The mean length of 7 childrens' index finger is 9.4cm. The mean length of 5 adults' index finger is 10.2cm. What is the mean length (rounded to 2 DP) of these 12 people's index finger?

Answer:

7/2                

Step-by-step explanation:

3 hours and 30 minutes = 7/2 in improper fraction

1 hour = 60 minutes

30 minutes = 30 minutes * 1 hour/60 minutes =30/60 = 1/2 hour

3 hours and 30 minutes:

= 3 hours + 1/2 hour

= 3 1/2 hours

= [(2 * 3)+1]/2

= [6+1]/2

= 7/2

Kate can see across the horizon by 3.33 times further than Paul.

The assumed shape of the horizon shows that it forms a cone shape. The volume of the cone can be used to determine how far they can see.

The volume of the cone [tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]

For Kate:

[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]

[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}[/tex]

V = 2.12526863 × 10¹⁵ m³

For Paul

[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]

[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}[/tex]

V = 6.3758059 × 10¹⁴ m³

To determine how much further can kate see across the horizon than Paul, we have:

= Volume of Kate/Volume of Paul

= 2.12526863 × 10¹⁵ m³/6.3758059 × 10¹⁴ m³

= 3.33 times further.

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Answer:

x=14

Step-by-step explanation:

collect like terms, like so

Answer:4(x−2)−8=4+2x

Use the distributive property to multiply 4 by x−2.

4x−8−8=4+2x

Subtract 8 from −8 to get −16.

4x−16=4+2x

Subtract 2x from both sides.

4x−16−2x=4

Combine 4x and −2x to get 2x.

2x−16=4

Add 16 to both sides.

2x=4+16

Add 4 and 16 to get 20.

2x=20

Divide both sides by 2.

x=

2

20

​

Divide 20 by 2 to get 10.

x=10

Step-by-step explanation:

Answer:

There are many ways we can write [tex]5^{11}[/tex] one of them being that we just write 11 fives being multiplied against each other like the following:

[tex]5*5*5*5*5*5*5*5*5*5*5[/tex]

This can seem very repetitive which is why powers are a lot more helpful.  We can also rewrite [tex]5^{11}[/tex] using the power in the bottom of a fraction.  The way that we do this is put [tex]5^{-11}[/tex] on the bottom which can then be flipped to the top with a positive power and will be the same.

[tex]\frac{1}{5^{-11}}[/tex]

The final way that we can rewrite [tex]5^{11}[/tex] is by using several different powers.  We can do [tex]5^6*5^5[/tex] which will equal the same thing as [tex]5^{11}[/tex] because the base is the same and what we basically do is just add up the powers together to get back to 11.

[tex]5^6*5^5[/tex]

Answer:the answer above is correct

Step-by-step explanation:

[tex]∠BAD≈65.22°[/tex]

Note:

The following formula is tan formula:

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

1) Finding the tan of ∠BAC

[tex]tan(\theta)=\dfrac{4}{5}[/tex]

[tex]\theta=tan^-1(\dfrac{4}{5})[/tex]

2) Finding the tan of ∠CAD

[tex]tan(\theta)=\dfrac{3}{6}[/tex]

[tex]\theta=tan^-1(\dfrac{3}{6})[/tex]

3) Add the value of ∠BAC to the value of ∠CAD

[tex]tan^-1(\dfrac{4}{5})+tan^-1(\dfrac{3}{6})≈65.22°[/tex]

4) The sum of interior angles in quadrilateral is 360°

Then

[tex]tan(∠BAC)+tan(∠ACB)+tan(∠CAD)+tan(∠ACD)=360°[/tex]

[tex]tan^-1(\dfrac{4}{5})+tan^-1(\dfrac{5}{4})+tan^-1(\dfrac{3}{6})+tan^-1(\dfrac{6}{3})=180°[/tex]

[tex]180°+∠CDA+∠CBA=^?360[/tex]

[tex]180°+90°+90°=^?360°[/tex]

[tex]360°=360°[/tex]

Answer:

$288

Step-by-step explanation:

We first need to find what 0.8% of 300 makes and to do that we multiply 300 with 0.8 and divide that by 100

300*(0.8)/100 = 2.4 this is the monthly interest

Now we need to find how much it'd be after 10 years

There are 10*12 = 120 months in 10 years

120*(2.4) = 288 is the interest Bob will earn after 10 years

Answer: The mean is 24, and the median is 26.5 .

Step-by-step explanation: To find the mean, one must add all the numbers in a set of data and divide it by the amount of numbers added. To find the median, one must line the numbers in a set of data from biggest to smallest. The number in the middle is the median. If the amount of numbers in the set are even, resulting in no middle, the two numbers closest to the middle are added and then divided by two. The resulting number is the median. In this case I had to add and divide.

Answer:

10 ft.

Step-by-step explanation:

Scale ⇒ 1 in. : 2 ft.

Scale factor

Width of model=5in

Width of structure

Answer:180 or halfwayStep-by-step explanation:90 is 1/4 and 360 is a full rotation so it rotated halfway all together.

Answer:

2n + 3n equals to 5n in the end, so just set n equal to literally any number :)

Step-by-step explanation:

Example:

Let n = 1000

2(1000) + 3(1000) = 5(1000)

5000 = 500

Basically, plug in the number and solve on both sides each time. You will know you've demonstrated it if it's equal on both sides

Answer:

2n + 3n equals to 5n in the end, so just set n equal to literally any number

Step-by-step explanation:

Example:

Let n = 1000

2(1000) + 3(1000) = 5(1000)

5000 = 500

Basically, plug in the number and solve on both sides each time. You will know you've demonstrated it if it's equal on both sides

Answer:

Step-by-step explanation:  interior angle of a regular polygon is 160 degrees, then the exterior angle is 20 degrees. The sum of all exterior angles is 360 degrees so there must be 360/20 sides = 18 sides.

yes it can have 160 degree as interior angel

Answer:

y=2/3x+4

Step-by-step explanation:

4 is y-intercept

2/3 is  the slope (rise/run)

Answer: y = [tex]\frac{2}{3}[/tex]x + 4

Step-by-step explanation:

    This is in slope-intercept form. We are missing the m and the b value. See attached for more information.

[m aka the slope]

   Starting from point (-6, 0), counting up 2 units, then right 3 units to point (-3, 2), gives us a slope of [tex]\frac{2}{3}[/tex] via rise-over-run

[b aka the y-intercept]

   The line intersects the y-axis at positive 4.

-> This value is "4"

Answer:

the answer is b

Step-by-step explanation:

you multiply 0.1% or 0.001 to 4200

the reason I am not multiplying 1.2% is because that is for yearly and 0.1% is for monthly

Answer:

A

Step-by-step explanation:

find 1.2% of £4,200 then multiply it

The answer would be [tex]\frac{1}{2}[/tex].

The probability of getting a 5 is [tex]\frac{1}{100}[/tex] and the probability of getting a number larger than 50 is [tex]\frac{49}{100}[/tex] (the 50 doesn't count). Add those up and you get [tex]\frac{50}{100}[/tex] and can be simplified to [tex]\frac{1}{2}[/tex].

Answer:

  51/100

Step-by-step explanation:

The probability is the ratio of the number of outcomes of interest to the total number of possible outcomes.

__

There is one number 5. There are 50 numbers in the range 1–100 that are greater than 50. So, the total number of outcomes of interest is 1+50 = 51.

The possible outcomes are any of the numbers 1–100, so there are 100 of them.

The probability of interest is ...

  P(n=5||n>50) = 51/100

Answer:

D

Step-by-step explanation:

(-10,6) got it correct

Answer:

I think no solution I'm not sure sorry if I'm wrong

The image of dilating the points by a scale factor 3.5 with centre of enlargement (4, -6) is (-7, 14), (0, 14), (-7,7) and (0, 7)

The coordinates are given as:

(2,-2) (4,-2) (2,-4) (4,-4)

The scale factor is given as:

k = 3.5

The center of enlargement is given as:

(a,b) = (4, -6)

The image of dilation is calculated using:

[tex](x,y) \to (k(x -a), k(y -b))[/tex]

So, we have:

A = (3.5(2 -4), 3.5(-2 +6))

A = (-7, 14)

B = (3.5(4 -4), 3.5(-2 +6))

B = (0, 14)

C = (3.5(2 -4), 3.5(-4 +6))

C = (-7,7)

D = (3.5(4 -4), 3.5(-4 +6))

D = (0, 7)

Hence, the image of dilating the points is (-7, 14), (0, 14), (-7,7) and (0, 7)

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Answer:

15° and 100°

Step-by-step explanation:

[tex]65 + 3x + 20x = 180[/tex]

[tex]23x = 115[/tex]

[tex]x = 5[/tex]

3 × 5 = 15, 20 × 5 = 100. So the other two angles measure 15° and 100°.

Answer:

I'm assuming you want me to do 18-23?  Okay:

Step-by-step explanation:

18) 8.6(10^−4)+6.7(10^−5)

=0.000927 --> 9.27 × 10^-4

19)  3.5(10^3)−9(10^1)

=3410 --> 3.41 × 10^3

20)  5.6(10^4)(4.5(10^6))

=252000000000 -->  2.52 × 10^11

21)  7.6(10^−7)(8.9(10^−2))

=0 --> 0

22)  3.9(10^−12)/4(10^4)

=0 --> 0

23)  1.75(10^5)/5(10^−3)

=35000000 -->  3.5 × 10^7

-

Please comment below if you would like me to solve #24 :)

The bolded numbers are the answer, the underlined numbers are to show the question number.  Hope this helped !!

The correct options are:

The probability you select a purple marble is 3/10

P(Red) + P(Yellow) + P(Purple) = 1

The probability you select a green marble is 0.

Probability calculates the chance that an event would happen. If it is certain that the event would not happen, it would have a value of 0. If it is certain that the event would happen, it would have a value of 1.

Probability of picking a red marble = total number of red marbles / total number of marbles

= 4/10

Probability of picking a purple marble =  total number of purple marbles / total number of marbles

3/10

P(Red) + P(Yellow) + P(Purple) = 4/10 + 3/10 + 3/10 = 1

Here is the complete question:

A bag contains four red marbles, three yellow marbles, and three purple marbles. You will randomly select one marble from the bag.

Which statements are true regarding the scenario? Check all that apply.

The probability you select a red marble is 3/10

The probability you select a purple marble is 3/10

P(Red) + P(Yellow) + P(Purple) = 1

The probability you select a green marble is 0.

The probability you select a yellow marble is 3.

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Answer:

b,c,d on edge

Step-by-step explanation:

trust

Answer: C. 30:1

Step-by-step explanation:

A ratio of x:y is created by taking the number of x and the number of y, plugging them in, and reducing if necessary. In this problem, x is orange trees and y is cherry trees. There are 30 orange trees and only 1 cherry tree, so the ratio is 30:1. It cannot be reduced.

Answer:

4289.4

Step-by-step explanation:

El valor que falta es 4289.4, 4289.4 ÷ 9 = 476.6

Answer:

  $37,500

Step-by-step explanation:

The amount of the fee is the product of the fee rate and the amount to which that rate is applied.

__

  3.75% × $1,000,000 = 0.0375 × $1,000,000 = 37.5 × $1000

  = $37,500

The fee on a $1M loan could range up to $37,500.

_____

Additional comment

If you're computing this by hand, it can be easier to (a) use scientific notation, or (b) adjust the decimal points as we have shown here. In this case, we multiplied the percentage by 1000 and divided the loan amount by 1000. The product remains the same, but the numbers are easier to deal with.

In scientific notation, this is 3.75E-2 × 1E6 = 3.75E4 = 37.5E3 = 37,500, where the "E" notation would be that used by a calculator or spreadsheet.

Answer:

  (x, y) = (12, 15)

Step-by-step explanation:

The given expression for y suggests that using substitution would be a good choice for the method of solution.

__

  x +(x +3) = 27 . . . . substitute for y using the second equation

  2x = 24 . . . . . . . subtract 3

  x = 12 . . . . . . . divide by 2

  y = 12 +3 = 15 . . . . use the second equation to find y

The solution is (x, y) = (12, 15).

Answer:

244.93

Step-by-step explanation:

area formula for trapezoid:1/2*(b1+b2)*h

area formula for semi circles: (3.14*r^2)/2

so then we cut the figure to make a semi cirlce and trapazoid

semicircle- 14 is the full diameter, divide by 2 to make 7, 7×3.14×7)/2=76.93

trapezoid: base one is 18. base 2 is 14. 18+14=32 then times that by 10.5 which is 336 and divide that by 2 is 168

add both and you get 244.93

Answer:

Soup A

Step-by-step explanation:

For this we need to find the number of sodium per cup. To do this, we divide the ratios by the number of cups. 8:10 would be 10/10 (1 cup) and 8/10 (.8 g per cup). 7:14 would be 14/14 (1 cup) and 7/14 (.5 g per cup). So, soup A has .8 g of sodium per cup and soup B has .5 g of sodium per cup. .8>.5, so soup A has more sodium.

Hope this helps!

Answer:

1.

Step-by-step explanation:

distance = √(X2 - X1)^2 + (Y2 - Y1)^2

= √(-1 - 2)^2 + (9 - 8)^2

= √(-3)^2 + (1)^2

= √ 9 + 1

= √10

Answer:The distance is √10

Step-by-step explanation:

The function best represents the given graph will be f(x) = (x + 3)(x − 3)(x - 1)

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

Given that:-

The polynomial for the given points will be written as:-

f(x) = (x + 3)(x − 3)(x - 1)

The coordinate is -3 so it will be written as (x+3) similarly 1, and 3 will be written as (x-3) and (x-1) .

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