Answer:
[tex]\bar x = 34.7[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Age} & {Fatalities} & {11 - 20} & {340} & {21-30} & {1527} & {31-40} & {866} & {41-50} & {693} & {51-60} & {423} & {61-70} & {123} \ \end{array}[/tex]
Required
Calculate the mean
The given data is a grouped data. So, we need to calculate the class mid -point first.
This is done by calculating the average of the class intervals.
So, we have:
[tex]\begin{array}{ccc}{Age} & {Fatalities} & {x} & {11 - 20} & {340} & {15.5} & {21-30} & {1527} &{25.5}& {31-40} & {866} & {35.5} & {41-50} & {693} & {45.5} & {51-60} & {423} & {55.5} & {61-70} & {123} & {65.5}\ \end{array}[/tex]
For 11 - 20, the midpoint is: [tex]x =\frac{1}{2}(11+20) = \frac{1}{2}*31=15.5[/tex]
For 21 - 30, the midpoint is: [tex]x =\frac{1}{2}(21+30) = \frac{1}{2}*51=25.5[/tex]
.....
For 61 - 70, the midpoint is: [tex]x =\frac{1}{2}(61+70) = \frac{1}{2}*131=65.5[/tex]
The mean is then calculated as:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{(15.5 * 340) + (25.5 * 1527) + (35.5 * 866) + (45.5 * 693) + (55.5 * 423) + (65.5 * 123)}{340 + 1527 + 866 + 693 + 423 + 123}[/tex]
[tex]\bar x = \frac{138016}{3972}[/tex]
[tex]\bar x = 34.7472306143[/tex]
[tex]\bar x = 34.7[/tex] --- approximated
The mean is approximately 34.7
Composite figures. PLEASE help me identify the area of the figure. Thank you!
Answer:
[tex] 84 \: {cm}^{2} [/tex]
Step-by-step explanation:
Area of the figure = Area of rectangle + Area of trapezoid
[tex] = 18 \times 3 + \frac{1}{2} \{(18 - 11) + 3) \}(9 - 3) \\ \\ = 54 + \frac{1}{2} \{7 + 3 \}6\\ \\ = 54 + 10 \times 3\\ \\ = 54 + 30 \\ \\ = 84 \: {cm}^{2} [/tex]
Select the correct answer.
A figure in the second quadrant is reflected over the y-axis. In which quadrant will the reflected figure appear?
Answer:
It would land on the first quadrant.
Step-by-step explanation:
Help plz:)))I’ll mark u Brainliest
9514 1404 393
Answer:
x = 18
Step-by-step explanation:
The parallel lines cut the transversals proportionally.
(2x -1)/40 = 21/24
2x -1 = 35 . . . . . . . multiply by 40
2x = 36 . . . . . . . . add 1
x = 18 . . . . . . . . . divide by 2
HELP ME PLS I NEED ANSWERS
I need help with this
Answer:
They multiplied by 100
Step-by-step explanation:
1 x 1.5 = 1.5
10 x 1.5 = 15
100 x 1.5 = 150
(25 + 19) + 15 = (19 + 25) + 15
What property is that equation
Answer:
Commutative Property
Step-by-step explanation:
It looks like Associative property which is when you change the GROUP, but actually it’s commutative because it didn’t change any numbers in the group, just the order of where they were.
Associative: (25 + 19) + 15 = (15 + 19) + 25
Commutative: (25 + 19) + 15 = (19 + 25) + 15
It didn’t change the numbers, only the order. Therefore, it would be commutative property
Answer:
25+19=44
44+15=59
19+25=44
44+15=59
10 points and will be marked BRAINLIEST if the answer you give is correct!
Answer:
the one on the bottom and Lewis made one less of whatever Bryan made
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
bryan- 7x4=28
lewis- 6x4=24
28+24=52
i need help asap due tonight
Answer:
The top right one 3(x+4)=30
Step-by-step explanation:
Answer:
The answer should be the one on the top right.
Step-by-step explanation:
So we know that the whole entire model equals 30, and each of the three sections are s+4. So, in order to get 30, the equation has to have something to do with three times s+4. We can eliminate the one on the top left because the model does not have a 12 involved. We can also eliminate the bottom left because it only represents one of the three s+4s. The bottom right can be taken off because the 3 in that equation is only multiplied to s, and not s+4. The top right works because it is saying that s+4 multiplied by 3 times is equal to 30. There you go! I hope this helps❤️
? Help if you know how to do this
Answer:
[tex]x = 2.5[/tex]
Step-by-step explanation:
Given
[tex]AC = 2x - 1[/tex]
[tex]AB = 2x + 1[/tex]
[tex]BC = 2\sqrt{7[/tex]
[tex]\angle A = 60^{\circ}[/tex]
Required
Find x
To find x, we make use of cosine formula which states:
[tex]a^2 = b^2 + c^2 - 2bcCosA[/tex]
In this case:
[tex]BC^2 = AB^2 + AC^2 - 2*AB*BC*CosA[/tex]
Substitute values
[tex](2\sqrt{7})^2 = (2x + 1)^2 + (2x-1)^2 - 2*(2x + 1)*(2x - 1)*Cos(60^{\circ})[/tex]
Evaluate all exponents
[tex]4*7 = (4x^2 + 4x + 1)+(4x^2 - 4x + 1) - 2(4x^2 - 1)*cos(60^{\circ})[/tex]
Open brackets
[tex]28 = 4x^2 + 4x + 1+4x^2 - 4x + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]
Collect Like Terms
[tex]28 = 4x^2 +4x^2+ 4x - 4x+ 1 + 1 - (8x^2 - 2)*cos(60^{\circ})[/tex]
[tex]28 = 8x^2+ 2 - (8x^2 - 2)*cos(60^{\circ})[/tex]
Substitute 0.5 for cos(60)
[tex]28 = 8x^2+ 2 - (8x^2 - 2)*0.5[/tex]
Open bracket
[tex]28 = 8x^2+ 2 - 4x^2 + 1[/tex]
Collect Like Terms
[tex]8x^2- 4x^2 + 2 + 1 - 28 = 0[/tex]
[tex]4x^2 -25 = 0[/tex]
Collect Like Terms
[tex]4x^2 =25[/tex]
Divide both sides by 4
[tex]x^2 =\frac{25}{4}[/tex]
[tex]x^2 =6.25[/tex]
Take positive square root of both sides
[tex]x = \sqrt{6.25[/tex]
[tex]x = 2.5[/tex]
Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times the inverse tangent of the quantity x squared divided by 4, plus C one fourth times the natural log of x to the 4th power plus 16, plus C one fourth times the inverse tangent of the quantity x squared divided by 4, plus C the product of negative one fourth and 1 over the quantity squared of x squared plus 16, plus C
Answer:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]
Step-by-step explanation:
Given
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx[/tex]
Required
Solve
Let
[tex]u = \frac{x^2}{4}[/tex]
Differentiate
[tex]du = 2 * \frac{x^{2-1}}{4}\ dx[/tex]
[tex]du = 2 * \frac{x}{4}\ dx[/tex]
[tex]du = \frac{x}{2}\ dx[/tex]
Make dx the subject
[tex]dx = \frac{2}{x}\ du[/tex]
The given integral becomes:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]
Recall that: [tex]u = \frac{x^2}{4}[/tex]
Make [tex]x^2[/tex] the subject
[tex]x^2= 4u[/tex]
Square both sides
[tex]x^4= (4u)^2[/tex]
[tex]x^4= 16u^2[/tex]
Substitute [tex]16u^2[/tex] for [tex]x^4[/tex] in [tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du[/tex]
Simplify
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
In standard integration
[tex]\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)[/tex]
So, the expression becomes:
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)[/tex]
Recall that: [tex]u = \frac{x^2}{4}[/tex]
[tex]\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c[/tex]
2(a+11)= -3(16-a) one solution, no solution, or infinite solutions
Answer:
the answer is one solution (70)
Step-by-step explanation:
2(a+11)=-3(16-a)
distribute
2a+22=-48+3a
subtract 2a from both sides
22=-48+a
add 48 to both sides
70=a
the answer is one solution (70)
n - 89 > 171. what inequality below true. 1. n=82. 2. n=105. 3. n=268. 4. n=300. 5. n=312
Answer:
1. Assume the contrary, namely that √2 + √3 + √5 = r, where r is a rational number.
Square the equality √2 + √3 = r − √5 to obtain 5 + 2
√6 = r2 + 5 − 2r
√5. It follows
that 2√6 + 2r
√5 is itself rational. Squaring again, we find that 24 + 20r2 + 8r
√30
is rational, and hence √30 is rational, too. Pythagoras’ method for proving that √2 is
irrational can now be applied to show that this is not true. Write √30 = m
n in lowest
terms; then transform this into m2 = 30n2. It follows that m is divisible by 2 and because
2( m
2 )2 = 15n2 it follows that n is divisible by 2 as well. So the fraction was not in lowest
terms, a contradiction. We conclude that the initial assumption was false, and therefore
√2 + √3 + √5 is irrational.
Step-by-step explanation:
P(AB)fxufucufgcidgfyzyfgx
Answer:
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Answer:
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Step-by-step explanation:
Find the value of X
Answer:
18
Step-by-step explanation:
This is a 5 sided shape, aka a pentagon, and we know that five sided shape's angles add up to 540, so our equation is:
(9x-6)+(3x+23)+95+(7x-4)+90=540.
Combine like terms:
We get 25x+90=540
x = 18
PLZZZZZZZZZZ HELP!!!!!!!!
Answer:
b
Step-by-step explanation:
cause a negative number is to the left of zero and a positive to the right
i literally have no clue how to do this can someone help
Peace and love
Peace
Can you help me with my math?
Answer:
y = -3x - 1
Step-by-step explanation:
First find the slope then the Y-intercept
What is the Answer pls help
Answer:48ft
Step-by-step explanation:
Find a, please do not guess or if your not sure. i need help not guesses for points. (it’s geometry)
Answer:
[tex]\huge\boxed{\boxed{a=6}}[/tex]Step-by-step explanation:
to understand thisyou need to know about:trigonometryPEMDASequationtips and formulas:sin(30°)=½sin(x)=opp/hypolet's solve:[tex] step - 1 : define[/tex]
[tex] \sin( {30}^{o} ) = \frac{a}{12} [/tex]
[tex] step - 2 : solve[/tex]
[tex] \tt substitute \: the \: value \: of \: \sin( {30}^{o} ) \\ \tt \frac{1}{2} = \frac{a}{12} [/tex][tex] \tt cross \: multiplication : \\ \tt2a = 12 [/tex][tex] \tt divide \: both \: sides \: by \: 2 : \\ \tt \frac{2a}{2} = \frac{12}{2} \\ \therefore a = 6[/tex]Find the Area of this figure.
Answer:
158 m²
Step-by-step explanation:
I made this into 3 rectangles.
Figure 1:
9•8=72
The 9 is from the 13 m side, but I've taken 4 m off from the overlapping square.
Figure 2:
6•7=42
The 7 is from the 10 m side, but I've taken 4m off from the overlapping square again.
Remaining Area:
If you extend the lines into figures 1 and 2 from the top left corner and bottom right corner vertically, you will get a rectangle that is (11 m) x (4 m). This is not yet accounted for.
11•4=44
Add together: 72 + 42 + 44 = 158
*Note: You could also find the area of the squares a much easier way by subtracting the overlapping part after finding the area of both figures , but this is how I did it*
The triangles are similar. Complete the similarity statement
Answer:
ABC
Step-by-step explanation:
Answer:
YZX ~ ABC
Step-by-step explanation:
For Angle Y, there is one curved line, so you must go to the other triangle and find which angle has one curved line too, in this case that is angle A. Then, Angle Z has three curved lines, and in the other triangle, Angle B has three curved lines, so you now have AB, which only leaves C left. So your final answer is ABC.
For what value of x is the following expression
sinx
undefined for Os x <211?
1+COS X
Answer:
ti 5
Step-by-step explanation:
its 5
If the midpoint of AB Is (5,-4) and the coordinates of Aare (10,-6), then the coordinates of B are
Answer:
Step-by-step explanation:
A(10,6), M(5, -4), B(x,y)
5 = (10+x)/2
x = 0
-4 = (6+y)/2
-8 = 6+y
y = -14
B(0, -14)
The required coordinate of B is given as (0, -2 ).
Given that,
To determine the coordinates of B, If the midpoint of AB Is (5,-4) and the coordinates of A are (10,-6).
What is the midpoint?The midpoint is that point the line whose length from both the ends of the line is equal.
Here,
We have given two coordinates one of the endpoints A of AB and the other is midpoint M i.e. A(10, -6) and M(5, -4).
Definition of midpoint says,
x = [x₁ + x₂] / 2 ; y = [y₁ + y₂] / 2
x₁ = 10, x = 5 , y₁ = -6 , y = -4
now,
5 = [10 + x₂] / 2 ; -4 = [-6 + y₂] / 2
x₂ = 10 - 10 ; y₂ = -8 + 6
x₂ = 0 : y₂ = -2
Thus, the required coordinate of B is given as (0, -2 ).
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Once sales tax is included, a $62 hammock ends up costing $67.58. What is the sales
tax percentage?
NEED ASAP WILL GIVE BRAINLIEST
Answer:
9%
Step-by-step explanation:
subtract 62 from 67.58 to get 67.58-62=5.58divide 62 by 5.58and your final answer is 9%A blogger has 400 subscribers to her blog in January. The number of subscribers has grown by a factor of 1.5 every month since then. Write a sequence to represent the number of subscribers in the 3 months that followed.
Answer:
Since a blogger has 400 subscribers to her blog in January, and the number of subscribers has grown by a factor of 1.5 every month since the, to write a sequence to represent the number of subscribers in the 3 months that followed, the following reasoning has to be made:
January: 400 subscribers
February: 400 x 1.5 = 600 subscribers
March: 600 x 1.5 = 900 subscribers
April: 900 x 1.5 = 1,350 subscribers
The sequence to represent the number of subscribers in the 3 months that followed are :
First month = 600 subscribers
Second month = 900 subscribers
Third month = 1350 subscribers
The blogger has 400 subscriber to her blog in January.
The number of subscriber has grown by a factor of 1.5 every month since then.
Therefore, the sequence to represent the number of subscribers in the 3 months that followed can be calculated below
January Subscribers = 400
February Subscribers = 1.5 × 400 = 600
March Subscribers = 1.5 × 600 = 900
April subscribers = 1.5 × 900 = 1350
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Which of these equations are true when the value of y is 27?
I. −9 + y = 18
II. −18 + y = −45
III. 5y = 135
IV. 2y = 29
Answer:
I. -9 + y = 18
Step-by-step explanation:
Double-check to see if I was correct
The equations I. and III. satisfies the condition when y = 27
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The value of y = 27
So , substituting the value of y in all of the given equations , we get
I.
-9 + y = 18
when y = 27
Substituting the value of y , we get
-9 + 27 = 18
18 = 18
So , I. satisfies the condition and the equation is TRUE
II.
-18 + y = 45
when y = 27
Substituting the value of y , we get
-18 + 27 = 45
9 ≠ 45
So , II. does not satisfy the condition and the equation is FALSE
III.
5y = 135
when y = 27
Substituting the value of y , we get
5 x 27 = 135
135 = 135
So , III. satisfies the condition and the equation is TRUE
IV.
2y = 49
when y = 27
Substituting the value of y , we get
2 x 27 = 29
54 ≠ 29
So , IV. does not satisfy the condition and the equation is FALSE
Hence , the equations I. and III. are TRUE
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? points
Simplify completely :
5x - 20
9x - 36
Answer:
5/9
Step-by-step explanation:
what is the slope of a line that passes through the point (3,29.25)
Answer:
The slope is 9 3/4 or 9.75
Step-by-step explanation:
slope= rise/run or y/x
29.25/3=9.75 or 9 3/4
What is the equation of a line, in general form, that passes through point (1,-2) and has a siope of 1/3?
9514 1404 393
Answer:
x -3y -7 = 0
Step-by-step explanation:
The general form of the equation for a line is ...
ax +by +c = 0
where a, b, c are mutually prime and the leading coefficient is greater than zero.
__
The general form equation for a line with slope m = rise/run through point (h, k) can be found by simplifying ...
rise(x -h) -run(y -k) = 0 . . . . where run has the sign of the slope
For the given point and slope, we have ...
1(x -1) -3(y -(-2)) = 0
x -3y -7 = 0
4) James Madison was born on March
16, 1751. John F. Kennedy was born on
May 29, 1917. If they were both still
alive today, how much older would
James Madison be than John F.
Kennedy?
Answer:
166 years older.
Step-by-step explanation: Subtract 1751 from 1917
