Which of the following will increase the standard error for the estimate of a specific y value at a given value of x? (Select all that apply) A. Higher variability in the y values about the linear model (o_ɛ). B. Larger sample size C. the value of x* is farther from x-bar D. the variability in the values of x is higher

Answers

Answer 1

A) Higher variability in the y values about the linear model (o_ɛ)and D) the variability in the values of x is higher  will increase the standard error for the estimate of a specific y value at a given value of x.

A. Higher variability in the y values about the linear model (σ_ε) will increase the standard error because it indicates greater uncertainty in the relationship between x and y, leading to a wider range of possible y values for a given x.

D. Higher variability in the values of x (σ_x) will also increase the standard error because it introduces more variability in the data, making it harder to estimate the true relationship between x and y accurately. This increased variability adds uncertainty to the estimate and widens the standard error.

So A and D are correct.

For more questions like Error click the link below:

https://brainly.com/question/13179711

#SPJ11


Related Questions

Seventy percent of kids who visit a doctor have a fever and 21% of kids have fever and sore throats .

What is the probability that a kid who goes to the doctor has a sore throat given that he has a fever?

Answers

The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 30%

How to determine the probability?

The given parameters are:

P(Fever) = 70%

P(Fever and sore throat) = 21%

The probability that a kid who goes to the doctor has a sore throat given that he has a fever is calculated as:

P = P(Fever and sore throat)/P(Fever)

So, we have:

P = 21%/70%

Evaluate

P = 30%

Hence, the probability is 30%

Read more about probability at:

https://brainly.com/question/24756209

#SPJ1

a) The cosine rule can be used to find the value of x in the triangle below.

What number completes the following calculation? x² = 12² +152 - 2 x 12 x 15 x cos(?)

b) What is the value of x? Give your answer to the nearest integer.​

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

(the side required )² = sum of squares of other 2 sides - ( 2 × product of other 2 sides and cos(angle opposite side required ) )

x² = 12² + 15² - (2 × 12 × 15 × cos71°)

(b)

x² = 144 + 225 - 360cos71°

   = 369 - 360cos71° ( take square root of both sides )

x = [tex]\sqrt{369-360cos71}[/tex]

  ≈ 16 cm ( to the nearest integer )

If f(x)= 2x/7+4 which of the following is the inverse of f(x)

Answers

The inverse of the function f(x)= 2x/7 + 4 is y = 7x/2 - 14.

What is the inverse of the function?

Given the function; f(x)= 2x/7 + 4

First. we write the function as an equation then interchange the variables.

y = 2x/7 + 4

x = 2y/7 + 4

We solve for y.

2y/7 = x - 4

2y = 7x - 28

y = 7x/2 - 28/2

y = 7x/2 - 14

Therefore, the inverse of the function f(x)= 2x/7 + 4 is y = 7x/2 - 14.

Learn more about inverse of function here: https://brainly.com/question/2541698

#SPJ1

Why cant the a value in the standard form of a quadratic function ax^2+bx+c=0 be equal to 0?

Answers

Answer:

  the equation is no longer quadratic

Step-by-step explanation:

A quadratic equation is a polynomial equation in which the highest-degree term has degree 2.

What happens when a = 0?

The value a=0 makes the squared term disappear. If 'a' is zero, the equation becomes a linear equation, not a quadratic equation:

  bx +c = 0

Write two expressions that have a solution of x = 4.
ASAP!! Ty

Answers

Answer:

X multiplied by 2 is 8

X divided by 2 is 4

Step-by-step explanation:

This is the quickest thing i can give you

Which series is convergent? check all that apply. sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction sigma-summation underscript n = 1 overscript infinity endscripts startfraction n squared minus 1 over n minus 2 endfraction sigma-summation underscript n = 1 overscript infinity endscripts (one-fifth) superscript n sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction) superscript n sigma-summation underscript n = 1 overscript infinity endscripts startfraction 1 over 10 endfraction (3) superscript n

Answers

These series show convergence of series which are

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction

sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

According to the statement

we have given the some series and we have to find that the out of these series which series is convergent.

So, For this purpose we have to check the convergence of series.

So,

we know that the for the convergent of series there is a one condition and if those condition will satisfy on the series then the series is convergent and if not then series is divergent.

So, the condition for convergent is a series converges if the absolute value of the sum of any finite number of sequential terms can become arbitrary small by starting the addition from a term which is far enough. So, if this condition is not satisfied the series diverges.

When we apply this condition on all given series then only 2 series satisfy this condition which is

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfractionsigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

So, These series show convergence of series  which are

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction

sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

Learn more about Convergence of series here https://brainly.com/question/1521191

#SPJ4

Answer:

B. The series converges because it has a sum of 2/3

Here are the answers for the rest of the assignment:

C.

B.

C and D

A and C

B and D

C.

B. 0.31 and A. 0.0025

B. 1.0317 and C. 1.9683

(please read below)

Step-by-step explanation:

Had the assignment and these are the correct answers, enjoy :)

p.s Take a break here for a second, this was your last assignment before the unit test and finals, pre-calc is a very hard subject to master and calc is going to be even harder so I just want to say that I am proud of you, you have done a great job this year.

I have also taken the course(and many others) and answered countless questions for brainly (you have probably seen some of them if you took pre-calc) and this is my final answer for edge(might do one or 2 more for the finals) and it has been my greatest pleasure to bring you guys edge answers for 3 years strait but sadly this is where my road ends, I have tried my hardest to make your lives easier with my answers as others have for me. I hope some of y'all continue on my legacy and continue bringing good to the world 1 answer at a time.

So long fellows, thank you for taking the time to listen I hope y'all do well in life :)

Alishia rides her bike 45.3 km in 143 minutes. what is her average speed in kilometers per hour?

Answers

Average speed of Alishia is 19 kilometers per hour

Average speed is calculated by dividing the total distance that something has traveled by the total amount of time it took it to travel that distance. Speed is how fast something is going at a particular moment. Average speed measures the average rate of speed over the extent of a trip

Given :

Distance = 45.3 km

Time taken = 143 minutes = 143/60 =2.384 hours

Average speed = 45.3/2.384 = 19 kilometers per hour

Thus the average speed of Alishia is 19 kilometers per hour.

Learn more about Average speed here :

https://brainly.com/question/17277454

#SPJ4

The side lengths of ABC are 2, 5, and 6, and DEF has side lengths of 12, 30, and 36. Find the ratios of the lengths of the corresponding sides of ABC
to DEF. Are the two triangles similar? Explain. Determine which two of the three given triangles are similar. Find the
scale factor for the pair.

Answers

Triangles ABC and DEF are similar. The scale factor for the pair is: 1/6.

What are Similar Triangles?

The ratios of the corresponding sides of similar triangles are equal, because they are proportional.

If triangles ABC and DEF are similar triangles, then:

AB/DE = BC/EF = AC/DF

Plug in the given values

2/12 = 5/30 = 6/36 = 1/6

This means that the triangles are certianly similar. The scale factor for the pair is: 1/6.

Learn more about similar triangles on:

https://brainly.com/question/2644832

#SPJ1

i need major help completing math questions (im terrible at it.)

Answers

Answer:

78.5 inches square is the answer

Step-by-step explanation:

area-3.14*(5)^2

What is the solution to the equation − = − − ? show your work.

Answers

The solution to the equation is 2

How to determine the solution

Given the equation

4 + 4(x-2) = 2(x+1) - x

First, we expand the bracket

4 + 4x - 8 = 2x + 2 - x

collect like terms

4x - 2x + x = 2 - 4 + 8

Add like terms

3x = 6

Make 'x' the subject

x = 6/3

x = 2

Thus, the solution to the equation is 2

The complete question is

What is the solution to the equation of 4 + 4(x-2) = 2(x+1) - x? show your work

Learn more about algebraic expressions here:

https://brainly.com/question/723406

#SPJ1

On four consecutive statistics quizzes, you receive the scores: 86 96 100 98 what is your median quiz score?

Answers

Answer:

98

Step-by-step explanation:

96+100=196

196÷2=98

Answer:

97.

Step-by-step explanation:

86 96 100 98

Place them in order:

86 96 98 100

The median is the middle value of an ascending sequence of numbers.

As there is an even number of values the median is the mean of the 2 middle ones:

So here it is (96 + 98) / 2

= 97.

A rectangle has a length of (3x - 1) and a width of (x + 1). part a determine the perimeter and area of the rectangle as polynomials. part b determine the perimeter and area of the rectangle if x equals 5. part c determine the perimeter and area of the rectangle if x equals 8.

Answers

Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..

Lets try to solve out the problem,

Length = 3x-1

Width = x+1

Perimeter = 2(l+b)

Area = l*b

Perimeter= 2 (3x-1 + x+1)

P= 8x

Area = (3x-1) (x+1)

=> 3x(x+1) -1 (x+1)

=> 3x^2 + 3x -x -1

=> 3x^2 + 2x -1.

Hence Perimeter of rectangle is 8x and Area is 3x^2 + 2x -1..

Learn more about Perimeter on:

https://brainly.com/question/397857

#SPJ4

A sample of 20 pages was taken from a Yellow Pages directory. On each page, the mean area devoted to display ads was measured in square millimeters (mm2). The sample mean is 346.5 mm2 and sample standard deviation is 170.38 mm2. The 95 percent confidence interval for the mean is:

Answers

The 95 percent confidence interval for the mean is (266.76,426.24).

A confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Confidence intervals are intrinsically connected to confidence levels.

The formula of Confidence Interval =  Mean ±   [tex]t\frac{Standard Deviation}{\sqrt{number of observations} }[/tex]

where t is a constant

Given:

Mean = 346.5

Standard Deviation = 170.378

t-critical value for 95% Confidence interval with degrees of freedom(df)=n-1= 19 is 2.093

∴ Substituting values in formula we get

E = [tex]2.093 X170.378/\sqrt{20}[/tex] = 2.0931.96 x 38.0976=79.74

95% Confidence interval : (346.5-79.74,346.5+79.74)

95% Confidence interval : (266.76,426.24)

Learn more about confidence intervals here :

https://brainly.com/question/24131141

#SPJ4

Find the additive inverse of the following. (a) -4 (b) -18 (c) 620 (d) 60 (e) -244 (f) -8921

Answers

The additive inverse is:

(a) 4   (b) 18   (c) -620  (d) -60  (e) 244  (f) 8921

What is additive inverse?

The additive inverse of a number x is the number that, when added to x  yields zero.

It is shown as [tex]x+(-x)=0[/tex]

To find the additive inverse of a number we just change the sign of the given number which means positive changes to negative and vice versa.

The additive inverse of the given numbers are:

(a) 4

(b) 18

(c) -620

(d)-60

(e) 244

(f) 8921

Learn more about additive inverse here:

https://brainly.com/question/13715269

#SPJ4

Outside a home, there is a 4-key keypad numbered 1 through 4. The correct six-digit code will open the garage door. The numbers can be repeated in the code
(a) How many codes are possible?
(b) What is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code?
(a) The number of possible codes is
(Type an integer or fraction. Simplify your answer)
(b) The probability that the correct code is given on the first try, assuming that the owner doesn't remember it is
(Type an integer or fraction Simplify your answer.)

Answers

Using the Fundamental Counting Theorem, it is found that:

a) 256 codes are possible.

b) The probability is [tex]\frac{1}{256}[/tex].

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

There are 4 keys, each with 4 options, hence the parameters are:

[tex]n_1 = n_2 = n_3 = n_4 = 4[/tex].

Then the number of codes is:

[tex]N = 4^4 = 256[/tex]

And the probability is:

[tex]p = \frac{1}{256}[/tex].

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866

#SPJ1

Total area=
Help me please
Thanks so much

Answers

Answer: 228

Explanation: In a bit more legible pic below

A random sample of n = 16 scores is obtained from a normal population with m = 40 and s = 8. what is the probability that the sample mean will be within 2 points of the population mean?

Answers

Using the normal distribution, there is a 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For this problem, the parameters are given as follows:

[tex]\mu = 40, \sigma = 8, n = 16, s = \frac{8}{\sqrt{16}} = 2[/tex]

The probability that the sample mean will be within 2 points of the population mean is the p-value of Z when X = 40 + 2 = 42 subtracted by the p-value of Z when X = 40 - 2 = 38, hence:

X = 42:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (42 - 40)/2

Z = 1

Z = 1 has a p-value of 0.8413.

X = 38:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (38 - 40)/2

Z = -1

Z = -1 has a p-value of 0.1587.

0.8413 - 0.1587 = 0.6826 = 68.26% probability that the sample mean will be within 2 points of the population mean.

More can be learned about the normal distribution at https://brainly.com/question/24537145

#SPJ1

pls help me on this one :((

Answers

Answer:

B

Step-by-step explanation:

Finding the area of the trapezoid using the lengths in the diagram, we get (c)(2d+a+b)/2.

This is equal to c(d+b), so:

(1/2)(c)(2d+a+b)=c(d+b)

(1/2)(2d+a+b)=d+b

d+0.5a+0.5b=d+b

0.5a+0.5b=b

0.5a=0.5b

a=b

A committee of three people needs to be chosen. There are three men and five women available to serve on the committee. If the committee members are randomly chosen, what is the probability that two of the three people chosen on the committee are women

Answers

Answer:

probability of choosing two women over people in a community=⅔

The standard deviation tells us a. the average value of the scores. b. the relative standing of a particular score. c. the skewness of the distribution. d. the dispersion of the scores.

Answers

Answer:

D.

Step-by-step explanation:

Standard deviation tells us the dispersion of data/scores around the mean.

We can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.

What is the standard deviation?

A standard deviation (or σ) is a measure of how widely distributed the data is about the mean (μ). A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out. A standard deviation around 0 suggests that data points are close to the mean, whereas a high or low standard deviation indicates that data points are above or below the mean, respectively.

We use the following formula to compute the standard deviation:

[tex]\sigma = \sqrt\frac{{\sum_{i=1}^{N}\left | x_i - \mu \right | }^2}{N}[/tex]

In this formula, σ is the standard deviation, [tex]x_i[/tex] is the data point in the set we are solving for, μ is the mean, and N is the total number of data points.

How to solve the question?

In the question, we are asked to tell what standard deviations tell us from the given options.

From the above discussion, we can say that the standard deviation tells us the dispersion of the scores, making option D the correct choice.

Learn more about the standard deviation at

https://brainly.com/question/475676

#SPJ2

Adam runs 100m in 14.5 seconds. Jenny runs the same distance 10% faster. How long does it take for Jenny to finish?

Answers

The time taken for Jenny to run the same distance at 10% faster is 13.05 seconds

Percentage

Distance Adam runs = 100mTime taken by Adam = 14.5 secondsDistance Jenny runs = 100m

Time taken by Jenny = 14.5 - (10% × 14.5)

= 14.5 - (0.1 × 14.5)

= 14.5 - (1.45)

= 13.05 seconds

Therefore, the time taken for Jenny to run the same distance is 13.05 seconds

Learn more about percentage:

https://brainly.com/question/843074

#SPJ1

__________ 11A. In Circle O, it is given that m∠A = 20°.

Find m∠B.

Answers

Answer:

70 degrees.

Step-by-step explanation:

As AB is a diameter M < C = 90 degrees.

Therefore m < B = 90 - 20 = 70.

A bakery offers a sale price of $3.30 for 3 muffins. what is the price per dozen?

Answers

Answer:

$13.20

Step-by-step explanation:

A dozen consists of 12 items. If you have 3 you must multiply the current amount by 4 to get 12. Therefore you must also multiply the price by 4.

3.30*4=13.20

The National Center for Education Statistics reported that 47% of college students work to pay for tuition and living expenses. Assume that a sample of 450 college students was used in the study.

Answers

Using the z-distribution, it is found that the 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).

If we had increased the confidence level, the margin of error also would have increased.

What is a confidence interval of proportions?

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96. Increasing the confidence level, z also increases, hence the margin of error also would have increased.

The sample size and the estimate are given as follows:

[tex]n = 450, \pi = 0.47[/tex].

The lower and the upper bound of the interval are given, respectively, by:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 - 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.4239[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 + 1.96\sqrt{\frac{0.47(0.53)}{450}} = 0.5161[/tex]

The 95% confidence interval for the proportion of college students who work to pay for tuition and living expenses is: (0.4239, 0.5161).

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Mark this and retum
S
R
Which statements are true about triangle QRS? Select
three options.
The side opposite ZQ is RS.
The side opposite ZR is RQ.
The hypotenuse is QR.
The side adjacent to ZR is SQ.
The side adjacent to 4Q is QS.
Save and Exit
Next
Submit

Answers

The  statements that are correct  about right triangle QRS are:

Side opposite ∠Q is RS not RQHypotenuse of the right triangle is QRAdjacent side to ∠Q is QS

What is a Right Triangle?

A right triangle posses  a right angle which is in opposite direction to the  hypotenuse.

Considering the right angle triangle, it can be deduced that Side opposite ∠Q is RS not RQ,  and  Adjacent side to ∠Q is QS.

Learn more about right triangles on:

brainly.com/question/2217700

Joel spends 272727 more minutes playing soccer after school on Tuesday than he did on Monday. He still exercises for a total of 606060 minutes after school.
What percent of his time exercising after school did Joel spend playing soccer on Tuesday?

Answers

Joel spent 72.5% of his time exercising after playing soccer on Tuesda

How to determine the percentage?

The given parameters are

Minutes spent on Tuesday = 27 more minutes than Monday

Total minutes spend = 60

This means that

Tuesday = Monday + 27

Monday + Tuesday = 60

Make Monday the subject in Tuesday = Monday + 27

Monday = Tuesday - 27

Substitute Monday = Tuesday - 27 in Monday + Tuesday = 60

Tuesday - 27 + Tuesday = 60

Evaluate

2 * Tuesday = 87

Divide by 2

Tuesday = 43.5

The percentage of time spent exercising on Tuesday is then calculated as

Percentage = 43.5/60 * 100%

Evaluate the expression

Percentage = 72.5%

Hence, Joel spent 72.5% of his time exercising after playing soccer on Tuesday

Read more about percentages at:

https://brainly.com/question/843074

#SPJ1

Which relationship describes a function?
O (bedrooms, sale price)
(acres of land, appraised value)
(sale price, bedrooms)
(appraised value, property tax)

Answers

The relationship which best defines a function, for the houses on Katrina's street exists appraised value, property tax.

How to read the data from the table?

Table exists a form to describe the data of the two or more variables.

To read the data from the table, examine for the value of one variable, and obtain the resultant value of other variables from the related block.

The table below details some of the characteristics of the houses on Katrina’s street. Let's estimate the most suitable choice whose relationship defines a function.

The function exists in the relationship between various variables. This relation or the expression provides the output, by accepting some input value of variables.The output for a function is related to the input and provides various outputs with various input values.Only appraised value and property tax, in the given table, supplies a unique value per time.

The relationship which nicely illustrates the function, of the houses on Katrina's street exists between the appraised value and property tax.

Therefore, the correct answer is option d) (appraised value, property tax).

To learn more about appraised value and property tax refer to:

https://brainly.com/question/11533884

#SPJ9

Answer: D

Step-by-step explanation: Appraised Value , Property Tax

The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is symbolized by _____.

Answers

Considering that the value of 126.07 is valid for the population, it is a parameter.

What is the difference between a statistic and a parameter?

If the measure is defined only for the sample, it is a statistic.If the measure can be defined for the population, it is a parameter.

In this problem, the mean blood pressure is calculated for all employees, which means that it is valid for the population, hence it is a parameter.

More can be learned about parameters and statistics at https://brainly.com/question/13794992

#SPJ1

What term describes the brief time-out of the heart's electrical impulse that allows for sufficient time for ventricular filling between beats

Answers

Refractory period brief time-out of the heart's electrical impulse that allows for sufficient time for ventricular filling between beats.

At what time is the volume of blood in the ventricle at a maximum?

End-diastolic pressure is at its resting level (end-diastolic pressure) and ventricular volumes are at their maximum value when the heart muscle is relaxed (end-diastolic volume).

What is the state of the heart during systole?

Describe what occurs during systole in the heart. Describe where the blood is sent from each ventricle. Right ventricle transfers blood into the pulmonary artery during ventricular contraction and pumps it to the heart.

What are the 4 phases of cardiac cycle?

There are four main stages of activity in the cardiac cycle: Isovolumic contraction, inflow, ejection, and relaxation are the order of events. (See Wiggers graphic, which labels the stages in the following order: 3, 4, 1, and 2, from left to right.)

Learn more about Refractory period

brainly.com/question/13044654

#SPJ4

The triangle below is equilateral. Find the length of side x to the nearest tenth.

Answers

Answer:

[tex]\sqrt{\frac{15}{2} }[/tex] or 2.738

Step-by-step explanation:

Let’s just look at the triangle on the top with the [tex]\sqrt{10}[/tex] on the top and x on the bottom. (Basically the top half to the equilateral triangle)

There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]

We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b=[tex]\frac{1}{2}(\sqrt{10})[/tex] or [tex]\frac{\sqrt{10} }{2}[/tex]

Plugging these values into the equation:

x^2+ (\frac{\sqrt{10} }{2})^{2}=\sqrt{10} ^{2}

[tex]x^{2}=\sqrt{10} ^{2}-\frac{\sqrt{10} }{2} ^{2}[/tex]

[tex]x^{2} =10-\frac{10}{4}[/tex]

[tex]x^{2} =\frac{15}{2}[/tex]

[tex]x=\sqrt{\frac{15}{2} }[/tex]

This approximately equals 2.738

Answer:

[tex]x=\sqrt{\frac{15}{2} }[/tex]. Another form of this answer is [tex]x=\frac{\sqrt{15} }{\sqrt{2} }[/tex](it's the same thing)

Step-by-step explanation:

Because the triangle is equilateral, all other sides of the triangle are also [tex]\sqrt{10}[/tex]. Also, x is the altitude of this triangle as it forms a right angle with the base and is therefore perpendicular. We know that this triangle is equilateral and in any triangle that has at least two sides that are equal(in other words isosceles), the altitude is also the median and angle bisector. A median would cut the side it reaches into half. So, x would cut the base into two equal parts. Since the base is [tex]\sqrt{10}[/tex], divide it by two and both halves are [tex]\frac{\sqrt{10}}{2}[/tex]. What we are left with is two right triangles, both with legs [tex]\frac{\sqrt{10} }{2}[/tex] and x. Using the Pythagorean Theorem, we know that [tex]a^{2}+b^{2}=c^{2}[/tex], with [tex]a[/tex] and [tex]b[/tex] being the legs and [tex]c[/tex] being the hypotenuse. So, we plug in the values and get [tex]\frac{\sqrt{10} }{2} ^{2}[/tex][tex]+x^{2}=\sqrt{10}^{2}[/tex]. Squaring, we get [tex]\frac{10}{4}+x^{2}=10[/tex]. This becomes [tex]x^{2}=10-\frac{10}{4}[/tex] which equals [tex]x^{2}=\frac{40}{4}-\frac{10}{4}[/tex]. Finally, [tex]x^{2}=\frac{30}{4}[/tex]. This is [tex]x^{2}=\frac{15}{2}[/tex]. Square rooting this we get [tex]x=\sqrt{\frac{15}{2} }[/tex]. Another form of this answer is [tex]x=\frac{\sqrt{15} }{\sqrt{2} }[/tex]

Other Questions
The Tully-Fisher relation exists between the galaxy's luminosity and its:Select one:A. size.B. rotation.C. age.D. mass.E. color. basic dimensions defining hole positions should all originate at the datums to prevent the tolerance accumulation that could result from chain dimensioning with basic dimensions.T/F Every year thousands of people in the UK have heart attacks.A heart attack is caused when the heart muscle cells do not get enough oxygen, causing the cells to die.Statins and stents are two treatments used to reduce the risk of someone having a heart attack.Evaluate the use of statins compared with the use of a stent to reduce the risk of a heart attack. [6 marks] . a powerful way that communication shapes the self is the self-fulfilling prophecy. which of the following best describes a self-fulfilling prophecy? Suppose that A is annxnsquare and invertible matrix with SVD (Singular Value Decomposition) equal toA = U\Sigma T^{T}. Find a formula for the SVD forA^{-1}. (hint: If A is invertable,rankA = n, this also gives information about\Sigma). write a menu driven program that implements the following binary search tree operations find (item) insert (item) delete (item) delete_tree (delete all nodes - be careful with the traversal!) The security team received a report of copyright infringement from the IP space of lire corporate network. The report provided a precise time stamp for the incident as well as the name of the copyrighted file. The analyst has been tasked with determining the infringing source machine and instructed to implement measures to prevent such incidents from occurring again. Which of the following is MOST capable of accomplishing both tasks?A. HIDSB. Allow listC. TPMD. NGFW FILL IN THE BLANK a healthy expanding company would most likely show a ______ cash flow from investing activities. fort20, the velocity ofaparticle moving along the x-axis is given by v(t)=t6t 10t4. a sound wave in air has a frequency of 1280 hz and travels with a speed of 343 m/s. how far apart are the wave crests (compressions) ? the distance between wave crests is the wavelength of the wave. A jewlary shop sells 240 necklaces in a month 180 of the necklaces were sold in a via the shops website the rest were sold in a high street shop .Work out the ratio of online sales to shop sales Give ur answers in its simplest form find an equation of the plane. the plane through the points (2, 1, 3), (7, 4, 6), and (3, 3, 2) A 12. 45 kg stone falls from the top of a cliff and strikes the ground at a speed of 46. 2 m/s what is the height of the cliff? Sketch the area of the region bounded by the curves y= x^2 2x + 3; x axis; x = 2; x = 1? A doctor knows from experience knows that the time for patient to complete a psychological test has an average of 21 minutes and standard deviation of 2 minutes. The shape of the test distribution is symmetric, bell-shaped, and normal. Please make a graph for each part. Use the 68-95-99.7 Empirical rule to find the mid 99.7% quiz completion test ranges. What percentage of the patients will complete the test in more than 22 minutes? a. b. Use z scores: C. Suppose he wants to allow sufficient time so that mid 95% of the patients to complete the test in the allotted time. What is the range of time for the mid 95% of the patients? Find the 75 percentile score for the psychological test. d. What is happening in the first step of the mechanism of the reaction between Oxone, NaCl and borneol? a. Oxidation of chloride b. Oxidation of Oxone c. Oxidation of bisulfite d. none of the above For which reaction is G expected to be closest to H?CO2(g) CO2(s)2NO(g) N2(g) + O2(g)H2O() H2O(s)NaCl(s) Na+(aq) + Cl-(aq)N2(g) + 3H2(g) 2NH3(g) A 4-pack of frappuccinos costs $10. 88 how much does each individual can cost The sum of two numbers is -6. One number is 14 more than the other one. Find the numbers. true/false. fe2o3 and al2o3 have similar chemical properties