In a party of 60 people, 35 had vanilla ice-cream, 35 had chocolate ice-cream. All the people has at least one ice cream then how many of them had i) both vanilla and chocolate ice-cream ii) only Vanilla ice-cream iii) Only chocolate ice-cream​

Answer : 72

Step-by-step explanation:

It's above in the pic .

Answer:

y=2 x=4

Step-by-step explanation:

Substitute x with 2y so the second equation is 2y+y=6

Then simplify your new equation:

3y=6

y=2

If y=2 and x=2( 2) then x=4

Using proportions, it is found that the length of the sculpture using the new scale is given by:

D. 20 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The initial scale is of 1 cm = 2 feet, with a sculpture of 8 feet, hence the length of the drawing is given by:

l = 8/2 = 4 cm.

For the new scale, 1 cm = 5 feet, and you keep the drawing of 4 cm, hence the length of the sculpture is given by:

l = 4 x 5 = 20 feet.

Hence option D is correct.

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An ordered pair is simply the x-coordinate and the y-coordinate of a point.

The ordered pair of the bullseye is (4,-2.5)

From the given image (see attachment), we have:

[tex](x_1,y_1) = (9,3)[/tex]

[tex](x_2,y_2) = (-1,-8)[/tex]

The bullseye is at the midpoint of these two points.

So, the ordered pair of the bullseye is calculated using the following midpoint formula.

[tex](x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

So, we have:

[tex](x,y) = (\frac{9-1}{2},\frac{3-8}{2})[/tex]

[tex](x,y) = (\frac{8}{2},\frac{-5}{2})[/tex]

[tex](x,y) = (4,-2.5)[/tex]

Hence, the ordered pair of the bullseye is (4,-2.5)

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Answer:

An integer is any positive whole number or its opposite. Here, opposite means sign. So a positive integer has a negative opposite and vice versa

Step-by-step explanation:

-5 and 5 are an example.

Answer:

radius is 7 cm

Step-by-step explanation:

formular for volume:

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

r is radius

h is height

[tex]1540 = 3.14 \times {r}^{2} \times 10 \\ {r}^{2} = 49.0 \\ r = 7 \: cm[/tex]

Answer:

a = 5, b = - 13

Step-by-step explanation:

The Remainder theorem states that the remainder when f(x) is divided by (x - a) is equal to f(a)

Thus the remainder for division by (x + 2) is zero , then by substituting x = - 2 into the expression.

2(- 2)³ + a(- 2)² + b(- 2) - 30 = 0

2(- 8) + 4a - 2b - 30 = 0

- 16 + 4a - 2b - 30 = 0

- 46 + 4a - 2b = 0 ( add 46 to both sides )

4a - 2b = 46 → (1)

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Similarly when f(x) is divided by (cx - a) the remainder is f([tex]\frac{c}{a}[/tex] )

The remainder on dividing by (2x - 1) is - 35, then by substituting x = [tex]\frac{1}{2}[/tex]

2([tex]\frac{1}{2}[/tex] )³ + a([tex]\frac{1}{2}[/tex] )² + [tex]\frac{1}{2}[/tex] b - 30 = - 35

2([tex]\frac{1}{8}[/tex] ) + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b - 30 = - 35 ( add 30 to both sides )

[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] a + [tex]\frac{1}{2}[/tex] b = - 5 ( multiply through by 4 to clear the fractions )

1 + a + 2b = - 20 ( subtract 1 from both sides )

a + 2b = - 21 → (2)

Solve (1) and (2) simultaneously )

Add (1) and (2) term by term to eliminate b

5a = 25 ( divide both sides by 5 )

a = 5

Substitute a = 5 into (2)

5 + 2b = - 21 ( subtract 5 from both sides )

2b = - 26 ( divide both sides by 2 )

b = - 13

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). The value of a and b are 5 and -13, respectively.

According to the remainder theorem, when a polynomial P(x) is divided by (x-t) then the remainder of the division is equal to P(t). If P(t)=0, then the (x-t) is the factor of the polynomial.

Using the remainder theorem we can write,

f(x) = 2x³+ ax² + bx - 30

f(-2) = 2(-2)³ + a(-2)² + b(-2) - 30 = 0

-16 + 4a - 2b - 30 = 0

4a - 2b = 46   ........ equation 1

f(x) = 2x³+ ax² + bx - 30

f(1/2) = 2(1/2)³ + a(1/2)² + b(1/2) - 30 = -35

(1/4) + a(1/4) + b(1/2) = -35 + 30

(1+a+2b)/4 = -5

1 + a + 2b = -5 × 4

a + 2b = -21   .......... equation 2

Adding the two equations,

4a + 2b + a - 2b = 46 - 21

5a = 25

a = 25/5

a = 5

Substitute the value of a in any one of the equation,

a + 2b = -21

5 + 2b = -21

2b = -21 - 5

2b = -26

b = -26/2

b = -13

Hence, the value of a and b are 5 and -13, respectively.

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Answer:

C

E

Step-by-step explanation:

Step-by-step explanation:

Steps are in the picture above.

Answer:

3

Step-by-step explanation:

[tex]log(3x^{3}) - log(x^{2}) = log(\frac{3x^{3}}{x^{2}})\\log(27) - log(x) = log(\frac{27}{x} )\\[/tex]

therefore,

[tex]\frac{3x^{3} }{x^{2} } = \frac{27}{x} \\3x=\frac{27}{x} \\3x^{2} =27\\x= +3\\x=-3[/tex]

however, since logarithms cannot have negative arguments, x can only be +3

i.e. log(-3) is impossible, and will return MATH ERROR on a calculator.

Answer:

14

Step-by-step explanation:

√36+√64

√36=6

√64=8

6+8

14

THANK YOU

Answer: Yes it is.

Step-by-step explanation:

Mixed to proper

7/3 = 2 1/3

Answer:

54.895

Step-by-step explanation:

hopes it's help you

Answer:

Step-by-step explanation:

Apply the natural log to both sides we have

[tex](-(2/3)x -1 ) \ln 2 = (3-2x)\ln 3\\-x(2/3)\ln 2 + 2x\ln 3 = 3\ln 3 -\ln 2\\x\left(\frac{-2}{3}\ln 2 +2\ln 3\right)=\ln (27/2)\\x\left(\ln 9 -\ln \sqrt{8}) =\ln(27/2)\\\\x\ln (9/\sqrt{8})=\ln(27/2)\\\\x= \ln(27/2) / \ln(9/\sqrt{8})[/tex]

Probabilities are used to determine the chance of an event. The following are the summary of the solution.

Given that:

[tex]n = 8[/tex]

[tex]G = 6[/tex] --- Green

[tex]Y = 2[/tex] --- Yellow

(a) Probability that the two cellphones are green (without replacement).

Since the cellphone is not replaced, the probability is calculated as follows:

[tex]Pr = \frac Gn \times \frac{G - 1}{n-1}[/tex]

So, we have:

[tex]Pr = \frac 68 \times \frac{6 - 1}{8-1}[/tex]

[tex]Pr = \frac 68 \times \frac 57[/tex]

[tex]Pr = \frac{30}{56}[/tex]

[tex]Pr = \frac{15}{28}[/tex]

Hence, the probability that the two cellphones are green (without replacement) is 15/28

(b) Probability that one green and one yellow is selected (without replacement).

Since the cellphone is not replaced, the probability is calculated as follows:

[tex]Pr = \frac Gn \times \frac{Y}{n-1} + \frac Yn \times \frac{G}{n-1}[/tex]  ---- The subtraction means the cellphones are not replaced

This gives

[tex]Pr = \frac 68 \times \frac{2}{8-1} + \frac 28 \times \frac{6}{8-1}[/tex]

[tex]Pr = \frac 34 \times \frac{2}{7} + \frac 14 \times \frac{6}{7}[/tex]

[tex]Pr = \frac 32 \times \frac17 + \frac 12 \times \frac 37[/tex]

[tex]Pr = \frac{3}{14} + \frac{3}{14}[/tex]

Take LCM

[tex]Pr = \frac{3+3}{14}[/tex]

[tex]Pr = \frac{6}{14}[/tex]

[tex]Pr = \frac{3}{7}[/tex]

Hence, the probability that one green and one yellow is selected (without replacement) is 3/7

(c) Probability that the all three cellphones are yellow (with replacement).

Since the cellphone is replaced, the probability is calculated as follows:

[tex]Pr = \frac Yn \times \frac Yn \times \frac Yn[/tex]

So, we have:

[tex]Pr = \frac 28 \times \frac 28 \times \frac 28[/tex]

[tex]Pr = \frac 14 \times \frac 14 \times \frac 14[/tex]

[tex]Pr = \frac 1{64}[/tex]

Hence, the probability that all three cellphones are yellow (with replacement) is 1/64

(d1) Probability that the two cellphones are green (with replacement).

Since the cellphone is replaced, the probability is calculated as follows:

[tex]Pr = \frac Gn \times \frac{G}{n}[/tex]

So, we have:

[tex]Pr = \frac 68 \times \frac{6}{8}[/tex]

[tex]Pr = \frac 34 \times \frac{3}{4}[/tex]

[tex]Pr = \frac{9}{16}[/tex]

Hence, the probability that the two cellphones are green (with replacement) is 9/16

(d2) Probability that one green and one yellow is selected (with replacement).

Since the cellphone is replaced, the probability is calculated as follows:

So, we have:

[tex]Pr = \frac Gn \times \frac{Y}{n} + \frac Yn \times \frac{G}{n}[/tex]

This gives

[tex]Pr = \frac 68 \times \frac{2}{8} + \frac 28 \times \frac{6}{8}[/tex]

[tex]Pr = \frac 34 \times \frac{1}{4} + \frac 14 \times \frac{3}{4}[/tex]

[tex]Pr = \frac 3{16} + \frac{3}{16}[/tex]

Take LCM

[tex]Pr = \frac {3+3}{16}[/tex]

[tex]Pr = \frac {6}{16}[/tex]

[tex]Pr = \frac {3}{8}[/tex]

Hence, the probability that one green and one yellow is selected (with replacement) is 3/8

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Answer:

No.

Step-by-step explanation:

No because it can be written as a fraction, 6606/10

Answer:

Ans : the length of 5/9 is 5m

Answer:

Answer is 4 I think!!

Answer:

Step-by-step explanation:

t=2g+3.

9514 1404 393

Answer:

  14xv^3

Step-by-step explanation:

Coefficients are 28 and 14, which have a GCF of 14.

x exponents are 1 and 6, so the GCF is x^1 = x

y exponents are 8 and 0, so the GCF is y^0 = 1

v exponents are 7 and 3, so the GCF is v^3

The GCF of the two terms is the product of the factors just found:

  14xv^3

[tex](2a - 5)(4a - 7)[/tex]

[tex]2a(4a - 7) - 5(4a - 7)[/tex]

[tex]8 {a}^{2} - 14a - 20a + 35[/tex]

[tex]8 {a}^{2} - 34a + 35[/tex]

Step-by-step explanation:

( 2a - 5 ) ( 4a - 7 )

2a ( 4a - 7) - 5 ( 4a - 7 )

8a² - 14a - 20a + 35

8a² -34a + 35

Answer:

ALU stands for arithmetic logic unit. which is part of the central processing unit of a computer which performs arithmetic and logical operations.

I hope this helps

Answer:

In computer science: Architecture and organization. …of a control unit, an arithmetic logic unit (ALU), a memory unit, and input/output (I/O) controllers. The ALU performs simple addition, subtraction, multiplication, division, and logic operations, such as OR and AND.

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

AB is the hypotenuse of the right triangle

sin34 = opp/hyp = 29/hyp

hyp = 29/sin34 = 51.860457849...

Answer:

[tex]let \: |ab| \: be \: x \\ \\ \frac{ \sin(90) }{x} = \frac{ \sin(34) }{29} \\ x \sin(34) = 29 \sin(90) \\ x = \frac{29 \sin(90) }{ \sin(34) } \\ x = 51.86(2.d.p) \\ |ab| = 51.86[/tex]

Step-by-step explanation:

Given line y=1/3x-4

slope of given line m=1/3

Slope of required line :

m=1/3

As lines are parallel then slope of lines are equal.

Using point slope form:

y-y1=m(x-x1)

p(x1,y1)=(9,8)

y-8=1/3(x-9)

3y-24=x-9

x-3y-9+24=0

x-3y+15=0

Note:if you need to ask any question please let me know.

The answer is 56. work is shown below.

Step 1: apply 2nd power to everything inside parentheses

(7 - 1)² = 7² - 1²

Step 2: apply exponents (remember, exponents are a shorter way to express a number multiplied by itself a number of times).

1 x 1 = 1

7 x 7 = 49

Step 3: subtract

49 - 1 = 48

Step 4: apply exponent

2 x 2 x 2 x 2 = (2 x 2) x (2 x 2)

2 x 2 = 4

2 x 2 = 4

4 x 4 = 16

2⁴ = 16

Step 5: add

48 + 16 = 64

Step 6 (final step): subtract

64 - 8 = 56

final answer: 56

Answer:

300

Step-by-step explanation:

I hope it will help you.

Answer:

y = - [tex]\frac{1}{2}[/tex] x - 4

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

y -  [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~~~~

m = - [tex]\frac{1}{2}[/tex]

( - 10, 1 )

y - 1 = - [tex]\frac{1}{2}[/tex] [ x - ( - 10 )]

y - 1 =  - [tex]\frac{1}{2}[/tex] x + ( - [tex]\frac{1}{2}[/tex] )(10)

y = - [tex]\frac{1}{2}[/tex] x - 4

Answer:

It is 1/10

Step-by-step explanation:

One decade has 10 years

[tex]{ \sf{1 \: decade = 10 \: years}} \\ { \sf{ \frac{1}{10} \: decade = 1 \: year}}[/tex]

Answer:

10% , 1/10, or 10/100

Step-by-step explanation:

There are 10 years in a decade

1/10 represents the 1 year out of the 10!