47.4 is the mean of the data summarized in the given frequency distribution.
What is a frequency distribution?
The number of times a value appears in a dataset is its frequency. The pattern of frequencies for a variable is known as a frequency distribution. The frequency with which each potential value of a variable appears in a dataset.speed m f m*f
42-45 43.5 22 957
46-49 47.5 14 665
50-53 51.5 7 360.5
54-57 55.5 4 222
58-61 59.5 2 119
Total 49 2323.5
mean = 2323.5/49 = 47.4
The computed mean is not close to the actual mean because the difference between the means is more than 5%.
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Solve each formula for the indicated variable. V = lwh , for w
The solution of the given formula V = lwh for the variable w is V/lh.
According to the given question.
We have a formula.
V = lwh
Since, we have to solve this given formula V = lwh for the variable w.
Which means we have to write separate variable w to one side from the other variables which are in the given formua V = lwh .
Thereofre, the solution of the given formula V = lwh for the variable w is given by
V = lwh
⇒ V/l = wh (dividing both the sides by l)
⇒ V/lh = w (dividing both the side by h)
or w = V/lh
Hence, the solution of the given formula V = lwh for the variable w is V/lh.
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Henry had a piece of rope that was 23 1/2 inches long. Henry cut the rope into two pieces so that one pieces was 8 1/4 inches long. what was the length of the other piece of rope(also hello again! :)
Answer:
15 1/4 inches
Step-by-step explanation:
Length of the other piece
= 23 1/2 - 8 1/4
= 47/2 - 33/4
= 94/4 - 33/4
= 61/4
= 15 1/4 inches.
PQ= 6x+25 and QR=16-3z
Question 1 (1 point)
Find the missing side of the right triangle. ROUND TO THE NEAREST TENTH (one decimal place). Of 88 and 81
The length of the missing side of the given triangle is 2√2×11.
What are triangles?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.So, the missing length of the given triangle:
The formula of the hypotenuse.
H² = B² + L²Now, substitute values in the formula:
H² = B² + L²13² = 9² + L²13² - 9² = L²169 - 81 = L²88 = L²L = √88L = √2×2×2×11L = 2√2×11Therefore, the length of the missing side of the given triangle is 2√2×11.
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F(x)=x^2-6x , what value of x is f(x) at its minimium
The function value at the minimum is -9
How to determine the function value at the minimum?The function is given as:
f(x) = x^2 - 6x
Differentiate the function
So, we have
f'(x) = 2x - 6
Set the function to 0
So, we have
2x - 6 = 0
This gives
2x = 6
Divide by 2
x = 3
Substitute x = 3 in f(x) = x^2 - 6x
f(3) = 3^2 - 6(3)
Evaluate
f(3) = -9
Hence, the function value at the minimum is -9
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For each function, find the y -intercept
y = -(2/3)(x-9)².
Answer:
(0, -54)
Step-by-step explanation:
The y-intercept is when x=0.
[tex]y=-(2/3)(0-9)^2 \\ \\ =-(2/3)(81) \\ \\ =-54[/tex]
Write an explicit and a recursive formula for each sequence. 0, 1/8, 1/4, 3/8 . . . . . .
an=a1+d(n−1) is the explicit and a recursive formula for each sequence .
What is sequence?
See the pattern
1/8-0 =1/8
1/4-1/8 = 1/8
3/8-1/4 = 1/8
the explicit and a recursive formula for each sequence is an=a1+d(n−1).
An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.
Arithmetic sequences are sequences containing these patterns. The distance between succeeding terms in an arithmetic series is always the same. The difference between consecutive words is always two, hence the sequence 3, 5, 7, 9... is arithmetic.
An explicit formula that states a = d (n - 1) + c, where d is the common difference between succeeding words, and c = a1, can be used to establish an arithmetic sequence.
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What is the value of the left side of the statement?
4³ + 2 · (5 + 4) =
Answer:
awnser value is 64
Step-by-step explanation:
4³ is an exponential multiplied by itself 3 times an added to 2
Answer:
82
Step-by-step explanation:
Follow BIDMAS: 1. Brackets, 2. Indices, 3. Division, 4. Multiplication, 5. Addition, 6. Subtraction
1. Brackets, 5+4=9
therefore the equation is now
[tex]4^3+2*9[/tex]
2. Indices
[tex]4^3=4*4*4=64[/tex]
therefore the equation is now
[tex]64+2*9[/tex]
3. Multiplication
2*9=18
therefore the equation is now
64+18
now add,
=82
therefore, [tex]4^3+2*(5+4)=82[/tex]
Compare √180 and 102/8 using <, >, or =.
HELP ASAP
Answer:
√180 > 102/8
Step-by-step explanation:
√180 = 13.416407865
102/8 = 12.75
Answer:
Yes
Step-by-step explanation:
Because 180 is greater than 102
_____
8
help me....................................................................................................,,....
Answer:
f. 4+3=7
g. 23+8+4=35
h. 53+3+28=84
i. 11+17+92=120
j. 24+8+3=35
Step-by-step explanation:
Answer:
F = 4 + 4 = 8
G = 23 + 8 + 4 = 35
H = 53 + 3 + 27 = 83
I = 11 + 17 + 93 = 121
J = 24 + 8 + 3 = 35
Step-by-step explanation:
Describe a pair of events that are mutually exclusive and a pair of events that are not mutually exclusive.
The two events are mutually exclusive if they cannot occur at the same time. A triangle is equiangular if it is equilateral. Never can one preclude the other. The two events are mutually exclusive if they cannot occur at the same time.
What pairs of occurrences can never coexist?
Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously. A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.What are some examples of mutually exclusive events?
Several instances of occurrences that can never occur simultaneously include: The outcomes of receiving head or tail while flipping a coin are mutually exclusive.Learn more about probability
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Polygon B C D E ≅ polygon R S T U . Find each value.
To ensure that sailboat races are fair, the boats and their sails are required to be the same size and shape.
c. Name six pairs of congruent angles.
Six pairs of congruent angles are:
∠B≅∠R∠C≅∠S∠D≅∠T∠E≅∠U∠CBD≅∠SRT∠EDB≅∠UTRWhat is a Polygon?A polygon is a plane figure described by a fixed amount of straight-line segments connected to form a closed polygonal chain in geometry. A polygon is defined as a bounded plane region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.To name six pairs of congruent angles:
Given: BCDE ≅ RSTU
Then,
∠B≅∠R∠C≅∠S∠D≅∠T∠E≅∠UNow, connect diagonals BD and RT.
So,
∠CBD≅∠SRT∠EDB≅∠UTRTherefore, six pairs of congruent angles are:
∠B≅∠R∠C≅∠S∠D≅∠T∠E≅∠U∠CBD≅∠SRT∠EDB≅∠UTRKnow more about Polygons here:
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A tailor used 5 meters of string to make 7 Halloween masks. He used ____ of a meter for each mask.
Answer:
.715 meters
Step-by-step explanation:
Steven buys 6 movie downloads.
The total cost is $3 above or below
$35. Write an equation that models
the cost x, in dollars, of each movie
download.
The equation that models the cost x, in dollars, of each movie download is x = $(35 ± 3)/6
Writing an EquationFrom the question, we are to write an equation that models the cost x, in dollars, of each movie download
From the given information,
Steven buys 6 movie downloads and the total cost is $3 above or below
$35
That is,
6x = $(35 ± 3)
Then,
The cost x, in dollars, of each movie download is
x = $(35 ± 3)/6
Hence, the equation is x = $(35 ± 3)/6
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The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she knows that the paper will last about 80 days.
c. How many packs of printer paper should the manager expect to have after 30 days?
5.25 pack of printer paper the manager should expect to have after 30 days.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
If 140 paper are used in 80 days then
in days 80 ⇒ 140 pack paper used
in day 1 ⇒ 140/80 pack paper used
in days 30 ⇒ 140/80 × 30
⇒ 21/4 pack paper used or 5.25 pack paper used
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In Exercises 7-9, solve the formula for the indica
7. Force: f = ma; Solve for m.
Answer:
F= ma is the formula of Newton’s Second Law of Motion.
Newton’s Second Law of Motion is defined as Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.
raise the difference of r and s to the 9th power
Answer:
(r-s)⁹
Step-by-step explanation:
The difference means to subtract, so we have r-s.
Raising this to the 9th power gives (r-s)⁹.
Chemistry The time required for a certain chemical reaction is related to the amount of catalyst present during the reaction. The domain of the relation is the number of grains of catalyst, and the range is the number of seconds required for a fixed amount of the chemical to react. The table shows the data from several reactions.
b. If the domain and range were interchanged, would the relation be a function? Explain.
x= 6, y = 3 are the domain and range were interchanged, would the relation be a function.
What is domain ?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.If the terms in range and domain were interchanged, one term 6 of domain relates with two different values of range,
x = 6, y = 2.5
x= 6, y = 3
Since, a term of domain can't have two different values in range,
Therefore, interchanged relation will not be a function.
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Help please
10 points
Answer: A number is divisible by 3 if the sum of the digits is divisible by 3.
If the last two digits of a number are divisible by 4, the whole number is. For example, in 1,012, 12 is divisible by 4.
A large number is divisible by 8 if the last three digits are also divisible by 8 or are 000.
Find the slope of the line through each pair of points. (0,0) and (5,-3)
The slope of the line passing through the pair of points, (0 , 0) and (5 , -3), is -3/5.
The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:
m = (y2 - y1)/(x2 - x1)
where m is the slope
x1 and y1 are the coordinates of one point
x2 and y2 are the coordinates of the 2nd point
Given two points in the line, (0 , 0) and (5 , -3), plug in the values to the formula for the slope.
m = (y2 - y1)/(x2 - x1)
m = (-3 - 0)/(5 - 0)
m = -3/5
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Suppose y varies directly with x , and y-15 when x-3 . What is y when x=12 ?
If y varies directly with x , and y-15 when x-3, y is 60 when x is equal to 12.
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
y = kx (Where k is the constant)
Here, we have given
15 = k3
k = 15/3
= 5
So, y = 5x
When x = 12,
y = 5(12)
= 60
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Correct question
Suppose y varies directly with x, and y = 15 when x = 3. What is y when x = 12?
Cindy is deciding between a striped red-and-purple lunch box and a polka-dotted blue lunch box to buy for school. Each lunch box is shaped like a rectangular prism with a volume of 300 cubic inches. The red-and-purple lunch box is 7.5 inches wide and 4 inches tall. The blue lunch box is 8 inches wide and 3 inches tall.
How much longer is the blue lunch box than the red-and-purple lunch box?
============================================
Explanation:
x = length of the red and purple lunch box
y = length of the blue lunch box
volume = length*width*height
The volume expression for the red and purple lunch box is x*7.5*4 = 30x
Set this equal to the stated volume 300 cubic inches, and solve for x.
30x = 300
x = 300/30
x = 10
The red and purple lunch box has length of 10 inches.
-----------------
The blue lunch box has volume of
length*width*height = y*8*3 = 24y
Set this equal to 300 and solve for y
24y = 300
y = 300/24
y = 12.5
The blue lunch box has length of 12.5 inches
Therefore the blue lunch box is longer and is longer by 12.5-10 = 2.5 inches.
Three polynomials are factor below but some coefficients and constants are missing all of the missing values of a,b,c, and d are intergers
1. The coefficients of the factored polynomial x² - 8x + 15 are
a = 1,b = -5,c = 1 andd = -32. The coefficients of the factored polynomial 2x³ - 8x² + 24x are
a = 1, b = -2, c = 1 and d = 63. The coefficients of the factored polynomial 6x² + 14x + 4 are
a = 2, b = -4, c = 3 and d = 1How to factor the polynomials?1. How to factor the polynomial x² - 8x + 15Sincw we want to factor the polynomial x² - 8x + 15 in the form (ax + b)(cx + d), we have that
x² - 8x + 15 = x² - 3x - 5x + 15
= x(x - 3) - 5(x - 3)
= (x - 5)(x - 3)
comparing (x - 5)(x - 3) with (ax + b)(cx + d), we see that the coefficients of the polynomial are
a = 1, b = -5, c = 1 and d = -32. How to factor the polynomial 2x³ - 8x² + 24xSincw we want to factor the polynomial 2x³ - 8x² + 24x in the form 2x(ax + b)(cx + d), we have that
2x³ - 8x² - 24x = 2x(x² - 4x - 12)
Factorizing the expression inthe bracket, we have
= 2x(x² - 2x + 6x - 12)
= 2x[x(x - 2) + 6(x - 2)
= 2x(x - 2)(x + 6)
comparing 2x(x - 2)(x + 6) with 2x(ax + b)(cx + d), we see that the coefficients of the polynomial are
a = 1, b = -2, c = 1 and d = 63. How to factor the polynomial 6x² + 14x + 4Sincw we want to factor the polynomial 6x² + 14x + 4 in the form (ax + b)(cx + d), we have that
6x² + 14x + 4 = 6x² + 2x + 12x + 4
= 2x(3x + 1) - 4(3x + 1)
= (2x - 4)(3x + 1)
comparing (2x - 4)(3x + 1) with (ax + b)(cx + d), we see that the coefficients of the polynomial are
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Sue is fishing. she catches a bass weighing 5_ 1/4 lb. then she catches three more weighing 3_ 1/2 lb, 1_3/4 lb, and 2 lb. she releases the smallest fish. what is the total weight of the fish sue keeps?
Answer:
10 3/4 lb
Step-by-step explanation:
she releases the 1 3/4 lb fish and keeps the 5 1/4lb, 3 1/2lb, and 2lb
The total weight of these three fish are
5 1/4lb
+
3 1/2lb
+
2lb
which equals 10 3/4lb
Determine the 20th term of the sequence
1,4,7,... in arithmetic sequence
Answer: 58
Step-by-step explanation:
Increment of 3
4th term is 10,
5th term is 13,
6th term is 16,
7th term is 19,
8th term is 22,
9th term is 25,
10th term is 28,
11th term is 31,
12th term is 34,
13th term is 37
14th term is 40
15th term is 43
16th term is 46
17th term is 49
18th term is 52
19th term is 55
Meaning that the 20th term is 58
Answer:
a₂₀ = 58
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = a₂ - a₁ = 4 - 1 = 3 , then
a₂₀ = 1 + (19 × 3) = 1 + 57 = 58
solve 2x + 13 = 17 for x, and then use that number to find the value of 3x + 1
Step-by-step explanation:
2x+13=17
2x=17-13
2x=4
x=4/2
x=2
then,
3x+1
= 3*2+1
= 6+1
= 7
Answer: 7
Step-by-step explanation:
To solve the problem you need to use algebra.
[tex]2x+13=17\\[/tex]
Subtract 13 on both sides.
[tex]2x=4[/tex]
Proceed to divide by 2 to solve for x.
[tex]x=2[/tex]
Now using your x-value, plug that into 3x+1 to get your solution.
[tex]3x+1\\3(2)+1=7[/tex]
Determine whether set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 13,15,16
Given set of numbers 13, 15, 16 represent an acute triangle.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.
Now we find the type of triangle.
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
The sum of the squares of the two smaller sides is,
= 13² + 15²
= 169 + 225
= 394
And 16² = 256
Since the sum of the squares of the two smaller sides is greater than the square of the largest side, the triangle must be an acute triangle.
Therefore, given set of numbers 13, 15, 16 represents an acute triangle.
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Compare the two numbers. Use > or < .
√75, 9
As the value of Square root √75 is equals to 8.66, and the number 9 is larger than the number 8.66.
What exactly is a square root?The square root of a number x is a number y whose square (the result of multiplying the number by itself, or y y), equals x in mathematics.The term "radicand" refers to the expression (or quantity) whose square root is being considered.The term or number under the radical sign in this instance is referred to as the radicand, and it is 9.Square roots of negative integers can be discussed in the context of complex numbers.In any circumstance where the idea of an object's "square" is established, square roots can be considered more generally.These include square matrices and function spaces, among other mathematical constructs.The value of Square root √75 is equals to 8.66, and the number 9 is larger than the number 8.66.
So, √75 < 9
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Prove the following.
If VZ ≅ VY and WY ≅ XZ , then VW ≅ VX .
The expression of the segment as the sum of the parts, gives VW = VX
How can the segment parts be used to prove that VW = VX?The given parameters are;
VZ = VY, WY = XZ, then VW = VX
From the given drawing obtained from a similar question, we have;
VZ = VW + WY (Segment Addition Postulate)
VY = VX + XZ, by segment addition
Therefore;
By substitution property, we have;
VW + WY = VX + XZ
Which gives;
VW + WY = VX + WY (substitution)
VW + WY - WY = VX + WY - WY
VW = VX by subtraction property
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When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?
Answer:
When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?
https://www.louisianabelieves.com/docs/default-source/assessment/grade-7-answer-key.pdf
Step-by-step explanation:
