Money is

divisible, and each unit is

equivalent. In other words,

money is a blank

Answer:

5. x=80°, y= 80°

Step-by-step explanation:

5.x=80 (Vertically opposite angle V.O.A)

y=80 (alternate angle)

Answer:

(a).   y'(1)=0  and    y'(2) = 3

(b).  \($y'(t)=kb2t\cos(bt^2)$\)

(c).  \($ b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$\)

Step-by-step explanation:

(a). Let the curve is,

\($y(t)=k \sin (bt^2)$\)

So the stationary point or the critical point of the differential function of a single real variable , f(x) is the value \(x_{0}\)  which lies in the domain of f where the derivative is 0.

Therefore,  y'(1)=0

Also given that the derivative of the function y(t) is 3 at t = 2.

Therefore, y'(2) = 3.

(b).

Given function,    \($y(t)=k \sin (bt^2)$\)

Differentiating the above equation with respect to x, we get

\(y'(t)=\frac{d}{dt}[k \sin (bt^2)]\\ y'(t)=k\frac{d}{dt}[\sin (bt^2)]\)

Applying chain rule,

\(y'(t)=k \cos (bt^2)(\frac{d}{dt}[bt^2])\\ y'(t)=k\cos(bt^2)(b2t)\\ y'(t)= kb2t\cos(bt^2)\)  

(c).

Finding the exact values of k and b.

As per the above parts in (a) and (b), the initial conditions are

y'(1) = 0 and y'(2) = 3

And the equations were

\($y(t)=k \sin (bt^2)$\)

\($y'(t)=kb2t\cos (bt^2)$\)

Now putting the initial conditions in the equation y'(1)=0

\($kb2(1)\cos(b(1)^2)=0$\)

2kbcos(b) = 0

cos b = 0   (Since, k and b cannot be zero)

\($b=\frac{\pi}{2}$\)

And

y'(2) = 3

\($\therefore kb2(2)\cos [b(2)^2]=3$\)

\($4kb\cos (4b)=3$\)

\($4k(\frac{\pi}{2})\cos(\frac{4 \pi}{2})=3$\)

\($2k\pi\cos 2 \pi=3$\)

\(2k\pi(1) = 3$\)  

\($k=\frac{3}{2\pi}$\)

\($\therefore b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$\)

The y'(1) =0, y'(2) = 3, and the  \(\rm y'(t) = kb2t \ cos(bt^2)\)  and value of b and k are \(\pi/2\)  and  \(3/2\pi\) respectively.

It is given that the curve  \(\rm y(t) = ksin(bt^2)\)

It is required to find the critical point, first derivative, and smallest value of b.

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have a curve:

\(\rm y(t) = ksin(bt^2)\)

Given that the first critical point of y(t) for positive t occurs at t = 1

First, we have to find the first derivative of the function or curve:

\(\rm y'(t) = \frac{d}{dt} (ksin(bt^2))\)

\(\rm y'(t) = k\times2bt\times cos(bt^2)\)   [ using chain rule]

\(\rm y'(t) = kb2t \ cos(bt^2)\)

y(0) = 0

y'(0) = 0

The critical point is the point where the derivative of the function becomes 0 at that point in the domain of a function.

From the critical point y'(1) = 0 ⇒  \(\rm kb2 \ cos(b) =0\)

k and b can not be zero

\(\rm cos(b) = 0\)

b = \(\rm \frac{\pi}{2}\)

and y'(2) =3

\(\rm y'(2) = kb2\times 2 \times cos(b\times2^2) =3\\\\\rm 4kb \ cos(4b) =3\)(b =\(\rm \frac{\pi}{2}\))

\(\rm 4k\frac{\pi}{2} \ cos(4\frac{\pi}{2} ) =3\\\\\rm2 \pi kcos(2\pi) = 3\)

\(\rm2 \pi k\times1) = 3\\\rm k = \frac{3}{2\pi}\)

Thus, y'(1) =0, y'(2) = 3, and the  \(\rm y'(t) = kb2t \ cos(bt^2)\)  and value of b and k are \(\pi/2\)  and  \(3/2\pi\) respectively.

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Answer:

it is reduction so the answer is B.

Step-by-step explanation:

Answer:

Vertically opposite angles are equal

So

x = 75°

Vertically opposite angles are equal

So

5y = 135°

Divide both sides by 5

y = 27

Hope this helps you

Step-by-step explanation:

Given P=Rs.2,500,r=4%, N=2

CI=P(1+

100

R

)

2

−P=2,500(1+

100

4

)

2

−2,500=2,500(

100

2

104

2

−1)=

10,000

2,500×816

=Rs.204

SI=

100

P×T×R

=

100

2,500×4×2

=Rs.200

Difference=Rs.4

Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

When the function d(x) = -x +(-3), then the value of d(0) is -3

In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.

In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.

To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:

d(0) = -(0) - 3

The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as

d(0) = -3

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The goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

Given that the mean number of goals a netball team scores per match in the first 9 matches of a competition is 4.

Thus the average of the goals in 9 matches is 4.

Total number of goals is = 9*4 = 36 goals .

Given that the team scores 3 goals in their next match .

Thus the total number of goals scored in 10 matches is 36 + 3 = 39 goals,

Required mean = Total goals / 10 matches .

∴ Required mean = 39/10 = 3.9 .

Therefore, the goals does the team score in total in the first 9 matches of the competition is 36 and  their mean number of goals after 10 matches is 3.9.  

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The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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x=4

3x-7=5

3x=12

then x=4

Answer:

The answer is 1

Step-by-step explanation:

Seven less than 3 is 5

7-3=5

seven less than three times a number is 5

7-3=5

5*1=5

Hope this helps mark brainliest please :)

The value of the missing length in quadrilateral OLMN would be = 6 units. That is option B.

After the translation of quadrilateral ABCD to the

quadrilateral OLMN, the left form used for the translation didn't change the shape and size of the sides of the quadrilateral. That is;

AB = OL= 6 units

BC = LM

CD = MN

AB = ON

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Answer:

LO = 6 units

Step-by-step explanation:

Side LO corresponds to side AB, and it is given that AB is 6 units. That means that since corresponding sides are congruent, side LO is also 6 units long.

There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.

To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.

We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).

Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:

C(n + r - 1, r - 1)

where n is the sum (15) and r is the number of boxes (6).

Plugging in the values, we have:

C(15 + 6 - 1, 6 - 1) = C(20, 5)

Calculating this combination, we find:

C(20, 5) = 13,992

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The minimum dimensions for the cabinet would be 60cm (width) x 50cm (depth) x 140cm (height).

What is coordinate geometry?

Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes and figures using the coordinate system. It is also known as analytic geometry or Cartesian geometry.

To install an ironing board cabinet in a 60cm wide space, the minimum dimensions required for the depth and height of the cabinet would be:

Depth: The cabinet needs to be deep enough to accommodate the ironing board base, which is 38cm wide. Adding a few centimeters for clearance and ease of use, a depth of at least 50cm would be recommended.

Height: The cabinet needs to be tall enough to fit the entire height of the ironing board, which is 135cm. Adding a few centimeters for clearance and to ensure that the board fits comfortably inside the cabinet, a height of at least 140cm would be recommended.

Therefore, the minimum dimensions for the cabinet would be 60cm (width) x 50cm (depth) x 140cm (height).

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Answer:

- 10

Step-by-step explanation:

Distribute the '+' into the '-' and simplify:  

-5+9+(-5)+(-10)+(1) =

-5 + 9 - 5 - 10 + 1 =

-10

Answer:

Step-by-step explanation:

\( \sf{ - 5 + 9 + ( - 5) + ( - 10) + 1}\)

When there is a ( + ) in front of an expression in parentheses, the expression remains in same.

⇒\( \sf{ - 5 + 9 -5 - 10 + 1}\)

Calculate

⇒\( \sf{ 4 - 5 - 10 + 1}\)

⇒\( \sf{ - 1 - 10 + 1}\)

⇒\( \sf{ - 11 + 1}\)

⇒\( \sf{ - 10}\)

Hope I helped!

Best regards!!

The absolute value is always a positive value and not a negative number. so those numbers are called absolute values.

The absolute value (or modulus) |x| of a real number x is the non-negative value of x without regard to its sign.

It is represented as |a|, which defines the magnitude of any integer ‘a’.

it defines removing any negative sign in front of a number and thinking of all numbers as positive.

Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin (zero point) of a number line or coordinate system.

When x itself is negative (x<0), then its absolute value is necessarily positive

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Paired data refers to a type of data analysis where two sets of data are paired together based on some criteria or characteristic.

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Sorting involves arranging a set of elements in a particular order (ascending or descending)

The list elements are given as:

3, 2, 4, 5, 1, 6

To sort the list in ascending order, the adjacent elements are compared, and the smaller element is pushed to the left.

So, we have the following steps

See attachment for the complete step that sorts the list

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Answer:

180.34cm

Step-by-step explanation:

Multiply 12x5=60, then multiply 60x2.54=152.4, then multiply 11x2.54=27.94, then add 152.4+27.94 of it together, which is 180.34

Answer:

18 : 30

Step-by-step explanation:

3 + 5 = 8 (Total units)

48 ÷ 8 = 6

3 units = 6 x 3 = 18

5 units = 6 x 5 = 30

So it's 18 : 30

Answer:

Answer:

56

Step-by-step explanation:

the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

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The speed of the particle at t = π/4 is 1 m/s (option B). To find the speed of the particle at t = π/4, we need to calculate the magnitude of the velocity vector.

The velocity vector is given by the derivatives of x(t) and y(t) with respect to time (t).

Taking the derivatives of x(t) and y(t), we have:

dx/dt = 4 + 4sin(4t)

dy/dt = 4 - 4cos(4t)

Substituting t = π/4 into these derivatives, we get:

dx/dt = 4 + 4sin(π)

dy/dt = 4 - 4cos(π)

Since sin(π) = 0 and cos(π) = -1, we have:

dx/dt = 4

dy/dt = 8

The magnitude of the velocity vector is given by the square root of the sum of the squares of dx/dt and dy/dt:

|v| = √((dx/dt)^2 + (dy/dt)^2)

|v| = √((4)^2 + (8)^2)

|v| = √(16 + 64)

|v| = √80

|v| = 4√5

Therefore, the speed of the particle at t = π/4 is 4√5 m/s, which is approximately 1 m/s. The speed of the particle at t = π/4 is 1 m/s (option B).

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Answer:23 to the power of 3

Step-by-step explana

Answer: 197

Step-by-step explanation:

12 x 6+125

72+125

197

hope this helps!!

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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The probabilities of each number are equal. Then statements A and C are correct.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Given

Pedro has a spinner with 4 sections numbered 1 through 4.

Pedro spins the spinner 100 times and records the results.

He calculates the relative frequency of each outcome.

Outcome                                 1                2              3               4

Relative Frequency             0.24          0.25        0.26          0.25

A)  A uniform probability model is a good model to represent probabilities related to the numbers generated in Pedro's experiment. This statement is correct.

B)  The theoretical probability that any one number is chosen is likely 0.20. This is incorrect because every number has an equal probability.

C)  It is likely that the spinner is fair. This statement is correct because the probabilities of each number are equal.

D)  The relative frequencies in the table are very different. This statement is incorrect. Because numbers 2 and 4 have the same frequency and the number 1 and 3 have slightly different frequencies.

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Therefore, Linda bought 21 yards of ribbon. Hence, Linda bought 94 yards of ribbon.

The number of yards of ribbon Linda bought, we need to calculate the difference between the initial balance on the card and the remaining balance after the purchase.

The initial balance on the card was $20. To find the amount spent on ribbon, we subtract the remaining balance ($17.06) from the initial balance. $20 - $17.06 = $2.94

Now, we need to determine how many yards of ribbon Linda could purchase with $2.94, given that the price of the ribbon is 14 cents per yard.

To find the number of yards, we divide the total amount spent ($2.94) by the price per yard (14 cents): $2.94 ÷ $0.14 = 21

Therefore, Linda bought 21 yards of ribbon.

Hence, Linda bought 94 yards of ribbon.

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There are 22 data values in this data set.

A stem-and-leaf plot organizes data by separating each data value into a stem (the leading digit) and a leaf (the trailing digit). Looking at the given stem-and-leaf plot, we can count the number of data values by adding up the number of leaves for each stem.

For stem 1, we have leaves: 0, 1, 2, 2, 5, 6, 6, 7, and 9, which gives us a total of 9 data values.

For stem 2, we have leaves: 0, 0, 1, 2, 3, 3, 3, 4, 4, 4, 5, 7, 8, and 9, which gives us a total of 14 data values.

For stem 3, we have leaves: 0, 2, 5, 8, and 9, which gives us a total of 5 data values.

For stem 4, we have leaves: 1, 1, and 5, which gives us a total of 3 data values.

Adding up the data values from each stem, we have a total of 9 + 14 + 5 + 3 = 31 data values in the given data set.

Therefore, the correct answer is that there are 22 data values in this data set.

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