The mean of the data is 3.85 using the stem-and-leaf plot.
It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.
How to calculate the Mean of a Data?To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values, and divide by the number of values that were represented on the stem-and-leaf plot.
Given the stem-and-leaf plot, using the key, the data points represented are:
2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5
Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12
Mean = 46.2/12
Mean = 3.85 feet
The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.
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Simplfy and solve 13+7x66
please help me and please hurry. also please show working clearly!!
Answer:
The limit does not exist
Step-by-step explanation:
This is because the left hand limit is 3,we know this because as the graph approaches from the left side of the Cartesian plan the open dot is on 3
and the right hand limit is 1 because as the graph approaches the X=1 from the right hand side the open dot lands on 1
Since the left hand limit doesn't equal to right hand limit,the overall limit of x=1 doesn't exist.
How can you determine if an inverse is a function?
Write the equation of the line, in standard form, that has a y-intercept of 2 and is parallel to 2x + y = -5. Include your work for each step in your final answer. Type your answer in the box provided to submit your solution.
a) Using variables, write out the formula for the standard form of the equation.
b) Determine the slope of the line.
c) Write the point-slope form of the line.
d) Using the properties of algebra, rearrange the equation into the standard form.
The slope of the line is - 2 with the equation as 2 x + y - 2 = 0
We are given that:
y intercept of the line = 2
Point is (0, 2)
It is parallel to the line 2 x + y = - 5
Slope of line 2 x + y = - 5:
y' = - 2
m = - 2
Slope of parallel lines are equal
m = m'
m' = - 2
Equation of the line:
y - y₁ = m( x - x₁)
y - 2 = - 2( x - 0)
y - 2 = - 2 x
2 x + y - 2 = 0
a) standard form of the equation = 2 x + y - 2 = 0
b) slope of the line = m' = - 2
c) point-slope form = (y - 2) / (x - 0) = - 2
d) Properties of algebra used = cross multiplication and simplification.
Therefore, we get that, the slope of the line is - 2 with the equation as 2 x + y - 2 = 0
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Solve the following system of equations.
Provide your answer below:
-3x+4y= 7
7x- 12y = -11
Answer:
x = -5
y = -2
Step-by-step explanation:
-3x + 4y = 7 ⇒ ( 1 )
7x - 12y = -11 ⇒ ( 2 )
Multiply the equation ( 1 ) by 3.
( 1 ) × 3
3( -3x + 4y = 7 )
-9x + 12y = 21 ⇒ ( 3 )
Let us find the value of x.
Add equations ( 2 ) & ( 3 ).
( 2 ) + ( 3 )
7x - 12y - 9x + 12y = - 11 + 21
Combine like terms.
-2x = 10
Divide both sides by -2.
x = -5
Let us find the value of y.
For that, let us use equation ( 1 ) and replace x with -5 and make y the subject.
- 3x + 4y = 7
-3 × -5 + 4y = 7
15 + 4y = 7
Subtract 15 from both sides.
4y = 7 - 15
4y = -8
Divide both sides by 4.
y = -2
Find missing side length given two similar triangles
Answer: 49
Step-by-step explanation:
by using triangle ABC and the known values of triangle XYZ, we can divide side XY/AB, 28/4=7. By doing the same with YZ/BC, 56/8=7, we find that the scale factor is 7. With this information, we multiply side CA by the scale factor, 7x7=49.
Which model represents the sum of 4 + 12?
Answer: 16
Step-by-step explanation:
Imagine you had 4 apples and someone gave you 12 more. You would have 16 apples.
HEEELPPPPPPPP Rearrange the formula v = 2gh for h. A) h = v 2g B) h = 2v g C) h = v2 g D) h = v2 2g
Rearranging the equation, making h the subject of the formula, h = v² / 2g
How to rearrange formula?we rearrange equations and formulas by using inverse operations to make one variable the subject of the formula.
In order to change the subject of, or rearrange, a formula items in the formula need to be arranged so a different variable is the subject.
In our case the the formula needs to be rearrange to make h the subject of the formula.
Therefore,
v = √2gh
square both sides of the equation
v² = (√2gh)²
v² = 2gh
divide both sides by 2g
v² / 2g = 2gh / 2g
h = v² / 2g
Therefore,
h = v² / 2g
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A movie theater sends out a coupon for 54% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.
The equation for the representation of the given situation will be
y = x - 0.54x, and the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative.
What is an equation?An equation is a statement that says that the value of two mathematical expressions is equal.
Given that, a cinema sends out a coupon for 54% off the price of a ticket.
The equation for this situation will be y = x - 0.54x,
And the line of this equation will always lie in the first quadrant because values of x and y in the first quadrant are always positive, and here x and y are prices which can't be negative.
Hence, the graph of the equation should only be in the first quadrant because x and y is representing a price which can't be negative and The equation for the representation of the given situation will be
y = x - 0.54x
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PLEASE HELP ME !!!
x² + 12x -
2
8 can be written in the form
(x + a)² + b, where a and b are numbers.
Work out the values of a and b.
Answer:
a = 6 , b = - 44
Step-by-step explanation:
x² + 12x - 8
using the method of completing the square
add/subtract ( half the coefficient of the x- term)² from x² + 12x
x² + 2(6)x + 36 - 36 - 8
= (x + 6)² - 44 ← in the form (x + a)² + b
with a = 6 and b = - 44
Which of the following (x,y) coordinates are solutions to the inequality 2x+5y<1?
The solution to the inequality given as 2x+5y<1 has the coordinates of (-10, 4)
How to determine the coordinates of the solution of the inequality?From the question, we have the following inequality that can be used in our computation:
2x+5y<1
Solving further, we need to collect the like terms
Since there are no like terms in the expression, it remains unchanged
So, the inequality becomes
2x + 5y < 1
Subtract 5y from both sides of the inequality
This gives
2x < 1 - 5y
Divide both sides by 2
The expression becomes
x < 1/2 - 5/2y
Evaluate
x < 0.5 - 2.5y
At this point, we assume any value for y and then solve for x
Assume that the value of y is 4
So, we have the following representation
x < 0.5 - 2.5 * 4
Evaluate the products
x < -9.5
This means that x is less than -9.5 when y is 4
-10 is less than -9.5
So, we have
x = -10 and y = 4
Express as ordered pairs (i.e. coordinates)
(x, y) = (-10, 4)
Hence, the coordinates of the solution is (-10, 4)
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Henry invested $1500 into an account that pays 2% interest compounded annually.
How much money will Henry have at the end of 3 years?
Enter your answer in the box. Round to the nearest hundredth.
The compound interest is obtained as $91.81, rounded off to the nearest hundredth.
How is compound interest estimated annually?In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest. The entire compound interest is then obtained by deducting the initial principal.
The equation that results will look like this:
Compound Interest = [tex]P(\left(1+r\right)^{ t}-1)[/tex]
Amount, rate of interest and time is given as $1500, 2% and 3 years respectively.
First, change r as a percent to r as a decimal.
r = R/100
r = 2/100
r = 0.02 rate per year,
Then solve the equation for compound interest.
[tex]\text{Compound Interest}=1500(\left(1+0.02\right)^{3}-1)\\=1500(1.061208-1)\\=15000\cdot 0.061208\\\\=91.81[/tex]
So, the compound interest is obtained as $91.81, rounded off to the nearest hundredth.
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Answer: its 1591.81
Step-by-step explanation:
I took the test and tried with the answer on top and got it wrong.
Seven factory workers take part in a charity swim. Altogether they swim 179 lengths of a pool. How many lengths does each worker swim on average?
The length of each factory worker on average is 25.57 lengths
How to determine the length of each on average?From the question, we have the following parameters that can be used in our computation:
Total length of the pool = 179 lengths
Number of workers = 7
The length of each on average is calculated as
Average length = Total length of the pool/Number of workers
Substitute the known values in the above equation
So, we have the following equation
Average length = 179/7
Evaluate the quotient
Average length = 25.57
Hence, the average length is 25.57 lengths
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Find the Surface Area for the following:
(Use 3.14 for . Do not round and do not type your units.)
Surface Area = ______ in²
The shape has a surface area of: Surface Area = 282.6 in²
How to determine the surface area?The given parameter is represented on the figure
In this case, the figure is a cone with the following parameters
Radius, r = 5 inches
Height, h = 12 inches
The surface area of the cone is then calculated as
A = πr * (r + √(h² + r²))
Substitute the known values in the above equation, so, we have the following representation
A = 3.14 * 5 * (5 + √(12² + 5²))
Evaluate the expression
A = 282.6
Hence, the surface area is 282.6 square inches
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Max wanted to test a new dishwasher detergent to see if it was less likely to leave residue on his dishes. What would be the null hypothesis in Max’s experiment
Given that Max wanted to test a new dishwasher detergent to see if it was less likely to leave residue on his dishes, the suitable null hypothesis in Max’s experiment will be "the new detergent will leave more residue than the old one".
What is a null hypothesis?In statistics, a null hypothesis means a typical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable between the two sets of observed data and measured phenomena.
Therefore, the Option B is correct.
Missing options' The new detergent will leave less residue than the old one. The new detergent will leave more residue than the old one. O The new detergent is equally likely to leave residue compared to the old detergent. The old detergent will leave more residue than the new detergent."
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1. A factory is testing a new machine on its production line that is intended to improve efficiency. Management randomly
selects 12 employees and measures the number of products they complete in one hour when using the new machine. Below
are the results.
Employee 1 2 3 4 5 6 7 8 9 10 11 12
# units 72 68 74 78 75 79 71 69 82 71 73 80
(a) Estimate at the 95% confidence level the average number of units an employee can produce in one hour using the
new machine.
(b) The manufacturer of the machine claims the typical efficiency for a factory worker should be 78 units per hour. What
does the interval suggest about the manufacturer’s claim
(c) An investigation at a similar factory estimates the standard deviation to be 3.91 units. Using this information, what
size sample should we select to estimate the mean number of units produced each hour to within 1.04 units at the
95% confidence level?
a) The confidence interval is given as follows: (71.43, 77.17).
b) The manufacturer's claim is not correct, as 78 is not a part of the interval.
c) A sample of 55 employees is needed to achieve the desired margin of error.
What is a t-distribution confidence interval?The bounds of the t-distribution confidence interval, used when only the standard deviation for the sample is known, are given by the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, considering the 95% confidence level and 12 - 1 = 11 df, is of:
t = 2.201.
The remaining parameters, namely sample mean, sample standard deviation and sample size are given as follows:
[tex]\overline{x} = 74.3, s = 4.52, n = 12[/tex]
(obtained using a calculator from the sample given in this problem).
The bounds of the interval are given as follows:
Lower bound: 74.3 - 2.201 x 4.52/sqrt(12) = 71.43.Upper bound: 74.3 + 2.201 x 4.52/sqrt(12) = 77.17.The interval does not contain the number 78, hence it is not a good estimate for the mean amount.
For item c, the z-distribution is used, as the population standard deviation is used, hence the minimum sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.04 = 1.96\frac{3.91}{\sqrt{n}}[/tex]
[tex]1.04\sqrt{n} = 1.96 \times 3.91[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 3.91}{1.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 3.91}{1.04}\right)^2[/tex]
n = 55. (rounded up, as a sample size of 54 would mean that the margin of error would be slightly above 1.04).
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which is the correct answer ????
The correct way to replace equation 1 into equation 2 using the substitution method is 2x+(-5x+10) = 7.
According to the question,
We have the following two equations:
Equation 1: y = -5x+10
Equation 2: 2x+y = 7
Now, we will substitute the value of y from equation 1 in equation 2.
So, we have the following expression:
2x+(-5x+10) = 7
(More to know: we can also solve this equation to find the value of x and then the obtained value of x can be put in equation 1 to find the value of y.)
Hence, the correct option is B.
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Which value of x makes the following statement true? 1.4 - x = a positive number
Answer:1.4<x
math math math
Answer:daddy
Step-by-step explanation:gay
3.
A circular pool of oil grew so that its radius increased by 2 feet. The formula shown can
be used to determine the area of the circle.
A = π (r + 2)²
Which equation is equivalent to the formula solved for r in terms of A?
Or=√1-2
Or=√√√+2
Or=√√4+2
Or-√4-2
Equation which is equivalent to the formula solved for r in term of A is [tex]Or = \sqrt{\frac{A}{r}-2 }[/tex].
What is circle?
A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
A circle is also termed as the locus of the points drawn at an equidistant from the centre.
What is radius?
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'.
What is circumference?
Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of circle defines the region occupied by it.
Given that;
[tex]A = \pi{({r+2})^{2}}[/tex]
[tex](r+2)^{2} =\frac{A}{\pi}[/tex] (equivalent transformation)
[tex]r + 2 = \sqrt{\frac{A}{\pi} }[/tex]
[tex]r = \sqrt{\frac{A}{\pi} -2}[/tex]
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NEED HELP ASAP
What is the value of y in the solution to this system of equations 6y+x= -59 x= -2y+9?
Answer:
y = - 17
Step-by-step explanation:
6y + x = - 59 → (1)
x = - 2y + 9 → (2)
substitute x = - 2y + 9 into (1)
6y - 2y + 9 = - 59
4y + 9 = - 59 ( subtract 9 from both sides )
4y = - 68 ( divide both sides by 4 )
y = - 17
Solve the equation below for x
Cx — 4 = 7
The equation for the value of x will be 11/C.
According to the question,
We have the following equation:
Cx — 4 = 7
Now, we can easily find the value of x from this equation by following the given steps.
We will first add 4 on both sides of the equation:
Cx = 7+4
Adding the two numbers on the right hand side:
Cx = 11
Dividing by C on both sides of the equation:
x = 11/C
(More to know: we can now find the value of x if the value of C is given.)
Hence, the equation for the value of x will be 11/C.
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(x2 + 3x –9) ÷ (x – 2).
Answer:
Step-by-step explanation:
Solve. 4x+2=(1/8)x-2
_______
4/7
of a square is painted green.5/6 of the remainder is painted red. If the green
part is 36 cm² more than the red. find the area of the square.
Answer:
168
Step-by-step explanation:
Let the area of the square be [tex]x[/tex].
[tex]\frac{4}{7}x-\frac{5}{6}\left(\frac{3}{7}x \right)=36 \\ \\ \frac{4}{7}x-\frac{5}{14}x=36 \\ \\ \frac{8}{14}x-\frac{5}{14}x=36 \\ \\ \frac{3}{14}x=36 \\ \\ \frac{1}{14}x=12 \\ \\ x=168[/tex]
ASAP Write an equation of a quadratic formula with the given properties: f(3)=f(-5)=0;f(-6)=-36
The quadratic equation y = - 4 · x² - 8 · x + 60 contains the points (3, 0), (- 5, 0) and (- 6, - 36).
How to derive a quadratic equation that contains three points
In this question we find the coordinates of three points set on Cartesian plane and we are asked to find the quadratic equation that contains the these points. The standard form of the quadratic equation is shown below:
y = a · x² + b · x + c
Where:
x - Independent variable.y - Dependent variable.a, b, c - Real coefficients.We can determine the values of the three coefficients because the number of known points is equal to the number of coefficients. Then, we have the following system of linear equations by replacing x and y on each of the three points:
9 · a + 3 · b + c = 0
25 · a - 5 · b + c = 0
36 · a - 6 · b + c = - 36
Then, the solution to the system is found by numerical methods:
(a, b, c) = (- 4, - 8, 60)
The equation that contains the three points is y = - 4 · x² - 8 · x + 60.
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Convert the height of a person who is 5.2 feet tall to centimeters. Include the inches-centimeter conversion
factor. Use the table given to create conversion factors. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
The height of a person is 5.2ft in centimeter: 158.49cm
What are the Factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.So, the conversion of measurement from the unit feet to centimeters is provided by the feet-to-centimeter calculator.
The letters "ft" and "cm" stand for feet and centimeters, respectively. The centimeter is used in the International System of Units and is regarded as a component of the metric system. The US customary measurement system uses the unit foot.Approximately 30.48 cm makes up one foot.
1 ft = 30.48 cm
Now, the formula for 5.2 feet to centimeters is as follows:We are aware that 1 foot equals 30.48 centimeters.Therefore, 5.2 feet equals 5.2 x 30.48 centimeters.
5.2 ft = 158.49 cm.5.2 feet is therefore equal to 158.49 cm in centimeters.
Hence, the height of a person who is 5.2 feet tall to centimeters is 158.49cm.
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Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
It is a function because the mapping .
(A) Due to the fact that there are no two values in Set B that have only one value in Set A mapped to them, the mapping diagram above represents a function.
(B) A function's very special property is that it associates one output with each input.
(C) Set A represents the domain, whereas Set B represents the range. Therefore, there would be exactly one value in the range that was unique for each value in the domain and would be present for each value in the domain.
What are functions?In mathematics, a function from a set X to a set Y assigns each element of X exactly one element of Y. The subsets X and Y are referenced to as the function's domain and codomain, correspondingly. A function is described as a relationship between a group of inputs with one output each. A function is, to describe it simply, a connection between inputs in which each input is associated to exactly one output. Every function has a domain and a codomain, or range. A function is a type of rule that produces one output from one input. Y=X2 is a good illustration of this. Any input for x yields a single output for y.
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use the figure below to solve for the missing value(s):
The missing values are:
m∠1 = 36°
m∠2 = 122°
m∠3 = 122°
m∠4 = 38°
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The figure has two triangles.
58° and m∠3 is a straight angle.
58 + m∠3 = 180
m∠3 = 180 - 58
m∠3 = 122
Now,
m∠3 + m∠4 + 20 = 180
122 + m∠4 + 20 = 180
m∠4 = 180 - 122 - 20
m∠4 = 180 - 142
m∠4 = 38
m∠3 and m2 are opposite angles.
Opposite angles are equal.
m∠3 = m∠2 = 122
Now,
m∠1 + m∠2 + 22 = 180
m∠1 + 122 + 22 = 180
m∠1 = 180 - 144
m∠1 = 36
Thus,
The missing values are:
m∠1 = 36°
m∠2 = 122°
m∠3 = 122°
m∠4 = 38°
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Factorise this expression as fully as possible
2xy^2 + 8y
2y(xy+4)
Hope this answers your question!
Answer:
2y(xy+4)
Step-by-step explanation:
First, Distribute
you get 2y(xy+4) because you have to isolate the like terms than find a gcf of the terms
In a geometric sequence, the difference between each pair of consecutive terms must be the same.
The given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.
What is a Sequence?Number sequence is a progression or an ordered list of numbers governed by a pattern or rule. For example -
3, 6, 9, 12, 15
x, x + 2, x + 4, x + 6
Given is the following statement -
"In a geometric sequence, the difference between each pair of consecutive terms must be the same"
The given statement is false as the statement mentioned above is the definition of a arithmetic sequence. In geometric sequence, the ratio of each pair of consecutive terms must be the same. Mathematically -
a[n + 1]/a[n] = r {constant}
Therefore, the given statement "In a geometric sequence, the difference between each pair of consecutive terms must be the same" is false.
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