A can of soup is a cylinder with diameter 7 cm.

The can is 10 cm high

The can is full of soup

soup

The soup is poured into a saucepan.

The saucepan is a cylinder with diameter 12 cm.

Work out the depth of the soup in the saucepan.

Give your answer correct to 1 decimal place.

Answer:

Answer:

Raff = 38

Suzie = 19

Step-by-step explanation:

Raff gets 2x

Suzie gets x

2x + x = 57 dollars

3x = 57 dollars

x = 19 dollars

2x = 38 dollars

Answer:

Many test takers have found the Reading and English section to be moderately difficult. However, many TEAS takers vouch that the Science and Math section are more complex and challenging. The timed nature of the exam can be difficult for some.

Step-by-step explanation:

Therefore, the possible values for x are 1, 4, and 5.

First, let's use long division to factor the polynomial 3x³-16x²+31x-20, which represents the area of the trapezoidal desktop, by x²-5x+x-5:

           ____________________________

\(x^{2} -5x+x-5 | 3x^{3} - 16x^{2} + 31x - 20\)

\(- (3x^{3} - 15x^{2} + 3x^{2} - 15x)\)

           ____________________________

                  \(- x^{2} + 31x - 20\)

                    \(-(- x^{2} + 5x - 5)\)

                     ________________

                          \(26x - 15\)

The result of the long division is x - 5 with a remainder of 26x - 15.

Therefore, we can rewrite the polynomial as:

\(3x^{3} - 16x^{2} + 31x - 20 = (x - 5)(x^{2} - 5x + 4) + (26x - 15)\)

Now, let's use the formula for the area of a trapezoid to set up an equation using the polynomial above:

\(area = 1/2h(b_1 + b_2)\)

We know that the bases of the trapezoid are represented by the expressions x + 5 and x² - 5x, so we can substitute them in the formula:

\(3x^{3} - 16x^{2} + 31x - 20 = 1/2h((x + 5) + (x^{2} - 5x))\)

Simplifying the expression:

\(3x^{3} - 16x^{2} + 31x - 20 = 1/2h(x^{2} - 4x + 5)\)

Multiplying both sides by 2:

\(6x^{3} - 32x^{2} + 62x - 40 = h(x^{2} - 4x + 5)\)

Now, we can substitute the remainder of the long division we did earlier (26x - 15) for h:

\(6x^{3} - 32x^{2} + 62x - 40 = (x - 5)(x^{2} - 5x + 4) + (26x - 15)\)

\(6x^{3} - 32x^{2} + 62x - 40 = (x - 5)(x^{2} - 5x + 4) + h\)

\(6x^3 - 32x^2+ 62x - 40 = (x - 5)(x^2 - 5x + 4) + (26x - 15)\)

Simplifying the expression again:

\(6x^3 - 32x^2 + 36x - 25 = (x - 5)(x^2 - 5x + 4)\)

Now we have a quadratic equation that we can solve for x:

\(x^3 - 5x^2 + 4x + 5x^2 - 25x + 20 = 0\)

\(x^3 - 21x + 20 = 0\)

\((x - 1)(x - 4)(x - 5) = 0\)

Therefore, the possible values for x are 1, 4, and 5.

Now we can substitute these values in the expression we derived for h:

\(h = (6x^3 - 32x^2 + 62x - 40)/(x^2 - 4x + 5)\)

For x = 1:

\(h = (6(1)^3 - 32(1)^2 + 62(1) - 40)/2\\h = 6-32+62-40/2\\h = 68-72/2\\h = -4/2\\ h= -2\)

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Answer:

2+4a

Step-by-step explanation:

Answer:

where's the picture. to the nearest mile...

Step-by-step explanation:

;-;

The radius of the circle with equation x² +y² =1 is 1.

The radius of a circle is the separation between any two points on its circumference. R or r is typically used to indicate it. This amount is significant in practically all formulas involving circles. A circle's radius can also be used to calculate its surface area and circumference.

To see this, we can rewrite the equation in the standard form for the equation of a circle: (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.

In this case, we have:

x² + y² = 1

This can be rewritten as:

(x-0)² + (y-0)² = 1

Thus, the radius of the circle is 1.

The complete question is;-

What is the radius of the circle with the equation x² +y²= 1?

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Step-by-step explanation:

\(1 + 5a + 7a^{2}+a+3\\\)

so you have \(7a^{2}\)

5a + a = 6 a

and 1 + 3 = 4

Answer: \(7a^{2} + 6a + 4\)

Answer:

7a² + 6a + 4

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 1 + 5a + 7a² + a + 3

Let's simplify the expression,

→ 1 + 5a + 7a² + a + 3

→ 7a² + 5a + a + 1 + 3

→ (7a²) + (5a + a) + (1 + 3)

→ 7a² + (6a) + (4)

→ 7a² + 6a + 4

Hence, answer is 7a² + 6a + 4.

The snail will take approximately 0.43 hours or 25.8 minutes to travel 12 feet at the speed of 8.5 meters per hour.

Given, A snail moves at a speed of 8.5 meters per hour, 1m = 3.28ft. Let's convert meters per hour into feet per hour by multiplying it with 3.28ft/m. So, 8.5 meters per hour = 8.5 × 3.28 feet per hour ≈ 27.88 feet per hour.

Now, to calculate the time taken by a snail to travel 12 feet, we can use the formula: Time = Distance ÷ Speed

Time taken = 12 feet ÷ 27.88 feet per hour ≈ 0.43 hours (rounded to two decimal places)

Now, let's convert 0.43 hours to minutes by multiplying it with 60 minutes per hour: 0.43 hours × 60 minutes per hour ≈ 25.8 minutes (rounded to one decimal place). Therefore, it will take approximately 0.43 hours or 25.8 minutes for the snail to travel 12 feet at the speed of 8.5 meters per hour.

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The value of dx/dt = 16/3 when x = 2.

To solve this problem, we will need to use implicit differentiation. We start by differentiating both sides of the equation xy = 3 with respect to time t:

d/dt (xy) = d/dt (3)

Using the product rule for differentiation, we can rewrite the left-hand side as:

x (dy/dt) + y (dx/dt) = 0

Substituting the given value of dy/dt = -4 and the given value of xy = 3, we get:

x (-4) + y (dx/dt) = 0

Simplifying this expression, we get:

-4x + y (dx/dt) = 0

Now we can solve for dx/dt by plugging in the given value of x = 2 and solving for y:

xy = 3

2y = 3

y = 3/2

Substituting y = 3/2 and x = 2, we get:

-4(2) + (3/2) (dx/dt) = 0

Simplifying this expression, we get:

-8 + (3/2) (dx/dt) = 0

Multiplying both sides by 2/3, we get:

-16/3 + dx/dt = 0

Therefore, we have:

dx/dt = 16/3

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Answer:

He would have received $33 if he exchanged 22 dinars

Step-by-step explanation:

Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

The terms adjacent, neighboring, contiguous, and juxtaposed all denote being close by. Although adjacent might indicate a touch or not, it is usually assumed that there is nothing of the same sort in between. a home with a garage close by. Adjoining clearly means coming together and touching at a certain location or line.

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to a stop. When adjacent angles have the same vertex and side, they might be a complimentary angle or supplemental angle.

Thus, adjacent angles are two angles that lie in the same plane and have a common vertex and a common side but have no common interior points.

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1- True: Linear programming can be used to identify the critical path for a PERT network.

2- False: The probabilistic approach characterized by PERT does not use median activity times.

3- False: The critical path is the sequential path of activities from the first to the last, defined by activities with zero slack.

4- False: Linear programming can be used for both profit and nonprofit organizations.

Linear programming can indeed be used to identify the critical path for a PERT network. The critical path represents the sequential path of activities from the first activity to the last, and it is defined by activities with zero slack. By analyzing the dependencies and constraints between activities, linear programming techniques can be applied to determine the optimal schedule and identify the critical path.

The probabilistic approach characterised by PERT does not use median activity times. Instead, it utilises three time estimates for each activity: optimistic, most likely, and pessimistic activity times. These estimates are used to calculate the expected duration and variability of the project.

Regarding the statement about linear programming and profit optimization, it is incorrect to say that linear programming cannot be used for nonprofit organizations. Linear programming can be applied to various optimisation problems, including those related to resource allocation, cost minimisation, and efficiency improvement, which are relevant to both for-profit and nonprofit organisations.

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Answer:

C. five samples.

Step-by-step explanation:

To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first plot the curve on a polar graph.

From the graph, we can see that the curve has two loops - one larger loop and one smaller loop. The larger loop encloses the smaller loop.

To find the area inside the larger loop and outside the smaller loop, we can use the formula:

Area = 1/2 ∫[a,b] (r2 - r1)2 dθ

where r2 is the equation of the outer curve (larger loop) and r1 is the equation of the inner curve (smaller loop).

The limits of integration a and b can be found by setting the angle θ such that the curve intersects itself at the x-axis. From the graph, we can see that this occurs at θ = π/2 and θ = 3π/2.

Plugging in the equations for r1 and r2, we get:

r1 = 1/2 + cos(θ)
r2 = 1/2 - cos(θ)

So the area inside the larger loop and outside the smaller loop is:

Area = 1/2 ∫[π/2, 3π/2] ((1/2 - cos(θ))2 - (1/2 + cos(θ))2) dθ

Simplifying and evaluating the integral, we get:

Area = 3π/2 - 3/2 ≈ 1.07

Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is approximately 1.07. Note that this area is smaller than the total area enclosed by the curve, since it excludes the area inside the smaller loop.
To find the area inside the larger loop and outside the smaller loop of the limaçon given by the polar equation r = 1 + 2cos(θ), follow these steps:

1. Find the points where the loops intersect by setting r = 0:
1 + 2cos(θ) = 0
2cos(θ) = -1
cos(θ) = -1/2
θ = 2π/3, 4π/3

2. Integrate the area inside the larger loop:
Larger loop area = 1/2 * ∫[r^2 dθ] from 0 to 2π
Larger loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 0 to 2π

3. Integrate the area inside the smaller loop:
Smaller loop area = 1/2 * ∫[r^2 dθ] from 2π/3 to 4π/3
Smaller loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 2π/3 to 4π/3

4. Subtract the smaller loop area from the larger loop area:
Desired area = Larger loop area - Smaller loop area

After evaluating the integrals and performing the subtraction, you will find the area inside the larger loop and outside the smaller loop of the given limaçon.

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The slope of the line is  m = 14 / 17

The line representing  "rise" and " run" is given below

The vertical distance is said to be "rise" and from the graph it is equal to 14.

The horizontal distance is said to be "run" and from the graph it is equal to 17 .

According to the slope formula , we get

     m = 14 / 17

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We can infer here that in order to fairly distribute the remaining water to the residents of the state, a distribution channel/strategy will be needed to properly distribute the same volume of water to each resident. Therefore, I will collaborate with local officials to create a distribution strategy for fair distribution.

Lake Mead is actually known to be reservoir that is located in Nevada and Arizona. It is actually known as the largest reservoir in the US when it comes to water capacity. This reservoir actually serves the states of Nevada, Arizona and California. Some part of Mexico also benefit from it.

The Lake Mead reservoir is said to sustain about 20 million people and also serves large areas of farmlands.

To fairly distribute the remaining water to residents, a distribution strategy must be applied.

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1.46% probability that fewer than 700 children received their vaccine.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

95% of children have received their DTaP vaccine p = 0.95

Sample of 750, n = 750

For the approximation, the mean and the standard deviation are given by:

u = np = 750×0.95 = 712.5

σ = \(\sqrt{np(1-p)}\)

σ = \(\sqrt{750(0.95)(0.05)}\)

σ = 5.97

Using continuity correction, the probability that fewer than 700 children received their vaccine is P(X < 700 - 0.5) = P(X < 699.5), which is the p-value of Z when X = 669.5.

Z = X-u/σ

Z = 669.5 - 712.5/5.97

Z = - 2.18

The p-value of Z = - 2.18 is 0.0146.

Hence, 1.46% probability that fewer than 700 children received their vaccine.

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-( ( 7 - u )( u - 2 ) ) is the factorized form of the polynomial -7u² + 12u + 4, using the AC method.

Given the polynomial in the question;

-7u² + 12u + 4

Factor out -1 out of the polynomial

-1( 7u² - 12u - 4 )

Compare to the form ax² + bx + c

To factor, compare to the form ax² + bx + c and rewrite the middle term as a sum of two terms whose product is;

a × c = 7 × -4 = -28

and whose sum is;

b = -12

Now, factor -12 out of -12x

-1( 7u² - 12(u) - 4 )

We know that -13 is the same as 2 plus -14

-1( 7u² - ( 2 - 14 )u - 4 )

Apply distributive property

-1( 7u² - 2u - 14u - 4 )

Group the terms

-1( u(7u - 2) - 2(7u - 2 ) )

-1( (7-u)(u-2) )

-( (7-u)(u-2) )

Therefore, the factorized form of the polynomial is -( ( 7 - u )( u - 2 ) ).

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-(7u+2)(u-2) is the factorized form of expression -7u²+12u+4.

An expression is combination of variables, numbers and operators.

The given expression is -7u²+12u+4.

We need to find the factors of this expression.

-7u²+12u+4.

This can be written as

-7u^2+14u-2u+4.

Take 7u from first two terms and 2 from last two terms in the expression.

-7u(u-2)-2(u-2)

(-7u-2)(u-2)

-(7u+2)(u-2)

Hence -(7u+2)(u-2) is the factorized form of -7u^2+12u+4.

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Answer

d

Step-by-step explanation:

Answer:

1000 km^3

Step-by-step explanation:

1 km=1000m

1 cubic kilometer is equivalent to 1,000,000,000 cubic meters, due to cubing the conversion factor of 1,000 (meters per kilometer).

1 cubic kilometer is equivalent to 1,000,000,000 (one billion) cubic meters. When converting units, you need to remember the relationships between those units. In this case, 1 kilometer is equivalent to 1000 meters. Therefore, to convert from cubic kilometers to cubic meters, you need to cube the conversion factor (1000 meters/kilometer). Hence, 1 cubic kilometer = 1,000^3 cubic meters = 1,000,000,000 cubic meters.

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The statement that best describes "willing suspension of disbelief" is: A dynamic in which the audience agrees to accept the fictional world of the play on an imaginative level while knowing it to be untrue.

The concept of "willing suspension of disbelief" is an essential element in experiencing and appreciating works of fiction, particularly in theater, literature, and film. It refers to the voluntary act of temporarily setting aside one's skepticism or disbelief in order to engage with the fictional narrative or performance. It involves consciously accepting the imaginative world presented by the creator, even though it may contain unrealistic or fantastical elements. By willingly suspending disbelief, the audience allows themselves to become emotionally invested in the story and characters, making the experience more enjoyable and meaningful. This dynamic acknowledges the inherent fictional nature of the work while acknowledging that the audience is aware of its fictional status. It creates a mutual understanding between the audience and the creators, enabling the audience to fully immerse themselves in the narrative and connect with the intended emotions and themes of the work.

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When B is the circumcenter of  triangle ADG the lengths of AE and DG are 4 and 12 respectively

The intersection of the perpendicular bisectors of a triangle's sides is known as the circumcenter of that particular triangle.

In other terms, the circumcenter is the point at which the bisector of a triangle's sides coincides.

The perpendicular lines radiating from the sides of the triangle are the bisectors hence the line it radiates from shares the is shared into two halves at that point

Having this in mind

AE = DE = 4

and

DF = GF = 6

Also, DF + GF = DG

DG = DF + DF

DG = 6 + 6

DG = 12

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The equation of the line shown is y = 4 x

A straight line is the shortest distance between two points. the equation of straight line is represented as \(y = mx + c\)

m is the gradient

y2, y1, x2, x1 are gotten from the graph

\(m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

\(m = \frac{8 - 4}{2 - 1}\)

\(m = \frac{4}{1}\)

m = 4

c is the intercept on x-axis

from the graph c = 0

substituting the values give:

y = 4 x

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Answer:

infinite many solutions

Step-by-step explanation:

As L.H.S = R.H.S, there are infinite many solutions

\(\\ \rm\Rrightarrow 5(2b+1)=10b+5\)

\(\\ \rm\Rrightarrow 10b+5=10b+5\)

\(\\ \rm\Rrightarrow 0=0\)

Answer:

x = -3

Step-by-step explanation:

Answer:

x= -11

Step-by-step explanation:

you multiple 4 times the things in the parentheses and solve for x

Answer:

[D] \(\displaystyle \lim_{h \to 0} \frac{[5(x + h)^2 - 2(x + h)] - (5x^2 - 2x)}{h}\)

General Formulas and Concepts:

Calculus

Limits

Derivatives

Definition of a Derivative: \(\displaystyle f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\)

Step-by-step explanation:

Step 1: Define

Identify

\(\displaystyle f(x) = 5x^2 - 2x\)

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e