the sum of two numbers, one of which is two-third of the other, is 45. find the smaller number​

Step-by-step explanation:

a)

we have 400 people. that is 10/10 of the whole group.

7/10 of the whole group drink tea. that is

400 × 7/10 = 40 × 7 = 280

that leaves 3/10 of the whole group not drinking tea

400 × 3/10 = 40 × 3 = 120

from the 280 tea drinkers 20% drink at lay e cups of tea each day. that is

280 × 20/100 = 28 × 2 = 56

because 20 out of 100 is the meaning of 20%.

and the remaining 80% of the tea drinkers drink less then 3 cups each day.

280 × 80/100 = 28 × 8 = 224

b)

out of the 400 people 56 drink at least 3 cups of tea each day. that is

56/400 = 7/50

The expression (3a + 2b)^7 is a binomial expression;

The coefficient of the fourth term is 15120

The equation is given as:

(3a + 2b)^7

The above expression is a binomial expression;

Assume the expression is:

(x + y)^n

The equation of the expansion is:

[tex](x + y)^n = ^nC_r * x^{n-k} * y^k[/tex]

When the expression is expanded, the parameters of the fourth term are

n = 7

r = 4

x = 3a

y = 2b

So, we have:

(3a + 2b)^7 = 7C4 * (3a)^(7-4) * (2b)^4

Evaluate each factor

(3a + 2b)^7 = 35 * (3a)^3 * (2b)^4

Evaluate the powers

(3a + 2b)^7 = 35 * 27a^3 * 16b^4

Evaluate the product

(3a + 2b)^7 = 15120a^3b^4

The coefficient of the above expression is 15120

Hence, the coefficient of the fourth term is 15120

Read more about binomial expressions at:

https://brainly.com/question/13602562

Answer:

Box 4

Step-by-step explanation:

negative divided by negative is positive so both negatives cancel out and u get (5/6) / (1/3)

Answer:

83

Step-by-step explanation:

first add whatever is in the 1's place so for 38, 8 is in the 1's place and for 45, 5 is in the 1's place

so first it will be 8+5 which is 13 so you are going to carry the 1 over to the tens place so now it will be 30 + 40 + 10 and that equals 80 so you add 80 and 3 which looks like 80+3 and that equals 83

Answer:

10

Step-by-step explanation:

The Interquartile Range (IQR) is the difference between Q3 and Q1.

From the diagram we see that Q1 = 40, and Q3 = 50

IQR = Q3-Q1 = 50 - 40 = 10

[tex]\boxed{\bold{x = 2, 3}}[/tex]

Stepwise Solving:

[tex]\rightarrow \sf x^2-5x + 6 = 0[/tex]

[tex]\sf use \ the \ formula : x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \ \ when \ ax^2 + bx + c = 0[/tex]

Identify the coefficients:

Solve for x:

[tex]\dashrightarrow \ \sf x=\dfrac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4 \ x \ 1 \ x \ 6}}{2 \ x \ 1}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{\left25-24}}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm \sqrt{1}}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right\pm1}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{\left5\right+ 1}{2} \ , \dfrac{\left5\right- 1}{2}[/tex]

[tex]\dashrightarrow \ \sf x=\dfrac{6}{2} \ , \ \dfrac{4}{2}[/tex]

[tex]\dashrightarrow \ \sf x= 3, \ 2[/tex]

Step-by-step explanation:

I hope its helped ! studied well.

Answer:

a: The tape diagram represents the story because there’s 5 boxes representing the 5 weeks and x-2 in each box since x represents the amount Andre’s neighbor will pay him weekly to mow the lawn. This all equals 40 because that’s how much money he has to save.

B: Andre’s neighbor pays him 10 dollars each week to mow the lawn.

Step-by-step explanation:

b: For this part you have to make an equation combining all the five weeks which would be 5x-10. Then you would make it equal 40 because that’s how much he needs to save 5x-10=40. The you solve to find x by adding 10 to both sides of the equation and get 5x = 50. Then if you divide 5 on both sides you get 10!
You can check you work by plugging in 10 as x into the diagram.

[tex]\cfrac{6}{5}~~ + ~~\boxed{?}~~ = ~~\cfrac{27}{10}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10\left( \cfrac{6}{5}~~ + ~~\boxed{?} \right)~~ = ~~10\left( \cfrac{27}{10} \right)}\implies 12+10\boxed{?}=27 \\\\\\ 10\boxed{?}=15\implies \boxed{?}=\cfrac{15}{10}\implies \boxed{?}=\cfrac{3}{2}[/tex]

Answer: 30 units^2

Step-by-step explanation:

[tex]\mathrm{From \ the \ figure \ we \ know \ this \ is \ a \ right \ triangle. \ The \ area \ of \ the \ triangle}:[/tex]

[tex]A = \frac{1}{2}bh \\= \frac{1}{2} \times 6 \times 10\\= 30 \ units^2[/tex]

(Formula for area of right triangle: Half of the product of two right edges)

Therefore, the area of the triangle is 30 units^2

Answer:

Yes.

Step-by-step explanation:

because 9 feet converted to inches equals 108 inches, we know this because we can convert feet to inches via multiplication. To do this, simply multiply the given number (9) by 12 to get your answer.

Answer:

I believe a is equal to -54

Answer:

706.5m^2

Step-by-step explanation:

The sign is a circle

Area of a circle is (pi)r^2

d = 30 in -> r = d/2  = 30/2 = 15

Area = 3.14 x (15)^2 = 706.5m^2

Answer:

about 706.5 or 706.86

Step-by-step explanation:

to find this answer we need to use the area formula of a circle which is A = πr ^2

we know the diameter is 30, and the radius is half the of diameter, so we take 30 and divide it by 2, which should give us 15 for the radius. ( 30/2 = 15, so r = 15)

depending on how your teacher wants u to answer this you can use π on a calculator or use 3.14

now just plug in your numbers to formula

A = 3.14 * 15^2 or A = π * 15^2

and should equal about 706.5 or 706.86 (depending on if you use 3.14 or π)

Answer:

9

Step-by-step explanation:

Add all numbers together: 36

divide by the amount of numbers in the list: 9

                                      :)

Answer:

x = 110

y = 23

Step-by-step explanation:

For X :

100 = x -10

110 = x

Corresponding angles are equal

For Y :

180 - 110 = 70

(2y + 24) = 70

2y = 46

y = 23

Adjacent Angles on a straight line add up to 180 Degrees

Answer:

1/7 and 1/2

Step-by-step explanation:

The probability of orange marble is 1/7

Probability of tails is 1/2

If you need to add this, then it'll be 1/14

7 x 2 = 14

1 x 1 = 1

Artificial selection picks previously existing qualities by breeding individuals with favourable traits, whereas genetic engineering affects the genetic composition of plants or animals by adding new genes or silencing genes.

The question asked by Troy is a statistical question because there would be variability in the answers he get fro the 12 maths teachers.

A statisical question is a question that can only be answered through the collection of data. Thhere would be variablility in the results gotten from the data.

A non- statistical question is a question that has only one answer. For example, how old are you? is a non-statistical question.

To learn more about a statisitcal question, please check: https://brainly.com/question/21508412

Answer:

Step-by-step explanation:

Working with the top equation, subtract 2x from both sides.

y = 9 - 2x

Put this value for y in the second equation

3x - 4(9 - 2x) = 8                 Remove the brackets

3x -36 + 8x = 8                   Add 36 to both sides

3x + 8x = 8 + 36                 Combine

11x = 44                               Divide by 11

x = 4

2x + y = 9

2*4 + y = 9                          

8 + y = 9                              Subtract 8 from both sides

y = 9-8

y = 1

The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.

Volume is the amount of space occupied by a three dimensional shape or object.

Let us assume the cone and cylinder has a radius of 7 cm and height of 10 cm, hence:

Volume of the cone = (1/3) * π * radius² * height = (1/3) * π * 7² * 10 = 513.33 cm³

Volume of the cylinder = π * radius² * height = π * 7² * 10 = 1540 cm³

The volume of the cone and cylinder with a radius of 7 cm and height of 10 cm is 513.33 cm³ and 1540 cm³ respectively.

Find out more on volume at: https://brainly.com/question/12410983

Answer:

I have no idea ask 567 9922 mathe teacher

Hey there!

[tex] \rm{\frac{5}{x} = \frac{7}{x + 2} }[/tex]

Solve:--

[tex] \sf\rightarrow \: (7)(x) = (5)(x + 2)[/tex]

[tex] \sf\rightarrow \: 7x = 5(x + 2)[/tex]

[tex] \sf\rightarrow \: 7x = 5x + 10[/tex]

[tex] \sf\rightarrow \: 7x - 5x= 5x + 10 - 5x[/tex]

[tex] \sf\rightarrow \: 2x= 10 [/tex]

[tex] \sf\rightarrow \: \frac{ 2x}{2}= \frac{10 }{2}[/tex]

[tex] \sf\rightarrow \: x= 5[/tex]

~Done~

Step-by-step explanation:

Answer:

y = 60 :)

Step-by-step explanation:

Triangle angle total measure: 180

We need to add upp the angles we know and subtract from the total 180, so we can figure out y.

60 + 60 + y = 180

120 + y = 180

180 - 120 = 60

y = 60

Now you know how to solve this type of problem!

Have a great day!!

Please rate and mark brainliest!!

Answer:

The value of y should be 60

Step-by-step explanation:

Tell me if its not right

Answer:

the answer without rounding is 147 but with its 100

Step-by-step explanation:

firsts you add up both sides of the triangle and then you subtract by 180 and now that you your answer but you had to round AN anyting above 150 you would have to run to 200 but you had one 47 so it's 100

Answer:

Mary has $1120

Step-by-step explanation:

money mary has at first : x

money jane has at first : y

Mary brought twice as much money as Jane : x=2y

Mary had spent $800 and Jane had spent $240, they had equal amount of money left : x-800=y-240

=> [tex]\left \{ {{x=2y} \atop {x-800=y-240}} \right.[/tex]

=> x=1120

y=560

Answer:

Step-by-step explanation:

Let the amount mary and jane had be 2x and x respectively.

Let the equal amount be y:

[tex]mary \: (y = 2x - 800) \\ jane \: (y = x - 240)[/tex]

Using the simultaneous equation method, multiply the first equation by the coefficient of x(1) of the second equation and the second equation by the coefficient of x(2) of the first equation:

[tex]y = 2x - 800 \\ 2y = 2x - 480[/tex]

Subtract the second equation from the first equation:

[tex] - y = - 320 \\ y = 320[/tex]

$320 was their equal amount.

Substitute 320 for y in any equation:

[tex]y = x - 240 \\ 320 = x - 240 \\ x = 320 + 240 \\ x = 560 \\ \\ 2x = 1120[/tex]

Therefore, Jane had $560 at first and Mary had $1120 at first.

Answer:

D is d because when You have to do they graph You have multiplicar

Answer:

182 m

Step-by-step explanation:

The shape is a trapezoid. The area of the trapezoid formula is [tex]\frac{a + b}{2}h[/tex].

The two bases (AKA a and b) are 8 + 18.

The height is 14.

[tex]\frac{18+8}{2} 14[/tex], Add 18 + 8

[tex]\frac{26}{2}14[/tex], Divide 26 by 2

[tex]13 *14[/tex], 182

Answer:

B. 4

Step-by-step explanation:

To undo multiplication (which is what is being asked of us) you must divide. 28 divided by 7 is 4

so

4 x 7 is 28

If Brianna is taking care of 7 chickens, Tamara is taking care of 4 times the number of chickens because she is taking care of 28

Answer:

Length: 20, Width=34

Step-by-step explanation:

Say the length of the width is w, and the length of the length is l. Then, we can establish an equation of W=2L-6. Since the area of a rectangle is W*L, we can substitute W with 2L-6. If we multiply 2L-6 and L, we get [tex]2L^{2} -6L[/tex]=680. We can simplify this equation by dividing everything by 2. We then get [tex]L^{2}-3L=340[/tex]. If we solve for L, we get 20. Now, we plug 20 into the equation, W=2L-6. Since W=2(20)-6, which simplifies to W=40-6 which is 34, we get a width of 34.

Hope this helps