Answer:
Mean = 45.178
Standard Deviation = 10.33
Step-by-step explanation:
class m frequency, f m [tex]\times[/tex] f f [tex]\times[/tex] [tex]m^{2}[/tex]
25 - 34 29.5 22.1 651.95 19232.525
35 - 44 39.5 31.5 1244.25 49147.875
45 - 54 49.5 37.7 1866.15 92374.425
55 - 64 59.5 25.3 1505.35 89568.352
116.6 5267.7 250323.15
mean = [tex]\frac{5267.7}{116.6} = 45.178[/tex] standard deviation = [tex]\sqrt{\frac{250323.15 - \frac{(5267.7)^2}{116.6} }{(116.1 - 1)} } = 10.33[/tex]
The mean of a distribution is the average of the distribution ; it is the sum of observation divided by the count of the observation.
The mean age is 45.18The standard deviation is 10.29
Given that:
[tex]\begin{array}{ccccc}{Age}&25-34&35-44&45-45&55-64\\{Number}&22.1&31.5&37.7&25.3\end{array}[/tex]
First, we calculate midpoint of each class.
This is the sum of the class interval divided by 2.
So, we have:
[tex]x_1 = \frac{25+34}{2} = 29.5[/tex]
[tex]x_2 = \frac{35+44}{2} = 39.5[/tex]
And so on...
The table becomes:
[tex]\begin{array}{ccccc}{Age}&25-34&35-44&45-45&55-64&{Number(f)}&22.1&31.5&37.7&25.3&{x}&29.5&39.5&49.5&59.5\end{array}[/tex]
The mean of the distribution is:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \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]\bar x = \frac{5267.7}{116.6}[/tex]
[tex]\bar x = 45.18[/tex]
The standard deviation is calculated as follows:
[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]
[tex]\sigma= \sqrt{\frac{(29.5 - 45.1)^2\times 22.1 + (39.5 - 45.1)^2 \times 31.5 + (49.5 - 45.1)^2 \times 37.7 + (59.5 - 45.1)^2 \times 25.3}{22.1 + 31.5 + 37.7 +25.3}}[/tex]
[tex]\sigma= \sqrt{\frac{12342.176}{116.6}}[/tex]
[tex]\sigma= \sqrt{105.85}[/tex]
[tex]\sigma= 10.29[/tex]
Hence:
The mean age is 45.18The standard deviation is 10.29Read more about mean and standard deviation at:
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I need help please and thank you
(A AND B ARE NOT ANSWERS THEY ARE SEPARATE PROBLEMS)
Answer:
Part a) Wayne's savings before he spent $28 was $31.08
Part b) Stef's savings after she spent $28 was $9.29
Step-by-step explanation:
Part a)
Let
x ----> original amount of Wayne's savings
y ----> original amount of Stef's savings
we know that
Original ratio
[tex]\frac{x}{y}=\frac{5}{6}[/tex]
[tex]x=\frac{5}{6}y[/tex] ----> equation A
After spending $28 each
[tex]\frac{x-28}{y-28}=\frac{1}{4}[/tex]
Multiply in cross
[tex]4x-112=y-25\\y=4x-112+25[/tex]
[tex]y=4x-87[/tex] ----> equation B
substitute equation A in equation B
[tex]y=4(\frac{5}{6}y)-87[/tex]
solve for y
[tex]\frac{20}{6}y-y=87[/tex]
[tex]\frac{7}{3}y=87[/tex]
[tex]y=37.29[/tex]
Find the value of x
[tex]x=\frac{5}{6}(37.29)=31.08[/tex]
so
The original amount of Wayne's savings was $31.08 and the original amount of Stef's savings was $37.29
therefore
Wayne's savings before he spent $28 was $31.08
Part b) Find Stef's savings after she spent $28
Subtract $28 from the original savings
so
$37.29-$28=$9.29
therefore
Stef's savings after she spent $28 was $9.29
What is 4 equal expressions to 4(2x^2+16)
Answer:
8x^2+64
Step-by-step explanation:
What is the scale factor on the map (10 points
Answer:
2785
Step-by-step explanation:
the sum of 7 times a number and 9 is 4
The length of a rectangle is 2 units more than the width. The area is 63 units. What is the width, in units, of the rectangle?
Answer:
the width is 7. i just did this in deltamath
Step-by-step explanation:
For what value of x is the rational expression below equal to zero?
X-4/x-6
Answer:
Step-by-step explanation:
When x equals to 4
4-4 = 0
-------------
4-6 = -2
0/-2 = 0
The rational expression X-4/x-6 equals zero when X equals 4, as long as the denominator is not zero, which avoids division by zero.
The question asks: For what value of x is the rational expression below equal to zero? The expression given is X-4/x-6. To find when this expression is equal to zero, we need to understand that a rational expression equals zero when its numerator is zero (and the denominator is not zero, to avoid division by zero).
To solve X-4 = 0, we simply add 4 to both sides of the equation, getting X = 4. This means that the rational expression is equal to zero when X equals 4, given that X is not equal to 6 to avoid making the denominator zero, which would be undefined. Hence, the value of X that satisfies the condition is 4.
You want to draw an enlargement of a design that is printed on a card that is 5 in. by 6 in. You will be drawing this design on an piece of paper that is 8.5 in. by 11 in. What are the dimensions of the largest complete enlargement you can make?
Answer:
The dimensions of the largest enlargement are
[tex]8\frac{1}{2}\ in\\10\frac{1}{5}\ in[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the scale factor is the ratio of its corresponding sides
step 1
Divide 8 1/2 by 5
[tex]8\frac{1}{2}=\frac{8*2+1}{2}=\frac{17}{2}\ in[/tex]
so
[tex]\frac{17}{2}/5=1.7[/tex]
step 2
Divide 11 by 6
so
[tex]\frac{11}{6}=1.83[/tex]
step 3
Find the largest complete enlargement
The scale factor is the smaller of the two previous values
so
The scale factor is 1.7
The dimensions are
[tex]5(1.7)=8.5=8\frac{1}{2}\ in[/tex]
[tex]6(1.7)=10.2=10\frac{1}{5} \ in[/tex]
The largest complete enlargement of the original 5 in by 6 in design that can be made on an 8.5 in by 11 in paper has dimensions of 8.5 in by 10.2 in, determined by the limiting width dimension and maintaining the aspect ratio.
Explanation:The question involves finding the dimensions of the largest complete enlargement of a design with an original size of 5 in. by 6 in. onto a piece of paper that is 8.5 in. by 11 in. To determine the largest complete enlargement, we must consider the scale factor that will allow the design to fit within the dimensions of the larger paper while maintaining the aspect ratio of the original design.
To maintain the aspect ratio, the scale factor for width and height must be the same. We compare the ratio of the widths and the heights of the original and target sizes to find the limiting dimension:
For width: 8.5 in / 5 in = 1.7For height: 11 in / 6 in = 1.833...Since the scale factor for the width (1.7) is less than the scale factor for height, the width is the limiting factor. Thus, we can enlarge the original design by a factor of 1.7 to fit the paper. Now, we calculate the enlarged dimensions:
Width: 5 in * 1.7 = 8.5 inHeight: 6 in * 1.7 = 10.2 inThe largest complete enlargement of the design that can be made on an 8.5 in by 11 in paper will have dimensions of 8.5 in by 10.2 in.
Find two consecutive even integers whose sum is 30
Answer:
14 & 16
Step-by-step explanation:
30÷2=15
15+15=30, so we can make the conclusion...
14+16=30
The high temperature on Monday was -14 F.on Tuesday the high temperature was 24 F. What is the difference in high temperatures on theses 2 days
If a number is divisible by 3 and 5 then it is divisible by 15
Answer:
Yes!
Step-by-step explanation:
Besides 15 and one, 3 and 5 are the greatest common factors of 15. Those numbers are therefore divisible by any product of 15.
Example:
45
45/3 = 15
45/5 = 9
45/15 = 3
Answer:
Yes it is
Step-by-step explanation:
Since the multiplication of 3 and 5 will give 15
I.e 3 × 5 = 15
Then any number that can be divided by 3 and 5, can also be divided by 15.
What is wrong with this solution?
-5m - 16 = 19
5m - 16 + 16 = 19 + 16
Step One:
Step Two:
Solution:
m = 7
Final answer:
The solution shown is incorrect because the equation is not simplified before performing operations.
Explanation:
The solution shown is incorrect. Let's go step by step to find the error:
Step One: -5m - 16 = 19
Step Two: 5m - 16 + 16 = 19 + 16
Step Three: 5m = 35
Step Four: Divide both sides by 5: m = 7
The mistake in the solution occurs in Step Two. The previous equation should be simplified to 5m = 35 before dividing by 5. The addition of 16 on both sides should be taken care of first by canceling it out, resulting in 5m = 35 instead of 5m + 0 = 35.
Therefore, the correct solution is m = 7.
Final answer:
The solution to the equation -5m - 16 = 19 is m = -7, not m = 7. The student initially misplaced the sign after dividing by -5.
Explanation:
The student has made a mistake in the initial steps of solving the equation -5m - 16 = 19. The correction process involves isolating the variable m on one side of the equation to find its value.
Step One
Add 16 to both sides of the equation to eliminate the -16:
-5m - 16 + 16 = 19 + 16
-5m = 35
Step Two
Divide both sides by -5 to solve for m:
-5m / -5 = 35 / -5
m = -7
The correct solution is m = -7, not m = 7. It is important to follow the addition rules and subtraction rules carefully and to remember to divide by the coefficient of m, which in this case is -5, resulting in changing the sign of the solution.
At midnight the temperature is -6°C. At midday the temperature is 9°C. By how much did the temperature rise?
Answer:
15 degrees
Step-by-step explanation:
It went from -6 to 0 which is 6 degrees of change then from 0 to 9 degrees which is 9 degrees of change 9+6=15
The amount of temperature that has been increased from midnight to midday is 15°C.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Midnight temperature = -6°C
Midday temperature = 9°C
The difference between the temperature.
= 9 - (-6)
= 9 + 6
= 15°C.
Thus,
The temperature is raised by 15°C.
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an elephant eats about 2500 pounds of food in 10 days. About how muck food does an elephant eat in 1000 days
Final answer:
An elephant that eats about 2500 pounds of food in 10 days would eat approximately 250,000 pounds in 1000 days. You find this by dividing 2500 pounds by 10 to get a daily consumption rate and then multiply that rate by 1000 days.
Explanation:
If an elephant eats about 2500 pounds of food in 10 days, to find out how much food it eats in 1000 days, you should first calculate how much it eats per day and then multiply that number by the total number of days (1000). To find the daily food consumption, you divide the total food consumed in 10 days by the number of days:
2500 pounds ÷ 10 days = 250 pounds per day.
Now multiply the daily consumption by 1000 days to find the total amount for that period:
250 pounds per day × 1000 days = 250,000 pounds.
So the elephant would eat approximately 250,000 pounds of food in 1000 days.
Solve for y.
2(-4y + x) = 4
Answer:
Step-by-step explanation:
-4y + X = 2
-4y = 2 - x
y = 2 - x/ -4
hope this helps!!
The value of y in terms of x is -1/2 + x/4.
To solve for y, we start with the equation 2(-4y + x) = 4.
Distribute the 2 inside the parentheses: -8y + 2x = 4.
Move the term with x over to the other side by subtracting 2x from both sides: -8y = 4 - 2x.
Isolate the y by dividing both sides by -8: y = (4 - 2x) / -8.
Simplify the right side by dividing both terms by -8: y = -1/2 + x/4.
29+x+41=90 and 113-y=90
29+x+41 = 90
x+70 = 90 ..... combine like terms
x+70-70 = 90-70 .... subtract 70 from both sides
x = 20 answer---------------------------------------
113 - y = 90
113 - y = 90 - 113 ... subtract 113 from both sides
-y = -23
y = 23 answerDonato is 6 feet 2 inches tall. His sister is 68 inches tall. Donato is how many inches taller.
6 inches taller
Step-by-step explanation:
There’s 12 inches in a foot. So 12•6 is 72 then plus another 2 then you get 74. Then subtract 74 by 68 and you get 6
Answer:
Step-by-step explanation: since 1 foot =12 inches then we multiply 12*6=72 inches +2 inches =74 inches therefore Donato is 74 inches which is obviously bigger than 64 inches so we subtract 74-64=10
As a result ,Donato is 10 inches taller than his sister
Max spent 35 minutes doing research on the internet. She finished at 7:10 P.M. At what time did max start her reserch
Answer:
6:35
Step-by-step explanation:
Answer: 6:35
Step-by-step explanation:
7:10 take 10 from 35 and you get down to 7:00 and then subtract 25 from 7:00 and get your answer
5. Name the property the equation illustrates.
3. You want to leave a tip for a meal that
costs $17.95. If all you have is $3.00, what
percentage tip will you be able to leave?
Answer:
17%
Step-by-step explanation:
3/17.95 = 0.167
0.167 × 100 = 16.7 *rounding to 17
12.95 × 0.17 = 3.0515
Apply the distributive property to factor out the greatest common factor 70-40p
Answer:
10(7-4p)
Step-by-step explanation:
A pair of shoes is priced $35.99, but is on sale for 20% off.What is the sale price of the shoes
Answer: $7.20
Step-by-step explanation:
20% equals 1/5 and 35.99 divided by 1/5 is 7.198 now round to the nearest tenth and you got 7.20.
Movies are on sale for 1/4 the original price. If the original price is $20, which expression gives the sale price?
You can buy 5 cans for green beans at the Village Market for $3.70. You can buy 10 of the same cans of beans at Sam’s club for $6.30. Which place is the the better buy?
Answer:
Sams club
Step-by-step explanation:
3.70/5= $.74 per can
6.30/10=$.63 per can
Eden spent half of her weekly allowance on candy. To earn more money her parents let her weed the garden for $5. What is her weekly allowance if she ended with 12?
Answer:
her weekly allowance would be 7
Step-by-step explanation:
Answer:
$24
Step-by-step explanation:
12 is 1/2 of 24.
So, when she weeds the garden, she will have $17.
If she gets her weekly allowance and the $5, she will have $41, assuming she doesn't spend any of the money she already has.
10. A student studied 18 hours in 7 days, if he wants to study average 2 hours each day for 14 days. How many hours he needs to study for next 7 days?
Answer:
2 x 14 = 28
28 - 18 = 10
He needs to study for 10 hours that week or, about one and half hours per day.
2. If the whole bar is 3 units long, what is the length of the shaded part of the bar? Write a multiplication
equation for the diagram, and then solve.
Answer:
The length of the shaded part is [tex]\frac{9}{4}[/tex]
Step-by-step explanation:
The original figure, which you may have unintentionally missed to add, is attached below.
From the figure, it is easy to figure out that:
The whole bar is 3 units long.The bar has 4 total parts.The shaded region has 3 parts.So, the ratio of shaded parts to total parts will be: [tex]\frac{3}{4}[/tex]
In order to determine length of the shaded part, just multiply the ratio of the shaded parts to total parts by the total length of the bar.
So,
[tex]\frac{3}{4} \times3=\frac{9}{4}[/tex]
Therefore, the length of the shaded part is [tex]\frac{9}{4}[/tex]
Keywords: ratio, length
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Answer:
see the explanation
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The fraction of the shaded part is equal to divide the number of shaded parts divided by the total number of parts
so
Let
x ----> the number of shaded parts
y ----> the total number of parts
we have
x=3, y=4
so
[tex]\frac{3}{4}[/tex]
To find out the length of the shaded part, multiply the fraction of the shaded parts by the total length of the bar
so
[tex]\frac{3}{4}(3)=\frac{9}{4}=2.25\ units[/tex]
Chang drove 315 miles in 5 hours.
At the same rate, how long would it take him to drive 567 miles?
I hours
Answer:
AROUND 6-7 HOURS
Step-by-step explanation:
Solve the equation for y plz -1.2y-4.2y=-3.78
Answer:
y=0.7
Step-by-step explanation:
-1.2y-4.2y=-3.78
Simplify:
-5.4y=-3.78
5.4y=3.78
3.78/5.4=0.7
y=0.7
PLSSSSS HELP What is the period of the function f(x)=sin1/6x ? π/6 12/π 6π 1/6
the answer is 12pi
just took the quiz :)
The period of the function is 12π, the correct option is B.
What is the period of a function?The period of a function is the distance in which the graph repeats itself.
For a trigonometric function, the length of one complete cycle is called the periodic function.
For the function
y = a sin (bx + c)
Here,
a is the amplitude,
b is the period of the sine curve, and
c is the phase shift of the sine curve
The amplitude is the height of the curve.
The coefficient of b = 1, for a period of 2π
To find the period of the sine curve for any coefficient b,
Divide 2π by the coefficient of b to get the new period of the curve.
The coefficient b and the period of the sine curve have an inverse relationship,
As b gets smaller, the length of one cycle of the curve gets bigger. Similarly, on increasing the value of b, the period will decrease.
The function is y = sin1/6x
The period of the function is,
= 2π / ( 1/6)
= 12π
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Find the missing number
45-9=46-
The answer is 10 because 45-9 is 36, so 46-x must be 36, which would result in 10