(a) Sum of values = Mean × Number of values = 64 × 5 = 320
(b) Sum of values = Mean × Number of values = 8.2 × 5 = 41
Fifth value = Sum of values - sum of known values = 41 - (6 + 10 + 7 + 12) = 41 - 35 = 6
How to solve(c) The resulting middle number when computing 10, 20, 30, 40, 50;that is (10 + 20 + 30 + 40 + 50)/5, totals up to 150 and dividing that number by 5 reflects a mean of 30.
i) Forming an average of 20, 30, 40, 50, 60;that is (20 + 30 + 40 + 50 + 60)/5 provides an outcome of 200 and divided by 5 reveals a mean of 40.
ii) With 0, 10, 20, 30, 40 used, (0 + 10 + 20 + 30 + 40)/5 practices calculation yielding a total of 100 which, split into five parties, imparts a mean of 20.
iii) Taking into consideration the input of 100, 200, 300, 400, 500;whereby (100 + 200 + 300 + 400 + 500)/5 develops a collective of 1500, cut in half produces a mean of 300.
iv) Calculating 1, 2, 3, 4, 5's mean; namely (1 + 2 + 3 + 4 + 5)/5 ascertains a collective amount of 15, divide that figure by five culminates with a mean of 3.
v) Accordingly, the following general assumptions can be made:
i) Introducing a constant to each value augments the mean by that very same constant.
ii) Extracting a constant from all values decrements the mean by such said constant.
iii) Multiplying every value by one constant multiplies the mean by the same specific constant.
iv) Dividing all values by a particular constant divides the mean by that given constant.
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Which relation is a function?
The only graph that represents a function is: Graph D
How to identify a function?A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.
From the graphs, we can see that:
Graph A has 2 outputs at x = -2
Graph B has 2 outputs at x = 0
Graph C has two outputs at x = -1
Graph D has a unique output for every input and as such it is a function
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A beaker is shaped like a cylinder with a radius of 1.8 inches and a height of 4.6 inches. It is filled to the top with a solution. Caleb wants to pour it into a different beaker with a radius of 1.25 inches. What is the minimum height the second beaker must be so it does not overflow? Round to the nearest tenth.
The minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.
Now, For the minimum height of the second beaker, we need to find its volume first.
The volume of the first beaker is given by;
⇒ V₁ = πr₁²h₁
where r₁ is the radius and h₁ is the height.
Substituting the given values, we get:
V₁ = π(1.8)²(4.6)
V₁ ≈ 66.85 cubic inches
Since, the first beaker is filled to the top, its volume equals the volume of the solution.
Therefore, the volume of the solution is also 66.85 cubic inches.
To find the minimum height of the second beaker, we need to use the formula for the volume of a cylinder:
V₂ = πr₂²h₂
where r₂ is the radius and h₂ is the height of the second beaker.
We want to find h₂ such that V₂ is equal to 66.85 cubic inches.
Dividing both sides of the equation by πr₂², we get:
h₂ = V₂ / (πr₂²)
Substituting the given value for r₂, we get:
h₂ = 66.85 / (π(1.25)²)
h₂ ≈ 13.5 inches
Therefore, the minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.
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what is the value of sin B?
8/17
17/15
15/17
8/15
The sine of angle B is obtained dividing the length of the opposite side to angle B by the length of the hypotenuse.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined on the bullet points below:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse of the triangle.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse of the triangle.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle of the triangle.Missing InformationThe problem is incomplete, hence the general procedure to obtain the sine of angle B is presented.
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A rectangular prism has a volume of 2288 cubic meters a height of 13 meters and a length of 22 meters. What is the measure of the missing dimension?
The measure of the missing dimension is 8 meters.
We are given that;
Volume= 2288 cubic meters
Height= 13meter
Length= 22meter
Now,
To find the width.
You can rearrange the formula to solve for width by dividing both sides by length and height:
Width = Volume / (length × height)
Plug in the given values:
Width = 2288 / (22 × 13)
Simplify:
Width = 2288 / 286
Width = 8
Therefore, by the given rectangular prism the answer will be 8 meters.
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WHats this answer?
Please help!
The measure of angle 3 is 52⁰.
The measure of angle 5 is 38⁰.
The measure of angle 6 is 52⁰.
What is the measure of angle 3, 5 and 6?
The measure of angle 3, 5 and 6 is calculated as follows;
angle 1 + angle 2 + angle 3 = 180 (sum of angles in straight line )
90 + 38 + angle 3 = 180
angle 3 = 180 - 128
angle 3 = 52⁰
The measure of angle 5 is calculated as follows;
angle 5 = angle 2 (vertical opposite angles are equal)
angle 5 = 38⁰
The measure of angle 6 is calculated as follows;
angle 6 = angle 3 (vertical opposite angles are equal)
angle 6 = 52⁰
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How do l do this? Help please
By expanding and simplifying the algebraic expression (y + 7)(y - 5), we have the result y² + 2y - 35
How to expand and simplify algebraic expression in bracketsTo expand an algebraic expression in brackets, we need to use the distributive property to make is easy for simplification, thus we expand and simplify the expression as follows:
(y + 7)(y - 5) = y(y - 5) + 7(y - 5) {distributive property}
(y + 7)(y - 5) = y² - 5y + 7y - 35
by simplification, we have;
(y + 7)(y - 5) = y² + 2y - 35
Therefore, the expansion and simplification of the algebraic expression (y + 7)(y - 5), gives the result y² + 2y - 35.
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Please help !!!!!!!!!!!!!!!!
length LD = 6 units
length DF = 9 units
length HF = 6 units
length LH = 9 units
length L'D' = 2 units
length D'F' = 3 units
length H'F' = 2 units
length L'H' = 3 units
What is dilation?Dilation is the scaling of an object, where it gets bigger or smaller.
Scale factor = new dimension/old dimension
length LD = 15-9 = 6units
length DF = 6-(-3) = 9units
length HF = 15-9 = 6 units
length LH = 6-(-3) = 9 units
Since the scale factor is 1/3, we divide the preimage dimension by 3 to get the dimensions of the new image.
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LAST QUESTION FOR THE NIGHT I NEED HELP WITH IT I’M KINDA STRUGGLING HERE
The solution to the system of equations in this problem is given as follows:
(-1, -5).
How to solve the system of equations?The system of equations in the context of this problem is defined as follows:
y = x - 4.y = -3x - 8.The x-coordinate of the solution in the context of this problem is obtained equaling the two equations, as follows:
x - 4 = -3x - 8
4x = -4
x = -1.
Hence the y-coordinate of the solution is obtained as follows:
y = -1 - 4
y = -5.
Thus the solution is:
(-1, -5).
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The British government has a consol bond outstanding paying per year forever. Assume the current interest rate is per year.
a. What is the value of the bond immediately after a payment is made?
b. What is the value of the bond immediately before a payment is made?
A toy ball can be modeled as a sphere. Moussa measures its circumference as 56.3 cm. Find the ball’s volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
Answer:
3013.5 cm³
Step-by-step explanation:
Given a ball with a circumference of 56.3 cm, you want to know its volume.
RadiusThe formula for circumference is ...
C = 2πr
Solving for radius, we get ...
r = C/(2π) = 56.3 cm/(2π) ≈ 8.96042 cm
VolumeThe volume of a sphere is given by ...
V = 4/3πr³
V = 4/3π(8.96042 cm)³ ≈ 3013.5 cm³
The ball's volume is about 3013.5 cubic centimeters.
__
Additional comment
Alternatively, we could use the formula ...
V = C³/(6π²)
to get the same result.
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what is this pls help
what is the aswer nk
Answer: 2x + 12
Step-by-step explanation:
Let the cost of each sweater be x.
since she's buying 2, the total cost of the sweaters will be 2x.
Just tack on the + 12 at the end for the sunglasses :)
Solve the following for θ, in radians, where 0≤θ<2π.
−sin2(θ)−4sin(θ)+4=0
Select all that apply:
1.1
2.52
0.98
0.69
1.43
2.17
Answer:0.98
2.17 are correct
Step-by-step explanation:
-u^2 - 4u + 4 = 0
Multiplying both sides by -1, we get:
u^2 + 4u - 4 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 4, and c = -4. Substituting these values, we get:
u = (-4 ± sqrt(4^2 - 4(1)(-4))) / 2(1)
u = (-4 ± sqrt(32)) / 2
u = (-4 ± 4sqrt(2)) / 2
u = -2 ± 2sqrt(2)
Therefore, either:
Select the correct answer. Determine which statement is true about the zeros of the function graphed below. An upward parabola f on a coordinate plane vertex at (1, 4) and intercepts the y-axis at 5 units. A. Function f has one real solution and one complex solution. B. Function f has exactly one real solution and no complex solutions. C. Function f has exactly two real solutions. D. Function f has exactly two complex solutions.
The correct option is D, the equation has two complex solutions.
Which is the correct statement about the quadratic equation?Here we can see that we have the graph of a quadratic equation.
It opens upwards, and we can see that it has a vertex at (1, 4), which intercepts the y-axis at y = 5.
Now, we say that the solutions of a quadratic are the values of x such that the function becomes zero.
Particualrly, in this graph we can see that the graph never intercepts the x-axis, that means that this equation has no real roots.
Then the correct option is:
"Function f has exactly two complex solutions."
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There may be many polynomial equations with integer coefficient which have the square root of 8 - 1 and the square root of 8 + 1 as its roots. Construct an equation of smallest degree with integer coefficients that has the square root of 8 - 1 and the square root 8 + 1 as its roots
The equation of smallest degree with integer coefficients will be f(x) = x^2 - (3 + √7)x + 3√7
How to explain the equationIt should be noted that to begin, let us establish the following:
x = √(8 - 1) which is equal to √7.
y = √(8 + 1) which is equivalent to √9. Therefore, y equals 3.
For the value of x, its conjugate coincides with √7; hence:
(x - x') × (x - y') = (x - √7)(x - 3)
Equation expansion yields:
f(x) = x^2 - (3 + √7)x + 3√7
By substituting for both values x and y in the equation above, we can show that f(x) satisfies the given specifications:
When x takes on a value of √7:
f(√7) = (√7)^2 - (3 + √7)√7 + 3√7 = 7 - 7 = 0
With an input value of 3:
f(3) = 3^2 - (3 + √7)(3) + 3√7 = 9 - 9 - 3√7 + 3√7 = 0
The lowest degree polynomial with rational coefficients having √(8 - 1) and √(8 + 1) as its roots is: f(x) = x^2 - (3 + √7)x + 3√7
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Can someone help me with the 4 questions
The list represents the ages of students in a gymnastics class. 10, 10, 11, 12, 12, 13, 13, 14, 14, 15 If another student of age 15 joins the class, how is the mean affected? The mean will remain the same at 13. The mean will remain the same at about 12.4. The mean will increase to about 12.6. The mean will decrease to about 11.
The required mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.
The original mean is the sum of the ages divided by the number of students:
Mean = (10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15) / 10
Mean = 124 / 10
Mean = 12.4
If another student of age 15 joins the class, the new sum of the ages is:
Sum = 10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 15
Sum = 139
The new mean is the new sum of ages divided by the new number of students:
New mean = Sum / (Number of students + 1)
New mean = 139 / 11
New mean = 12.63636... or about 12.6 (rounded to one decimal place)
Therefore, the mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.
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ASAP.
jack goes for a ride on a ferris wherl thst has a radius of 51 yards. the center of the ferris sherl is 61 yards above the ground. he starts bis rifr at the 9 oclock position and travels counter clockwise. define a function g that tepresents jacks verticL distance above the grihdn in yards in terms of the angel ( meassured in radians) jack has swept out measured grom the 9 oclock positions
Answer:
112 yards
Step-by-step explanation:
The center of the Ferris wheel is 61 yards above the ground and the radius is 51 yards. When Jack is at the 9 o'clock position, he is at a distance of 112 yards from the center of the Ferris wheel (51 yards from the center plus 61 yards above the ground). Let θ be the angle that Jack has swept out measured from the 9 o'clock position, in radians.
The function g that represents Jack's vertical distance above the ground in yards in terms of the angle θ is:
g(θ) = 61 + 51sin(θ)
where sin(θ) represents the vertical component of the distance Jack has traveled.
Note that when θ = 0, sin(θ) = 0, which means Jack is at the very top of the Ferris wheel, 112 yards above the ground. When θ = π/2, sin(θ) = 1, which means Jack is at the 12 o'clock position, 112 + 51 = 163 yards above the ground. Similarly, when θ = π, sin(θ) = 0, which means Jack is at the very bottom of the Ferris wheel, 112 yards above the ground.
After running a 100 meter dash, Jane turns left 40 degrees and walks 60 meter. True or false: she is closer now to her starting position than when she crossed the finish line. What about if Jane turns left 90 degrees or 120 degrees?
False. When Jane turns left 40 degrees and walks 60 meters, she is farther away from her starting position than when she crossed the finish line.
If Jane turns left 90 degrees or 120 degrees, then she will also be farther away from her starting position than when she crossed the finish line. Turning left 90 degrees or 120 degrees will take her in a different direction, and thus she will be farther away from her starting position than when she crossed the finish line.
Therefore, the given statement is false.
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Rachel works at a lemonade stand at the park on Monday. She used 1 2/5 bags of lemons on Tuesday. She used 1 1/4 times as many lemons as on Monday. How many bags of lemons did Rachel use on Tuesday?
Let's start by finding how many bags of lemons Rachel used on Monday. We know she used a whole number of bags plus a fraction, so we'll need to convert the mixed number to an improper fraction:
1 2/5 = 7/5
So Rachel used 7/5 bags of lemons on Monday.
On Tuesday, Rachel used 1 1/4 times as many lemons as on Monday. To find out how many bags of lemons that is, we can multiply the amount Rachel used on Monday by 1 1/4:
1 1/4 = 5/4
5/4 times 7/5 = 35/20 = 7/4
So Rachel used 7/4 bags of lemons on Tuesday, which is the same as 1 3/4 bags of lemons.
Therefore, Rachel used 1 3/4 bags of lemons on Tuesday.
In the month, what percent of Dinesh’s time was spent on Project X? Be sure to show your work, and answer the question below.
The percentage of Dinesh’s time spent on Project X is 36.90%.
We have,
From the table,
The total time spent on the X-project each week is given as:
= 23(1/3) + 16(1/3) + 9.33 + 4.20
= 23.33 + 16.33 + 9.33 + 4.20
= 53.19
This is the time spent on X-project for the month.
Now,
The total time spent on all the events in the table.
= 144.13
The percent of Dinesh’s time spent on Project X.
= 53.19/144.13 x 100
= 36.90%
Thus,
The percentage of Dinesh’s time spent on Project X is 36.90%.
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The endpoints of WX are W(-5,-1) and X(2,6).
What is the length of WX?
A. 7
B. 14
C. 4√2
D. 7/2
The sum of three numbers is -3. If the second number is subtracted from the sum of the first and third numbers, the result is -3. If the third number is subtracted from the sum of the first and second numbers, the result is -5. Find the three numbers.
[Hint: let x represent the first number, y the second number, and z the third number. Use the given conditions to write and solve a system of equations.]
Answer:
The three numbers are -4, 0, and 1.
Step-by-step explanation:
mark brainliest
Suppose that 3 items will be chosen from a group with 7 total items.
Given that order does not matter, how many different ways can the items be chosen?
A) 35
B)70
C)140
D)210
The number of ways of selecting 3 items from a total of 7 items, where order does not matter is (a) 35 ways.
The number of ways to choose three items from a group of seven, where order does not matter, is given by the combination formula:
⇒ C(n,r) = n!/(r! × (n-r)!),
where n is = total number of items, and r is = number of items to be chosen,
We have, total items (n) = 7 and items to be selected (r) = 3.
Substituting the values,
We get;
⇒ C(7,3) = 7!/(3! × (7-3)!),
⇒ 7!/(3! × 4!),
⇒ (7 × 6 × 5)/(3 × 2 × 1),
⇒ 35 ways.
Therefore, the correct option is (a).
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We can approximate the amount of current in amps I
The measure of the third outgoing current will be 0.5 amperes.
We know that,
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.
Then the measure of the third outgoing current will be
We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.
Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆.
Then we have
I₁ + I₂ + I₃ = I₄ + I₅ + I₆
0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆
1.85 = 1.35 + I₆
I₆ = 0.5
Thus, the measure of the third outgoing current will be 0.5 amperes.
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complete question:
The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing current measure 0.8 amps and 0.55 amps find the measure of the third outgoing current
Prove the following:
Based on the information, HH is a subset of Ha, which is a subset of aH, which is a subset of H, which is a subset of HH
How to make the proofIt should be noted that to demonstrate this theory, we must show that each of these collections are components of the others and consequently all are equivalent.
At first, let's evaluate HH. As H is a subgroup of G, it is dependent on multiplication so for any two elements h1, h2 in H, the product h1h2 is also in H. Thus, every entity within HH can be expressed as the aggregate of h1h2 for certain elements h1, h2 from H. Since H is a subgroup, it is also subject to inverse property, so h2^-1h1^-1 remains inside H. Clearly, h1h2 thus translates to h'(h2^-1h1^-1)h'', where h', h'' are members of H.
This illustrates that every component of HH can be presented as h'h'' for a pair of h', h'' which exist in H, therefore approximating with accuracy the definition of H. Thus, we have demonstrated that HH is part of H.
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Select the correct answer. Which point lies on the circle represented by the equation (x − 3)2 + (y + 4)2 = 62? A. (9,-2) B. (0,11) C. (3,10) D. (-9,4) E. (-3,-4) Reset Next
Answer: The point that satisfies the equation is E. (-3, -4).
Explanation:
To determine which point lies on the circle represented by the equation (x − 3)² + (y + 4)² = 6², we can substitute the coordinates of each point into the equation and see which one satisfies the equation.
A. (9, -2): (9 − 3)² + (-2 + 4)² = 6²
(6)² + (2)² = 36
36 + 4 = 40 ≠ 36
B. (0, 11): (0 − 3)² + (11 + 4)² = 6²
(-3)² + (15)² = 36
9 + 225 = 234 ≠ 36
C. (3, 10): (3 − 3)² + (10 + 4)² = 6²
(0)² + (14)² = 36
0 + 196 = 196 ≠ 36
D. (-9, 4): (-9 − 3)² + (4 + 4)² = 6²
(-12)² + (8)² = 36
144 + 64 = 208 ≠ 36
E. (-3, -4): (-3 − 3)² + (-4 + 4)² = 6²
(-6)² + (0)² = 36
36 + 0 = 36
The point that satisfies the equation is E. (-3, -4).
help asap im so lost
Answer:250
Step-by-step explanation:
I think they just want you to multiply the 25 and the 10 (radius squared times the height)
The admission fee at an amusement park is $2.25 for children and $5.60 for adults. On a certain day, 269 people entered the park, and the admission fees collected totaled 1091 dollars. How many children and how many adults were admitted?
PLEASE HURRY!!!!
The height h in feet of an object shot straight up with initial velocity v in feet per second is given by h = −16t^2 + vt + c, where c is the initial height of the object above the ground. A model rocket is shot vertically up from a height of 6 feet above the ground with an initial velocity of 22 feet per second. Will it reach a height of 10 feet? Identify the correct explanation for your answer.
A. No; The discriminant is positive so the rocket will reach a height of 10 feet.
B.Yes; The discriminant is positive, so the rocket will reach a height of 10 feet.
C.No; The discriminant is negative, so the rocket will not reach a height of 10 feet.
D.Yes; The discriminant is zero, so the rocket will reach a height of 10 feet.
Answer:
B.
Step-by-step explanation:
We can use the given formula to find the time it takes for the rocket to reach a height of 10 feet:
10 = -16t^2 + 22t + 6
Rewriting the equation in standard quadratic form:
16t^2 - 22t + 4 = 0
Using the quadratic formula:
t = (22 ± sqrt(22^2 - 4(16)(4)))/(2(16))
t = (22 ± sqrt(36))/32
t = 3/4 or 1/4
Since the rocket reaches a height of 10 feet at two different times (3/4 and 1/4 seconds), it must pass through that height twice during its flight. Therefore, the rocket will reach a height of 10 feet. The correct answer is B.