A machinist who had been producing 40 parts per day increased to the out put of 60 parts per day by going to a faster machine. How many times faster is the new machine? Wright your answer as a mixed number.​

P(B|A) expressed in simplest form is 4/15. Option C is correct answer.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Here, probability of event A = 4/15

         probability of event B = 4/15

P(B|A) = P(A ∩ B)/P(B)

P(A ∩ B) = P(A) X P(B)

              = (4/15)(4/15)

              = 16/225

Now, conditional probability;

P(B|A) = (16/225) / (4/15)

          = (16/225)(15/4)

          = (16 X 15) / (225 X 4)

          = 4/15

Thus, P(B|A) expressed in simplest form is 4/15. Option C is correct answer.

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The value of the variables are y = -45/2, r = -9, x = 2/9 and x = 2

(1) y/3 + 6 = -3/2

Multiply through by 3

y + 18 = -9/2

Subtract 18 from both sides

y = -18 - 9/2

Take LCM

y = (-18 * 2 - 9)/2

Evaluate

y = -45/2

(2) -2r/3 - 3 = 3

Multiply through by 3

-2r - 9 = 9

Add 9 to both sides

-2r = 18

Divide by 2

r = -9

(3) 2/3 - 2x = x

Multiply through by 3

2 - 6x = 3x

Add 6x to both sides

2 = 9x

Divide by 9

x = 2/9

(4) 7x/2 + -5/2 = 9/2

Multiply through by 2

7x - 5 = 9

Add 5 to both sides

7x = 14

Divide by 7

x = 2

Hence, the value of the variables are y = -45/2, r = -9, x = 2/9 and x = 2

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The profit from selling 30 designer cakes in a single month is; $2130.

It follows from the task content that the income function as given is; d(x) = 125 × a.

Hence, when 30 designer cakes are sold, thee income is; 125 × 30 = 3750$.

The profit which is a function of the income y is given as; p (y) = y - 1620.

On this note, if follows that the profit is; p (y) = 3750 - 1620 = $2130.

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Answer: 3x+1

Step-by-step explanation: See attachment

Answer:

x = - 6 , x = 4

Step-by-step explanation:

the absolute value function always gives a positive value but the expression inside can be positive or negative , that is

2x + 2 = 10 or - (2x + 2) = 10

solving both

2x + 2 = 10 ( subtract 2 from both sides )

2x = 8 ( divide both sides by 2 )

x = 4

or

- (2x + 2) = 10

- 2x - 2 = 10 ( add 2 to both sides )

- 2x = 12 ( divide both sides by - 2 )

x = - 6

The cost of the path around the swimming pool with length 15m and width 12m is $1,190

Pathway with 2m wide:

Area of the path = length × width

= 17m × 14m

= 238 square meters

Total cost of the path = 238 square meters × $5

= $1,190

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Answer:

[tex]\frac{7}{9}[/tex] and [tex]\frac{7163}{9900}[/tex]

Step-by-step explanation:

we require 2 equations with the repeating digits placed after the decimal point.

(1)

let x = 0.777... (1) ← multiply both sides by 10

10x = 7.777... (2)

subtract (1) from (2) thus eliminating the repeating digits

9x = 7 ( divide both sides by 9 )

x = [tex]\frac{7}{9}[/tex]

(2)

let x = 0.723535.. ( multiply both sides by 100 and 10,000 )

100x = 72.3535.... (1)

10,000x = 7235.3535..... (2)

subtract (1) from (2) thus eliminating the repeating digits

9900x = 7163 ( divide both sides by 9900 )

x = [tex]\frac{7163}{9900}[/tex]

Answer:

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y

.

x-intercept(s): None

y-intercept(s): (0,5)

Step-by-step explanation:

Answer:

P= 2l + 2W

Step-by-step explanation:

(P-2W)/2= l

(P-2W)= 2l

P-2W= 2l

P= 2l + 2W

Answer:

26% increase

Step-by-step explanation:

Initial temperature= t

5% increase= t+ 5%= 1.05t

20% increase= 1.05t +20%= 1.05t*1.2= 1.26t

1.26 t= t + 26%

So temperature increased by 26%

The points would you find on the graph for |x| +1 < 3 are -1, 0 and 1

The inequality is given as:

|x| + 1 < 3

Subtract 1 from both sides

|x| < 2

This means that the absolute value of x is less than 2

From the list of options, the true values are -1, 0 and 1.

Because their absolute values are less than 2

Hence, the points would you find on the graph for |x| +1 < 3 are -1, 0 and 1

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The function over the interval is an increasing exponential function.

A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".

The complete question is

An investment group compares returns on an account

against the function represented in the table, where x is the

time in years and f(x) is the total return on investment.

Which describes the function over the interval given in the

table?

х

a decreasing quadratic function

an increasing quadratic function

a decreasing exponential function

an increasing exponential function

0

5

f(x)

10,000

12,201.90

14,888.64

22,167.15

10

20

A decreasing quadratic function is the vertex of the parabola lies on the axis parabola. So, time in years change does not give maximum total return on investment.

For increasing quadratic equation, the graph increasing at one side of the axis and decreases at other side.

For, Exponential function          

When the exponential function then it shows total return on investment is not maximum.

When the exponential function is increasing it shows time goes, total return on investment is maximum.

Hence, the exponential function is increasing.

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Step-by-step explanation:

the circumference of a whole circle is

2×pi×r

with r being the radius. which is in our case a.

so,

2×pi×a

the part arc of just a sector of the circle is just the angle/360 part (as the whole circle is 360°).

we therefore know

27×pi = 2×pi×a × 60/360 = 2×pi×a × 1/6 = pi×a × 1/3

3×27×pi = pi×a

81×pi = pi×a

a = 81

Thw measurements based on the arrow on the rulers will be:

A= 1.3cm

B = 2.1 cm

C = 3.4cm

D = 4.4cm

E = 5.5cm

F = 7cm

G = 8.2cm

H = 10.3cm

I = 11cm

J = 11.7cm

K = 12.7cm

L = 14.7cm

It should be noted that 10 millimeters make 1 cm. Therefore, to convert the centimeters to millimeters, you simply have to multiply by 10.

A = 1.3cm × 10 = 13mm

B = 2.1cm = 21mm

C = 3.4 × 10 = 34m

Using same method, the value of the remaining will be:

D = 44mm

E = 55mm

F = 70mm

G = 82mm

H = 103mm

I = 110mm

J = 117mm

K = 127mm

L = 147mm

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The centre of the circle is (1/2, 1) and the radius of the circle is 2 if the circle equation is x² + y² − x − 2y − 11/4 = 0

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

The question is incomplete.

The complete question is:

A circle is defined by the equation given below.

x² + y² − x − 2y − 11/4 = 0

What are the coordinates for the centre of the circle and the length of the radius?

We know the standard form of a circle:

(x - h)² + (y - k)² = r²

Here (h, k) is the centre of the circle and r is the radius of the circle

[tex]\rm x^2 - x + \dfrac{1}{4} + y^2 - 2y + 1= \dfrac{11}{4} +\dfrac{1}{4} + 1\\\\[/tex]

[tex]\rm (x - \dfrac{1}{2})^2+(y-1)^2 = 2^2[/tex]

Thus, the centre of the circle is (1/2, 1) and the radius of the circle is 2 if the circle equation is x² + y² − x − 2y − 11/4 = 0

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Answer:

£69

Step-by-step explanation:

Given information:

Cost of buying a dress and shoes:

⇒ £50 + £43 = £93

Discount:

⇒ 1/3 of £93 = 1/3 × 93 = £31

Cost of goods after discount is applied:

⇒ £93 - £31 = £62

Addition of shipping and handling:

⇒ £62 + £7 = £69

Therefore, Ruth will pay £69 if she buys a dress and shoes.

Answer:

10

Step-by-step explanation:

Evaluate for x=4

[tex]\frac{3(4+4)(4+1)}{(4+2)(4-2)}[/tex]

[tex]=\frac{120}{12}[/tex]

[tex]=10[/tex]

I Hope This Helps :)

Can you Mark Me As Brainliest

Answer:

c

Step-by-step explanation:

3*8*5/（6*2）=10

The correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.

If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics.

a x b = b x a

So for the expression 5(2a − 3) = (2a − 3) ⋅ 5 suppose 5 is a and ( 2a - 3 ) is b so.

a x b = b x a

5(2a − 3) = (2a − 3) ⋅ 5

Therefore the correct answer is option C which is 5(2a − 3) = (2a − 3) ⋅ 5 showing commutative property.

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Answer:

28

Step-by-step explanation:

similar triangles are proportional

and add all the sides of the bigger triangle

Answer:

ln(x)

Step-by-step explanation:

ln(x) can be rewritten as e^ln(x)=x. so if e^ln(1)=1 the exponent is just 0. because anything to the power of 0 is 1 according to the Zero Exponent Rule

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

The amount of money you saved by receiving a discount of 25% is $5.5

Step-by-step explanation:

Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price. Selling price is the actual price at which an article is sold after any reduction or discounts in the cost price.

discount is always calculated on the cost price of the article

formula to calculate the discount and discount %

Discount = List Price - Selling Price

Discount (%) = (Discount/cost price) × 100

here, in the question discount % is given = 25%

cost price of the item = $22

therefore using the above mentioned discount percentage formula:

25 = (Discount/22)×100

25/100 = Discount/ 22

0.25 × 22 = Discount

$5.5     = Discount

thus ,  

the amount of many you saved by receiving a discount of 25% is $5.5

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A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The radius of the cylindrical tin is 7 cm.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

The height of the cylindrical tin can is 7 cm, while the total surface area is 462 cm². Therefore, the total surface area of the tin will be,

The total surface area = area of base + Lateral surface area

462 cm² = πR² + 2πRH

462 = π(R² + 2R7)

147 = R² + 14R

R² + 14R - 147 = 0

R = 7, -21

Since the radius can not be negative.

Hence, the radius of the cylindrical tin is 7 cm.

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Answer:

Graph B

Step-by-step explanation:

In order for a graph to represent a function, it needs to pass the vertical line test.  In this case, graph B is the only one that passes the vertical line test.

Hope this helped :)

3 packages of bread would produce more utility than 2 jars of jam

The marginal utility function of jam is given as:

f(x) = 55 - 4x

Integrate the above function to determine the total utility function

f'(x) = 55x - 2x^2

Hence, the total utility function of the jam is f'(x) = 55x - 2x^2

The marginal utility function of bread is given as:

g(x) = 37 - x

Integrate the above function to determine the total utility function

g'(x) = 37x - 0.5x^2

Hence, the total utility function of the bread is g'(x) = 37x - 0.5x^2

We have:

Jam = 2 jars

Bread = 3 packages

Substitute 2 for x in f'(x) = 55x - 2x^2

f'(2) = 55 * 2 - 2 * 2^2

f'(2) = 102

Substitute 3 for x in g'(x) = 37x - 0.5x^2

g'(3) = 37 * 3 - 0.5 * 3^2

g'(3) = 106.5

106.2 is greater than 102

Hence, 3 packages of bread would produce more utility

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Answer:

54x + 36

Step-by-step explanation:

Simplify:

First open the brackets by multiplying  each term by 7.

 5x - 6 + 7(7x + 6) = 5x - 6 + 7*7x + 7*6

                              = 5x - 6 + 49x + 42

                              = 5x + 49x - 6 + 42

Combine like terms. Like terms have same variable with same power. Here 5x and 49x are like terms & (-6) and 42 are like terms (Constants)

                              =  54x + 36

Answer:

54x +36

Step-by-step explanation:

5x - 6 + 7(7x+6)       multiply                

5x -6 +49x+42         add like terms

54x + 36                   that's the answer

Answer:

Step-by-step explanation:

truth to the power 6 15 raised to the power x

Answer:

0.346

Step-by-step explanation:

brainiest pls ty

Answer:

.,..

Step-by-step explanation:

0.346 ............ I'm..............

The average rate of change is 4.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The rate of change in interval [0, 2]

r=[h(2)-h(0)]/2

h(2)=(2)²+2(2)-6

h(2)=4+4-6

h(2)=2

h(0)=(0)²+2(0)-6

h(0)=0+0-6

h(0)=-6

So, r=[h(2)-h(0)]/2

r=[2-(-6)]/2

r=(8)/2

r=4

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