hich of the these are steps for a proof by mathematical induction that P(n) is true for all positive integers n? a. Verify that P(1) is true. b. Demonstrate that the conditional statement Plk) implies Plk+1) is true for all positive integers k. c. Verify that P(1), P(2), P(3), ..., P(k) are all true, where k is a specific large, positive integer. d. Demonstrate that if P(k) is false, then Plk+1) is false for all positive integers k. e. Demonstrate that P(k+1) implies plk) is true for all integers k.

The answer is c): 17 and one-half quarts

To answer the question, we need to find the total amount of juice Sam made by adding the given quantities. However, the given quantities are in different units, which makes the addition difficult. Therefore, we need to convert all quantities to the same unit before adding them.

1 gallon = 4 quarts (since 1 gallon is equal to 128 ounces, and 1 quart is equal to 32 ounces,

thus 1 gallon = 128/32 = 4 quarts)

1 quart = 2 pints

1 pint = 2 cups

Therefore, 3 gallons = 3 x 4 = 12 quarts

2 quarts = 2 x 1 = 2 quarts

4 pints = 4 / 2 = 2 quarts

6 cups = 6 / 4 = 1.5 quarts

Now, we can add all the quantities in quarts to get the total amount of juice that Sam made:

12 + 2 + 2 + 1.5 = 17.5 quarts

Therefore, Sam made 17 and one-half quarts in all. Thus, the correct option is (c) seventeen and one half.

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Grace need to buy the jump rope, the game, and the ball $8.

$7 will get you a jump rope.

$10 will get you a board game.

$4 will get you a playground ball.

total amount to be spent: $7 + $10 + $4 = $21

She has ten dollars.

$3 was all her uncle gave her.

13 dollars are all she has.

She needed $8, therefore 21 - 13 = $8.

a sum of money awarded as compensation, a bounty, or to cover costs. a wage that comes with a cost-of-living supplement. especially: a regular amount set aside for household or personal costs.

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Answer: Let x be the number of hamburgers sold.

Then, the number of cheeseburgers sold is 3x.

The total number of burgers sold is x + 3x = 4x.

Given that the total number of burgers sold is 416, we have:

4x = 416

x = 416/4

x = 104

Therefore, 104 hamburgers were sold.

Step-by-step explanation:

To find the next two terms of the sequence, we need to first find the common difference between consecutive terms:

52 - 44 = 8

64 - 52 = 12

80 - 64 = 16

We notice that the common difference is increasing by 4 for each term. Therefore, the next two terms of the sequence are:

80 + 20 = 100

100 + 24 = 124

To determine the nth term of the quadratic sequence, we can use the formula:

an = a1 + (n-1)d + bn^2

where a1 is the first term, d is the common difference, b is the coefficient of n^2, and n is the term number.

Using the first four terms of the sequence, we can form a system of equations:

44 = a1 + b

52 = a1 + d + b

64 = a1 + 2d + b

80 = a1 + 3d + b

Solving for a1 and b, we get:

a1 = 20

b = 24

Substituting these values into the formula for an, we get:

an = 20 + (n-1)4 + 24n^2

an = 24n^2 + 4n - 4

To find the 30th term of the sequence, we simply substitute n = 30 into the formula we just derived:

a30 = 24(30)^2 + 4(30) - 4

a30 = 21,596

To prove that the quadratic sequence will always have even terms, we notice that the first term is even (44 = 2 x 22), and the common difference is even (8 = 2 x 4). Therefore, every term of the sequence can be expressed as an even number plus an even multiple of n^2, which is always even. Hence, the quadratic sequence will always have even terms.

Step-by-step explanation:

Sequence is 44;52;64;80;.....44;52;64;80;.....

General formula is Tn=2n2+2n+40

Sec x is the simplified expression cos(−x)+tan(−x)sin(−x) involving a single trigonometric function with no fractions.

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

The Given expression is

cos(−x)+tan(−x)sin(−x)

Now,

cos(−x) + tan(−x)sin(−x)

= cos x + (- tan x) (- sin x)

= cos x + tan x * sin x

= cos x + (sin x / cos x) * sin x

= (cos²x + sin²x) / cos x     ( As sin²x + cos²x = 1)

= 1/ cos x

= sec x       (As sec x = 1/cos x)

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Answer: x = -2

Step-by-step explanation:

Since both equations are in the y-slope form,

we can use substitution for y in finding x.

Hence,

4x=x-6

4x-x=x-x-6

Subtract x from both sides to get x on one side and integer on one side.

[tex]\frac{3x}{3} =\frac{-6}{3}[/tex]

Divide 3 to find the value of x

x=-2

Answer: The one that has the best deals.

Step-by-step explanation:

The calculation shows that 9,000 scientists have seen the deep ocean through Alvin's windows; and

a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

1) If on each of the 4,500 dives Alvin carried a new pilot and two new scientists, then the total number of scientists who have seen the deep ocean through Alvin's windows is:

4,500 dives x 2 scientists per dive = 9,000 scientists

Therefore, 9,000 scientists have seen the deep ocean through Alvin's windows.

2) To calculate the total number of people who traveled in Alvin, we can add the number of pilots and scientists on each dive and multiply by the number of dives:

4,500 dives x (1 pilot + 2 scientists)

= 4,500 x 3

= 13,500 people

Therefore, a total of 13,500 people have traveled in Alvin over the course of its 4,500 dives.

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Answer:

345.6

Or 345 full cubes

Step-by-step explanation:

To answer this question we first need to find the volume of the cuboid!

To find volume we use the equation...

For the cuboid we are given the dimensions 60, 24 and 30 so we just need to multiply them...

We now need to the the volume of the cube which we can just do by cubing the value given

We now need to divide the two results together to find out how many cubes would fit...

Hope this helps, have a lovely day!

Answer:

A

Step-by-step explanation:

Answer:

Y=x^2+7x-3

complete the square to re-write the quadratic function in vertex form.

pls help

Step-by-step explanation:

To complete the square, we need to add and subtract a constant term inside the parentheses, which when combined with the quadratic term will give us a perfect square trinomial.

y = x^2 + 7x - 3

y = (x^2 + 7x + ?) - ? - 3 (adding and subtracting the same constant)

y = (x^2 + 7x + (7/2)^2) - (7/2)^2 - 3 (the constant we need to add is half of the coefficient of the x-term squared)

y = (x + 7/2)^2 - 49/4 - 3

y = (x + 7/2)^2 - 61/4

So the quadratic function in vertex form is y = (x + 7/2)^2 - 61/4, which has a vertex at (-7/2, -61/4).

As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.

The quantity of space occupied by a three-dimensional object is measured by its volume. Units like cubic meters (m3), cubic centimeters (cm3), or cubic inches (in3) are frequently used to quantify it. Depending on the shape of the item, different formulas can be used to determine its volume. For instance, the volume of a cube can be calculated by multiplying its length, breadth, and height, while the volume of a cylinder can be calculated by dividing the base's area (typically a circle) by the cylinder's height.

given

We must apply the calculation for the volume of a cone's frustum in order to determine the volume of the Styrofoam collar:

[tex]V = (1/3)\pi h(R^2 + Rr + r^2)[/tex]

where h is the height of the frustum, r is the small radius, and R is the large radius.

Given the numbers, we can determine:

R = 5 in.

3 centimeters is r.

24 inches tall

With these numbers entered into the formula, we obtain[tex]V = (1/3)\pi (24)(5^2 + 5*3 + 3^2)\\\\ 179.594 cubic inches[/tex]

As a result, the Styrofoam collar has a volume of roughly 179.594 cubic inches.

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As Masons backyard deck is rectangular, the length of the deck is 22 feet.

Let's start by using algebra to solve for the length of the rectangular deck.

Let L be the length of the deck.

Then, the width of the deck is L - 12.

The perimeter is the sum of all four sides, so we have:

Perimeter = 2L + 2(L - 12) = 64

Simplifying the equation, we get:

2L + 2L - 24 = 64

Combining like terms, we get:

4L - 24 = 64

Adding 24 to both sides, we get:

4L = 88

Dividing both sides by 4, we get:

L = 22

Therefore, the length of the deck is 22 feet.

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Victor bought 10 packages of the largest-grain sandpaper.

Total money spent (20+15+9+6) = 50; total money left over (30+15+6+0) = 51. Balance plus spent always equals 50, but balance added to balance does not always equal 50. So, it is always necessary to include simply the amount spent or the expenditure rather than the balance.

Thus, we know how much he spent:

2S + (61 - 2S) = 61 - S

$1 on sandpaper with the biggest grit. We can condense this phrase as follows:

61 - S = 61 - 2S

Adding S to both sides, we get:

S = 0

Then we know that he spent:

2L + Ly = 61

Spending money on sandpaper. Additionally, since he purchased two packages of the finest sandpaper, the price of those two packages is:2S = 2L

We can substitute 2L for 2S in the first equation:

2L + Ly = 61

Simplifying, we get:

2L + L(2/3)L = 61

Multiplying both sides by 3/2, we get:

3L² = 91.5

Taking the square root of both sides, we get:

L ≈ 5.27

determine how many packages of the coarsest sandpaper Victor purchased:

2L + Ly = 61

2(5.27) + 5.27y = 61

10.54 + 5.27y = 61

5.27y = 50.46

y ≈ 9.56

Rounding to the nearest whole number, we get:

y = 10

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The simplified square expression for[tex]\sqrt{3a^2/10b^6}[/tex] is [tex]|3a| / (\sqrt{10} * b^{3})[/tex].

What is square root ?

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9.

The square root is denoted by the symbol √, also known as the radical symbol. For instance, the square root of 16 is written as √16 = 4.

The square root can be used to solve various types of equations, including quadratic equations and problems involving areas and volumes. It is also used in various fields such as physics, engineering, and finance.

According to the question:
To simplify the expression [tex]\sqrt{3a^{2}/10b^6}[/tex], we can first separate the numerator and denominator inside the square root:

[tex]\sqrt{3a^2/10b^6} = \sqrt{3a^2}/\sqrt{10b^6}[/tex]

Next, we can simplify the square root of the numerator:

[tex]\sqrt{3a^2} = |3a|,[/tex] where |За| represents the absolute value of За.

Finally, we can simplify the square root of the denominator by factoring out the perfect square[tex]b^2[/tex]:

[tex]\sqrt{10b^6} = \sqrt{10} * \sqrt{b^6} = \sqrt{10} * b^{3}[/tex]

Substituting these values back into the original expression, we get:

[tex]\sqrt{3a^2/10b^6} = |3a| / \(sqrt{10} * b^3[/tex]

Therefore, the simplified expression for[tex]\sqrt{3a^2/10b^6}[/tex] is [tex]|3a| / (\sqrt{10} * b^{3})[/tex].

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The number of papers xavier have remaining after working for 12 hours is 18

Xavier can grade 6 papers per hour, so in 12 hours he can grade:

6 papers/hour x 12 hours = 72 papers

Therefore, after working for 12 hours, Xavier would have

90 - 72 = 18 papers remaining to grade.

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Over the range [5, 7], the definite integral of f(x) = 1 / (x² + 10x + 25) is around -1/60.

To find the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7], we can use the following formula:

∫[a,b] f(x) dx = F(b) - F(a)

where F(x) is the antiderivative of f(x).

First, we need to find the antiderivative of f(x):

∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx

To do this, we can use a technique called partial fraction decomposition:

1 / (x² + 10x + 25)

= A / (x + 5) + B / (x + 5)²

Multiplying both sides by the denominator (x² + 10x + 25), we get:

1 = A(x + 5) + B

Setting x = -5, we get:

1 = B

Setting x = 0, we get:

A + B = 1

A + 1 = 1

A = 0

Therefore, the partial fraction decomposition of f(x) is:

1 / (x² + 10x + 25) = 1 / (x + 5)²

Now we can find the antiderivative:

∫ f(x) dx = ∫ 1 / (x² + 10x + 25) dx = ∫ 1 / (x + 5)² dx

Using the substitution u = x + 5, du = dx, we get:

∫ 1 / (x + 5)² dx = -1 / (x + 5) + C

where C is the constant of integration.

Now we can evaluate the definite integral over the interval [5, 7]:

∫[5,7] f(x) dx = F(7) - F(5)

∫[5,7] f(x) dx = [-1 / (7 + 5) + C] - [-1 / (5 + 5) + C]

∫[5,7] f(x) dx = [-1 / 12 + C] - [-1 / 10 + C]

∫[5,7] f(x) dx = -1 / 12 + C + 1 / 10 - C

∫[5,7] f(x) dx = -1 / 60

Therefore, the definite integral of f(x) = 1 / (x² + 10x + 25) over the interval [5, 7] is approximately -1/60.

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Using pythagoras' theorem in the right-angled triangle

A right-angled triangle is a polygon with 3 sides in which one angle is a right angle

Now, since we have 3 triangles, using Pythagoras' theorem in all three triangles, we have

h² + (12 - x)² = 12² - 6² (1)

Also, h² + x² = 6²  (2)

So, h² + (12 - x)² = 12² - 6²

h² + (12 - x)² = 144 - 36

h² + (12 - x)² = 108  (3)

From equation (2), h² = 36 - x²

Substituting this into equation (3), we have that

h² + (12 - x)² = 108  (3)

36 - x² + (12 - x)² = 108  (3)

Expanding the brackets, we have that

36 - x² + 144 - 24x + x² = 108

36 + 144 - 24x = 108

180 - 24x = 108

-24x = 108 - 180

-24x = -72

x = -72/-24

x = 3

Since  h² = 36 - x²

h = √(36 - x²)

So, substituting the value of x = 3 into the equation, we have that

h = √(36 - x²)

h = √(36 - 3²)

h = √(36 - 9)

h = √27

h = 3√3

So,

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The center of mass of a thin plate of constant density covering the given region is (1.8, 3.6).

To find the center of mass, we must calculate the weighted average of all the points in the region. The region is bounded by the parabola y = 3x - x² and the line y = -3x.

We must calculate the integral of the region and divide by the total mass. The mass is equal to the area times the density, .

The integral of the region is calculated using the limits of the two curves, yielding a final integral of 32/15. Dividing this integral by the density gives the total mass, and multiplying by the density gives us the center of mass, (1.8, 3.6).

We can also find the center of mass by calculating the moments of the plate about the x-axis and y-axis.

The moment about the x-axis is calculated by finding the integral of the parabola and line using the x-coordinate, and the moment about the y-axis is calculated by finding the integral of the parabola and line using the y-coordinate. Once the moments are found, we can divide each moment by the total mass to get the center of mass.

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the sale price of the cell phone after the 35% discount is $315.25.

How to solve and what is sale?

To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:

Sale price = Regular price - Discount amount

Sale price = $485 - (0.35 x $485)

Sale price = $485 - $169.75

Sale price = $315.25

Therefore, the sale price of the cell phone after the 35% discount is $315.25.

A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.

In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.

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Answer:

yo your dûmb asl

Step-by-step explanation:

The total area under the curve for x ≥ 6 is 449/4500.

The area under the curve y = 2x-3 from x = 6 to x = t and its evaluation at t = 10 and t = 100The area under the curve y = 2x-3 from x = 6 to x = t can be calculated as follows:

We know that the area of the region under the curve f(x) between x = a and x = b is given by [tex]A = ∫abf(x)dx[/tex]

Since the given function is y = 2x-3, we can write it as y = 2x^(-3) by applying the power rule.

Hence,A = [tex]∫62x^(-3)dx = [-2x^(-2)]6t = -2/t^2 + 2/36[/tex]We need to evaluate this area for t = 10 and t = 100, so we get[tex]A = -2/10^2 + 2/36 = -1/25 + 1/18 = 7/450andA = -2/100^2 + 2/36 = -1/5000 + 1/18 = 449/4500[/tex]Total area under this curve for x ≥ 6

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Answer:

54

Step-by-step explanation:

Answer:

y=54

as x=3

so y=2*x^3

y= 2*3^3

y=2*27

y=54

The theoretical probability for the 1 horned, 1 eyed,  flying, people eater purple is found to be 1/120.

Experimental Probability: Based on actual results rather than mathematical calculations, the experimental probability of an occurrence is the likelihood that the event will actually occur.

Theoretical Probability: Considering that the event is ideal, the theoretical chance that it will occur is the theoretically ideal probability of a specific result. The flaws in the system are not taken into consideration by theoretical probability.

Theoretical Probability = Number of favorable outcomes / Number of possible outcomes.

The given probability are;

Let P(E)  be the theoretical probability  1 horned, 1 eyed,  flying, people eater purple.

Then,

P(E) =  3/4 * 1/5* 2/3* 3/8* 1/2

P(E) =  1/120

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The system of inequalities that represents the number of quarters, x, and the number of dimes, y, that Mai could have is given by:

x + y ≥ 10 and 0.25x + 0.1y < 2

These are the two systems of inequalities that represent the number of quarters, x, and the number of dimes, y, that Mai could have.

Let x be the number of quarters and y be the number of dimes that Mai has. Then, the system of inequalities can be represented as:

Thus, the first inequality is x + y ≥ 10.

Also, Mai has less than $2.00, therefore, the second inequality is 0.25x + 0.1y < 2. The value of x and y are assumed to be non-negative integers.+

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To determine the degree of the Maclaurin polynomial required for the error in the approximation of the function f(x) = -x+1 at the indicated value of x to be less than 0.001, we can use the formula: N ≥ ln(error)/ln(absolute value of x) + 1.

For our given function, the error is 0.001, and the value of x is 0.2. Plugging these values into the formula, we get: N ≥ ln(0.001)/ln(0.2) + 1, which is equivalent to N ≥ 6.64 + 1 = 7.64. Therefore, we need the degree of the Maclaurin polynomial to be 7.64 in order for the error in the approximation of the function at the indicated value of x to be less than 0.001.

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The value of the expression z + 3x4 using arithmetic operation where z = 15, is 27. The answer is A) 27.

The given expression is z + 3x4, where z = 15. To evaluate this expression, we substitute 15 for z and perform the multiplication. First, we multiply 3 and 4, which gives us 12. Then, we add 15 and 12 to get the final result of 27.

z + 3x4 = 15 + 3x4

= 15 + 12

= 27

Therefore, the value of the expression when z = 15, is 27. In other words, using arithmetic operation of multiplication and addition, which gives us the final answer of 27. So, the correct answer is option A).

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____The given question is incomplete , the complete question is given below:

Evaluate the expression, where z = 15

z + 3x4

A. 27

B. 32

C. 56

D. 1,304

Answer:

100 minutes

Step-by-step explanation:

We know

It takes 3 hrs to run a distance of 180 km.

180 / 3 = 60 km / h

60 minutes = 60 km

40 minutes = 40 km

What time it will take to run 100 km?

60 + 40 = 100 minutes

So, it takes 100 minutes to run 100 km.

Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.

Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.

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