Answers
Length of third side = 10 units.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
Here, given that,
Height = 7 units
Base = √51 units
And, we have, it is a right angle triangle
and we have to find the hypotenuse.
By Pythagorean theorem we get,
Hypotenuse = √7²+ 51
=√100
=10 units.
Hence, Length of third side = 10 units.
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Related Questions
help
Given the sides of a rectangle are in the proportion 9:14 and the perimeter of the rectangle is 230 cm,
the larger side length is:
What is the area
Answers
The larger side of the rectangle is 70 cm and the area is 3150 cm²
What is a rectangle?A 4-sided flat shape with straight sides where all interior angles are right angles (90°). Also, opposite sides are parallel and of equal length.
Given that, the sides of a rectangle are in the proportion 9:14 and the perimeter of the rectangle is 230 cm
Let the smaller side of the rectangle be 9x and larger side be 14x
We know that the perimeter of a rectangle = 2(l+w)
Therefore, perimeter = 2(9x+14x)
2(9x+14x) = 230
2×23x = 230
2x = 10
x = 5
Therefore, the smaller side of the rectangle is 45 cm and larger side is 70 cm
Area of a rectangle = (l×w)
Area = 70×45 = 3150 cm²
Hence, required answers are 70 cm and 3150 cm²
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7(4n-6)=6+4(4+3n) what’s the answer show work please
Answers
Step-by-step explanation:
7(4n−6)=6+4(4+3n)
Step 1: Simplify both sides of the equation.
7(4n−6)=6+4(4+3n)
(7)(4n)+(7)(−6)=6+(4)(4)+(4)(3n) (Distribute)
28n+−42=6+16+12n
28n−42=(12n)+(6+16) (Combine Like Terms)
28n−42=12n+22
Step 2: Subtract 12n from both sides.
28n−42−12n=12n+22−12n
16n−42=22
Step 3: Add 42 to both sides.
16n−42+42=22+42
16n=64
Step 4: Divide both sides by 16.
[tex]\frac{16n}{16} = \frac{64}{16}[/tex]
n=4
Determine whether enough information is given to show that the
triangles are congruent. If so state the congruence postulate or theorem that you would use
Answers
The given triangles are congruent due to the congruent postulate AAS.
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
As per the given figure,
In ΔCDE and ΔABF has :
m∠C = m∠A
m∠D = m∠B
side DC = side AB
According to AAS, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.
Hence, ΔCDE ≅ ΔABF
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Implementing a new system into an organization module by module is called a ____________.
A.
pilot study
B.
phased approach
C.
module strategy
D.
parallel strategy
E.
direct cutover strategy
Answers
Implementing a new system into an organization module by module is called a phased approach.
A phased approach is one of two common methods used to develop an ERP system solution. In this strategy, the system's functionalities are introduced in a certain order, gradually replacing previous systems and processes.
This frequently indicates that a business starts off with core functionality that is given top attention, and then other applications are gradually added in stages over time. An alternative implementation strategy, however, uses an all-at-once model in which the system and all apps "Go Live" simultaneously.
The optimal implementation plan for your firm will depend on the needs, goals, and strategies you have for it. This might involve a hybrid strategy where crucial functionality is added to the core ERP programs first, and then desirable features are added later on in a staged implementation. By considering all of your options, your firm can decide which will serve its interests the most effectively.
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List the data in the following stem-and-leaf plot. The leaf represents the tenths digit. 14 15 1447 16 56 17 8 18 366 Separate the numbers in the list by a comma. The list is: 151, 154, 154, 157, 165, 166, 178, 183, 186, 186 0,0,... X
Answers
The leaf representation is given as
14 l
15 l 1447
16 l 56
17 l 8
18 l 366
The 10th means that after the decimal, So the foundation must be the 15.1. This will be the 15.4, 15.7, 16.5 16.6 17.8 18.3 18.6 and 18.6.
In order to help visualize the shape of a distribution, a stem-and-leaf display or stem-and-leaf plot is a tool for presenting quantitative data in a graphical manner, comparable to a histogram.
The adoption of monospaced (typewriter) typestyles during that period contributed to their appeal since they made it simple for then-current computer technology to create the images. The improved graphic capabilities of modern computers have reduced the employment of these techniques.
While a stemplot is another name for a stem-and-leaf plot, it frequently refers to a different kind of chart. The term "simple stem plot" may refer to the mapping of a matrix of y values to a common x axis, along with the identification of the common x value by a vertical line and the individual y values by symbols on the line.
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. A soccer team spent $183 on 15 new soccer balls. Each ball cost the same. Find the exact cost of each soccer ball. Show all work.
Answers
Answer:
Each soccer ball cost $12.20
Step-by-step explanation:
183/15 = 12.20
183 / 15 = 12.2
So each soccer ball costs $12.2
Find the x-intercept of the line 18x–5y=12.
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.
Answers
The x-intercept of the line 18x – 5y = 12 is 2/3
How to determine the x-intercept of the line?From the question, we have the following parameters that can be used in our computation:
A linear equation
The linear equation is represented as
18x–5y=12
Express properly
So, we have the following representation
18x – 5y = 12
Set y to 0 to determine the x-intercept of the line
So, we have the following representation
18x – 5 * 0 = 12
Evaluate the products
18x = 12
Divide by 18
So, we have
x = 12/18
Simplify
x = 2/3
Hence, the intercept is 2/3
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1. what is the next number in the series 99, 33, 11, 11/3 11/9 ___?_
a. 11/11
b. 11/18
c. 11/27
d. 11/33
e. 11/99
f. None of these 2. Which number in the following group represents the smallest amount 3 .7 .59 15 .18 6 3. in the following set words, which words is different from the others a. citizen
b. villager
c. habitat
d. resident e. native
Answers
1) The next number in the series 99, 33, 11, 11/3, 11/9, . . . is 11/27
The correct answer is an option (c)
2) In the given group the smallest amount is .18
1.
We have been given a sequence of numbers 99, 33, 11, 11/3, 11/9,. . .
We need to find the next number in given sequence .
We can observe that given series is geometric sequence with the first term a₁ = 99 and the common ratio r = 1/3
We know that the formula for the n-th term of gemetric sequence is:
an = a₁ × r^(n - 1)
For n = 6,
a₆ = 99 × (1/3)⁽⁶ ⁻ ¹⁾
a₆ = 99 × (1/3)⁵
a₆ = 11/27
Hence, the next number in the series is 11/27
2.
If we arrange the numbers in ascending order then it would be,
0.18, 0.59, 0.7, 3, 6, 15
So, the smallest amount is .18
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a basketball team's players were successful on $50\%$ of their two-point shots and $40\%$ of their three-point shots, which resulted in 54 points. they attempted $50\%$ more two-point shots than three-point shots. how many three-point shots did they attempt?
Answers
The team attempted 30 three-point shots.
Let x be the number of three-point shots the team attempted.
We know that the team attempted 50% more two-point shots than three-point shots, so the number of two-point shots is 1.5x.
We also know that 50% of the two-point shots were successful and 40% of the three-point shots were successful, so we can set up the following equation:
(1.5x)(0.5) + (x)(0.4) = 54
Solving for x yields x = 30.
Therefore, the team attempted 30 three-point shots.
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find the scale of a map. 50 km in real disstance is 2dm on a map
Answers
The scale of the map is 1 dm : 25 km
How to determine the scale of the map?From the question, we have the following parameters that can be used in our computation:
Mathematical statement
The mathematical statement is given as
50 km in real distance is 2dm on a map
The scale is then calculated as
Scale = Map distance : Actual distance
Substitute the known values in the above equation, so, we have the following representation
Scale = 2 dm : 50 km
Divide by 2
Scale = 1 dm : 25 km
Hence, the scale is 1 dm : 25 km
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What is a function of the form f/x Logbx?
Answers
The logarithmic function [tex]f(x)=\log _{x} b[/tex] is the inverse of the exponential function [tex]g(x)= b^{x}[/tex].
The logarithm function is of the form [tex]f(x)=\log _{x} b[/tex] where [tex]x[/tex] is the base and [tex]b > 0[/tex].
The exponential function is of the form [tex]g(x)= b^{x}[/tex] where [tex]x[/tex] represents variable and [tex]b[/tex] represents constant. [tex]b[/tex] is also called the base of the function and must be greater than 0.
The inverse of a function exists if and only if the function is one-one and onto function. When the function has inversed the range of the function changes to the domain of the inversed function and the domain of the function changes to the range of the inverse function.
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Which function depicts f (x)
Answers
We have depicted the function f(x).
If the function is stretched vertically by a factor of 5 -> 5f(x).
If the function is shrunk horizontally by a factor of 5 -> f(5x).
If the function is shifted to the right five units -> f(x) - 5
If the function is shifted to the down five units -> f(x - 5)
If the function is shifted to the up five units -> f(x) + 5
If the function is shifted to the right five units -> f(x + 5)
What is a function?
A function is a mathematical relationship between a set of inputs, known as the domain, and a set of outputs, known as the range. In other words, it's a rule that assigns a unique output to each input.
If the function is stretched vertically by a factor of 5 -> 5f(x).
If the function is shrunk horizontally by a factor of 5 -> f(5x).
If the function is shifted to the right five units -> f(x) - 5
If the function is shifted to the down five units -> f(x - 5)
If the function is shifted to the up five units -> f(x) + 5
If the function is shifted to the right five units -> f(x + 5)
Hence, we have depicted the function f(x).
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Which equation has no solution?
|4x - 2| = - 6, |-2 - x| = 9, |3x + 6| = 6, |-2x + 8| = 0
Answers
This is because the absolute value equation is equal to a negative value. This cannot occur because absolute value is the distance from 0, and distance is always a positive measurement. Thus, absolute value always produces a positive output. For example, if we were to find the absolute value of 6, it would look like:
|x|=6
So, x must be two numbers that are 6 units from 0; there is a positive and negative value, but the negative value turns positive since there is no negative distance.
Thus, we’d know that x=-6, 6 because |-6|=6 and |6|=6, so -6 is 6 units from 0 and 6 is 6 units from 0.
However, what if we said the absolute value of a number, x, must equal -6? Well, here’s what happens:
|x|=-6
|-6|≠-6 and |6|≠-6
So, there are no solutions to this equation because distance can’t negative. There is no value that is -6 units from 0.
5 - 8 + 2 x 8 - 5 + 6 divided by 3 x 8
Answers
Answer:
-18.66666666666667
Step-by-step explanation:
How much did McCandless weigh when he died?
Answers
McCandless weighed a hundred and forty pounds when he died.
It was apparent that McCandless had been deceased for nineteen days based on a mysterious journal that was discovered among his belongings.
According to a driver's license that was granted eight months before he passed away, he was 24 years old and weighed 140 pounds. After being taken out of the woods, his body underwent an autopsy, which found that it weighed only 66.7 pounds and had no subcutaneous fat that could be seen.
The coroner's findings said that malnutrition was the death's most likely cause.
Thus, McCandless weighed a hundred and forty pounds when he died.
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McCandless weigh when he died is at the amount of sixty-seven pounds.
The term weigh in math is defined as the measure of the force of gravity on an object and the mass of an object will never change, but the weight of an item can change based on its location.
Here we have know that the driver's license issued eight months before he perished indicated that he was twenty-four years old and weighed a hundred and forty pounds. Therefore his body was flown out of the wilderness, and at the time of autopsy determined that it weighed sixty-seven pounds and lacked discernible subcutaneous fat and the cause of death was officially reported as starvation.
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Find the length of the third side. If necessary, write in simplest radical form.
Show steps
Answers
Answer:
b = 2sqrt(5)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
4^2 + b^2 = 6^2
16+b^2 = 36
b^2 = 36-16
b^2 = 20
Taking the square root of each side
sqrt(b^2) = sqrt(20)
b = sqrt(20)
b = sqrt(4*5)
b = sqrt(4) sqrt(5)
b = 2sqrt(5)
b = 2sqrt(5)
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
4^2 + b^2 = 6^2
16+b^2 = 36
b^2 = 36-16
b^2 = 20
Taking the square root of each side
sqrt(b^2) = sqrt(20)
b = sqrt(20)
b = sqrt(4*5)
b = sqrt(4) sqrt(5)
b = 2sqrt(5)
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GEOMETRY FIND LENGTH OF THIRD SIDE
Answers
The other side length is √20 after applying the Pythagoras and other two sides are 2 and 2√3.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
One side length = 2
Other side length = 2√3
Apply Pythagoras
x^2 = 2^2 + (2√3)^2
x^2 = 4 + 12
x = √20
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Let N represent the number of solutions of the equation 3 times open paren x minus A close paren is equal to 3(x - a) = 3x - 6 Which statements are correct? Select all that apply.
Answers
The statements which are correct about the equation 3(x - a) = 3x - 6 are;
When a = 3; N < 1.When a = 2; N > 1.When a = x; N = 1.When a = -x; N = 1.Identifying statements which are correct about the equation.According to the task content; the equation which is to be considered is;
3(x - a) = 3x - 6
Therefore, it follows from the distributive property that we have;
3x - 3a = 3x - 6
Therefore
When a = 3; 3x - 9 = 3x - 6; Therefore, since -9 ≠ -6; the number of solutions N is 0. TRUE.When a = -3; 3x + 9 = 3x - 6; Therefore, since +9 ≠ -6; the number of solutions N is 0. FALSE.When a = 2; 3x - 6 = 3x - 6; Therefore, since -6 ≠ -6; the number of solutions N is infinite; N > 1. TRUE.When a = -2; 3x + 6 = 3x - 6; Therefore, since +6 ≠ -6; the number of solutions N is 0. FALSE.When a = x; 3x -3x = 3x - 6; Therefore, since x = 2; the number of solutions N is 1. TRUE.When a = -x; 3x +3x = 3x - 6; Therefore, since x = -2; the number of solutions N is 1. TRUE.On this note, the true statements are as indicated above.
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Tips to divide large numbers and decimals (or literally, any number) quickly anyone? 100 Points for a helpful answer!
Answers
Answer:
Step-by-step explanation:
Here are a few tips for quickly dividing large numbers and decimals:
Use estimation: Estimate the quotient by rounding the dividend and divisor to easy numbers. This can save time and give you a rough idea of the answer.
Use long division: This method can be used to divide larger numbers, and it involves breaking down the dividend into smaller parts, dividing each part by the divisor, and then combining the results.
Use a calculator: A calculator can quickly divide large numbers and decimals, and it eliminates the need for long division or estimation.
Use the reciprocal: Dividing by a number is the same as multiplying by its reciprocal, so if you know the reciprocal of the divisor, you can use it to quickly divide any number.
Use mental math: If you are comfortable with mental math and good at it, you can use it to quickly divide numbers. This can help you to quickly divide large numbers and decimals.
Use the method of repeated subtraction or shifting the decimal point: Instead of dividing by repeatedly subtracting the divisor from the dividend or shifting the decimal point, this method can also be used to divide large numbers and decimals.
Practice: The more you practice dividing large numbers and decimals, the better and faster you will get at it.
Answer:
calculator. the one I usually use is the casio fx-97SGX
Multiply.
6 2/3 × 3 6/7
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
The multiplication of the fraction 6 2/3 × 3 6/7 is 25 5/7 as a mixed number in simplest form.
How to multiply fraction?Fraction refers to a number which consists of a numerator and a denominator. A numerator is the upper value of a fraction while a denominator is the lower value of a fraction.
6 2/3 × 3 6/7
= 20/3 × 27/7
= (20 × 27) / (3 × 7)
Multiply the numerator and denominator respectively.
= 540 / 21
= 25 15/21
It can also be written in simplest form as;
= 25 5/7
Therefore, 25 5/7 is the result of the multiplication of the fraction 6 2/3 × 3 6/7 in its simplest form
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What is the domain of the relation graphed below?
Answers
Domain of the given graph is {x/-4≤x≤4}
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The domain of a function or relation is the set of all possible independent values the relation can take.
The graph is passing through the points (4, 0)(-4, 0)(0, 1) and (0, -1)
Four comma zero, minus four comma zero, zero comma one and zero comma minus one.
The x is between -4 and 4
The domain of the given graph is {x/-4≤x≤4}
Hence, domain of the given graph is {x/-4≤x≤4}
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2. A sequence of patterns is made using lines and dots. The first three patterns in the sequence are shown below. Pamer 1 Param: P1 (a) Draw Pattern 4 on the grid. (b) Copy and complete the table Pattern 1st Number of dots Number of lines 2 4 point tog starting point toget 2nd 3rd 4th 3 5 7 10 13 P4 10th (c) Find an expression, in terms of n, for (i) The number of dots in Pattern n. (ii) The number of lines in Pattern n. (d) A pattern has 76
pattern
Answers
Answer:
my answer is one
Step-by-step explanation:
I don't know why but when i ask it in my brother he is an engineer so he know that
a.
The image shows the pattern with 7 dots and 10 lines. The dots are arranged in a square, with 3 dots on each side.
b. The complete table is seen below
ci. the expression for the number of dots in Pattern n is n + 1.\
cii. the expression for the number of lines in Pattern n is n + 2.
d. the 76th pattern has 77 dots and 78 lines.
How do we explain?(a)
b.
Pattern Number of dots Number of lines
1st 2 4
2nd 3 5
3rd 5 7
4th 7 10
5th 9 13
6th 11 16
7th 13 19
8th 15 22
9th 17 25
10th 19 28
(c)
(i) The pattern of dots in Pattern n can be found by adding 1 to the number of lines in Pattern n - 1 and the expression for the number of dots in Pattern n is n + 1.
(ii) The number of lines in Pattern n can be found by adding 2 to the number of lines in Pattern n - 1 and the expression for the number of lines in Pattern n is n + 2.
(d)
If a pattern has 76 lines, then it is the 76th pattern in the sequence. So, n = 76.
The number of dots in the 76th pattern is 76 + 1 = 77.
The number of lines in the 76th pattern is 76 + 2 = 78.
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In which of the following options does x varies inversely as y?
x+y=5x plus y is equal to 5
x=5yx is equal to 5 y
x=5yx is equal to 5 over y
x=5y+5
Answers
Answer: The meaning of the statement “ x vary inversely as y “ is “x is inversely proportional to y".
Final Answer // x=5yx is equal to 5 over y
Step-by-step explanation:
Step by step answer please
Answers
Answer: 48°
Step-by-step explanation:
We know that the angles of a triangle are equal to 180 degrees when added together. Using this logic, we will create an equation to solve for x. Then we will substitute this value of x back into the expression for angle F.
Given:
E + D + F = 180°
Substitue:
(8x - 18)° + (6x - 4)° + (5x - 7)° = 180°
Reorder and combine like terms:
8x° + 6x° + 5x° - 18° - 4° - 7° = 180°
19x° - 29° = 180°
Add 29 to both sides of the equation:
19x° = 209°
Divide both sides of the equation by 19:
x = 11
Substitute this value of x into the expression for angle F:
(5x - 7)°
(5(11) - 7)°
(55 - 7)°
48°
Find the x -intercept of a line with a slope of - 2 and a point ( 3 , 4 ) .
Answers
let's firstly get its equation and then find the x-intercept, keeping in mind that the x-intercept occurs when y = 0.
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- 2}(x-\stackrel{x_1}{3}) \qquad \implies\quad \stackrel{\textit{setting y = 0}}{0-4=-2(x-3)} \\\\\\ -4=-2x+6\implies -10=-2x\implies \cfrac{-10}{-2}=x\implies 5=x~\hfill \boxed{\stackrel{x-intercept}{(5~~,~~0)}}[/tex]
Point-slope: (y-y₁)=m(x-x₁), where y₁ = first y-coordinate, m=slope, and x₁=first x-coordinate.
Let’s plug the given information into point-slope form:
(y-(4))=2(x-(3))
*( ) indicate a value has been substituted in for a variable*
Now, let’s transform the equation into standard form. We will do this because standard form is the easiest, equivalent form to calculate the x-intercept.
Standard Form: Ax+By=C
Translating to standard form:
y-4=2(x-3)
Distribute the 2:
y-4=2x-6
Combine like terms - add 4 to both sides:
y=2x-6+4
y=2x-2
Subtract 2x from both sides:
-2x+y=-2
We are now in standard form. To calculate the x-intercept, y must equal 0 because there will not be any vertical change when y=0, so we can determine what value lies on the x-axis with 0 vertical change.
When y=0, x=….
-2x+(0)=-2
-2x=-2
Divide both sides by -2:
x=-2/-2
x=1
Therefore, x=1 is the x-intercept or the point (1, 0).
In a regression analysis, the error term ε is a randomvariable with a mean or expected value of
a) Zero
b) One
c) any positive value
d) any value
Answers
In a regression analysis, the error term ε is a random variable with a mean or expected value of zero. The correct option is a.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Given:
Analysis is a regression analysis.
And the error term in regression analysis:
The error term, which refers to the total of the deviations within the regression line and explains the discrepancy between the theoretical value of the model and the actual observed results, denotes the margin of error inside a statistical model.
ε = Epsilon or error term.
The variation in the dependent variable that the independent factors do not explain is taken into account by the error term.
The values of the error term should be determined by random chance.
The average value of the error term must be equal to zero in order for your model to be impartial.
Therefore, error term is zero.
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What is the slope of the equation 5/4x-7/4
Answers
Answer:
3rd option ==> 5/4
Step-by-step explanation:
5x/4 means that for every time x increases by 1, y increases by 5/4.
5/4 is the coefficient for x.
Answer:
[tex]\dfrac{5}{4}[/tex]
Step-by-step explanation:
The general slope-intercept form of a line equation is
[tex]y = mx + b[/tex]
where m is the slope and b the y-intercept
The given line has the equation:
[tex]y = \dfrac{5}{4}x - \dfrac{7}{4}[/tex]
Comparing the general equation to this equation tells us that the slope
[tex]\textr{m } = \dfrac{5}{4}[/tex]
and y-intercept
[tex]b = -\dfrac{7}{4}[/tex]
If the basin is completely filled with water, how much water will it hold? round the answer to the nearest tenth of a foot. ft3
Answers
A cylindrical basin is 2 feet tall and has a diameter of 5 feet, as shown. If the basin is completely filled with water, how much water will it hold? Round the answer to the nearest tenth of a foot.
The basin holds 39.3 cubic feet of water.
The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm3, m3, in3, etc. Let us see the formula used to calculate the volume of a cylinder. We know that the base of a right circular cylinder is a circle and the area of a circle of radius 'r' is πr2. Thus, the volume (V) of a right circular cylinder, using the above formula, is,
V = πr²h
Here,
⇒ 'r' is the radius of the base (circle) of the cylinder
⇒ 'h' is the height of the cylinder
⇒ π is a constant whose value is either 22/7 (or) 3.142.
Thus, the volume of cylinder directly varies with its height and directly varies with the square of its radius. i.e., if the radius of the cylinder becomes double, then its volume becomes four times.
We are given that the height of the basin h = 2 ft and the diameter = d = 5 ft.
So, radius r = d/2 = 5/2 = 2.5 ft
The amount of water the basin holds is equal to the volume of cylindrical basin.
Volume =πr²h
=3.1416×2.5²×2
=39.27 cubic feet
= 39.3 cubic feet
Thus, the basin holds 39.3 cubic feet of water.
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A consumer watchdog organization estimates the mean weight of 1-ounce "Fun-Size"
candy bars to see if customers are getting full value for their money. A random sample
of 25 bars is selected and weighted, and the organization reports that a 95% confidence
interval for the true mean weight of the candy bars is 0.982 to 0.988 ounces.
a) What is the point estimate (=sample mean) from this sample?
b) What is the margin of error?
(Hint: find the distance between the sample mean and the upper limit).
c) Interpret the confidence level of 90% in the context of the problem?
Answers
Point estimate from the sample is 0.985, margin error is 0.003.
What is Confidence Interval?Confidence interval is defined as the interval which is the estimate for the parameter of the sample or population to be contained.
(a) To calculate point estimate or sample mean :
Point estimate is the mid point of the confidence interval.
Given that true mean weight of candy bars is 0.982 ounces to 0.988 ounces.
Point estimate = (0.982 + 0.988) / 2 = 1.97 / 2 = 0.985
(b) Margin error is the one half of the total width of the interval.
Margin error = (0.988 - 0.982) / 2 = 0.003
(c) The confidence level of 90% in this problem can be interpreted as , if we do the interval construction for many times, about 90% of the total constructed intervals has the true population mean of weight of fun size candy bars.
Hence the point estimate and margin error are 0.985 and 0.003 respectively.
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Evaluate 4ª - 4(2) (-8)
Answers
On solving the provided question, we can say that let the equation be X = 4ª - 4(2) (-8) => X = -15
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
let the equation be
X = 4ª - 4(2) (-8)
here, a = 0
X = 1 - 8-8
X = -15
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