you need 418 yards of blue silk to make one bridesmaid’s dress and 358 yards of the same fabric to make another. How many yards of blue silk do you need to make both dresses?

Answer:

Find the GCD (or HCF) of numerator and denominator. GCD of 47 and 94 is 47.

47 ÷ 4794 ÷ 47.

Reduced fraction: 12. Therefore, 47/94 simplified to lowest terms is 1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

You just keep simplifying.

Find the GCD of the numerator and denominator. The GCD of 47 and 94 is 47.

47 divided by 4794 divided by 47

Reduced fraction: 12. So 47/94 simplified is 1/2

Answer:

26 ft

Step-by-step explanation:

A=bh

40= 8h

h=5

P=2(l+w)

P= 2(8+5)

P = 2(13)

P = 26

Answer:

X=2,3

Step-by-step explanation:

Answer:

1/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the encoded message defined by the function f(x) = x³-1,  the inverse function that the decoder would need when the message is received can be expressed as thus:

let the inverse of the function be represented as y such that y = x³-1.

Making x the subject of the formula from the equation above;

x³ = y+1

Taking the cube root of both sides:

∛x³ = ∛(y+1)

x = ∛(y+1)

replacing y with x:

y = ∛(x+1)

f⁻¹(x) = ∛(x+1)

The encoded message is the inverse function ∛(x+1)

Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).

Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)

The area of the surface formed by revolving the polar equation over the given interval about the given line , r = 4cosθ is 16π .

Polar coordinate system is a two dimensional coordinates system like Cartesian system with the variables r, θ ( polar coordinates) and axis called polar axis . Consider the polar equation

r = 4cosθ --(1) ; 0≤θ ≤π/2

The axis of a rotation is in polar axis.

We know that, the surface area about θ = π/2 is

S = 2π ∫(r sinθ√(r² + (dr/dθ)²) dθ with limits

so, differenatiate equation (1) with respect to θ we get , dr/dθ = - 4 sinθ

Now, S =2π₀∫ˣ [4cosθsinθ√(4²cos²θ + (-4 sinθ)²)]dθ where x = π/2

S = 2π ₀∫ˣ[ 4cosθsinθ√(4²cos²θ + 4²sin²θ)]dθ

S = 2π₀∫ˣ [ 4cosθsinθ√4²(cos²θ+sin²θ)]dθ

S = 2π ₀∫ˣ [ 16cosθsinθ√(cos²θ+sin²θ)]dθ

S = 32π ₀∫ˣ [cosθ sinθ √1 ]dθ

S = (32π/2) ₀∫ˣ 2cosθsinθdθ

S = (16π) ₀∫ˣ sin2θdθ

S = 16π ₀[- cos2θ/2]ˣ

putting the upper limit θ = x = π/2 and lower limit θ = 0

S = (- 16π/2) [ cos2 (π/2) - cos2(0)]

S = (- 8π )[ cosπ - cos0° ] = - 8π[ - 1 - 1]

S = 16π

Hence, surface area is 16π .

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Complete question :

Find the area of the surface formed by revolving the polar equation over the given interval about the given line_ Polar Equation r = 2 cosQ

Interval 0 < Q <π/ 2 Axis of Revolution Polar axis.

The Distance from the point P(2, 1, 4) to the plane is approximately -0.9487.

The equation of a plane can be found using the normal vector and a point on the plane.

First, we can find the normal vector of the plane by finding the cross product of two vectors connecting the points on the plane.

The vector from point Q to R is (0, 2, 0) - (1, 0, 0) = (-1, 2, 0)

The vector from point Q to S is (0, 0, 3) - (1, 0, 0) = (-1, 0, 3)

The normal vector is the cross product of these two vectors:

n = cross(-1, 2, 0), (-1, 0, 3)) = (3, 3, -2)

Next, we can find the equation of the plane using the normal vector and a point on the plane, say Q(1, 0, 0):

ax + by + cz = d

3x + 3y - 2z = d

3x + 3y - 2z = 3(1) + 3(0) - 2(0) = 3

Finally, we can find the distance from the point P(2, 1, 4) to the plane by finding the perpendicular distance between the point and the plane. This can be done using the formula:

\(d = (Ax + By + Cz + D)/\sqrt{ {A^2 + B^2 + C^2}\)

\(d = (3x + 3y - 2z + 3)/\sqrt{ (3^2 + 3^2 + (-2)^2)\)

\(d = (3(2) + 3(1) - 2(4) + 3)/\sqrt{ (3^2 + 3^2 + (-2)^2)\)

\(d = (-3)/\sqrt{(18)\)

d = -3/3.162 = -0.9487

So the distance from the point P(2, 1, 4) to the plane is approximately -0.9487.

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Answer:

Option A: 3.59% is the correct answer

Step-by-step explanation:

Z-score is used to calculate the probabilities when mean and standard deviation is given.

Given

Mean = μ = 21

SD = σ = 5

We have to find the probability of selling 12 or less water heaters so our x value is 12

x = 12

The z-score of a value is calculated as:

z-score = (x-μ)/σ

Putting the values

\(z-score=\frac{12-21}{5} \\=\frac{-9}{5}\\=-1.8\)

Now z-score table will be used to calculate the probability for z= -1.8

So we will go for the row with -1.8 and column 0, which gives us: 0.03593

As we have to calculate the probability in percentage

\(=0.03593*100\\= 3.593\%\)

Hence,

Option A: 3.59% is the correct answer

The distance Luciano walked more on Sunday is given by the equation A = ( 1/6 ) of a mile

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance Luciano walked more on Sunday be A

Now , the equation will be

The distance walked by Luciano on Sunday = ( 5/9 ) mile

The distance walked by Luciano on Saturday = ( 7/18 ) mile

So , the distance Luciano walked more on Sunday A = distance walked by Luciano on Sunday - distance walked by Luciano on Saturday

Substituting the values in the equation , we get

The distance Luciano walked more on Sunday A = ( 5/9 ) - ( 7/18 )

On simplifying the equation , we get

The distance Luciano walked more on Sunday A = ( 10 - 7 ) / 18

The distance Luciano walked more on Sunday A = 3/18 miles

The distance Luciano walked more on Sunday A = 1/6 miles

Hence , the equation is A = 1/6 of a miles

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Answer:

1) Already in scientific notation

2) 2 x 10^5

3) 3 x 10^5

4) 1.5 x 10^5

Answer:

7:43 am.

Step-by-step explanation:

it was  1/2 full one minute ago then another 1/2 = 1/4 full 2 minutes ago.

Knowing how the bus fills, we want to find the time where the bus is one-quarter full.

The bus is one-quarter full at 7:43 am.

We know that at 7:45 am the bus is full. Let's say that the full bus has N people inside.

Each minute the population doubles, so if we go backwards, each minute the population is divided by 2.

One minute before, the bus must have half of the above population, meaning that at 7:44 am, the bus has N/2 people.

Another minuter before the people inside is halved again, then at 7:43 am we will have (N/2)/2 = N/4 people.

And if N is the people in a full bus, then N/4 represents the buss a quarter full.

Then we can answer the question as:

The bus is one-quarter full at 7:43 am.

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Answer:

-30x+147= -171-24x

+24x                +24x

-6x+147= -171

     -147   -147

       -6x= -318

           x=53

Hope this helps!

The mass of the water is 7880.1 grams.

Specific heat capacity is the amount of heat energy required to raise the temperature of a substance per unit of mass.

Mathematically -

Q = mcΔT

where -

{Q} = heat energy

{m} = mass

{c} = specific heat capacity

{ΔT} =change in temperature

Given is the water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it.

Specific heat capacity of water = 4.186 J/g°C

205 calories = 857720 Joules

We can write -

Q = mcΔT

857720 = m x 4.186 x (38 - 12)

857720 = 108.836 x m

m = 857720/108.836

m = 7880.1 grams

Therefore, the mass of the water is 7880.1 grams.

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{QUESTION IN ENGLISH -

The water in a container changes its temperature from 12°C to 38°C, when 205 calories are transferred to it. What is the mass of water in the container?}

Answer:

There is a 0.2 chance or 20% change that he will choose a nonfiction book. PLease mark as helpful if it is! thanks

Answer:

B

Step-by-step explanation:

5•x=5x

5• (-5)=-25

5x-25 and 5(x-5) are equivalent

Answer:

awnsrer is b 5(x-5) and 5x - 25

The angle measure that belongs in the green box is given as follows:

70.67º.

We consider a triangle with side lengths and angles related as follows, as is the case for this problem:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(x)/12  = sin(76º)/12.34

Applying cross multiplication, the missing angle measure is given as follows:

sin(x) = 12 x sine of 76 degrees/12.34

sin(x) = 0.9436.

x = arcsin(0.9436)

x = 70.67º.

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Answer:

0.75 g ≤ 35

Step-by-step explanation:

if each games costs $0.75, then the answer of g will be given by 35/0.75.

he can go up to exactly $35 but not over

so, the inequality is given by 0.75 g ≤ 35

Answer:

800 books

problem solving steps：

adults:60%

young people:5%

children=100%-60%-5%

=35%

35%=280 books

1%=280÷35

=8

100%=800

so,there are 800 books

The solution to the problems are;

1.  Area = 108 square feet

2. Area = 342 square feet

3. x = $1, 890, x = $1764

4. Cost, x = $151. 2, $117. 6

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that;

From the diagram shown, we have that;

The deck is gray

The garden is white

1. The area of the garden in design A

Area = 9(12) = 108 square feet

2. The area of the deck in design A is;

Area = 18(25) = 450 square feet

The area of the deck without the garden = 450 - 108

Area = 342 square feet

3. If $4. 20 = 1 square feet in design A

Then, x = 450 square feet

x = $1, 890

Area of deck of design B = 21(20) = 420 square feet

cost = $1764

4. If $1. 40 = 1 square feet of garden A

Then, x = 108 square feet

Cost = $151. 2

For garden of design B

Area = 1/2 × (12)(14) = 84 square feet

Then, cost = $117. 6

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Answer: +3

Step-by-step explanation:

5 + (-2) ( + × - = - )  ∴ 5 - 2 = 3

Answer:  26 and 1/4

Step-by-step explanation:

Using the Factor Theorem, it is found that the statements that could describe all zeros of F are:

\(f(x) = a(x - x_1)^{n_1}(x - x_2)^{n_2} \cdots (x - x_n)^{n_n}\)

In this problem:

Then, the correct statements are:

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Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

To write a quadratic function to represent the height h of the acrobat t seconds after the jump, we can use the following formula:

\(h(t) = -16t^2 + vt + h0\)

Where h0 is the initial height of the acrobat, which is 25 feet, and v is the initial vertical velocity, which is 4 ft/s. Plugging in these values, we get:

\(h(t) = -16t^2 + 4t + 25\)

To find how long it will take for her to land safely on the net, we need to find the time at which h(t) = 5. In other words, we need to solve the equation:

\(-16t^2 + 4t + 25 = 5\)

Simplifying this equation, we get:

\(-16t^2 + 4t + 20 = 0\)

Dividing both sides by -4, we get:

\(4t^2 - t - 5 = 0\)

Now we can use the quadratic formula to solve for t:

\(t = (-b ± \sqrt(b^2 - 4ac)) / 2a\)

Where a = 4, b = -1, and c = -5. Plugging in these values, we get:

\(t = (1 ± \sqrt(1 + 4(4)(5))) / 8\)

Simplifying this equation, we get:

\(t = (1 ± 9) / 8\)

So, the two solutions are:

\(t = 1 and t = -5/4\)

Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The probability that a defective component will be detected only by the first inspector is 0.19

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

The probability that all three defective components in a batch escape detection by both inspectors is 0.

It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.

Therefore P(A)=P(B)=81%=0.81

At least one inspector does not detect a defect on 38% of all defective components.

Therefore, bar P(A∩B)=0.38

As we know:

bar P(A∩B)=1-P(A∩B)=0.38

P(A∩B)=1-0.38=0.62

A defective component will be detected only by the first inspector.

P(A∩barB)=P(A)-P(A∩B)

=0.81-0.62

P(A∩barB)=0.19

The probability that a defective component will be detected only by the first inspector is 0.19

Part (B) A defective component will be detected by exactly one of the two inspectors.

This can be written as: P(A∩barB)+P(barA∩B)

As we know:

P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)

Substitute the respective values we get:

P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)

=0.81+0.81-2(0.62)

=1.62-1.24

P(A∩ barB)+P(bar A∩B)=0.38

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

Part (C) All three defective components in a batch escape detection by both inspectors

This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)

As we know bar P(A∩B)=P(bar A∪ bar B)=0.38

From part (B): P(bar A∩B)+P(A∩bar B)=0.38

This can be written as:

P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0

The probability that all three defective components in a batch escape detection by both inspectors is 0

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Answer:

C. 15 Miles

Step-by-step explanation:

3 multiplied by 5 is 15 :)

Anna moves 100 jellybeans from bottle a to bottle b, changing the number of red jellybeans in bottle a to 80% and the number of yellow jellybeans in bottle b to 40 percentage

Let x be the number of jellybeans Anna moves from bottle a to bottle b

Original:

Bottle a: 400 jellybeans, 75% red, 25% yellow

Bottle b: 300 jellybeans, 50% red, 50% yellow

After:

Bottle a: 400 jellybeans, 80% red, 20% yellow

Bottle b: 300 + x jellybeans, 40% yellow, 60% red

Equations:

75% of 400 = 300 red jellybeans in bottle a

50% of 300 = 150 red jellybeans in bottle b

80% of 400 = 320 red jellybeans in bottle a

60% of (300 + x) = 180 red jellybeans in bottle b

320 red jellybeans in bottle a - 300 red jellybeans in bottle b = 20 red jellybeans

180 red jellybeans in bottle b - 150 red jellybeans in bottle b = 30 red jellybeans

20 red jellybeans in bottle a = 30 red jellybeans in bottle b

x = 100 jellybeans

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Answer:

Is the question 'Rewrite 3^-7 using a fraction'

If yes, Then

It can be written as 1/3^7

THIS IS DONE BY USING  A LAW i.e., a^-1=1/a^1