003 (part 1 of 2) 10.0 points
a 0.58 kg object is at rest. a 2.65 n force
to the right acts on the object during a time
interval of 1.51 s.
a) what is the velocity of the object at the
end of this time interval?
answer in units of m/s.
004 (part 2 of 2) 10.0 points
at the end of this interval, a constant force of
3.60 n to the left is applied for 2.86 s.
b) what is the velocity at the end of the
2.86 s?
answer in units of m/s.

The solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and            k = 1,3,5,7,9...

Let d = [tex](2a^{2} +29a + 65, a+ 13)[/tex]

Now, we can split [tex]2a^{2} + 29a + 65[/tex] in the following way, so that it becomes easier to factorise.

[tex]2a^{2} + 29a + 65 = (2a^{2} + 29a + 39) + 26[/tex]

From this, we can quantify and notice that -13 is one root of this equation, while the other root is -3/2.

Therefore, [tex]2a^{2} + 29a + 39 = (a+13)(2a+3)+26[/tex]

Thus, [tex]d = ((a+13)(2a+3)+26, a+ 13)[/tex]

The greatest common divisor (GCD) of two or more numbers is the greatest common factor number that divides them, exactly. It is also called the highest common factor (HCF).

Now, we can use Euclid's Algorithm.

[tex]= gcd (2a^{2} + 29a + 65, a + 13)\\= gcd (2a^{2} + 29a + 65 - 2a(a+13), a+13)\\= gcd (3a + 65, a + 13)\\= gcd (3a + 65 - 3a(a+13), a+13)\\= gcd (26, a + 13)[/tex]

This is necessarily 1, 2, 13, or 26, which we can see by just looking at the first term. By factoring 1183 and considering that [tex]a[/tex] is an odd multiple, then we should be able to conclude the answer.

Hence, the conclusion is that the solution is 26, since gcd (26, a + 13) = 26 when a = 1183k, and k = 1,3,5,7,9...

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Answer:

Step-by-step explanation:

x / 12 = 3 / 8

x = 3 / 8 x 12

x = 3 / 94

x = 32

32 / 12 = 3 / 8

Answer:

The angle in radians is 4.6.

Note that it is expressed in radians, to convert it to degrees you need to multiply it by 180/π, but it is already rounded to the nearest 10th.

Step-by-step explanation:

To find the angle in radians to the nearest 10th, you need to use the relationship between the length of an arc, the radius of the circle, and the angle of the arc:

arc length = (angle in radians) * (radius)

In this case, the radius of the circle is 8.5 and the arc length is 38.9, so you can substitute these values into the equation:

38.9 = (angle in radians) * (8.5)

To solve for the angle in radians, you need to divide both sides of the equation by the radius:

angle in radians = 38.9 / 8.5

The angle in radians is 4.6.

Note that it is expressed in radians, to convert it to degrees you need to multiply it by 180/π, but it is already rounded to the nearest 10th.

Answer:

---------------------------------------

Find the distance between the given point (-3, 2) and the center of circle (4, 0) using distance formula:

As we see the distance is greater than radius, hence it is outside circle.

Answer:

To solve this problem, we will use the following steps:

Step 1: We know that the amount of time it takes Susan to get from her residence to class averages 50 minutes, with a standard deviation of 5 minutes. So we can use this information to calculate the proportion of Susan's trips to class that would take less than 40 minutes.

Step 2: To calculate the proportion of Susan's trips to class that would take less than 40 minutes, we need to find the z-score for the value of 40 minutes. We can use the following formula to find the z-score:

z = (x - μ) / σ

Where x is the value we are interested in (40 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).

z = (40 - 50) / 5 = -2

Step 3: We can use a standard normal table or a calculator to find the proportion of Susan's trips to class that would take less than 40 minutes.

The proportion of Susan's trips to class that would take less than 40 minutes is 0.0228 or 2.28%.

Step 4: To calculate the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes, we need to find the proportion of Susan's trips to class that would take more than 50 minutes and add it to the proportion of Susan's trips to class that would take less than 40 minutes.

Step 5: To find the proportion of Susan's trips to class that would take more than 50 minutes, we need to find the z-score for the value of 50 minutes.

z = (50 - 50) / 5 = 0

Using a standard normal table or a calculator, the proportion of Susan's trips to class that would take more than 50 minutes is 0.5 or 50%.

Step 6: Finally, we can add the proportion of Susan's trips to class that would take more than 50 minutes and the proportion of Susan's trips to class that would take less than 40 minutes to find the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes.

0.50 + 0.0228 = 0.5228 or 52.28%

Final Answer: The proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes is 0.5228 or 52.28%.

The required inequality describes for the given problem is  x < 8.5.

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

she used 3.5 pounds of the wax to make vanilla-scented candles and has less than 5 pounds of wax left to make orange-scented candles.

let x represent the weight of the block of wax originally

then,inequality can be written as,

x - 3.5 < 5

x < 8.5

Thus, required inequality is x < 8.5.

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The number of integers N less than 1000 that can be written as the sum of j consecutive positive odd integers from exactly 5 values of j ≥ 1 is 15.

Arithmetic sequence is a sequence of numbers/terms that has a fixed pattern, based on the operation of subtraction or addition. Thus, each sequence of numbers will have a common difference.

Formula: aₙ = a₁ + (a - 1)d,

where aₙ is the nᵗʰ term and a₁ is the first term in the sequence, and d is the common difference between terms

Sum of n terms = n (a₁ + aₙ) / 2

We want to know the number of integers N less than 1000 that can be written as the sum of j consecutive positive odd integers from exactly 5 values of j ≥ 1

First, we determine:

- the first odd integer in the list: 2n + 1, where n ≥ 1

- the last odd integer in the list: 2n + 1 + 2(j - 1) = 2(n + j) - 1

These odd integers form a sequence with the following sum:

N = n (a₁ + aₙ) / 2

   = j (2n + 1 + 2(n + j) - 1) / 2

   = j (2n + 1 + 2n + 2j - 1) / 2

   = j (4n + 2j) / 2

   = j (2n + j)

We also know that there are exactly 5 values of j that satisfy the equation, there must be either 9 or 10 factors of N.

This means N = p₁².p₂² or N = p₁.p₂⁴

If N is odd, then j is also odd, which means that 2n+j is also odd. It is valid for all odd j.  Given the boundary of 1000, the possibilities of odd N are (3².5²), (3².7²), (3⁴.5), (3⁴.7), and (3⁴.11) ---> 5 possibilities

If N is even, then j is also even. If we substitute j = 2k into the N, we get:

  N = j (2n + j)

      = 2k (2n + k)

      = 4k (n + k)

N/4 = k (n + k)

This formula implies that the new upper bound is 250. So the possibilities of even N are (2².3²), (2².5²), (2².7²), (3².5²), (2⁴.3), (2⁴.5), (2⁴.7), (2⁴.11), (2⁴.13), and (3⁴.2) ---> 10 possibilities

Thus, the total number of integer N is 5 + 10 = 15

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If the point (3√5,d+3) is 3d Units away from the origin , then the smallest possible value of d is 3 .

The point (3√5,d+3) is 3d Units away from the origin , that means ,

the distance between the points (0,0) and (3√5,d+3) is 3d units ;

By using the distance formula , the given situation can be represented as

⇒ [tex](3d)^{2} =(3\sqrt{5} -0)^{2} + (d+3)^{2}[/tex] ;

On simplifying the equation ,

we get ;

⇒ [tex]9d^{2} = 45+d^{2} +6d+9[/tex] ;

⇒ [tex]4d^{2} -3d--27 = 0[/tex] ;

Writing in factor form ,

we get ;

⇒ [tex](4d+9)(d-3)= 0[/tex] ;

On solving we have [tex]d=-\frac{9}{4}[/tex] and [tex]d=3[/tex] .

Since the distance is only positive , So we can write d = 3 ;

Therefore , the smallest possible value of d is 3 .

The given question is incomplete , the complete question is

A point (3√5,d+3) is 3d Units away from the origin. What is the smallest possible value of d ?

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2^8, 4^4 and 16^2 are equivalent to 256. We can find this out by using the concept of Factors.

Factors are numbers or algebraic expressions that divide another number of expression without leaving a remainder.

In the question, the number given is 256.

Options are: 2^8, 4^4, 16^2, and 128^2

We will break down all the numbers into the product of their factors and using multiplication, we will verify if they are equivalent to 256 or not.

2^8 = 2*2*2*2*2*2*2*2 = 256

4^4= 4*4*4*4 = 256

16^2= 16*16 = 256

128^2 = 128*128 = 16384

As we can observe, only 128^2 is not equivalent to 256.

Therefore, 2^8, 4^4 and 16^2  are equivalent to 256.

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Answer:

50

Step-by-step explanation:

Answer:

Step-by-step explanation:

0

The lengths of q and r are 2.5 , 2.5 respectively if the perimeter of an isosceles triangle pqr is 9 cm.

What is a triangle ?

triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.

Given ,

The perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm.

the length of side p is 4 cm

Let the lengths of q and r are x and y respectively.

The perimeter of an isosceles triangle  =  (p+2q)

So,

p+2q = 9

4+2q = 9

2q = 9-4

2q = 5

q = 5/2

q = 2.5 cm

Hence , the lengths of q and r are 2.5 , 2.5 cm respectively .

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An equation Dividing 4x^2+6x by 4x+2 gives : Therefore , the expression ... 4x + 2, as follows: 4x^2 + 2x + 4x + 2 − 2, or x(4x + 2) + (4x + 2) − 2.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here,

the given equation is

this above equation is equivalent to

2X - 10/2X+2,

as root of both equation are same

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By using a trigonometric relation, we will see that the hypotenuse of the right triangle measures 160 units.

On the image, we can see a right triangle where we know one of the angles and one of the cathetus.

We want to find the value of x, which is the hypotenuse of the right triangle, and the cathetus that we know is the adjacent cathetus to the known angle.

Then we can use the trigonometric relation:

cos(a) = (adjacent cathetus)/hypotenuse

cos(60°) = 80/x

Using that we can find the value of x, we will get:

x = 80/cos(60°) = 160

The value of x is 160 units.

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Answer:

Option B

Step-by-step explanation:

The peak, the largest deposit, made in July

It's the tallest one in the plot.

Let's arrange the number from smallest to greatest:

50<80=80<95<100<110<250<300<320

Jan<Feb=Sep<May<Apr<Mar<June<Aug<July

So, the greatest amount of deposit was in July.

These trades took place between June and August 2020. June 1 After giving it some deliberation, Natalie decides to offer Curtis a mixer for $1,150 (mixer cost: $620) on credit with terms of n/30. 30 Curtis gives Natalie a call. He signs a one-month, 8.35% note payable since he won't be able to pay the sum due for another month. Curtis calls on July 31.

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Answer:

Step-by-step explanation:

You need to know trigonometry for this.\

You can't solve this without a scientific calculator.

TOA means Tan x = Opposite/Adjacent or in this case, 5.1/4.2

tan x = 5.1/4.2

arctant(tanx) = arctan(5.1/4.2)

x = arctan(5.1/4.2)

≈ 50.5°

arctan x is also known as tan inverse x

Answer: 7.4

Step-by-step explanation:

[tex]\frac{x}{\sin 46^{\circ}}=\frac{5}{\sin 29^{\circ}}\\\\x=\frac{5\sin 46^{\circ}}{\sin 29^{\circ}}\\\\x \approx 7.4[/tex]

e6z = xyz,  implicit differentiation of the following equation-

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. 

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. 

We have LHS = RHS (left hand side = right hand side) in every mathematical equation. 

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.  To determine the value

To determine the value A statement is not an equation if it has no "equal to" sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

According to our question-

Given e6z = xyz

To find ∂z/∂x → consider z as a function of x and take y to be a constant

So differentiating with respect to x, we get

e6z × 6 × ∂z/∂x = z × y + xy × 1 × ∂z/∂x

[using the chain rule on the LHS and the product rule on the RHS]

Factor out the ∂z/∂x:

∂z/∂x [6e6z - xy] = yz

∂z/∂x = yz / [6e6z - xy]

Do the same thing to find ∂z/∂y except consider z to be a function of y and take x to be a constant

Differentiating with respect to y:

e6z × 6 × ∂z/∂y = z × x + xy × 1 × ∂z/∂y

∂z/∂y [6e6z - xy] = xz

∂z/∂y = xz / [6e6z - xy]

Therefore, ∂z/∂x = yz / [6e6z - xy] and ∂z/∂y = xz / [6e6z - xy]

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Answer:

4am, it's 4 am.

The likelihood that a student chosen at random has any siblings is 0.777. This is determined by deducting from 1 the probability of having no siblings (0.223).

1. Get the probability of 0 siblings : 0.223

2. Subtract the probability of 0 siblings from 1 :

1 - 0.223

= 0.777

3. Round the result to 3 decimal places :

0.777

The probability of a student not having 0 siblings can be calculated by subtracting the probability of having 0 siblings from 1. The probability model created from the survey results is a 2-column table with 5 rows. Column 1 is labeled number of siblings with entries 0, 1, 2, 3, 4 or more. Column 2 is labeled probability with entries

0.223, 0.532, 0.121, 0.085, 0.039.

The probability of having 0 siblings is 0.223. To calculate the probability of not having 0 siblings, we subtract 0.223 from 1. This gives us 0.777, which is the probability of not having 0 siblings. This result should be rounded to 3 decimal places, giving us 0.777 as the final answer.

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If a fisheries biologist is stocking fish in a lake. She knows that when there are n fish per unit of water. The value of n that will maximize the total fish weight per unit of water is 125 fish . The weight is 31,250g.

a. Value of n that will maximize the total fish weight per unit of water?

W(n) = 500 -2n

W=n(500 -2n)

W = 500n -2n

0=500 -4n

n =500/4

n = 125 fish

b. Weight

Weight = Number of fish/ Average weight of fish

Weight = 125 × (500/2)

Weight = 125 × 250

Weight = 31,250g

Therefore the value of n that will maximize the total fish weight per unit of water is 125 fish . The weight is 31,250.

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On solving the provided question, we can say that the roasting approach, which represents sets as 3, 5, 7, and 8, is one way to write domains

The domain of a function is the set of possible values that it can accept. The x-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. This set is the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.

A set of ordered pairs (x, y), {(3,6),(5,7),(7,7),(8,9)}.

The collection of x values that make up the domain of the function f(x) include,

The roasting approach, which represents sets as 3, 5, 7, and 8, is one way to write domains. Another is the arrow diagram method.

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The approximate percentage of daily phone calls numbering between 46 and 82 is 95%.

The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations.

In this case, the mean is 64 and the standard deviation is 9. Therefore, approximately 68% of the daily phone calls answered by each receptionist fall between 64 - 9 = 55 and 64 + 9 = 73.

Additionally, approximately 95% of the data falls between 64-18 = 46 and 64 + 18 = 82.

So, the approximate percentage of daily phone calls numbering between 46 and 82 is 95%.

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The vertex form of equation is discussed below,

The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants. of the parabola is at (h, k).

As, A parabola has a lowest point if it opens upward.

Additionally, a parabola has a highest point if it opens downward.

The vertex of the parabola is located at this lowest or highest point.

Now, the parent function f(x) = x² has its vertex at the origin.

Also, The vertex form of a quadratic function is

f(x) = a(x – h)² + k, where a, h, and k are constants.

For example, The parent function f(x) = x² is vertically stretched by a

factor of 4/3 and then translated 2 units left and 5 units down.

So, the vertex form : g(x) = 4/3 (x+2)² - 5.

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9,900 codes that are available for reckha.

There are a total of 10,000 possible three-digit codes when each digit is in the set {0,1,2,3,4,5,6,7,8,9}. Since each digit can take 10 different values, we can use the formula 10^3 = 1000 to calculate the total number of codes.

However, since reckha cannot choose a code that is the same as yours or one that is the same as yours except for switching the positions of two digits, we have to subtract these possibilities from the total. We can calculate the number of codes forbidden by subtracting the number of codes with the same digits in all three positions (10) and the number of codes with the same digits but different positions (90) from the total. This leaves us with 10,000 - (10 + 90) = 9,900 codes that are available for reckha.

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The solution to the given exponential equation is 0.791.

What is a logarithm?

The logarithm is the inverse function of exponentiation in mathematics. That is, the exponent to which b must be raised to produce x is the logarithm of a number x to the base b.

Given exponential function is

5x⁻² = 8

Divide both sides by 5:

x⁻² = 8/5

x⁻² = 1.6

Taking logarithm of base x:

[tex]log_x(x^{-2})=log_x1.6[/tex]

-2 [tex]=log_x(1.6)[/tex]

Now applying the logarithm of change of base formula:

-2 = log 1.6/log x

Divide both sides by -2:

1 = log 1.6/( -2log x)

Multiply both sides by log x:

log x = log 1.6/-2

log x = -0.1021

Now applying the formula [tex]log_xa = b[/tex] implies [tex]a = x^b[/tex]:

x = 10^(-0.1021)

x = 0.7905

x = 0.791

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Answer:

I can provide you with a description of the graph.

The graph would have the distance on the y-axis and the time on the x-axis.

The first 60 miles of the journey would be represented by a straight line with a slope of 60/1=60, since the car is traveling at a constant speed of 60 mph.

The point where the first 60 miles ends would be (1,60) which is the time of one hour from London, the distance of 60 miles from London.

After the 30-minute break at the motorway services, the car would continue its journey at a constant speed of 70 mph. This part of the journey would be represented by a straight line with a slope of 70/1=70.

The point where the whole journey ends would be (4,200) which is the time of 4 hours from London, the distance of 200 miles from London.

Please note that it is assumed that the car doesn't stop during the second part of the journey.

Answer:

y-1=2/3(x+9)

Step-by-step explanation:

Sorry cant really explain well but I am positive this is the right answer.