Find the equation of the sphere if one of its diameters has endpoints (-8, -3, -10) and (-6, 1, -4) which has been normalized so that the coefficient of x2 is 1.

Answers

Answer 1

Answer:

The  equation is  [tex]x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0[/tex]

Step-by-step explanation:

From the question we are told that  

    The  diameter endpoints is   (-8, -3, -10) and (-6, 1, -4)

Generally the equation of a sphere with center coordinates (a, b , c ) and  radius  r   is mathematically represented as

           [tex](x - a )^2 + (y -b )^2 + (z -c)^2 = r^2[/tex]

Now since we are given the endpoints of the diameter then we can obtain the center coordinates as follows

         [tex](a, b , c) = [ \frac{ -8 +(-6)}{2} , \frac{-3 + (1)}{ 2} , \frac{ -10 + (-4)}{2} ][/tex]

         [tex](a, b , c) = [ -7 , -1.5 , -7 ][/tex]

Now the length of the diameter is evaluated as

    [tex]|d| = \sqrt{ (-8 - (-6 ))^2 + ( -3 - (1) )^2 + ( -10 - (-4))^2 }[/tex]

   [tex]|d| = \sqrt{56 }[/tex]

   [tex]|d| = \sqrt{4 * 14 }[/tex]

   [tex]|d| = 2 \sqrt{ 14 }[/tex]

Now the radius is mathematically represented as

    [tex]r = \frac{|d|}{2}[/tex]

    [tex]r = \frac{ 2 \sqrt{14} }{2}[/tex]

    [tex]r = \sqrt{14}[/tex]

So

   [tex](x - -7 )^2 + (y --1.5 )^2 + (z --7)^2 = ( \sqrt{14} )^2[/tex]

   [tex](x +7 )^2 + (y +1.5 )^2 + (z +7)^2 = 14[/tex]

    [tex]x^2 + 14 x + 49 + y^2 + 3y + 2.25 +z^2 14z + 49 = 14[/tex]

    [tex]x^2 + y^2 +z^2 + 14 x + 3y \ + 14z + 86.25=0[/tex]


Related Questions

As the sample size for a t-distribution increases, the differences between the t-distribution and the standard normal distribution ______.

Answers

Answer:

The differences become smaller

Step-by-step explanation:

Normally, we use the t-distribution table rather than the normal distribution when the population standard deviation is unknown and when the sample size is small i.e. less than 30.

Now, as the sample size gets bigger, we will be getting closer to the point where we have to use the normal distribution.

This means that as the sample size increases, the values of the t-distribution will be getting close to that of the normal distribution because normal distribution is used when sample is more than 30.

For example the t-value for a sample of 25 people would be closer to the normal distribution value for a sample of 35 people while a t-value for a sample of 15 people will be far away from the normal distribution value for a sample of 35 people.

Thus, as the sample size increases, the differences between the t-distribution and standard normal distribution becomes smaller.

Solve m +9 = 2.


Please and thank you.

Answers

Answer:

the answer is -7

Step-by-step explanation:

m+9=2-9

-9

m=. -7

PLEASE HELP!!!! I will award brainliest!! Look at the figure shown below. A student made the table shown below to prove that PQ is equal to RQ. 1. Provide the missing statement and justification in the proof. 2. Using complete sentences, explain why the proof would not work without the missing step.

Answers

Answer:

See below.

Step-by-step explanation:

1.

Statement 8. triangle SQR is congruent to triangle TQP

Reason 8. ASA

2.

The only way to prove those two sides are congruent is to first prove that the triangles that contain those sides are congruent. Then you can use CPCTC to prove those sides congruent.

Picture 1
Soap, Face, cream, Fragrance mist
Common​

Answers

All face products and have sulfates in them

m∠C= step by step thank you so much

Answers

Answer:

please mark my answer brainliest

Step-by-step explanation:

in tri ABD and bcd...

AD =DC ...given

AB =BC.....given

BD =BD.....common

therefore...both tri are congruent...by SSS CRITERION

therefore angle adb...and angle bdc are equal...cpct...

therefore angle bdc =32°

angle dbc =90°

therefore angle bcd =angle C=180- (90 +32) =58°

angle C=58°....answer

If it took 4 hours to clean 8 houses, how many houses could be cleaned in 7 hours

Answers

Answer:

14

Step-by-step explanation:

you clean 2 a hour so 7*2=14

Answer:

14 houses

Step-by-step explanation:

In which of the following scenarios will conducting a two-sample t-test for means be appropriate? Check all that apply.
A. To test if there is a difference between the proportion of low-income families in British Columbia and a known national proportion.
B. To test if the mean annual income of Ontarians is higher than that of British Columbians.
C. To test if there is a difference between the mean annual income of husbands and that of wives in Canada.
D. To test if the proportion of low-income families is higher than that of high-income families in British Columbia.
E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.
F. To test if there is a difference between the mean annual income of British Columbians and a known national mean.
G. None of the above

Answers

Answer:

B. To test if the mean annual income of Ontarians is higher than that of British Columbians

E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.

Explanation:

The options chosen have two populations that are independent. For example in option B, the annual income of Ontarians is a different population from annual income of British Columbians and they are also independent. The two sample t test can only be used when the populations are independent, it can also be used when computing difference between the means of two populations

The scenarios where conducting a two-sample t-test for means be appropriate include:

A. To test if there is a difference between the proportion of low-income families in British Columbia and a known national proportion.E. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.

It should be noted that the two sample t-test is used when the populations are independent band the sample size is small.

Therefore, it will be appropriate to test if there is a difference between the proportion of low-income families in British Columbia and a known national and the difference between the mean annual income of male British Columbians and that of female British Columbians.

Read related link on:

https://brainly.com/question/17042228

Multiply the place value of 6 in 37651 by 11​

Answers

Answer: Hi!

The place value of 6 in 37651 is equal to 600, as it is in the hundreds place.

All we need to do is multiply 600 by 11:

600 * 11 = 6600

Hope this helps!

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

So in 37,651, the 6 is in the hundreds place since it's the third digit (from right to left).

6 in the hundreds place is 600.

600 times 11 equals 6600.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

♡ Hope this helps! ♡

❀ 0ranges ❀

(90) points ill give brainly immideatly but gotta be right -------- Maria and her parents are hiking in the mountains. During one hike, Maria monitored their changing elevation and displayed it in the graph below. Which of the following BEST describes a functional relationship shown in the graph? A Maria's elevation remained constant for two hours. B Maria's elevation decreased between 1:00 and 3:00. C Maria's elevation increased between 9:00 and 12:00. D Maria spent more time decreasing her elevation than increasing her elevation.

Answers

Answer:

(C) Maria's elevation increased between 9:00 and 12:00

Step-by-step explanation:

Looking at the graph, we can test each statement.

For A, it says Maria's elevation remained constant for 2 hours. Looking at the graph, we can see that it remained constant for just one hour, so this is eliminated.

For B, Maria's elevation decreased between 1:00 and 3:00, we can see that while x is between 1:00 and 3:00, the y is decreasing, meaning this statement is false - this is eliminated.

For C, Maria's elevation increased between 9:00 and 12:00, we can see that while x is between 9:00 and 12:00, the graph is increasing - which means this is correct.

For D, Maria spent more time decreasing her elevation than increasing, we can count how many hours were spent doing each. Comparing the x-axis, we can see that Maria spent 5 hours increasing and 3 hours decreasing, meaning that Maria spent more time INCREASING than decreasing, making this statement false.

Hope this helped!

Answer: C A B C D

Step-by-step explanation: I HAVE NONE IM JUST SMART

I THINK?

Which fraction is equal to k in the equation below?
1\3 / 2= k

Answers

Answer:

0_10 =0_2

Step-by-step explanation:

Convert the following to base 2:

0_10

Hint: | Starting with zero, raise 2 to increasingly larger integer powers until the result exceeds 0.

Determine the powers of 2 that will be used as the places of the digits in the base-2 representation of 0:

Power | \!\(\*SuperscriptBox[\(Base\), \(Power\)]\) | Place value

0 | 2^0 | 1

Hint: | The powers of 2 (in ascending order) are associated with the places from right to left.

Label each place of the base-2 representation of 0 with the appropriate power of 2:

Place | | | 2^0 |  

| | | ↓ |  

0_10 | = | ( | __ | )_(_2)

Hint: | Divide 0 by 2 and find the remainder. The remainder is the first digit.

Determine the value of 0 in base 2:

0/2=0 with remainder 0

Place | | | 2^0 |  

| | | ↓ |  

0_10 | = | ( | 0 | )_(_2)

Hint: | Express 0_10 in base 2.

The number 0_10 is equivalent to 0_2 in base 2.

Answer: 0_10 =0_2

Your anula salary of $42,500 is about to he increased by 2%.Explain the steps you would take to determine your new salary.What will your new salary be?

Answers

Answer:

$43,350

Step-by-step explanation:

To find the increase in the salary we need to find the percentage.

2 percent of $42,500 = $850.

$42,500 + $850 =  $43,350.

New salary = $43,350.

DUE TONIGHT !! determine whether the statement is true or false. justify your answer. A line with a slope of -5/7 is steeper than a line with a slope of -6/7

Answers

False.

Slope is the "rise over run" (y/x) in a linear equation. Because the denominators are the same in both fractions, it means you can just focus on the numerator with the larger number as that one will be the steeper line.

Plz HELP ASAP (algebra)

Answers

Answer:16

Step-by-step explanation:

Given: 15% of 60 is 9.

so 9 kids are 15 year old.

and 1 other kid is 16 year old.

Thus, there are total of (15+1) kids that are either 15 or 16 year old. you can also draw venn diagram to find that.

Find the equation of the line that contains the points (4,2) and (6,10). Write the equation in the form y=mx+b and identify m and b.

Answers

Points (4,2) and (6, 10)

Eqn:
y - y = m(x - x)
y - 2 = [(2-10)/(4-6)] (x - 4)
y - 2 = (-8/-2) (x - 4)
y - 2 = 4(x-4)
y - 2 = 4x - 16
y - 2 + 2 = 4x - 16 + 2
y = 4x - 14

Therefore the slope (m) would be 4 and the y intercept (b) would be -14.

What is another name for AC

Answers

Answer:

air conditioning or air cooling or climate control

hope this helps :)

The stem-and-leaf plot shows the number of words in the classified ads in a newspaper one day.



How many ads had at least 20, but fewer than 45, words?



1 0 3 3 5 7 9

2 0 0 1 4 5

3 3 8 8

4 7

5 2



key:1|0 = 10



A. 6

B. 3

C. 10

D. 8

Answers

Answer:

D. 8

Step-by-step explanation:

We can see the numbers from 20 (inclusive) to 45 on the plot:

20, 20, 21, 24, 25, 33, 38, 38In total 8 ads

Correct answer choice is: D. 8

The answers listed below are characteristics of a Type I error EXCEPT for one. Select the characteristic that is not for Type I errora) upsetting status quo for falsehoodb) reject null hypothesis when null is truec) a "missed opportunity"

Answers

Answer:

c

Step-by-step explanation:

:)

In the healthy handwashing survey conducted by Bradley Corporation, a study was found that 64% of adult Americans operate the flusher of toilets in public restrooms with their foot. Suppose a random sample of n=20 adult Americans is obtained, and the number x who flush public toilets with their feet is recorded.
A) Explain why this is a binomial experiment.
B) Find and interpret the probability that exactly 12 flush public toilets with their foot.
C) Find and interpret the probability that at least 16 flush public toilets with their foot.
D) Would it be unusual to find more than 17 who flush public toilets with their foot? Why?

Answers

Answer:

A) It fulfills the condition of binomial experiment

B) P (x=12) =0.1678

C)P ( x ≥16)= 0.1011

d) P (x>17) =0.0096 < 0.5

Step-by-step explanation:

A. The binomial probability distribution has the following four properties

1. the outcomes of each trial maybe classified into success and failure.

2) the probability of success p remains constant for all trials.

3) the successive trials are all independent.

4) the experiment is repeated a fixed number of times ,n.

These all conditions are fulfilled by the given question so it is a  binomial experiment.

B) P (x=12) = 20C12 (0.64)^12 * (1-0.64)^8= 0.1678

C) P ( x ≥16) = P (x=16) + P (x=17) + P (x=18) + P (x=19)+ P (x=20)

where

P (x=16)= 20C16 (0.64)^16 * (1-0.64)^4= 0.0645

P (x=17)= 20C17 (0.64)^17 * (1-0.64)^3= 0.0270

P (x=18)= 20C18 (0.64)^18 * (1-0.64)^2= 0.0080

P (x=19)=20C19 (0.64)^10 * (1-0.64)^1= 0.0015

P (x=20)= 20C20 (0.64)^20 * (1-0.64)^0= 0.0001

so

P ( x ≥16)= 0.0645+ 0.0270 +0.0080+ 0.0015+0.0001= 0.1011

d) P (x>17)= P (x=17) + P (x=18) + P (x=19)+ P (x=20)

                    =0.0270 +0.0080+ 0.0015+0.0001

                         =0.0096

From this we see that the probability of  more than 17  people who flush public toilets with their foot is unusual because it is far away from the mean which is supposed to be somewhere 0.5 in a given distribution.

Darren picked 25 flowers that he plans to divide evenly into 3 vases. He will use as many flowers per vase as he can, but may have flowers left

Answers

Answer:

He will use flowers per vasebut will have one left

Step-by-step explanation:

In this problem we are required to place flowers evenly across  3 flower vases.

Given that we have 25 flower to collect from and distribute evenly.

we are going to divide 25 by 3

We have

[tex]= \frac{25}{3}\\\\ =8\frac{1}{3}[/tex]

From the result in the improper fraction we can see the Darren can place 8 flowers evenly of the 25 flowers and there will be just one left over

Given: 2x + 3y= 6.
What is the y-intercept?
(0,3)
(2,0)
(0,2)
no intercept

Answers

Answer: (0,2) Explanation: You plug in the coordinates into the equation and find which points make the equation true. Plugging in (0,2) turns the equations into (2•0) + (3•2) = 6. Simplify it and you get 6 = 6 which is true.

Determine if the two triangles shown are similar. If so, write the similarity statement. options:

A) ΔWUV ∼ ΔFGH

B) ΔUVW ∼ ΔFGH

C) Impossible to determine.

D) The triangles are not similar.

Answers

Answer:

B

Step-by-step explanation:

∠ U = ∠ F = 76° thus are congruent

Consider the ratios of corresponding sides

[tex]\frac{UW}{FH}[/tex] = [tex]\frac{9}{21}[/tex] = [tex]\frac{3}{7}[/tex]

[tex]\frac{UV}{FG}[/tex] = [tex]\frac{18}{42}[/tex] = [tex]\frac{3}{7}[/tex]

Thus Δ UVW ~ Δ FGH by the SAS postulate

Yes the given two triangles are similar.

The similarity statement is B) ΔUVW ∼ ΔFGH

What do we mean by similar triangles ?

The triangles that have similar shape but the sizes of the triangles may be different, are called similar triangles.

Are the given triangles similar or not ?

Here, in the given triangles,

∠U = ∠F = 76°

Therefore they are congruent.

The ratio of corresponding sides, [tex]\frac{UW}{FH} =\frac{9}{21} = \frac{3}{7}[/tex]

Again the ratio of corresponding sides, [tex]\frac{UV}{FG}=\frac{18}{42}=\frac{3}{7}[/tex]

Thus, ΔUVW ∼ ΔFGH by SAS rule of similarity.

Learn more about Similarity of triangle here :

https://brainly.com/question/14285697

#SPJ2

50 Points! PLEASE ANSWER ASAP

Answers

Answer:

a. 1120 is the area b. max # of ppl is 80

Step-by-step explanation:

a. Area= Length* width = 28 * 40 = 1120

(8,10) and (8,38) have 28 units between them

(8,10) and (48,10) have 40 units between them

b. Since the area is 1120 and they say that only one person is allowed per 14 square feet, you would divide 1120 by 14 to get 80 people

If each coordinate equals 1 foot then:

(8,10) to (48,10) is 40 feet (48-8)

(8,10) to (8,38) is 28 feet (38-10)

so now you got length 40 and width 28

40 x 28 = 1120

a. 1120ft^2

b. 1120 / 14 = 80

Please help. I’ll mark you as brainliest if correct

Answers

Answer: He doesn't have any money left that period point blank

Step-by-step explanation

7-6=1

1-3= you cant do that

so he doesn't get soda at all.

7 -6 =1. . . . . . . - . . . . . . = . 1-3= nope. - . . . = nahhh
He is in debt for $2. He bought the sandwich and soda for a total of 9. But he only had $7. So it won’t be a positive number. The amount of money he could have had after these purchases is


-2.

factorise : 64a cube minus 27b cube minus 144a square b plus 108ab square ​ .


Plz Answer this question

Answers

Answer:

[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]

Step-by-step explanation:

The question is not properly formatted, here is a good format for proper understanding and readability

[tex]64a^3-27b^3-144a^2+108ab^2[/tex]

let us first collect/ group like terms

[tex]64a^3-144a^2+108ab^2-27b^3[/tex]

we can now bring out the common factors we have

[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]

The simplified expression is

[tex]16a(4a^2-9a)+27b^2(4a-b)[/tex]

A chef orders carrots and celery in bulk. The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb
combined.
What is the weight of the carrots?

Answers

Answer:

Y= 7.9 lb

X= 10.1 lb

Step-by-step explanation:

The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb combined.

Let carrot= x

Let celery= y

X+y = 18...... equation one

X= 2.2 +y.... equation two

Substituting the value of x into equation one

2.2 +y +y =18

2y= 18-2.2

2y= 15.8

Y= 7.9 lb

Substituting the value of yinto equation 2

X= 2.2 +y

X= 2.2 + 7.9

X= 10.1 lb

This is the question.

Answers

Answer:

B

Step-by-step explanation:

Hello!

A function is a equation that every input has one output

To find if an equation is a function we put in a number for one variable and solve

I'll use 0

y^2 = 0^2 + 5(0) + 4

Simplify

y^2 = 0 + 0 + 4

Combine like terms

y^2 = 4

To remove the square from y you put 4 in the square root in both negative and positive

[tex]y=\sqrt{4}[/tex] [tex]y=-\sqrt{4}[/tex]

Simplify

y = 2, y = -2

For one input (0) we get two outputs (2 and -2) this means it is not a function. So the answer is B

Hope this Helps!

Consider a graph of the equation y = −3x + 4. What is the y-intercept? Answers: −3, 3, 4, −4

Answers

Answer:

When finding the y-intercept it indicates that the x-coordinate will be zero.

So,when letting x=0 you will get

y=-3(0)+4

Hence,

y=4

Step-by-step explanation:

Among the four northwestern states, Washington has 51% of the total population, Oregon has 30%, Idaho has 11%, and Montana has 8%. A market researcher selects a sample of 1000 subjects, with 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana. At the 0.05 significance level, test the claim that the sample of 100 subjects has a distribution that agrees with the distribution of state populations.

Answers

Answer:

Step-by-step explanation:

H₀ : The distribution of the sample agrees with the population distribution.

H₁ : the distribution of the does not agree with the population distribution.

Using the  Chi-square test statistics

we will compute the expected frequencies

Now expected frequency for Washington will be

Fe = Npi = 1000×51% = 5100

expected frequency for Oregon

Fe = Npi = 1000×30% = 300

expected frequency for Idaho

Fe = Npi = 1000×11% = 110

expected frequency for  Montana

Fe = Npi = 1000×8% = 80

The Chi=square test statistics is;

x² = ∑ [ (Fo - Fe)² / Fe )

now we substitute

Given our Fo ( 450 in Washington, 340 in Oregon, 150 in Idaho, and 60 in Montana) from the question

x² =  (450-510)²/510 + (340-300)²/300 + (150-110)²/110 + (60-80)²/80

x²= 31.9376

so the chi-square test statistics is 31.9376

Now the chi-square critical value

first we compute for degree of freedom

d.f = k -1 = 4 - 1 = 3

So from the critical value table, degree of freedom 3 and significance level 0.05,

the chi-square critical value is 7.8147

Therefore chi-square test statistics 31.9376 is greater than the chi-square critical value 7.8147, so NULL HYPOTHESIS IS REJECTED at 5% significance.

There is sufficient evidence to warrant rejection  of the claim that the distribution of the sample agrees with the distribution of the state populations.

t takes one person 2 hours to grade 1 exam and it takes another 4 hours to grade 1 exam. If both work together, how many exams they can grades in 8 hours

Answers

Answer:

4

Step-by-step explanation:

2×4 equals 8 4 papers in 8 hours

PLEASE HELP ME, I DON'T UNDERSTAND THIS! :(

Answers

Answer Choice 1

Take it step by step!

First find what sqrt(x-7) is like. Compare it to sqrt(x).

You can see that in sqrt(x), when x = 0, y = 0. However, in sqrt(x-7), when x = 7, y = 0. When y = 0, sqrt(x-7) is 7 more, which means it is shifted 7 units to the right.

Similarly, +8 means that whatever sqrt(x-7) is, you add 8 more to y. Adding on extra for y is just moving it up by 8 units.

Hope that helped,

-sirswagger21

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