In a toy​ store, the ratio of the number of teddy bears to the number of dolls is 7:3 . If the store has 140 teddy bears ​, how many dolls are in the​ store?

[tex]\rule{200}4[/tex]

Answer : The required ratio is (14m-6):(8m+23) .

[tex]\rule{200}4[/tex]

Here we are given that the ratio of sum of first n terms of two AP's is (7n + 1):(4n + 27) .

That is.

[tex]\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{7n +1}{4n +27} \\[/tex]

As , we know that the sum of n terms of an AP is given by ,

[tex]\small\sf\longrightarrow \pink{ S_n =\dfrac{n}{2}[2a +(n-1)d]} \\[/tex]

Assume that ,

Using this we have ,

[tex]\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{\dfrac{n}{2}[2a + (n-1)d]}{\dfrac{n}{2}[2a' +(n-1)d'] } \\[/tex]

[tex]\small\sf\longrightarrow \dfrac{7n+1}{4n+27}=\dfrac{2a + (n -1)d}{2a' + (n -1)d' } . . . . . (i) \\[/tex]

Now also we know that the nth term of an AP is given by ,

[tex]\longrightarrow\sf\small \pink{ T_n = a + (n-1)d}\\[/tex]

Therefore,

[tex]\longrightarrow\sf\small \dfrac{T_{m_1}}{T_{m_2}}= \dfrac{ a + (n-1)d }{a'+(n-1)d'}. . . . . (ii)\\[/tex]

[tex]\longrightarrow\sf\small \dfrac{T_1}{T_2}=\dfrac{2a + (2n-2)d}{2a'+(2n-2)d'} . . . . . (iii)\\[/tex]

From equation (i) and (iii) ,

[tex]\longrightarrow\sf\small n-1 = 2m-2\\[/tex]

[tex]\longrightarrow\sf\small n = 2m -2+1 \\[/tex]

[tex]\longrightarrow\sf\small n = 2m -1 \\[/tex]

Substitute this value in equation (i) ,

[tex]\longrightarrow \sf\small \dfrac{2a+ (2m-1-1)d}{2a' +(2m-1-1)d'}=\dfrac{7(2m-1)+1}{4(2m-1) +27}\\[/tex]

Simplify,

[tex]\longrightarrow\sf\small \dfrac{ 2a + (2m-2)d}{2a' +(2m-2)d'}=\dfrac{14m-7+1}{8m-4+27}\\[/tex]

[tex]\longrightarrow\sf\small \dfrac{2[a + (m-1)d]}{2[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\[/tex]

[tex]\longrightarrow\sf\small \dfrac{[a + (m-1)d]}{[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\[/tex]

From equation (ii) ,

[tex]\longrightarrow\sf\small \underline{\underline{\blue{ \dfrac{T_{m_1}}{T_{m_2}}=\dfrac{ 14m-6}{8m+23}}}}\\[/tex]

[tex]\rule{200}4[/tex]

Answer:

108 : 1

Step-by-step explanation:

1 foot = 12 inches

81 foot = 81 * 12 = 972 inches

Scale factor = 81 feet  : 9 inches

                    = 972 : 9

                    = 972 ÷ 9  : 9÷9

                    = 108 : 1

Answer:

12x+4x-7y+45b+78a-44b+1a+1z+0d+1.1a+1.1a+2+2+2

Answer: 2nd option: 9-i

Step-by-step explanation:

We can add the numbers and the terms with i separately.

12 - 5i - 3 + 4i = (12 - 3) + (-5i + 4i)

= 9 + (-i)

*Adding a negative is essentially subtracting a positive*

= 9-i

Answer:

15+15+40+40+40= 150

Step-by-step explanation:

Triangle x2]

(5 x 6) / 2

15

Rectangle x3]

(8 x 5)

40

only for a triangle, we divide by 2

Your answer is 150cm square.

But you do not have that option so I would pick the closes one if I were you. Have a good day.

Not sure what you meant... but your answer is 6.

2x1 is 2. 2x1 is 2 again. 2x3 is 6.

Answer:

119.32 m

Step-by-step explanation:

[tex]\textcolor{violet}{\text{Circumference of circle = 2πr = πd}} [/tex]

In the formula above, r is the radius and d stands for diameter.

Circle's circumference

= 3.14(38)

= 119.32 m

Answer:

I believe the answer is A.

Step-by-step explanation:

Hope that helps!

Answer:

[tex]-\frac{27(-\frac{20t}{10}+x)^{n} }{50} +2.56[/tex]

Step-by-step explanation:

Answer:

x should be eliminated

hope it helps

Answer: 4

Step-by-step explanation:

When x=0, y=4

Answer:

Sis 97,U is 30,Tis19,R is 21and m is 37

Answer:

Hey bro ur answer is 5-10g +20h

Step-by-step explanation:

5(1-2g+4h)=5 x 1- (5 x 2g) + ( 5 x 4h) = 5-10g +20h

Answer:

She will ride 13 miles in one hour

Step-by-step explanation:

(8 2/3) / (2/3) = x / 1....8 2/3 miles to 2/3 hr = x miles to 1 hr

cross multiply

(2/3)(x) = (8 2/3)(1)

2/3x = 26/3

x = 26/3 * 3/2

x = 26/2...which equals 13....she will ride 13 miles in 1 hr

Answer/Step-by-step explanation:

Explain the role of the GCF in factoring a polynomial.

The role of the GCF in factoring a polynomial is the largest monomial that divides evenly into each term. GCF is a factor that is shared by all terms within a polynomial. For instance, if we have a polynomial of the form A*B + A*C, the GCF is A since both terms have A as a factor.

Where is the GCF placed after factoring the GCF?

After factoring out the GCF, it's placed outside the parentheses, in front of the rest of the polynomial. Like the sample we previous use A*B+A*C = A(B+C).

How do you verify factoring is correct?

To Verify factoring is correct distributing the GCF to the polynomial within the parentheses.

~Learn with Lenvy~

[tex]\left[Hello!\;Answer\;- > \;Below:][/tex]

Answer:

Decimal Form: 16.25

Fraction Form :16 1/4

Step-by-step explanation:

Given:

James Grows Corn 1/4 of his land

Note: 1/4 = .25

Question:

If he has 65 acres of land, how much of the land is used for growing corn?

Solve:

Thus;

65 x 1/4 or 65 x .25

which given you the answer;

16 1/4 or 16.25

[RevyBreeze]

The graph of the direct variation passes through the origin

From the graph, we have the following points

(x.y) = (0,0) and (2,10)

Where:

x represents the number of revolutions

y represents the distance in feet

The revolution per foot of travel (r) is then calculated as:

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

This gives

[tex]r = \frac{2 - 0}{10 - 0}[/tex]

[tex]r = 0.2[/tex]

This means that, the revolution per foot of travel is 0.2

This is the reciprocal of the revolution per foot of travel

In (a), we have:

[tex]r = 0.2[/tex]

So, the slope is:

[tex]Slope = \frac 1{0.2}[/tex]

[tex]Slope = 5[/tex]

Hence, the slope of the graph is 5

Read more about direct variation at:

https://brainly.com/question/6499629

Answer:

2. b) New amount = £6200

Same ratio → Jon : Bon = 3 : 7

6200 ÷ (3 + 7) = 620

⇒ 620 × 3 : 620 × 7

⇒ 1860 : 4340

Jon = £1860

Bon = £4340

3.

  Tom : Thom : Thomas

= 2 : 3 : 5

= 2x: 3x : 5x

Given Tom received £2400:

⇒ 2x = 2400

⇒ x = 1200

   2x: 3x : 5x

⇒ (2 × 1200) : (3 × 1200) : (5 × 1200)

⇒ 2400 : 3600 : 6000

Tom = £2400

Thom = £3600

Thomas = £6000

4.

  cats : dogs

= 1 : 5

= 1x : 5x

Given there are 8 cats:

⇒ 1x = 8

⇒ x = 8

   1x : 5x

⇒ (1 × 8) : (5 × 8)

⇒ 8 : 40

Therefore, there are 40 dogs

Answer:

SAA

Step-by-step explanation:

This is because we see the triangles share two equal congruent angles and the one side where they touch each other. We don't know anything about the other sides so it cannot be ASA.

The two right-angled triangles are congruent by RHS so the correct option is neither.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

From the given figure two triangles share a common side which is their height.

The two triangles have the same measure of angles opposite to their base,

Therefore the bases of the triangles are also congruent.

Now, we know if two right-angled triangles have the same height and base

their hypotenuse must also be the same.

Now, the hypotenuse and one of the legs of the triangle is congruent to another right-angled triangle they are congruent by RHS or right-angled hypotenuse.

learn more about congruency here :

https://brainly.com/question/7888063

#SPJ2

Answer:

80% of 75 = 60

Step-by-step explanation:

first make 80% a decimal so 0.8 because 80/100 = 0.8

the multiply 0.8 by 75

this will give you 60

Therefore Helen's necklace has 60 blue beads

Answer:

Length of the volleyball court in drawing = 2 mm

Step-by-step explanation:

8 meter  = 8 *1000 = 8000 mm

Scale factor = 1 : 8000

Length of the volleyball court in drawing = x

1 : 8000 :: x : 16000

[tex]\dfrac{1}{8000}=\dfrac{x}{16000}\\\\\\\dfrac{1}{8000}*16000=x\\\\[/tex]

x = 2 mm

Answer:

26

Step-by-step explanation:

[tex]5^{2}[/tex] = 5 · 5 = 25

then add 1

Answer:

26

Step-by-step explanation:

(5 x 5) + 1

25 + 1

26

Have an amazing day!!!

PLEASE RATE AND MARK BRAINLIEST!!!

Answer:

E = 27.125

Step-by-step explanation:

Hope this helps you.

Answer:

e=56

Step-by-step explanation:

since the denominator is 8, what can you divide by 8 to get something that you can add to 23 and get 30.

30-23=7

56//8=7

Answer:

x < 6

Step-by-step explanation:

Step 1: Subtract 12 from both sides.

Therefore, the answer is x < 6.

The goal of this is to get 24 by multiplying the p value with q. q can be any number, as long as it gets to 24 in this scenario.

So your first p value is 4, so you can take 24, and divide it by 4 to get your answer.

24/4=6 then you can check it by multiplying 6*4=24. That means 6 is your first q value.

This will work for the rest of them in that table, except for the 0, because no matter what you multiply that by you cannont get 24. Try it out for yourself, goodluck!

Answer:

q- 24/4=6

24/2=12

24/0=0

24/-2= -12

24/-4= -6

Answer:

$4825.80

Step-by-step explanation:

Answer:

102in2

Step-by-step explanation:

The formula for surface area is 2(wl+hl+hw). So plug in the measurements of the prism into the formula to get 102.

Answer:

(2x + 14)° + (7x + 13)° = 180°

(2x + 14)° = 48°

(7x + 13)° = 132°

All 3 statements are true

Step-by-step explanation:

Answer:

=5x5x5

Step-by-step explanation:

5x5^2

=5x(5x5)

=5x5x5

Answer:

625

Step-by-step explanation:

5×5 to the power of 2

25 to the power of 2

25×25 = 625