25. The wight to the nearest (kg) of a group of 50 people under a special diet are given below. Use the information to: (i) prepare a grouped frequency table using Sturges formula (ii) compute mean, mode and media. [17.5 marks] 65, 70, 60,46, 51, 55, 59, 63, 68, 53 47, 53, 72, 53, 67, 63, 64, 70, 57, 56 73, 56, 48, 51, 53, 72, 65, 62, 49, 64 53, 59, 63, 50, 43, 62, 67, 56, 61, 64 66, 52, 49, 62, 71, 58, 69, 53, 63, 59
​

The ordered pairs that are solutions of the given system of equations are:

(a) (0,−4)

The ordered pairs are a numerical value that occupies a specific position in the Cartesian plane, these pairs can have at least two components and these are:

P = (x, y)

First we will write the equations in a more organized way, then we will evaluate each of the pairs and validate that the equality is fulfilled.

[tex]y = -4e^{x}[/tex]

[tex]7x - y = 4[/tex]

(a) (−4,0)

y = -4e⁻⁴

y = -0.0732

Not true since the value of "x" does not make the value of "y" zero.

(b) (0,−4)

y = -4e⁰

y = -4

7(0) - y = 4

0 - y = 4

y = -4

If it complies

(c) (0,−2)

y = -4e⁰

y = -4  This pair is not a solution

(d) (−1,−3)

y = -4e⁻¹

y = -1.47    This pair is not a solution

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Answer:

4 in

Step-by-step explanation:

Surface area = 1/2 ( 5x12) *2   + 5 x h  + 13 * h +  12 x h

                                 60 + 30h = 180

                                          h = 4 in

just a quick addition to "jsimpson11000" posting above

keeping in mind that for a triangular prism, the base is always the triangular face.

Check the picture below.

[tex]5h~~ + ~~12h~~ + ~~\stackrel{\textit{two triangles}}{2\left[\cfrac{1}{2}(12)(5) \right]}~~ + ~~13h~~ = ~~180 \\\\\\ 60+30h=180\implies 30(2+h)=180\implies 2+h=\cfrac{180}{30} \\\\\\ 2+h=6\implies \boxed{h=4}[/tex]

The only graph that has a function referred to as  many-to-one function  is; Graph A

A many-to-one function is defined as a function that have y-values associated to more than one x-value.

Graphically speaking, if a horizontal line is drawn through the graph, such horizontal line would cross the graph at least twice.

In the graphs, we can see that A is a parabola, and that if a horizontal line is drawn above y = 0, the line will go through the parabola twice. For example, in y = 10 it will cross the parabola at the point (-3, 10) and (3, 10). Therefore, this is a many-to-one graph.

The second graph is a one-to-one graph since there is only one y-value associated to each x-value.

The third graph is not even a function because by definition of function, each element of x should be associated with ONE element of y. In this case, x= 5 and x = 9 are associated to more than one y elements (the vertical lines that form two sides of the square) and therefore is not a function.

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The percent of change from 400 to 600 is 33.34%.

What is Percentage Increase?

It is given that the percent of change is from 400 to 600.

There is an increase from 400 to 600, so the percent of change is an increase.

[tex]\% \text Increase = \frac{\text FV - IV}{FV} \times 100[/tex]

Here, the final value (FV) = 600 and initial value (IV) = 400.

Substituting the given values in the above formula, we get

[tex]\% \text Increase = \frac{600-400}{600} \times 100\\\implies \% \text Increase = \frac{200}{600} \times 100\\\implies \% \text Increase = 33.34 \%[/tex]

Therefore, the percent of change from 400 to 600 is 33.34%.

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The exact value of trigonometric function is ,

sin(60°+45°)= [tex]\frac{\sqrt6+\sqrt2}{4}[/tex]

cos[tex](\frac{\pi}{3}-\frac{\pi}{4})[/tex] = [tex]\frac{\sqrt2+\sqrt6}{4}[/tex].

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here the given is

a) sin(60°+45°)

Now using formula sin(t+s)= sin t cos s+ cos t sin s then

=> sin60°cos45°+cos 45°sin60°

=> [tex]\frac{\sqrt3}{2}\times\frac{\sqrt2}{2}+\frac{1}{2}\times\frac{\sqrt2}{2}[/tex]

=> [tex]\frac{\sqrt6}{4}+\frac{\sqrt2}{4}[/tex]

=> [tex]\frac{\sqrt6+\sqrt2}{4}[/tex]

b) cos[tex](\frac{\pi}{3}-\frac{\pi}{4})[/tex]

Now using formula cos(t-s)=cos t cos s + sin t sin s then

=> [tex]cos\frac{\pi}{3} cos\frac{\pi}{4}+ sin\frac{\pi}{3}sin\frac{\pi}{4}[/tex]

=> [tex]\frac{1}{2}\times\frac{\sqrt2}{2}+\frac{\sqrt3}{2}\times\frac{\sqrt2}{2}[/tex]

=> [tex]\frac{\sqrt2}{4}+\frac{\sqrt6}{4}[/tex]

=> [tex]\frac{\sqrt2+\sqrt6}{4}[/tex]

Hence the exact value of trigonometric function is ,

sin(60°+45°)= [tex]\frac{\sqrt6+\sqrt2}{4}[/tex]

cos[tex](\frac{\pi}{3}-\frac{\pi}{4})[/tex] = [tex]\frac{\sqrt2+\sqrt6}{4}[/tex].

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Answer:i don't know maybe C

Answer:

The power set of a set B = {a, b, c, d, e, f, g} is the set of all possible subsets of B.

In mathematical notation, the power set of B is represented as P(B).

The number of elements in the power set of B is 2^n, where n is the number of elements in B. In this case, n = 7, so the number of elements in P(B) = 2^7 = 128.

The power set of B is:

{{}, {a}, {b}, {c}, {d}, {e}, {f}, {g}, {a, b}, {a, c}, {a, d}, {a, e}, {a, f}, {a, g}, {b, c}, {b, d}, {b, e}, {b, f}, {b, g}, {c, d}, {c, e}, {c, f}, {c, g}, {d, e}, {d, f}, {d, g}, {e, f}, {e, g}, {f, g}, {a, b, c}, {a, b, d}, {a, b, e}, {a, b, f}, {a, b, g}, {a, c, d}, {a, c, e}, {a, c, f}, {a, c, g}, {a, d, e}, {a, d, f}, {a, d, g}, {a, e, f}, {a, e, g}, {a, f, g}, {b, c, d}, {b, c, e}, {b, c, f}, {b, c, g}, {b, d, e}, {b, d, f}, {b, d, g}, {b, e, f}, {b, e, g}, {c, d, e}, {c, d, f}, {c, d, g}, {c, e, f}, {c, e, g}, {d, e, f}, {d, e, g}, {e, f, g}, {a, b, c, d}, {a, b, c, e}, {a, b, c, f}, {a, b, c, g}, {a, b, d, e}, {a, b, d, f}, {a, b, d, g}, {a, b, e, f}, {a, b, e, g}, {a, c, d, e}, {a, c, d, f}, {a, c, d, g}, {a, c, e, f}, {a, c, e, g}, {a, d, e, f}, {a, d, e, g}, {b, c, d, e}, {b, c, d, f}, {b, c, d, g}, {b, c, e, f}, {b, c, e, g}, {b, d, e, f}, {b, d, e, g}, {c, d, e, f}, {c, d, e, g}, {a, b, c, d, e}, {a, b, c, d, f}, {a, b, c, d, g}, {a, b, c, e, f}, {a, b, c, e, g}, {a, b, d, e, f}, {a, b, d, e, g}, {a, c, d, e, f}, {a, c, d, e, g}, {b, c, d, e, f}, {b, c, d, e, g}, {a, b, c, d, e, f}, {a, b, c, d, e, g}​,{a, b, c, d, f, g}​,{a, b, c, e, f, g}​,{a, b, d, e, f, g}​,{a, c, d, e, f, g}​,{b, c, d, e, f, g}​,{a, b, c, d, e, f, g}​}

Equation graphed along with the parent function is, g(x) = ∛(x-3) + 4

The correct option is B.

The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x).

Given that;

Graph of a parent function.

And, Equation is graphed along with the parent function.

Here, The Parent function is,

f(x) = ∛x

Hence, By the graph,

There is 3 unit horizontal shift to positive side, and 4 unit vertical shift to upwards in parent function

Thus, The function drawn along with it is;

g(x) = ∛(x-3) + 4

Hence, g(x) = ∛(x-3) + 4 is the equation, graphed along with the parent function.

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The complete question is this,

Which equation is graphed along with the parent function?

g(x)= ^3 √x+3 +4

g(x)= ^3 √x-3 +4

g(x)= ^3 √x-4 +3

g(x)= ^3 √x+4 +3

The value of y is 28.

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,

The water level rises 14 centimeters every 3 minutes.

This means,

14 cm = 3 minutes

This can be written as,

(3, 14)

Now,

14 cm = 3 minutes

Multiply with 2 on both sides.

2 x 14 cm = 6 minutes

28 cm = 6 minutes

This can be written as,

(6, 28)

Thus,

The y value is 28.

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Answer:2x+4.4=85.8

Step-by-step explanation:

pretty sure this is the answer

Gavyn doubles the number and adds 4.4 so -> 2x+4.4 and that equals to 85.8

so it's 2x+4.4=85.8

Answer:

Step-by-step explanation:

If the original number is x, then we can say:

2x+4.4=85.8

2x=85.8-4.4

2x=81.4

x=40.7

To check,

40.7*2=81.4

81.4+4.4=85.8

Hence, x is 40.7

im stuck on the same thing

The matching of equations with their characteristic is as shown:

a) Neither parallel nor perpendicular lines

b)  these are perpendicular lines

c) these are parallel lines

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Rewrite the equations that need to be in y=mx+b form, then compare the slopes ( m values )

a) y= -4x +5 , y=(-1/4)x - 6

Neither parallel nor perpendicular lines

b)  y=3x+5 , y= (-1/3)x - 7

The slopes are m and -1/m , these are perpendicular lines

c)  The slopes are equal

So, these are parallel lines

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Answer:

A) The independent variable is the number of books (b) and the dependent variable is the total amount paid in fees (t).

Step-by-step explanation:

B) The input/output table for this function would be as follows:

b t

1 9

2 13

3 17

4 21

5 25

So some of the ordered pairs of the function are (1, 9), (2, 13), (3, 17), (4, 21) and (5, 25)

C) The domain of the function is discrete because it only includes specific values of b, the number of books. This is the only possible values of b are the natural numbers.

D) The domain of the function is all natural numbers b>=1, since it doesn't make sense for the number of books to be negative or zero. The range of the function is all natural numbers t>=5, since it doesn't make sense for the total amount paid to be negative or zero.

The salary after sixth year of employment will be $45918.34. The total compensation after six years are $250914.15.  

The amount raised over a period of time is given by the equation ,

Xₙ = X₀ (1+r)ⁿ

Xₙ is the final amount or number

X₀  is the initial amount or number

r is the rate

n is the number of years or period of time.

Here the annual rise is given as $1200. So we can calculate the rate.

r = 1200/36500 = 0.039

The salary rise during the sixth year, Xₙ = 36500 ×(1+0.039)⁶

                                                     = 45918.34

Total salary in all six years = 36500 + [36500×(1+0.039)¹] + [36500× (1+0.039)²] + [36500× (1+0.039)³] + [36500×( 1+0.039)⁴] +[36500×(1+0.039)⁵] + [36500× (1+0.039)⁶]

 =250914.15

So the 6th year salary is $45918.34 and total compensation for 6 years will be 250914.15.

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Answer:

n=0.2(6x+12y-5mx)/my

Step-by-step explanation:

If Joe can only reserve rooms in blocks, and each block contains 8 rooms and costs $900 , then inequality describes this scenario is (b) 16 + 8B ≥ 50  .

the number of rooms that Joe has already reserved = 16 rooms  ;

the number of additional blocks that Joe reserved is = 8 blocks

they need at least 50  total rooms , which  means that the total number of rooms that Joe has reserved, including the blocks he needs to reserve.

The expression "16 + 8B" represents the total number of rooms that Joe has reserved, as he has already reserved 16 rooms and each block contains 8 rooms.

Therefore, The inequality represents the constraint that Joe must meet in order to ensure that the company has enough rooms for the trip is 16 + 8B ≥ 50  .

Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50  total rooms. Joe had already reserved and paid for 16 rooms, so he needs to reserve additional rooms.

He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900 , "B" represent the number of additional blocks that Joe reserves

Which inequality describes this scenario?

(a) 16 + 8B ≤ 50

(b) 16 + 8B ≥ 50

(c) 16 + B ≤ 50

(d) 16 + B ≥ 50

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Answer:

0

Step-by-step explanation:

[tex] {x3 \: - 4 {x \: }^{2} + 3x \: = 0}^{} [/tex]

solve for x

[tex]x 1 = 0 \\ x2 \: = 1 \\ x3 \: = 3[/tex]

Answer:

$32,648

Step-by-step explanation:

1-  find 12% of 37,100         ( 37,100x12= 445,200  445,200/100= $4452)

2-  37,100- 4452= $32,648

(im not sure if its correct

https://brainly.com/question/25317034Assuming t is the number of hours since noon, a slope equation for the temperature, D, in terms of t is 80 ± 10t.

The slope refers to the change in y value resulting from a change in x.

The slope is also described as the quotient of the rise and run.

The slope refers to the rate of change along the regression line.

Temperature at noon = 80 degrees

High temperature during the day = 90 degrees

Increase in temperature from noon = 10 degrees (90 - 80)

Low temperature during the day = 70 degrees

Decrease in temperature from noon = -10 degrees (70 - 80)

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The number of hotdogs would you have to eat every minute to beat the last winner is about 21 hotdogs per minute

The statement reads that the 95th annual hotdog eating contest consumed 207 hotdogs (and buns!) in 10 minutes.

This implies that 208/10= 20.8 hotdogs (and buns) per minute to beat the record of 207 in 10 minutes or about 21 hotdogs per minute.

(2) In two minutes, you would be able to eat 21 hotdogs times 2 = 42 hotdogs

(3)At the average rate needed to win the contest, the number of total hotdogs will you consume in three minutes is 21 hotdogs  times 3 = 63 hotdogs

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Answer: To convert cubic meters (m³) to gallons, we can use the conversion factor 1 m³ = 264.172 gallons.

First, we need to find the amount of water needed to fill the pool to 94% of its capacity. We can do this by multiplying the volume of the pool (60 m³) by 94% (0.94).

60 m³ * 0.94 = 56.4 m³

Now we can use the conversion factor to convert the volume in cubic meters to gallons:

56.4 m³ * 264.172 gallons/m³ = 14,958.2 gallons

So the number of gallons of water that will be needed to fill the empty swimming pool to 94% of its capacity is 14,958.2 gallons.

Rounded to 3 decimal values is 14,958.2 gallons.

Step-by-step explanation:

The solution of the inequality means p = { range of values greater than $175 up until $400 }

We need to write and solve an inequality to find the prices p of coats that the shopper can afford.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Given that the value of price, p of coats the shopper can afford is greater than $175.

p > 175 can be translated as 175 < p

The shopper has $400 to spend on a winter coat such, p ≤ $400 .

The two inequalities can therefore be combined to yield a single inequality thus;

175 < p ≤ $400

The solution for prices of coat, p that the shopper can afford ranges between;

p = { range of values greater than $175 up until $400 }

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There are two different combinations, these are:

We will use the variables:

x = number of 5¢ stamps used.

y = number of 3¢ stamps used.

z = number of 2¢ stamps used.

We can write this:

x*5 + y*3 + z*2 + 44 = 62

5x + 3y + 2z = 62 - 44

5x + 3y + 2z = 8

There are two ways in which we can do that, these are:

x = 1

y = 1

z = 0

5*1 + 3*y + 2*0 = 8

8 = 8

The other solution is:

x = 0

y = 0

z = 4

5*0 + 3*0 + 2*4 = 8

8 = 8

So there are two different ways.

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Answer:

three times

Step-by-step explanation:

Please find the attachment for detail

Answer:

width = 4.2 units

Step-by-step explanation:

Easy, if the length is 65 units

65 * width = 273

width = 273 / 65

width = 4.2

the answer is 4.2

if you have the lenght and area just divided both in the equation and then you will have the answer

Answer:

48$

Step-by-step explanation:

6 times 4 equals 24 and 8 times 3 equals 24. 24 plus 24 equals 48.

Answer:

$ 48

Step-by-step explanation:

Smiths payment:

           To find the amount Maeve earned for 4 hours, multiply the unit rate (per hour $6) by 4.

           Payment made to Maeve for 1 hour = $ 6

            Payment made to Maeve for 4 hour = 6 * 4

                                                                         = $ 24

Blacks payment:

To find the amount Maeve earned for 3 hours, multiply the unit rate (per hour $8) by 3.

          Payment made to Maeve for 1 hour = $ 8

        Payment made to Maeve for  3 hours = 3 * 8

                                                                       = $ 24

To find the total earnings, add the amount given by Smith and Black

Maeve earnings = 24 + 24

                           = $ 48

Answer: $81.92

Step-by-step explanation:

First you must convert the 45% to a decimal.

0.45

You must multiply 0.45 by the total cost and then subtract what you get.

The algebraic equation of the total area of all of the pieces is 4x + 6y + 6x² + 2xy + y².

What is the linear equation?

Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.

We have given,

Collection of tiles of the same dimensions.

x,  x², y,  y², and xy.

The question examines the calculation,

Total Area = 1* x * 4 + 1 * y * 6 + x * x * 6 + x * y * 2 + y * y *1

= 4x + 6y + 6x² + 2xy + y²

Area =  4x + 6y + 6x² + 2xy + y².

Therefore, The algebraic equation of the total area of all of the pieces is 4x + 6y + 6x² + 2xy + y².

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Answer:

Solve for p:

p = q + z

Solve for v:

v = (p - q - z) / m

Step-by-step explanation:

You provided an algebraic equation with multiple variables: p, m, v, x, q, and z. To solve for a specific variable, we need to isolate that variable on one side of the equation and all the other variables on the other.

To solve for p:

p = mv + x = q + z

The variable "p" is already on one side of the equation, so we don't need to do anything else.

To solve for v:

v = (p - q - z) / m

We need to isolate v on one side. Therefore we can subtract q and z from both sides to obtain the equation v = (p - q - z) / m, where v is the isolated variable on one side of the equation, and all the other variables are on the other side.