By using the formula for the distance between the two points, it is found that S could lie on the perpendicular bisector QR.
Distance between points:
The distance between two points, (x1,y1) and (x2,y2) is calculated as,
D = √(x2 - x1)² + (y2 - y1)²
Given,
Here we have the coordinates: Q(-5, 4), R(8, -3), S(-2,-5)
Now, we have to determine if S could lie on the perpendicular bisector of QR with the given coordinates.
Here we have the endpoints are: Q(-5, -1), R(3, 7)
Point S is (4,-2).
The distance of S to Q is calculated as,
D = √(4 - (-5))² + (-2 - (-1))²
D = √82
Now, the distance of S to R is calculated as,
D = √(4 - 3)² + (-2 - 7)²
D = √82
Both have the Same distance, thus states the S could lie on the perpendicular bisector QR.
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suppose the probability of an event is 29 30 . what are the odds for the event happening? to what are the odds against the event happening? to
The probability of winning is 30/59.
What is a probability simple definition?
A probability is a number that expresses the possibility or likelihood that a specific event will take place.
Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
probability = wanted outcomes / total outcomes
odds = wanted outcomes / unwanted outcomes
odds of 29/30 losing means 29 losing outcomes and 30 winning outcomes.
The total outcomes is 59
The probability of losing is 29/30. Yet we want the probability of winning.
Provability of winning is 1 - probability of losing.
1 - 29/59 = 30/59
The probability of winning is 30/59.
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Tranlate the entence into an inequality. A number c divided by 8 i greater than or equal to 26
A number c divided by 8 is greater than or equal to 26:
c/8 ≥ 26
What is the median of 4 and 7?.
The mean of the 4 and 7 numbers is 5.5.
What is mean?
A amount that includes a price intermediate between those of the acute members of some set is known as mean.
Main body:
In this question we have to find the mean of the 4 and 7 numbers. Whole numbers are all non-negative integers which start from 0. Now the mean of the 4 and 7 numbers as the count of numbers from 4 and 7 is 2. Use this concept to reach the answer.
Mean of numbers is equal to the sum of the numbers divided by the count of the numbers that is
Mean = sum of numbers/ total numbers
mean = 4+7/2
= 5.5
HENCE , mean of 4 and 7 is 5.5
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HELP PLEASE!!!!!!
For the data in the table, does y vary directly with x? If it does, right and equation for the direct variation.
X: 4.5, 7.5, 10.5
Y: 3, 5, 7
Does y vary directly with x?
Write an equation for the direct variation:
ANSWER
13.5
EXPLANATION
It was given that, y varies directly as x.
Therefore, the variation equation is of the form:
If y is 4.5 when x is 3, then we can substitute to find the constant of variation.
Divide both sides by 3;
Hence the equation becomes:
When x=9,
Use the formula for the sum of a geometric series to calculate the given sum. (Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the series diverges.) 72 73 74 A 75 7 + ... = 123 * 126 Use the formula for the sum of a geometric series to find the sum. (Use symbolic notation and fractions where needed. Enter DNE if the series diverges.) 3 C 19 t 4 - t + - + .. = DNE 934
In mathematics, a geometric series is defined as the sum of an infinite number of terms that have a constant ratio say "r" between successive terms.
a) Sum of first infinite geometric series is 49/8640
b) Sum of second infinite geometric series is 68/9.
In general, a geometric series is written as
a+ar+ar²+ar³+... ..
where 'a' is the coefficient of each term and 'r' is the common ratio between adjacent terms.
We have given that
a) 7²/12⁴ + 7³/12⁵ + ......
it is a geometric infinite series with a = 7²/12⁴and r = 7/12
we have find out the sum of series.
Using sum geometric infinite terms formula,
Sₙ= a /(1-r)
where, n = ∞ ; |r| <0
put all known values we get ,
Sₙ = 7²/12⁴ + 7³/12⁵ + ......
=> Sₙ = 7/12( 7/12³ + 7²/12² +---)
=> Sₙ = 7²/12³ ( 1 - 7/12)
=> Sₙ = 7²/12³ × 5/12
=> Sₙ = 49/8640
b) Second series is
16/9 + 4/3 + 1 + 3/4 + 9/16 + ------
= 16/9 + 4/3 +( 1 + 3/4 + 9/16 + ------ )
= 16/9 + 4/3 + ( 1 + 3/4 + (3/4)² + ------ )
= 16/9 + 4/3 + B
B = 1 + 3/4 + (3/4)²+ ------
it is geometric infinite series with a = 1 , r = 3/4
Sₙ = a/(1-r) = 1/(1- 3/4 ) = 1/1/4 = 4
16/9 + 4/3 + 1 + 3/4 + 9/16 + ------ = 16/9 + 4/3 + 4
= (16+16+36)/9 = 68/9
Hence, the sum of first geometric infinite series is
49/8640 and second series is 68/9.
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Find the missing length. (the ?)
The value of the side EC for the given triangle is 28.75 .
What is triangle proportionality theorem?A line parallel to one side of a triangle splits the other two sides of the triangle proportionally if the line also crosses the other two sides.
In the given triangle,
Side AD = 12, BD = 20 and AC = 56,
Also, the side BC is parallel to side DE.
Let the side EC is x,
Then side AE = 56-x
Since, lines BC and DE are parallel
Therefore, by triangle proportionality theorem,
AD/BD = AE/EC
12/20 = 56-x/x
3/5 = 56-x/x
3x = 230 - 5x
8x = 230
x = 230/8
x = 28.75
The required side EC is 28.75.
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What are the types of symmetry?.
Four different symmetry types are translation symmetry, rotational symmetry, reflection symmetry, and glide symmetry can be seen in a variety of contexts.
A balanced and proportionate likeness between two sides of an item is referred to as symmetry. It implies that one half is the other's mirror image. The term "line of symmetry" refers to the fictitious axis or line that may be used to fold a figure into symmetrical halves.
If an object exhibits translational symmetry, it indicates that no matter how it is translated, the thing remains unchanged. The translations for a particular object that fall under this constitute the object's symmetry group or, if the object has other types of symmetry, a subgroup of the symmetry group.
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URGENT!!!!!!!!!!!!!!!!!!
The hexagon can be split into 6 equilateral triangles. The length of a side of a triangle if x + 2
The perimeter of one triangle is 54 units, what is the perimeter of Honeycomb Salon?
=Answer: x+2
Step-by-step explanation:
which of the following instructions clears all the bits in register $8 except for the low order byte, which is unchanged?
andi $8,$8,0xFF is the instructions that clears all the bits in register $8 except for the low order byte, which is unchanged.
What is low order byte?The byte with the least amount of the value would be the low-order byte. For instance, a 16-bit int with the value 5,243 might be represented in hex as 0x147B. The low-order byte is 0x7B, whereas the high-order byte is 0x14. A word's bits are numbered 0 through 15, with bit 0 being the least important. The word's low byte, which contains bit 0, and high byte, which contains bit 15, are referred to as such. Byte ordering comes in two flavors. Big-endian format places the byte with the most important bit in the first memory location, followed by bytes whose importance decreases.
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a fair coin is flipped 10 times. the probability that there are an equal number of heads and tails or the first three flips are heads is the sum of the probabilities that there are an equal number of heads and tails and that the first three flips are heads.
The probability of getting 5 heads and 5 tails is 0.246
Given that,
No. of head = No of tail,
The probability of getting 5 heads and 5 tails
P(X = x ) = nCₓPˣQⁿ⁻ˣ
There x = 5, n=10 p= 1/2 and Q=1/2
P ( x = 1 ) = 10C₅(1/2)⁵(1/2)⁵
= 252 ( 0.000 9765625 )
P ( X = 5 )= 0.2460
First three flips are head stored no of Outcome 2^10 = 1024
X = {H,H,H....}
The remaining 7 position can be flued with Either head or tail
Therefore ,the possible favourable outcomes = 2^7
No of favourable outcomes
: P(X) =No of favorable outcomes /total no of outcomes
P(X) = 0.125
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How many strings can be formed by ordering the letters salespersons if no two s’s are consecutive?.
There are 2,540,160 strings of SALESPERSONS with no consecutive S's.
Explanation:
The number of r-combinations of a set of n distinct objects is C(n,r) = [tex]\frac{n!}{r!(n-r)!}[/tex]
Multiplication principle : If one event can occur in m ways AND a second event can occur in n ways, then the number of ways that the two events can occur in sequence is then mn.
We want to place the 4S's in the string of the other letters such that there are not consecutive. Since there are 9 positions including spaces between two consecutive letters in the 8-letter string and two positions on either side of the string, we need to place 4 of the 9 positions to contain a single S each.
By the definition of combination, there are ⁹C₄ ways to select 4 of the 9 positions to place the S's (as the order of the positions is not important since a different order of the S's leads to the same string).
By the multiplication principle, there are then ⁹C₄. [tex]\frac{8!}{2}[/tex] (divided by 2 since , in remaining 8 characters 2E are identical) possible strings of SALESPERSONS with no consecutive S's.
⁹C₄ . [tex]\frac{8!}{2}[/tex] = [tex]\frac{9!}{4!(9-4)!}[/tex] [tex]\frac{8!}{2}[/tex]
= [tex]\frac{9!}{4!.5!} . 20,160[/tex]
= 126.20,160
= 2,540,160
Thus, there are 2,540,160 strings of SALESPERSONS with no consecutive S's.
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How much should she expect to pay on rent and utilities each year? $1,300 $2,400 $13,200 $15,600
The amount Amy is expected to pay on rent and utilities each year is $15,600. (Option D)
Rent and utilities refer to the amount paid each month for utilization of accommodation and for utility services which are products, services and equipment related to energy, telecommunications, water, and sewerage respectively.
Based on the information provided in the salary analysis table, Amy’s monthly rent and utilities are:
Total = Amy’s Rent + Amy’s Utilities = $1100 + $200 = $1300
As there are 12 months in a year, the yearly total is:
Total = $1300 x 12 = $15,600
Hence, the amount Amy is expected to pay on rent and utilities each year is $15,600.
Note: The question is incomplete. The complete question probably is Amy is analyzing a job offer. How much should she expect to pay on rent and utilities each year? A) $1,300 B) $2,400 C) $13,200 D) $15,600.
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3. (03.01 lc) rewrite the radical expression as an expression with a rational exponent. (1 point) the cube root of five to the seventh power x21 x4 five to the seven thirds power five to the three sevenths power
Five to the seven thirds power is the correct answer. This expression can be rewritten as the cube root of five to the seventh power, which is equal to five to the seven-thirds power.
What is meant by exponents?When a term is multiplied by itself several times, it is said to have "power" or exponents in mathematics. An exponent, which is expressed as a little number above and to the right of the base number, serves as a representation for this. For instance, the number 2 to the power of 3 (23) is represented as 222 and equals 8.Power can alternatively be written as xy, in which x is the base number and y is the exponent. The equation 23 is represented as 23 in this notation, and it still equals 8.Power, in addition to representing repeated multiplication, may also be used to indicate a number's root.
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Air conditioner system cuirculates 440 cubic feet per minute. how many cubic yards of air can it circulate per minute
The air conditioner can circulate 16.2963 cubic yards of air per minute.
The air conditioner circulates 440 cubic feet of air per minute.
We know that 3 feet = 1 yard
Therefore cubic feet when converted to yard we have to divide the data by 27.
Therefore 440 cubic feet = 440 / 27 = 16.2963 cubic yards.
Therefore the air conditioner can circulate 16.2963 cubic yards of air per minute.
A conversion factor must be added, subtracted, multiplied, or divided throughout the multi-step process of unit conversion. It can also be essential to round the numbers and select the right number of significant digits. Different units of metric conversion are used to measure different parameters.
Unit conversion is a multi-step procedure that involves adding, subtracting, or multiplying by a number. There are many ways to measure weight, distance, volume and temperature.
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the product of 5 and the sum of -5 and a number is -25
Answer:
The number is 0.
Step-by-step explanation:
Let's say the number is "n"
5(-5+n)=-25
rearrange:
5(n-5)=-25
Simplify:
5n-25=-25
rearrange:
5n=-25+25
simplify:
5n=0
n=0
How do you know if a triangle is HL congruent?.
if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.
How do you know if a triangle is HL congruent?
Hypotenuse-Leg (HL) for Right Triangles. There is one case where SSA is valid, and that is when the angles are right angles. Using words: In words, if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.
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A six-foot person walks from the base of a streetlight directly toward the tip of the shadow cast by the streetlight... (more down below)When the person is 12 feet from the streetlight and 5 feet from the tip of the streetlight's shadow, the person's shadow starts to appear beyond the streetlight's shadow.(a) Draw a right triangle that gives a visual representation of the problem. Show the known quantities and use a variable to indicate the height of the streetlight. (b) Use a trigonometric function to write an equation involving the unknown quantity.
h =(c) What is the height of the streetlight?
______ ft
b) h = [tex]tan \theta[/tex] x 17 is the required equation.
c) The height of the streetlight is 20.4 ft.
The height of the person is 6 ft.
The distance at which the person is standing from the streetlight = 12 ft.
The distance at which the person's shadow appears = 5ft.
a) Hence, we can make the following diagram.
The right triangle below gives a visual representation of the problem. It shows the known quantities and a variable 'h' to indicate the height of the streetlight.
b) Let's now find an equation trigonometric function involving the unknown quantity 'h'.
from the below diagram, we can say that,
[tex]tan \theta[/tex] = h/base
base= 12+5=17
hence we have, [tex]tan \theta[/tex] = h/17
h = [tex]tan \theta[/tex] x 17 is the required equation.
c) Now we have to find the height of the streetlight.
firstly let's find the value of [tex]\theta[/tex],
[tex]\theta[/tex] = tan 6/5.
[tex]tan^{-1}[/tex](6/5) = 50.2°
hence, tan 50.2 = h/17
1.20 = h/17
h= 1.20 x 17
h= 20.4 ft.
Hence, the height of the streetlight is 20.4 ft.
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consider an airfoil at 12o angle of attack. the normal and axial force coefficients are 1.2 and 0.03, respectively. calculate the lift and drag coefficients.
The coefficient of lift is 1.17
C1 = Cn cos α - Ca sin α
Here, α
Cn is the normal force coefficient, and Ca is Substitute 12· for the axial force coefficient for α
C1 = 1.2cos12.-0.03sin 12.
= 1.16
≈1.17
What is the coefficient of normal force?
The Greek letter mu () typically serves as a symbol for it. From a mathematical perspective, = F/N, where F is the normal force and N is the frictional force. The coefficient of friction has no dimensions because both F and N are measured in force units like newtons or pounds.
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What is the triple of 6 answer?.
Answer:
Not sure what you are asking, but 6 to the third power = 216 and 6 times 3 = 18. Hopefully one of those is the answer you are looking for.
three more than eight times a number is less than 15
Answer:
8x+3<15
x<1.5
Step-by-step explanation:
8x+3<15
-3. -3
8x<12
/8. /8
x<1.5
Hopes this helps please mark brainliest
Consider the following hypothesis test:
H0: μ ≤ 27
Ha: μ 27
A sample of 50 provided a sample mean of 28.4. The population standard deviation is 6.
a. Compute the value of the test statistic (to 2 decimals).
b. What is the p-value (to 4 decimals)? Use the value of the test statistic rounded to 2 decimal places in your calculations.
c. At α = .01, what is your conclusion? (pick one)
p-value is Selectgreater than or equal to 0.01, rejectgreater than 0.01, do not rejectless than or equal to 0.01, do not rejectless than 0.01, rejectequal to 0.01, do not rejectnot equal to 0.01, do not rejectItem 3 H0
d. What is the rejection rule using the critical value? (pick one)
Reject H0 if z is Selectgreater than or equal to 2.33greater than 2.33less than or equal to 2.33less than 2.33equal to 2.33not equal to 2.33Item 4
What is your conclusion? (pick one)
Select1.65 is greater than or equal to 2.33, do not reject1.65 is greater than 2.33, do not reject1.65 is less than or equal to 2.33, reject1.65 is less than 2.33, do not reject1.65 is equal to 2.33, reject1.65 is not equal to 2.33, do not rejectItem 5 H0
A sample of 50 provided a mean of 28.4. The population standard deviation is 6. the value of test statistic is 1.65
The following hypothesis test:
H₀ : μ ≤ 27
Ha: μ 27
A sample of 50 provided a mean of 28.4. The population standard deviation is 6.
We need to find the value of test statistics
test statistic = (28.4 - 27)/(6/√50)
test statistic= 1.4/0.848
test statistic = 1.65
Therefore, a sample of 50 provided a mean of 28.4. The population standard deviation is 6. The value of test statistic is 1.65.
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How many electrons are required for the reduction of one molecule of oxygen?.
Four electrons are required for the reduction of one molecule of oxygen to water in the mitochondria
Reduction means that a reaction in which electrons are added to a compound or molecule; the compound or molecule that gains electrons is said to be reduced
Water has 2 hydrogen and each hydrogen needs only one electron. Hence, four electrons along with four hydrogen atoms are required to reduce one molecule of oxygen (O₂) to two molecules of water (H₂0) in the mitochondria
Therefore, four electrons along with four hydrogen atoms are required to reduce one molecule of oxygen (O₂) to two molecules of water (H₂0) in the mitochondria
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In Game 1, Emeron truck out 30 time in 90 time at bat. In Game 2, he truck out 40 time in 120 time at bat. In Game 3, Emeron truck out 42 time in 140 time at bat. What i the percent of time her hit the ball
Emerson actually hit the ball 32% of times at bat.
Since in Game 1, Emerson struck out 30 times in 90 times at bat; in Game 2, he struck out 40 times in 120 times at bat; and in Game 3, Emerson struck out 42 times in 140 times at bat; To determine what percentage of times at bat did Emerson actually hit the ball, the following calculation must be performed:
(30 + 40 + 42) / (90 + 120 + 140) = X
112/350 = X
0.32 = X
Therefore, Emerson actually hit the ball 32% of times at bat.
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Write an equation uing ""x"" and olve the equation. The rate changed for a tandard room $250 dollar. A couple tayed in the tandard room for x night and their total room change $750
The equation which describes the problem statement would be 250x = 750.
What is the equation in one variable?
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable.
The rent for staying one night is $250.
and if a couple stays in the standard room for x night and their total rent was $750 then this can be expressed as
250x = 750
Hence, the equation which describes the problem statement would be 250x = 750.
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Mia plans to go running. She wants to make sure she takes
enough water and snacks with her. She usually drinks a bottle
of water after every 2 miles and eats a snack after every
4 miles. She decides to pack 5 bottles of water and 2 snacks.
How far can Mia run with the items she has packed?
Explain your answer.
Answer:
10 miles---------------------------------
Mia has 5 bottles of water, it gives her:
5×2 = 10 milesWithin this 10 miles Mia can eat a snack twice and this will limit her further run.
The items Mia has allow her to run 10 miles maximum.
Answer:
12 miles
Step-by-step explanation:
Given information:
Mia drinks a bottle of water after every 2 miles.Mia eats a snack after every 4 miles.Mia drinks water after every 2 miles she runs. Therefore, if Mia has packed 5 bottles of water she can run:
⇒ 2 + 5 × 2 = 12 miles
Mia eats a snack after every 4 miles she runs. Therefore, if Mia has packed 2 snacks she can run:
⇒ 4 + 2 × 4 = 12 miles
Therefore, Mia can run 12 miles with the items she has packed.
0 miles: Begins running.
2 miles: Drinks bottle 1.
4 miles: Drinks bottle 2 and eats snack 1.
6 miles: Drinks bottle 3
8 miles: Drinks bottle 4 and eats snack 2.
10 miles: Drinks bottle 5.
---------------------------------------------------------------
12 miles: Drinks another bottle.
Remember that Mia drinks a bottle of water after she has run 2 miles, and eats a snack after she has run 4 miles.
Therefore, drinking a bottle of water allows Mia to run for 2 further miles, and eating a snack allows her to run for 4 further miles.
So when she drinks her last bottle of water at 10 miles, she can only continue running for a further 2 miles before she needs to drink again. As she doesn't have a 6th bottle of water, she will have to stop running at 12 miles.
For a given arithmetic equence, the term, , i equal to , and the term, , i equal to. Find the value of the term,
The value of the 60th term is -721 in given arithmetic progression or we call as AP
What is arithmetic progression?
The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP).
It is possible to obtain a formula for the nth term of the AP using this kind of development.
A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by adding 4 to the previous term.
The nth term in this series equals 4n-2. You can get the sequence's terms by inserting n=1,2,3,...
Given:
-13, -25, -37, -49,..
a = -13
d = t₂ - t₁
= -25 - (-13)
= -25 + 13
d = -12
tₙ = a +(n-1) d
t₆₀ = -13 + (60-1) (-12)
= -13 + (59) (-12)
= -13 - 708
t₆₀ = -721
Hence, the value of the 60th term is -721 in given arithmetic progression.
complete question is
Find a formula for the
nth term, Tn, of the following arithmetic sequence:−13,−25,−37,−49
,. . . Hence, or otherwise, find the value of the 60th term,
T60
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write and solve an equation to find the value of x so that the figures have the same area
1÷2×8x+32=3x+18
4x+16=3x+18
4x-3x=18-16
x=2
Think of 5 positive integers that have a
mode of 3 and 4, a median of 4 and a
mean of 6.
The required set of 5 positive integers is 3, 3, 4, 4, 16.
What is the mean?The mean is the mathematical average of a group of integers.
Given, to find a set of 5 positive integers such that their mode is 3 and 4, the median is 4, and the mean is 6.
Since the median is 4, the middle number or the number at the 3rd position will be 4.
Since the mode of the data set is 3 and 4, the frequency of 3 and 4 must be 2.
Now, the numbers found so far are 3,3,4,4.
Let the fifth number be x.
The mean of the data set is given by:
mean = (3 + 3 + 4 + 4 + x)/5
Given that mean is 6, therefore,
(3 + 3 + 4 + 4 + x)/5 = 6
14 + x = 30
x = 30 -14
x = 16
Hence, the required set of 5 positive integers is 3, 3, 4, 4, 16.
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A six-sided die with sides labeled through will be rolled once. Each number is equally likely to be rolled. What is the probability of rolling a number greater than ?.
The probability of rolling a number greater than 2 is 2/3
Given that a six sided die with sides labelled with numbers 1,2,3,4,5 and 6 is rolled once.
Since die is said to be equally likely for each number, die is unbiased
P(1) = P(2)=...=P(6) = 1/6
For a number greater than 2, we must not include 2 and hence numbers can be 3 or 4 or 5 or 6
Probability of rolling a number >2 = Probability of rolling 3 or 4 or 5 or 6
= P(3)+P(4)+P(5)+P(6)
= 1/6+1/6+1/6+1/6
=4/6
=2/3
Therefore, the probability of rolling a number greater than 2 is 2/3
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What is the ratio 1 to 3 mean?.
for every one (1) you have, you have 3 times the first
Ok,
for example for every 1 penny you have, you have 3dollars,
you counted and you have 4 pennies, in order to find out how many dollars you have, you have to times 4 by 3 to get 12
altogether you would have 4 pennies: 12 dollars.
