Natalie is scuba diving in the ocean. She starts 30 feet below sea level. She then dives down another 20 feet. From there, she goes up 15 feet. Which equation shows Natalie's current level?

Answer:

a) The height decreases at a rate of [tex]\frac{7}{12}[/tex] ft/sec.

b) The area increases at a rate of [tex]\frac{527}{24}[/tex] ft^2/sec

c) The angle is increasing at a rate of [tex]\frac{1}{12}[/tex] rad/sec

Step-by-step explanation:

Attached you will find a sketch of the situation. The ladder forms a triangle of base b and height h with the house. The key to any type of problem is to identify the formula we want to differentiate, by having in mind the rules of differentiation.

a) Using pythagorean theorem, we have that [tex] 25^2 = h^2+b^2[/tex]. From here, we have that

[tex]h^2 = 25^2-b^2[/tex]

if we differentiate with respecto to t (t is time), by implicit differentiation we get

[tex]2h \frac{dh}{dt} = -2b\frac{db}{dt}[/tex]

Then,

[tex]\frac{dh}{dt} = -\frac{b}{h}\frac{db}{dt}[/tex].

We are told that the base is increasing at a rate of 2 ft/s (that is the value of db/dt). Using the pythagorean theorem, when b = 7, then h = 24. So,

[tex]\frac{dh}{dt} = -\frac{2\cdot 7}{24}= \frac{-7}{12}[/tex]

b) The area of the triangle is given by

[tex]A = \frac{1}{2}bh[/tex]

By differentiating with respect to t, using the product formula we get

[tex] \frac{dA}{dt} = \frac{1}{2} (\frac{db}{dt}h+b\frac{dh}{dt})[/tex]

when b=7,  we know that h=24 and dh/dt = -1/12. Then

[tex]\frac{dA}{dt} = \frac{1}{2}(2\cdot 24- 7\frac{7}{12}) = \frac{527}{24}[/tex]

c) Based on the drawing, we have that

[tex]\sin(\theta)= \frac{b}{25}[/tex]

If we differentiate with respect of t, and recalling that the derivative of sine is cosine, we get

[tex] \cos(\theta)\frac{d\theta}{dt}=\frac{1}{25}\frac{db}{dt}[/tex] or, by replacing the value of db/dt

[tex]\frac{d\theta}{dt}=\frac{2}{25\cos(\theta)}[/tex]

when b = 7, we have that h = 24, then [tex]\cos(\theta) = \frac{24}{25}[/tex], then

[tex]\frac{d\theta}{dt} = \frac{2}{25\frac{24}{25}} = \frac{2}{24} = \frac{1}{12}[/tex]

Answer:

To compute the probabilities, just divide the number of times a number was landed by the total amount of outcomes.

Spinning 2: 30/120 = 0.25  

Spinning 3: 19/120  = 0.16

Spinning 4:  25/120  = 0.21

Spinning 5:  29/120  = 0.24

Spinning 6:  17/120  = 0.14

Stacy would spin a 6 approximately 0.14*50 = 7 times in 50 tries.

Answer:

a) The third quartile Q₃ = 56.45

b) Variance [tex]\mathbf{ \sigma^2 =2633.31}[/tex]

Step-by-step explanation:

Given that :

[tex]Q_1[/tex]  =  30.8

Median [tex]Q_2[/tex] =  48.5

Mean  = 42

a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :

[tex]SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}[/tex]

[tex]-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}[/tex]

[tex]-0.38Q_3 + 11.704 = Q_3 +30.8 - 97[/tex]

[tex]1.38Q_3 = 77.904[/tex]

Divide both sides by 1.38

[tex]Q_3 = 56.45[/tex]

b) The objective here is to determine the approximate value of the variance;

Using the relation

[tex]SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}[/tex]

[tex]-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}[/tex]

[tex]-0.38= \dfrac{(-19.5) }{\sigma}[/tex]

[tex]-0.38* \sigma = {(-19.5) }{}[/tex]

[tex]\sigma =\dfrac {(-19.5) }{-0.38 }[/tex]

[tex]\sigma =51.32[/tex]

Variance =  [tex]\sigma^2 =51.32^2[/tex]

[tex]\mathbf{ \sigma^2 =2633.31}[/tex]

Answer:

a)

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Step-by-step explanation:

a)

Given data population proportion 'p' = 19% =0.19

                                                          q  = 1-p = 1- 0.19 =0.81

Given  two people are randomly​ selected

 Given n = 2

Let 'X' be the random variable in binomial distribution

[tex]P(X=r) =n_{C_{r} } p^{r} q^{n-r}[/tex]

The probability that both will be hopelessly romantic is

                   [tex]P(X= 2) =2_{C_{2} } (0.19)^{2} (0.81)^{2-2}[/tex]

                     P(X = 2)   = 1 × 0.0361

The probability that both will be hopelessly romantic is  

                                                             P(X = 2)   =  0.0361

b)

The probability that at least one person is hopelessly romantic is

               P( X>1) = 1-P(x<1)

                            = 1 - ( p(x =0)

                            = [tex]1- 2_{C_{0} } (0.19)^{0} (0.81)^{2-0}[/tex]

                           = 1 - (0.81)²

                           = 1 -0.6561

                           = 0.3439

The probability that at least one person is hopelessly romantic is

               P( X>1) = 0.3439

Answer:

  the sum shown is (20/21)a -(1/7)

Step-by-step explanation:

As written, the sum is ...

  [tex]a-\dfrac{\frac{3}{7}}{3}-\dfrac{a}{21}=\boxed{\dfrac{20}{21}a-\dfrac{1}{7}}[/tex]

__

We wonder if you mean the quotient ...

  ((a-3)/7)/((3-a)/21)

  [tex]\dfrac{\left(\dfrac{a-3}{7}\right)}{\left(\dfrac{3-a}{21}\right)}=\dfrac{a-3}{7}\cdot\dfrac{21}{3-a}=\dfrac{-21(3-a)}{7(3-a)}=\boxed{-3}[/tex]

_____

Comment on the problem presentation

Parentheses are required when plain text is used to represent fractions. The symbols ÷, /, and "over" all mean the same thing: "divided by." The denominator is the next item in the expression. If arithmetic of any kind is involved in the denominator, parentheses are needed. This is the interpretation required by the Order of Operations.

When the expression is typeset, fraction bars and text formatting (superscript) serve to group items that require parentheses in plain text.

__

Please note that some authors make a distinction between the various forms of division symbol. Some use ÷ to mean ...

  (everything to the left)/(everything to the right)

and they reserve / solely for use in fractions. Using this interpretation, your expression would be ...

  (a -(3/7))/(3 -(a/21)) = (21a -9)/(63 -a)

That distinction is not supported by the Order of Operations.

Answer:

Down below

Step-by-step explanation:

   a. Net income= $100,000 (as given in the question)

   b. Return on equity= (net income)/(shareholder’s equity)

Shareholder’s equity= $400,000

Thus return on equity= 100000/400000 = 0.25  or 25%

   a. Net income= $100000 + 50000 –  12800 (debt interest 8% of     $160000)

= $137,200

b. Return on equity= (net income)/(shareholder’s equity)

= 137200/400000

=0.343  or 34.3%

a. Net Income= $100000 + 50000

= $150000

b. Return on equity= (net income)/(shareholder’s equity)

= 150000/(400000 + 160000)

Where ($560,000) 400000 + 160000 is shareholder’s equity

= 0.27 or 27%

Answer:

  8.5

Step-by-step explanation:

For continuous compounding, the account value formula is ...

  A = Pe^(rt)

where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...

  3550 = 2400e^(.046t)

  ln(355/240) = 0.046t

  t = ln(355/240)/0.046 ≈ 8.5

It will take 8.5 years for the value to reach $3550.

Answer:

32/25 walls per gallon.

Step-by-step explanation:

Martin uses 5/8 Of a gallon of paint to cover 4/5 Of a wall

Hence 1 gallon would be 4/5÷5/8=

4/5 × 8/5= 32/25 walls per gallon.

Answer:

a. The Poisson approximation is good because n is large, p is small, and np < 10.

The parameter of thr Poisson distribution is:

[tex]\lambda =np\approx1.6[/tex]

b. P(r=0)=0.2019

c. P(r>1)=0.4751

d. P(r>2)=0.2167

e. P(r>3)=0.0789

Step-by-step explanation:

a. The Poisson distribution is appropiate to represent binomial events with low probability and many repetitions (small p and large n).

The approximation that the Poisson distribution does to the real model is adequate if the product np is equal or lower than 10.

In this case, n=963 and p=1/596, so we have:

[tex]np=963*(1/596)\approx1.6[/tex]

The Poisson approximation is good because n is large, p is small, and np < 10.

The parameter of thr Poisson distribution is:

[tex]\lambda =np\approx1.6[/tex]

We can calculate the probability for k events as:

[tex]P(r=k)=\dfrac{\lambda^ke^{-\lambda}}{k!}[/tex]

b. P(r=0). We use the formula above with λ=1.6 and r=0.

[tex]P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\[/tex]

c. P(r>1). In this case, is simpler to calculate the complementary probability to P(r<=1), that is the sum of P(r=0) and P(r=1).

[tex]P(r>1)=1-P(r\leq1)=1-[P(r=0)+P(r=1)]\\\\\\P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\P(1)=1.6^{1} \cdot e^{-1.6}/1!=1.6*0.2019/1=0.3230\\\\\\P(r>1)=1-(0.2019+0.3230)=1-0.5249=0.4751[/tex]

d. P(r>2)

[tex]P(r>2)=1-P(r\leq2)=1-[P(r=0)+P(r=1)+P(r=2)]\\\\\\P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\P(1)=1.6^{1} \cdot e^{-1.6}/1!=1.6*0.2019/1=0.3230\\\\P(2)=1.6^{2} \cdot e^{-1.6}/2!=2.56*0.2019/2=0.2584\\\\\\P(r>2)=1-(0.2019+0.3230+0.2584)=1-0.7833=0.2167[/tex]

e. P(r>3)

[tex]P(r>3)=1-P(r\leq2)=1-[P(r=0)+P(r=1)+P(r=2)+P(r=3)]\\\\\\P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\P(1)=1.6^{1} \cdot e^{-1.6}/1!=1.6*0.2019/1=0.3230\\\\P(2)=1.6^{2} \cdot e^{-1.6}/2!=2.56*0.2019/2=0.2584\\\\P(3)=1.6^{3} \cdot e^{-1.6}/3!=4.096*0.2019/6=0.1378\\\\\\P(r>3)=1-(0.2019+0.3230+0.2584+0.1378)=1-0.9211=0.0789[/tex]

Answer:

  7 and 8

Step-by-step explanation:

  54 is between 7^2 = 49 and 8^2 = 64.

The square roots have the same relationship.

  49 < 54 < 64

  √49 < √54 < √64

  7 < √54 < 8

Answer:

V =2744 cm^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

V = 14^3

V =2744 cm^3

Answer: 2,744 cm³

Step-by-step explanation: Since the length, width, and height of a cube are all equal, we can find the volume of a cube by multiplying side × side × side.

So we can find the volume of a cube using the formula s³.

Notice that we have a side length of 14cm.

So plugging into the formula, we have (14 cm)³ or

(14 cm)(14 cm)(14 cm) which is 2,744 cm³.

So the volume of the cube is 2,744 cm³.

Answer:

   {-7, -4, -1, 3, 7}

Step-by-step explanation:

The range is the list of y-coordinates of the points:

  range = {-7, -4, -1, 3, 7}

Answer:

1.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Surface Area is the combined area of all two-dimensional surfaces of a shape. Just like ordinary area, the units are the squares of the units of length (that is, if a shape's sides are measured in meters, then the shape's area is measured in square meters

Answer:

y = - 3x + 9    or     (y - 6) = - 3(x - 1)

Step-by-step explanation:

I'm assuming you are looking for the equation of the line.

First, let's find the slope of the line, which we use equation (y1-y2) / (x1-x2)

x1: 1      x2: 2

y1: 6     y2: 3

(6-3) / (1-2) = 3 / -1 = -3

The slope of the line is -3.

The equation for slope-intercept form is y = mx + b, where m is slope and b is the y - intercept.

y = -3x+b

Now substitute a set of points in (any coordinates work). I'll use (1, 6)

6 = -3(1)+b

6 = - 3 + b

b = 9

So our equation in slope intercept form is y = - 3x + 9

You can also write this in point slope form,   (y-y1) = m (x-x1)     m is still slope

(y - 6) = - 3(x - 1)

Answer:

1/52

Step-by-step explanation:

Answer:

200.96 units

Step-by-step explanation:

Use the formula for the volume of a cone [tex]V=\pi r^{2} \frac{h}{3}[/tex]

Plug in the values ([tex]\pi[/tex]=3.14) and multiply them all out

Answer:

≈ 201

Step-by-step explanation:

V= πr²h/3

V= 3.14*4²*12/3= 200.96 ≈ 201

Answer:

Option D,four is correct

Step-by-step explanation:

The tax withholding from the gross income of $951 is the gross income itself minus the income after tax withholding i.e $189  ($951-$762)

The percentage of the withholding =189/951=20% approximately

Going by the multiple  choices provided,option with 4,189 dollars seems to the correct option as that is the exact of the tax withholding on Robert's gross income and his earnings fall in between $950 and $960

The number of allowances that Robert has claimed is four. Option d is correct.

A withholding tax is a tax that an employer deducts from an employee's paycheck and delivers it straight to the government (federal income tax).

From the given information:

The tax allowance = Gross income - savings amount

The tax allowance = $951 - $762

The tax allowance = $189

From the weekly income between 950 and 960 data, we can see that the number of allowances claimed related to the withholding allowances are:

0  → $259

1   →  $242

2   → $224

3   → $207

4  → $189

5   → $173

6  →  $162

7   → $151

8  →  $140

Therefore, we can conclude that the number of allowances that Robert has claimed is four.

Learn more about tax withholding here:

https://brainly.com/question/25927192

Answer:

Option C.

Step-by-step explanation:

Let a point (x, y) has a sequence of transformations,

Option A).

Reflects across x-axis then the coordinates will be,

(x, y) → (x, -y)

Then reflects across the y-axis,

(x, -y) → (-x, -y)

Image (x, y) gets changed to (-x, -y) therefore, point (x, y) doesn't map onto itself.

Option B).

(x, y) rotate 90° counter clockwise about the origin.

(x, y) → (-y, x)

Then reflect across x-axis,

(-y, x) → (y, x)

Since coordinates of the image and the actual are not same therefore, image doesn't map itself.

Option C).

(x, y) when reflected across x-axis,

(x, y) → (x, -y)

Then reflected over the x-axis,

(x, -y) → (x, y)

In this option point (x, y) maps onto itself after these transformations.

Option D).

(x, y) rotated 90°counterclockwise about the origin

(x, y) → (-y, x)

Then translated up by 2 units.

(-y, x) → (-y, x+2)

Therefore, (x, y) gets changed after these transformations and doesn't maps itself.

Option (C) will be the answer.

Answer:

you have it correct the answer is option c

Step-by-step explanation:

Answer:

X=-2or,-3

Step-by-step explanation:

X^2+5x+6=0

or,x^2+(2+3)x+6=0

or,x^2+2x+3x+6=0

or,x(x+2)+3(x+2)=0

or,(x+3) (x+2)=0

Either,

x+3=0 x+2=0

or,x=-3 or,x=-2

Therefore,the value if x is -2 or -3 .

I HOPE IT WILL HELP YOU

Answer:

x = pi/6

x = 11pi/6  

x = 5pi/6  

x =7pi/6

Step-by-step explanation:

2 sec^2 (x) + tan ^2 (x) -3 =0

We know tan^2(x) = sec^2 (x) -1

2 sec^2 (x) +sec^2(x) -1 -3 =0

Combine like terms

3 sec^2(x) -4 = 0

Add 4 to each side

3 sec^2 (x) = 4

Divide by 3

sec^2 (x) = 4/3

Take the square root of each side

sqrt(sec^2 (x)) = ±sqrt(4/3)

sec(x) = ±sqrt(4)/sqrt(3)

sec(x) = ±2 /sqrt(3)

Take the inverse sec on each side

sec^-1 sec(x) = sec^-1(±2 /sqrt(3))

x = pi/6 + 2 pi n    where n is an integer

x = 11pi/6 + 2 pi n  

x = 5pi/6 + 2 pi n  

x =7pi/6 + 2 pi n  

We only want the solutions between 0 and 2pi

Answer:

i think it's c.)3.5 i may be wrong

Step-by-step explanation:

Answer:

The differential equation which describes the mixing process is [tex]\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}[/tex].

Step-by-step explanation:

The mixing process within the tank is modelled after the Principle of Mass Conservation, which states that:

[tex]\dot m_{salt,in} - \dot m_{salt,out} = \frac{dm_{tank}}{dt}[/tex]

Physically speaking, mass flow of salt is equal to the product of volume flow of water and salt concentration. Then:

[tex]\dot V_{water, in, 1}\cdot c_{salt, in,1} + \dot V_{water, in, 2} \cdot c_{salt,in, 2} - \dot V_{water, out}\cdot c_{salt, out} = V_{tank}\cdot \frac{dc_{salt,out}}{dt}[/tex]

Given that [tex]\dot V_{water, in, 1} = 9\,\frac{L}{min}[/tex], [tex]\dot V_{water, in, 2} = 7\,\frac{L}{min}[/tex], [tex]c_{salt,in,1} = 0.04\,\frac{kg}{L}[/tex], [tex]c_{salt, in, 2} = 0.05\,\frac{kg}{L}[/tex], [tex]\dot V_{water, out} = 16\,\frac{L}{min}[/tex] and [tex]V_{tank} = 1000\,L[/tex], the differential equation that describes the system is:

[tex]0.71 - 16\cdot c_{salt,out} = 1000\cdot \frac{dc_{salt,out}}{dt}[/tex]

[tex]1000\cdot \frac{dc_{salt, out}}{dt} + 16\cdot c_{salt, out} = 0.71[/tex]

[tex]\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}[/tex]

Answer:

(a) See below

(b) r = 0.9879  

(c) y = -12.629 + 0.0654x

(d) See below

(e) No.

Step-by-step explanation:

(a) Plot the data

I used Excel to plot your data and got the graph in Fig 1 below.

(b) Correlation coefficient

One formula for the correlation coefficient is  

[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}[/tex]

The calculation is not difficult, but it is tedious.

(i) Calculate the intermediate numbers

We can display them in a table.

   x            y             xy                      x²             y²    

   36       0.22              7.92               1296           0.05

   67        0.62            42.21              4489           0.40

   93         1.00            93.00           20164           3.46

 433        11.8          5699.4          233289        139.24

 887      29.3         25989.1          786769       858.49

1785      82.0        146370          3186225      6724

2797     163.0         455911         7823209    26569

3675   248.0         911400        13505625   61504        

9965   537.81     1545776.75  25569715   95799.63

(ii) Calculate the correlation coefficient

[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}[/tex]

(c) Regression line

The equation for the regression line is

y = a + bx where

[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}[/tex]

(d) Residuals

Insert the values of x into the regression equation to get the estimated values of y.

Then take the difference between the actual and estimated values to get the residuals.

   x            y       Estimated   Residual

    36        0.22        -10                 10

    67        0.62          -8                  9

    93        1.00           -7                  8

   142        1.86           -3                  5

  433       11.8             19               -  7

  887     29.3             45               -16  

 1785     82.0            104              -22

2797    163.0            170               -  7

3675   248.0            228               20

(e) Suitability of regression line

A linear model would have the residuals scattered randomly above and below a horizontal line.

Instead, they appear to lie along a parabola (Fig. 2).

This suggests that linear regression is not a good model for the data.

Answer:

Step-by-step explanation:

Using the formula for finding range in projectile, Since range is the distance covered in the horizontal direction;

Range [tex]R = U\sqrt{\frac{H}{g} }[/tex]

U is the velocity of the arrow

H is the maximum height reached = distance below the bullseye reached by the arrow.

R is the horizontal distance covered i.e the distance of the target from the archer.

g is the acceleration due to gravity.

Given R = 60ft, U = 250ft/s, g = 32ft/s H = ?

On substitution,

[tex]60 = 250\sqrt{\frac{H}{32}} \\\frac{60}{250} = \sqrt{\frac{H}{32}}\\\frac{6}{25} = \sqrt{\frac{H}{32}[/tex]

Squaring both sides we have;

[tex](\frac{6}{25} )^{2} = (\sqrt{\frac{H}{32} } )^{2} \\\frac{36}{625} = \frac{H}{32} \\625H = 36*32\\H = \frac{36*32}{625} \\H = 1.84feet[/tex]

The arrow will hit the target 1.84feet below the bullseye.

Answer:

8.7

Step-by-step explanation:

on edge . You're welcome

Answer:

  B.  g(x)

Step-by-step explanation:

g(x) is a function of odd degree, so will tend toward negative infinity as an extreme value.

f(x) is an even-degree function with a positive leading coefficient. Its minimum value is -2.

g(x) has the smallest minimum value

Answer:

The coordinates of point A after both transformations becomes (0, 3)

Step-by-step explanation:

Translation 4 units down is equivalent to -4 units in the y direction, therefore, we have;

A(-3, 4), B(6, 4), and C(2, -3) becomes

A(-3, 4 - 4), B(6, 4 - 4), and C(2, -3 - 4) which is A(-3, 0), B(6, 0), and C(2, -7)

Rule on operation on coordinates due to rotation of a triangle 90° clockwise is as follows;

For vertex coordinate, (x, y), we change it to (y, -x)

Therefore, we have the coordinates of the point A(-3, 0) after a rotation of 90° clockwise becomes A(0, 3).

Answer:

T = £85.87

the cost of the petrol the car used in November is £85.87

Step-by-step explanation:

Given;

In November Hillary drove 580 miles in her car;

Distance travelled d = 580 miles

the car travelled 33.5 miles for each gallon of petrol used;

Fuel consumption rate r = 33.5 miles per gallon

Number of gallons N consumed by the car is;

N = distance travelled/fuel consumption rate

N = d/r = 580/33.5 = 17.3134 gallons

Given that;

Petrol cost £1.09 per litre

Cost per litre c = £1.09

1 gallon = 4.55 litres

Converting the amount of fuel used to litres;

N = 17.3134 gallons × 4.55 litres per gallon

N = 78.77612 litres

The total cost T = amount of fuel consumption N × fuel cost per litre c

T = N × c

T = 78.77612 litres × £1.09 per litre

T = £85.87

the cost of the petrol the car used in November is £85.87

Answer:

The Probability that the sample average was 289 yards or less

P(x⁻≤ 289) = P( Z≤ -1.909) =  0.0287

Step-by-step explanation:

step(i):-

Mean of the Population = 292.5 yards

Standard deviation of the Population = 14.2 yards

sample size 'n' =60 drives

               N = 4244 drives

Step(ii):-

Let X⁻ be random sample average

[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

Let  X⁻ = 289

[tex]Z = \frac{289 -292.5}{\frac{14,2}{\sqrt{60} } }[/tex]

Z  = - 1.909

The Probability that the sample average was 289 yards or less

P(x⁻≤ 289) = P( Z≤ -1.909)

                = 0.5 -A(1.909)

                = 0.5 -0.4713

               = 0.0287

Conclusion:-

The Probability that the sample average was 289 yards or less = 0.0287

Answer: The area of circle V is 196π ft² (196Pi feet squared)

Step-by-step explanation:

From the equation for area of a circle,

A = πr²

Where A is the area of the circle

r is the radius of the circle

In Circle V, the radius, r of the circle is 14 feet

That is,

r = 14ft

Hence, Area is

A = π × (14ft)²

A = π × 14ft × 14ft

A = 196π ft²

Hence, the area of circle V is 196π ft² (196Pi feet squared)

Answer:

The answer is D on Edge 2020

Step-by-step explanation:

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