The integral So'sin(x - 2) dx is transformed into 1, g(t)dt by applying an appropriate change of variable, then g(t) is: g(t) = sin g(t) = sin g(t) = 1/2 sin(t-3/2) g(t) = 1/2sint-5/2) g(t) = 1/2cos (t-5/2) = cos (t-3)/ 2

Answer:  No. The grasshopper cannot cover exactly 101 cm in exactly 100 jumps.

Step-by-step explanation:  

If the grasshopper makes 50 forward jumps of 19 cm and 50 backward jumps of 17 cm (in any order) the jumps total 950-850 for a net result of 100.

Changing to any other amount just gets farther away from the goal.

A system of equations yields no solution of integers.

x + y ==100

19x - 17y =101

You can try it, but the result has a decimal. This grasshopper cannot make partial jumps!

Answer:

The ratio of quarters to nickels is:

Step-by-step explanation:

To solve the exercise, you must first consider how big is the ratio of each one to the other, when it is mentioned that the ratio of quarters to dimes is 5:2 it means that for every 5 quarters, Jon has 2 dimes, for the more quarters there are with respect to the dimes, we simply divide the larger value by the smaller:

Thus, we know that there are 2.5 more quarters than dimes. Now the following proportion: the ratio of dimes to nickels is 3:4, which means that for every 3 dimes there are 4 nickels, as the nickels are greater in quantity, we are going to see how many times they are greater in proportion than the dimes making again a division of the major over the minor:

As we can see, the nickels are a little more than 1 with respect to the dimes, now we are going to create two formulas with those values:

Where:

As you see. We only express the calculated proportions, at first glance you can identify that the number of quarters is greater, but to know how much greater with respect to nickels we are going to divide the two values ​​that accompany "d" in the formulas:

If we express it in ratio as it is in the exercise, we obtain:

So, 15:8 is the ratio of quarters to nickels, which means that for every 15 quarters, jon has 8 nickels.

The critical points are (0, 0) and (1/2, 1/8).

To find the critical points of the function f(x, y) = 8x^3 + y^3 - 6xy + 2, we need to find the points where the partial derivatives of f with respect to x and y are equal to zero.

a.) Finding the critical points:

∂f/∂x = 24x^2 - 6y = 0

∂f/∂y = 3y^2 - 6x = 0

From the first equation, we have:

24x^2 - 6y = 0

4x^2 - y = 0

y = 4x^2

Substituting y = 4x^2 into the second equation:

3(4x^2)^2 - 6x = 0

48x^4 - 6x = 0

6x(8x^3 - 1) = 0

This gives two possible cases:

6x = 0, which implies x = 0.

8x^3 - 1 = 0, which implies 8x^3 = 1 and x^3 = 1/8. Solving this equation, we find x = 1/2.

For x = 0, we can substitute it back into y = 4x^2 to find y = 0.

So, the critical points are (0, 0) and (1/2, 1/8).

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Answer:

47 zeros

Step-by-step explanation:

Therefore, there will be approximately 20,480 bacteria after 30 minutes. The correct answer is (b) 20,480 bacteria.

In this experiment, we have an initial bacterial count of 5,000 at time 0 and a count of 8,000 at 10 minutes. Since the growth is exponential, we can use the exponential growth formula:

\(N(t) = N₀ * (1 + r)^t\)

Where N(t) is the number of bacteria at time t, N₀ is the initial number of bacteria, r is the growth rate, and t is the time.

First, let's find the growth rate using the data provided:

\(8000 = 5000 * (1 + r)^{10\\\\(1 + r)^{10} = 8000 / 5000 = 1.6\)

Now, let's find the 10th root of 1.6 to find the growth rate (1 + r):

\(1 + r = 1.6^{1/10} =1.0481\)

So, the growth rate (r) is approximately 0.0481.

Next, we want to find the number of bacteria after 30 minutes:

N(30) = 5000 * (1.0481)^30 ≈ 20480.18

Therefore, there will be approximately 20,480 bacteria after 30 minutes. The correct answer is (b) 20,480 bacteria.

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Using the arithmetic operations, the total change in her monthly electric bill over 5 months is +$10.58

For the past 5 months,

The change in her July electric bill = +$18.02

The change in her August electric bill =  +$1.03

The change in her September electric bill = -$0.44

The change in her October electric bill = -$6.84

The change in her November electric bill = -$1.19

The total change in her monthly electric bill over 5 months = Sum of all changes in her electric bill over 5 months

= +18.02+1.03-0.44-6.84-1.19

= +$10.58

Hence, the total change in her monthly electric bill over 5 months is +$10.58

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The missing area or side length in the triangles are:

1: Area = 145 units²

2: Area =  17 units²

3: Area  = 29 units²

4: Area= 27 units²

5: length = √37 units

6: length = 2√26 units

7: length = 3√11 units

8: length  = 5√3 units

Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. That is:

c² = a² + b²

Where  a and b are the lengths of the legs, and c is the length of the hypotenuse

No. 1

Area (hypotenuse)  = 81 + 64 = 145 units²

No. 2

Area (hypotenuse)  = 16 + 1 = 17 units²

No. 3

Area (hypotenuse)  = 5² + 2² = 29 units²

No. 4

Area (leg)  = 36 - 9 = 27 units²

No. 5

length (hypotenuse)  = √(6² + 1²) = √37 units

No. 6

length (hypotenuse)  = √(10² + 2²) = 2√26 units

No. 7

length (leg)  = √(10² - 1²) = 3√11 units

No. 8

length (leg)  = √(10² - 5²) = 5√3 units

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Answer:

10√2

Step-by-step explanation:

This is a 45-45-90 triangle which means that the two non-hyptonouse lenghts are the same which means that the bottom lenght of the triangle is also 10 units

We can then use a^2+b^2=c^2 to solve for the last side

so we have

10^2+10^2=x^2

200=x^2

sqrt200=x

and I see that they want an exact answer so you simplify sqrt200 to

10√2

There are 96 ways for four people to sit in six chairs so that the leftmost chair is occupied and the rightmost is empty.

There are 4 guests and the leftmost seat is to be occupied, so there are 4  such ways to choose the occupant of that seat.

Then, for each of those 4 ways, there are 4 ways to decide the occupant for the second seat -- the remaining three people plus the possibility of that seat being empty, that makes a total of 16 ways to decide the configuration of the first two seats.

Then, for each of those 16 ways, there are 3 ways to choose the occupant for the third seat (either 3 remaining guests if the second seat was left empty, or the two remaining guests plus the possibility of leaving the 3rd seat empty). Hence, 16 times 3 is 48. For each of those ways, there are two choices for the next seat, i.e. 48 times 2 = 96, and finally one choice for the fifth seat. So in all, there are 96 ways.

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Answer:

$1656

Step-by-step explanation:

(12*74)+768

(888)+768

1656

78.740 inches in 2 meters. 2 meters equals 6.56168 ft. One meter is equivalent to 3.28084 ft.

2 meters into inches

1 inch = 39.370

2 meters = 2 × 39.370

Then we get ,

= 78.740 inches

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The rate of change, based on y is a function of the distance traveled, z, and what it means is B. The ride costs $3 per mile.

The rate of change is the unit rate or the slope.

The rate of change also refers to the variable cost per unit.

The variable cost can be differentiated from the fixed cost since it varies according to the quantity involved.

Distance (mi), z Total Cost ($) y  Rate of Change

       0                        2                        $0

       1                         5                        $3 ($5 - $2)

      2                         8                        $3 ($8 - $5)

      3                         11                       $3 ($11 - $8)

      4                         14                       $3 ($14 - $11)

The Rate of Change = The Slope = Rise/Run = ($5 - $2)/(1 - 0)

Thus, based on the total cost of a ride-sharing trip, the unit rate is $3 per mile.

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Required area of the composite figure is 69 cm²

What is area of a composite shape?

the area covered by any composite shape. A composite shape is a shape in which some polygons are put together to form the required shape is called the area of composite shapes . These figures can consist of combinations of triangles, rectangles, squares etc. To determine the area of composite shapes, divide the composite shape into basic shapes such as square, rectangle,triangle, hexagon, etc.

Basically, a compound shape consists of basic shapes put together. This is also called a "composite" or "complex" shape. This mini-lesson explains the area of compound figures with solved examples and practice questions.

Here in this figure, we have two figures.

First one is rectangle and second one is triangle.

Length and breadth of the rectangle are 12 cm and 4 cm respectively.

So, area = Length × Breadth = 12 × 4 = 48 cm²

Again height of the triangle is (11-4) = 7 cm and base of the triangle is (12-6) = 6 cm.

So, area of the triangle = 1/2 × 7 × 6 = 3×7 = 21 cm²

Now if we add both area of rectangle and triangle then we will get area of the composite figure.

So, required area of the composite figure is ( 48+21) = 69 cm²

Therefore, option A is the correct option.

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Answer: 13

Step-by-step explanation:

Answer:

$25.75

Step-by-step explanation:

$30.00 - $4.25 = $25.75

Answer:

-10

Step-by-step explanation:

hope this can help :)

Answer:

-10

Step-by-step explanation:

because 0 is greater than all the other numbers and -5 is closer to 0 than -10.

The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To fill in the blanks, we need to use the given information to complete the probability distribution table.

We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

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The value of x that results in short circuit evaluation, causing (y < 4) not to be evaluated, is any value that is greater than or equal to 7.

Short Circuit Evaluation is a concept in computer programming where certain expressions are evaluated only if necessary.

In this case, the expression (x >= 7) (y < 4) 678, we need to find the value of x that results in short circuit evaluation and causes (y < 4) not to be evaluated.

In this expression, the first expression (x >= 7) is evaluated first. If the value of x is greater than or equal to 7, then the expression is considered true and the evaluation process moves to the next expression (y < 4).

However, if the value of x is less than 7, then the expression is considered false and the evaluation process stops.

In this case, (y < 4) is not evaluated because the result of the expression is already known to be false, and therefore, evaluating it would be a waste of resources.

If x is less than 7, then (y < 4) will be evaluated. It is important to keep in mind that short circuit evaluation is a technique used to optimize the evaluation process and make it more efficient.

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Answer:

0

Step-by-step explanation:

A tangent line is a line that touches the circle's circumference at only one point.

Given two concentric circles one with radius \(r_1\) and the second with radius \(r_2\), and \(r_1>r_2\). SInce \(r_2\) is inside the smaller circle, there is no way it would intersect with the tangent line t.

Therefore, there are no points of intersection between the tangent line t and    \(r_2\) .

Answer:

Infinity

Step-by-step explanation:

Look it up, its how it works. 0 can go into 3.2 infinity times.

Answer:

addition property of equality

Step-by-step explanation:

The volume of the solid obtained by rotating the region bounded by the curves y = 3x^6 and y = 3x (where x ≥ 0) about the x-axis is π/2 cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves y = 3x^6 and y = 3x (where x ≥ 0) about the x-axis, we can use the method of cylindrical shells.

First, we need to find the limits of integration. The curves intersect at x = 1, where y = 3. Therefore, we can integrate from x = 0 to x = 1 to obtain the volume of the solid.

Next, we need to find the radius and height of the cylindrical shells. The radius of each shell is x, which is the distance from the axis of rotation (the x-axis) to the curve. The height of each shell is the difference in y-coordinates between the curves at a given value of x.

Thus, the volume of each cylindrical shell is given by:

dV = 2πx (y2 - y1) dx

where y2 is the equation of the upper curve (y = 3x), y1 is the equation of the lower curve (y = 3x^6), and dx is an infinitesimal thickness of the shell.

Substituting the equations for y1 and y2, we have:

dV = 2πx (3x - 3x^6) dx

Integrating this expression from x = 0 to x = 1, we get:

V = ∫[0,1] 2πx (3x - 3x^6) dx

Evaluating this integral, we obtain:

V = π/2.

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a) the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b)a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

The definition of an equation is the claim that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The LHS and RHS can contain variables, constants, operations, and functions.

a) The two formulae for cooking times are:

(66 x weight in kg) + (35 x time in an electric oven

Microwave oven time = (26 x weight in kg) + 15

We can compare the two formulae by looking at their coefficients and constants.  This suggests that the electric oven takes longer to cook the meat than the microwave oven, and that the difference in cooking times will increase with larger weights.

b) (66 x weight in kg) + (35 x time in an electric oven

2 x 60 = (66 x weight in kg) + 35

120 - 35 = 66 x weight in kg

85 = 66 x weight in kg

weight in kg = 85 / 66

weight in kg ≈ 1.29

So, a joint of meat that takes about 2 hours to cook in an electric oven weighs approximately 1.29 kg.

Microwave oven time = (26 x weight in kg) + 15

Microwave oven time = (26 x 1.29) + 15

Microwave oven time ≈ 48.34 minutes

Therefore, a 1.29 kg joint of meat would take about 48 minutes to cook in a microwave oven.

c) The answer to part a seems sensible, as the formula for the electric oven predicts longer cooking times than the formula for the microwave oven.

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a. Cοnditiοnal statement: If a pοlynοmial has three terms, then it is a trinοmial.

Pοlynοmials appear in many areas οf mathematics and science. Fοr example, they are used tο fοrm pοlynοmial equatiοns, which encοde a wide range οf prοblems, frοm elementary wοrd prοblems tο cοmplicated scientific prοblems; they are used tο define pοlynοmial functiοns, which appear in settings ranging frοm basic chemistry and physics tο ecοnοmics and sοcial science; they are used in calculus and numerical analysis tο apprοximate οther functiοns

a. Cοnditiοnal statement: If a pοlynοmial has three terms, then it is a trinοmial.

b. Cοnverse statement: If a pοlynοmial is a trinοmial, then it has three terms.

c. Inverse statement: If a pοlynοmial dοes nοt have three terms, then it is nοt a trinοmial.

d. Cοntrapοsitive statement: If a pοlynοmial is nοt a trinοmial, then it dοes nοt have three terms.

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It takes 1/5 hours or 12 minutes for 1 centimeter of snow to accumulate in Harper's yard.

We are given that the depth of snow that accumulates in Harper's yard during the first h hours of a snowstorm is given by the equation d = 5h.

To find out how many hours it takes for 1 centimeter of snow to accumulate, we need to find the value of h when the depth of snow d is equal to 1 centimeter.

Substituting d = 1 in the equation d = 5h, we get:

1 = 5h

Dividing both sides by 5, we get:

h = 1/5

In summary, the equation d = 5h gives the depth of snow in centimeters that accumulates in Harper's yard during the first h hours of a snowstorm. To find how many hours it takes for 1 centimeter of snow to accumulate, we substitute d = 1 and solve for h, which gives us h = 1/5 hours or 12 minutes.

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Complete question is:

We can calculate the depth d of snow, in centimeters, that accumulates in Harper's yard during the first h hours of a snowstorm using the equation d = 5h. How many hours does it take for 1 centimeter of snow to accumulate in Harper's yard?

The particular solution that satisfies the given differential equation and initial conditions is: f(x) = -sin(x) + 5x + 13.

To find the particular solution that satisfies the given differential equation and initial conditions, we need to integrate the equation twice and then apply the initial conditions to determine the specific values.

Given the differential equation f''(x) = sin(x), integrating it once gives us:

f'(x) = -cos(x) + C₁,

where C₁ is the constant of integration.

Integrating again:

f(x) = -sin(x) + C₁x + C₂,

where C₂ is the constant of integration.

Applying the initial condition f'(0) = 4:

f'(0) = -cos(0) + C₁ = 4,

-1 + C₁ = 4,

C₁ = 5.

Now, let's apply the second initial condition f(0) = 13:

f(0) = -sin(0) + C₁(0) + C₂ = 13,

0 + 0 + C₂ = 13,

C₂ = 13.

Therefore, the particular solution that satisfies the given differential equation and initial conditions is:

f(x) = -sin(x) + 5x + 13.

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Answer:

20

Step-by-step explanation:

Total no of plants in a garden = 36

The ratio of tomato plants to cucumber plants to be 4:5.

Let tomato plants are 4x and cucumber plants is 5x.

ATQ,

4x+5x=36

9x = 36

x = 4

For cucumber plant, 5x = 5(4) = 20

So, there are 20 cucumber plants will be in Reggie's garden

Answer:

This is the answer. Hope it helps

Step-by-step explanation:

3/25<22/25

The derivative of h(x) is h'(x) = √x²+1.

To find the derivative of h(x), we can apply the Leibniz  rule, which states that if the upper limit of the integral is a function of x, then we need to differentiate both the integrand and the limits of integration. Using this rule, we get:

h'(x) = (√x²+1)(z²/z⁴+1) ∣ z=1 - (1²/1⁴+1) ∣ z=√x

To simplify this expression, we need to evaluate the limits of integration and simplify the integrand. First, we evaluate the limits of integration:

√x → 1: (z²/z⁴+1)dz = arctan(z) ∣ z=√x → 1 = arctan(1) - arctan(√x)

1 → 1: (z²/z⁴+1)dz = arctan(z) ∣ z=1 → 1 = arctan(1) - arctan(1) = 0.

Now, we can simplify the expression for h'(x):

h'(x) = (√x²+1)(1) - 0 = √x²+1.

Therefore, the derivative of h(x) is h'(x) = √x²+1.

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