given the missing unit ​

The information provided hows an investment that yields a simple interest.

A simple interest is calculated as follows;

Therefore, Dante's investment after 3 years at the rate of 2% (that is 0.02) would be;

ANSWER:

After 3 years, Dante would have $3,710 in his account

Answer:

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Step-by-step explanation:

Answer:

The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

Step-by-step explanation:

Natural Numbers are known as 1, 2, 3, 4, ..., ∞

Now,

For Cube of first six natural numbers

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Thus, The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

-TheUnknownScientist

To prove that ∠BDA + ∠CDA = 180°, we will use the information given and the properties of quadrilaterals and angles.

Given:

Quadrilateral ABCD

AC = BC

∠ABD = ∠CAD = 30°

∠BAD is compound

To begin the proof, we need to establish some relationships between the angles in the quadrilateral. Since AC = BC, we can conclude that triangle ABC is an isosceles triangle, and therefore, ∠ABC = ∠ACB. Let's denote these angles as α.

Since ∠ABD = ∠CAD = 30°, we can conclude that ∠ADB = ∠CDA = 180° - 30° - 30° = 120°.

Now, let's analyze the compound angle ∠BAD. Since ∠BAD is compound, it can be expressed as ∠BAD = ∠BAC + ∠CAD. We know that ∠BAC = ∠ABC = α. Substituting this information, we have ∠BAD = α + 30°.

Since ∠BDA + ∠BAD = ∠ADB, we can substitute the values we obtained: ∠BDA + (α + 30°) = 120°. Rearranging the equation, we have ∠BDA = 120° - (α + 30°) = 90° - α.

Finally, let's substitute these values into ∠BDA + ∠CDA = 90° - α + ∠CDA. Since ∠ADB = ∠CDA = 120°, we have 90° - α + 120° = 210° - α.

Now, to prove that ∠BDA + ∠CDA = 180°, we need to show that 210° - α = 180°. This can be proven by showing that α = 30°.

Since triangle ABC is isosceles, ∠ABC = ∠ACB = α. Since the sum of the angles in a triangle is 180°, we have α + α + 30° = 180°, which simplifies to 2α + 30° = 180°. Solving for α, we find α = 75°.

Substituting this value back into ∠BDA + ∠CDA = 210° - α, we have 210° - 75° = 135°, which is indeed equal to 180°.

Therefore, we have proven that ∠BDA + ∠CDA = 180°.

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Answer:

The area of the square 45 \(meters^{2}\)

Step-by-step explanation:

Width 3 meters

3x5=15

Length 15 meters

3x15=45

Answer:

45%

Step-by-step explanation:

1,450 - 1,000 = 450

the 450 becomes 0.45

to make 0.45 a percent, we multiply it by 100

0.45 x 100 = 45

45%

The volume of the solid generated when the region bounded by y = 9x and y = 27x/x is revolved around the x-axis is given by V = 27lnx - 9x + c

To calculate this volume, we need to calculate the area of the cross-section of a shell at x.

The cross-section is found by taking the difference of the two curves, y = 9x and y = 27x/x, at that particular x in the form of a rectangle.

The height of the rectangle is y₂ - y₁ and the width is the interval dx. Therefore, the area of the cross-section is given by

A(x) = (y₂ - y₁)dx = [(27x/x - 9x)dx].

The volume of the solid is then given by the formula

=> V = ∫A(x)dx.

Substituting in the expression for A(x), we have

=>  V = ∫(27x/x - 9x)dx.

Integrating this expression, we get V = 27lnx - 9x + c, where c is an arbitrary constant.

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Answer:

(x + 5)(x + 12) = 0

What are the solutions?

x = -12 or -5

Step-by-step explanation:

Hope it helps! :D

Answer:

(x + 5)(x + 12) = 0

and

x = -12 or -5

Step-by-step explanation:

Answer:  B) \(+\infty\)

=================================================

Explanation:

As x goes to positive infinity, we're moving forever to the right.

If we have a point on the curve, then the point will move to the right and it will also move upward forever.

So as \(x \to \infty\) we have \(y \to \infty\)

Because y = f(x), this is the same as saying \(f(x) \to \infty\)

The notation \(+\infty\) is the same as \(\infty\)

In terms of words, we can say "the curve rises to the right" to describe the end behavior on the right.

Answer: Hence the ratio will be 2 : 30, and then divide both sides by 2 to get 1 : 15 as the ratio in its simplest terms.

Step-by-step explanation:

By examining the relationships between different traits and methods, we can determine whether a measure is measuring what it is intended to measure, and identify any sources of error or bias in the measurement process.

Multitrait-Multimethod (MTMM) is a statistical technique that is commonly used in psychology and other social sciences to evaluate the validity of measures.

The MTMM correlation matrix is a square matrix that contains the correlations between each combination of traits and methods.

For example, suppose we want to evaluate the validity of a measure of social anxiety. We might use three different methods of measurement: self-report questionnaires, behavioral observation, and physiological measures such as heart rate. We might also measure social anxiety using multiple traits such as shyness, fear of social situations, and self-consciousness.

To arrange the MTMM correlation matrix for this example, we would first identify the traits and methods that we want to examine.

We would then collect data on each measure and calculate the correlations between each combination of traits and methods. We would then arrange these correlations in a square matrix, where the rows and columns represent the traits and methods, respectively.

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Answer:

Answer is in attached image

I hope it help...

The integral is equal to zero, since the divergence of a constant vector is always zero.

The integral ∫ (∇ × a® ).® is equal to zero. This is due to the fact that the curl of a constant vector is always zero. The vector a® is given to be eˆ eˆ eˆ, therefore it is a constant vector. Since the divergence of a constant vector is always zero, the integral is equal to zero.

To further illustrate this point, we can expand the integral in terms of its components. ∇ × a® is equal to 0 as it is the curl of a constant vector. Similarly, a® .® is equal to 0 since the inner product of two constant vectors is always zero. Therefore, the integral is equal to 0.

The surface defined by the paraboloid is not used in this calculation, as the surface does not affect the value of the integral. The surface is used to define the range of the integral, but not to calculate the value of the integral itself.

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The greater principal is there for Account A as $400.

Simple interest can be defined as a type of interest where the rate is applied on the same principal.

Given that,

The interest for Account A is $15.75 and Account B is  $28.

The total time for interest is 21 months.

Rate of interest for Account A is  3% and Account B is 4%.

Now, the time period can be written in years as,

21 months = 21 / 12 years

                  = 7 / 4

Suppose the principal for Account A and Account B is P₁ and P₂ respectively.

The formula for simple interest is given as,

(P × r × t) / 100

Substitute the respective values for both the accounts to get,

For Account A,

15.75 = (P × 3 × 7 / 4) / 100

⇒ P = (1575 × 4) / (3 × 7)

⇒ P = 300

For Account B,

28 = (P × 4 × 7 / 4) / 100

⇒ P = 2800 / 7

⇒ P = 400

Hence, Account B had greater principal.

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The required answer is the current in the second parallel wire is approximately 0.446 A.

we can determine the current in the second wire using Ampere's law. Here's a step-by-step explanation:

1. A vertical straight wire carries an upward 29-A current.
2. The force per unit length between the two wires is given as 8.3×10^-4 N/m.
3. The distance between the two parallel wires is 5.5 cm, which is equal to 0.055 m.
The attractive force per unit length of 8.3×10−4 n/m is exerted by the first vertical wire, which carries an upward 29-aa current, on the second parallel wire located 5.5 cm away.
We'll use Ampere's law to find the current in the second wire. The formula for the force per unit length between two parallel wires is:
F/L = (μ₀ × I₁ × I₂) / (2π × d)

where F is the force, L is the length of the wires, μ₀ is the permeability of free space (4π × 10^-7 T·m/A), I₁ and I₂ are the currents in the wires, and d is the distance between the wires.
Rearranging the formula to find I₂, we get:
I₂ = (2π × d × F/L) / (μ₀ × I₁)
Now, plug in the given values:
I₂ = (2π × 0.055 × 8.3 × 10^-4) / (4π × 10^-7 × 29)
I₂ ≈ 0.446 A

So, the current in the second parallel wire is approximately 0.446 A.

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The solutions to the given algebraic expressions are;

1) 3x + 4 = 7x - 8; Letter C

2) 2x = 7x - 5; Letter E

3) 5x - 8 = 5x + 12; Letter D

1) We are given the algebraic expression as;

3x + 4 = 7x - 8

Add 8 to both sides to get;

3x + 12 = 7x

Subtract 3x from both sides to get;

12 = 4x

divide both sides by 4 to get;

x = 3

2) 2x = 7x - 5

Add 5 to both sides to get;

2x + 5 = 7x

Subtract 2x from both sides to get;

5x = 5

divide both sides by 5 to get;

x = 1

3) 5x - 8 = 5x + 12

Subtract 5x from both sides gives;

-8 = 12

Thus, no solution

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The magnitude of the projection of f1 onto the line of action of f2 is 5.55.

The magnitude of the projection of f1 onto the line of action of f2 can be calculated using the dot product of the two vectors. The dot product is given by the formula:

f1 • f2 = |f1| |f2| cos θ

Where f1 • f2 is the dot product of f1 and f2, |f1| and |f2| are the magnitudes of f1 and f2 respectively, and θ is the angle between the two vectors.

To find the magnitude of the projection, we need to find the dot product of f1 and f2 and divide it by the magnitude of f2. The magnitude of the projection is given by:

Magnitude of the projection = (f1 • f2) / |f2|

Let's calculate it step by step:

Step 1: Calculate the dot product of f1 and f2:
f1 • f2 = (3.8 * 9.3) + (6.3 * 3.0) = 35.34 + 18.9 = 54.24

Step 2: Calculate the magnitude of f2:
|f2| = √(9.3^2 + 3.0^2) = √(86.49 + 9) = √95.49 = 9.772

Step 3: Calculate the magnitude of the projection:
Magnitude of the projection = (f1 • f2) / |f2| = 54.24 / 9.772 = 5.55

Therefore, the magnitude of the projection of f1 onto the line of action of f2 is 5.55.

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Answer: 5h+4=A

Step-by-step explanation:

She gets five dollars an hour so for one hour she gets five dollars, for two hours she gets 2 times 5 dollars (10 dollars), for three hours she gets 3 times 5 dollars (15 dollars) etc...

Now replace the 1,2,3... with the variable representing the hour. In this case it would be h. So 5h=five dollars per hour. Because you only put the kid to bed once, you add four at the end

Answer:

DSSD

Step-by-step explanation:

Hello there! :)

If Mark has 4 times as many songs as Chloe, then it means that we must take the amount of songs Mark has and divide it by 4 to figure out how many songs Chloe has.

440:4=110 songs

So Chloe has 110 songs.

If Cici has 42 pairs of shoes, and Aubree has half of 42, then it means that in order to figure out how many pairs of shoes Aubree has, we must take 42 and divide it by 2. So Aubree has 21 pairs of shoes.

Tito walked 3 more miles than Danielle. Danielle walked 2 miles.

3+2=5 miles

Tito walked 5 miles.

Hope this helps and good luck! :)

\(GraceRosalia\)

Answer:  first problem 3rd choice  The graph shifts vertically up 5 units

11.) the y intercept is  -5

19.)  f(-8) = -18

last item  third choice  All real numbers such that  are ≥ 0 and ≤ 40

Step-by-step explanation:

19.)  f(x)=2(-8 -3) + 4

              2 (-11)  + 4

                -22 + 4

        f(-8) = -18

The evaluation of the given expressions involving complex numbers is as follows: (a) addition: (a+jb)+(c+jd)= (a+c) + j(b+d), (b) subtraction: (a+jb)-(c+jd)= (a-c) + j(b-d), (c) multiplication: (a+jb)(c+jd)= (ac-bd) + j(ad+bc), (d) division: (1+j)/(1-j)= -j, (e) real part of (a+jb)= a, (f) imaginary part of (a+jb)= b, (g) conjugate: (a+jb)*= a-jb, (h) magnitude: |a+jb|= \(\sqrt{ (a^2+b^2)}\), (i) angle: arg(a+jb)= atan(b/a).

(a) Addition: When adding two complex numbers, you combine the real parts and the imaginary parts separately. So, (a+jb)+(c+jd) simplifies to (a+c) + j(b+d).(b) Subtraction: Similarly, when subtracting two complex numbers, you subtract the real parts and the imaginary parts separately. Therefore, (a+jb)-(c+jd) simplifies to (a-c) + j(b-d).(c) Multiplication: To multiply two complex numbers, you can use the distributive property. So, (a+jb)(c+jd) expands to (ac-bd) + j(ad+bc).

(d) Division: To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. Here, (1+j)/(1-j) can be simplified by multiplying both the numerator and denominator by (1+j). The result is -j.(e) Real Part: The real part of a complex number (a+jb) is simply a.(f) Imaginary Part: The imaginary part of a complex number (a+jb) is b.(g) Conjugate: The conjugate of a complex number (a+jb) is obtained by changing the sign of the imaginary part. So, (a+jb)* becomes (a-jb).(h) Magnitude: The magnitude (or absolute value) of a complex number (a+jb) is calculated using the formula |a+jb| =\(\sqrt{(a^2+b^2)}\).(i) Angle: The angle (or argument) of a complex number (a+jb) is given by arg(a+jb) = atan(b/a), where atan represents the inverse tangent function.

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The cylinder express r in terms of V and H as:\(r = \sqrt{v/(\pi h)}\) in volume.

What is volume ?

Volume is the amount of space that an object or substance occupies in three-dimensional space. It is a physical quantity that is usually measured in cubic units, such as cubic meters or cubic feet.

For example, the volume of a rectangular box can be calculated by multiplying its length, width, and height. The volume of a sphere can be calculated using the formula \((4/3)\pi r^3\), where r is the radius of the sphere. The volume of a cylinder can be calculated using the formula \(\pi r^2h,\) where r is the radius of the circular base and h is the height of the cylinder.

According to the question:
To express r in terms of V and H, we can rearrange the formula for the volume of a cylinder as follows:

\(v = \pi r^2h\)

Dividing both sides by πh, we get:

\(r^2 = v/(\pi h)\)

Taking the square root of both sides, we get:

\(r = \sqrt{v/(\pi h)}\)

Therefore, r is expressed in terms of V and H as:

\(r = \sqrt{v/(\pi h)}\)

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Answer:

100%

Step-by-step explanation:

The formula to calculate the return on investment is:

ROI=(Net Profit/Total Investment)*100

Net profit=Revenues-expenses=500-(500*0.6)=500-300=200

Total investment=250-(250*0.2)=250-50=200

Now, you can replace the values:

ROI= (200/200)*100

ROI= 100%

According to this, the answer is that If Angelo Company can reduce its capital investment by 20% in Adams Company, return on investment will be 100%.

Answer:

Step-by-step explanation:

You just have to distribute all the equations. Start with the parenthesis. I'll do one for you. 2(x-5) +7 = x+8. Distribute 2(x-5) and you gest 2x-10+7=x+8. subtract x from the right and you get x-10+7=8. Combine like terms so you get x-3=8. Then add 3 on both sides and you get x=11.

The correct graph of the ellipse is identified and attached below.

Given the equation is (x₋3)²/16 ₊ (y₋4)²/9 = 1

step 1: identify the center (h,k) of the ellipse in standard form:

(x₋h)²/a² ₊ (y₋k)²/b² = 1

In the standard form of an ellipse, notice that there is a minus sign in front of the h and k.

In our equation  (x₋3)²/16 ₊ (y₋4)²/9 = 1 , we have:

h = 3 and k = 4

Therefore, center (h,k) = (3,4)

Step 2: Identify the orientation by determining the major axis and minor axis in (x₋h)²/a² ₊ (y₋k)²/b² = 1

if a>b, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.

if a<b, the minor axis is horizontal and the major axis is vertical, making the ellipse a vertical ellipse.

For  (x₋3)²/16 ₊ (y₋4)²/9 = 1

a² = 16, a = 4 and b² = 9 , b = 3

so, 4>3, the major axis is horizontal and the minor axis is vertical, making the ellipse a horizontal ellipse.

Step 3:

Plot the co-vertices along the minor axis and the vertices along the main axis (endpoints). No matter which way around, draw points a horizontal distance of a to the left and right from the center and points b above and below the center.

Therefore the vertices are marked along the major axis.

vertices are (3,7) and (3,1)

and co vertices are marked along the minor axis

co vertices are (₋1,4 ) and (7,4)

step 4: connect the vertices and co vertices making a smooth horizontal ellipse.

Hence a horizontal ellipse is made.

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The smaller number is -17, and the quadratic equation that can be used to find it is\(x^2 + x - 272 = 0.\)

The correct answer would be \(x^2 + x - 272 = 0.\)

To find the quadratic equation that can be used to find the smaller number, we can set up the equation using the given information. Let's assume that the smaller number is x.

Since the product of two consecutive integers is 272, we can express this as an equation: x(x + 1) = 272.

Expanding the equation, we have:

\(x^2 + x = 272.\)

To find the quadratic equation, we need to rearrange the equation in the standard form, which is\(ax^2 + bx + c = 0\). In this case, we have:

\(x^2 + x - 272 = 0.\)

Therefore, the correct quadratic equation that can be used to find the smaller number is\(x^2 + x - 272 = 0.\)

This equation can be solved by factoring, completing the square, or using the quadratic formula. Factoring may not be straightforward in this case since 272 does not have obvious factors, so let's use the quadratic formula to find the solutions.

The quadratic formula states that for an equation of the form \(ax^2 + bx + c = 0\), the solutions for x can be found using the formula:

x = (-b ± √\(\sqrt{(b^2 - 4ac)}\)) / (2a).

For the equation\(x^2 + x - 272 = 0,\)we have a = 1, b = 1, and c = -272. Substituting these values into the quadratic formula, we get:

x = (-(1) ± \(\sqrt{((1)^2 - 4(1)(-272))) / (2(1)).}\)

Simplifying further, we have:

x = (-1 ±\(\sqrt{ (1 + 1088)) / 2.}\)

x = (-1 ± \(\sqrt{1089)}\) / 2.

Since we are looking for the smaller number, we take the negative square root:

x = (-1 -\(\sqrt{ 1089}\)) / 2

Calculating the value, we have:

x = (-1 - 33) / 2.

x = -34 / 2.

x = -17.

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Answer:

125.6

Step-by-step explanation:

Circumference = 2 x pi x r (radius)

                         = 2 x 3.14 x 20

                         = 125.6

Answer: 120

Step-by-step explanation: 20x3x2

20x3=60

60x2=120

Answer:

hope this helps:)

Step-by-step explanation:

The two probabilities for events U and V are:

A) P(U and V) = 0

B) P(U or V) =  0.67

We know that if two events A and B are mutually exclusive events, then these two events can't occur at the same time, this means that:

P(A and B) is always zero, and:

P(A or B) = P(A) + P(B)

Here we know the probabilities:

P(U)= 0.38

P(V) = 0.29

Then we can write:

P(U and V) = 0  (by definition)

And:

P(U or V) = P(U) + P(V) = 0.38 + 0.29 = 0.67

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Histograms generally do not reveal the option b. exact data range.

The term "histogram" refers to a visual representation of data points arranged into user-defined ranges. The histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual by taking many data points and organizing them into logical ranges or bins.

The histogram is one of the most popular graphing tools. It is used to present summary summaries of continuous or discrete data that have been interval scaled. The main characteristics of the data distribution are frequently illustrated using it as a practical example.

To create a histogram, the data must be divided into class intervals. Make a tally to show the frequency (or relative frequency) of each interval's data. The frequency in a particular class is divided by the total number of observations to determine the relative frequency.

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