Find the mean of the data summarized in the given frequency distribution . Compare the computed mean to the actual mean of 57.6 Degrees.
Low Temperature ( F) 40-44 45-49 50-54 55-59 60-64 Frequency 2 5 9 6 3
Answers
The mean of the frequency distribution is 52.6° F. The computed mean of 52.6° F is lesser than the actual mean of 57.6° F.
What is the mean of a distribution?The mean of the distribution can be defined as the average value of the distribution, It can be expressed as the total sum of all the observed values divided by the frequency of the distribution.
From the parameters given:
Low-temperature Frequency
40 - 44 2
45 - 49 5
50 - 54 9
55 - 59 6
60 - 64 3
The first thing to do is to determine the class midpoint. The class midpoint is the sum of the class interval divided by 2.
The class midpoint of 40 - 44 is \(\mathbf{\dfrac{40 + 44}{2} = 42}\)
The class midpoint of 45 - 49 is \(\mathbf{\dfrac{45 + 49}{2} = 47}\)
The class midpoint of 50 - 54 is \(\mathbf{\dfrac{50 + 54}{2} = 52}\)
The class midpoint of 55 - 59 is \(\mathbf{\dfrac{55 + 59}{2} = 57}\)
The class midpoint of 60 - 64 is \(\mathbf{\dfrac{60 + 64}{2} = 62}\)
Now, the table can be represented as:
Low-temperature Frequency x
40 - 44 2 42
45 - 49 5 47
50 - 54 9 52
55 - 59 6 57
60 - 64 3 62
The mean can now be determined as follows:
\(\mathbf{\bar x = \dfrac{\sum fx}{\sum f }}\)
\(\mathbf{\bar x = \dfrac{(2 \times 42)+ (5 \times 47) + ( 9\times 52) +(6\times 57) + (3 \times 62)}{2 + 5 + 9 + 6 + 3 }}\)
\(\mathbf{\bar x = \dfrac{1315}{25}}\)
\(\mathbf{\bar x = 52.6}\)
Therefore, we can conclude that the mean of the frequency distribution is 52.6° F. The computed mean of 52.6° F. is lesser than the actual mean of 57.6° F
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Related Questions
the bill at the restaurant is $18.79 .estimate the amount to leave as 10% tip.
solve to show solutions
Answers
Step-by-step explanation:
The question should be:
"The bill at the restaurant was $18.79 estimate the amount to leave as a 10% tip. A. $2.00 B. $3.00 C. $9.00 D. $21.00"
The general case is:
When we have a quantity A (where A is the 100%) the X% of A is:
(X%/100%)*A
In this problem, we have a bill of $18,79 and we want to leave a 10% tip.
Then $18,79 is the 100% we want to see how much is the 10% of $18,79
If we use the above equation we get:
Tip = (10%/100%)*$18,79 = $1,879
The option that approaches the best to this amount is option A, $2.00
Then the tip should be $2
The correct option is A.
What is the value of x? Round only your final answer to the nearest hundredth.
Answers
The length of the hypotenuse is 12.52 yards.
Given that a right triangle, we need to find the value of the hypotenuse x,
Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle.
We can evaluate the third side using the Pythagoras theorem, given the measure of the other two sides. We can use the abbreviated form of trigonometric ratios to compare the length of any two sides with the angle in the base.
Let us consider a right-angled triangle with one of its acute angles to be x. Then the cosine formula is, cos x = (adjacent side) / (hypotenuse), where "adjacent side" is the side adjacent to the angle x, and "hypotenuse" is the longest side (the side opposite to the right angle) of the triangle.
We know that, the cosine of the angle is the ratio of the base to the hypotenuse,
So,
Cos 37° = 10 / x
x = 10 / Cos 37°
x = 12.52
Hence the length of the hypotenuse is 12.52 yards.
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For F(x)=x^2+8 and g(x)=x^2-8 , find
( f o g) (x)
(g o f) (x),
(f o g)(2)
thanks!!
Answers
The final answer is (f o g)(x) = x^4 - 16x^2 + 72
(g o f)(x) = x^4 + 16x^2 + 56
(f o g)(2) = 24
To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.
(f o g)(x):
To find (f o g)(x), we substitute g(x) into f(x):
(f o g)(x) = f(g(x))
Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:
(f o g)(x) = f(g(x)) = f(x^2 - 8)
Now we replace x in f(x^2 - 8) with x^2 - 8:
(f o g)(x) = (x^2 - 8)^2 + 8
Simplifying further:
(f o g)(x) = x^4 - 16x^2 + 64 + 8
(f o g)(x) = x^4 - 16x^2 + 72
Therefore, (f o g)(x) = x^4 - 16x^2 + 72.
(g o f)(x):
To find (g o f)(x), we substitute f(x) into g(x):
(g o f)(x) = g(f(x))
Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:
(g o f)(x) = g(f(x)) = g(x^2 + 8)
Now we replace x in g(x^2 + 8) with x^2 + 8:
(g o f)(x) = (x^2 + 8)^2 - 8
Simplifying further:
(g o f)(x) = x^4 + 16x^2 + 64 - 8
(g o f)(x) = x^4 + 16x^2 + 56
Therefore, (g o f)(x) = x^4 + 16x^2 + 56.
(f o g)(2):
To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:
(f o g)(2) = 2^4 - 16(2)^2 + 72
(f o g)(2) = 16 - 64 + 72
(f o g)(2) = 24
Therefore, (f o g)(2) = 24.
In summary:
(f o g)(x) = x^4 - 16x^2 + 72
(g o f)(x) = x^4 + 16x^2 + 56
(f o g)(2) = 24
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The manager of a pizzeria collected data from customers on whether they prefer cheese, veggie, or pepperoni pizza and whether they prefer thin or regular crust pizza. The two-way table below shows the data collected.
Which association does the two-way table suggest?
A. Those who prefer regular crust pizza tend to prefer cheese pizza.
B. Those who prefer regular crust pizza tend to prefer pepperoni pizza.
C. None of the associations listed are correct.
D. Those who prefer thin crust pizza tend to prefer pepperoni pizza.
Answers
The correct option is D. Those who prefer regular crust pizza tend to prefer pepperoni pizza are shown by two-way table.
Explain about the term two-way table?a table where each cell shows the frequency (as well as proportion) obtained for that particular row and column combination for said two variables.
The rows represent the classifications for one classification variable, the figures below show the categories of either a second category variable.
Customers' preferences for cheese, veggie, or pepperoni pizza, as well as for thin or standard crust, were gathered by the pizzeria management. The data gathered are displayed in the two-way table below.In the given data, the number of people taking pepperoni pizza are maximum for those who prefer regular crust pizza.
Thus, according to a two-way table, pepperoni pizza tends to be preferred by people who favor regular crust.
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You have two recipes that together use a pound of butter. One recipe takes a 1/4 pound more than the other one. How much butter does each recipe use?
Answers
Answer:
First recipe needs = 3/8
Second recipe needs = 5/8
Step-by-step explanation:
Given:
Two recipes needs butter = 1 pound
One recipe needs 1/4 pound more
Find:
Each recipe needs butter
Computation:
Assume;
First recipe needs = x
Second recipe needs = x + (1/4)
Two recipes needs butter = First recipe needs + Second recipe needs
x + x + (1/4) = 1
2 x = 1 - (1/4)
2 x = 3/4
x = 3/8 pound
First recipe needs = 3/8
Second recipe needs = x + (1/4) = (3/8) + (1/4) = 5/8
Second recipe needs = 5/8
Which of the following equations is 2x + 3y = 6 written in slope-intercept form.
oy--(2/3)x + 6
y=-2/3)x+ 2
y=-(3/2)x+ 2
Answers
The equation in the slope-intercept form is y = (-2/3)x + 2. Then the correct option is B.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The equation is given below.
2x + 3y = 6
Then arrange the equation in the slope-intercept form. Then we have
3y = -2x + 6
y = (-2/3)x + 2
Then the correct option is B.
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The equation of a circle is:
(x-2)^2 + (y+4)^2 = 25
Part A:
Determine the center and the radius of the circle.
...is this correct?
Answers
The requried center and radius of the given circle are (2, -4) and 5.
The standard equation of a circle is given as,
(x - h)² + (y - k)² = r²
Where, (h, k) is the center of the circles and r is the radius of the circle,
The equation of the given circle is,
(x - 2)² + (y + 4)² = 25
Comparing the above equation with the standard equation we have,
(h, k) = (2, -4)
r² = 5²; r =5
Thus, the requried center and radius of the given circle is (2, -4) and 5.
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Un comerciante tiene en cartera una letra de 14000 con vencimiento a 2 años y le somete a un descuento bancario 1 año y 8 meses antes de su vencimiento a una taza de 14%anual con capitalización trimestral ¿cuanto recibira el propetario de la letra ?
Answers
Answer:
dud
Step-by-step explanation:
fjfn
kgoipyx
vbjjkkkkkkjjjjhcblxkcjl
help please and fast!
Answers
= [3x3^-2x(-2)^6/2x3^-1x(-2)^5]^2 = 1
Answer:
1
Step-by-step explanation:
\([\frac{3a^{-2} b^6}{2a^{-1}b^5}] ^{2} \\=[1.5 a^{-2-(-1)} b^{6-5}]^2\\=[1.5a^{-2+1}b]^2\\=[1.5a^{-1}b]^2\\\\Substituting\ a=3,b=-2, we\ get,\\=[1.5*3^{-1}*-2]^2\\=[1.5*1/3*-2]^2\\=[1/2*-2]^2\\=[-1]^2\\=1\)
This is the table answer this please
Answers
Answer:
so answer is b.42
Step-by-step explanation:
3 7
6 14
9 21
every time width increase by 3 length increase by 7 so:
12 28
15 35
18 42
help!!! Pleasee thank youuuu
Answers
Answer:
a
Step-by-step explanation:
it is the reflection or mirror image
A teacher is making 7 identical supply boxes
for each table in her classroom. Each box
contains some pencils and 11 pens. The
teacher uses a total of 182 pencils and pens.
Determine the number of pencils that are in
each box.
Answers
Answer:
26
Step-by-step explanation:
182 pencils devided by 7 identical boxes
182÷7
=26 pencils are in each box
Answer:
15 pencils in each box
Step-by-step explanation:
If each box has 11 pens,then there are 77 pens
In total 182 pencils and pens
182-77 = 105 (105 pencils)
105/7 = 15
15x7 = 105
11x7 = 77
105 +77 = 182
what is the value of x^2 - 6x + 9 when x = 2 + i?
Answers
The Expression x^2 - 6x + 9 when x = 2 + i is -2i
To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:
(2 + i)^2 - 6(2 + i) + 9
Simplifying the first term, we get:
(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2
Since i^2 = -1, we can substitute that in and simplify further:
(2 + i)^2 = 4 + 4i - 1 = 3 + 4i
Now we substitute this into the original expression:
(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9
Simplifying further, we get:
= 3 + 4i - 12 - 6i + 9
= 0 - 2i
= -2i
Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.
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Use the drop-down menus to complete each statement about the functions f and g.
Note: Exponential functions are of the form f(x) = abx.
The function f is (linear, exponential, neither)
.
Consecutive (differences, quotients)
are (constant, nonconstant )
.
The function g is (options are same for the rest)
.
Consecutive
are
.
Answers
The function f(x) is the linear and the function g(x) is the exponential. Then the equations are f(x) = 6x and g(x) = 3(2)ˣ.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The functions f(x) and g(x).
The table is shown below.
Let the function f(x) be the linear function and the function g(x) be the exponential. Then we have
Then the function f(x) will be
f(x) = mx + c
Then we have
12 = 2m + c
6 = m + c
Then we have
m = 6 and c = 0
Then the equation will be
f(x) = 6x
Then the function g(x) will be
g(x) = abˣ
Then we have
48 = ab⁴
24 = ab³
We have
a = 3 and b = 2
Then the function g(x) will be
g(x) = 3(2)ˣ
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Find m angle c 14.5in 97.5 degrees and 13.7in (please solve step for step pleasee )
Answers
Based on law of sine, the value of angle C is equal to 94.5 degree.
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
\(\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}\)
\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)
we have, by law of sines,
We will use the law of sines to find c as;
sin c sin 97.5
--------------- = -------------
14.5 13.7
(13.7)sin c= 14.5 sin 97.5
sin c = 14.5 sin 97.5 / (13.7)
sin c = - 0.1168
Angle c = 94.5
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(I'll be giving brainliest and extra points to who ever helps me!!)
Solve one and three fourths times two fourths.
A) fourteen sixteenths
B) fifteen sixteenths
C) seventeen sixteenths
D) eighteen sixteenths
Answers
Answer:
A. fourteen sixteenths
Step-by-step explanation:
\(1\frac{3}{4} x \frac{2}{4}\)
\(\frac{7}{4} x \frac{2}{4}\)
\(\frac{14}{16}\)
Hope I helped you out!
~PumpkinSpice1
♥☼☺
Answer:
A it didnt let me answer at first and it dose now
Step-by-step explanation:
What is the remainder and quotient of 23 divided by 861
Answers
Answer:
37 r10
explanation
0 3 7
2 3 L 8 6 1
− 0
8 6
− 6 9
1 7 1
− 1 6 1
1 0
Mr. Hooper has a tree in his front yard that grows every year. If the tree was 3 feet tall when he planted it 6 years ago , what is the current height of the tree in terms of f?
A. 3f + 6 feet
B. 6f + 3 feet
C. 3f + 18 feet
D. 6f + 18 feet
Answers
The height of the tree after 6 years can be expressed as "3 feet + 6f feet."
The correct answer is A. 3f + 6 feet.
To determine the current height of the tree in terms of "f,"
let's analyze the given information.
We know that the tree was initially 3 feet tall when it was planted 6 years ago.
Since the tree grows every year, we can assume that its growth rate is consistent.
Let's denote the current height of the tree as "h" (in feet).
After 6 years, the tree has grown by a certain amount, which we'll represent as "6f" (6 years multiplied by the growth rate "f").
Therefore, the height of the tree after 6 years can be expressed as "3 feet + 6f feet."
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match the function equations to their graphs. please help!
Answers
Answer:
y goes from the top to the bottom postive to negative. Then x is from left to right. The left is negative the right is postive.
Step-by-step explanation:
Make frequency tables for the following data sets. Include columns for relative frequency. Also, make a bar graph for the frequency
Final grades of 30 students in a math class: AAAAAABBBBBBCCCCCCCCCCFFF
Answers
Solve for x
0.5(5-7x)=8-(4x+6)
Answers
Answer:
Problem: 0.5(5-7x)=8-(4x+6)
Answer: x= -1
Two sides of a triangle have lengths 43 and 67. The angle included between these sides measures 27degrees°. To the nearest hundreth, what is the length of the third side?
Answers
The length of the third side of the triangle, to the nearest hundredth, is approximately 54.75 units.
1. We have a triangle with two known side lengths: 43 and 67 units.
2. The angle included between these sides measures 27 degrees.
3. To find the length of the third side, we can use the Law of Cosines, which states that \(c^2 = a^2 + b^2\) - 2ab * cos(C), where c is the third side and C is the included angle.
4. Plugging in the known values, we get \(c^2 = 43^2 + 67^2\) - 2 * 43 * 67 * cos(27).
5. Evaluating the expression on the right side, we get \(c^2\) ≈ 1849 + 4489 - 2 * 43 * 67 * 0.891007.
6. Simplifying further, we have \(c^2\) ≈ 6338 - 5156.898.
7. Calculating \(c^2\), we find \(c^2\) ≈ 1181.102.
8. Finally, taking the square root of \(c^2\), we get c ≈ √1181.102 ≈ 34.32.
9. Rounding to the nearest hundredth, the length of the third side is approximately 34.32 units.
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Calculator What is the approximate volume of the sphere? Use 3.14 to approximate pi and round to the nearest hundredth if necessary. 36 in³ 84.78 in³ O 113.04 in³ O339.12 in 3 in
Answers
The volume of the sphere can be calculated using the formula V = 4/3πr³
What is a sphere?A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. It is a perfectly-round 3D shape with one continuous curved surface
We have a sphere.
Since the dimensions of a sphere are not given, we will assume it. Assume the radius of sphere be [r]. Then the approximate value of the volume of the sphere can be calculated using the formula -
V = 4/3πr³
Where -
[r] is the radius of sphere
Therefore, the volume of the sphere can be calculated using the formula V = 4/3πr³
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Hello everyone-SOLVING nonlinear system of equations- ALGEBRA 1
Answers
The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.
To solve the nonlinear system of equations:
Equation 1: \(y = -x^2 + 7\)
Equation 2: y = 2x + 4
We can equate the right sides of both equations since they both represent y.
\(-x^2 + 7 = 2x + 4\)
To simplify the equation, we can rearrange it to be in the standard quadratic form:
\(x^2 + 2x - 3 = 0\)
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:
(x + 3)(x - 1) = 0
From this equation, we get two possible solutions:
x + 3 = 0 => x = -3
x - 1 = 0 => x = 1
Now, we substitute these x-values back into either equation to find the corresponding y-values.
For x = -3:
y = 2(-3) + 4
y = -6 + 4
y = -2
For x = 1:
y = 2(1) + 4
y = 2 + 4
y = 6
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Plsssss Help i have no idea how to do this
Answers
Answer:
500
Step-by-step explanation:
someone please answer this its confusing me
Answers
the line AB will be congruent to line DC so 8t + 7 = 9t - 2 which gives you t = 9
line AD will also be congruent to line BC so 4s + 1 = 2s + 25 which gives you s = 12
a teacher created two way table for four different classrooms the tables track whether each student has an after school job or not and whether they are in art class only, music class only, both classes, or neither class.
Answers
Answer:
1) Classroom 2
2) Classroom 3
3) Classroom 2
4) Classroom 4
When you half a whole number that ends in 6, you always get a number
ends in 3."
Answers
Answer:
This actually is false, it doesn't always work.
Step-by-step explanation:
Such as,
256 x 1/2 =
128.
The last digit isn't a 3, it's an 8.
Another Example,
176 x 1/2 =
88.
The last digit is also an 8 here, and not a 3.
It does work for some equations, but not for most of them, hope this helps!
Could someone please help! I will give brainlyist!
Answers
Answer: It would be 7.5.
Answer:
the answer would be 7 1/2
Step-by-step explanation:
convert the mixed number into fractions so it would become :
3/1 ÷ 2/5
multiply :
3/1 × 2/5 which equals 15/2
simplify and get : 7 1/2
Hello! I really need help on these two questions please!
Answers
Answer:
1. y-4=1/3(x-3)
used (3,4)
2. y-7=3(x-3)
used (3,7)