The approximate mean age is [tex]\(45.15\)[/tex] years, and the approximate standard deviation for age is [tex]\(9.22\)[/tex] years, both rounded to two decimal places.
To approximate the mean and standard deviation for the age groups provided, we can calculate the weighted average based on the midpoint of each age group and use the formula for the standard deviation of a weighted dataset.
First, calculate the midpoints of the age groups:
- For 25-34 years: midpoint = (25 + 34) / 2 = 29.5
- For 35-44 years: midpoint = (35 + 44) / 2 = 39.5
- For 45-54 years: midpoint = (45 + 54) / 2 = 49.5
- For 55-64 years: midpoint = (55 + 64) / 2 = 59.5
Next, calculate the weighted mean using the formula:
[tex]\[ \text{Weighted Mean} = \frac{\sum (\text{Midpoint} \times \text{Number of People})}{\sum \text{Number of People}} \][/tex]
[tex]\[ \text{Weighted Mean} = \frac{(29.5 \times 22.1) + (39.5 \times 31.5) + (49.5 \times 37.7) + (59.5 \times 25.3)}{22.1 + 31.5 + 37.7 + 25.3} \][/tex]
[tex]\[ \text{Weighted Mean} \approx \frac{651.45 + 1244.25 + 1867.35 + 1503.35}{116.6} \][/tex]
[tex]\[ \text{Weighted Mean} \approx \frac{5266.4}{116.6} \][/tex]
[tex]\[ \text{Weighted Mean} \approx 45.15 \text{ years (approx)} \][/tex]
Now, calculate the standard deviation using the formula:
[tex]\[ \text{Weighted SD} = \sqrt{\frac{\sum (\text{Number of People} \times (\text{Midpoint} - \text{Weighted Mean})^2)}{\sum \text{Number of People}}} \][/tex]
[tex]\[ \text{Weighted SD} = \sqrt{\frac{(22.1 \times (29.5 - 45.15)^2) + (31.5 \times (39.5 - 45.15)^2) + (37.7 \times (49.5 - 45.15)^2) + (25.3 \times (59.5 - 45.15)^2)}{116.6}} \][/tex]
[tex]\[ \text{Weighted SD} \approx \sqrt{\frac{9919.575}{116.6}} \][/tex]
[tex]\[ \text{Weighted SD} \approx \sqrt{85.004} \][/tex]
[tex]\[ \text{Weighted SD} \approx 9.22 \text{ years (approx)} \][/tex]
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ZX is the perpendicular bisector of wY, and YZ = 13.75. Find wz.
The required values are WZ = 13.75 and YZ = 27.
What is a perpendicular bisector?A perpendicular bisector is defined as a line that divides an angle into two equal angles. Draw the given angle first, then cut it in half, and then draw the angle's bisector.
As per question 1,
We have been given that ZX is the perpendicular bisector of WY
YZ = 13.75
13.75 + 13.75 = 27.5
27.5 / 2 = 13.75
WZ = 13.75
As per question 2,
We have been given that ZX is the perpendicular bisector of WY
WZ = 4n - 13 and YZ = n + 17
To find YZ
According to the property of the perpendicular bisector,
WZ = YZ
4n - 13 = n + 17
4n - n = 17 + 13
3n = 30
n = 30/3
n = 10
Substitute the value of n = 10 in YZ = n + 17
So, YZ = 10 + 17 = 27
Thus, the required values are WZ = 13.75 and YZ = 27.
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Can anyone help with my math problems because I need help and you need to be quick. I will mark brainliest.
Please answerrrr I need it desperately and please EXPLAIN how.!!
Answer:
B
Step-by-step explanation:
The opposite of negative one half is the one half and the opposite of 5/2 is -5/2, or -2.5
Check the picture below.
Pls help me with this!
Step-by-step explanation:
5-in 5-in five interest answer
If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (x)?
Question:
If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (x)?
h (x) = StartFraction x + 5 Over 11 EndFraction
h (x) = StartFraction 11 Over x minus 1 EndFraction
h (x) = StartFraction 11 Over x minus 4 EndFraction
h (x) = StartFraction 11 Over x minus 3 EndFraction
Answer:
Option C: [tex]h(x)=\frac{11}{x-4}[/tex] has the same domain as [tex]$(m \circ n)(x)$[/tex]
Explanation:
It is given that [tex]m(x)=\frac{x+5}{x-1}[/tex] and [tex]n(x)=x-3[/tex]
Let us find the domain of [tex]$(m \circ n)(x)$[/tex]
[tex]$\begin{aligned}(m \circ n)(x) &=m(n(x))\\&=m(x-3) \\ &=\frac{(x-3)+5}{(x-3)-1} \\ &=\frac{x+2}{x-4} \end{aligned}$[/tex]
Now, let us equate the denominator equal to zero to determine the domain.
[tex]$x-4=0$[/tex]
[tex]x=4[/tex]
Thus, the function becomes undefined at the point [tex]x=4[/tex]
Hence, the domain of [tex]$(m \circ n)(x)$[/tex] is [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Now, we shall find the function which has the same domain as [tex]$(m \circ n)(x)$[/tex]
Option A: [tex]h(x)=\frac{x+5}{11}[/tex]
The function h(x) has the domain of set of all real numbers [tex]$-\infty<x<\infty$[/tex]
Thus, the interval [tex](-\infty,\infty)[/tex] is not the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Hence, Option A is not the correct answer.
Option B: [tex]h(x)=\frac{11}{x-1}[/tex]
Equating the denominator equal to zero, the function becomes undefined at the point [tex]x=1[/tex]
Thus, the function h(x) has the domain of [tex]$(-\infty,-1) \cup(-1, \infty)$[/tex] is not the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Hence, Option B is not the correct answer.
Option C: [tex]h(x)=\frac{11}{x-4}[/tex]
Equating the denominator equal to zero, the function becomes undefined at the point [tex]x=4[/tex]
Thus, the function h(x) has the domain of [tex]$(-\infty, 4) \cup(4, \infty)$[/tex] is the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Hence, Option C is the correct answer.
Option D: [tex]h(x)=\frac{11}{x-3}[/tex]
Equating the denominator equal to zero, the function becomes undefined at the point [tex]x=3[/tex]
Thus, the function h(x) has the domain of [tex]$(-\infty,3) \cup(3, \infty)$[/tex] is not the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]
Hence, Option D is not the correct answer.
Answer:
It’s C
Step-by-step explanation:
YOU PROBABLY CAN'T ANSWER THIS :/
Using the exponential function 2x + 3, what is the average rate of change between the values 1 ≤ x ≤ 5?
explain your answer step by step
Rate of change of the function: 60
Step-by-step explanation:
The exponential function in this problem is
[tex]f(x)=2^{x+3}[/tex]
The rate of change of a function between a certain interval [tex]x_1 \leq x \leq x_2[/tex] is given by
[tex]r=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
where
[tex]f(x_1)[/tex] is the value of the function calculated in [tex]x_1[/tex]
[tex]f(x_2)[/tex] is the value of the function calculated in [tex]x_2[/tex]
In this problem, the interval is
[tex]1\leq x \leq 5[/tex]
So we have:
[tex]f(x_1)=f(1)=2^{1+3}=2^4=16[/tex]
and
[tex]f(x_2)=f(5)=2^{5+3}=256[/tex]
Therefore, the rate of change is:
[tex]r=\frac{256-16}{5-1}=60[/tex]
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Write the Contrapositive of the statement Below.⬇
If you have, 400$, then you can afford a new laptop computer.
Answer:
If you can't afford a new laptop computer, then you haven't got 400$.
Step-by-step explanation:
The contrapositive is:
If A implies B then not B implies not A.
3=3/4(b-8)
Please help me thank you!
So you need to isolate/get "b" by itself in the equation:
[tex]3=\frac{3}{4}(b-8)[/tex] Distribute/multiply 3/4 into (b - 8)
[tex]3=(\frac{3}{4}(b))+(\frac{3}{4}(-8))[/tex]
[tex]3=(\frac{3}{4} b)+(-6)[/tex] Don't know which goes into the parentheses....think the one above makes more sense...maybe....sorry
[tex]3=\frac{3}{4} b-6[/tex] Add 6 on both sides
[tex]9=\frac{3}{4} b[/tex] Multiply the reciprocal of 3/4 to get rid of the fraction and get b by itself, which would be 4/3 [basically flipping the fraction or switching the numerator and the denominator]
[tex]\frac{36}{3} =b[/tex] Simplify the fraction
12 = b
List the next four multiples of the fraction 3/5
Answer:
6/10,9/15,12/20,15/25
Step-by-step explanation:
Solve the equation 11x + 7 = 73?
Answer:
6
Step-by-step explanation:
If 5 worksites take 31.5 hours to prepare, how long will it take to prepare 13 worksites
(Answer to be in hours pls)
Answer:
81.9 hours.
Step-by-step explanation:
5 work sites take 31.5 hours to prepare, so
1 work sites take 31.5 / 5 hours to prepare, and
13 work sites take . (31.5 * 13) / 5 hours to prepare
= 409.5 / 5
= 81.9 hours.
a rectangle has a perimeter of 204 feet. Its length is six feet longer that twice its width. find the dimensions
Answer:
The length of the rectangle is 70 cm
The width of the rectangle is 32 cm
Step-by-step explanation:
Given:
perimeter of the rectangle = 204 feet
Its length is six feet longer that twice its width
To Find:
The dimensions of the rectangle = ?
Solution:
Let the width of the rectangle be x
Then its length is six feet longer that twice its width.
That is length = 6 + 2x
Now we know that the perimeter of the rectangle is
perimeter = 2(length + width)
204 = 2(6+2x+x)
204 = 2(6+3x)
204 = 12 +6x
204 - 12 = 6x
192 = 6x
x =[tex]\frac{192}{6}[/tex]
x = 32
Thus the width is 32 cm
Its length is
=6 + 2x
=6 + 2(32)
=6 + 64
= 70 cm
convert the rate 175 miles per 5 gallons to feet per quart.
Answer: 46200 feet per quart.
Step-by-step explanation:
We know that 1 gallon = 4 quarts
1 mile = 5280 feet
Therefore , 5 gallons = 5 x 4 quarts
= 20 quarts (i)
175 miles = 175 x 5280 feet
i.e. 175 miles = 924000 feet (ii)
Now , 175 miles per 5 gallons = [tex]\dfrac{\text{ 175 miles }}{\text{5 gallons}}[/tex]
[tex]=\dfrac{ 924000 \text{ feet}}{\text{20 quarts}}[/tex] [From (i)and (ii)]
[tex]\dfrac{46200\text{ feet }}{1\text{ quart}}\\\\=46200\text{ feet per quart}[/tex]
Hence, 175 miles per 5 gallons = 46200 feet per quart.
Answer:
175 miles per 5 gallons = 46200 feet per quart.
What is the area of the following circle?
the diameter is 10.
Answer: The area of the circle with a diameter of 10 cm is 78.5 cm2.
Answer: 78.5 units²
Step-by-step explanation: To find the area of a circle, start with the formula for the area of a circle.
Area = πr²
Notice that here, we're given the diameter instead of the radius. It's important to understand that the radius is equal to half of the diameter so the radius of this circle will be equal to half of 10 or 5.
So plugging into the formula, we have (π)(5)².
A common mistake is to plug 10 into the formula but remember that we must plug in the radius and not the diameter.
Multiplying, (5)² is equal to 5 x 5 or 25 so we have 25π.
So the area of the circle is 25π.
Now, remember that π is approximately equal to 22/7 or 3.14 so we can estimate the area of the circle by plugging in 3.14 for π.
So we have (25)(3.14) which is equal to 78.5 units².
Since there were no labels, I just add units to the end.
So the area of the circle is approximately equal to 78.5 units².
Molly is saving money to buy a new bike that costs $189. He has save $99 so far. He plans on saving $10 each week. Write and solve an equations to determine after how many weeks Molly will have enough money to buy the bike.
Answer: Molly will have to save $10 each week for 9 weeks to get $189.
Step-by-step explanation:
Start at $99, count $10 every week until you get $189. Your answer is 9 weeks.
Two cars start from towns 805 miles apart and travel toward each other. They meet after 7 hours. Find the speed of each car if one travels 15 mph faster than the other.
Answer:
One car was going 50 mph and the other was going 65 mph.
Step-by-step explanation:
At a basketball practice you made 59 out of 80 shots. What percentage did you score
Answer:
You have scored 73.75 percentage
Step-by-step explanation:
Given:
Total number of shots = 80
Total number shot made = 59
To find:
The percentage of the score = ?
Solution:
The percentage of the score = [tex]\frac{\text{number of shots made}}{\text {total number of shots}} \times 100[/tex]
Now on substituting the values
The percentage of the score =[tex]\frac{59}{80} \times 100[/tex]
The percentage of the score =[tex]0.7375 \times 100[/tex]
The percentage of the score = 73.75 %
What is the solution to the system of equations below?
y=3x-4 and Y =-2x-9
A(-2, -5)
B(-2,-3)
C(2,-3)
D(2,-13)
C(2,-3)
That is your answer
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My answer might be wrong
9. What is the area of the largest square?
A=2
A=36units2
A=64units2
Answer:
If you mean Area=2 and Area=36units times 2 and Area=64units times 2, then the answer is that A = 64units times 2 would be the largest square.
Step-by-step explanation:
The larger the area, the larger the square. The first square has an area of 2. The second square has an area of 72, and the third square has an area of 128, so the third square is the biggest.
I really don't get it can you give me the answer then explain why it is that one please
Answer:
[tex]\frac{100}{9}[/tex] is the answer.
Step-by-step explanation:
Well the first thing we would do is simplify all the exponents first inside the parenthesis. So 2^-3 is equal to 1/8. To solve negative exponents you would just divide the number instead of multiply, so 2 divided by 2 divided by 2 is equal to ⅛ or .125
Next would be to do the 2^-9. This would equal 1/512
Now would be to simplify 5^0. Anything to the power of 0 is always one. So now we simplify all the products meaning 7*5*2 and 7*3.
Now we would simplify both fractions.
The picture are pretty much self explanatory. If you have any questions feel free to ask in the comments - Mark
Also when you have the chance please mark me brainliest.
Answer:
e (i said this so the other dude could be mark brainlist)
Step-by-step explanation:
Simplify : a) [tex]\sqrt{x} 0.49x^1^8[/tex] when x<0
Simplify : b) [tex]15\sqrt{x} 0.16c^1^2[/tex] x can be anything
(a) The simplified expression is [tex]\[-0.49 \cdot |x|^{18.5} \cdot i\][/tex]. (b) The simplified expression remains [tex]\[15\sqrt{x} + 0.16c^{12}\][/tex].
Let's simplify the given expressions step-by-step.
a) Simplify [tex]\(\sqrt{x} \cdot 0.49x^{18}\) for \(x < 0\)[/tex]
Since [tex]\(x < 0\), \(x\)[/tex] is negative. This affects the interpretation of [tex]\(\sqrt{x}\)[/tex] in the real numbers because the square root of a negative number is not real. However, if we consider complex numbers, we need to include the imaginary unit [tex]\(i\).[/tex]
Given:
[tex]\[\sqrt{x} \cdot 0.49x^{18}\][/tex]
First, let's express [tex]\(\sqrt{x}\)[/tex] in terms of the imaginary unit:
[tex]\[\sqrt{x} = \sqrt{|x|} \cdot i\][/tex]
Next, rewrite \(x^{18}\):
[tex]\[x^{18} = (x^2)^9 \\= |x|^{18} \cdot (-1)^9 \\= -|x|^{18}\][/tex]
Thus, the expression becomes:
[tex]\[\sqrt{|x|} \cdot i \cdot 0.49 \cdot -|x|^{18}\][/tex]
Simplify the coefficients and combine terms:
[tex]\[0.49 \cdot -1 = -0.49\\\sqrt{|x|} \cdot |x|^{18} = |x|^{\frac{1}{2}} \cdot |x|^{18} = |x|^{18.5}\][/tex]
Therefore, the simplified expression is:
[tex]\[-0.49 \cdot |x|^{18.5} \cdot i\][/tex]
b) Simplify [tex]\(15\sqrt{x} + 0.16c^{12}\)[/tex]
Here, [tex]\(x\) and \(c\)[/tex] can be anything.
Given:
[tex]\[15\sqrt{x} + 0.16c^{12}\][/tex]
There are no common factors to combine these terms, so the expression is already simplified. The terms involve different variables and exponents, and cannot be further simplified together.
So the simplified expression remains [tex]\[15\sqrt{x} + 0.16c^{12}\][/tex]
a) The simplified expression is [tex]\[-0.49 \cdot |x|^{18.5} \cdot i\].[/tex]
b) The expression remains as usual given in the question:
[tex]\[15\sqrt{x} + 0.16c^{12}\][/tex]
You earned a 75% on a test. You answered 24 questions correctly.How many questions were on the test?
Answer: 32questions
Step-by-step explanation:let the total number of test = x
Therefore: 24/x * 100 = 75
x = 24*100 / 75
= 32questions
In a certain school 75% of the students in first year chemistry have had algebra if there are 300 students in first year chemistry how many of them have had algebra?
Answer:
225
Step-by-step explanation:
Total number of students =300
75% have had algebra
Number of students that have had algebra will be
= 75%/100% x 300
= 0.75 x 300
= 225
So, 225 of the 300 students have had algebra
Answer:225 students
There are 2 simple ways to get the answer.
Which of the following numbers is irrational?
Select all that apply.
2.3
n
8/9
1.5
Answer:
N
Step-by-step explanation:
On the distant plant, Mathology, a sports area covers 7400 yodels2. How many square deckles would this be if 1 deckle = 75.9 yodels?
Answer:
It would be 97.50 square deckles.
Step-by-step explanation:
Given:
On the distant plant, Mathology, a sports area covers 7400 yodels².
1 deckle = 75.9 yodels.
Now, to get the square deckles.
As given, 1 deckle = 75.9 yodels.
So, to get the square deckles by using conversion factor:
75.9 yodels = 1 deckle.
7400 yodels² = [tex]7400\div 75.9[/tex]
= [tex]97.50\ deckels ^2.[/tex]
Therefore, it would be 97.50 square deckles.
The area is approximately 1.286 deckles².
To convert the area from square yodels to square deckles, we need to use the given conversion factor: 1 deckle = 75.9 yodels.
First, we'll find out how many yodels one square deckle is by squaring the conversion factor.
1. Calculate the area of one square deckle in yodels: (75.9 yodels)² = 5752.81 yodels².
2. Convert the given area of the sports area from yodels² to deckles²: 7400 yodels² ÷ 5752.81 yodels²/deckle² ≈ 1.286 deckles².
Therefore, the sports area covering 7400 yodels² is approximately 1.286 square deckles.
A bag contains five white balls and five black balls. Your goal is to draw two black balls.
a) You draw two balls at random. What is the probability that they are both black?
b) You draw two balls at random. Once you have drawn two balls, you put back any white balls, and redraw so that you again have two drawn balls. What is the probability that you now have two black balls? (Include the probability that you chose two black balls on the first draw.)
The probability of drawing two black balls from a bag containing 5 white and 5 black balls is 2/9 (approximately 0.22) if you do not replace balls after drawing them, and 1 if you replace any white balls that are drawn.
Explanation:This question relates to the concept of probability in mathematics. The total number of balls in your bag is 10 (5 white balls and 5 black balls). If you want to draw two black balls, the probability will change based on the conditions of the question.
a) For the first draw, there are 5 black balls out of a total of 10 balls, so the probability is 5/10 or 0.5. If a black ball is drawn in the first draw, there are now 9 total balls and 4 of them are black, so the probability for the second black ball is 4/9. For both balls to be black, multiply the individual probabilities: (5/10) * (4/9) = 20/90 = 2/9 approximately equal to 0.22.
b) If you draw two balls and put back any white balls, then redraw until you have two balls, you are essentially ensuring that white balls are not counted. In this case, every draw will either be a black ball or a redraw with a white ball, so the probability is essentially 1 that you will eventually draw a black ball. Therefore, the probability of drawing two black balls using this method is (1/1) * (1/1) = 1.
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If f(1) = 7 and f(n) = f(n − 1) – 4 then find the value of f(6).
Answer:
- 13
Step-by-step explanation:
f(1) = 7
f(n) = f(n − 1) – 4
f(₂) = f(1) – 4 = 7 - 4 = 3
f(₃) = f(₂) – 4 = 3 - 4 = -1
f(₄) = f(3) – 4 = (-1) - 4 = - 5
f(₅) = f(₄) – 4 = (- 5) - 4 = - 9
f(₆) = f(₅) – 4 = (- 9) - 4 = - 13
The value of f(6) is -13, calculated based on the provided recursive formula where each term is four less than the previous.
Explanation:We are given that f(1) = 7, and the recursive equation for n is f(n) = f(n − 1) – 4. Since the equation shows that each next term is four less than the previous one, we can calculate the following iterations:
f(2) = f(2-1) - 4 = f(1) - 4 = 7 - 4 = 3f(3) = f(3-1) - 4 = f(2) - 4 = 3 - 4 = -1f(4) = f(4-1) - 4 = f(3) - 4 = -1 - 4 = -5f(5) = f(5-1) - 4 = f(4) - 4 = -5 - 4 = -9f(6) = f(6-1) - 4 = f(5) - 4 = -9 - 4 = -13So, the value of f(6) is -13.
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Suppose a basketball player typically makes one-third of his foul shots. Which simulation could be used to generate frequencies and determine the probability that the player will make his next two foul shots?
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Roll two fair dice, when a 1 or 2 is rolled for both dice simultaneously it is recorded as both foul shots being made. This process is repeated for 50 trials.
The probability of a 1 or 2 from a roll of a die is
2
6
or
1
3
which equals the probability of the player making a single foul shot. Therefore, the compound event of two foul shots being made is equal to a 1 or 2 being rolled on both dice simultaneously, (
1
3
)(
1
3
) =
1
9
.
Simplify the expression. 7y+3x+3-2y+6
What is the coefficient of y
What is the constant
Answer:
Step-by-step explanation: combine like terms 7y minus 2y is 5y then combine 3 plus 6 which is 9 then u get 3x+5y+9
If 3/7 of Z is 42, what is 5/7 of Z?
Answer:
x = 70
Step-by-step explanation:
First to make the equation easy, divide 42 by 3 to get what 1/7 of Z equals.
42 / 3 = 14
Now to get 5/7 of Z, just multiply 14 by 5.
14 x 5 = 70
x = 70
Hope this helped.
Answer:
70
Step-by-step explanation:
convert the decimal & solve for Z.
(3/7)Z = 42
(0.4286)Z = 42
Z = 98
Now,
(5/7)Z = ?
putting the value of Z
(0.714) (98) = 70