What is the remainder when a^3 - 4 is divided by a+2?
a)0
b)-6
c)-2
d)-12

Answer:

3x²

im lazy to solve right now

hope it helps

Answer:

Step-by-step explanation:

half of the circle is 180 degrees

so x + 3x = 180

4x = 180

x = 45

To be sure that a figure is a scaled copy there are some features we need to check:

One of them, is that no matter what, the angles of the figure must conserve the same measure to the original one.

Another one, is that the lengths of the sides of the figure, must conserve the same proportions compared to the original one (this is the scale factor).

And those are the most important features to check to know if a figure is a scaled copy.

I will show you an example:

The rectangle ABCD is a figure. Check if the rectangle EFGH is a scaled copy.

The angles of the rectangle EFGH are equal to the ones of ABCD. Nevertheless, it is necessary to check if they conserve the same proportions.

The ratio of segment AB to segment EF is 1:2. And the ratio of segment BD to segment FH is also 1:2.

The ratio of the segment AB to segment AC is 1:2. The ratio of segment EF to segment EG is also 1:2.

Once we check these feauture, we can be sure that rectangle EFGH is a scaled copy of rectangle ABCD.

Answer:

(55-54)²=1²=1 is your answer

Answer:

your answer will be 1

Step-by-step explanation:

......

93 because 100% of any number is that number

Answer: 93

Step-by-step explanation:

First, put 100% of what = 93 into an equation, when the missing number is x, and 100% is equal to 1:

1x=93

Then, divide each side by 1:

1x/1 = 93/1

Which means you get x = 93

You can also simplify 1x to x and get x=93

I hope this makes sense! :)

Answer:

22

Step-by-step explanation:

I factor out the radicand and get 22

Let's test if my answer is correct!

22 times 22 = 484

So, my answer is correct!

Answer:

Number of Nickels is 12

Number of Dimes is 9

Number of Quarters is 15

Step-by-step explanation:

Given that there are a total of 36 coins, which consists of nickels, dimes, and quarters.

That is, when we sum the numbers of nickels, dimes, and quarters, we have 36.

Let number of nickels be N

Let number of dimes be D

Let number of quarters be Q

Then

N + D + Q = 36 .................................(1)

- There are three fewer quarters than nickels.

This implies that

N = Q - 3 ..............................................(2)

Or

Q = N + 3 .............................................(3)

- There are six more dimes than quarters.

This implies that

Q = D + 6 .............................................(4)

Comparing (3) with (4), we see that

N + 3 = D + 6

N - D = 6 - 3

N - D = 3 ................................................(5)

Using (3) in (1)

N + D + (N + 3) = 36

2N + D = 36 - 3

2N + D = 33 ..........................................(6)

Solving (5) and (6) simultaneously

From (5): D = N - 3

From (6): D = 33 - 2N

=> N - 3 = 33 - 2N

N + 2N = 33 + 3

3N = 36

N = 36/3 = 12..........................................(7)

Using (7) in (6)

2(12) + D = 33

24 + D = 33

D = 33 - 24

D = 9 ........................................................(8)

Using (7) and (8) in (1)

12 + 9 + Q = 36

21 + Q = 36

Q = 36 - 21 = 15.......................................(9)

Therefore,

Number of Nickels, N = 12

Number of Dimes, D = 9

Number of Quarters, Q = 15

The student's claim is incorrect because , ( x + 9 ) ( x - 9 ) = x² - 81 , therefore the right side of the equation does not equal to the left side of the equation

Given data ,

Let the polynomial equation be represented as A

Now , the value of A is

A = ( x + 9 ) ( x - 9 )

On simplifying , we get

A = ( x + 9 ) ( x ) - ( x + 9 ) ( -9 )

A = x² + 9x - 9x - 81

On further simplification , we get

A = x² - 81

Hence , the equation is solved and A = x² - 81

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Bangladesh has 2962 people for each square mile of land in the country this describes Bangladesh's population density.

This describes Bangladesh's population density. Population density is a measure of the number of people per unit of land area, Population density is the concentration of individuals within a species in a specific geographic locale usually expressed as the number of individuals per square mile or square kilometer. In the case of Bangladesh, the average population density is 2962 people per square mile of land. This indicates that Bangladesh has a high population density, as it has a large number of people living in a relatively small area.

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Answer:

1. 1/2 6/10 2/3 4/5

2. 3/10 1/3 1/2 3/5

3. 1/10 1/5 1/3 2/4

Step-by-step explanation:

Hope this helps! :)

The number of independent variables that can be tested in a single experiment depends on various factors, including the research design, resources, and the complexity of the study. In general, it is best to limit the number of independent variables to maintain control over the experiment and facilitate clear interpretation of results.

In simpler experiments, researchers often focus on a single independent variable to study its effect on the dependent variable while controlling for other factors. This allows for a clear cause-and-effect relationship to be established.

However, in more complex experiments, researchers may introduce multiple independent variables to examine their combined effects or interactions. This can provide insights into how different factors influence the outcome simultaneously.

The exact number of independent variables that can be tested in a single experiment varies, but it is generally recommended to keep the number manageable and avoid excessive complexity. This ensures that the experiment remains feasible, interpretable, and effectively addresses the research question or hypothesis.

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Answer:

1/9

Step-by-step explanation:

The vertex form is

y =a(x-h)^2 +k where (h,k) is the vertex

The vertex is (-2,-3)

y =a(x--2)^2 +-3

y =a(x+2)^2 -3

Substitute the point into the equation

-2 = a(-5+2)^2 -3

-2=a(-3)^2-3

Add 3 to each side

-2+3 = a(9)

1 = 9a

1/9 =a

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

The coefficient of the x^2 is 1/9

Answer:

\(\frac{1}{9}\)

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (- 2, - 3) , then

y = a(x + 2)² - 3

To find a substitute (- 5, - 2 ) into the equation

- 2 = a(- 5 + 3)² - 3 ( add 3 to both sides )

1 = a(- 3)² = 9a ( divide both sides by 9 )

\(\frac{1}{9}\) = a

y = \(\frac{1}{9}\) (x + 2)² - 3

The coefficient of the x² term is therefore \(\frac{1}{9}\)

The equation f(x) = L can have at most two solutions for any real number L.

To show that the equation f(x) = L can have at most two solutions for any real number L, we can use the Intermediate Value Theorem and the fact that f"(x) ≠ 0 for all x ∈ R.

Assume that the equation f(x) = L has three distinct solutions, denoted as a, b, and c, where a < b < c.

By the Intermediate Value Theorem, since f is continuous and takes on the values L at a and c, there must exist a point d ∈ (a, c) such that f(d) = L.

Consider the interval [a, d]. Since f is twice differentiable, we can apply Rolle's Theorem. By Rolle's Theorem, there exists at least one point e ∈ (a, d) such that f'(e) = 0.

Now, consider the interval [d, b]. Similarly, there exists at least one point f ∈ (d, b) such that f'(f) = 0.

Since f'(e) = 0 and f'(f) = 0, by the Mean Value Theorem, there exists at least one point g ∈ (e, f) such that f"(g) = 0.

However, this contradicts the given information that f"(x) ≠ 0 for all x ∈ R. Therefore, the assumption that the equation f(x) = L has three distinct solutions is false.

Hence, the equation f(x) = L can have at most two solutions for any real number L.

This shows that the statement is true, and the equation f(x) = L can have at most two solutions for any real number L.

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The radius of table can be 13 inches or 73 inches.

Let r inches be the table's radius.

Make the corner the starting point or origin.

the coordinates for the table's center are as follows: (r, r).

So  \((x-r)^{2} +(y-r)^{2}=r^{2}\)  is the equation for the table's diameter.

The distance between the mark at the table's edge and one wall is 18 inches and 25 inches, respectively. Consequently, this point's coordinates are (18, 25). It might alternatively be (25, 18), but our calculations would not be affected.

Given that the mark is on the edge, it satisfies the criteria established by the table's circumference equation.

\((18-r)^{2} +(25-r)^{2} =x^{2}\)

\(324-36r+r^{2} +625-50r+x^{2} =x^{2}\)

\(r^{2} -86r+949=0\)

(r−13)(r−73)=0

r=13 inches or r=73 inches

As a result, the table's radius can be either 13 inches or 73 inches.

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The surface area of the given shape above would be = 47.2

To determine the surface area of the solid shape above,the surface area of a cone and a cylinder is first determined and then added together.

The formula for the surface area (SA) of cone = πrs + πr²

where;

r = 1

s = 6

S.A = 3.14×1×6 + 3.14×1×1²

= 18.84+3.14

= 21.98

Formula for Surface area of cylinder = 2πr(r+h)

where;

r = 1

h = 3

SA = 2×3.14×1 (1+3)

= 25.12

Therefore, the surface area of the solid shape = 21.98+25.22 = 47.2

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Answer:

6

Step-by-step explanation:

The perimeter of a rectangle with a length of 9x - 4 and a width of (5x + 2) will be 18x - 4.

Let W be the rectangle's width and L its length. The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be given as,

Perimeter of the rectangle = 2(L + W) units

The dimension of the rectangle is given as,

L = 9x - 4
W = 5x + 2

Then the perimeter of the rectangle is given as,

P = 2(L + W)

P = 2(9x - 4 + 5x + 2)

P = 2(14x - 2)

P = 18x - 4

The perimeter of a rectangle with a length of 9x - 4 and a width of (5x + 2) will be 18x - 4.

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Answer:

3a

\( 3a { }^{7} {x}^{7} \)

Step-by-step explanation:

Answer:

x=18

Step-by-step explanation:

First, multiple both sides by reciprocal 3/2.

It will look like this: x=12*3/2

Then, simplify:

x=18

Hope it helped.

Answer:

1/4

Step-by-step explanation:

The step that is included in the graph of the ceiling function is given as follows:

y = -2 for -2 ≤ x ≤ -1.

The ceiling function is represented by the symbol ⌈x⌉ used in this problem, and represents the least integer greater than or equal to x,

For example, we have that:

⌈0 ≤ x < 1⌉ = 1.

In this problem, we have that the function is translated one unit right, hence the correct step is given as follows:

⌈x - 1⌉ = -2 for -2 ≤ x ≤ -1.

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Answer:

c

Step-by-step explanation:

The limit definition of the derivative is written as \(f '(x) &= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\). Here, h is defined as (x₂ – x₁) or ∆x or the change in x.

The limit definition of the derivative is also known as the difference quotient or increment definition of the derivative.  This is a product of the input value difference, (x + h) - x, and the function value difference, f(x + h) - f(x). This can be calculated using the difference quotient formula as follows,

\(\begin{aligned}f '(x) &= \lim_{h \to 0}\;\text{(difference quotient)}\\f '(x) &= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\end{aligned}\).

Here, f(x) represents (y₁), f(x+h) represents (y₂), x represents x₁, x+h represents x₂, h represents (x₂ – x₁) or ∆x or the change in x, Lim represents the slope M as h→0, and f (x+h) – f (x) – represents (y₂ – y₁).

This provides a measurement of the function's average rate of change over an interval. In other words, this provides the current rate of change.

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a) the angular speed in rad/minute is 1382.48 radians/ minute

b) the speed in ft/ min is 1105.98ft/min.

Angular speed is the rate at which an object changes its angles .It is measured in radians/ given time. Angular speed has a magnitude . ω = θ /t.

converting 220 revolution to radians

1 revolution = 360°

180°= π

36

0°= 2π

220 revolutions= 220× 2π=440π

angular speed=220revolution/min= 440×3.142=1382.48rad/min

The speed of a circular motion is given as

v= wr

r = 1.6/2= 0.8ft

v= 1382.48×0.8ft

= 1105.98ft/min

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Answer:

Hey buddy whatsup? All good

Coming to the question fig 1 and 3 aren't functions

Coz.... Reason for fig 1... Every distinct element of domain must have a unique element in codomain, but in this fig the same element has more than two unique elements which is a relation not a function.

Reason for fig 3 every element in domain must have an unique element in codomain but in this fig the element c doesn't have any unique element hence it isn't a function.....

Thank you

Answer:

fig 1 is not function because x-componet (A) has two range

Answer:

40

Step-by-step explanation:

Answer:

40

here is the awnser buddy I hope it's right

Answer:

4.8 Liters

Step-by-step explanation:

Sundaes at her next birthday party. She thinks each person will eat 200 milliliters of ice cream, and there will be 24 people at her party. How many liters of ice cream should she buy

Step 1

1 person = 200ml of ice cream

24 persons = x

Cross Multiply

x = 24 × 200ml of ice cream

x = 4800 ml of ice cream

Step 2

How many liters of ice cream should she buy

We convert from Milliliters to Liters

1 milliliters= 0.001 liters

4800 millilitres = x

Cross Multiply

= 4800 × 0.001 liters

= 4.8 Liters

Therefore, she should buy 4.8 Liters of ice cream

Answer:

-1/7

Step-by-step explanation:

(4-3)/(3-10)=1/-7

1. The implementation that faster is P1 than P2.

2. The global CPI for each implementation are:

Global CPI = (10% x 3) + (30% x 2) + (40% x 1) + (20% x 4) = 1.9

Global CPI = (10% x 2) + (30% x 2) + (40% x 2) + (20% x 2) = 2

3. The clock cycles required in both cases are:

Clock cycles = 1.9 x 1.0E5 = 190,000

Clock cycles = 2 x 1.0E5 = 200,000

P1: 10% x 3 + 30% x 2 + 40% x 1 + 20% x 4 = 1.9 CPI

Execution time P1 = (1.9 x 1.0E5) / 3GHz = 63.33 microseconds.

P2: 10% x 2 + 30% x 2 + 40% x 2 + 20% x 2 = 2 CPI

Execution time P2 = (2 x 1.0E5) / 2.5GHz = 80 microseconds.

Therefore, P1 is faster than P2.

Global CPI = (Percentage of class A instructions x CPI of class A) + (Percentage of class B instructions x CPI of class B) + (Percentage of class C instructions x CPI of class C) + (Percentage of class D instructions x CPI of class D)

For P1:

Global CPI = (10% x 3) + (30% x 2) + (40% x 1) + (20% x 4) = 1.9

For P2:

Global CPI = (10% x 2) + (30% x 2) + (40% x 2) + (20% x 2) = 2

Clock cycles = Global CPI x Instruction count

For P1:

Clock cycles = 1.9 x 1.0E5 = 190,000

For P2:

Clock cycles = 2 x 1.0E5 = 200,000

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Answer:

The answer is A. f(1) = 5

Step-by-step explanation:

If f(x) is a function it can have only one value per x value, so f(1) = 1 cannot be true

Answer:The answer is B. f(2) = 1

Step-by-step explanation:

If f(x) is a function it can have only one value per x value, so f(1) = 1 cannot be true

The median of X is 1;  P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and  the value of q such that P(X < q) = 0.95 is 1.9.

(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.

Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.

For 0 < x < 2, the CDF is:

F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x

Setting (1/2) * x = 0.5 and solving for x:

(1/2) * x = 0.5;  x = 1

Therefore, the median of X is 1.

(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.

For x > 2, the PDF is 0, so P(X > x) = 0.

Therefore, P(X > 2) = 0.

(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.

P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)

Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.

Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.

(d) The variance of X can be calculated using the formula:

Var(X) = E(X²) - [E(X)]²

To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:

E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3

To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:

E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Now we can calculate the variance:

Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33

Therefore, Var(X) is approximately 0.33.

(e) The expected value of X, E(X), is given by:

E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1

Therefore, E(X) is 1.

(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:

∫(0 to q) f(x) dx = 0.95

Since the PDF is constant at 1/2 for 0 < x < 2, we have:

(1/2) * (x) | (0 to q) = 0.95

(1/2) * q = 0.95

q = 0.95 * 2 = 1.9

Therefore, the value of q such that P(X < q) = 0.95 is 1.9.

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Answer:

D. -3 for every 1 to the right, in goes down 3.

E. 0, the graph could represent no change over time.

F.

assume the point on the graph is the origin, you can graph these

(2,-4)

(1,-2)

(0,0)

(-1,2)

(-2,4)

(-3,6)

Step-by-step explanation: