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5. The constant of proportionality is 1.5

The equation is p = 1.5×s

6. The constant of proportionality is 1.99

The equation is p = 1.99 × a

7. The variables Number of Pens and Cost  are not proportional

Please find attached the required graph

8. The variables Number of minutes and Words Typed are not proportional

Please find attached the required graph

The procedure for finding the answers are as follows;

5. The given data are presented as follows;

[tex]\begin{array}{ccc}Shirts \ (s)&&Profit \ (p)\\5&&7.50\\10&&15.00\\15&&22.50\end{array}[/tex]

Where two variables, s and p are proportional, we get;

p ∝ s

Therefore;

p = C × s

C = p/s

Where;

C = The constant of proportionality

Therefore, the constant of proportionality, C, of the given variables, (number of shirts, s, and profit, p, is found as follows;

C = 7.50/5 = 15.00/10 = 22.50/15 = 1.5

The constant of proportionality, C = 1.5

The equation that relates the two values is p = 1.5×s

6.  For the apples to price relationship, we have;

[tex]\begin{array}{ccc}Apples \ (a)&&Price\ (p)\\4&&7.96\\5&&9.95\\6&&11.94\end{array}[/tex]

Therefore;

p ∝ a

p = C × a

C = p/a

Plugging in the values gives;

C = 7.96/4 = 9.95/5 = 11.94/6 = 1.99

The constant of proportionality, C = 1.99

Therefore, the equation relating the two values is p = 1.99 × a

7. The given data is presented in a tabular form as follows;

[tex]\begin{array}{ccc}Number \ of \ pens &&Cost\ \\1&&52\\2&&54\\3&&56\\4&&58\end{array}[/tex]

A set of data is proportional or has a proportional relationship if their x, and therefore, y-intercept is (0, 0)

From the graph of the data, created with MS Excel, the y-intercept is 50 which is not equal to zero, therefore, the relationship between the data is not a proportional relationship

8. The given data is presented in a tabular form as follows;

[tex]\begin{array}{ccc}Number \ of \ Minutes&&Words \ Typed\ \\1&&50\\2&&90\\3&&140\\4&&180\end{array}[/tex]

From the graph of the data, we have that the y-intercept of the line of best fir is 5, therefore, the relationship is not a proportional relationship

Learn more about proportional relationships here;

https://brainly.com/question/24289972.

Answer:

Step-by-step explanation:

Answer:

11.2 cm

Step-by-step explanation:

Given that;

Arc Length Formula (if θ is in radians): l = ϴ × r

ϴ = angle subtended in radians

r= radius of the circle

l = 8cm × 1.4 radians

l= 11.2 cm

Answer:

what can i help u with

Step-by-step explanation:

I really can't help u with that sorry i am bad at math

Answer:

Step-by-step explanation:

Prime numbers are basically numbers that don't have any factors that multiply to get that number except for 1 and the number itself. (For example: 2, 3, 5, 7, 11, 13 and so on are all prime numbers)

The question is asking to express 60 into prime numbers. 60 is 30*2, and since 2 is a prime number, we can circle it. Then we continue on with 30, which can divide into 15*2. Again, since 2 is a prime number, we circle it, while 15 can be factored further because 5*3 is 15. Since 5 and 3 are prime numbers, we circle them too. In the end, we have the prime numbers 5, 3, 2, and 2. There are two 2's in our factorization, so therefore we can simplify that to 2^2 since they ask for your answer in index form. There is only one 5 and one 3, and they ask to write them  in asscending order, and so the answer would be (2^2)*3*5. Hope this helps!

Answer:

[tex]\angle 1 + \angle 2 = 180^o[/tex]

Step-by-step explanation:

Given

[tex]\angle 1[/tex] and [tex]\angle 2[/tex]

Required

The relationship between them [tex]\angle 1[/tex] and [tex]\angle 2[/tex]

From the question, we understand that [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are supplementary

Supplementary angles add up to 180.

So, the relationship between [tex]\angle 1[/tex] and [tex]\angle 2[/tex] is:

[tex]\angle 1 + \angle 2 = 180^o[/tex]

Answer:

The ratio of senior members to junior members at the company is 1 : 3

Step-by-step explanation:

The given average number of years of experience of the senior employees, x = 16 years

The given average number of years of experience of the junior employees, y = 7 years

Let a represent the number of senior employees in the company, and let b represent the number of junior workers in the company, we have;

(16·a + 4·b)/(a + b) = 7

∴ (16·a + 4·b) = (a + b) × 7 = 7·a + 7·b

16·a - 7·a = 7·b - 4·b

9·a = 3·b

a/b = 3/9 = 1/3

a/b = 1/3

The above equation, expressed as a ratio is, a : b = 1 : 3

Therefore;

The ratio of senior members to junior members at the company, a : b = 1 : 3.

Answer:

the answer is 3.81

but rounding it it will be 3.8 meters

Step-by-step explanation:

Pythagorean theorem says

a²+b²=c²

so,

take take the Lowest measurement as a² which will be 7 and take 8 as the hypotenuse or the longest side which is c²

then put it all together you get

7²+x²=8²

we made b as x because we will be finding b

then substitute the values

x²=8²-7²

x²=64-49

x²=15

to remove that square from the x you then put square root in both

✓x²=✓15

press in the calculator, root of 15 will be about 3.81

now we got

x=3.81

x is the missing measurement

Answer:

$943.39622

Step-by-step explanation:

A = final amount, = 1000

Interest, r = 6% = 0.06

Time, t = 1

Principal, P = amount you can borrow today

Using the simple interest formula :

A = P(1 + rt)

1000 = P(1 + 0.06*1)

1000 = P(1 + 0.06)

1000 = P(1.06)

P = 1000 / 1.06

P = 943.39622

lllStep-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

a + b =1

Step-by-step explanation:

Write the given quadratic as x^2 – 1x – 90 = 0.  This factors into

(x - 10)(x + 9) = 0, and so the roots/solutions are {-9, 10}.

If we call -9 "a" and 10 "b," then the sum a + b is -9 + 10, or a + b =1.

Answer:

Step-by-step explanation:

Volume of pyramid = Base area * height

                              = 41.57 * 10

                               = 415.7 cubic inches

Answer:

y =1/2x -4

Step-by-step explanation:

x1 y1  x2 y2

2 -3  4 -2

(Y2-Y1) (-2)-(-3)=   1  ΔY 1

(X2-X1) (4)-(2)=    2  ΔX 2

slope=   1/2    

B= -4          

Y =0.5X -4    

Answer:

B.y = 3x - 1

Step-by-step explanation:

Pick two points on the line

(0,1) and (2,5)

The slope using the slope formula

m = (y2-y1)/(x2-x1)

   = ( 5-1)/(2-0)

  = 4/2

  = 2

We want a slope that is greater than 2

The slope intercept form of the equation is

y = mx+b where m is the slope

y = 3x - 1  has a slope of 3 which is greater than 2

Answer:

82

Step-by-step explanation:

You are looking for the hypotenuse.

c = ?

a = 80

b = 18

c^2 = a^2 + b^2

c^2 = 18^2 + 80^2

c^2 = 324 + 6400

c^2 = 6724

sqrt(c^2) = sqrt(6724)

c = 82 inches

Answer:

[tex]\boxed {\boxed {\sf 82 \ inches}}[/tex]

Step-by-step explanation:

We are asked to find the length of the rake.

We know it hits the wall 80 inches above the ground and the bottom of the rake is 18 inches away from the wall. The point where the top of the rake hits the wall and the distance away from the wall are the legs that form a right angle and the rake is the hypotenuse.

We want to find the hypotenuse or the length of the rake. We will use the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

In this theorem, a and b are the legs and c is the hypotenuse.

The length of the legs are 80 inches (distance from ground to top of rake)  and 18 inches (distance from wall to bottom of rake). The hypotenuse is unknown.

Substitute the known values into the formula.

[tex](80 \ in)^2+(18 \ in)^2= c^2[/tex]

Solve the exponents.

[tex]6400 \ in^2+ 324 \ in^2= c^2[/tex]

Add.

[tex]6724 \ in^2=c^2[/tex]

We are solving for c, the hypotenuse, so we must isolate the variable. It is being squared. The inverse of a square is a square root, so we take the square root of both sides.

[tex]\sqrt {6724 \ in^2}= \sqrt{c^2}[/tex]

[tex]\sqrt{6724 \ in^2}=c[/tex]

[tex]82 \ in =c[/tex]

The length of the rake is 82 inches.

Answer:

√85

Step-by-step explanation:

We can find the distance between two points by using this formula

d = √(x2 - x1)² + (y2 - y1)²

Where the x and y values are derived from the two given points

The two given points are (-2,5) and (4,-2)

Remember that coordinates are written as (x,y)

Next we want to define our variables ( x2, x1, y2 and y1 are the variables)

x2 = 4

x1 = -2

y2 = -2

y1 = 5

Now to find the distance between the two points we simply substitute the values of the variables into the formula

Formula: d = √(x2 - x1)² + (y2 - y1)²

x2 = 4, x1 = -2, y2 = -2 and y1 = 5

d = √(4 - (-2))² + (-2 - 5)²

The two negative signs before the 2 cancel out and it changes to + 2

d = √(4 + 2)² + (-2 - 5)²

Add 4 and 2

d = √6² + (-2 - 5)²

Subtract -2 and -5

d = √6² + -7²

Apply the exponents

d = √36 + 49

Add 36 and 49

d = √85

We can conclude that the distance between the two points is √85

Answer:

11314.87379 (This is still rounded).

Step-by-step explanation:

Year 1:

9300*4%=372. 9300+372=9672.

Year 2:

9672*4%=386.88. 386.88=10058.88.

Year 3:

10058.88*4%=402.3552. 402.3552+10058.88=10461.2352.

Year 4:

10461.2352*4%=418.449408. 418.449408+10461.2352=10879.68461

Year 5:

10879.68461*4%=435.1873843. 435.1873843+10879.68461=11314.87379.

Some of the sub-questions have been answered. I will provide explanation to the already answered questions and then answer the unanswered parts

1. The graph type

The three graph displayed are stem-and-leaf plots. The single numbers at the left-hand side are referred to as the stem, while the numbers at the right are called leaves.

2. The type of data

The three graphs display numerical data (i.e. numbers). Hence, the data are quantitative

3. The correct graph

To know the correct graph; the leaves on each line must be in ascending order and the delimiter to use is a blank space.

Only graph A obey the above illustration

4. Skewness

In graph A, the length of the leaves increases as we move from one stem to the other. This means that the graph is negatively skewed.

For a negative skewed stem plot, the mean is less than the median

5. The population size

This means that we count the number of leaves in the stem plot

The leaves are:

[tex]Leaves = \{0,8,4,8,0,4,6,2,2,2,6,6,6,0,0,0,0,2,4\}[/tex]

So, the population size is: 19

6. The data set

To do this, we include the stem to the corresponding leaves.

So, we have:

[tex]Dataset= \{50,58,64,68,70,74,76,82,82,82,86,86,86,90,90,90,90,92,94\}[/tex]

Learn more about stem and leaf plots at:

https://brainly.com/question/22141441

Step-by-step explanation:

People also ask

What is Heron's formula of area of triangle?

Then the semi-perimeter is, s = (a + b + c)/2 = (3 + 6 + 7)/2 = 8. We will find the area of the triangle using the Heron's formula. This formula was derived by a mathematician known as the Hero of Alexandria.

...

Area of Triangle With 3 Sides.

1. Area of Triangle with 3 Sides Formula

3. FAQs on Area of Triangle with 3 Sides

....

Answer:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Step-by-step explanation:

Heron's formula allows us to find the area of any triangle when given the length of the three sides of the triangle. Let [tex]s[/tex] represent the semi-perimeter of the triangle and let the three sides be [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex].

The semi-perimeter is equal to half the perimeter and is calculated by:

[tex]s=\frac{a+b+c}{2}[/tex]

After you've found [tex]s[/tex], multiply it by the difference between it and each of the sides of the triangle. Then take the square root of that value to find the area of the triangle. Therefore, Heron's Formula is:

[tex]\boxed{A=\sqrt{s(s-a)(s-b)(s-c)}}[/tex]

Answer:

x = 2

Step-by-step explanation:

0.3 (4 - x) = x - 1.4

1.2 - 0.3x = x - 1.4

-0.3x - x = -1.4 - 1.2

-1.3x = -2.6

x = 2

Answer:

Step-by-step explanation:

[tex]\displaystyle\ \Large \boldsymbol{} 0,3(4-x)=x-1,4 \\\\1,2-0,3x=x-1,4 \\\\x+0,3x=1,2+1,4\\\\1,3x=2,6 \\\\\underline{x=2 \ \ \ \ \ \ \ } \\\\0,3(4-2)=2-1,4 \\\\2\cdot 0,3=0,6 \\\\0,6=0,6[/tex]

Answer:

30. 2x²-x-1=0

or, 2x²-2x+x-1=0

or, 2x(x-1)+1(x-1)=0

or, (x-1)(2x+1)=0

so, x-1 = 0 or, x = 1

and 2x+1 = 0 or, 2x = -1 or, x = -1/2

so, x = 1 and 1/2

31. 3x²-14x=5

or, 3x²-14x-5=0

or, 3x²-15x+x-5=0

or, 3x(x-5)+1(x-5)=0

or, (x-5)(3x+1)=0

so, x-5=0 or, x=5

and 3x+1=0 or, 3x=-1 or, x=-1/3

so, x = 5 and -1/3

Answered by GAUTHMATH

Answer:

its 16

Step-by-step explanation:

rotation doesnt effect length

Answer:

180 degrees

Step-by-step explanation:

ABCD is now opposite where it started, so it was rotated 180 degrees

I hope this helps!

Answer:

180 degrees

Step-by-step explanation:

The question is incomplete. The complete question is :

Let [tex]p(t) = -0.0375t^2 + 0.225t[/tex]  be the density function for the shelf life of a brand of banana which lasts up to 4 weeks. Time, t, is measured in weeks and [tex]$0 \leq t \leq 4$[/tex]. Incorrect answer icon Your answer is incorrect. Find the mean shelf life of a banana using . Round your answer to one decimal place.

Answer:

2.4

Step-by-step explanation:

 Given :

[tex]p(t) = -0.0375t^2 + 0.225t[/tex]

Mean :

[tex]$=\int_0^4 tp (t) \ dt$[/tex]

[tex]$=\int_0^4 t (0.0375 t^2 + 0.225t) \ dt$[/tex]

[tex]$=-0.0375 \int_0^4 t^3 \ dt + 0.225 \int_0^4 t^2 \ dt$[/tex]

[tex]$=-0.0375 \left[ \frac{t^4}{4} \right]^4_0 + 0.225 \left[ \frac{t^3}{3} \right]^4_0$[/tex]

[tex]$=-0.0375 (64) + 0.225 \left( \frac{64}{3} \right)$[/tex]

[tex]$=-2.5 + 4.8$[/tex]

= 2.4

Therefore, the mean is 2.4

Answer:

Step-by-step explanation:

r = d/2

r = 10.2/2 = 5.1

Area = pi * r^2

Area = 3.14 * 5.1^2

Area = 81.67 in^2

To the nearest 1/10, this is 81.7 in^2