The sphere's equation that passes through the given point is:
(x - 3)² + (y - 8)² + (z - 1)² = 30What is the standard equation of a sphere?A sphere's standard equation is defined by its center and radius. Remember that the radius is the distance between any two points on the sphere. The standard formula is: [tex]\left(x-x_c\right)^2+\left(y-y_c\right)^2+\left(z-z_c\right)^2=r^2[/tex]To find the equation of the sphere:
The radius of a sphere is equally distant between any two points on the sphere. The sphere's center is: (3, 8, 1)So,
P = (4, 3,−1)C = (3, 8, 1)r = d(C, p)Now,
[tex]\begin{aligned}&=\sqrt{\left(x_c-x_p\right)^2+\left(y_c-y_p\right)^2+\left(z_c-z_p\right)^2} \\&=\sqrt{(3-4)^2+(8-3)^2+(1-(-1))^2} \\&=\sqrt{(-1)^2+(5)^2+(2)^2} \\&=\sqrt{1+25+4} \\\therefore r &=\sqrt{30}\end{aligned}[/tex]
Supplement the center point and radius into the standard sphere equation:
[tex]\left(x-x_c\right)^2+\left(y-y_c\right)^2+\left(z-z_c\right)^2=r^2\\(x-3)^2+(y-8)^2+(z-1)^2=(\sqrt{30})^2\\(x-3)^2+(y-8)^2+(z-1)^2=30[/tex]
Therefore, the sphere's equation that passes through the given point is:
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The correct question is given below;
Find an equation of the sphere that passes through the point (4, 3,−1) and has to center (3, 8, 1).
The formula for the area of a trapezoid is given. Solve this equation for h, height. a=H(B1+B2)/2
The solution of the equation for h is H = 2a/(B1 + B2)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to solve the equation for h?The equation is given as
a=H(B1 + B2)/2
The above means that the variable h is represented by the variable H
Multiply both sides of the equation by 2
So, we have
2a = H(B1 + B2)
Divide both sides of the equation by (B1 + B2)
H = 2a/(B1 + B2)
Hence, the solution of the equation for h is H = 2a/(B1 + B2)
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what is the answer for this 3x+4x+5x+...+43x
Answer:
1032x
Step-by-step explanation:
[tex]3x+4x+\cdots+43x=x(3+4+\cdots+45) \\ \\ =43x\left(\frac{45+3}{2} \right) \\ \\ =43(24x) \\ \\ =1032x[/tex]
solve the inequality for y
3y+8<65
Answer:
Step-by-step explanation:
y < 19
hope this helps :)
What is the value of the expression?
40÷[20−4⋅(7−4)]
Please help im giving brainiest
Answer:5
Step-by-step explanation:
7 times what makes 2555?
365
304
200
1000
365 is your answer...
Find the first four multiples of 15.
Answer:
15, 30, 45, 60
Step-by-step explanation:
ALL OF THE MULTIPLES OF 15
15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495, 510, 525, 540, 555, 570, 585, 600, 615, 630, 645, 660, 675, 690, 705, 720, 735
All numbers can be divided or the product of 15 is a multiple of 15.
the number of questions marked incorrect on a statistics midterm, y, is dependent on the pages of notes a student wrote over the semester, x, and can be modeled by the function y(x)
The another point is (2,23) of the function y(x).
What does regression analysis mean?
Finding the variables that have an effect on an interest issue can be done with accuracy using regression analysis. You can confidently establish which elements are most important, which ones can be ignored, and how these factors interact when you do a regression.The given Regression is -
y (X) = 30 - 3. 5 x .......................(1)
now when x = 0 , y(x) = 30 ..........................(1)
thus , y- intercept = 30
one point is ( 0 , 30 )
Again taking x = 0 we get
y(x) = 30 - 3. 5 x 2 by (1)
y(X) = 23
Thus the another point is (2,23).
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-6 ≤ x + 3 < 10 solve x
Answer:
-6 ≤ x + 3 < 10
-6 - 3 ≤ x + 3 - 3 < 10 -3
-9 ≤ x < 7
In a chi-square test, as the value of the χ2 increases, the likelihood of rejecting the null hypothesis ________.
If the chi-square value is going on English the likelihood of rejecting the null hypothesis also increases because there is a chance that the chi-square value increases more than the significant value that is given in the question. So the required answer is that increases as the required answer.
For example, if, according to Mendel's laws, you expected 10 of 20 offspring from a cross to be male and the actual observed number was 8 males, then you might want to know about the "goodness to fit" between the observed and expected.
Were the deviations (differences between observed and expected) the result of chance, or were they due to other factors? How much deviation can occur before you, the investigator must conclude that something other than chance is at work, causing the observed to differ from the expected.
The chi-square test is always testing what scientists call the null hypothesis, which states that there is no significant difference between the expected and observed result.
The formula for calculating chi-square ( 2) is:
2= (o-e)2/e
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Children shorter than 48 inches get into the water park free. Howard is currently 32 inches tall. He grows approximately 3 inches per year. Write an inequality to represent the number of years, y, that he can get in free.
Answer:
5 year
3 inches every year 48 minus 32 equals 16 3 Inches divided into 16 equal 5.333333 round it equals 5 years y = 5 years
How about members of a local professional sports team who are conducting a survey? which data collection method would provide biased results for the q
This is because they are likely to report their favorite game as soccer or some other related game.
What is survey explain?
In order to gather information about a service, product, or process, a survey is described as the act of looking at a process or questioning a predetermined sample of people. Surveys used to gather data ask a specific set of people about their beliefs, actions, or knowledge.What three sorts of surveys are there?
Most studies fall into one of three categories: exploratory, descriptive, or causal. Each has a distinct function and can only be applied in specified ways.
The biased result would be provided by the -
Ask people attending a soccer game
This is because they are likely to report their favorite game as soccer or some other related game.
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Select 3 collinear points.
r
A
B
D
s
N
C
Use the numbers 1,2,3,4,5,6 to fill in the circles to make the equations true. Use each number once.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Revision 1. Find the value of the variable that makes these number sentences true: a) h+8=19 b) 2p-6=4 c) y = 12 2. Substitute the value for x in order to find the value of y in the following: a) y=3x+2 ifx=8 b) y=4x-1 ifx=! c) y=0,2x+5 ifx=10 d) y = 10x+12 if x=0,3 3. Write the following as number sentences: a) The difference between two numbers is 25 b) The product of 5 and p is equal to the quotient of q and 2 c) The difference between 14 and 2y is equal to 6 d) The product of 15 and 4 is equal to four less than the sum of x and y. that represent these word problems.
1. The values which the given number sentences true are:
a) 11 b) 5 c) 36
2. After substituting the value of x we get the value for y as :
a) 6 b) 0 c) 7 d) 15
3. The number sentences are :
a) x ₋ y = 25
b) 5 × p = q ÷ 2
c) 2y ₋ 14 = 6
d) 15 × 4 = 4 ₋ (x₊y)
Given in the first bit we need to find the variables:
a) h ₊ 8 = 19
arrange the constants on one side.
h = 19 ₋ 8
h = 11
b) 2p ₋ 6 = 4
arrange the constants on one side.
2p = 4 ₊ 6
2p = 10
p = 10/2
p = 5
c) 1/3 y = 12
cross multiply.
y = 36
Now in the second exercise we are asked to substitute the x value and get the value of y.
a) y = 3x ₊ 2 if x =8
substitute x value in the equation.
y = 3(8) ₊ 2
y = 24 ₊ 2
y = 26
b) y = 4x ₋ 1 if x = 1/4
y = 4(1/4) ₋ 1
y = 1 ₋ 1
y = 0
c) y = 0.2x ₊ 5 if x = 10
y = 0.2(10) ₊ 5
y = 2 ₊ 5
y = 7
d) y = 10x ₊ 12 if x = 0.3
y = 10(0.3) ₊ 12
y = 3 ₊ 12
y = 15
In the last third bit we need to frame equations for the given word problems.
a) The difference between two numbers is 25.
let the two numbers be x and y.
x ₋ y = 25.
b) The product of 5 and p is equal to quotient of q and 2.
5 × p = q ÷ 2
c) The difference between 14 and 2y is equal to 6.
2y ₋ 14 = 6
d) The product of 15 and 4 is equal to four less than the sum of x and y.
15 × 4 = 4 ₋ (x₊y)
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the points (-3,1), (-1,1), (0,-1), (-1,-3), (-3,-3) and (-4,-1) are vertices of a polygon. what type of polygon is formed by these points?
Answer:
10
Step-by-step explanation:
Bxhwbdjnqbxkabxjb iqbdnannsmxns
Find the distance between the two points in simplest radical form.
(-8, 7) and (-4,5)
The distance between the two points in simplest radical form is 2√5.
Given the points are (₋8 , 7) and (₋4 , 5)
Let (₋8 , 7) be (x₁ , y₁) and
(₋4 , 5) be (x₂ , y₂)
we know that distance between two points is:
√(x₂ ₋ x₁)² ₊ (y₂ ₋ y₁)²
Substitute (₋8 , 7) and (₋4 , 5) into the above distance formula.
√(₋4 ₊ 8)² ₊ (5 ₋ 7)²
calculate the sum or the difference.
√(4)² ₊ (₋2)²
Determine the sign for radical or exponential expressions.
√16 ₊ 4
√20
Now factor and rewrite the radicand in the exponential form.
√2²×5
Rewrite the expression using ⁿ√ab = ⁿ√a . ⁿ√b
√2² × √5
simplify the radical expression.
2√5
hence we get the distance between two points in radical form as 2√5 units.
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HELP PLEASE !!! Phone will die soon
Answer:
The overall change was 58 degrees
Step-by-step explanation:
-2 + 58 = 56
Graph the inequality.
y ≥ |x+5|-3
The graph that represents the inequality is graph b
Graph of inequalitiesFrom the question, we are to graph the given inequality
The given inequality is
y ≥ |x+5|-3
To graph the inequality, we will write the inequality as an equation and we will find some of the points on the line
When x = 0
y = |x+5|-3
y = |0+5|-3
y = |-3
When y = 0
y = |x+5|-3
0 = |x+5|-3
0 = (x + 5) - 3 and 0 = -(x + 5) -3
3 = x + 5
x = 3- 5
x = -2
and
0 = -(x + 5) -3
x + 5 = -3
x = -3 - 5
x = -8
The graphs that has the points above are graphs b and d.
Since the inequality sign is ≥ when y is the subject, the solution to the inequality is above the lines.
Hence, the graph of the inequality is graph b.
The graph of the inequality is shown below
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GEOMETRY [35 POINTS]
What is the value of X?
What is the measure of angle A?
What is the measure of angle B?
Answer:
Step-by-step explanation:
Comment
The key to this is to know what a remote angle is. A remote angle is one that has one leg in common with the exterior angle. Make this a little simpler.
The exterior angle is outside the triangle. In this case it is the 157 degree angle.
The two remote angles each contribute just one side to the exterior angle. <B contributes BC and <A
Theorem
The two remote angles = the exterior angle.
Equation
x + x - 21 = 157
Solution
x + x - 21 = 157 Combine the left side
2x - 21 = 157 Add 21 to both sides
2x - 21 + 21 = 157+21 Combine
2x = 178 Divide by 2
2x/2 = 178/2
x = 89
Answer
x = A = 88
89 - 21 = B =68
(5,-4), (1, -7) distance formula
Answer:
The distance between both points is 5 units
Step-by-step explanation:
The distance formula is: d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}
A student in a big city lives on the 44th floor of her building. On rainy days, when she gets home from school, she takes the elevator all the way up to her floor. But on sunny days, she goes up to floor 20 and walks the rest of the way. Why?.
She is diminutive (a very, very small person). She can ask others to hit the top elevator buttons for him because he can't reach them. On rainy days, he presses the buttons with his umbrella.
What is a riddle?A statement, question, or phrase with a hidden or double meaning that is presented as a problem to be answered is called a riddle. Enigmas, which are difficulties typically presented in metaphorical or allegorical language that call for inventiveness and careful thought to solve, and conundra, which are questions that rely on puns in either the question or the answer, are two different forms of riddles.
Riddles from hundreds of various civilizations, including Finnish, Hungarian, American Indian, Chinese, Russian, Dutch, and Filipino sources, are cited by Archer Taylor in his statement that "we may definitely claim that riddling is a global art. Riddles and riddle motifs are common across the world.
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Which number rounds to 3,000 if you round it to the nearest thousand, AND to 2,500 if you round it to the nearest hundred?
Answer:
2,739 and 2,489
Step-by-step explanation:
There are many solutions to both problems:
(Rules)
If the number is 5 or higher round (up)
If the number is 4 or lower round (down)
2,739⇒3,000
↑↑↑
Higher than 500 so round up to get 3,000
2,489⇒2,500
↑↑
Higher than 50 so round up to get 2500
2,739 and 2500 are both possible solutions.
*HURRY help i’m taking a test*
mario will purchase 2 rare coins each month at a cost of $50 each. how much money will mario have spent on his coin collection after 2 years if he purchases an additional 3 coins at the end of the 2 years?
a. $1200
b. $2550
c. $2400
d. $1750
c. $1250
Answer:
it should be b.
Step-by-step explanation:
2 rare coins will make them $100 each month. There are 12 months in a year.
12 × 2 = 24 months
so $100 × 24 months will give us 2400.
Then Mario purchases 3 coins making it cost $150 ($50 + $50 + $50)
2400 + 150 = 2550
Brainliest plss :,)
What is Ah Fo's reply to the magician giving him the three brass pennies?
A. Ah Fo asks for a day to think about the decision.
B. Ah Fo immediately tells the magician what he wants.
C. Ah Fo asks the magician for suggestions.
D. Ah Fo tells the magician that he doesn't want a reward for his help.
The inference is that Ah Fo's reply to the magician giving him the three brass pennies is D.
Ah Fo tells the magician that he doesn't want a reward for his help.
How to illustrate the information?It should be noted that the information is about how the character helped the magician. Despite the help, he didn't request for anything in return.
Therefore, the inference is that Ah Fo's reply to the magician giving him the three brass pennies is that Ah Fo tells the magician that he doesn't want a reward for his help.
In conclusion, the correct option is D.
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Read the excerpt from "The Three Brass Pennies."
“And what might your decision be?” asked the magician, as he spread out the three brass pennies before him.
“I would ask first,” went on Ah Fo, “for the power to read accurately the thoughts of others; secondly, for the power to foretell my own future at least a month in advance of any given moment; third, for the power to acquire all learning without any effort!”
When he had finished, the magician sat back with a gasp, took off his spectacles and wiped them, put them on once more, and stared at Ah Fo in astonishment and not a little dismay. “This is most unusual,” he stammered, “not to say somewhat dangerous! Have you duly considered, my son, the extent of all you ask?”
Please help asap the picture has everything needed to answer the question. Thank you!
Answer:
Step-by-step explanation:
f(x) = 0
then x =
-2 and +2
f(x) = 5
then x = +3 and -3
David has 10 yd. Of material that he wiil cut into 15in. Thick mats. How many mats can David make?
Step-by-step explanation:
10 yards is equal to 360 inches. If you divided 360 inches by 15 inches, the answer will be 24. So the answer is 24 mats.
Evaluate the function.
f(x) = x² - 4x – 12
Find f(-7)
Answer:
Your answer is 65
Step-by-step explanation:
f(x) = x² - 4x - 12
f(-7) = (-7)² - 4 x (-7) - 12
= 49 - (-28) - 12
= 49 + 28 - 12
= 77 - 12
= 65
which function below has the largest slope? f(x) x f(x) −3 −10 −1 −7 1 −4 g(x) equals one half x plus 3 h(x) lance gains 1 level each time he plays his favorite video game. he started at level 10. (2 points) f(x) g(x) h(x) the functions all have the same slope
The function with the largest slope would be f(x) = 1.5
What is the slope in math?
The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").For f(x), choose any two points say (-3,-10) and (-1,-7) where
x1 = -3 ; y1 = -10 ; x2 = -1 ; y2 = -7
Find the slope (m)
m=(y2 - y1) / (x2 - x1) = (-7 - -10)/ (-1 - -3) = 3/2 or 1.5
slope of f(x) = 1.5
g(x) = 1/2 x + 3
standard formula: y = mx + b where m is the slope.
slope of g(x) = 1/2 or 0.5
Since lance gains 1 level every time he plays,
slope = 1/1 = 1 so, slope of h(x) = 1
the function with the largest slope would be f(x) = 1.5
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If the domain of the function f(x) = 3x -2 is {-1, 0, 1}, what is the range of the function?
When x = -2:
f(-2) = -3 (-2) + 1
f(-2) = 6 +1
f(-2) = 7
y = 7
When x = 0:
f(0) = -3 (0) + 1
f(0) = 0 +1
f(0) = 1
y = 1
When x = 3:
f(3) = -3 (3) +1
f(3) = -3 (3) + 1
f(3) = -9 +1
f(3) = -8
y = -8
So, the Range is {7, 1, -8}
Find the lowest common denominator for the following set of fractions: 4/21, 3/7, 4/9
The lowest common denominator for 4/21, 3/7, 4/9 is 63.
Lowest common denominator is the lowest number that is divisible by the denominators of the set of fractions.
Step 1: we will write down the prime factors of all the denominators.
[tex]21=7^{1} *3^{1}[/tex]
[tex]7=7^{1}[/tex]
[tex]9=3*3=3^{2}[/tex]
Step 2 : write down highest power of each prime number.
[tex]7^{1} ,3^{2}[/tex]
Step 3 : Multiply the values
7x9=63
Therefore , The lowest common denominator for 4/21, 3/7, 4/9 is 63.
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