Using the normal distribution we find that P(X=8) equals zero.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome.According to our question-
Measures how many standard deviations a measurement is from its mean.
After finding the Z-score, look at the Z-score table to find the p-value (percentile of x) associated with that Z-score.
As with any continuous distribution, the probability of an exact value, P(X = x), is 0.
So t we know that P(X=8) equals zero.
Hence, Using the normal distribution we find that P(X=8) equals zero.
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What is 18.92 divided by11 equals 18.92 at the top 11 at the bottom explain your answer PLEASE I HAVE TO SUMMIT THIS IN 19 MIN!
The value of 18.92/11 is 1.72.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
The given term is 18.92 divided by 11,
The mathematical expression for 18.92 divided by 11,
= 18.92/11
= 1.72
The value of 18.92 divided by 11 is 1.72.
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what is the probability of drawing (without replacement) an ace, then a king, and then a queen, from a regular deck of 52 cards?
Three cards are drawn from a standard deck. Thus, the probability to get an ace, followed by a king, and then a queen, is 16/34,425
The formula for conditional probability is:
P(A∩B) = P(B|A) . P(A)
In the given problem:
P(ace) = 4 / 54
After an ace was drawn, the number of cards now is 51.
Hence,
P(king | ace) = 4/51
After the second drawn, the remaining cards is 50. Hence,
P(queen | (king | ace)) = 4/50
Therefore,
P(ace,king,queen) = 4/54 x 4/51 x 4/50 = 64 / 137,700 = 16/34,425
Thus, the probability to get an ace, followed by a king, and then a queen, is 16/34,425
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A multiple regression model Y^=?^0+?^1X1+?^2X2+?^3X3 is fit to a data set with 14 observations. If a 95% confidence interval for the mean response at X1=2,X2=?4,X3=7 is (?1,1), and a 95% prediction interval for a new observation at X1=2,X2=?4,X3=7 is (?2,2), then to three decimal places the mean square error (MSE) equals
The mean square error (MSE) for that multiple regression model is 0.604
How to calculate MSE?
MSE = mean square error
n = total data
[tex]x^*[/tex] = predictor
[tex]\bar x[/tex] = mean
df = degree of freedom
α = significance level = 1 - 95% = 0.05
x, y = variable
assumed,
[tex]\hat y[/tex] = predicted value = 0
Formula for confidence interval (CI) for mean response is
CI = [tex]\hat y\pm t_{\alpha/2,df}\times \sqrt{MSE(\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]
Formula for confidence interval (CI) for prediction response is
CI = [tex]\hat y\pm t_{\alpha/2,df}\times \sqrt{MSE(1+\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]
Since, given confidence interval for mean response is (-1,1) and confidence interval for prediction response is (-2,2) at 95% confidence.
CI for mean response,
For CI = 1 = [tex]0+ t_{\alpha/2,df}\times \sqrt{MSE(\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]
For CI = -1 = [tex]0- t_{\alpha/2,df}\times \sqrt{MSE(\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]
simplified to
[tex]2\times t_{\alpha/2,df}\times \sqrt{MSE(\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 2
[tex]t^2_{\alpha/2,df}\times MSE\times (\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 1
CI for predicted response,
For CI = 2 = [tex]0+ t_{\alpha/2,df}\times \sqrt{MSE(1+\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]
For CI = -2 = [tex]0- t_{\alpha/2,df}\times \sqrt{MSE(1+\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex]
simplified to
[tex]2\times t_{\alpha/2,df}\times \sqrt{MSE(1+\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 4
[tex]t^2_{\alpha/2,df}\times MSE\times (1+ \frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 4
[tex]t^2_{\alpha/2,df}\times MSE+ t^2_{\alpha/2,df}\times MSE \times (\frac{1}{n}+\frac{(x^*-\bar x)^2}{\sum(x_i-\bar x)^2})[/tex] = 4
substitute CI for mean response to CI for predicted response
[tex]t^2_{\alpha/2,df}[/tex] x MSE + 1 = 4
[tex]t^2_{\alpha/2,df}[/tex] x MSE = 3
Now, for [tex]t^2_{\alpha/2,df}[/tex], we first find degree of freedom
df = n - 4
= 14 - 4
= 10
Look on t table for [tex]t_{0.05/2,10}[/tex], and we get 2.228. So,
MSE = [tex]\frac{3}{2.228^2}[/tex]
MSE = 0.604
Thus, the MSE is 0.604 for that multiple regression model.
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does the data suggest that true average total body bone mineral content during post weaning exceeds that during lactation by more than 25 g? state and test the appropriate hypotheses using a significance level of 0.05. (note: the appropriate normal probability plot shows some curvature but not enough to cast substantial doubt on a normality assumption.)
The appropriate hypotheses using a significance level of 0.05 reject H0.
The hypothesis :
H0 : μL - μP ≥ 25
H0 : μL - μP < 25
The sample mean difference; Xd
d = L - P
Xd = Σd/n
d = -198,-336,-70,-18,-122,-9,-50,-5,-163,-86
Xd = - 1057 / 10
Xd = - 105.7
Using calculator ;
Standard deviation of difference, Sd = 103.845
The test statistic :
T = Xd ÷ (Sd/√n)
T = -105.7 ÷ (103.845/√10)
T = - 3.219
Decision region :
Reject H0 ; If P-value < α
The P-value : df = n - 1 ; 10 - 1 = 9
P-value(-3.219, 9) ; two-tailed = 0.00525
Hence the answer is, the appropriate hypotheses using a significance level of 0.05 reject H0.
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Match each circle on the left-hand side with its circumference on the right
Answer:
1 - 4
2 - 2
3 - 5
4 - 3
5 - 1
Step-by-step explanation:
Hope this helps
Why is the treaty important?.
A Treaty is important because it settled downs the global issues with diplomatic approach.
A treaty is an agreement between two countries with the set of rules defining the responsibilities and obligations for the countries.
Some issues which are not only important for the country but also for the issues which need attention globally.
A Treaty can be made for any purpose. It is stabilizes the relationship between two countries in a diplomatic manner without the unnecessary loss of resources and valuable human life.
A Treaty is a long term solution for the problems.
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which of these af3 molecules will have a nonzero dipole moment? choose all that apply. which of these molecules will have a nonzero dipole moment?choose all that apply. request answer
The first molecule will have a ZERO dipole moment since all the F atoms are at 120 degree making the net dipole zero.
What exactly is a molecule?A molecule is a group of two or more atoms held together by chemical bonds; depending on the context, the term may or may not include ions that meet this criterion.
A molecule is a particle composed of two or more atoms that are chemically bonded together; the number of atomic nuclei constituting a molecule is fixed. HCl(g), for example, is a molecule composed of one hydrogen atom bonded to one chlorine atom. It is a diatomic molecule because it is composed of two atoms.
The second molecule will have a NON ZERO dipole moment. The net dipole moment will be downwards. The third molecule will have a NON ZERO dipole moment.
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Part (c) In words, state what your random variable X represents X represents the number of hours a woman works in a week X represents the number of women who work over 80 hours a week. X represents the average number of women who work over 80 hours a week. X represents the average number of hours women work in one week. Correct! The investigation involves the average number of hours that women work in a given week.
There is sufficient evidence to conclude that the average number of hours women work each week is more than 80 hours
The hypothesIs are
Ha : μ>80
Given the sample size n=68 and sample mean X 83 , sample standard deviation s=10
The test statistic is
t = x~ - 80/s/√n
t= 83-80/10/√68
t- 2.4738634
The P-value of the test is
P-value P(T> 2.4738634)
P-value 0.0080
When α=0.05,
Reject the null hypothesis since P-value 0.0080 a 0.05
i) The -a) 10090 two-sided confidence interval for mean based on the sample data is
{x}\pm t_{1-\α /2,n-1}\frac{s}/{√n}
Here the 95% confidence interval is
= 83 ± t1-0.05/2,67 10/V68
= (80.58,85.42)
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suppose that you had consumer group wanted to test to see if weight of participants in a weight loss program changed (up or down). they computed a 95% confidence interval of the result (2.177, 4.977). what do we know about the p-value for the test?
The required P-values for the result is 0.05.
How to calculate P-value?The p-value is determined utilizing the inspecting conveyance of the test measurement under the invalid speculation, the example information, and the kind of test being finished (lower-followed test, upper-followed test, or two-sided test).
According to question:The hypothesis test was done to claim that the weight of participants has changed.
The null and alternative hypothesis could be written as:
H₀ : a =0
Hᵃ : a [tex]\neq[/tex] 0
being μ the population mean change in weight.
With that data, we can perceive that is a two followed test. Test implies that fall in any of the tails, with a z-measurement over 1.96 or under - 1.96 (at an importance level of 0.05), will be proof to dismiss the invalid speculation.
The data we have about the example is the 95% certainty stretch determined from the example data.
This certainty stretch does exclude the worth μ=0.
Then, there is 2.5% of probability that the populace mean is under 2.177, the lower bound of the stretch, which incorporates the worth μ=0.
Thus, we can reason that the P-esteem must be under 0.05.
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Please help! There is 2 answers for this. thank you so much!
x = I9I
or:
x = I-9I
so:
x = 9 or -9
calculate the mass of camphor that contains a million carbon atoms. be sure your answer has a unit symbol if necessary, and round it to significant digits.
By using Unitary method, it can be calculated that
[tex]1 \times 10^7[/tex] atoms of carbon is contained in [tex]2.53 \times 10^{-17}[/tex] g of camphor
What is Unitary Method?
Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity
Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.
Here, Unitary method will be used
Formula for Camphor = [tex]C_{10}H_{16}O[/tex]
Gram Molecular mass = [tex]12 \times 10 + 16 \times 1 + 16[/tex] = 152g
[tex]10 \times 6 \times 10^{23}[/tex] atoms of carbon is contained in 152 g of camphor
1 atoms of carbon is contained in [tex]\frac{152}{6 .023 \times 10^{24}}[/tex] g of camphor
[tex]1 \times 10^{7}[/tex] atoms of carbon is contained in [tex]\frac{152 \times 1 \times 10^7}{6 .023 \times 10^{24}}[/tex] g of camphor
[tex]1 \times 10^7[/tex] atoms of carbon is contained in [tex]\frac{152 \times 1 \times 10^7}{6 .023 \times 10^{24}}[/tex] g of camphor
[tex]1 \times 10^7[/tex] atoms of carbon is contained in [tex]2.53 \times 10^{-17}[/tex] g of camphor
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Help!!!!!!!!!!!??????
PLS
Answer:
Slope of line e is 2/3
Step-by-step explanation:
you know that equation for line d is y= 2/3x+3. because that line e is parallel to line d, it means that line e and d will never intersect which can only happen if both lines have the same slope. so that means line e's slope is 2/3
Answer:
2/3
Step-by-step explanation:
when a line is parallel to another line we say that the slopes are equal hence the slope of line e is 2/3.
NOTE: if a line is perpendicular to another the slope of line B the line is the negative reciprocal of the slope of Line A
for instance: if the slope was 2/3 the slope of the perpendicular line is -3/2
hope this helps.
Which of the following correctly states the relationship between SST (total sum of squares), SSB (sum of squares between), and SSW (sum of squares within)?
SST = SSB + SSW
The relationship between SST, SSB and SSW is SST = SSB + SSW
The SSW is stands for sum of squares within and the SSW is defined as the sum of squared differences between a number and its sample mean for all numbers
The SSB stands for sum of squares between and the SSB is defined as the the sum of squared differences between a value and the grand mean.
The SST stands for the the total sum of squares and SST is defined as the the squared differences between the observed dependent value and the mean
The total sum of squares is the sum of the sum of squares between and the sum of square within
Therefore
SST = SSB + SSW
Hence, the relationship between SST, SSB and SSW is SST = SSB + SSW
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Which of the following is a solution of x^2+5x=-2
Answer:
x = [tex]\frac{-5 + \sqrt{17} }{2}[/tex]
Step-by-step explanation:
HOW TO SOLVE YOUR PROBLEM
1. Move terms to the left side
x² + 5x = -2
x² + 5x - (-2) = 0
2. Use the quadratic formula
x = [tex]\frac{-b + \sqrt{b^2 - 4ac} }{2a}[/tex]
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x² + 5x + 2 = 0
a = 1
b = 5
c = 2
x = [tex]\frac{-5 + \sqrt{5^2 - 4 * 1 * 2} }{2 * 1}[/tex]
3. Simplify
Evaluate the exponent
Multiply the numbers
Subtract the numbers
Multiply the numbers
Solution:
x = [tex]\frac{-5 + \sqrt{17} }{2}[/tex]
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 12 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
At the Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 26 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.
a. In words, define the Random Variable X.
b. List the values that X may take on.
c. Give the distribution of X.
d. How many fencers are expected to not use the foil as their main weapon? (Round your answer to the nearest whole number.)
e. Find the probability that fifteen do not use the foil as their main weapon.
f. Based on numerical values, would you be surprised if all 26 did not use foil as their main weapon?
The correct answers listed below :
A)The percentage of fencers that don't utilize the foil as their primary weapon in A.
B.) X : 0, 1, 2, 3,..., 21
C.) X ~ p(X) ; 10.4
D.) 21 ~ 0.4
E.) 0.0895
F.) Yes. There is a low (less than 1%) chance that all 21 fencers will not use the foil as their primary weapon.
A.) Considering that 60% of fencers reportedly utilize the foil as their primary weapon;
Number of fencers who do not utilize foil as their primary weapon is the random variable (x);
( 100% - 60%) = (1 - 0.6) = 0.4
B.) Possible values for X include:
The sample size is 26;
X : 0, 1, 2,..., 26
The breakdown of X
X ~ B ; X ~ p(X) ; 26 *0.4
=10.4
How many fencers are anticipated to not utilize the foil as their primary weapon in Part (d)?
X * p(x) (x)
=26 * 0.4
= 8.4
= 8 (nearest whole number) (nearest whole number)
Determine the likelihood that eleven will not utilize the foil as their primary weapon in part (e).
P(x = 11)
Using the link between binomial probabilities:
P(x =x) is equal to nCx * px * (1 - p) (n - x)
P(x = 11) = 26C11 * 0.4^11 * 0.6^10
P(x = 11) = 0.0895
Would you be shocked if none of the 21 used foil as their primary weapon based on the numbers?
P(x = 26) = 26C21 * 0.4^26 * 0.6^0
P(x = 26) = < 0.00001 ( about 0) ( approximately 0)
It will therefore be surprising if all 26 do not employ foil as their primary weapon given this extremely low value, which is virtually equal to 0.
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Assuming that julia is equally likely to have a spelling mistake on each of the 444 pages, what is the probability that she will have no spelling mistakes on at least one of them?.
The probability that she will have no spelling mistakes on at least one of them = 0.9919.
Let, X be the random variable denoting the no. of pages among those 444 pages which Julia writes where she makes no spelling mistake.
clearly we know that,
X Binomial (444, 0.7)
So, P(X = x) = [tex]4c_{x} * (0.7)^{x} * (0.3)^{(4-x)}[/tex]
[when x = 0, 1, 2, 3, 4 ..... so on until 444]
= 0 otherwise
According to the question, we have to find out P(X ≥ 1) .
Now, P(X ≥ 1)
= 1 - P(X = 0)
= [tex]1 - (444c_{x} * (0.7)^{0} * (0.3)^{(4)})[/tex]
= 1 - 0.0081
= 0.9919
So, the required probability is given by, 0.9919
Hence the answer is the probability that she will have no spelling mistakes on at least one of them = 0.9919.
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I am having trouble finding 2 square roots to estimate the square root of 10. Can someone please help me?
Answer:
sqrt9 and sqrt16
Step-by-step explanation:
Since you're trying to find the sqrt10, find a perfect square less than 10 and another perfect square greater than 10.
sqrt9 is 3. And sqrt16 is 4. So the estimate of sqrt10 is much closer to sqrt9.
sqrt10 ~= 3.2
if a within-subjects experiment produces 50 scores in treatment 1 and 50 scores in treatment 2, then the experiment must have employed .
If a between-subjects experiment produces 50 scores in treatment 1 and 50 scores in treatment 2, then the experiment must have employed 100 participants.
Why do between-subjects experimental designs employ random assignment?
Because it ensures that there are no systematic differences between the participants in each group, random assignment improves the study's internal validity. You can draw the conclusion from this that the independent variable is to blame for the results.
What is the metric that denotes the degree to which all scores typically differ from the mean?
Because it is reported in the original units of measurement and takes into account all of the scores in the data set, the standard deviation is the most widely used measure of variability. It reveals the average (or standard) distance that separates each score from the distribution's mean.
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Full Question = If a between-subjects experiment produces 50 scores in treatment 1 and 50 scores in treatment 2, then the experiment must have employed ____.
a. 100 participants
b. 25 participants
c. 50 participants
d. 200 participants
In 2012, there were approximately 980 thouand
retaurant in the United State. In 2016, there
were 1046 thouand retaurant. A. Write an equation decribing the relationhip
between time and the number of retaurant. Ue
ordered pair of the form (year pat 2012, number
of retaurant in thouand). B. Ue thi equation to predict the number of eating
etablihment in 2018
In 2018 there are 1079 restaurants using the equation y=980+16.5x .
What is equation?
In algebra, in its simplest form, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x 5 = 14 is an equation where 3x 5 and 14 are two terms separated by an equal sign. There are two types of equations: identities and conditionals. Equality applies to all values of the variable. A conditional expression applies only to specific values of a variable. Equations are written as two expressions joined by an equal sign ("=").
Here restaurants in the United States is ,
=> 2012 = 980
=> 2016 = 1,046
Here in 4 years difference (2016 - 2012),
=> 1046-980 = 66 more restaurants .
Then in 4 years = 66 restaurants, Then
In 1 year = 66/4 = 16.5 .
Now slope m = 16.5
The order pair of the relationship between years and restaurants ,
(0, 980) and (4, 1,046)
Now the equation ,
=> y = 980+16.5 x
where Y = number of restaurants in one year
x = number of years in the past.
Number of restaurants in 2018,
=> Y = 980 + 16.5x
Years 2018-2012 = 6 years
Forecast number of restaurants,
=> Y = 980 + 16.5(6)
=> 1,079
Therefore the equation is y=980+16.5x and In 2018 there are 1079 restaurants.
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Is there a series of rigid transformations that could map triangle QRS to triangle ABC if so which transformations could be used?.
The transformations that could be used is option D) ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.
A geometric transformation known as a stiff transformation of a Euclidean space maintains the Euclidean distance between each pair of points. Stiff transformations include rotations, translations, reflections, or any combination of these. A rotation is known as a rigid transformation or isometry when the image and the pre-image are of the same size and shape. Despite the fact that the figures may be in different positions, an object's size, form, and rotation are all the same. These are the two different categories of transformations: The rigid transition does not change the size or shape of the preimage. The preimage's size but not its shape will change as a result of the non-rigid transformation.
Note that the full question is:
Is there a series of rigid transformations that could map ΔQRS to ΔABC? If so, which transformations could be used?
A No, ΔQRS and ΔABC are congruent but ΔQRS cannot be mapped to ΔABC using a series rigid transformations.
B No, ΔQRS and ΔABC are not congruent.
C Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C.
D Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.
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What is a translated image?.
Concept and uses of image translation are explain below.
What is a translated image?In math, a change is an activity that moves, flips, or changes a shape (called the preimage) to make another shape (called the picture). An interpretation is a sort of change that moves each point in a figure a similar distance in a similar course.
Benefits os translation of image.An interpretation is a kind of change that takes each point in a figure and slides it a similar distance in a similar course. This interpretation maps △ X Y Z \triangle{XYZ} △XYZtriangle, X, Y, Z onto the blue triangle. The outcome is another figure, called the picture. The picture is consistent to the first figure.
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what does it mean to say that the confidence interval methods for the mean are robust against departures from normality?
The confidence interval methods for the mean are robust against departures from normality, meaning they work well with distributions that aren't normal, provided that departures from normality are not too extreme.
What is confidence interval for a mean ?A confidence interval for a mean is a range of values that is likely to contain a population mean with a certain level of confidence.
We use the following formula to calculate a confidence interval for a mean:
Confidence Interval = x +/- z*(s/√n)
where:
x: sample mean
z: the chosen z-value
s: sample standard deviation
n: sample size
They work well with distributions that aren't normal, provided that departures from normality are not too extreme.
This means that the methods of this section are not robust against poor sampling method.
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10-29 locate the centroid y of the channel's cross-sectional area, and then determine the moment of inertia with respect to the x' axis passing through the centroid
The correct value of the moment of inertia is 128.
Let us consider the shaded area as rectangle 1 of 16 x 16 in minus the rectangle 2 of 12 x 4
Area of rectangle 1 = A₁ = 16 x 16
A₁ = 96
Area of rectangle 2 = A₂ = 12 x 4
A₂ = 48
y- coordinate of the centroid
y = [A₁*(6/2) - A₂*(2+2)] / (A₁-A₂)
y = [(96*3)-(48*4)] / 48
y = 2 in
Moment of inertia of 1 about x-axis
Iₓ = [{16*(6)²} / 12] + [A₁(3-2)²]
Iₓ = 384
Moment of inertia of 2 about x-axis
Iₓ' = [12(4)²/12] + A₂[2+(4/2)-2]²
Iₓ' = 256
Moment of inertia of the entire shaded area
Iₐ = Iₓ - Iₓ'
Iₐ = 384 - 256
Iₐ = 128
Therefore the moment of inertia of the cross sectional area with respect to x-axis is 128.
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Guys help me on #4 please
Answer:
Step-by-step explanation:
so we are told that he deposited 7/9 of his money. that mean the remaining is 2/9. because 9/9 - 7/9 = 2/9 get it?
we are also told that 2.50 = 2/9 of his pay
so use that info to find the total pay
also using my calculator tells me that 2/9 = 0.22222222222222222222
knowing that, we can divide 2.50 by 0.222222222222
2.50 / 0.2222222222 = 11.25
we now know that 2.50 is 0.222 of 11.25
if you want to check your answer just multiply 11.25 x .222222222 to see if you get 2.50
Do you understand?
Line k ha an equation of y=x 2 7. Line include the point (7, – 2) and i perpendicular to line k. What i the equation of line ?
The equation of Straight line, perpendicular to line [k]would be y = - x + 5
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of straight line also represents the directly proportional relation as -
y = mx + c
y = mx {c = 0}
m = y/x
or
m = Δy/Δx
where [m] is constant of proportionality.
We have a line [k] that has an equation of y = x - 7
We have the given equation of line -
y = x - 7
Slope of line will be 1.
Slope of the line perpendicular to line [k] will be -
m[p] = -1
Then, the general equation would become -
y = - x + c
For point (7, - 2), we can write -
- 2 = - 7 + c
c = - 2 + 7
c = 5
Therefore, the equation of Straight line, perpendicular to line [k]would be y = - x + 5
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Diego then says if we take half of the first number and double the second the sum is 14.
The equation for the given phrase is 1/2(x)+2y=14.
Given that, Diego then says if we take half of the first number and double the second the sum is 14.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the first number be x and the second number be y.
Now, half of the first number and double the second the sum is 14
So, 1/2(x)+2y=14
Hence, the equation for the given phrase is 1/2(x)+2y=14.
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A researcher has created a Bose-Einstein condensate in which the index of refraction is
20,000,000
. The velocity of light in this gas is closest to which of these? A snail in full speed run A car on a local street. A ray of light in acrylic or glass
5.996×10 15
meters/second
The velocity v=15 m/s that is equal to the speed of a car on a local street. So the option 2 is correct.
In the given question we have to find the velocity of light in this gas is closest to which of these.
A researcher has created a Bose-Einstein condensate in which the index of refraction is 20,000,000.
The given options are;
A snail in full speed run A car on a local streetA ray of light in acrylic or glass5.996×10^{15} meters/seconRefractive index of B-E condensate(n) = 20,000,000 = 2×10^7
n = c/v
v=c/n
where v = speed of light in B-E condensate
As we know that c=3×10^8 m/s
So v=3×10^8/2×10^7
v=30×10^7/2×10^7
v=15 m/s
This is the velocity equal to the speed of a car on a local street.
So the option 2 is correct.
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Hace 20 año tendre tre vece la edad que tenia hace 10 año. ¿Que edad tuve hace tre año
Three years ago , mine age was 6 years
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Let my present age be x
Age of mine , 20 years ago = x - 20
Age of mine , 10 years ago = x - 10
According to question,
(x - 20) = 13(x - 10)
⇒ x - 20 = 13x - 130
⇒ 13x - x = 130 - 20
⇒ 12x = 110
⇒ x = 110/12
⇒ x = 9.17
Age of mine , theree years ago = x - 3
= 9.17 - 3
= 6.17
≈ 6
Therefore, three years ago , mine age was 6 years
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help asap!
The quadratic equation x2 - 16x + 64 = 4 is to be rewritten in factored form. From the list of equations below, determine which equation correctly represents the above quadratic equation in factored form.
Type yes next to each correct representation. Type no next to each incorrect representation. You must type an answer in every text box.
(x+8)(x+8) = 4
(x-8)2 = 4
(x-8)(x+8) = 4
(x+8)2 = 4
(x-8)(x-8) = 4
Answer: (x-8)(x-8) = 4 (yes)
Step-by-step explanation:
x²-16x+64 = 4
(x-8) (x-8) =4
(x+8)(x+8)=4 NO
(x-8)2 =4 NO
(x-8)(x+8)=4 NO
(x+8)2 = 4 NO
(x-8)(x-8) = 4 YES
When the image is larger than the pre-image the scale factor would be larger than 1?.
If the scale factor is greater than 1, the image is larger than the preimage
What are dilations?A transformation called dilatation alters a figure's size without altering its shape. A figure might become bigger or smaller due to dilation. The initial figure in dilatation is referred to as the preimage. The image is an enlarged figure. The center of dilatation is a fixed location from which figures are distorted.
What are reductions and enlargements?The scale factor specifies how much smaller or larger the picture will be when you dilate a figure.
• The picture is smaller than the preimage when the scaling factor is between 0 and 1. Reductions are referred to as dilations with scale factors between 0 and 1.
• The picture is larger than the preimage if the scale factor is greater than 1. Enlargements are defined as a dilation with a scale factor greater than 1. The prime sign, ', can be used to identify each new point in a dilated figure. For instance, point ', which stands for "prime," would be the dilated image of point.
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