Babies in the United States have a mean birth length of 20.5 inches with a standard deviation of 0.90 inch. The shape of the distribution of birth lengths is approximately Normal. a) Find the birth length at the 2.5th percentile. b) Find the birth length at the 97.5 percentile. c) Find the z-score for the length at the 2.5th percentile. d) Find the z-score for the length at the 97.5th percentile.

Answer:

a. £564

b. £141

Step-by-step explanation:

a. Firstly, we add up the ratios

= 5 + 4 + 3 = 12

Amanda’s share was 5

Let the total amount be £x

Thus; 5/12 * x = 235

5x = 12 * 235

x = 2820/5 = 564

The total cost of the holiday is £564

b. We want to calculate what Bethany paid

That would be 3/12 * 564 = £141

Answer:

the base???

Step-by-step explanation:

Answer:

Exponent

Step-by-step explanation:

An exponent is a shorthand notation which tells how many times a number (or expression) is multiplied by itself.

Answer:

the length of the side opposite = 20.6 feet

Step-by-step explanation:

using SOHCAHTOA

Sin 40 = opp / hyp

Sin 40 = opp / 35

opp = sin 40 x 35

opp = 20.6 feet

Answer:

If you account 0 as your first term then the 6th term of the arithmetic sequence will be 20.

Step-by-step explanation:

Answer:

1.) No

2.) 40 goals

Step-by-step explanation:

Given the following :

Last season:

Games played = 15

Points scored = 41

Current season:

Games played = 9

Points scored = 24

A)

Last season:

Goals per game = total points / number of games

Goals per game = 41 / 15 = 2.733

Current season :

Goals per game = total points / number of games

Goals per game = 24 / 9 = 2.667

Last season's goal per game is greater than that of current season.

B)

Current rate = goals / games = 24/9 - - - (1)

Let points to be scored this season = y

Ratio of y to number of games played last season = y / 15 - - - (2)

Equate both

24 / 9 = y / 15

9 * y = 24 * 15

y = 360 / 9

y = 40

Answer:

Last option is the correct choice.

Step-by-step explanation:

Substitute the first equation in the second equation and then solve for the variable m.

[tex]\begin{bmatrix}3m+7-2m=1\end{bmatrix}[/tex]

[tex]m=-6[/tex]

[tex]n=3\left(-6\right)+7\\\\n=-11[/tex]

Best Regards!

D!!!!

n=−11

m=−6

I used a graph to show you what the lines and when they would intersect would look like!!

Answer:

C.) (1/2, 4)

Step-by-step explanation:

The solution is where the two lines intersect

The lines intersect at x = .5 and y =4

Answer:

C.) (1/2, 4)

Step-by-step explanation:

Answer:

The interquartile range of the players' weights = 48 pounds.

Step-by-step explanation:

The boxplot attached to this question is missing. It was obtained online and is attached to this solution of the question.

It should be noted that the following is true for a boxplot.

A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.

The elements of the box plot are described thus;

The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.

The horizontal line inside the box is the median.

The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.

Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.

So, it is evident that for this question,

First quartile = 174 pounds

Third quartile = 222 pounds

Inter Quartile Range = (Third quartile) - (First quartile)

= 222 - 174

= 48 pounds.

Hope this Helps!!!

Answer:

The measurement found using Ruler 2 is more accurate and more precise.

Step-by-step explanation:

Ruler 1 has fewer tick marks, Ruler 2 has more which indicates  a more precise, exact, accurate reading.

option B is correct on edge

Step-by-step explanation:

Answer:

[tex] t = 17.3 [/tex]

Step-by-step explanation:

Given:

∆TUV,

m < T = 87°

VT = u = 11

TU = v = 14

VU = t = ?

Use the Law of Cosines to find t as shown below:

[tex] t^2 = u^2 + v^2 - 2uv*cos(T) [/tex]

[tex] t^2 = 11^2 + 14^2 - 2*11*14*cos(87) [/tex]

[tex] t^2 = 121 + 196 - 308*0.0523 [/tex]

[tex] t^2 = 317 - 16.1084 [/tex]

[tex] t^2 = 300.89 [/tex]

[tex] t = 17.3 [/tex] (rounded to the nearest tenth)

Answer:

b / 4

Step-by-step explanation:

If you are splitting b bumper stickers between 4 members, you must divide the number of bumper stickers by the number of members, which is 4! Dividing is just like if you were to divvy something up between people, but it is a mathematical term! This will give you  b / 4.

Answer:

21/20.

Step-by-step explanation:

tan α = opposite side / adjacent side

= 21/20

Answer:because that’s what the answer is

Step-by-step explanation:

Answer:

Y=1/2x-3

Step-by-step explanation:

Answer:

1:3

Step-by-step explanation:

4:12 divides by 4 to give

1 : 3

Answer:

n = 3

Step-by-step explanation:

1:n = 4:12

1/n = 4/12

Cross multiply.

4n = 12

n = 12/4

n = 3

Answer:

5/4,1.3,1 8/25

Step-by-step explanation:

5/4 = 1.25

1 8/25=1.32

1.25<1.3<1.32

Answer:

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

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

[tex]\frac{y-1}{2}[/tex] = x

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , so

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

Answer:  " f⁻¹(x) = (x-1)/2  ";  or, write as:

___________________________________

              " f⁻¹(x) = (x/2) - (1/2) " .

___________________________________

Step-by-step explanation:

___________________________________

Given:   f(x) = 2x + 1 ;  Find the inverse:

___________________________________

1)  Rewrite as y = 2x + 1 ;

2) Replace the "x" with "y" ; and the "y" with "x" ; and rewrite:

         x = 2y + 1 ;

3)  Now, "solve"; with "y" standing alone as a single, isolated variable on the left side of the equation, with an "equals" sign following the "y" :

         x = 2y + 1 :

Subtract "1" from each side of the equation:

         x - 1 = 2y + 1 - 1 ;

to get:

         x - 1 = 2y ;

___________________________________

↔  Rewrite as :

2y = x - 1 ;

Now, divide each side of the equation by "2" ;

  to isolate "y" on the left-hand side of the equation;

  & to solve in terms of "y":

___________________________________

2y / 2 = (x-1)/2 ;

___________________________________

to get:

y = (x-1)/2 ;

or; write as:  y = (x/2) - (1/2);

___________________________________

Now, rewrite; by replacing the "y" with "f⁻¹(x) "; as follows (to indicate that this is the "inverse function"):

___________________________________

f⁻¹(x) = (x-1)/2 ;  or, write as:

___________________________________

f⁻¹(x) = (x/2) - (1/2) .

___________________________________

Hope this is helpful to you!

 Best wishes!

___________________________________

Answer:

The answer is given below

Step-by-step explanation:

In triangle EFG, let a = EG, A = ∠f, b= 1.3 in, B = ∠G, c = 2.4 in C = ∠E = 48°

Using cosine rule:

[tex]c^2=a^2+b^2-2ab*cos(C)\\a^2-2ab*cos(C)=c^2-b^2\\Substituting:\\a^2-2a(1.3)cos(48)=2.4^2-1.3^2\\a^2-1.74a=4.07\\a^2-1.74a-4.07=0\\a=3\ or\ -1.34\\a=EG=3\ inches[/tex]

EG = 3 inches

Using sine rule,

[tex]\frac{b}{sin(B)} =\frac{c}{sin(C)}\\ Substituting:\\\frac{1.3}{sin(B)} =\frac{2.4}{sin(48)}\\sin(B)=\frac{sin(48)*1.3}{2.4}=0.4025\\ B=sin^{-1}(0.4025)=23.7^0[/tex]

∠G = B = 23.7°

Given ΔXYZ ≅ ΔEGF,

Therefore: ZX = EF = 1.3 inches, m∠X = m∠G =23.7 °, m∠Z = m∠F = 107°

ZY = FG = 2.4

Answer:

ZX = 1.3 in.

EG = 3 in.

m∠X = 48°

m∠G = 25°

Step-by-step explanation:

ΔXYZ ≅ ΔEGF

107 + 48 = 155

m∠G = 180 - 155 = 25

Answer:

Area of sphere = 576 pi ft^2

Volume of sphere = 2,304 pi ft^3

Step-by-step explanation:

Radius of great circles are the same as radius of the sphere

So let’s calculate the radius of the sphere from the area given;

Mathematically;

pi * r^2 = 144pi

r^2 = 144

r = square root of 144

r = 12 ft

Volume of sphere = 4/3 * pi * r^3

= 4/3 * pi * 12^3 = 2,304 pi ft^3

Area of sphere = 4 * pi * r^2 = 4 * pi * 12^2 = 4 * 144 * pi = 576 pi ft^2

Answer:

Slope = [tex]-\frac{11}{7}[/tex]

Step-by-step explanation:

Slope = [tex]\frac{rise}{run}[/tex]

Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]

Slope = [tex]\frac{7+4}{-12+5}[/tex]

Slope = [tex]\frac{11}{-7}[/tex]

Slope = [tex]-\frac{11}{7}[/tex]

Answer:

11/-7

Step-by-step explanation

- First you get you X1 and Y1 then X2 and Y2

-after getting that your problem should look like this:

7 minus negative 4

over negative -12  minus negative -5

which when subtracted will get you 11/-7!

please give brainliest!

Answer:

If we look at the table we notice that 2 + 4 = 6, 3 + 4 = 7, 4 + 4 = 8 and so on so the equation is y = x + 4.

Answer:

x+4

Step-by-step explanation:  

To solve this question we must look at the examples :

6-2=4

7-3=4

so the aswer is : y = x + 4

Work Shown:

908 rounds to 900. This is because 908 is closer to 900, than it is to 1000.

While 67 rounds to 100, for similar reasoning as above.

Multiplying those rounded values gives 900*100 = 90,000. This is the number 90 thousand.

Note that 9*1 = 9 and its followed by four zeros (two each from 900 and 100). This is a quick way to mentally multiply things like this.

Using a calculator, we see that 908*67 = 60,836 which is fairly off from what we estimated. This is to be expected as estimates only give us a rough idea of how big a number is.

Answer:

a direct variation means that the ratio of the variables is constant.as we know y=kxrepresents a family of straight lines passing through the origin.

Step-by-step explanation:

thisthis means as x increases y increases and aspects decreases y increases and the ratio between them always stayed the same

Answer:

A direct variance implies that the ratio of the variables is constant, since we know that y= kx represents a straight line family that passes through the origin.

Answer:

It's (B)

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

He made 48 naira.

48 = 40% * 120

Answer:

6

Step-by-step explanation:

Let the number be x.

1/3 × 12 = 2/3 × x

Multiply.

12/3 = 2/3x

4 = 2/3x

Multiply both sides by 3/2.

4 × 3/2 = x

12/2 = x

x= 6

Answer:

1/3 of 12 = 2/3 of 6

Step-by-step explanation:

1/3 · 12 = 2/3 · x

12/3 = 2x/3

Multiply 3 on both sides.

12 = 2x

12 ÷ 2 = x

6 = x

Answer:

1.2x10^13

Step-by-step explanation:

Trillion=1x10^12

12 trillion=12x10^12

12 trillion=1.2x10^13

Answer:

Ans is 72 bags!!

Step-by-step explanation:

Call the original number of bags, B

After 1/6 of these were eaten, there were B - (1/6)B = (5/6)B left

After 50% of these were eaten.....there were (1/2)(5/6)B = (5/12)B left

And this = 30

So

(5/12)B = 30 multiply both sides by 12/5

B = 30(12/5)

B = 360 / 5

B = 72

Hope it helped

Tysm

Mark me BRAINLIEST!

Answer:

a = 3

b = -2

c = 5

Step-by-step explanation:

The general form of a quadratic equation is ax² + bx + c = 0.

3x² - 2x + 5 = 0

The value of a is 3.

The value of b is -2.

The value of c is 5.

Answer:

Step-by-step explanation: