A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.(b) If the water is rising at a rate of 3/8 inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough. ft3/min

Answer:

R ≈ 3.97 %

Step-by-step explanation:

The value of  g(x) is  [tex]\frac{x^{2} }{3x-1}[/tex] of a function f(x)=3x-1 and (f∘g)(x)=[tex]x^{2}[/tex] .

As the composite equation is  [tex]f(X)=3x^{}-1[/tex]

[tex](FOG)= x^{2}[/tex]

As  [tex](FOG) =f(gx^{})\\[/tex]  

∴  [tex]3x-1(gx)=x^{2}[/tex]

⇒  [tex]gx=\frac{x^{2} }{3x-1}[/tex]

(fog)(x) = f(g(x)) is pronounced "f of g of x" or "f constructed with g of x." Keep in mind that the letters in each expression for the composition remain in the same order.

A composite function is a fog. G(x) function is in f(x) function if (fog) is true. (Gof) indicates that f(x) function is in g(x) function.

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Answer:

10 cups

I hope this helps, have a great day/night!

The cost of each bottle of juice is $0.51.

The tape diagram can be used to illustrate the relationship between the numbers that are given.

Let the cost of each bottle of juice be x.

In this case, she bought a bag of oranges for $2.19 and a 12-pack of juice bottles and the total cost before tax was $8.31.

This will be:.

2.19 + 12x = 8.31

Collect like terms

12x = 8.31 - 2.19

12x = 6.12

Divide

x = 6.12 / 12

x = 0.51

The cost is solved. Note that the tape diagrams weren't given but the.coat is solved accordingly.

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-11 degrees is the expected daytime temperature for today

The daytime temperature yesterday in Montana = -4.5 degrees

Expected temperature drop today = 6.5 degrees

The term "temperature" describes how hot or cold the atmosphere is and is measured with a thermometer. Temperature is reported by meteorologists in both Celsius (C) and Fahrenheit (F).

Today's expected daytime temperature:

The daytime temperature yesterday in Montana + Expected temperature drop today

But since the temperature of yesterday is negative we will use a negative sign to add the expected temperature of today. A drop in temperature will lead to a more cold temperature

= -4.5 + (-6.5)

= -11 degrees

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The temperature at 7 P.M is 32 °F.

Fahrenheit temperature scale, scale based on 32° for the freezing point of water and 212° for the boiling point of water, the interval between the two being divided into 180 equal parts.

Given that,

Temperature at noon = 45 °F

At 7 A.M. the temperature was 17°F colder = 45-17

                                                                      = 28 °F

The temperature at 7 P.M. Was 4°F warmer than at 7 A.M

= At 7 A.M. the temperature was 17°F colder +  4°F

= 28+4

= 32 4°F

Hence, The temperature at 7 P.M is 32 °F.

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At (9, 0), the graph of the equation y = - 2/3 x + 6 intersect the x - axis.

How to create linear equation using two variables?
If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalizes the two sides of the equation. A specific point on the graph represents the solution of a linear equation in two variables, ax + by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b. Basically, there are infinitely many solutions to a linear equation with two variables.
The linear equations can be solved using substitution method.

Given, the equation of the graph is : y = (-2/3) x + 6 -(i)
Also, the equation of x-axis is: y = 0 -(ii)
Substituting (ii) in (i), we get,
0 = (-2/3)x + 6 ⇒ (-2/3)x = -6 ⇒ (2/3)x = 6 ⇒ x = 9
Thus, the point where the graph of the equation y = - 2/3 x + 6 intersect the x - axis is (9, 0).

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Answer:

U = -1

Step-by-step explanation:

Answer:

u=-1

Step-by-step explanation:

-3 + 2u + 6 = -8u - 7

2u-3+6=-8u-7

2u+3=-8u-7

we will collect like terms

2u+8u=-7-3

10u=-10

u=-1

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The statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) is the graph of f(x) translated 7 units right.

The graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them.

According to the question we have

g(x)=f(x−7).

Given that f(x) then f(x + a) represents a horizontal translation of f(x).

If a > 0 then shift units left

If a < 0 then shift units right

Therefore, f(x - 7) represents a shift right of 7 units.

Hence, The statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) is the graph of f(x) translated 7 units right.

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The probability that the sample mean would be greater than 101.5 gallons

P(x>101.5)=0.9382

This is further explained below.

Generally, From this population, a sample with the size n=38 is taken and analyzed.

Let's say that x is the sample's mean value.

It may be concluded that the sample distribution of the x-bar is about normal with

Mean =103

Standard deviation=0.9733

Now, the expression for the probability looked for is P(x>101.5)

[tex]=&\mathrm{P}\left[\left(\bar{x}-\mu_{\bar{x}}\right) / \sigma_{\bar{x}} > \left(101.5-\mu_{\bar{x}}\right) / \sigma_{\bar{x}}\right][/tex]

Where

P=Probabilty

x=mean

[tex]\mu[/tex] is population mean

[tex]\sigma[/tex]= Standard deviation

[tex]\\&=\mathrm{P}\left[\left(\bar{x}-\mu_{\bar{x})} / \sigma_{\bar{x}} > (101.5-103) / 0.97332852678\right]\right.\end{aligned}[/tex]

= P[Z > -1.54]

P(x>101.5)=0.9382

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Answer:

x = 7

Step-by-step explanation:

(10x - 2) and (9x + 5) are corresponding angles and are congruent , then

10x - 2 = 9x + 5 ( subtract 9x from both sides )

x - 2 = 5 ( add 2 to both sides )

x = 7

Part A:

Add all the values:

Convert the oz into pounds:

1oz = 16 pounds

Divide each value by 16:

55 oz = 55/16 = 0.3125 pounds

11 oz = 11/16= 0.6875 pounds

14 oz = 14/16 = 0.875 pounds

1 pound = 1 lb

3 3/4lb= 3.75 lb

2 1/4 = 2.25 lb

2lb

Now add:

Total weight = 3.75 + 0.3125+ 2.25+0.6875+0.875 = 7.875 lb

Answer:

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

5+5=10

Answer:

15

Step-by-step explanation:

There are 18 combinations that Lisa can wear by shuffling skirts, sweaters, and blouses together.

Given,

Number of skirts = 3

Number of sweaters = 2

Number of Blouse = 3

By using permutation and combination formula nCr = n! ÷ (r! (n-r)!),

3C1 × 2C1 × 3C1

= (3!) ÷ ((3-1)! × 1!) × (2!) ÷ ((2-1)! × 1!) × (3!) ÷ ((3-1)! × 1!)

= (3!) ÷ ((2)! × 1!) × (2!) ÷ ((1)! × 1!) × (3!) ÷ ((2)! × 1!)

= ((3 × 2 × 1) ÷ (2 × 1 × 1)) × ((2 × 1) ÷ (2 × 1 × 1)) × ((3 × 2 × 1) ÷ (2 × 1 × 1))

= (6 ÷ 2) × (2 ÷ 1) × (6 ÷ 2)

= 3 × 3 × 2

= 18

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Answer:

Product: 2091

Estimate: 2100

Step-by-step explanation:

Estimate 697 as 700

700 x 3 = 2100

Find Product

697 x 3 = 2091

4

1) Examining that graph, we can see that this is a decreasing function, due to the line direction. And that the initial value is the y-intercept.

2) Hence, the initial value is 4. Notice that all values after that goes decreasing for y.

[tex] a \times - b - c \\ =(5) \times - ( - 9) - ( - 32) \\ = 5 \times 9 + 32 \\ = 45 + 32 \\ = 77[/tex]

ATTACHED IS THE SOLUTION

Answer:

-77

Step-by-step explanation:

we replace a=5, b=-9, c=-32

5 * -9 - 32

-45 - 32

- 77

Answer:

Your answer is [tex]\frac{1}{864}[/tex]

Step-by-step explanation:

[tex]4^{-1}[/tex] ÷ [tex]6^{3}[/tex] [tex]= 0.0011574074[/tex] or [tex]\frac{1}{864}[/tex]

The number of minutes it takes for the earth to travel one full rotation around the sun is 529, 960

A proportion can simply be described as an equation in which varying elements, or given numbers are set equal to each other.

It is seen as  a mathematical method of comparing two elements or numbers.

It is also defined as a relation that entails comparison on the basis of size or magnitude of numbers, quantities or elements.

From the information given, we have that;

The earth travels for 365. 25 days round the sun.

If 24 × 60 minutes = 1 day

Then x minutes = 365. 25 days

cross multiply, we have;

x = 24 × 60 × 365. 25

Multiply the values

x = 529, 960 minutes

Hence, the value is 529, 960 minutes

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Let X represent the number of defects.

When n=20 and p = 0.01,

Likelihood = P(Acceptance) = P(X=0) + P(X=1)

= 20C0 * (0.01)^0 * (1-0.01)^(20) + 20C1 * (0.01)^1 * (1-0.01)^(20-1) = 0.9831

When n=20 and p = 0.02,

Likelihood = P(Acceptance) = P(X=0) + P(X=1)

= 20C0 * (0.02)^0 * (1-0.02)^(20) + 20C1 * (0.02)^1 * (1-0.02)^(20-1) = 0.9401

When n=20 and p = 0.05,

Likelihood = P(Acceptance) = P(X=0) + P(X=1)

= 20C0 * (0.05)^0 * (1-0.05)^(20) + 20C1 * (0.05)^1 * (1-0.05)^(20-1) = 0.7358

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The equation which is best representing the height above ground, y, of the model rocket and x seconds after it reaches the maximum height is 75x + y = 2000.

The height above ground, y, of the model rocket, x seconds after it reaches its maximum height can be represent by a linear equation,

The maximum height is 2000 feet, after this the rocket starts to descend with a rate of 75 feet per second.

Let us say that when the rocket starts descending, our time is started from zero,

So, on plotting these points of graph, we can one point, (0,2000).

The rate of descend is the slope m of the graph,

m = -75 ft/s

We are taking it negative because height is decreasing with time,

We can use the point slope form of equation of line,

It says, if a line passes through (a,b) and has slope m. Then the equation of line is,

(y-b) = m(x-a)

So, our line is passing through (0,2000) and has slope -75 ft/s.

So, equation of the line is,

(y-2000) = -75(x-0)

75x + y = 2000.

This above equation of line is representing the relation between the height above ground and time of the model rocket.

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On selling 38 boxes daily without giving extra box will profit him one box daily

Profit: A profit occurs when you sell something. for more than it cost.  A business profit occurs when a business. makes more money than it spends.

Every purchase of 30 boxes gets 1 extra Free box. Rizky Sejahtera Bersama shop sells to its regular Warung Rp 38.000,-/box (without giving extra)

On selling 38 boxes daily without giving extra box will profit him one box daily

for two days if we add 38+38=76 boxes which profit him 2 boxes

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The percent recovery of benzoic acid is equal to 80.0 if the mass of purified benzoic acid after recrystallization is 1.611 g.

The percent recovery can be described as the amount of a product available after its production and purification.

The percent recovery of benzoic acid can be calculated by using the following formula:

percent recovery of sample = (Mass of purified sample ÷ Mass of contaminated sample) × 100

Substituting the given values of contaminated and purified benzoic acid in this equation;

percent recovery = (1.611 ÷ 2.014) × 100

percent recovery = 0.7999 × 100

percent recovery = 79.99

Rounding it to the nearest tenth;

percent recovery = 80.0

Hence the percent recovery of benzoic acid is calculated to be 80.0

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Answer: 1.5923926292577

Step-by-step explanation: Count, N: 14

Sum, Σx: 49

Mean, μ: 3.5

Variance, σ2:  2.5357142857143

Steps

σ2 =  

Σ(xi - μ)2

N

=  

(1 - 3.5)2 + ... + (6 - 3.5)2

14

=  

35.5

14

=  2.5357142857143

σ =  √2.5357142857143

=  1.5923926292577