{0.004}=0.0632[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.2-0}{0.0632}=\dfrac{0.2}{0.0632}=3.1623[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-2=500+500-2=998[/tex]
This test is a two-tailed test, with 998 degrees of freedom and t=3.1623, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t>3.1623)=0.0016[/tex]
As the P-value (0.0016) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the two types of steel have different true average fracture toughness values.
Which graph shows the solution set for 2x+3>-9
Answer:
x > -6
Step-by-step explanation:
2x + 3 > -9
Subtract 3 on both sides.
2x > -9 - 3
2x > -12
Divide 2 into both sides.
x > -12/2
x > -6
Answer: c
Step-by-step explanation:
Just helped my daughter with quiz got 100%
Suppose the preliteracy scores of three-year-old students in the United States are normally distributed. Shelia, a preschool teacher, wants to estimate the mean score on preliteracy tests for the population of three-year-olds. She draws a simple random sample of 20 students from her class of three-year-olds and records their preliteracy scores (in points).
81,84,87,91,91,91,92,92,94,95,97,99,100,102,106,107,107,111,115,116
1. Calculate the sample mean (x⎯⎯⎯), sample standard deviation (????), and standard error (SE) of the students' scores. Round your answers to four decimal places.
2. Determine the ????-critical value (????) and margin of error (m) for a 99% confidence interval. Round your answers to three decimal places.
3. What are the lower and upper limits of a 99% confidence interval? Round your answers to three decimal places.
4. Which is the correct interpretation of the confidence interval?
a. Shelia is certain that the true population mean is between 91.537 points and 104.263 points.
b. Shelia is 99% confident that the true population mean is between 92.171 points and 103.629 points.
c. There is a 99% chance that the true population mean is between 92.171 points and 103.629 points.
d. Shelia is 99% confident that the true population mean is between 91.537 points and 104.263 points.
e. There is a 99% chance that the population mean is between 91.537 points and 104.263 points.
Answer: 1. sample mean = 97.7; sample standard deviation(s) = 9.9467; standard error (SE) = 2.2241
2. t-critical value = 2.861; margin of error (m) = 97.9 ± 6.363
3. Lower limits = 91.537; upper limit = 104.263
4. d. Sheila is 99% confident that the true population mean is between 91.537 points and 104.263 points.
Step-by-step explanation: Knowing that this sample has 20 individuals, which means n = 20:
1. Sample mean is the average of the data set:
mean = [tex]\frac{81+84+...+115+116}{20}[/tex] = 97.9
Sample standard deviation is the spread of the sample data set from the mean:
s = [tex]\sqrt{\frac{(81-97.9)^{2}+...+(116-97.9)^{2}}{20-1} }[/tex] = 9.9467
Standard Error shows how far the mean of the set is from the true popultaion mean:
SE = [tex]\frac{9.9467}{\sqrt{20} }[/tex] = 2.2241
2. The t-critical value (t) is the value you use to decide if you reject or accept the null hypothesis. It can be calculated by a calculator or found in the t-test table. To use the table:
Degrees of freedom for this set is: n - 1 = 19
Critical value (α) = 0.99. For the t-test: [tex]\frac{1-0.99}{2}[/tex] = 0.005
[tex]t_{19,0.005}[/tex] = 2.861
Margin of error (m) shows, in percentage, how different your results are from the real population value. It is calculated as:
m = 97.9 ± 2.861*2.2241 = 97.9 ± 6.363
3. Lower and Upper limits are the interval the true mean can assume with a determined certainty.
lower limit = 97.9 - 6.363 = 91.537
upper limit = 97.9 + 6.363 = 104.263
4. In this case, the statistics shows that the true population mean is between 91.537 and 104.263, 99% of the time.
c. Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $12 and $18
Answer:
0.0066
Step-by-step explanation:
The x has a distribution that is approximately normal. For normal distribution the probability of x will be,
u = 12 and 18
P (12 [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 18)
P (- 2.3 [tex]\leq[/tex] [tex]x[/tex] [tex]\leq[/tex] 2.85 )
P (0.9912 - 0.9978)
= 0.0066
Mari Seni works exactly 40 hours in a 5-day work week. She worked 6 1/2 hours on Monday, 8 3/4 hours on Tuesday, 6 5/6 hours on Wednesday, and 10 1/4 hours on Thursday. How many hours must Mari work on Friday.
Answer:
gdk
Step-by-step explanation:
Beverly drove from the Atlantic City to New York she drove 284 miles at a constant speed of 58 mph how long did it take Beverly to complete the trip
Answer:
Find the number of hours by dividing the distance by mph. The number of hours will be to the left of the decimal point:
284 miles / 58 mph
= 4.896551724
= 4 hours
2) Find the number of minutes by multiplying what is remaining from step 1 by 60 minutes. The minutes will be to the left of the decimal point:
0.896551724 x 60
= 53.79310344
= 53 minutes
3) Find the number of seconds by multiplying what is remaining from step 2 by 60 seconds. The seconds will be to the left of the decimal point:
0.79310344 x 60
= 47.5862064
= 47 seconds
The answer is 4 hours 53 minutes and 47 seconds approx
Suppose you were told that a 98% confidence interval for the population mean of mpg of a hybrid car was (22, 38). Determine the point estimate for this population mean.
Answer:
The point estimate for the mean mpg of hybrid cars is 30 mpg.
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this problem, we have that:
Lower bound: 22
Upper bound: 38
Point Estimate:
(22 + 38)/2 = 30
The point estimate for the mean mpg of hybrid cars is 30 mpg.
simplify: 3^4 x 2^0 x 6^1
A. 0
B. 486
C. 972
D. 81
Answer:
B. 486
Step-by-step explanation:
3^4 = 3 × 3 × 3 × 3 = 81
2^0 = 1
6^1 = 6
Find the product.
81 × 1 × 6
= 486
Answer:
option B; 486
Step-by-step explanation: 3 raised to the power 4 can be written as 3*3*3*3, 2 raised to 0 is 1( any number raised to to the power 0 is 1), 6 raised to 1 is the number itself( means that 6 is only repeated or mentioned once).
so, 3*3*3*3*1*6=486
Consider the function below. (If an answer does not exist, enter DNE.) g(x) = 190 + 8x3 + x4 (a) Find the interval of increase. (Enter your answer using interval notation.)
Answer:
The interval of increase of g(x) is [tex](-6,+\infty)[/tex].
Step-by-step explanation:
The interval of increase occurs when first derivative of given function brings positive values. Let be [tex]g(x) = 190 + 8 \cdot x^{3} + x^{4}[/tex], the first derivative of the function is:
[tex]g'(x) = 24 \cdot x ^{2} + 4\cdot x^{3}[/tex]
[tex]g'(x) = 4 \cdot x^{2}\cdot (6+x)[/tex]
The following condition must be met to define the interval of increase:
[tex]4\cdot x^{2} \cdot (x+6) > 0[/tex]
The first term is always position due to the quadratic form, the second one is a first order polynomial and it is known that positive value is a product of two positive or negative values. Then, the second form must satisfy this:
[tex]x + 6 > 0[/tex]
The solution to this inequation is:
[tex]x > - 6[/tex]
Now, the solution to this expression in interval notation is: [tex](-6,+\infty)[/tex]
Multiply: (−2x2 + 9x − 3) * (7x2 − 4x + 2)
Answer:
[tex]-14x^4+71x^3-61x^2+30x-6[/tex]
Step-by-step explanation:
All we are doing is distributing each number of the 1st equation to the 2nd equation to get our answer. Once we do so, we combine like terms and we get our answer.
–25(r − 989) = 175 r = _______
Answer:
r = 982
Step-by-step explanation:
[tex]-25(r-989)=175\\-25r+24725=175\\-25r=-24,550\\25r=24,550\\r=982[/tex]
What do you go by for the pattern 360,60,10 would it be add 60, divided by 6 ,multiply by 6 or subtract 300?
Answer:
divided by 6
Step-by-step explanation:
Given pattern
360,60,10
would it be add 60
lets
add 60 to each term
360 +60 = 420
but next term is 60, hence it incorrect choice
divided by 6
lets divide each term by 6
360/6 = 60 which is the next term in the series as well
60/6 = 10 which is also the next term in the series as well
hence divided by 6 is the correct option.
multiply by 6
multiply by 6 to each term
360 *60 = 21600
but next term is 60, hence it incorrect choice
subtract 60 from each term
360 -300 = 60 which is the next term in the series
60 -300 = -240 which is not same the next term in the series that is 10
hence this is incorrect choice
Find measure of arc or angle indicated
A
cat is sitting on a 2 m high fence when it sees a mouse
1.5 m away from
the foot of the fence The cat leaps along
the path y = - 0.6x - x2, where the origin is where the cat
was sitting and xis measured in metres. Find, by a
graphical method, whether the cat lands on
the mouse.
Answer:
what's this... ..........
In a certain city, 80% of the residents like coffee or tea . 30% of them like coffee. 60%
percent of them like tea. What is the probability of residents like (a) both? (b) tea but not
coffee? (c) only coffee (d) neither tea nor coffee ?
Answer:
a =10% b=50% c=20% d=20%
Step-by-step explanation:
n(CuT)=n(C)+n(T)-n(CnT)
so n(CnT)=10%
for b
tea but not coffee =nonly(T)
=n(T)-n(TnC)
=50%
for c
only coffee=nonly(C)
=n(C)-n(CnT)
=20%
Factorise x²+5x−6 the options are
(x+2)(x+3)
(x−1)(x+6)
(x+1)(x−6)
(x−2)(x+3)
Answer:
(x-1)(x+6)
Step-by-step explanation:
=> [tex]x^2+5x-6[/tex]
Using mid-term break formula to find it's factors
=> [tex]x^2+6x-x-6[/tex]
=> x(x+6)-1(x+6)
Taking x+6 common
=> (x-1)(x+6)
The board of directors of Midwest Foods has declared a dividend of $3,500,000. The company has 300,000 shares of preferred stock that pay $2.85 per share and 2,500,000 shares of common stock. After finding the amount of dividends due the preferred shareholders, calculate the dividend per share of common stock.
Answer:
$1,06
Step-by-step explanation:
Calculation for dividend per share of common stock for board of directors of Midwest Foods
First step is to find the amount of dividends due to the preferred shareholders
Using this formula
Total Dividend =Dividend- (Preferred stock *Per share of preferred stock )
Let plug in the formula
Total Dividend =$3,500,000-($300,000*$2.85)
Total Dividend =$3,500,000-$855,000
Total Dividend =$2,645,000
The second step is to find Dividend per share of common stock
Using this formula
Dividend per share of common stock=Total dividend/Shares of common stock
Let plug in the formula
Dividend per share of common stock=$2,645,000/$2,500,000
Dividend per share of common stock=$1.06
Therefore the dividend per share of common stock for board of directors of Midwest Foods will be $1.06
A shipment of 60 inexpensive digital watches, including 9 that are defective,is sent to a department store.The receiving department select's 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective.What is the probability that the shipment will be rejected?
Answer: 0.627 or 62.7 %
Step-by-step explanation:
The probability that shipment will be rejected P(rejected) = 1- probability that shipment will be accepted.
P(rejected)= 1-P(accepted)
P(accepted) is equal to probability when all 10 watches are not defective.
The probability that 1st one randomly selected watches are not defective is 51/60 (51 watches are not defective and 9 are defective)
The probability that 2-nd one randomly selected watches are not defective is 50/59 ( because the total number of the watches now is 1 unit less 60-1=59, and the total number of not defective watches is 1 unit less 51-1=50 units)
The probability that 3rd one randomly selected watches are not defective is 49/58 (49 watches are not defective total number of watches is 58)
Similarly P(4th)= 48/57 P(5th)=47/56 P(6th)=46/55 P(7th)=45/54
P(8th)=44/53 P(9th)=43/52 P(10th)=42/51
So P(accepted)= P(1st)*P(2nd)*P(3rd)*P(4th)*P(5th)*P(6th)*P(7th)*P(8th)*P(9th)*P(10th)=
=51*50*49*48*47*46*45*44*43*42/(60*59*58*57*56*55*54*53*52*51)=
= approx= 0.373
So P(rejected)=1-0.373=0.627
To compare the production techniques used by foreign and local firms in Brazil, a random sample of 80 foreign firms and a random sample of 80 local firms are selected.This study uses_________ design
Answer:
An independent sample.
Step-by-step explanation:
In this scenario, to compare the production techniques used by foreign and local firms in Brazil, a random sample of 80 foreign firms and a random sample of 80 local firms are selected. We can safely conclude that this study uses an independent sample design.
An independent sample design can be defined as a research method that usually involves the use of multiple experimental groups (two or more). The samples or participants are only in one group and as such each group has no relationship with the other. This simply means that, the samples in a particular group is having no relationship with the other samples in another group.
Ultimately this implies, each samples are independent and satisfies only one condition of the independent sample design during the experiment to compare the production technique used by foreign and local firms in Brazil.
Hence, the researcher would use only two variables or conditions: a random sample of 80 foreign firms and a random sample of 80 local firms are selected.
Graph the system of linear inequalities. Please help!
Answer: Third option is correct
Step-by-step explanation: The y-intercepts match the constants (b in y=mx+b format) The y-values shaded above the line y≥2x+4 are correct. The y-values shaded in the region below the y≤2x -2 are also correct.
Poly(3-hydroxybutyrate) (PHB), a semicrystalline polymer that is fully biodegradable and biocompatible, is obtained from renewable resources. From a sustain-ability perspective, PHB offers many attractive proper-ties though it is more expensive to produce than standard plastics. The accompanying data on melting point (°C) for each of 12 specimens of the polymer using a differential scanning calorimeter appeared in the article "The Melting Behaviour of Poly(3-1-1ydroxybutyrate) by DSC. Reproducibility Study" (Polymer Testing, 2013: 215-220).
180.5 181.7 180.9 181.6 182.6 181.6
181.3 182.1 182.1 180.3 181.7 180.5
Compute the following:
a. The sample range
b. The sample variance S2 from the definition (Hint: First subtract 180 from each observation.]
c. The sample standard deviation
d. S2 using the shortcut method
Answer:
(a) 2.3
(b) 0.5245
(c) 0.7242
(d) 0.5245
Step-by-step explanation:
The data provided is:
S = {180.5, 181.7, 180.9, 181.6, 182.6, 181.6, 181.3, 182.1, 182.1, 180.3, 181.7, 180.5}
(a)
The formula to compute the sample range is:
[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]
The data set arranged in ascending order is:
S' = {180.3 , 180.5 , 180.5 , 180.9 , 181.3 , 181.6 , 181.6 , 181.7 , 181.7 ,, 182.1 , 182.1 , 182.6}
The minimum value is, 180.3 and the maximum value is, 182.6.
Compute the sample range as follows:
[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]
[tex]=182.6-180.3\\=2.3[/tex]
Thus, the sample range is 2.3.
(b)
Compute the sample variance as follows:
[tex]S^{2}=\frac{1}{n-1}\sum(x_{i}-\bar x)^{2}[/tex]
[tex]=\frac{1}{12-1}\times [(180.5-181.41)^{2}+(181.7-181.41)^{2}+...+(180.5-181.41)^{2}]\\\\=\frac{1}{11}\times 5.7692\\\\=0.524473\\\\\approx 0.5245[/tex]
Thus, the sample variance is 0.5245.
(c)
Compute the sample standard deviation as follows:
[tex]s=\sqrt{S^{2}}[/tex]
[tex]=\sqrt{0.5245}\\\\=0.7242[/tex]
Thus, the sample standard deviation is 0.7242.
(d)
Compute the sample variance using the shortcut method as follows:
[tex]S^{2}=\frac{1}{n-1}\cdot [\sum x_{i}^{2}-n(\bar x)^{2}][/tex]
[tex]=\frac{1}{12-1}\cdot [394913.57-(12\times (181.41)^{2}]\\\\=\frac{1}{11}\times [394913.57-394907.80]\\\\=\frac{5.77}{11}\\\\=0.5245[/tex]
Thus, the sample variance is 0.5245.
9) brainliest & 10 + points!
Answer:
no supplement
Step-by-step explanation:
Supplementary angles add to 180 degrees,
This angle is larger than 180 degrees by itself, so it has no supplement
determine the number and type of zeros of the quadratic function based on the value of the discriminant
If [tex]D>0[/tex] then [tex]x_1,x_2\in\mathbb{R}[/tex].
If [tex]D=0[/tex] then [tex]x_1=x_2\wedge x_1,x_2\in\mathbb{R}[/tex].
If [tex]D<0[/tex] then [tex]x_1,x_2\in\mathbb{C}[/tex].
Hope this helps.
What is the slope of the line shown?
Slope=-1/2
Slope =7
Slope=2
Slope=-2
Answer:
-2
Step-by-step explanation:
To find the slope: Rise/Run
You go 2 steps down for every step you go right.
Your rise is -2 and your run is 1.
So your slope is -2.
Answer:
-2
Step-by-step explanation:
Get two points that intersect that line.
(1, 5) and (2, 3)
Find the rise and run.
As we can see to get from (1,5) to (2,3), we have to go to the right by 1 and go down by 2 (in this case the movement is -2 steps).
rise/run
-2/1 = -2
round to the nearest hundredth: 2.0625
Answer: 2.06
Step-by-step explanation:
Remember if the number is greater than 5 round up, if it is less than 5 don't round up.
After round off the number 2.0625 to its nearest hundredth, it is 2.06.
When we round to the nearest hundredth, we follow the rule that says:
If the digit in the thousandths place is less than 5 we round down the hundredths place.If the digit in the thousandths place is greater than 5, we round up the hundredths place.The given number is 2.0625
In this number, the thousandth digit is 2 that is less than 5.
So we round down the hundredth place. The hundredth digit is 6 which remain 6 after rounding down.
So, the rounded number will be 2.06.
Hence, when we round 2.0625 to its nearest hundredth, it will be 2.06.
Learn more about round off the numbers here:
https://brainly.com/question/30453145
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I need help with this question: Label: Coefficients, variables, terms, and constant. −2x2 + 9x − 3
Answer:
coefficients: {-2, +9, -3}
variables: {x}
terms: {-2x^2, 9x, -3}
constant: {-3}
Step-by-step explanation:
It is difficult to "label" here, so we'll list each, separated by commas.
Coefficients
Coefficients are the multiplicative factor of an expression. Depending on the expression of interest, it may consist of numbers, variables, or expressions. Here, we consider the expression of interest to be powers of x, so the coefficients are as listed. The last one (-3) is sometimes called a "constant coefficient." It multiplies x^0.
coefficients: {-2, +9, -3}
Variables
A variable is usually a letter, symbol, or sequence of letters and symbols, that stands for something else--usually an unknown quantity. Its meaning and value will depend on the context. Generic variables are usually taken from the end of the alphabet: x, y, z. Their capitalization, font, or face may give special meaning. For example bold-face capital letters may be used to represent vectors or matrices.
variables: {x}
Terms
A term is a product of coefficients and variables. Terms in a polynomial are separated by addition or subtraction symbols.
terms: {-2x^2, 9x, -3}
Constant
"Constant" usually refers to a term containing no variables. It generally refers to a value that doesn't change.
constant: {-3}
Find the gradient of the line segment between the points (4,-4) and (0,-12).
Answer: 2
Step-by-step explanation:
The equation for slope is change in y / change in x, which is (-4-(-12))/(4-0) in this case. That is equal to 2.
The gradient of the line segment between the points (4,-4) and (0,-12) is 2.
We have to determine, the gradient of the line segment between the points (4,-4) and (0,-12).
The gradient and slope of the line segment between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by the following formula;
The gradient of the line segment = [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Then, the gradient of the line segment between the points (4,-4) and (0,-12) is,
[tex]= \dfrac{-12-(-4)}{0-4}\\\\= \dfrac{-12+4}{-4}\\\\= \dfrac{-8}{-4}\\\\= 2[/tex]
Hence, The required gradient of the line segment between the points (4,-4) and (0,-12) is 2.
To know more about Slope click the link given below.
https://brainly.com/question/19072709
what is the slope of the line that contains the points (-1,8) and (2,-4)
HELPPPPPP!!!
Step-by-step explanation:
[tex]a = \frac{ - 4 - 8}{2 - ( - 1)} = \frac{ - 12}{3} = - 4[/tex]
The slope of the line passing through the points (-1, 8) and (2, -4) is -4.
To find the slope of a line passing through two points, we can use the slope formula:
[tex]slope = (y_2 - y_1) / (x_2 - x_1)[/tex]
Let's use the given points (-1, 8) and (2, -4) to calculate the slope:
[tex]x_1 = -1, y_1 = 8\\\\x_2 = 2, y_2 = -4[/tex]
slope = (-4 - 8) / (2 - (-1))
= (-12) / (2 + 1)
= -12 / 3
= -4
Therefore, the slope of the line passing through the points (-1, 8) and (2, -4) is -4.
To know more about slope, refer here:
https://brainly.com/question/4193335
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A set of data is summarized by the stem and leaf plot below.
Steam Leaf
1 0 0 2 4 4 4 7 8 8 8 8 9
2 2 2 5 5 7 8
3 3 4 4 5 5 5 6 6 6 7 9 9
4 3 3 3 5 5 7 9
a. There are _____ values in the data set which are greater than or equal to 10 and less than or equal to 19.
b. There are _____ values in the data set which are greater than or equal to 30 and less than or equal to 39.
c. There are ____ values in the data set which are greater than or equal to 40 and less than or equal to 49.
Answer:
(a) There are 12 values in the data set which are greater than or equal to 10 and less than or equal to 19.
(b) There are 12 values in the data set which are greater than or equal to 30 and less than or equal to 39.
(c) There are 7 values in the data set which are greater than or equal to 40 and less than or equal to 49.
Step-by-step explanation:
We are given a set of data that is summarized by the stem and leaf plot below;
Steam Leaf
1 0 0 2 4 4 4 7 8 8 8 8 9
2 2 2 5 5 7 8
3 3 4 4 5 5 5 6 6 6 7 9 9
4 3 3 3 5 5 7 9
This shows that the data values are: 10, 10, 12, 14, 14, 14, 17, 18, 18, 18, 18, 19, 22, 22, 25, 25, 27, 28, 33, 34, 34, 35, 35, 35, 36, 36, 36, 37, 39, 39, 43, 43, 43, 45, 45, 47, 49.
(a) From the data above, the number of values in the data set which are greater than or equal to 10 and less than or equal to 19 is 12, i.e; 10, 10, 12, 14, 14, 14, 17, 18, 18, 18, 18, 19.
(b) From the data above, the number of values in the data set which are greater than or equal to 30 and less than or equal to 39 is 12, i.e; 33, 34, 34, 35, 35, 35, 36, 36, 36, 37, 39, 39.
(c) From the data above, the number of values in the data set which are greater than or equal to 40 and less than or equal to 49 is 7, i.e; 43, 43, 43, 45, 45, 47, 49.
Answer:5,9
Step-by-step explanation: