A fruit bowl contains apples and bananas in the ratio 4 : 5. Two apples are removed changing the ratio to 2 : 3. Work out the total number of fruit that remain in the bowl.​

Answer:

x = 12 units

Step-by-step explanation:

In the picture attached,

Since, DE and BC are the parallel lines,AC and AB are the transverse.

Therefore, ∠AED ≅ ∠ABC [Alternate angles]

∠ADE ≅ ∠ACB [Alternate angles]

ΔADE ~ ΔACB [By AA postulate of similarity]

By the property of similarity,

If two triangles are similar then their corresponding sides will be proportional.

[tex]\frac{\text{AB}}{\text{AE}}=\frac{\text{AC}}{\text{AD}}[/tex]

[tex]\frac{(4+8)}{4}=\frac{(6+x)}{6}[/tex]

[tex]3=1+\frac{x}{6}[/tex]

x = 12

Therefore, length of missing segment is 12 units.

Answer:

B. √16 × √6

C. √96

Step-by-step explanation:

4√6

4 can be written as a square root.

4 = √16

√16 × √6

The square roots are multiplied, they can be written under one whole square root.

√(16 × 6)

√96

Answer:

x=3 y=11

Step-by-step explanation:

2x+3=9

2x=6

x=3

y-4=7

y=11

Answer:

T = 3(2)ᵈ⁻¹

Step-by-step explanation:

This is a geometric series, where the first term is 3 and the common ratio is 2.

T = 3(2)ᵈ⁻¹

This can be rewritten as:

T = ³/₂ (2)ᵈ

Answer:

10KB = 1MB

Step-by-step explanation:

Since 1KB => 2*10bytes

1MB => 2*20bytes

Therefore 10KB => 1MB

Answer:

10% off

Step-by-step explanation:

When $70 is discounted to $63, you can multiply 70 times 0.1 to get 7 which 70-63=7. To make 0.1 to a percentage, multiply by 100 to get 10%.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

Step-by-step explanation:

put (x+2)/(x-2)=a

a-1/a=5/6

[tex]multiply~by~6a \\6a^2-6=5a\\6a^2-5a-6=0\\6a^2-9a+4a-6=0\\3a(2a-3)+2(2a-3)=0\\(2a-3)(3a+2)=0\\either 2a-3=0,a=3/2 \\\frac{x+2}{x-2} =\frac{3}{2} \\cross~multiply\\3x-6=2x+4\\3x-2x=4+6\\x=10\\[/tex]

[tex]or~3a+2=0\\a=-2/3\\\frac{x+2}{x-2} =-\frac{2}{3} \\3x+6=-2x+4\\3x+2x=4-6\\5x=-2\\x=-2/5[/tex]

2.

put (x+3)/x=a

a+1/a=4  1/4

[tex]a+\frac{1}{a} =\frac{17}{4} \\multiply~by~4a\\4a^2+4=17a\\4a^2-17a+4=0\\4a^2-16a-a+4=0\\4a(a-4)-1(a-4)=0\\(a-4)(4a-1)=0\\either~a-4=0,a=4\\\frac{x+3}{x} =4\\4x=x+3\\4x-x=3\\3x=3\\x=3/3=1\\or\\4a-1=0\\a=1/4\\\\\frac{x+4}{x} =\frac{1}{4} \\4x+16=x\\3x=-16\\x=-16/3[/tex]

Answer:

First one is 41

Second one is 87

Step-by-step explanation:

Make the shaded part as a trapezoid which is (3+6)*10/2 you just have to get rid of 2*2. So you get 41 as the answer.

The unshaded part will be 16*8 then subtracts the shaded part which is 41.  Then you get the answer 87.

Answer:

Step-by-step explanation:

1.  4x = angle 4

x = angle 1

Angle 1 + angle 4 = 180

4x + x = 180

5x = 180

2. 55 = angle 2

angle 1 = 68

angle 3 = 55 + 68 = 123 = 180 - 123 = 57

Angle 4 = 57

Hope this helped,

kavitha

If the first term is [tex]a[/tex], then the second term is [tex]ar[/tex], the third is [tex]ar^2[/tex], the fourth is [tex]ar^3[/tex], and the fifth is [tex]ar^4[/tex].

We're given

[tex]\begin{cases}ar=6\\ar^4=48\end{cases}\implies\dfrac{ar^4}{ar}=r^3=8\implies r=2\implies a=3[/tex]

So the first five terms in the GP are

3, 6, 12, 24, 48

Adding up the first four gives a sum of 45.

If you were asked to find the sum of many, many more terms, having a formula for the n-th partial sum would convenient. Let [tex]S_n[/tex] denote the sum of the first n terms in the GP:

[tex]S_n=3+3\cdot2+3\cdot2^2+\cdots+3\cdot2^{n-2}+3\cdot2^{n-1}[/tex]

Multiply both sides by 2:

[tex]2S_n=3\cdot2+3\cdot2^2+3\cdot2^3+\cdots+3\cdot2^{n-1}+3\cdot2^n[/tex]

Subtract this from [tex]S_n[/tex], which eliminates all the middle terms:

[tex]S_n-2S_n=3-3\cdot2^n\implies -S_n=3(1-2^n)\implies S_n=3(2^n-1)[/tex]

Then the sum of the first four terms is again [tex]S_4=3(2^4-1)=45[/tex].

Answer:

last option

Step-by-step explanation:

Again, 1 cm represents 8 / 2 = 4 feet so the width is 4 * 4 = 16 and the length is 6 * 4 = 24.

Answer:

52.0 m

Step-by-step explanation:

The triangle formed by the flagpole, the ground and the 30° line is a right triangle, with x as the required length to be found.

Using the tangent ratio

tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{30}{x}[/tex] ( multiply both sides by x )

x × tan30° = 30 ( divide both sides by tan30° )

x = [tex]\frac{30}{tan30}[/tex] ≈ 52.0 m

Step-by-step explanation:

Answer:

The answer is C.) (2, -5)

Answer:

1/2*base*height

Step-by-step explanation:

All triangles have the area of 1/2*base* height.

Answer:

1/2 * b * h

Step-by-step explanation:

Answer:

Step-by-step explanation:

7(42 ÷ 3) + 4 (72 + 53) + 8 (-3)4

7(14) + 4(125) + 8(-12)

98 + 500 - 96

    598 - 96

        502

Answer:

Step-by-step explanation:

[tex]7(42 \div 3) + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]

Divide the numbers

[tex] = 7 \times 14 + 4(72 + 53) + 8 \times ( - 3) \times 4[/tex]

Add the numbers

[tex] = 7 \times 14 - 4 \times 125 + 8 \times ( - 3) \times 4[/tex]

Calculate the product

[tex] = 7 \times 14 + 4 \times 125 - 96[/tex]

Multiply the numbers

[tex] = 98 + 500 - 96[/tex]

Add the numbers

[tex] = 598 - 96[/tex]

Subtract the numbers

[tex] = 502[/tex]

Hope this helps..

Best regards!!

Answer:

[tex]\boxed{x < 7.5}[/tex]

Step-by-step explanation:

=> 2x < 15

Dividing both sides by 2

=> x < 15/2

=> x < 7.5

Answer:

[tex]\boxed{x<\frac{15}{2}}[/tex]

Step-by-step explanation:

[tex]2x<15[/tex]

Divide both parts by 2.

[tex]\displaystyle \frac{2x}{2} <\frac{15}{2}[/tex]

[tex]\displaystyle x<\frac{15}{2}[/tex]

Answer:

26.4ft²

Step-by-step explanation:

I first converted the centimeter values to feet

140Cm x 30.48 = 4.59

70cm x 30.48 = 2.3

the paper required is approximately equal to the area of the pyramid.

area of pyramid is equal to area of triangle + base²

Are of triangle = 1/2 x b xh

= 4 x 1/2 x4.59x2.3 + (2.3)²

= 2 x 4.59 x 2.3 + 5.29

= 26.4 feet²

therefore it will take 26.4 feet² paper to make each tree, including the bottom.

Answer:

It is actually 24500

Step-by-step explanation:

Hope this helped! I had the same lesson.

Answer:

Susan and 4 quests

5 people

Step-by-step explanation:

Take 9/10 and divide by 1/6

9/10 ÷1/6

Copy dot flip

9/10 * 6/1

54/10

50/10 + 4/10

5 4/10

We can only serve whole numbers

5 people

Susan and 4 quests

Answer:

∠AOB and ∠COD are vertical angles

∠DOE and ∠COD are complementary, adjacent

∠AOB and ∠AOD are supplementary, adjacent.

Step-by-step explanation:

Let's start with ∠AOB and ∠COD.

Looking at this, we can see they are the same angles formed by two lines that intersected. These are vertical angles as they are opposite each other.

∠DOE and ∠COD together form the angle ∠EOC, which is a right angle. Complementary angles are any of two that add up to 90°, so these two angles are complementary. They are also adjacent because they are right next to each other.

∠AOB and ∠AOD together form the angle ∠BOD, which has a measure of 180°. Supplementary angles are any of two that add up to 180°, so ∠AOB and ∠AOD are supplementary. They are also adjacent as they are touching/right next to each other.

I hope this helped!

Answer:

Option D is the correct option.

Step-by-step explanation:

Given,

Diameter ( D ) = 10 meters

Radius ( r ) = 10 ÷ 2 = 5 meters

Height ( h ) = 8 meters

Volume = ?

Now, let's find the volume of the given cylinder:

[tex]\pi \: {r}^{2} h[/tex]

Plug the values

[tex] = 3.14 \times {5}^{2} \times 8[/tex]

Evaluate the power

[tex] = 3.14 \times 25 \times 8[/tex]

Calculate the products

[tex] = 628 \: {m}^{2} [/tex]

Hope this helps...

Best regards!!

Complete question is;

Angela makes a pillow in the shape of a wedge to use for watching TV. The pillow is filled with 0.35 m³ of fluffy

material. The Height is 0.5 m and the

Base is 1 m.

What is the length of the pillow?

Give an exact answer (do not round)

Answer:

length of Pillow  = 1.4 m

Step-by-step explanation:

This wedge will be the shape of a triangular prism. The volume of a triangular prism is given as;

V = area of base x length = ½ × base × height × length

Thus;

Volume of Wedge = ½ × base × height × length

We are given;

base = 1 m

height = 0.5 m

Volume = 0.35m³

And we want to find the Length(L)

Thus;

½ × 0.5 × 1 × L  = 0.35

L/4 = 0.35

Multiply both sides by 4 to give;

L = 0.35 × 4

L = 1.4 m

length of Pillow  = 1.4 m

Answer:

1.4

Step-by-step explanation:

Khan

Answer:

6 bags

Step-by-step explanation:

Hey there!

Well first we need to find the area of the circle using,

π r^2

4*4 = 16

16 * pi ≅ 50.27

So now to find how much bags needed we do,

50.27 ÷ 9.42 = 5.34

Meaning 6 bags of soil is needed.

Hope this helps :)

Answer:

Caisha will need 6 bags of soil.

(B.) 6 bags :)

Answer:

The correct option is;

False

Step-by-step explanation:

The coefficient of x^k·y^(n-k) is nk,   False

The kth coefficient of the binomial expansion, (x + y)ⁿ is  [tex]\dbinom{n}{k} = \dfrac{n!}{k!\cdot (n-k)!} = C(n,k)[/tex]

Where;

k = r - 1

r = The term in the series

For an example the expansion of (x + y)⁵, we have;

(x + y)⁵ = x⁵ + 5·x⁴·y + 10·x³·y² + 10·x²·y³ + 5·x·y⁴ + y⁵

The third term, (k = 3) coefficient is 10 while n×k = 3×5 = 15

Therefore, the coefficient of x^k·y^(n-k) for the expansion  (x + y)ⁿ = [tex]C(n,k)[/tex] not nk

Answer:

True

Step-by-step explanation:

apec

Answer:

[tex]-24x^4+6x^3+25x^2+16[/tex]

Step 1:

We need to place the numbers in descending order of the power. Here, [tex]-24x^4[/tex] has the largest power, so that number goes first. We keep doing this until we end up with our final expression, placed in order based on the powers.

[tex]-24x^4+6x^3+25x^2+17-7+6[/tex]

Step 2:

We can see that the last three numbers, 17, -7, and 6, don't have variables or powers, so we simplify by adding (and subtracting) them.

[tex]17-7=10\\10+6=16[/tex]

Our final equation:

[tex]-24x^4+6x^3+25x^2+16[/tex]

Answer:

Probability that one type of candy will be chosen more than once in 10 trials = 0.2639

Step-by-step explanation:

This is a binomial experiment because

- A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.

- It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. (10 trials, with the outcome of each trial being that we get the required candy or not)

- The outcome of each trial/run of a binomial experiment is independent of one another.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 10 trials

x = Number of successes required = number of times we want to pick a particular brand of candy = more than once, that is > 1

p = probability of success = probability of picking a particular brand of candy from a bulk with 10 different types of candies = (1/10) = 0.10

q = probability of failure = Probability of not picking our wanted candy = 1 - p = 1 - 0.1 = 0.90

P(X > 1) = 1 - P(X ≤ 1)

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X = 0) = ¹⁰C₀ (0.10)⁰ (0.90)¹⁰⁻⁰ = 0.3486784401

P(X = 1) = ¹⁰C₁ (0.10)¹ (0.90)¹⁰⁻¹ = 0.387420489

P(X ≤ 1) = 0.3486784401 + 0.387420489 = 0.7360989291

P(X > 1) = 1 - 0.7360989291 = 0.2639010709 = 0.2639

Hope this Helps!!!

Answer:

a) 28 units

b) 0.0262 seconds

c) Minimum height of the nail = 1.923 units

Step-by-step explanation:

a) From the given equation, f(x) = -14×cos(720(t - 10)) + 14 comparing with the equation for periodic function, y = d + a·cos(bx - c)

Where:

d = The mid line

a = The amplitude

The period  = 2π/b

c/b = The shift

Therefore, since the length of the mid line and the amplitude are equal, the diameter of the bike maximum f(x) = -14×-1 + 14 = 28

b) Given that three revolution = 6×π, we have;

At t = 0

cos(720(t-10) = cos(720(0-10))  = cos(7200) = 1

Therefore, for three revolutions, we have

720(t - 10) = 720t - 7200

b = 720

The period = 2π/b = 6·π/720 = 0.0262 seconds

c) The minimum height of the nail is given by the height of the wheel at t = 0, as follows;

f(x) = -14×cos(720(t - 10)) + 14

At t = 0 gives;

f(x) = -14×cos(720(0 - 10)) + 14

Minimum height of the nail = -14×cos(-7200) + 14 = -14×0.863+14 =1.923

Minimum height of the nail = 1.923

by bargaining with the owner, vying for discounts or insisting on multiple products for a complimentary value deal

Answer:

x = 65°

y = 25° (equations in explanation)

Step-by-step explanation:

We know that EKD is 25° and we know that DKB is 90°.

EKD, DKB, and BKF are supplementary. This means that their angle measures add up to 180°.

So, since we know two, we can find the other very easily.

[tex]180 - (25+90)\\180 - 115\\65[/tex]

This means that BKF is 65°.

Now, BKF and EKC are alternate interior angles, so they have the exact same measurement. Therefore, EKC, x, is 65°.

Again, EKC, CKA, and AKF are supplementary. AKF is 90° and EKC is 65°, so we can find the measure of CKA easily.

[tex]180 - (65+90)\\180-155\\25[/tex]

Therefore y is 25° and x is 65°.

Hope this helped!

Answer:

¿De que solución habla?

Step-by-step explanation:

Answer:

B, D, F

Step-by-step explanation:

edge 2020

Answer:

  (-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)

Step-by-step explanation:

To make it easier to differentiate, we'll rewrite the function as ...

  h(x) = 2/(x-5) -1/(x-2)

Then the derivative is ...

  h'(x) = -2/(x-5)^2 +1/(x-2)^2

This will be zero when ...

  -2(x-2)^2 +(x-5)^2 = 0

  -2(x^2 -4x +4) +(x^2 -10x +25) = 0

  -x^2 -2x +17 = 0

  x^2 +2x +1 = 17 +1

  x +1 = ±√18 = ±3√2

  x = -1 ±3√2

The values of the function at these locations are ...

  h(-1-3√2) = -1 +(2/3)√2 ≈ -1.9428

  h(-1+3√2) = -1 -(2/3)√2 ≈ -0.0572

Then the range of h(x) is ...

  (-∞, -1-(2/3)√2] ∪ [-1+(2/3)√2, ∞)