Greta offers to buy a team photo for 15 of her teammates, but 6 of them don't want one. If a team photo costs $2, how much will Greta spend on her teammates? Choose the correct expression and solution to this problem .

The equation of the tangent line to the curve y = 16x sin(x) at the point (π/2, 8π) is y = 16x.

To find the equation of the tangent line to the curve y = 16x sin(x) at the point (π/2, 8π), we need to determine the slope of the tangent line and use the point-slope form of a linear equation.

The slope of the tangent line at a specific point on a curve can be found by taking the derivative of the function at that point.

Given y = 16x sin(x), let's find its derivative:

dy/dx = d/dx (16x sin(x))

      = 16 (sin(x) + x cos(x))

To find the slope of the tangent line at (π/2, 8π), substitute x = π/2 into the derivative:

dy/dx = 16 (sin(π/2) + (π/2) cos(π/2))

      = 16 (1 + (π/2) * 0)

      = 16

Therefore, the slope of the tangent line at (π/2, 8π) is 16.

Now, using the point-slope form of a linear equation, we can write the equation of the tangent line:

y - y₁ = m(x - x₁),

where (x₁, y₁) is the point (π/2, 8π), and m is the slope of the tangent line.

Substituting the values, we have:

y - 8π = 16(x - π/2).

Simplifying:

y - 8π = 16x - 8π.

Rearranging the terms, we get the equation of the tangent line:

y = 16x.

Therefore, the equation of the tangent line to the curve y = 16x sin(x) at the point (π/2, 8π) is y = 16x.

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Answer:

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Answer:

Step-by-step explanation:

D

On average, Madrid has a higher monthly temperature. Its monthly

temperatures also vary more. The correct option is D.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It offers us a sense of how variable a dataset is.

It is given that weather researchers compared Dublin, Ireland, to Madrid, Spain. She found data about their average monthly temperatures.

Mean:  Dublin      Madrid

            56.1°F      68.0°F

Mean average deviation:

Dublin      Madrid

6.4°F         12.1°F

From the given table it is observed that the mean temperature of Madrid is higher than the mean temperature of Dublin.

Similarly, the mean average deviation for Madrid is higher than the mean average deviation of Dublin.

Therefore, the correct option is D.

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The expression 6x - x + 5 as 6 + 5 are not equivalent expression because one of the expression contain a variable while the other doesn't.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expression:

Expression = 6x - x + 5

Expression = 5x + 5

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A.  This expression gives: AC = -38 + 150/Q

B.  The manufacturer receives a maximum weekly profit of £594.50 when it produces 12.25 units per week.

C. The profit function is maximized at this point, since it is increasing for smaller values of Q and decreasing for larger values of Q.

a) The total cost (TC) function is given by the sum of fixed costs and variable costs:

TC = FC + VC

where FC is the weekly fixed cost of £150 and VC is the weekly variable cost per unit, which is given by VC = 2Q - 40. Substituting this expression into the TC function gives:

TC = 150 + 2Q - 40Q

Simplifying this expression gives:

TC = -38Q + 150

The average cost (AC) function is given by the total cost divided by the quantity:

AC = TC/Q

Substituting the expression for TC gives:

AC = (-38Q + 150)/Q

Simplifying this expression gives:

AC = -38 + 150/Q

b) The profit function (π) is given by the difference between revenue and cost:

π = TR - TC

where TR is the total revenue, which is equal to price times quantity, or PQ. Substituting the demand function P = 60 - 4Q gives:

TR = PQ = (60 - 4Q)Q = 60Q - 4Q^2

Substituting the expression for TC gives:

π = TR - TC = (60Q - 4Q^2) - (-38Q + 150)

Simplifying this expression gives:

π = -4Q^2 + 98Q - 150

To find the profit-maximizing level of output, we take the derivative of the profit function with respect to Q and set it equal to zero:

dπ/dQ = -8Q + 98 = 0

Solving for Q gives:

Q = 12.25

To check that this is a maximum, we take the second derivative:

d²π/dQ² = -8 < 0

Since the second derivative is negative, we know that Q = 12.25 is a maximum.

Substituting this value of Q into the profit function gives:

π = -4(12.25)^2 + 98(12.25) - 150 = £594.50

Therefore, the manufacturer receives a maximum weekly profit of £594.50 when it produces 12.25 units per week.

c) At the profit-maximizing level of output, the marginal revenue (MR) is equal to the marginal cost (MC). The marginal cost function is given by the derivative of the total cost function:

MC = dTC/dQ = -38

The marginal revenue function is given by the derivative of the demand function:

MR = dTR/dQ = 60 - 8Q

At the profit-maximizing level of output Q = 12.25, we have:

MC = -38

MR = 60 - 8(12.25) = -1

Since MR < MC, the profit function is decreasing at this point and the maximum profit has been achieved. This can be seen in the graph as the profit function peaks at Q = 12.25 and decreases for larger or smaller values of Q.

Here is a sketch of the relationship between the marginal cost (MC), the marginal revenue (MR), and the profit function at the profit-maximizing level of Q:

     |

MR     |

/\    /  

/  _/     _

/              

-------------------> Q

MC

The vertical line indicates the profit-maximizing level of output, where MR = MC. The profit function is maximized at this point, since it is increasing for smaller values of Q and decreasing for larger values of Q.

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Answer:45.3592 kg

Step-by-step explanation:

The United States uses the cental of 100 pounds (45.36 kg), which is equal to 45.3592 kilograms.

A pound is defined as 16 ounces, 7,000 grains (or 0.45359237 kg) of avoirdupois weight and 12 ounces, 5,760 grains (or 0.37324171216 kg) of troy and apothecaries' weight. The initials "lb" come from the Latin word "libra," which was the Roman equivalent of the current "pound."

In ancient Rome, the term "libra" was used to refer to a balance or scales as well as a unit of measurement called "libra pondo," which can be rendered as "pound weight" or "a pound by weight." The measurement's "pondo" component is the source of the English term "pound," whereas the "libra" component is the orgin behind.

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The remote interior angles are (180 - 5) / 2 = 87.5 degrees each.

so option D and E are correct.

An interior angles is described as the inner of the two angles formed where two sides of a polygon come together.

In a triangle, the sum of the interior angles is 180 degrees.

so if angle 5 is an interior angle, then the two remote interior angles must add up to 180 degrees minus the measure of angle 5.

Then angle 5 is equal to x degrees, then the remote interior angles are (180 - x) / 2 degrees each.

Because  we are  looking for the remote interior angles of angle 5, we can set x = 5, so the remote interior angles are (180 - 5) / 2 = 87.5 degrees each.

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Answer:

2y +3x

Step-by-step explanation:

sjsjdjdsndnjssje

Answer:

23 poudsfgghhhhhhhxcvbnmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

Answer:

value/total value • 100 = percentage

Step-by-step explanation:

if 5 out 100 kids have red backpacks then 5% of kids have red backpacks

5/100 • 100 = percentage

0.05 • 100 = percentage

5% = percentage

if 13 cars out of 41 have flat tires, then 32% of the cars have flat tires

13/41 • 100 = percentage

0.31707317073... • 100 = 31.707317073... %

depending on your precision, you may include as many decimal places as you like, unless the question specifies it.  For our example, we will round to 2 decimal places.

31.707317073... % = 31.71%

if you're looking to find percentages for probability, you will use the same equation.

the odds of flipping a coin and it landing on heads are 50%

possibilities:

Heads, Tails

there is one outcome where our result occurs out of the two possible outcomes

1/2 • 100 = percentage

0.5 • 100 = percentage

50% = percentage

Hope this helps and wasn't confusing

To make a table of values for a linear relationship;

Choose a group of x values before creating the table. Add each x value from the left side column to the equation. Evaluate the equation (middle column) to arrive at the y value

Given,

Linear relationship;

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Here,

We have to make a table of values for a linear relationship;

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Answer:

Step-by-step explanation:

for the triangle:

1.9x8/2= 7.6mi (this is area)

perimeter=17mi

for the trapezoid:

area= 18.36+13.6=31.96yd

perimeter=24.1yd

The lengths of the diagonals are approximately 10.6 cm and 31.8 cm.

To solve this problem, we can use the formula for the area of a rhombus, which is A = (d₁ x d₂)/2, where A is the area, and d₁ and d₂ are the lengths of the diagonals.

We are given that the area of the rhombus is 168 square centimeters, so we can substitute this value into the formula:

=> 168 = (d₁ x d₂)/2.

We are also given that one diagonal is three times as long as the other, so we can express the length of one diagonal in terms of the other: d₁ = 3d₂.

Substituting this expression for d₁ into the formula for the area, we get:

168 = (3d₂xd₂)/2 336 = 3d₂²2 d₂² = 112 d₂ = √(112) = 10.6 (to the nearest tenth of a centimeter)

Using the expression for d₁ in terms of d₂, we can find the length of the other diagonal:

d₁ = 3d₂ = 3(10.6) = 31.8 (to the nearest tenth of a centimeter)

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Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

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Answer:

2*11+15=37

22+15=37

37=37

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Answer:

$74.5

Step-by-step explanation:

7(10) + 1.50(3) =

70 + 4.5 = 74.5

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

X is 3

Step-by-step explanation:

this is because you divide 3 by nine and it equal 3 therefore x equals 3

Answer:

x = 27

Step-by-step explanation:

x/3 = 9

you multiply both sides by 3 so you get the variable by its self

9 times 3 equals 27

so x = 27

hope this helps

Spherical coordinates are a system of coordinates that describe points in three-dimensional space using a distance from the origin, an angle of inclination from the positive z-axis, and an angle of rotation around the z-axis.

To calculate the triple integral of f(x, y, z)=x2 y2 over the region rho≤2 using spherical coordinates, we first need to express the function in terms of the spherical coordinates.

We know that in spherical coordinates,

x = ρ sin(φ) cos(θ)
y = ρ sin(φ) sin(θ)
z = ρ cos(φ)

where ρ is the radial distance, θ is the azimuthal angle, and φ is the polar angle.

So, f(x, y, z) = x2 y2 can be expressed as

f(ρ, φ, θ) = (ρ sin(φ) cos(θ))2 (ρ sin(φ) sin(θ))2

= ρ4 sin2(φ) cos2(θ) sin2(φ) sin2(θ)

= ρ4 sin4(φ) cos2(θ)

Now, we can set up the triple integral using spherical coordinates.

∫∫∫ f(ρ, φ, θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 f(ρ, φ, θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 ρ4 sin4(φ) cos2(θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 ρ6 sin5(φ) cos2(θ) dρ dφ dθ

= ∫0^2π ∫0^π/2 [ρ7/7 sin5(φ) cos2(θ)]0^2 dφ dθ

= ∫0^2π ∫0^π/2 32/7 sin5(φ) cos2(θ) dφ dθ

= 32/7 ∫0^2π cos2(θ) dθ ∫0^π/2 sin5(φ) dφ

= 32/7 [π sin6(π/2)/6]

= 32π/21

Therefore, the triple integral of f(x, y, z) = x2 y2 over the region rho≤2 using spherical coordinates is 32π/21.

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Yes, the AP Calculus BC exam includes multiple choice questions.

The exam is divided into two sections, with Section I consisting of 45 multiple choice questions and Section II consisting of 6 free-response questions.

The multiple choice section of the exam is further divided into two parts, with Part A including 30 questions that do not allow the use of a calculator and Part B including 15 questions that do allow the use of a calculator.

Each section of the exam is weighted equally and contributes to 50% of the overall score.

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Answer:

4 movies

Step-by-step explanation:

variables:

x = number of movies watched

disney = 80 + 30x

theatres = 50x

80 + 30x = 50x

80 = 20x

x = 4

The cost would be the same amount when 4 movies are watched.

Step-by-step explanation:

j = jana's age

m = mom's age = 2.5 j

g = grandma's age = 5.25 j      summed, they equal 149 IN THREE YEARS

j+3       +     2.5j +3     +    5.25 j + 3 = 149

8.75 j  + 9 = 149

8.75 j = 140

j = 16  y/o

   mom = 2.5 j = 40 y/o

         g-ma = 5.25 j = 84 y/o

Answer:

Step-by-step explanation:

1: no

2 yes

3 no

4 yes

5 no

6 no

7 always

8 always

9 never

10 always

11 always

12 never

13 108

14 80

15 70

16 123

17 38

18 167

19 10

20 154

Therefore, to find the p-value, we need the specific value of the test statistic z and the alternative hypothesis to determine the direction of the test.

To find the p-value for a hypothesis test with the standardized test statistic z, we need to calculate the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.

The p-value is defined as the probability of obtaining a test statistic more extreme than the observed value in the direction specified by the alternative hypothesis.

To decide whether to reject the null hypothesis for a given level of significance α, we compare the p-value to the significance level α. If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.

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If the RMS value of the sinusoidal input to a full wave rectifier is Vo / (2)^(1/2) then the RMS value of the rectifier’s output is  \(Vo * (2)^(1/2) / 2.\)

Full wave rectifier length = Vo / (2)^(1/2)

The peak value of the output voltage = Vo.

For a full-wave rectifier, the outcome voltage is the whole value of the input voltage.

The RMS value of a sinusoidal waveform can be calculated using the formula:

Vrms = Vp / \((2)^(1/2)\)

Vrms = Vo / \((2)^(1/2)\)

To simplify this equation, we can multiply both the numerator and the denominator by (2)^(1/2):

\(Vrms = (Vo / (2)^(1/2)) * ((2)^(1/2)/(2)^(1/2))\)

\(Vrms = Vo * (2)^(1/2) / 2\)

Therefore, we can conclude that the RMS value of the rectifier's output is \(Vo * (2)^(1/2) / 2.\)

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Answer:

\((-\frac{1}{2},\frac{1}{5} )\), aka Option D is correct.

Hope this helps!

Answer:

Step-by-step explanation:

the answer for this is

(-1/2, 1/5]  <---

remember that it is a bracket at the end not a parenthese  

the answer is B

Answer:

0.000005871

thats just what it is cuz yeah

Answer:

Step-by-step explanation:

0.000005871

A.

a number that can be written as a fraction but not as a decimal I think

Use analytic methods,

(a) The local extrema,

1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.

2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.

(b) The intervals on which the function is increasing

Write properties of function :

Increasing interval : ( - ∞ , 0 )

(c) The intervals on which the function is decreasing

Write properties of function :

Decreasing interval : ( 0 , ∞ )

Given that,

Use analytic methods (a) the local extrema, (b) the intervals on which the function is increasing, and (c) the intervals, then the function is,

A function's growing (or decreasing) periods match the periods when its derivative is positive (or negative). As a result, we can easily determine the intervals where a function increases or decreases by taking its derivative and analyzing it to determine if it is positive or negative.

Let f be continuous on an open interval (a , b) that contains a critical x-value.

1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.

2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.

(b) The intervals on which the function is increasing

Write properties of function :

Increasing interval : ( - ∞ , 0 )

(c) The intervals on which the function is decreasing

Write properties of function :

Decreasing interval : ( 0 , ∞ )

Therefore,

Use analytic methods,

(a) The local extrema,

1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.

2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.

(b) The intervals on which the function is increasing

Write properties of function :

Increasing interval : ( - ∞ , 0 )

(c) The intervals on which the function is decreasing

Write properties of function :

Decreasing interval : ( 0 , ∞ )

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When x = 2, f(g(x)) is approximately equal to 187/9.

To solve for f(g(x)) when x = 2, we need to substitute the value of x into the function g(x) and then substitute the result into the function f(x). Let's calculate it step by step:

Step 1: Calculate g(x) when x = 2:

g(x) = x + 4/3

g(2) = 2 + 4/3

g(2) = 2 + 4/3

g(2) = 10/3

Step 2: Substitute the result from step 1 into f(x):

f(x) =\(x^2\) + 2x + 3

f(g(x)) = f(10/3)

f(g(2)) = f(10/3)

Step 3: Calculate f(g(2)):

f(10/3) = (10/3\()^2\) + 2(10/3) + 3

f(10/3) = 100/9 + 20/3 + 3

f(10/3) = 100/9 + 60/9 + 27/9

f(10/3) = 187/9

Therefore, when x = 2, f(g(x)) is approximately equal to 187/9.

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