A univerity tudent completed coure were three credit, and ome coure worth four credit. The tudent earned a total of 54 credit after completing 15 coure. How many coure or four credit did the tudent complete?

The value of y0 for which the solution of the initial value problem y' − y = 1 + 3 sin t, y(0) = y0 is:

y(0) = 3√2 - 1 = 3.24

Now, According t o the question:

A linear equation or polynomial, with one or more terms, consisting of the derivatives of the dependent variable with respect to one or more independent variables is known as a linear differential equation.

The general solution y of this equation is y = y0 + y1

where y0  = A[tex]e^t[/tex] is the solution for the equation y' - y = 0 (homogeneous equation), an

  y1 = (3/2)(sint + cost) - 1 = 3√2 sin(t + (π/4)) - 1 -

particular solution of the inhomogeneous equation. Thus, we have

  y(t) =A[tex]e^t[/tex] + 3√2 sin (t + (π/4))  - 1

To have the function y(t) finite for t → ∞ ,

We have to put  A = 0. Then, it follows

y(0) = 3√2 - 1 = 3.24

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The probability that all five of the children get the disease is 0.012.

The probability of a single child getting the disease from the mother is 0.41. The probability that all five children will get the disease from their mother can be found by multiplying the probability of each child getting the disease. So, the probability that all five of the children get the disease is

= 0.41 * 5

= 0.41 * 0.41 * 0.41 * 0.41 * 0.41

= 0.012.

= 1.2%

This means that there is a 0.012, or 1.2%, chance that all five of the children will get the disease from their mother.

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If the dot indicates the center of the circle, the equation that must be true is

The diameter of the semicircle is shown by line segment bearing the dot at the center.

By drawing a line from each end of the diameter to any location on the semicircle, the inscribed angle is created anywhere you perform this is a 90-degree angle will result.

This mean that angle B = angle A = 90 degrees

hence there addition is 180 degrees

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Answer:

9 hours

Step-by-step explanation:

The time taken is inversely proportional to the number of men; if M = number of men and D = number of days this can be expressed as
[tex]D \displaystyle \propto } \dfrac{1}{M}\\\\\text{which can be expressed as an equation: }\\\\D = k \cdot \dfrac{1}{M}\\\\or\\\\D = \dfrac{k}{M}\\\\[/tex]

k is known as the constant of proportionality which can be expressed as

[tex]k = D\cdot M[/tex]

Inversely proportional means:
As the number of men increases, the time taken decreases

As the number of men decreases, the time taken  increases

We can find k from the given information with M = 3 and D = 6 hours

[tex]k = 6 \cdot 3 = 18[/tex]

[tex]\textrm{Therefore, given M= 2, D = $\dfrac{18}{2} = 9$ \;hours}[/tex]

For 2 men it will take 9 hours to repair the road

If Term I Week 1 5. A fruit shop bought 500 kg of apples for R900 and sold them for R2,80 per kg.

a)  The profit per kilogram is R1 per kilogram

b) The profit as a percentage of the cost price is 55.56%

c)  The profit as a percentage of the selling price is 35.71%

a) Selling price

Selling price for 500 kg of apples = 500 * 2.80

Selling price for 500 kg of apples = R1400

Profit per kilogram = R1400 - R900 = R500 / 500 kg

Profit per kilogram = R1 per kilogram

b) The profit as a percentage of the cost price:

= R500 / R900 * 100

= 55.56%

c) The profit as a percentage of the selling price:

= R500 / R1400 * 100

= 35.71%

Therefore the profit per kilogram is R1 per kilogram.

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Using interquartile ranges.

Interquartile range (IQR) indicates the middle half range of the data set. You can use IQR to create "fences" around your data and define outliers as values outside those fences.

This method is useful when you have some values on either end of your dataset, but you are not sure whether any of them should be considered outliers.

Outliers are data that deviate too far from other data in a data set (outlier). The existence of these data outliers will make the analysis of a series of data biased, or not reflect the actual phenomenon. The term outliers is also often associated with extreme values, both large extremes and small extremes.

As an illustration, if there are four students, the first student has a monthly allowance of Rp. 500 thousand, second students Rp. 600 thousand, third student Rp. 700 thousand, and the fourth student because he is the son of a rich man (sultan), has a monthly allowance of up to Rp. 5 million. At a glance it appears that the value of 5 million is relatively far compared to the pocket money of the other three students.

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The given function is a radical expression with a coefficient of -3, a radicand of x-5, and a constant of 1.

A function is a process or set of instructions that takes inputs, performs a specific task, and produces an output. Functions are key components of programming languages, allowing the coder to create complex commands with simple instructions. For example, a function can be used to add two numbers together or to generate a random number. Functions can also be combined to create more complex sequences of instructions.


This function can be graphed on a coordinate plane by plotting the points that satisfy the equation. The graph of the given function will look like a parabola that is shifted up 1 unit and shifted left 5 units. It can also be seen that this function has been vertically stretched by a factor of 3.

To transform this function, we can use the same rules that apply to linear functions. For example, we can shift the graph up 3 units by adding 3 to the constant of 1, making the new equation f(x) = -3√x-5+4. We can also shift the graph down 5 units by subtracting 5 from the radicand, making the new equation f(x) = -3√x-10+1. Additionally, we can shift the graph left 2 units by subtracting 2 from the radicand, making the new equation f(x) = -3√x-7+1. Finally, we can shift the graph right 4 units by adding 4 to the radicand, making the new equation f(x) = -3√x-1+1.

Overall, by applying the same transformation rules that apply to linear functions, it is possible to transform the given radical expression. The transformation will result in a graph that is shifted up or down, left or right, and vertically stretched or compressed.

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The value of y when x=4 is 24. However, the given value of y is 22, so the answer is incorrect

The given equation is written in slope-intercept form as y=6x. This is a linear equation where 'y' is a function of 'x', and the slope is 6.

To calculate the value of y when x=4, first substitute the value of x in the given equation.

y = 6x

 = 6 x 4

 = 24

Therefore, the value of y when x=4 is 24. However, the given value of y is 22, so the answer is incorrect.

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a) The pattern we noticed in the sequence is; A geometric sequence

b) The value of 3⁻¹ which is the fourth term is; 1/3

c) The value of 3⁻² which is the fifth term is; 1/9

The general formula for the nth term of a geometric progression is;

aₙ = arⁿ⁻¹

where;

a is first term

r is common ratio

We are given the sequence as;

3², 3¹, 3⁰,____

Thus;

First term a = 9

Common ratio; r = 3/9

r = 1/3

b) Thus; 3⁻¹ will be the 4th term and as such will be;

3⁰ * 1/3 = 1/3

c) Similarly, The fifth term is 3⁻² expressed as;

1/3 * 1/3 = 1/9

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The value of (16^x)/(2^y) if 4x-y=12 is 4096.

Therefore the answer is 4096.

We are given the equation 4x - y = 12. To find the value of (16^x)/(2^y), we need to find the values of x and y. To do this, we can isolate either x or y and solve for it:

4x - y = 12

y = 4x - 12

We can substitute the expression for y into the expression for (16^x)/(2^y) to find the value:

(16^x)/(2^y) = (16^x)/(2^(4x - 12)) = (16^x)/(2^(4x)) * (2^12)

Note that 2^4 = 16, so (16^x)/(2^4x) = 1, which means that (16^x)/(2^y) =2^12.

Therefore, the value of (16^x)/(2^y) is 4096.

--The question is incomplete, answering to the question below--

"If 4x-y=12, then what is the value of (16^x)/(2^y) "

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The hypotenuse is 5 of a right triangle with legs of length3 and4

The Pythagoras theorem goes as follows:

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

a²+b²=c²

'A' and 'B' are the other two legs, and '=' is the hypotenuse of the right triangle. As a result, the Pythagoras equation can be used for any triangle that has one angle that is exactly 90 degrees to create a Pythagoras triangle.

Here: a=3,b=4

32+42=c²

9+16=c²

25=c²

=√25=5

So, the hypotenuse is 5

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Notice that points ( i ), ., (vi) are approaching x=1 from the right and points

(vii), ., (xi) are approaching from the left.

The closer is a point Q to x=1, the closer is the slope of the line PQ to the slope of the tangent at x=1.

For this articular function you can treat a pair like (xi),(vi) as an upper and lower

bound on the slope of the tangent.

If you can find a pair (something like Q1=0.999, Q2=1.001) so close to x=1 that the two secant lines PQ1 and PQ2 have identical slopes within two decimal places, then you have your estimate.

The exact value of the slope at x=1 is -14π.

The thing about this function is that it alternates between up and down extremely quickly.

If I could attach a graph I would; I would recommend that you look at it in some graphing tool.

Just imagine what is happening around x=1:

The argument of sin is 14π, making the value of the function 0.

If you keep increasing x beyond 1, the argument of sin gets smaller;

when the argument of sin gets to 13.5π the value of the function reaches -1

and the direction of the slope reverses.

That means that to get any meaningful estimate of the slope you need x

such that 14π/x is in the interval (13.5π, 14.5π).

That means x must be in the interval (0.97, 1.03).

And you probably need to try values even closer to 1 to get accuracy to 2 decimal digits.

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1. Factor out the greatest common factor (GCF) from the coefficients.

2. Split the middle coefficient into two factors that add to the middle coefficient and multiply to the last coefficient.

1. First, identify the GCF of the coefficients, which is 1. Since there is no GCF, this step can be skipped.

2. Next, split the middle coefficient (17) into two factors that add to the middle coefficient and multiply to the last coefficient.

Since 17 = 8 + 9, we can use 8 and 9 as our two factors.

3. Group the terms by the common factors.

We can group the first and last term together (6x2 + 5) and the middle term separately (17x).

4. Factor out the common factor, which is x, from the first and last group. This gives us x(6x + 5).

5. Lastly, factor the remaining quadratic expression (6x + 5).

Since 8 and 9 are the two numbers that add to the middle coefficient and multiply to the last coefficient, we can use them as our two factors. This gives us (6x + 8)(x + 9).

Therefore, the factored form of 6x2 + 17x + 5 is x(6x + 8)(x + 9).

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volume= 127.31

if base side is 7 and height is 6

Answer: 14

Step-by-step explanation:

Volume = 1/3 x 7 x 6

Volume = 1/3 x 42

Volume = 14

You will see what the calculator thinks you entered (which may be a little different to what you typed), and then a step-by-step solution. There can be more than one way to find a solution.

What is meant by solution?

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The effect of changing from a 90% confidence interval estimate for a population proportion to a 99% confidence interval for a population proportion is an increase in the interval size by 57%.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence.

When you increase the level of confidence, for example from 90% to 99%, you increase the width of the confidence interval.

The reason for this is that a higher level of confidence requires a wider range of values to ensure that the true population proportion is included within the interval with the specified level of confidence.

This increase in interval size allows us to be more certain that the true population proportion is included within the interval, but also makes the interval less precise in terms of estimating the population proportion.

Answer choice (C) is correct. An increase in the confidence level from 90% to 99% results in an increase in the interval size by approximately 57%.

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The sample standard deviation between two of the given independent sets is 15.3.

A standard deviation can be defined as the amount of variation or difference between a given set of values. If we have a low standard deviation, it means that the values are closer to the mean of the data set. A higher standard deviation just means that the opposite - the values are far off in the range.

Given data items 84, 85, 83, 63, 61, 100, 98,

Number of data items, N = 7,

Let x represent the data item. The Mean of the data points can be calculated using the -

= 84+ 85+ 83+ 63+ 61+ 100+ 98 / 7

= 82

Hence, the sample standard deviation would be -

= [tex]\sqrt{\frac{x}{y} }[/tex]   where x = Σ(x₁ - μ)² and y = N

= 15.3

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The solution is Option B.

The system of equations is solved and the value of x and y is ( 3 , 7 )

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.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

-2x + 3y = 15   be equation (1)

Let the first equation be represented as B

Now , the value of B is

x + y = 10   be equation (2)

On simplifying the equation , we get

Subtracting y on both sides of the equation , we get

x = 10 - y   be equation (3)

Substituting the value of x from equation (3) in equation (2) , we get

-2 ( 10 - y ) + 3y = 15

On simplifying the equation , we get

-20 + 2y + 3y = 15

Adding 20 on both sides of the equation , we get

5y = 35

Divide by 5 on both sides of the equation , we get

y = 7

Substitute the value of y in equation (3) , we get

x = 10 - 7

x = 3

Hence , the value of x and y is 3 and 7 respectively

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Answer:

Option B: (3, 7)

Step-by-step explanation:

i took the test xx

The fencing around the perimeter of semicircular statuary garden of diameter 21 feet will altogether cost $300

given that the diameter of the garden is 21 feet

cost per linear foot is  $9.50

perimeter of semicircle = [tex]\pi r[/tex]

hence the perimeter of the garden will be  [tex]3.14*\frac{21}{2}[/tex]

which is equal to 32.97 feet

now since the cost of fencing per linear foot is $9.50

the cost of fencing the perimeter will be [tex]32.97*9.50[/tex]

i.e $313.215≈  $300

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Answer:-3, -1/2

Step-by-step explanation:

bro this was tough for me i f u kin hate algebra but yeah theres your answer my guy

Steel: σs = p/A_s; Brass: σb = p/A_b; Copper: σc = p/A_c , where A_s, A_b, A_c are the areas of the steel, brass, and copper, respectively.

To calculate the tensile stresses in the steel, brass, and copper due to the force p, we use the formula: σ = p/A, where σ is the tensile stress and A is the area of the material. For the steel, the area is A_s, so the tensile stress σs is equal to p divided by A_s. For the brass, the area is A_b, so the tensile stress σb is equal to p divided by A_b. Finally, for the copper, the area is A_c, so the tensile stress σc is equal to p divided by A_c. Therefore, the tensile stresses in the steel, brass, and copper due to the force p can be calculated using the formula σ = p/A, where A is the area of the material.

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The correct option for the given question of the vector is none of these.

Physical values may be represented mathematically using vectors, which have both magnitude and direction. They are helpful for resolving issues in physics, engineering, and many other disciplines. They are frequently depicted as directed line segments or arrows. The addition, subtraction, and scaling of vectors make it simple and flexible to express physical quantities and carry out mathematical operations. They are crucial for characterizing geometric objects and carrying out spatial transformations.

According to the question

The vector projection of a vector u onto a vector v is given by:

proj_v u = (u . v) / ||v||^2 * v

where (u . v) is the dot product of vectors u and v, and ||v|| is the magnitude of vector v.

For the vectors u = i + 2j + 3k and v = 3i - j + 2k, the projection of u onto v is:

proj_v u = (u . v) / ||v||^2 * v = ((i + 2j + 3k) . (3i - j + 2k)) / ||3i - j + 2k||^2 * (3i - j + 2k) = (15 + 4 - 3) / 14 * (3i - j + 2k) = 16 / 14 * (3i - j + 2k) = (8/7) * (3i - j + 2k) = 8/7 * 3i - 8/7 * j + 8/7 * 2k = 8/7 * i + 2/7 * j + 16/7 * k

Therefore, the vector projection proj_v u of u onto v is:

proj_v u = 8/7 i + 2/7 j + 16/7 k

The "None of the above", option is correct.

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They need to ride "x = 20 - (hours a first day + hours second day)" on the third day to make their goal of biking a total of 20 hours in the park.

Let's call the number of hours Rebecca and Dan rode on the third day "x".

Then, the total number of hours they rode in the park is given by:

total hours = hours first day + hours second day + x

And, we know that their goal is to bike a total of 20 hours in the park, so we can set the equation equal to 20:

total hours = hours first day + hours second day + x = 20

We can substitute in the values for hours first day and hours second day:

20 = hours first day + hours second day + x

So, to find the number of hours they need to ride on the third day to reach their goal, we just need to solve for x:

x = 20 - (hours first day + hours second day)

We would need to know the values for hours first day and hours second day to find the exact value of x.

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The answer will that the point 0.22 is located in between 0 and 1 in the number line.

A number line is a representation of numerical data that has been plotted along a straight line, either horizontally or vertically. Writing the numbers down on a number line makes it straightforward to compare the numbers and perform basic arithmetic operations on them. Zero is frequently used to denote the beginning of a number line (0).

While the numbers directly to the right of zero are all positive, those directly to the left of zero are all negative. We can therefore claim that on a number line, the value of numbers increases as we move to the right. According to this assertion, the numbers on the right are consequently larger than the ones on the left.

Before we begin, keep in mind that a number line is a line with a zero in the middle, increasing positive numbers to the right of the zero, and decreasing negative numbers to the left of the zero. Since the line is infinitely long, it is impossible to display the entire line; however, we will show where the value 0.22 is situated on the line.

Hence the answer will that point 0.22 is located between 0 and 1.

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Answer:

Below

Step-by-step explanation:

See image

By applying the definite integral concept, it can be concluded that ∫₀¹²⁰ r(t) dt represents the number of gallons of oil that leaked from the tank in the first two hours.

Integral is a form of continuous addition that is the inverse of the derivative (anti-derivative)

Definite integral is an integral form in which the integration variables have limits (upper and lower limits) written at the top and bottom of the integral notation.

If y = f(x) is continuous on the interval a ≤ x ≤ b, where a is the lower limit and b is the upper limit, then:

∫ₐᵇ f(x) dx = F(x) |ₐᵇ

               = F(b) - F(a) , where

F(x) = anti-derivative of f(x) on the interval a ≤ x ≤ b

In everyday life, integrals can be used to calculate the volume of a container when the flow rate is known.

r(t) = V'(t) , where:

r(t) = flow rate

V'(t) = anti-derivative of volume

We have a function ∫₀¹²⁰ r(t) dt where r(t) is the oil leaks rate.

As we know that r(t) = V'(t), we can substitute this into the function:

∫₀¹²⁰ r(t) dt = ∫₀¹²⁰ V'(t) dt

                = V(120) - V(0)

Now we understand that this function represents the change of volume from t = 0 to t = 120 minutes (2 hours).

Or in the other words, this function represents the number of gallons of oil that leaked from the tank in the first two hours.

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Answer:

6(2g+1) (2g-1)

Answer:

6(2g - 1)(2g + 1)

Step-by-step explanation:

24g² - 6 ← factor out the common factor of 6 from both terms

= 6(4g² - 1) ← 4g² - 1 is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

4g² - 1

= (2g)² - 1²

= (2g - 1)(2g + 1)

then

24g² - 6 = 6(2g - 1)(2g + 1) ← in factored form

Therefore, when CD is divided by XX, Is standard form 20

The fixed positive integers are represented by alphabets in roman numerals. I, II, III, IV, V, VI, VII, VIII, IX, and X are roman numerals that stand for the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 respectively

We know that

CD = (D – C)

CD = (500 – 100)

CD = 400

XX = (X + X)

XX = (10 + 10)

XX = 20

CD = 400 and XX = 20 in numbers.

On dividing 400 by 20

Now, 20

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The pair (3, 36) means 3 dozens required 36 cookies

And the unit rate is 12

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

x = dozen

y = cookies

This means that

(3, 36) means 3 dozens required 36 cookies

Using the ordered pair in (a):

The unit rate of the pair (3, 36) is 36/3 = 12.

This means that for every 1 dozen change, there is a corresponding 12 cookies change

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The starting value of the expression is, y = 3.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

The expression is,

⇒ y = 3 × q⁵

Now, For starting value substitute q = 1 in above equation,

⇒ y = 3 × q⁵

⇒ y = 3 × 1⁵

⇒ y = 3 × 1

⇒ y = 3

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The probability that the proportion of students who plan on majoring in a branch of STEM is greater for Ms. Keating than for Ms. Lewis can be found by looking up the z-table. This can be done by finding the standard deviation for the difference between the two proportions, which is calculated by (55-49)/sqrt(25+23). This gives a standard deviation of 0.6.

The probability of the proportion being greater for Ms. Keating can be found by taking the difference between the two proportions (0.06) and subtracting it from 1 (1-0.06). This gives a probability of 0.94, which can be found on the z table as 0.841. This means that the probability of the proportion of students who plan on majoring in a branch of STEM being greater for Ms. Keating than for Ms. Lewis is 0.841.

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