800 is 10 times more

[tex]|\Omega|=12^2=144\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{144}=\dfrac{1}{12}[/tex]

Answer:

Step-by-step explanation:

3.8 miles per week

the miles ran last month is 2.8

let 2.8 be original , that is 100%

an increase of 36.2% is then

100 + 36.2 = 136.2% = [tex]\frac{136.2}{100}[/tex] = 1.362

multiply 2.8 by this quantity

= 2.8 × 1.362 = 3.8 miles per week ( to nearest tenth )

Answer:

1) Volume of water displaced = 5.16 L

2) Copper sinks in water.

Explanation:

1)  Density of copper = 8.92[tex]g/cm^3[/tex]

 Mass of copper = 46 kg = 46000 g

 We know that, Density = Mass / volume

        So, Volume = Mass/ density

              Volume of copper = 46000/8.92 = 5156.95 [tex]cm^3[/tex]

  Since the density of copper 8.92[tex]g/cm^3[/tex] is greater than density of water 1[tex]g/cm^3[/tex], the copper immerses in water. Since it immerses it will displace a volume of water which is equal to the volume of copper.

  So volume of water displaced = volume of copper = 5156.95 [tex]cm^3[/tex] =5.16 L of water

2)  Since the density of copper 8.92[tex]g/cm^3[/tex] is greater than density of water 1[tex]g/cm^3[/tex], the copper immerses in water.  So copper sink in water.

Triangle ABC is equilateral, because AB=BC=AC=a. Then

m∠A=m∠B=m∠C=60°.

Let point D lie on the ray BC to the right from points B and C and let CD=x. Then BD=a+x, AB=a.

Consider triangle ACD. In this triangle, m∠ACD=180°-m∠ACB=180°-60°=120°.

By the cosine theorem,

[tex]AD^2=AC^2+CD^2-2\cdot AC\cdot CD\cdot \cos \angle ACD,\\\\AD^2=a^2+x^2-2\cdot a\cdot x\cdot \cos 120^{\circ},\\\\AD^2=a^2+x^2+ax,\\\\AD=\sqrt{a^2+x^2+ax}.[/tex]

Since [tex]a^2+x^2+ax=a^2+x^2+ax+ax-ax=(a+x)^2-ax,[/tex] then

[tex]AD^2=(a+x)^2-ax<(a+x)^2=BD^2\Rightarrow AD<BD[/tex]

and

[tex]AD^2=a^2+x^2+ax>a^2=AB^2\Rightarrow AD>AB.[/tex]

Therefore, you get double inequality

[tex]AB<AD<BD[/tex] or [tex]BD>AD>AB.[/tex]

Answer:

The proof is below

Step-by-step explanation:

Please look at the attachment below

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28.8

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28 4/5 That is the answer for the question

Answer:

The Average rate of the first plane is 560 mph

Step-by-step explanation:

x = first plane's average rate (in mph)

x−108 = second plane's average rate (in mph)

First planes total distance = 2.25x

Second planes total distance = 1.25(x−108)

2.25x + 1.25(x−108) = 1825

x = 560

subtracting term by term

(3.1x - 4.3x ) + (2.8z - (- 1.2z ) )

= - 1.2x + (2.8z + 1.2z ) = - 1.2x + 5z

For this case we have the following expressions:

[tex]x = -4y + 4\\\\2x + 8y = 8\\[/tex]

Rewriting the second equation we have:

[tex]2x = -8y + 8\\[/tex]

It is observed that by multiplying the first equation by 2, the second equation is obtained.

Thus, the equations are linearly dependent and since the lines are equal then they are intercepted in infinite points. Therefore, the system has endless solutions.

Answer:

Option D

Answer:

Question 7

Total area of the quadrilateral [tex]27[/tex].

Question 8

Angles on the side of a straight line adds up to 180°

Therefore we can write the sum of all the angles as;

[tex]x+4x+20=180[/tex]

Then you can solve the equation to find the [tex]x[/tex].

Step-by-step explanation:

(7)

First Plot the coordinates in the Cartesian plane. Then join all the points. Now you should get a graph as the graph shown in "red lines" in the attachment.

To make it easier we add another point in the graph as "E(2,3)". Now we have two shapes, one is a rectangle ABED and the other is a triangle BEC. Addition of these to makes the ABCD quadrilateral.

Before finding the areas we need to find the lengths of each side.

AB=3-(-1)=4

AD=BE=2-(-4)=6

EC=4-3=1

Area of ABED rectangle = AB*AD

                                        =[tex]4*6[/tex]

                                        =[tex]24[/tex]

Area of the BEC triangle= [tex]\frac{1}{2}[/tex]*BE*EC

                                        =[tex]\frac{1}{2} *6*1[/tex]

                                        =[tex]3[/tex]

Therefore, total area of the quadrilateral = [tex]24+3[/tex]

                                                                    =[tex]27[/tex]

(8)

Angles on the side of a straight line adds up to 180°

Therefore we can write the sum of all the angles as;

[tex]x+4x+20=180[/tex]

Then you can solve the equation to find the [tex]x[/tex] as follows.

[tex]5x+20=180[/tex]

[tex]5x=160[/tex]

[tex]x=32[/tex]

Then you can find 4x° also by multiplying x by 4.

Given slabs thicknesses 5in, 10in, and 15in.

Therefore, ratio of thicknesses in simplest form would be 1:2:3.

Metal 1 thicknesses =  150lbs, 300lbs, 600lbs

Dividing by 150, we get ratio of Metal 1 thicknesses = 1:2:4.

Metal 2 thicknesses = 130lbs, 260lbs, 390lbs.

Dividing by 130, we get ratio of Metal 2 thicknesses =  1:2:3.

Metal 3 thicknesses = 310lbs, 620lbs, 930lbs.

Dividing by 310, we get ratio of Metal 3 thicknesses = 1:2:3.

Metal 4 thicknesses = 140lbs, 280lbs, 420lbs.

Dividing by 140, we get ratio of Metal 4 thicknesses = 1:2:3.

We can see the ratios of thicknesses of Metal 1 are 1:2:4 but it should be 1:2:3.

Therefore, Metal 1 weight is not proportional to thickness.

Answer:

Weights of metal 1 is not proportional to thickness.

Step-by-step explanation:

We have been given 3 thicknesses of metal slabs and the weights of each thickness for each metal. We are asked to find out which of the metals weight is not proportional to thickness.

We can see that the thicknesses of slabs are first three multiples of 5 that is 5 inches, 10 inches and 15 inches.

Now let us see which of the metals have not their weights proportional to their thicknesses.

In our first option we can see that 300 is 2 times 150 and 600 is 4 times 150 which is not proportional to thickness. In order to metal 1's weight to be proportional with it's thickness it should be 450 lbs instead of 600.

Our second metal's weight is proportional to it's thickness as 130, 260 and 390 are 3 first consecutive multiples of 130.

Our third and fourth metal's weights are also proportional to their thicknesses.

Therefore, metal 1's weight is not proportional to thickness.

let h= history books

science books = s

h=2s  there are 2 times as many history as science so to get them equal we double the science

h+s=81    there are 81 total history and science books

2s+s=81   substitute 2s for h in the above equation

3s = 81   combine like terms

s = 27

There are 27 science books

h=2s

h=2(27)

h=54

there are 54 history books

Answer:

c

Step-by-step explanation:

The inequality equivalent to -m ≥ 15 is m ≤ -15, achieved by multiplying both sides of the inequality by -1, which reverses the inequality symbol. So the correct answer is C. m ≤ -15.

The question asks which inequality is equivalent to the inequality -m ">≥ 15. To find the equivalent inequality where m is positive, we need to multiply or divide both sides of the inequality by -1, remembering that doing so reverses the inequality symbol. Therefore, multiplying both sides by -1 gives m ≤ -15, which means that the inequality that is equivalent to -m ≥ 15 is m ≤ -15.

So the correct answer is C. m ≤ -15.

Answer:

1) C

2) A

3) D

Step-by-step explanation:

A) We substitute the values for a ,b , c and d in the given equation.[tex]\frac{6}{3} +4^2 (5) \\= 2+80\\=82[/tex]

Hence option c. 82 is the answer.

2) The product 6(-3)

Since positive x negative gives negative

we get -(6x3) = -18

Option A is the answer.

3) For this we have to find cube of a fraction with numerator 4 and denominator 7

We find cube of numerator first = 4x4x4 =64

Cube of denominator = 7x7x7 = 343

Hence cube of fraction = 64/343

Option D

Using order of operations , the expression ⇒4[2.5+3(20+7)] = 334

Order of mathematical operations are done in order with respect to PEDMAS rule.

PEDMAS: Parenthesis → Exponents→ Division→ Multiplication→ Addition→ Subtraction.

it states that we will start will solving brackets or Parenthesis then will solve powers or exponents , then division and so on in the same order as given in PEDMAS rule

For given expression 4[2.5+3(20+7)]

First solve brackets (20+7)

⇒4[2.5+3(20+7)] = 4[ 2.5 + 3(27)]

Then solve bracket 2(27) = 81

⇒4[2.5+3(20+7)] = 4[ 2.5 + 3(27)] =  4[ 2.5 + 81]

Solve the bracket [ 2.5 +81]

⇒4[2.5+3(20+7)] =  4[ 2.5 + 81] = 4[83.5] = 334

Also, Learn more about order of operation from the link below:

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the slope of a perpendicular line = - [tex]\frac{3}{5}[/tex]

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

rearrange 5x - 3y = 2 into this form

subtract 5x from both sides

- 3y = - 5x + 2 ( divide all terms by - 3 )

y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{2}{3}[/tex]

with slope m = [tex]\frac{5}{3}[/tex]

the slope of a line perpendicular = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{3}{5}[/tex]

According to question

[tex] 80\% of n = 72[/tex]

Change percentage to decimal by dividing it by 100

[tex] (80\div100)\mul n=72[/tex]

[tex]0.80\times n =72[/tex]

Now, crossmultiply we get,

[tex] n = \frac{72}{0.80}[/tex]

Now sloving we get

[tex] n = 90[/tex]

Answer:

2 1/10

Step-by-step explanation:

(5 1/4)/(2 1/2)

Change mixed fraction to improper fractions

(21/4)/(2 1/2)

(21/4)/(5/2) =21/10

=2 1/10

Answer:

2 1/10

Step-by-step explanation:

You want to get y by itself

y=1/2 x

y=mx+b

m=1/2 b=0

y = [tex]\frac{1}{2}[/tex] x + 0

given 2y = x ( divide both sides by 2 )

y = [tex]\frac{1}{2}[/tex] x + 0

[tex]\frac{8}{27}[/tex]

(2/3)^3 = [tex]\frac{2^{3} }{3^{3} }[/tex] = (2 × 2 × 2 )/(3 × 3 × 3 ) = [tex]\frac{8}{27}[/tex]

Answer:

Step-by-step explanation:

The function f(x) = e^x never crosses the x-axis and crosses the y-axis at point (0,1). It does not pass through the point (e,1), but it does pass through the point (1,e). Hence, the correct statement is 'It passes through the point (1,e)'.

The function f(x) = e^x is an exponential function where 'e' is Euler's number, approximately equal to 2.71828. Its graph has distinctive traits which are related to the options provided.

The statements 'It crosses the x-axis at e' and 'It crosses the y-axis at e' are incorrect because the graph of f(x) = e^x never crosses the x-axis, and it crosses the y-axis at the point (0,1), not e.

The statement 'It passes through the point (e,1)' is also incorrect. This function, f(x) = e^x, will pass through the point (1,e), not (e,1). Hence, the option 'It passes through the point (1,e)' is the true statement about the graph of the function.

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