5 ratio 4 = 35 ratio x​

Answer:

Step-by-step explanation: 2cos3 theta=1. Cos 3theta=1/2. Since cos 60°= 1/2. Therefore cos 3theta=cos 60°. Theta=20°.

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Answer:

10

Step-by-step explanation:

This is a combinations problem, involving factorials.

5!/3!*2!=5*4/2=20/2=10

The different sum of the 4 coins from the list of 5 coins is an illustration of combination or selection. There are 5 different possible sums.

Given

[tex]n = 5[/tex] --- number of coins

[tex]r = 4[/tex] --- coins to be selected to calculate sum

For the sum of the coin value to be calculated, the 4 coins must be selected. This means combination.

So, we make use of:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

This gives

[tex]^5C_4 = \frac{5!}{(5 - 4)!4!}[/tex]

[tex]^5C_4 = \frac{5!}{1!4!}[/tex]

Expand

[tex]^5C_4 = \frac{5*4!}{1*4!}[/tex]

[tex]^5C_4 = \frac{5}{1}[/tex]

[tex]^5C_4 = 5[/tex]

Hence, there are 5 different possible sums.

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Answer:

The load the large truck can carry  is 2400 pounds

Step-by-step explanation:

Let the load the large truck can carry  = X

Let the  load each of the four trucks owned by the neighbor can carry = Y

The given parameters are;

The load the large truck can carry X = 600 + Y......(1)

The number trucks owned by the neighbor = 4

The load the large truck can carry X ≤ 1/3 × 4 × Y

Therefore, X ≤ 4/3 × Y

At maximum capacity, we have;

X = 4/3 × Y

Substituting the value of X into equation (1), we have;

4/3 × Y = 600 + Y

600 = 4/3 × Y - Y = 1/3·Y

Y = 3 × 300 = 1800 pounds

Y =  = 1800 pounds

Therefore, the load the neighbors truck can carry = 1800 pounds

X = 600 + Y gives;

X = 600 + 1800 = 2400 pounds

∴ The load the large truck can carry  = 2400 pounds

Answer:

Length = 34 feet

Breadth = 30 feet

Step-by-step explanation:

Perimeter= 128 ft

Let the breadth be = [tex]x[/tex]

Let the length be = [tex]x+4[/tex]

∴by the problem ,

2(length+breadth)= perimeter

[tex]2(x+4+x)=128\\2(2x+4)=128\\4x+8=128\\4x=128-8\\4x=120\\x=120/4\\x=30[/tex]

Therefore, length of the garden = 30+4= 34 feet

breadth of the garden = 30 feet  

Answer:

x = 1.5

Step-by-step explanation:

6 - 2x = 3

→ Minus 6 from both sides to isolate -2x

-2x = -3

→ Divide -2 from both sides to isolate x

x = 1.5

Answer:

z=-3

Step-by-step explanation:

z=(-3)^2 - 3(4)

z=9 - 12

z=-3

Answer:

54.528

Step-by-step explanation:

Answer:

[tex]slope=0[/tex]

Step-by-step explanation:

Use the slope formula:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope".

Insert the values:

[tex](-1_{x1},2_{y1})\\\\(2_{x2},2_{y2})\\\\\frac{2-2}{2-(-1)}\\\\\frac{2-2}{2+1}\\\\[/tex]

Simplify:

[tex]\frac{2-2}{2+1}=\frac{0}{3} =0[/tex]

The slope of the line is 0. This means that the two points lie on the same horizontal line.

:Done

Answer:

Friday & Sunday

Step-by-step explanation:

Thursday: 287

Friday: 618

Saturday: 973

Sunday: 532

973 < 287 + 618 = 973 < 905

We now know this isn't true.

973 < 287 + 532 = 973 < 819

This isn't true either.

973 < 532 + 618 = 973 < 1150

This is true.  The two days with the time are Friday and Sunday.

I really hope this helps you!  Tell me if it's right or not! :D

Answer:

y+(21)=-4(x-7)

Step-by-step explanation:

the point slope equation , two point

m=y2-y1/x2-x1

m=23+21/-4-7=44/-11= -4

y+(21)=-4(x-7)

The ratio 3:4 means for every 3 pounds made in away team tickets versus home team tickets. Multiply both sides by 9000 to have that 4 turn into 36000. The ratio 3:4 will then turn into 27000:36000

With this new ratio, we see that the away team pulls in 27000 and the home team pulls in 36000. Add the two amounts to get the final answer

27000+36000 = 63000

------------

We could alternatively add 3 and 4 (from the ratio 3:4) to get 3+4 = 7. Then multiply by that same scale factor 9000 getting 9000*7 = 63000.

Answer:

B

Step-by-step explanation:

well if we draw the graph we have the following image, and the only one that applies is

B

because 4>3

Answer:

Mr. Lim will have $2500

Step-by-step explanation:

Given:

The total amount of money which Mr. Lim, Mr. Tan and Mr. Chan is $8650;

Mr. Lim has $450 more than what Mr. Tan has;

Mr. Chan has double the amount of money than what Mr. Tan has.

Therefore, if we assume that the amount of money Mr. Tan has as x, then...

Total money = Mr. Tan + Mr. Lim + Mr. Chan

therefore,

8650 = x + (x + 450) + 2x

8650 = x + 2x + x + 450

8650 = 4x + 450

8650 - 450 = 4x

8200 = 4x

8200/4 = x

2050 = x

As we assumed earlier, x will be equal to the amount of money Mr. Tan has and the question is asking us how much money Mr. Lim has. To find this out, you have to add $450 to the amount of money Mr. Tan has which is $2050. This is because the question also gives us that Mr. Lim has $450 more that Mr. Tan.

I hope this helped you :)

Answer:

60 tiles are used

Step-by-step explanation:

1m equals 100 cm.

5m equals 500

3m equals 300

the whole thing is 500 by 300 which when you multiply gives you

150,000. When you multiple 50 by 50 it gives you 2,500. So when you divide 150,000 by 2,500 it gives you a total of 60 tiles. HOPE THIS HELPS

Answer:

60 tiles

Step-by-step explanation:

First, I would convert cm to m to make it easier

50 cm is .5 m

Now we can find how many tiles across it takes to make one row (5m)

.5 goes into 5, 10 times

That means we need 10 tiles across to fill one row

Now we need to find how many tiles it takes to fill up a column (3m)

.5 goes into 3, 6 times

It takes 6 tiles to fill up a column

Now we know it takes 10 tiles across and 6 vertically

10x6=60

60 tiles

Answer:

[tex]\large \boxed{\sf \bf \ \ a^2+b^2=20 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex]a^b=b^a\\\\\text{ We can replace a by 2b.}\\\\(2b)^b=2^b\cdot b^b=b^{2a}=b^2\cdot b^b\\\\\text{ Let's assume that b is different from 0 and we can divide by }b^b \\ \\ \text{ both sides of the equation, and it come.}\\\\2^b=b^2\\\\\text{ We find b = 2 and then a = 4, So}\\\\a^2+b^2=4^2+2^2=16+4=20[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

1560 acres

Step-by-step explanation:

What we need to do is find 13% of 12000.

We can start by converting 13% to a fraction.

13%=13/100

Multiply.

13/100*12000

(13*12000)/100

156000/100

Divide.

1560

1560 acres are being logged.

The number of acres that will be logged is 1560 acres.

Since thirteen percent of a 12,000 acre forest is being logged, to calculate the number of acres that will be logged, we'll have to multiply 13% by 12000. This will be:

= 13% × 12000

= 0.13 × 12000

= 1560

Therefore, 1560 acres will be logged.

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Answer:

4x^2−2

Step-by-step explanation:

Let's simplify step-by-step.

7x^2−2−3x^2

=7x^2+(−2)+(−3x^2)

Combine Like Terms:

=7x^2(+−2)+(−3x^2)

=(7x^2+(−3x^2))+(−2)

=4x^2+−2

Answer:

=4x2−2

Answer:

Hey there!

1) To solve this, we want to know the volume of the first cylinder, which using the cylinder volume formula, we find is roughly 3079 cm^3. If the water is poured into the second cylinder, we find that the height is about 9.8 cm.

2) First, we should know that 1000 cm^3=1 liter. Volume of 1 cm tank height: 3848 cm^3, or 3.848 l. Volume for 20  cm tank height= 76.96 l. It takes about 7.7 hrs for the water level to fall 20 cm.

3) Cylinder volume formula gives us the answer to be 176 m^3 as the volume.

Hope this helps :)

Answer:

A. 3.8 grams

Step-by-step explanation:

A baking scale measures mass to the tenth of a gram, up to 650 grams. Which of the following measurements is possible using this scale?

a.3.8 grams

b.120.01 grams

c.800.0 grams

d.54 milligrams

Solution

The scale measures mass to the tenth of a gram

The scale measures up to 650 grams

a.3.8 grams

This measures to the tenth of a gram (to one decimal place) and it is not up to 650 grams

b.120.01 grams

This measures to hundredth of a gram ( 2 decimal places) and it is not up 650 grams.

c.800.0 grams

This measures to the tenth of a gram but exceeds the 650 grams limit

d.54 milligrams

This is in milligram, so it is wrong

Option a.3.8 grams is the only possible scale measurement among the options.

Answer:

68 ft³

Step-by-step explanation:

Take the above figure to be 2 rectangular prism. A smaller prism on top, and a bigger one under.

Volume of the smaller rectangular prism on top:

[tex] Volume = whl [/tex]

Where,

w = 2 ft

h = 4 ft

l = 4 ft

[tex] Volume = 2*4*4 = 32 ft^3 [/tex]

Volume of bigger Rectangle prism under:

w = 2 ft

h = 3 ft

l = 6 ft

[tex] Volume = 2*3*6 = 36 ft^3 [/tex]

Volume of composite figure = 32 + 36 = 68 ft³

Answer:

Step-by-step explanation:

The correct answer is 76

Big prism: 4x8x2=64

What's Left: (6-4)x2x3=12

64+12=76

Answer: [tex]x=\dfrac{25}{21}[/tex]

Step-by-step explanation:

Area of parallelogram = Base x height

If two parallelograms are similar, then their corresponding sides are proportional.

That means, [tex]\dfrac{\text{Area of first parallleogram}}{\text{Area of second parallleogram}}=\dfrac{\text{height of first parallelogram}}{\text{height of second parallelogram}}[/tex]

[tex]\Rightarrow \dfrac{3x+5}{9x}=\dfrac{16}{20}\Rightarrow \dfrac{3x+5}{9x}=\dfrac{4}{5}\\\\\Rightarrow 5(3x+5)=4(9x)\\\\\Rightarrow\ 15x+25 = 36x\\\\\Rightarrow\ 36x-15x=25\\\\\Rightarrow\ 21x = 25\\\\\Rightarrow\ x=\dfrac{25}{21}[/tex]

Hence, [tex]x=\dfrac{25}{21}[/tex]

Answer:

one fifth

Step-by-step explanation:

42

Answer:

The graph of g is one-fifth as steep as the graph of f.

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

The crocodile river is y = 4

The road will intersect at ( 6,4)

We have two points on the line

(6,7) and (6,4)

The slope is

m = (y2-y1)/(x2-x1)

   = (4-7)/ (6-6)

  = -3/0

The slope is undefined

That means the equation is in the form

x=

Since the x coordinate is 6

x=6

Answer:

546 - 25 x 13 (divided by) 13

546 - (25 x 13) / 13

Step-by-step explanation:

25 x 13 = 325

546 - 325 = 221

221 / 13 = 17

17 mens teams can register.

Answer:

[tex]25(13)+13m\leq 546[/tex]

A

Step-by-step explanation:

Each team can only consists of thirteen players. Therefore, by letting w represent the number of women's teams and m the number of men's teams, the total number of players is represented by the equation:

[tex]13w+13m[/tex]

The total number of players cannot surpass 546. In other words, it must be less than or equal to. Therefore:

[tex]13w+13m\leq 546[/tex]

We are given that that 25 women's teams have already signed up. To find out the possible number of men's teams that can sign up, we can substitute 25 for w and then solve for m.

Therefore:

[tex]25(13)+13m\leq 546[/tex]

In conclusion, the answer is A.

Answer:

f(g(x)) = [tex]\sqrt{8x-22}[/tex]

Step-by-step explanation:

Substitute x = g(x) into f(x), that is

f(g(x))

= f(8x - 13)

= [tex]\sqrt{8x-13-9}[/tex]

= [tex]\sqrt{8x-22}[/tex]

Answer:

17.25 miles

1 hour, 56 minutes, and 20 seconds.

4 hours, 47 minutes, and 38 seconds.

Step-by-step explanation:

Part I:

For his three cycling sessions, he had traveled for 25.8 miles, 17.25 miles, and 27.42 miles.

The shortest distance he cycled is 17.25 miles.

Part II:

For his three cycling sessions, he spent: 1) 1 hour, 56 minutes, and 20 seconds, 2) 1 hour, 1 minute, and 13 seconds, and 3) 1 hour 50 minutes and 5 seconds.

The longest time he cycled for was 1 hour, 56 minutes, and 20 seconds.

Part III:

Lance's total cycling time is all the times added together. Therefore:

[tex]1\text{ hr} +1\text{ hr} +1\text{ hr} +56\text{ min} +1\text{ min}+50\text{ min} +20\text{ sec}+13\text{ sec} +5\text{ sec} \\\\=3\text{ hr} +107\text{ min}+38\text{ sec} \\\\=4\text{ hours, }47\text{ minutes}\text{ and 38 seconds}[/tex]

Answer:

i) 17.25 miles.

ii) 1 hrs :56 mins :20 secs

iii) 4 hrs :47 mins: 38 secs total.

Zoologists are studying two newly discovered species of insects in a previously unexplored section of rain forest. They estimate the current population of insect A to be 1.3 million and the current population of insect B to be 2.1 million. As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.

If P represents the population of each species of insect in millions, and t represents the elapsed time in years, then which of the following systems of equations can be used to determine how long it will be before the populations of the two species are equal?

Answer:

the  system of equation that  can be used to determine how long it will be before the populations of the two species are equal is :

[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]

Step-by-step explanation:

Given that :

the current population of insect A to be 1.3 million

the current population of insect B to be 2.1 million.

As development is encroaching on the section of rain forest where these insects live, the zoologists estimate the populations of insect A to be reducing at a rate of 3.8% and insect B to be reducing at a rate of 4.6%.

The equation that can be used to determine how long it will be before the populations of the two species are equal is an equation for exponential decay, which can be represented as follows:

[tex]\mathtt{y = pe^{-rt}}[/tex]

where;

P represents the population of each species of insect in millions

t represents the elapsed time in years

r is the rate of decrease

So, we can have:

[tex]\mathtt{p_1 = 1.3 }[/tex] in million   and  [tex]\mathtt{p_2 = 2.1}[/tex] in million

Also for rate of decrease;

[tex]\mathtt{r_1 = 0.038}[/tex]     and [tex]\mathtt{r_2 = 0.046}[/tex]

Therefore;

the exponential decay for Population of insect A can now be:

[tex]\mathtt{P = 1.3 e^{-0.038 \ t}}[/tex]

the exponential decay for Population of insect B can now be:

[tex]\mathtt{P = 2.1 \ e^{-0.046 \ t}}[/tex]

Hence, the  system of equation that  can be used to determine how long it will be before the populations of the two species are equal is :

[tex]\begin{cases} {\mathtt{P = 1.3 e^{-0.038 \ t}} & \\ \mathtt{P = 2.1 \ e^{-0.046 \ t}} & \end{cases}[/tex]

Answer:

A!

Step-by-step explanation:

Plato

Answer:

2nd 3rd last one

Step-by-step explanation:

Angles, lines, rays, and segments can be found in a plane. The terms shown on the diagram are: Ray KM, Line JK, and Ray MJ

A line is an unending, straight path that has no endpoints and travels in both directions along a plane. A line segment is a finitely long portion of a line with two endpoints. A line segment that goes on forever in one direction is known as a ray.

To identify the terms shown on the diagram, we need to note the following: A ray has no endpoint; it is represented with an arrow on one side line segment has two endpoints.

It is represented with dots on both sides. An angle is a space between intersecting lines, line segments, or rays. There is no connection between J and L. So, JL is not a line segment

Ray KM

KM has a dot at point K and an arrow that points in the direction of M. So, KM is a ray.

Line JK

JK has dots on both ends (at J and K). So, JK is a line.

Ray PK

PK has dots on both sides (at P and K). So, PK is a line; not a ray.

Angle LJK

There is no connection between points L, J, and K. Hence, LJK is not an angle.

Ray MJ

MJ has a dot at point M and an arrow that points in the direction of J. So, MJ is a ray.

The diagram is attached with the answer below.

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Answer:

150 pounds

the weight is directly proportional to the volume. hence:

138/23 = 6

now, 25*6 = 150

Answer:

B. 150 pounds

Step-by-step explanation: