Which of the following is an equation of the line in the graph?

Answer: \(A = 500(1.0125)^{100}\)

Step-by-step explanation:

Compound interest

A = P(1 + r/n)^nt

A is the final amount (what we are solving for)

P is the initial principal balance (P=500)

r is the interest rate as a decimal (r=0.05)

t is the time (25 years)

n is the number of times it is compounded yearly (every three months so n=4)

A = 500(1 + 0.05/4)^4(25)

A = 500(1 + 0.0125)^4(25)

A = 500(1.0125)^4(25)

A = 500(1.0125)^100

Answer:

300 dollars

Step-by-step explanation:

60% of 500

(60/100) * 500 = 300

Given picture is not a graph of inequality y < 6x + 1

In this question, we have been given a graph.

We need to determine whether the picture is a graph for the inequality y < 6x + 1 or not.

We know that the graph of equation y = 6x + 1 is a straight line and we represent a straight line graph by a solid line.

This graph represents a shaded region below dotted line. This means, this is the graph of inequality.

From this graph we can see that x-intercept of the equation is (2, 0) and y-intercept is (0, - 4)

If we find the x and y-intercept of y = 6x + 1 then it would be,

x - intercept = (-1/6 , 0)

y - intercept = (0, 1)

This means, given picture is not a graph of inequality y < 6x + 1

Therefore, given picture is not a graph of inequality y < 6x + 1

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Answer:

i'ts very simple.What fraction of shape c IS shaded? sorry i don't understand

Nick's z -score is -1.833.

According to the given question.

Total points scored by Nick, x = 24

Mean score for the test was, μ = 35

Standard deviation, σ = 6

As, we know that z-score can be caluated by using the formula

z = (x - μ)/σ

Where, x is a score

μ is mean score

σ is standard deviation

z is z-score

Therefore, Nick's z-score is given by

z = (24 - 35)/6

z = -1.833

ence, Nick's z -score is -1.833.

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Answer:

the answer is number 2

Step-by-step explanation:

hope this helps u

Answer:

You can get the answer of 1,2,3,4,5 or 6. Each are 1/6 likely to be rolled.

Step-by-step explanation:

The die has 6 sides. If you were to roll the die 6 times you have the chance to roll the side with 1. The chances of rolling a 1 are 1/6.

Answer:

That is an alternate exterior angle.

Answer:

x = 9 , y =3

Step-by-step explanation:

-3x + y = 0 ---- 1

2x -2y = -12 -----2

By elimination method:

let's first eliminate x

we can do that by making x equal in both equations

multiply equation 1 by 2 ( because 2 is the coefficient of x in equation 2 and remember we want to equate both equations)

multiply equation 2 by -3 ( because -3 is the coefficient of x in equation 2 and remember we want to equate them both)

-3x + y = 0 ×2

2x -2y = -12 ×-3

-6x + 2y = 0 ----3

-6x + 6y = 36 -----4

subtract equation 4 from 3

that will give

0-4y = -36

which is

-4y = -36

divide both sides by coefficient of y which is-4

(-4y) ÷ (-4) = (-36)÷(-4)

answer : y= 9

substitute 9 for y in equation 1

-3x + y = 0

-3x + 9 = 0

subtract 9 from both sides

-3x +9-9= 0-9

-3x = -9

divide both sides by coefficient of x which is-3

(-3x)÷(-3) = (-9÷-3)

x = 3

Answer:

Kenny found 80% of the eggs.

Step-by-step explanation:

(4 ÷ 5) × 100 = x

0.8 × 100 = x

80% = x

Kenny found 80% of the eggs.

Probability of random variables

a) P[2Y < 1.9] = 0.475.

b) P[Y(n) < 1.9] ≈ 0.999999999999973

a) Since Y follows a Uniform(0, 2) distribution, we know that its density function is f(y) = 1/2 for 0 <= y <= 2. Therefore, we have:

P[2Y < 1.9] = P[Y < 0.95]

= \(\int^{0.95}_0 (1/2)dy + \int^{2}_{1.9/2} (1/2)dy\)= (0.5)(0.95-0) + (0.5)(0-0.05/2)

= 0.475

Therefore, P[2Y < 1.9] = 0.475.

b) Since the Y's are independent, we have:

P[min(Y1, Y2, ..., Y100) < 1.9] = 1 - P[Y1 >= 1.9, Y2 >= 1.9, ..., Y100 >= 1.9]

\(= 1 - (P[Y > = 1.9])^{100}\\= 1 - ((2-1.9)/2)^{100}\\= 1 - (0.05/2)^{100}\\\)

≈ 0.999999999999973

Therefore, P[Y(n) < 1.9] ≈ 0.999999999999973.

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Answer:

iii) R2

Step-by-step explanation:

Answer:

Super easy, 3360

Step-by-step explanation:

just multiply the total amount by the missing percentage and BOOM you got your answer

0.28 times 12,000 and boom problem solved

now go read a book

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.

To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.

The system of equations is as follows:

Equation 1: -x + y - z = 0

Equation 2: 2x - y = 0

Equation 3: 2x - 3y - 4z = 0

We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.

Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.

Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).

To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.

The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.

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Answer: We can start by using the information given to find the total bill amount.

If the water/sewer/garbage portion of the bill is 72% of the total bill, then the remaining 28% of the bill must be for other utilities. We can use a proportion to set up the equation:

72/100 = 94.41/x

where x is the total bill amount.

We can cross-multiply and solve for x:

72x = 100 * 94.41

x = (100 * 94.41) / 72

x = 123.84

To the nearest cent, the total amount of the utility bill was $123.84.

Step-by-step explanation:

Triangle ABC is congruent to Triangle CDA using the SSS rule.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

SSS rule states that,

If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

To prove:

ΔABC ≅ ΔCDA.

AB = DC ( given)

AD = BC (given)

AC = AC (common to both the triangles)

ΔABC ≅ ΔCDA ( By SSS rule )

Thus,

ΔABC ≅ ΔCDA by SSS rule.

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According to the given statement the total number of ordered pairs is: (2 - 1) * (3 - 1) * (5 - 1) * (7 - 1) * ... * (97 - 1) = 1 * 2 * 4 * 6 * ... * 96 = 2⁴⁹ * 3²⁴* 5⁹* 7⁴ * ... * 97 .

To find the number of ordered pairs (x, y) where both xy and x1y1 are integers, we need to consider the prime factorization of the given expressions.

Let's first analyze xy.

For xy to be an integer, x and y must have a common factor.

Since y < x and x ≤ 100, we can consider all the prime numbers up to 100.

There are 25 prime numbers up to 100.

For each prime number p, we need to find the number of values of y that are less than x and have p as a factor.

For a given prime p, the number of such values of y is equal to p - 1.

So, the total number of values of y for each prime p is (p - 1).

Now, let's consider x1y1. Similar to the previous case, we consider all the prime numbers up to 100.

For each prime p, the number of values of y1 that are less than x1 and have p as a factor is again (p - 1).

Since x and y are positive integers, the total number of ordered pairs (x, y) where both xy and x1y1 are integers is the product of the number of values of y and y1 for each prime p.

The total number of ordered pairs (x, y) is equal to 2⁴⁹ * 3²⁴ * 5⁹ * 7⁴ * ... * 97.

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The moment of inertia for an area is a measure of an object's resistance to rotational forces and is calculated using an integral involving the distance of small area elements from a reference axis.

Moment of inertia for an area, also known as the second moment of area or area moment of inertia, is a fundamental geometric property of a shape that reflects how its mass is distributed relative to a specific reference axis. It plays a crucial role in mechanics, as it is directly related to an object's resistance to bending and torsion.

In mathematical terms, the moment of inertia for an area is calculated using an integral of the form:

I = ∫(y^2 + z^2) dA

Where I represents the moment of inertia, y and z are the distances of a small area element dA from the reference axis (usually the centroid of the shape), and the integral is computed over the entire area of the shape.

The moment of inertia has units of length to the fourth power (L^4), and its value depends on both the shape's geometry and the axis around which it is calculated. For simple shapes like rectangles, circles, and triangles, the moment of inertia can be calculated using standard formulas. However, for more complex shapes, numerical methods like finite element analysis or integral calculus might be required.

In summary, the moment of inertia for an area is a measure of an object's resistance to rotational forces and is calculated using an integral involving the distance of small area elements from a reference axis. It plays a crucial role in mechanics and is essential in understanding an object's behavior under bending and torsion.

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Answer:

\(\boxed {\boxed {\sf D. \ 23.5}}\)

Step-by-step explanation:

The median is the number in the middle of a set of data. To find, we place the numbers in order from least to greatest and pick the middle number.

The data set is:

This is already in order from least to greatest, so we can begin removing numbers from each side of the list until the middle is reached.

Now we have 2 numbers that are in the middle. To find the median, we take the mean or average of these 2 numbers. Add them together, then divide by 2.

The median of this data set is 23.5 and choice D is correct.

Answer:

3rd term of this sequence = 2

5th term of the sequence = -14

Step-by-step explanation:

nth term = 11 - n²

(i) Find the third term of this sequence

When n = 3

nth term = 11 - n²

3rd term = 11 - 3²

= 11 - 9

= 2

3rd term of this sequence = 2

nth term = 11 - n²

Find the fifth term of this sequence.

When n = 5

5th term = 11 - 5²

= 11 - 25

= -14

5th term of the sequence = -14

Answer:

Answer option 2

Step-by-step explanation:

When a shape is rotated counterclockwise by 90°, each point of the shape is moved in a circular motion in the counterclockwise direction by 90° around the fixed point of rotation.

As the triangle is rotated about point O, the position of point O does not change (i.e. it is "fixed").

Line segment OA is horizontal in the original figure. When it is rotated 90° counterclockwise, it becomes vertical, where A is above O.

Line segment BA is vertical in the original figure. When it is rotated 90° counterclockwise, it becomes horizontal, where B is to the left of A.

Therefore, the figure that represents the image after the given rotation is the second answer option.

Answer:

Answer option number two.

No, there is no sufficient evidence to support the claim that the technique performs differently than the traditional method.

It is a statistic used in statistical hypothesis testing. It is typically specified in terms of a test statistic. It is considered as the numerical summary of a data set. It reduces the data to one value and it can be used to perform the hypothesis test. It is a number that is used to describe how much the research results differ from the null hypothesis. It is derived from statistical test and it shows how close our experimental scores matches the distribution. In test statistic, we have null hypothesis and alternative hypothesis.

Given, Population mean, μ = 95 hours

Sample mean,  = 97 hours

Sample size, n = 90

Alpha, α = 0.02

standard deviation, σ =  49hours

We have to use, the null hypothesis and the alternate hypothesis

And we use Two-tailed z test to do this hypothesis,

z=(x-μ)/(σ/√n)

Substituting all the values, we get

z= 97-95/(49/√90)

z=0.3872

z-critical at 0.02 level of significance=-2.0537

There is no sufficient evidence to support the claim that the technique performs differently than the traditional method.

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Answer:

a. 4×2 = 8

b. E = 120

c. F = 400

if radius is 45

V≈1.78×10^5

if radius is 28

V≈1.11×10^5

volume = pi times radius squared times height

if radius is 45

volume = pi times 45 squared times 28

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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p represent the perimeter of the base, assuming that the pentagon is regular we get:

h represents the hight of the prism, which in this case is:

B represents the base area, which in this case is:

The surface area is:

The values of k for which the augmented matrix follows the consistent  linear system are all the real numbers except 2 i.e. R- {2}

The linear equations become consistent when it has unique or infinitely many solutions. We have to find k according to the linear system which is consistent.

Consider the given matrix,

\(\left[\begin{array}{ccc}1&k&-4\\4&8&2\end{array}\right]\)

After dividing R2 by 2,

\(\left[\begin{array}{ccc}1&k&-4\\2&4&1\end{array}\right]\)

Now the linear equations will be,

x+ky = -4

2x+4y = 1

For infinitely many solutions it should be coincident lines so a1/a2=b1/b2=c1/c2 which is not going to happen for any value of k.

Therefore it should follow the condition of a unique solution i.e.

a1/a2\(\neq\)b1/b2

1/2\(\neq\)k/4

k\(\neq\)2

Therefore the value of k other than 2  i.e R-{2} will satisfy the linear equations.

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