​Recently, a random sample of 2534 year olds was​ asked, "How much do you currently have in​ savings, not including retirement​ savings?" The data in the table represent the responses to the survey. Approximate the mean and standard deviation amount of savings.

Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3

Answers

Answer 1

The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively

How to determine the mean?

The table of values is given as:

Savings Lower Limit Upper Limit     Frequency

0-199         0         199                       345

200-399   200   399                         97

400-599   400   599                         52

600-799   600   799                         21

800-999   800   999                         9

1000-1199 1000  1199                         8

1200-1399 1200  1399                      3

Rewrite the table to include the class midpoint and the frequency

x               f

99.5         345

299.5        97

499.5        52

699.5        21

899.5        9

1099.5        8

1299.5        3

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]

Evaluate

[tex]\bar x = 233.331775701[/tex]

Approximate

[tex]\bar x = 233.3[/tex]

Hence, the approximation of the mean is 233.3

How to determine the standard deviation?

The standard deviation is calculated as:

[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]

So, we have:

[tex]\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]

Evaluate

[tex]\sigma = 229.82[/tex]

Hence, the approximation of the standard deviation is 229.82

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Related Questions

Math Topic: Sum, Difference, and Product of two functions

Help with this!

Answers

The expression are; [tex](h - g) (x) = 3x^{3} -x^{2}[/tex], [tex](h + g) (x) = 3x^{3} +x^{2}[/tex] , [tex](h.g) (-1) = -3[/tex].

What is a function?

The function is a type of relation, or rule, that maps one input to specific single output.

Given function;

g(x) = [tex]x^{2}[/tex]

h(x) = [tex]3x^{3}[/tex]

The expression;

[tex](h - g) (x) = 3x^{3} -x^{2}[/tex]

[tex](h + g) (x) = 3x^{3} +x^{2}[/tex]

[tex](h.g) (-1) = x^{2} .3x^{3} \\\\(h.g) (-1) = 3x^5\\\\(h.g) (-1) = 3(-1)^5\\\\(h.g) (-1) = -3[/tex]

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a die is tossed twice and the number of dots facing up in each toss is counted and noted in the order of occurrence. (a) find the sample space. (b) find the set a corresponding to the event “number of dots in first toss is not less than number of dots in second toss.” (c) find the set b corresponding to the event “number of dots in first toss is 6.” (d) does a imply b or does b imply a? (e) find and describe this event in words. (f) let c correspond to the event “number of dots in dice differs by 2.”

Answers

A die is tossed twice and a number of dots facing up in each toss are counted and noted in the order of occurrence.

a) The sample space is given as:

Sample Space (S)= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5),(2,6),(3,1),(3,2),(3,3)(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1)(5,2)(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),c),(6,6)}.

What is the sample space?

A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol S.

b) the set corresponding to the event number of dots in the first toss is not less than the number of dots in the second toss.

{(6,6),(6,5)(6,3)(6,2)(6,1)(6,4),(5,1)(5,2)(5,3),(5,4),(5,5),(4,1),(4,2),(4,3),(4,4),(3,1),(3,2), (2,1), (2,2),(1,1)}

c) find the set b corresponding to the event number of dots in the first toss is 6.

{(6,1),(6,2),(6,3),(6,4),c),(6,6)}.

e) a does not imply b or does b imply a.

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Expand each expression A ( x+1)^2 B(x-3)^2. C ( x+4)^2 D (x-1/2)^2

Answers

The expanded expressions are shown below:

(x + 1)² = x² + 2 · x + 1(x - 3)² = x² - 6 · x + 9(x + 4)² = x² + 8 · x + 16(x - 1/2)² = x² - x + 1/43 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75(1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2

How to expand perfect square trinomials

Perfect square trinomials are polynomials of grade 2 with the form (a + b)² = a² + 2 · a · b + b². In this case, we have to expand six perfect square trinomials:

a) (x + 1)² = x² + 2 · x + 1

b) (x - 3)² = x² - 6 · x + 9

c) (x + 4)² = x² + 8 · x + 16

d) (x - 1/2)² = x² - x + 1/4

e) 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75

f) (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2

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RATS is a parallelogram. M

Answers

Answer:

Answer:

x = 12

Step-by-step explanation:

m∠S + m∠T = 180

8x + 7x = 180

15x = 180

x = 12

does this help?

Given the function f ( x ) = x 2 − 6 x + 10 , what is the average rate of change of the function over the interval [ 4 , 8 ] ?

Answers

The rate of change of the function over the interval [ 4, 8 ] will be 6.

What is the rate of change of the function?

The rate of change function represents the rate at which one quantity changes in relation to another. Simply put, the rate of change is the difference between the amount of change in one item and the comparable amount of change in another.

Given function:-

F(x) = x² - 6x + 10

The formula for calculating the rate of change will be given as:-

[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]

We have x₁ = 4 and x₂ = 8 given in the question

F(x₂) =  x²₂ - 6x₂ + 10 = (8)² - ( 6 x 8 ) + 10 =

F(x₂) = 64 - 48 + 10

F(x₂) = 26

F(x₁) =  x²₁ - 6x₁ + 10 = (4)² - ( 6 x 4 ) + 10 =

F(x₁) = 16 - 24 + 10

F(x₁) = 2

[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]

[tex]ROC = \dfrac{26 -2}{8-4}=\dfrac{24}{4}=6[/tex]

Therefore the rate of change of the function over the interval [ 4, 8 ] will be 6.

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if the length of a side of a square is x CM its perimeter is​

Answers

Square perimeter =4x cm.

The complete length that a square's edge encompasses is referred to as its perimeter. Any enclosed geometric shape's perimeter may be computed by measuring the space around it.

By calculating the total of all the sides of a square, the perimeter may be determined. The perimeter of a square will be stated as,

The perimeter of square = s + s + s + s

Perimeter of square = 4s, where "s" is the side length of the square.

This is because all edges of a square are equal and each edge measures "s" units.

Calculating the perimeter of a square:

Mathematically, the formula for calculating a square's perimeter is: Square perimeter, (P) = 4 Side

P= 4x cm

It is concluded that the solution is 4x cm.

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2. Mike is looking to purchase a Ford Explorer, which has a sticker price of $32,415. He's able to negotiate $3,000
off sticker price, and the tax rate is 6.5%. License and title fees are $395. If he trades in his minivan for $9,000
(deducted from the negotiated price before taxes), the monthly payment will be $500.95 for 60 months. He is
also offered a lease with $2,900 down and payments of $429 for 36 months.
a) How much will Mike pay total if he chooses the lease option?
b) How much more will he pay in the first three years if he chooses to buy instead?
c) How much interest will he pay if he buys?
d) Which option would you choose? Explain.
3. Maya bought a new Ford Focus for $17,400. She made a down payment of $4,000 and made monthly payments
of $396 for three years. Find the APR.

Answers

Answer:

.wfhytrsssssssssd

Step-by-step explanation:

dddddddddddddddddd

Solve the following triangle. Round side measure to the nearest tenth and angle measure to the nearest degree:

Answers

Answer: [tex]AB=4.7, BC=8.8, \angle C=28^{\circ}[/tex]

Step-by-step explanation:

As angles in a triangle add to 180 degrees,

[tex]\angle C=180^{\circ}-90^{\circ}-62^{\circ}=\boxed{28^{\circ}}[/tex]

We know that:

[tex]\sin 62^{\circ}=\frac{BC}{10}\\\\BC=10\sin 62^{\circ} \approx \boxed{8.8}[/tex]

Similarly,

[tex]\cos 62^{\circ}=\frac{AB}{10}\\\\AB=10\cos 62^{\circ} \approx \boxed{4.7}[/tex]

-
Find the area of a rectangle with a length of 15 inches and a width of 9 inches. The area of the rectangle is
inches. Enter only the number.
The solution is
square

Answers

135inches2

Step-by-step explanation:

by multiplying both length and width you can get the sum

ƒ(x) = x² - x - 1
What is the average rate of change of f over
the interval -1 ≤ x ≤ 1?

Answers

Answer: -1

Step-by-step explanation:

[tex]f(-1)=(-1)^2 - (-1)-1=1\\\\f(1)=1^{2}-1-1=-1\\\\\therefore \frac{f(-1)-f(1)}{-1-1}=\frac{1-(-1)}{-1-1}=\frac{2}{-2}=\boxed{-1}[/tex]

La diferencia de las medidas de dos ángulos suplementarios es 20% determina el complemento del menor de dichos ángulos

Answers

Smaller angle = 50
Larger angle = 130

Let smaller angle be x degree

=> larger angle= [tex]3x - 20[/tex]

Since these angles are supplementary , So

[tex]= > x + 3x - 20 = 180\\= > 4x = 200\\= > x = 50\\= > 3x - 20\\ = > 150 - 20 = 130[/tex]

So smaller angle would be 50 deg & larger angle would be  130 deg.

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Shauna solved the polynomial equations given in the table.
Determine whether each polynomial is correct. Select Correct or Incorrect for each equation.
Equation
-
(5a - 8) + (2a² + 2a − 1) = 2a² + 7a - 9
(6² +6b-4) (3b +6²) = 26² +36-4
(9c-4c²) - (2c² + c) = -6c² + 10c
-
Correct
Incorrect

Answers

Answer:

(5a - 8) + (2a² + 2a − 1) = 2a² + 7a - 9 - correct.

Step-by-step explanation:

(5a - 8) + (2a² + 2a − 1) = 2a² + 7a - 9 - correct;

(6² +6b-4) (3b +6²) = 26² +36-4 - incorrect (correct is: 18b²+...36²);

(9c-4c²) - (2c² + c) = -6c² + 10c - incorrect (correct is: -6c² + 8c).

A cell phone towerbcast a shadow that is 40 feet long . An 10- foot- tall stop sign located near the tower casts a shadow that is 8 feet long. How tall is the cell phone tower?

Answers

Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:

8 feet - 10 feet

40 feet - h feet

Applying cross multiplication:

8h = 10 x 40

Simplifying by 8:

h = 10 x 5 = 50 feet.

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The box plots below show attendance at a local movie theater and high school basketball games:
Two box plots are shown. The top one is labeled Movies. Minimum at 130, Q1 at 162, median at 185, Q3 at 195, maximum at 290. The bottom box plot is labeled Basketball games. Minimum at 85, Q1 at 170, median at 200, Q3 at 225, maximum at 230.

Which of the following best describes how to measure the spread of the data?
- The IQR is a better measure of spread for movies than it is for basketball games.
- The standard deviation is a better measure of spread for movies than it is for - basketball games.
- The IQR is the best measurement of spread for games and movies.
- The standard deviation is the best measurement of spread for games and movies.

Answers

The standard deviation is a better measure of spread for movies than it is for basketball games.

What is box- plot?

A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

As, Movies is more centric to mean and not skewed on a particular side whereas basketball games is not centric to mean but is skewed right then left.

Now, Standard deviation just measures the deviation or spread with respect to mean of collected data.

So, In the movies the data is more collected. Thus standard deviation is best suited for movie data.

Now, interquartile range. IQR relies on if the data is skewed.

So, in the basketball data the standard deviation will not give the information.

Hence, the  standard deviation is a better measure of spread for movies than it is for basketball games.

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look at the picture

Answers

the answer to the question is the first answer choice

Create a real-life representation of the following multiplication problem. Explain what the result represents in the problem.
24(1/3) = 8

Answers

The real-life problem will be:- The total number of chocolates is 24 and there are 3 boxes what will be the number of chocolates filled in each box. The number of chocolates in each box will be 8.

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression is:-

[tex]24\times \dfrac{1}{3}[/tex] = 8

The real-life problem will be given the as:-The total number of chocolates is 24 and there are 3 boxes what will be the number of chocolates filled in each box. The number of chocolates in each box will be 8.

Hence the number of chocolates in each box will be 8.

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If the sides of a square measure 9sqrt3 units, then find the length of the fishbowl.

Answers

The length of the diagonal of the square is 22.05 units

How to find the diagonal of a square?

A square have all its sides equal to each other.

Therefore, using Pythagoras theorem,

c² = a² + b²

c² = (9√3)² + (9√3)²

c² = 81 × 3 + 81 × 3

c² = 243 + 243

c² = 486

square root both sides

c = √486

c = 22.045407685

c = 22.05 units

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What is 3/4 divided by 1/2

Answers

Answer:
Fraction: 3/2
Decimal: 1.5

Answer:

1 1/2

Step-by-step explanation:

Convert both fractions into decimals

⇒ 3/4 (0.75) and 1/2 (0.50)

Divide the decimals:

⇒0.75 ÷ 0.50

Find the quotient

⇒ 1.5

Convert the quotient to a fraction

⇒ 1 1/2

Terms:

Operations with fractions

A dairy farmer wants to make 45% protein supplement and a standard 15% protein ration to make 1800 pounds of high grade 35% protein ration how many pounds of each should be used.

Answers

1200 pounds of protein supplement and 600 pounds of standard protein is used.

Let a be the protein supplement and b be the standard protein.

Given that protein supplement and standard protein make 1800 pounds of high grade protein.

i.e., a+b = 1800 ------- (1)

45% a + 15% b = 35% 1800

0.45a + 0.15b = 1800 (3.5)

By (1), a = 1800 - b

Substituting, we get

0.45 (1800-b) + 0.15b = 630

810 - 0.45 b + 0.15b = 630

- 0.3 b = - 180

b = -180/-0.3

b = 600

Substituting b = 600 in (1),

we get

a = 1200.

Hence, 1200 pounds of protein supplement and 600 pounds of standard protein is used.

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A new element with atomic number 116 was discovered in 2000. In 2012 it was named livermorium, Lv. Although Lv is radioactive and short-lived, its chemical properties and reactivity should follow periodic trends.

a. Determine the electron configuration for the valence electrons of Lv in the ground state. (2 pts)

Answers

Answer:

7s²7p⁴

Step-by-step explanation:

Livermorium is located in the seventh period and sixteenth column of the periodic table. The noble gas configuration for livermorium is [Rn]7s²5f¹⁴6d¹⁰7p⁴. The valence electrons are the ones in the orbitals with the highest quantum number (coefficient). Remember, there can be up to 8 valence electrons at one time. Therefore, the valence electron configuration is 7s²7p⁴.

Let's check

116 is the atomic no

Electronic configuration

1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶5s²4d¹⁰5p⁶4f¹⁴6s²5d¹⁰6p⁶7s²5f¹⁴6d¹⁰7p⁴

Valence electrons

7s²7p⁴

patulong po,thankyou

Answers

The answer is 27 cubic meters. Why? Well, the formula for the volume of a rectangular box is length times width times height (or base times height because length and width make up what is known as the base). Provided these measurements, all we need to do in this equation is multiply the length, width, and height to get our volume.

1.8 x 1.2 = 2.16

2.16 x 12.5 = 27

Because we just multiplied all three numbers by each other, we have identified our missing volume. The volume of the rectangular box is 27 cubic meters.

Your final answer: A.

The table below shows the participation in the town soccer league during its first five seasons.
Town Recreational Soccer League Participation
Number of participants
88
95
100
108
115
Year
1
2
23
3
4
fo
5
Which is the equation of the trend line that can be generated by using the data from years 1 and 5?
Oy-6.75x-688.25
Oy-6.75x-1.75
O y-6.75x+81.25
Oy-6.75x+148.75

Answers

Using a calculator, the equation of the trend line that can be generated by using the data from years 1 and 5 is:

y = 6.75x + 81.25.

How to find the equation of linear regression using a calculator?

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points, in the format (x,y), are given as follows:

(1,88), (2,95), (3,100), (4,108), (5,115).

Hence, using a calculator, the regression line is:

y = 6.75x + 81.25.

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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Indicate the equation of the given line in standard form. The line that contains the point Q( 1, -2) and is parallel to the line whose equation is y - 4 = 2/3 (x - 3)

Answers

The value of x, y, and z are 15/2,  (15√3)/2, and  (15√3)/2 after applying the trigonometric ratios.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

To find the value of x:

In right-angle triangle x-z-15:

sin30 = x/15

x = 15sin30 = 15/2

To find the value of y:

sin60 = y/x = y/(15/2)

sin60 = 2y/15

√3/2 = 2y/15

y = (15√3)/2

To find the value of z:

cos30 = z/15

√3/2 = z/15

z = (15√3)/2

Thus, the value of x, y, and z are 15/2,  (15√3)/2, and  (15√3)/2 after applying the trigonometric ratios.

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What algebraic expression is a product with a factor of 5

Answers

Answer:

y=5x

Step-by-step explanation:

A product means multiplication, and you need to multiply x by 5 in order to make the product have a factor of 5.

Which algebraic expression is a trinomial?
O x³ + x²-√x
O 2x³-x²
○ 4x³ + x²-1/x
O x-x+√6

Answers

Answer:

D. x^6 - x + √6

Step-by-step explanation:

Last option:

⇒  x^6 - x + √6

Cannot be simplified further and has three terms.

Therefore is a trinomial.

The algebraic expression that is a trinomial is 2x³-x².

What is a polynomial?

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

A trinomial is a polynomial that has three terms.

In the given options, the only expression that has three terms is "2x³-x²". It has the terms 2x³, -x², and 0x (which is often omitted).

The other options have different numbers of terms or they have terms with fractional or radical exponents, which do not fit the definition of a trinomial.

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A tree is making a shadow 22 feet long. The angle of elevation from the tip of
the shadow to the top of the tree is 50°.
feet. Round your answer to the nearest
The height of the tree is about
foot.

Answers

Answer:

26.2 feet

Step-by-step explanation:

tan(50°) = h/22

h = 22 × tan(50°) = 26.2 feet

The price p in dollars that a store sets for an items is given by the equation p=c + 1/10c where c dollars is the stores cost for the items if the store sets a price of $55 for an ideal what is the cost for the item

Answers

The cost of the item whose price $ 55 is $ 50.

What is Cost Price?

The cost price is the price paid by an individual to buy an item or any other commodity. Or this can also be taken as the total amount of money spent by the manufacturer to assemble a product or deliver a service.

Here, Price equation in terms of cost

       P = C + C/10

      P =  (10C+C)/10

      P = 11C/10

      C = 10P /11

For P = $ 55, the cost will be

      C = 10 X 55 / 11

      C = 10 X 5

      C = $ 50

Thus, the cost of the item whose price $ 55 is $ 50.

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the height of a plant in centimeters is modeled as a function of time, in days. consider this graph of the function enter the average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20

Answers

The average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20 is 1.32 cm per day.

What is average height?

The average height is the ratio of change in height of the plant and the time taken taken for that change.

Given is the height of a plant in centimeters is modeled as a function of time, in days.

For day 0, the height is 18cm and the height for day 20 is 42 cm, then the average height change is

height per day = 42 - 18/ 20 -0

height per day  = 1.2 cm/day

Thus, the average height of plant is  1.2 cm/day.

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Find the x-intercept of 2x+2y=2

Answers

Answer:

x-intercept: (1,0)

y-intercept: (0,1)

Step-by-step explanation:

Given: Find the x and y intercepts of 2x + 2y = 2

X-intercept

To solve for a x - intercept we have to substitue 0 in for y and solve for [tex]x[/tex]

Lets do it:

2x + 2(0) = 2

2x + 0 = 2

2x = 2

x = 1

Therefore, this means that when y = 0, x = 1 or (1,0)

Y-intercept

To solve for a y - intercept we have to substitue 0 in for x and solve for [tex]y[/tex]

Lets do it:

2(0) + 2y = 2

0 + 2y = 2

2y = 2

y = 1

Therefore, this means that when x = 0, y = 1 or (0,1)

PLEASE HELP WITH THIS PROBLEM!

Answers

Answer: Options 1 and 2

Step-by-step explanation:

To model exponential decay, the base of the exponential has to be less than 1.

Model exponential decay equation are

y = 0.34(0.98)^x

y = 8 (0.28)^x

Model exponential decay equation

Model exponential decay equation has the base value which is less than 1.Exponential decay is the process of reducing amount by consistent percentage rate over a time period. It can be expressed by the equation y=a(1-b)x where y is the final amount, a original amount, b decay factor, and x is the amount of time that has passed.

Option C and D have the base value greater than 1. So it can't be model exponential decay equation.

Hence, the model exponential decay equation are

y = 0.34(0.98)^x

y = 8 (0.28)^x

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