Andy is comparing how long two tablets can be used after being fully charged.
-
Tablet A Tablet B
(minutes) (minutes)
540
593
Mean
Median
580
589
NOR
21
13
MAD
6
2

Answer:

x=7

Step-by-step explanation:

Alternate interior angles so they are congruent. So, 13x+5=12x+12. Subtract 12x and get x+5=12. Subtract 5 and you get x=7

Answer:

3

Step-by-step explanation:

-48/16 = 48/16

-48/16 = -3/1 = -3

Answer:

There was a 45% increase in furniture sales.

Furniture sales rose by 9 percentage points.

Step-by-step explanation:

absolute difference = new - old

29-20= 9 percentage points

absolute difference / initial value = 9/20 = .45 * 100 = 45%

Two statements which are true about furniture sales are  [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and  [tex](f)[/tex]  Furniture sales rose by [tex]9[/tex] percentage points.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage [tex]=\frac{Obtained\ number}{Total\ number}\ * 100[/tex]

We have,

Sales of furniture in [tex]2015=20\%[/tex]

Sales of furniture in [tex]2016=29\%[/tex],

So,

Change in Percentage [tex]=29-20=9\%[/tex]

i.e.

Sales rise by [tex]9\%[/tex] points,

And,

Increase in Percentage [tex]=\frac{9}{20}\ *100=45\%[/tex]

Hence, we can say that Two statements which are true about furniture sales are [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and [tex](f)[/tex] Furniture sales rose by [tex]9[/tex] percentage points.

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Answer:

D x is all real numbers

R y ≥ -3

Step-by-step explanation:

The domain is the values that x can take

The domain is all real numbers

The range is the values that y can take

The range is y is greater than or equal to -3

Any relation that has an inverse is a function

The function is given as:

[tex]\mathbf{f(n) = 0.4n + 6}[/tex]

(a) Evaluate [tex]\mathbf{f^{-1}(33)}[/tex]

First, we calculate the inverse function

We have:

[tex]\mathbf{f(n) = 0.4n + 6}[/tex]

Rewrite as:

[tex]\mathbf{y = 0.4n + 6}[/tex]

Subtract 6 from both sides

[tex]\mathbf{y -6= 0.4n + 6 - 6}[/tex]

[tex]\mathbf{y -6= 0.4n}[/tex]

Divide both sides by 0.4

[tex]\mathbf{\frac{1}{0.4}(y -6)= \frac{0.4n}{0.4}}[/tex]

[tex]\mathbf{\frac{1}{0.4}(y -6)= n}[/tex]

[tex]\mathbf{2.5(y -6)= n}[/tex]

Make n the subject

[tex]\mathbf{n = 2.5(y -6)}[/tex]

Rewrite as:

[tex]\mathbf{n = 2.5(f(n) -6)}[/tex]

So, the inverse function is:

[tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]

Substitute 33 for n to calculate [tex]\mathbf{f^{-1}(33)}[/tex]

[tex]\mathbf{f^{-1}(33) = 2.5(33 -6)}[/tex]

[tex]\mathbf{f^{-1}(33) = 2.5(27)}[/tex]

[tex]\mathbf{f^{-1}(33) = 67.5}[/tex]

(b) The rule of [tex]\mathbf{f^{-1}(n)}[/tex]

In (a), we have: [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]

Hence, the rule of [tex]\mathbf{f^{-1}(n)}[/tex] is [tex]\mathbf{f^{-1}(n) = 2.5(n -6)}[/tex]

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Answer:

335

Step-by-step explanation:

To convert meters to centimeters, move the decimal point two spaces to the right.

Answer:

335

Step-by-step explanation:

a centimeter is one hundredth of a meter so multiply 3.35x100

Answer:

173 949 pounds

Step-by-step explanation:

radius of the hemisphere = diameter / 2 = 11 feet

Volume of the hemisphere = (2/3  * radius^3 * pi) = = (2/3 * 11^3 * pi) = 2.787,639881 ft^3

Total weight = volume of the hemisphere * 62.4 = 173,948.728592

Answer:

The car uses less gas

They use the same amount of gas after [tex]\frac{640}{7}[/tex] miles

Step-by-step explanation:

Given

The table represents the car mileage

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

First, calculate the car's slope (m)

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

From the table, we have:

[tex](x_1,y_1) = (60,13.5);\ \ (x_2,y_2) = (180,10.5)[/tex]

So, we have:

[tex]m = \frac{10.5 - 13.5}{180 - 60}[/tex]

[tex]m = \frac{-3}{120}[/tex]

[tex]m = -\frac{1}{40}[/tex]

Calculate the equation using:

[tex]y = -\frac{1}{40}(x - 60)+13.5[/tex]

[tex]y = -\frac{1}{40}x + 1.5+13.5[/tex]

[tex]y = -\frac{1}{40}x + 15[/tex]

[tex]m = -\frac{1}{40}[/tex] implies that for every mile traveled, the car uses 1/40 gallon of gas

Also:

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

By comparison to: [tex]y = mx + b[/tex]

[tex]m = -\frac{1}{5}[/tex]

This implies that for every mile traveled, the van uses 1/5 gallon of gas.

By comparison:

[tex]1/40 < 1/5[/tex]

This means that the car uses less gas

Solving (b): Distance traveled for them to use the same amount of gas.

We have:

[tex]y = -\frac{1}{5}x + 31[/tex] --- The van

[tex]y = -\frac{1}{40}x + 15[/tex] --- The car

Equate both

[tex]-\frac{1}{5}x + 31 =-\frac{1}{40}x + 15[/tex]

Collect like terms

[tex]\frac{1}{40}x -\frac{1}{5}x =-31 + 15[/tex]

[tex]\frac{1}{40}x -\frac{1}{5}x =-16[/tex]

Take LCM

[tex]\frac{x - 8x}{40} = -16[/tex]

[tex]\frac{- 7x}{40} = -16[/tex]

Solve for -7x

[tex]-7x = -640[/tex]

Solve for x

[tex]x = \frac{640}{7}[/tex]

Answer:

A) P ( chicken is small ) = 0.3085,  P ( chicken is medium ) = 0.6621

   P (chicken is large ) = 0.0294

B) C = 3.9233

C) 0.1404

Step-by-step explanation:

A) Probabilities

i) P ( chicken is small )

 P( w ≤ 3.5 ) = Fw ( 3 .5 )

                    = F ( 3.5 - 3.8 / 0.6 )

                    = F ( -0.5 ) = 1 - F( 0.5 ) [∵ F(-x) 1 - F(x) ]

                    = 1 - 0.6915 ( from Table )

                    = 0.3085

ii) P ( chicken is medium )

  P ( 3.5 < w < 4.9 )

  P ( w < 4.9 ) - P ( w < 3.5 )

= Fw ( 4.9 ) - Fw ( 3.5 )

= F ( 4.9 - 3.8 / 0.6 ) - 0.3085

= 0.9706 - 0.3085 = 0.6621  

iii) P (chicken is large )

= P ( w > 4.9 )

= 1 - P ( w < 4.9 )

= 1 - Fw ( 4.9 ) = 1 - 0.9706 = 0.0294

B) Find c

Given:  P( w < c ) = 0.6

Fw ( c ) = 0.6

F ( c - 3.8 / 0.6 ) = 0.6

c - 3.8 / 0.6 = 0.2055 ( from table )

∴C = 3.9233

C) P ( 3 out of 5 = small )

P ( 3 of 5 = small ) = 0.1404

attached below is a detailed solution

Answer:

x=1

y=-1

Step-by-step explanation:

Answer:

x = 1

y = -1

Step-by-step explanation:

[tex]x = 2x - 1 \\ 1 = 2x - x \\ 1 = x \\ x = 1 \\ [/tex]

[tex]y = 3y + 2 \\ - 2 = 3y - y \\ - 2 = 2y \\ \frac{ - 2}{2} = y \\ - 1 = y \\ y = - 1 \\ [/tex]

51

Step-by-step explanation:

uajdnensjdkalsnnamakksls

Answer:

x= 62

first take linear pair angle with any line then once again with x then you're done

Answer:

x value is 62 degree

because they are vertically opposite angles

Answer:

in this tiangle tanA = 8/15

Answer:

See image below:) :)

Step-by-step explanation:

9514 1404 393

Answer:

  a) MBE; b) EBY; c) MBY; d) MBE; e) YME; f) XEW; g) EBM, EBY; h) EBY, EBM

Step-by-step explanation:

There are many choices here. We'll use choices that make as much use as possible of the same points and segments.

a) ∠MBE is an acute angle

b) ∠EBY is an obtuse angle

c) ∠MBY is a straight angle

d) ∠MBE is an angle with vertex B

e) ∠YME is an angle with side MY

f) ∠XEW is another name for ∠BER

g) ∠EBM and ∠EBY are adjacent angles

h) ∠EBY and ∠EBM are supplementary angles

__

Additional comments

An acute angle measures less than 90°; an obtuse angle measures more than 90°. A straight angle measures exactly 180°. A linear pair is a pair of adjacent angles that together measure 180°. That is, they are supplementary and combine to make a straight angle. (Supplementary angles only need to have a sum that is 180°. They do not need to be a linear pair. However, in a figure like this, where angle measures are not marked, angles are guaranteed to be supplementary only if they are a linear pair.)

9514 1404 393

Answer:

  k = 2/15

Step-by-step explanation:

We can solve the given equation for k:

  k = s/p . . . . . . divide the given equation by p on both sides

Using the first values from the table (15 pounds, 2 scoops), we have ...

  k = 2/15

The value of k is 2/15.

Replace f(x) to 5x-3 and g(x) to 3x-3 then subtract f(x) by g(x).

[tex] \large{f(x) - g(x) = (5x - 3) - (3x - 3)}[/tex]

Cancel the brackets, remember that multiplying or expanding the negative symbol will switch the sign. From plus to minus and minus to plus.

[tex] \large{ f(x) - g(x)= 5x - 3 - 3x + 3 }[/tex]

Combine like terms.

[tex] \large{f(x) - g(x) = 2x + 0 \longrightarrow \boxed{2x}}[/tex]

Answer

Answer:

5x-3-(3x-3)

5x-3-3x+3

5x-3x

2x

Answer: The probability when neither of the accidents is severe and at most one is moderate is 0.65

Step-by-step explanation:

Given values:

Probability when the accident is minor = 0.5

Probability when the accident is moderate = 0.4

Probability when the accident is severe = 0.1

As two accidents are occurring independently and we need to calculate the probability of an event that neither accident is severe and at most one is moderate.

So, the equation for the probability becomes:

[tex]=\text{P[moderate, minor]}+\text{P[minor, moderate]}+\text{P[minor, minor]}\\\\= (\text{P[moderate]}\times \text{P[minor]}) + (\text{P[minor]}\times \text{P[moderate]}) + (\text{P[minor]}\times \text{P[minor]})[/tex]

Putting values in above equation, we get:

[tex]=[(0.40)\times (0.5)] + [(0.5)\times (0.4)] +[((0.5)\times (0.5)]\\\\= 0.65[/tex]

Hence, the probability when neither of the accidents is severe and at most one is moderate is 0.65

Answer:

12

Step-by-step explanation:

Just substitute 3 for n and solve.

Solve the expression [tex]2+(3-1)5\\[/tex]

Use PEMDAS and solve.

(3-1) = 2 so it becomes 2 + (2)5

Then multiply 2 and 5 to get 10.

Then add 2 so you get 12.

[tex]a_{3}[/tex]=12

Answer:

is it correct if yes you may follow me for more helps ☺️

Answer:

The answer is B ;)

Step-by-step explanation:

4x+5 is greater than or equal to 13

subtract 5 from each side to get 4x is greater than or equal to 8

then divide both sides by 2 to get

x is greater than or equal to 2

Answer:

ST = 15

Step-by-step explanation:

Given:

QR = 3x

LM = x + 9

ST = 6x - 3

Required:

ST

Solution:

First, we need to find the value of x by creating an equation.

Based on the trapezoid mid-segment theorem, we have the following equation:

LM = ½(QR + ST)

Substitute

x + 9 = ½(3x + 6x - 3)

x + 9 = ½(9x - 3)

Multiply both sides by 2

2(x + 9) = 9x - 3

2x + 18 = 9x - 3

Collect like terms

2x - 9x = -18 - 3

-7x = -21

Divide both sides by -7

x = -21/-7

x = 3

Find ST:

ST = 6x - 3

Plug in the value of x

ST = 6(3) - 3 = 18 - 3

ST = 15

Answer:

h(t) = -16t2 + 186t + 43

at the ground h = 0

hence;  -16t2 + 186t + 43 = 0  

solving this quadratic equation using the quadratic formula ; a = -16, b = 186, c = 43 ; x = (-b +-(b2 - 4ac)1/2)/2a

gives t = 11.8 seconds to the nearest tenth (note that the negative root has no practical significance)

Step-by-step explanation:

Answer:

60 square meters

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

Think of line AE as a transversal. with DE and AB cutting across it. If we draw it out, looking at the picture, we can see that angles A and E correspond, meaning that angle A = angle E = 50

Answer:

x = 111

Step-by-step explanation:

180- 82 -29 is 69 and 180-69 is x which x is equal to 111

Answer:

111°

Step-by-step explanation:

By exterior angle theorem:

[tex]x = 82 \degree + 29 \degree \\ = 111 \degree[/tex]

Answer:

using Pythagoras theorem

bc²=ac²-ab²

bc²=100-64

bc=√36

bc =6

Answer:

5 and 3 is vertical. 4 and 6 are vertical. 2 and 1 are supplementary angles.

Let x,y be the two numbers.

Given that one number is 8 greater than another.

Let x be the smaller number ans y be the greater number.

That is y=x+8. Let this be the first equation.

And also given that product of the two numbers is 84.

That is x × y = 84, let us plugin y=x+8 here.

x × (x+8) = 84

x²+ 8x -84 = 0.

x²+12x-4x-84 = 0

x(x+12)-4(x+12) =0

(x-4)(x+12)=0

That is x= 4 or -12.

Hence two positive numbers corresponding to given conditions are 4,12.

And two negative numbers corresponding to given conditions are -12,-4.

Step-by-step explanation:

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