The standard equation of the sphere with the given endpoints of a diameter is x^2 - 7x + y^2 - 8y + z^2 - 4z + 20 = 0.
The center of the sphere is the midpoint of the given diameter. Using the midpoint formula, we have:
Center = ((6+1)/2, (1+7)/2, (5+(-1))/2) = (3.5, 4, 2)
The radius of the sphere is half the length of the diameter, which can be found using the distance formula between the given endpoints:
diameter = √[(6-1)^2 + (1-7)^2 + (5-(-1))^2] = √(146)
radius = diameter/2 = √(146)/2
Therefore, the standard equation of the sphere is:
(x - 3.5)^2 + (y - 4)^2 + (z - 2)^2 = (√146/2)^2
Expanding and simplifying this equation gives:
x^2 - 7x + y^2 - 8y + z^2 - 4z + 20 = 0
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please help with this
Answer: the initial points is 30.
and per pair of shoes is 15.
Step-by-step explanation:
Julie went to the post office and bought both $0.41 stamps and $0.26 postcards. She spent $51.40. The number of stamps was 20 more than twice the number of postcards. How many of each did she buy?
The number of postcards she bought is 40.
What are a formula and an equation?Your example is an equation since an equation is any expression with an equals sign. Due of mathematicians' love of equal signs, equations are commonly used in mathematical expressions.
A formula is a collection of guidelines for producing a specific outcome.
Write the equation by adding the total values of each item.
0.41 (2p+20)+0.26p = 51.40
We can solve this equation for p to find the number of postcards.
0.41(2p+20)+0.26p =51.40
0.82p+8.20+0.26p=51.40
1.08p=43.2
p=40
So, the number of postcards she bought is 40. Since the number of 41-cent stamps is 20 more than twice the number of postcards, the number of 41-cent stamps is 2(40)+20=100.
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Help!! I need this ASAP!
The given expression rewritten in simplified exponential form is \(5x^{\frac{3}{2}}\)
Simplifying an expressionFrom the question, we are to rewrite the given expression is simplified exponential form.
The given expression is
\(\sqrt{\sqrt{25^{2} x^{6} } }\)
First, we will evaluate the inner square root
\(\sqrt{25^{\frac{2}{2} } x^{\frac{6}{2} } }\)
\(\sqrt{25 x^{3 } }\)
Simplifying further
\(\sqrt{25 } \times \sqrt{x^{3}}\)
\(5\times x^{\frac{3}{2}}\)
= \(5x^{\frac{3}{2}}\)
Hence, the expression in simplified form is \(5 x^{\frac{3}{2}}\)
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Identify the equation for the line of the graph below.
Circle the two smallest numbers.
3.68
3.06
3.7
3.08
36.8
3.068
The Smallest numbers is 3.068 and 3.6
What is meant by smallest numbers ?Check the whole number portion of each decimal number before placing them in ascending order. Since 4 is the smallest whole number, the smallest decimal number is 4.926. The remaining decimal digits all contain the same whole number, or 18.
The least number among those given is 1.
The smallest three-digit number in the number system is 100, which becomes a two-digit number, which is 99, when one is deducted from the number (a two-digit number). Therefore, in the number system, 100 is the smallest three-digit number. The smallest three-digit number is 100, which is so proven.
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Mookie betts of the boston red sox had the highest batting average for the 2018 major league baseball season. His average was 0.364. So, the likelihood of his getting a hit is 0.364 for each time he bats. Assume he has seven times at bat tonight in the red sox-yankee game. This is an example of what type of probability?
An example where Mookie betts of the boston red sox had the highest batting average in 2018 with probability of average batts is 0.364 for each is a binomial Probability example.
In the statistics, the concept of probability is handy in figuring out the likelihood a particular outcome would occur for an event or decision. On the basis of probability, one can figure out other related probabilities like the probability of not having that particular outcome or the probability of having only that outcome every time. There is Mookie betts of the boston red sox had the highest batting average in league baseball season.
The average probability = 0.364 for each time of bats.
That is Probability of hitting or success, p = 0.364
Number of trials, n = 7
That is Probability distribution is written as \(X \: \tilde \: \: Binom( n,p) \).
After reading all seniror, the probability for seven seven times at bat tonight in the red sox-yankee game is an example of binomial Probability.
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Pls help!! I have no idea what to do
The barrel has 60 gallons and water leaks at a rate of 1 gallon per 10 minutes.
The graph goes by 100 minutes so 100x1 = 10 gallon leaked per 100 minutes.
The graph would be a line segment as you would start at 60 gallons and end at 0 gallons, you cannot have negative gallons.
The graph is a negative line as you are losing gallons.
1/3 +1/6 in fraction form
\(\Large\texttt{Answer}\)
\(\bf{\cfrac{1}{2}}\)
\(\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}\)
\(\Large\texttt{Process}\)
Do you remember that we cannot add fractions when they have unlike denominators? We can onyl add fractions as long as they have the same denominator!
So here's the big idea: fractions must have the same denominator.
If we multiply the first fraction by 2, then both fractions will have the same denominator. *
* Why 2??
- Because:
We need to find the least common multiple of 3 and 6, which is 6. Next, what should 3 be multiplied by to result in 6? That's right, 2.
Also, we can only multiply the denominator by 2 as long as we multiply the numerator by 2!
So that's why we multiply the whole fraction by 2
\(\bf{\cfrac{1\times2}{3\times2}+\cfrac{1}{6}}\)
Watch what happens
\(\bf{\cfrac{2}{6}+\cfrac{1}{6}}\)
Add the numerators
\(\bf{\cfrac{2+1}{6}}\)
\(\bf{\cfrac{3}{6}}\)
Simplifying the fractions
\(\bf{\cfrac{3\div3}{6\div3}}\)
\(\bf{\cfrac{1}{2}}\)
Hope that helped
Answer: 1 / 2
Step-by-step explanation:
Given information
\(\frac{1}{3} ~+~\frac{1}{6}\)
Convert the denominator (3, 6) into the same common denominator
Least Common Multiple (LCM) of 3 and 6 = 6
\(=\frac{1~*~2}{3~*~2} ~+~\frac{1}{6}\)
\(=\frac{2}{6} ~+~\frac{1}{6}\)
Combine two fractions
\(=\frac{2~+~1}{6}\)
\(=\frac{3}{6}\)
Simplify the fraction by dividing 3 on both numerator and denominator
\(=\frac{3~/~3}{6~/~3}\)
\(=\Large\boxed{\frac{1}{2} }\)
Hope this helps!! :)
Please let me know if you have any questions
How many ounces of a 4% acid solution and how many ounces of a 10% acid solution must be mixed to make 24oz of a 6% acid solution
a = acid solution 4%
b = acid solution 10%
a + b = 24
0.04*a+0.1*b=0.06*24
a=24-b
0.04*(24-b) + 0.1*b = 1.44
0.96 - 0.04b + 0.1*b = 1.44
0.06*b = 0.48
b = 8 oz
a=24-b
a = 24 - 8
What is equivelant to 9b + 24?
a
3(3b + 24)
b
3(3b + 8)
c
3(3b + 216)
d
3(9b + 8)
Answer:
it is b.
Step-by-step explanation:
hope this helps
Mo is wrapping a gift in a rectangular box for his mother. What is the surface area of the box Mo needs to wrap?
Answer:
The perimeter of the rectangular box.
Step-by-step explanation:
If 10 2.29=195, find the value of log10 19.5
Answer:
log10 195 = 2.29
Answer:
I found this
To solve for the value of log10 19.5, we can use the property of logarithms that states:
loga(b^c) = c * loga(b)
In this case, we can express 19.5 as 10^2.29:
19.5 = 10^2.29
So, we can find the logarithm of 19.5 by solving for c:
log10(19.5) = log10(10^2.29)
By using the property of logarithms mentioned above, we can simplify the equation to:
log10(19.5) = 2.29 * log10(10)
Since log10(10) = 1, we can further simplify the equation to:
log10(19.5) = 2.29
Therefore, the value of log10 19.5 is 2.29.
what type of sampling is used when it is not possible to select individuals directly from the target population?
Answer:
If a researcher cannot gain access to a target population, snowball sampling procedures can assist in locating subjects. In regard to sampling procedures, if a researcher wants to be able to generalize results to the total population of interest, then a purposeful sampling technique is the best approach.
Answer:
Non-probability sampling
Step-by-step explanation:
Non-probability sampling is a method of selecting units from a population using a subjective method.
HELPPP!??? PLS ANSWER!!???
Answer:
FE = 9 , DE = 15
Step-by-step explanation:
Δ FDE and Δ HGE are similar , then the ratios of corresponding sides are in proportion , that is
\(\frac{FE}{HE}\) = \(\frac{FD}{HG}\) ( substitute values )
\(\frac{FE}{6}\) = \(\frac{12}{8}\) ( cross- multiply )
8 × FE = 6 × 12 = 72 ( divide both sides by 8 )
FE = 9
and
\(\frac{DE}{GE}\) = \(\frac{FD}{HG}\)
\(\frac{DE}{10}\) = \(\frac{12}{8}\) ( cross- multiply )
8 × DE = 10 × 12 = 120 ( divide both sides by 8 )
DE = 15
Is the triangle congruent by SSS, SAS, or ASA. What is the congruent statement for the shape
Answer:
SAS
Step-by-step explanation:
I hope this helps you out!
Which one?
A. B. C. or D?
Answer:
Its B
Step-by-step explanation:
Its B prob
At an athletics event, gold, silver and bronze medals are awarded. The ratio of gold to silver medals won by a country is 1:3 . The ratio of silver to bronze medals won by the country is 2:3 . Find the ratio of gold to bronze medals won by the country in the form 1 / n .
Answer:
1:3
Step-by-step explanation:
gold to silver
1:3
silver to bronze
2:3
gold to bronze
1:3
Answer:
1:3 I think
Step-by-step explanation:
1:3 I think im pretty sure but im not good at math so
Suri makes 15$ per hour and gets a weekly bonus of 25$.Juan makes 14$ per hour and gets weekly bonus of 50$.Is it possible for Suri and Juan to make the same amount of wages,y, by working the same number of hours,x,in one week? Explain
Answer:
Yes, it is possible for Suri and Juan to make the same amount of wages if they both work 25 hours in one week.
Step-by-step explanation:
Let x = number of hours worked
Let y = total wages earned
Suri: 15x + 25 = y
Juan: 14x + 50 = y
Equate equations and solve for x:
15x + 25 = 14x + 50
Subtract 14x from both sides: x + 25 = 50
Subtract 25 from both sides: x = 25
Yes, it is possible for Suri and Juan to make the same amount of wages if they both work 25 hours in one week.
Subtract-3c2 + 12cd – 4d2 from 4c2 + 3cd + 2d?.
Your answer should be a polynomial in standard form.
Answer:
Subtract \(-3c^2 + 12cd - 4d^2\) from \(4c^2 + 3cd + 2d^2\) we get \(\mathbf{7c^2-9cd+6d^2}\)
Step-by-step explanation:
We need to Subtract \(-3c^2 + 12cd - 4d^2\) from \(4c^2 + 3cd + 2d^2\)
(Note: Considering 2d^2 instead of 2d as thinking it typo error)
Subtracting from means we have to subtract \(4c^2 + 3cd + 2d^2 -(-3c^2 + 12cd - 4d^2)\)
Subtracting:
\(4c^2 + 3cd + 2d^2 -(-3c^2 + 12cd - 4d^2)\\=4c^2 + 3cd + 2d^2 +3c^2 - 12cd + 4d^2\)
Combining like terms (Like terms are those that have same variables like 4c^2 and 3c^2 are like terms, 3cd and -12cd are like terms, 2d^2 and 4d^2 are like terms)
\(=4c^2+3c^2 + 3cd-12cd + 2d^2+4d^2 \\=7c^2-9cd+6d^2\)
So, Subtract \(-3c^2 + 12cd - 4d^2\) from \(4c^2 + 3cd + 2d^2\) we get \(\mathbf{7c^2-9cd+6d^2}\)
Kelsey knit a total of 6 centimeters of scarf over 2 nights. After 4 nights of knitting, how many centimeters of scarf will Kelsey have knit in total? Assume the relationship is directly proportional.
Answer:
\(12\) cm
Step-by-step explanation:
If Kelsey knit a total of \(6\) cm of scarf over \(2\) nights, then we know that she can knit \(\frac{6}{2}=3\) cm each night. Therefore, after \(4\) nights of knitting, Kelsey would have knit a total of \(3*4=12\) cm of scarf in total. Hope this helps!
help with angle sum theorem please
7. call a positive integer an uphill integer if every digit is strictly greater than the previous digit. for example, 1357,89 , and 5 are all uphill integers, but 32,1240, and 466 are not. how many uphill integers are divisible by 15 ?
Answer:
6
Step-by-step explanation:
You want to know the number of uphill integers divisible by 15, where an uphill integer is one that has its digits strictly increasing.
Divisible by 15An integer will be divisible by 15 if and only if it is divisible by 3 and 5. An integer is divisible by 5 if it ends in 5 or 0. An uphill integer cannot end in 0, so must end in 5.
An integer is divisible by 3 if the sum of its digits is divisible by 3
Uphill integersAn uphill integer will have differences between successive digits that are positive integers. In order for the final digit to be 5, the sum of these differences must be 5. Hence we can find uphill integers by considering the "integer partitions" of 5: the sets of positive integers whose total is 5. Those sets would be ...
{5}, {4, 1}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, {1, 1, 1, 1, 1}
Uphill integers will also have digit differences that are some permutation of each of these sets. For example, the digit differences may be {4, 1} or {1, 4}, corresponding to the numbers 45 or 15.
The uphill integers that end in 5 are ...
5, 45, 15, 35, 25, 345, 145, 125, 245, 235, 135, 2345, 1345, 1245, 1235, 12345
Divisible by 3We already know each of these is divisible by 5. The ones that have a digit total that is a multiple of 3 are ...
15, 45, 135, 345, 1245, 12345
There are 6 uphill integers divisible by 15.
A clerk enters 75 words per minute with 6 errors per hour. What probability distribution will be used to calculate probability that zero errors will be found in a 255-word bond transaction
The probability of having zero errors is approximately 0.711.
The probability distribution that can be used to calculate the probability that zero errors will be found in a 255-word bond transaction is the Poisson distribution.
The Poisson distribution is a discrete probability distribution that is used to model the number of events occurring within a fixed interval of time or space, given the average rate of occurrence of the events.
In this case, the average rate of occurrence of errors is 6 per hour, which can be converted to 0.1 errors per minute. Therefore, the expected number of errors in a 255-word bond transaction is (255/75)*0.1 = 0.34 errors.
Using the Poisson distribution, the probability of having zero errors in a 255-word bond transaction can be calculated as:
\(P(X = 0) = (e^{(-\lambda)} * \lambda^0) / 0! = e^{(-0.34)} * 0.34^0 / 1! \approx 0.711\)
where λ is the expected number of errors in the 255-word bond transaction.
Therefore, the probability distribution used to calculate the probability of having zero errors in a 255-word bond transaction is the Poisson distribution, and the probability of having zero errors is approximately 0.711.
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How much the statistic varies from one sample to another is known as the ____ _____ of a statistic.
How much a statistic varies from one sample to another is known as the sampling variability of a statistic.
Testing variability arises due to the reality that exceptional samples of the same size can produce special values of a statistic, although the samples are described from the same populace. the quantum of slice variability depends on the scale of the sample, the variety of the populace, and the unique statistic being calculated.
The end of statistical conclusion is to apply the data attained from a sample to make consequences about the population, while counting for the slice variability of the statistic. ways similar as thesis checking out and tone belief intervals do not forget the sampling variability of a statistic to make redundant accurate consequences about the populace.
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find volume of figure down below
The volume of figure down below is 470.996 cubic in.
The volume of the cone is the product of one-third of the height, pie, and square of the radius that is;
The volume of the cone = 1/3(πr²)(height)
Since we can see that there are two cones combined together to form one figure.
So, Volume of first cone = 1/3(πr²)(height)
= 1/3(π 5²)(7)
= 1/3(π 25)(7)
= 183.166
Volume of second cone = 1/3(πr²)(height)
= 1/3(π 5²)(11)
= 1/3(π 25)(11)
= 287.83
Therefore, the volume of the figure is;
287.83 + 183.166
470.996
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A parabola can be drawn given a focus of
(3, -9) and a directrix of y = -5. Write
the equation of the parabola in any form.
The equation of parabola is y = -8(x -3)² - 9.
Define parabola.A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
Given Data
Focus = (3, -9)
Directrix: y = -5
The focus-passing line has an equation of x = -5 that is perpendicular to the directrix. The symmetry line of a parabola is seen here.
The parameter of the parabola is the separation between the focus and the directrix, so
p = -9 - 3
p = -12
p = 12
The distance between the focus and the directrix is divided into two equal portions by the parabola's vertex, which is located on the line of symmetry. Its coordinates are as follows: (3,-9).
Since a parabola moves in the opposite direction of y, its equation is
y -(-9) = -2(4(x -3)²)
y + 9 = -8(x-3)²
y = -8(x -3)² - 9
The equation of parabola is y = -8(x -3)² - 9.
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Noelle is making a rectangular place mat that is 15 inches wide and 18 inches long. What is the least amount of fabric that she will need to make the place mat?
Answer:
270 in
Step-by-step explanation:
the least amount of fabric she would need is equal to the area of the mat
the mat is in the shape of a rectangle
Area of a rectangle = length x width
15 x 18 = 270 in²
Can any body help Me with Factoring this
(5a+5a)=
Find the equation of the tangent line to the curve when x has the given value. F(x) = x^2 + 5x ; x = 4 Select one: A. y =13x-16 B. y=-4x/25 +8/5 C. y=x/20+1/5 D.y=-39x-80
The correct answer for tangent line is A. y = 13x - 16.
What is tangent line?A line that barely touches a curve (or function) at a specific location is said to be its tangent line. In calculus, the tangent line may cross the graph at any other point(s) and may touch the curve at any other point(s).
To find the equation of the tangent line to the curve defined by \(F(x) = x^2 + 5x\) at x = 4, we can use the concept of differentiation.
First, let's find the derivative of F(x) with respect to x. Taking the derivative of \(x^2 + 5x\), we get:
F'(x) = 2x + 5.
Now, to find the slope of the tangent line at x = 4, we substitute x = 4 into F'(x):
F'(4) = 2(4) + 5 = 8 + 5 = 13.
So, the slope of the tangent line is 13.
To find the y-intercept of the tangent line, we substitute x = 4 into the original function F(x):
\(F(4) = 4^2 + 5(4) = 16 + 20 = 36.\)
Therefore, the point (4, 36) lies on the tangent line.
Using the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept, we can write the equation of the tangent line:
y = 13x + b.
To find b, we substitute the coordinates (x, y) = (4, 36) into the equation:
36 = 13(4) + b,
36 = 52 + b,
b = 36 - 52,
b = -16.
Therefore, the equation of the tangent line to the curve \(F(x) = x^2 + 5x\) at x = 4 is:
y = 13x - 16.
Thus, the correct answer is A. y = 13x - 16.
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how many factors of 10 does 1000 have?
Answer:it has 16
Step-by-step explanation:
The answer of your question is 16 factors