Use the formula for continuous compounding to compute the balance in the account after​ 1, 5, and 20 years.​ Also, find the APY for the account.

A $17,000 deposit in an account with an APR of 4.5%

The balance in the account after 1 year is approximately $____

We prooved the paragraph proof of Theorem 3.8 that if two lines are perpendicular to the same line, then they are parallel to each other.

In the given question we have to explain the a paragraph proof of Theorem 3.8.

Let the lines that cross line a be m and n. Let m be parallel to a. As a result, the intersection of m and a produces four 90° angles.

Let n be parallel to a. This indicates that each of the four angles created by the intersection of n and an is 90 degrees.

The same-side internal angles (between lines m and n) are also congruent because all of the angles are congruent. The lines are parallel if two internal angles on the same side are congruent.

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The right question is:

Write a paragraph proof of theorem 3-8: in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

The area of the path is 456 square feet

The formula for determining area of a rectangle is given as;

A = lw

Where;

Now, substitute the values into the formula, we have;

Area of the rectangle  = 40 × 70

Area of the rectangle = 2800 square feet    (1)

Bordered fence with a 4 ft path so dimensions 44 ft by 74 ft

Area of rectangular garden with Path = 44 × 74

= 3256 square feet       (2)

Area of the walk = (2) - (1) = 3256 - 2800 = 456 square feet

Hence, the value is 456 square feet

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Option B, The table does not show a probability distribution.  the sum of all the probabilities is not equal to 1 .

A statistical function called a probability distribution explains the range of values and probabilities that a random variable might have. A statistical function known as a probability distribution explains the possibility of obtaining each potential value that a random variable can have.

The sum of the values is given as 0.001 + 0.008 + 0.034 + 0.057

= 0.1

Due to the fact that this is not a probability distribution.

We must choose the standard deviation as well. There is no probability distribution displayed in the table. These exist because sum = 1, which is not present here, is required for a probability distribution.

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Answer:

11 pizza rolls

6 chicken wings

Answer:

11 pizza Rolls and 6

Step-by-step explanation:

The cost of the car is 500000 and by selling it with an 8% gain he earned 40000.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A car dealer gained 40,000 on a sale which is 8% profit.

Assuming the cost of the car to be x.

∴ (108/100)x - x = 40000.

1.08x - x = 40000.

0.08x = 40000.

x = 40000/0.08.

x = 500000

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Answer:

0.80

Step-by-step explanation:

The hundredth is 2 digits after the decimal.

Rounding 0.799, we want 0.xx

Look at the third digit, 9, meaning we round up.

However, since the second digit after the decimal is also a 9, we can make that a 0 by adding 1 to the first digit after the decimal.

We get 0.80

Answer:

2x - 9

Step-by-step explanation:

x = unknown number

2 * x -9

2x - 9

The amount of paper required to make the model is 94.2 square cm

The given parameters in the question are

Slant height = 7 cm

Diameter = 6 cm

This means that

Radius = Diameter/2 = 6 cm/2

So, we have

Radius = 3 cm

The amount of paper required to make the model is then calculated as

A = πr(r + l)

So, we have

A = 3.14 * 3 * (3 + 7)

Evaluate

A = 94.2

Hence, the amount needed is 94.2 square cm

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The total number of cartons needed more to pack small 15 cartons than 35 large cartons is108 cartons.

Division is defined as one of the four basic operations of arithmetic in mathematics.

The parameters for this question are:

Total number of cartons =2835

Number of small cartons needed = 15 cartons

Number of large cartons needed = 35 cartons

To package the orange juice in large cartons we need [tex]\frac{2835}{35} =81 cartons[/tex]

Also, to package 15 small cartons we need [tex]\frac{2835}{15} =189 cartons[/tex]

Number of more small cartons than large cartons is

Small cartons -large cartons

=189-81=108 more cartons.

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Answer: y=x−2 y = x − 2

Step-by-step explanation:

Answer:

expanded: 7+0.08

standard: 7.08

Step-by-step explanation:

The hundredths place is the second digit after the decimal, so 8 hundredths is 0.08.

Answer:

A trapezoid is isosceles if and only if its diagonals are congruent. So if we can prove that the bases are parallel and the diagonals are congruent, then we know the quadrilateral is an isosceles trapezoid, as Cool Math accurately states.

Step-by-step explanation:

The true statements are

The side length of the transparent cube is given as

Length = 10 millimetres

The volume of the cube is calculated as

Volume = Length³

Substitute the known values in the above equation, so, we have the following representation

Volume =10³

Evaluate

Volume = 1000 cubic millimetres

1000 cubic millimetres and 30 cubic millimetres do not have the same value

So, the co-worker is incorrect.

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Using the graph of the relationship, the missing values are:

x   | y    

2     6

4     12

6     18

Given the graph attached below where:

The graph shows the relationship between the number of gallons (x) and the cost in dollars (y).

For example, if an ordered pair on the graph is (2, 8), it means it would cost $8 for 2 gallons.

Thus, to find the respective values for each missing pair of values, trace the corresponding value on the graph that is given.

The complete table is therefore:

x   | y    

2     6

4     12

6     18

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Answer:

x = 4

y = 1

Step-by-step explanation:

x + 3y = 7 --> Eq1

4x - y = 15 --> Eq2

Find x in term of y using Eq1

x = 7 - 3y

Substitute x in Eq2

4(7-3y) -y = 15

28 - 12y - y = 15

-12y-y = 15 - 28

-13y = -13

y = -13/-13

y = 1

Find x

x = 7-3(1) = 4

If you have to solve for x first

Find y in term of x using Eq 2

y = 4x - 15

Substitute y in Eq 1

x + 3(4x -15) = 7

x + 12x - 45 = 7

x + 12x = 7 + 45

13x = 52

x = 52/13

x = 4

Find y

y = 4(4) -15 = 16 - 15 = 1

Answer:

No.

Step-by-step explanation:

Because the equation has an exponent, it is quadratic, and not linear.

Answer:1

Step-by-step explanation:

The number of nickels and the number of dimes that Joseph has are 12 and 5 respectively.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Let the no. of nickels be N and no. of dimes be D.

∴ N + D = 17...(i) and 0.05N + 0.1D = 1.45...(ii)

Multiplying (ii) by 100 we get 5N + 10D = 145...(iii)

Now multiply (i) by 5 we get 5N + 5D = 85...(iv)

Now subtracting (iv) from (iii) we get,

5D = 60.

D = 12 hence N = 5.

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Answer:

I'm not sure but based on my work I would say option 2.

Hope this helps!

Step-by-step explanation:

Answer:3/2

Step-by-step explanation:

3/8 divided by 1/4 is the same as multiplying 3/8 by 4/1

= 12/8

=3/2

The polynomial that is in standard form is: B. [tex]x^4 - 8x^2 - 16[/tex].

A polynomial that is expressed in standard form is given in such a way that the terms of the expression are written in ordered from from the term with the highest degree, to the term with the lowest degree. The constant comes last in a polynomial that is expressed in standard form.

5 - 2x is not expressed in standard form because it is not properly ordered. The constant needs to come last.

[tex]x^4 - 8x^2 - 16[/tex] is well ordered, therefore, it is a polynomial that is expressed in standard form.

[tex]5x^3 + 4x^4 - 3x + 1[/tex] is not well ordered. It is not in standard form.

The answer is therefore: B. [tex]x^4 - 8x^2 - 16[/tex].

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The inverse function of the function f(x) = 2x - 4 will be x/2 +2.

What is inverse function?

A function that returns the initial value for which a function has produced output is called an inverse function. If f(x) is a function that produces the value y, then f-1(y), which is the inverse function of y, will produce the value x. Inverse and reciprocal functions should not be confused. The output's original value is returned by the function's inverse, which is represented by the symbol f-1 (x). While the reciprocal of a function is represented by 1/f(x) or f(x)-1

Those that do are referred to as invertible. For a function f: X Y to have an inverse, it must possess the characteristic that there is exactly one x in X such that f(x) = y for every y in Y. This characteristic guarantees the existence of a function g: Y X that has the required connection to f.

f(x) = 2x - 4

y = 2x - 4

So x = y +4 /2

x = y/2 +2

Now to get the inverse of the function  put the x value in y

So [tex]f^{-1}[/tex](x) = x/2 +2

Hence, inverse function will be x/2 +2.

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Answer:

4 [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Answer:

The integers could be 8 and 4, just checked with a calculator

Answer:

change 5 weeks to days(5*7)-35days

then convert the days to seconds

35*86400/10*86400

answer 7/2

The transformed equation of  is  y = x³ is y =-1/7(x+8)³

Given that :

The equation of y=x^3 and Vertical compression by a factor of 1/7 ,horizontal shift 8 units to the left, reflection across the x axis

Applying the given transformations, we have:

To have a vertical compression by a factor of 1/7, we need to multiply the function by 1/7. So, we have:

y=1/7x³

We must add 8 to x in order to have a horizontal shift of 8 units to the left. We thus have:

y=1/7(x+8)³

A reflection over the x-axis would be the final step, we need to multiply the function by −1. So, we have:

y= -1/7(x+8)³

Therefore, the transformed equation is y= -1/7(x+8)³

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Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.

Given that,

We have to find the missing reasons in the two column.

Given

AC bisects ∠DAB and CA bisects ∠DCB

Prove

ΔDAC≅ΔABC

Statement                                                          Reasons

1. AC bisects ∠DAB                                           Given

2. ∠DAC≅∠BAC                                              definition of angle bisects

3.AC≅AC                                                         reflexive property
4.CA bisects ∠DCB                                           given

5. ∠DCA≅∠BCA                                              definition of angle bisects

6. ΔDAC≅ΔABC                                               ASA postulate

Therefore, Option A is correct that is ASA postulate AC bisects ∠DAB and CA bisects ∠DCB then we proved ΔDAC≅ΔABC.

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1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].

We are given that polynomial [tex]$3 x^2+x-4$[/tex] is being divided by factor [tex]$(\mathrm{x}-1)$[/tex]

It is also said that when David perform the mathematical operation it gives remainder 0 .

Remainder 0 represents that divisor [tex]$(\mathrm{x}-1)$[/tex] is a factor polynomial [tex]$3 x^2+x-4$[/tex].

As x-1 is a factor of the given ploynomial, we can get one of the root of by setting it equal to 0 and solve for x.

Therefore,

x-1=0

Adding 1 on both sides, we get

[tex]$$\begin{aligned}& x-1+1=0+1 \\& x=1 .\end{aligned}$$[/tex]

Therefore, 1 must be the root of the polynomial [tex]$3 x^2+x-4$[/tex].

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials. This video covers common terminology like terms, degree, standard form, monomial, binomial and trinomial.

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Applying the definition of an Isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.

In geometry, an isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.

The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.

An Isosceles triangle has a vertex angle and two equal base angles.

Given that triangle TIC is an isosceles triangle:

angle I is the vertex angle = 90 degrees

angle T is a base angle

angle C is also a base angle

Thus:

angle C and angle T are congruent or equal to each other.

Therefore,

    Angle T = (180 - 90)/2

⇒ Angle T = 90/2

⇒ Angle T = 45 degrees.

applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.

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Based on the concept of ASA, when two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Congruent triangle:

Congruent triangle means all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Given,

Here we need to prove that triangle congruence by ASA.

In order to prove this one, we have to know that definition of ASA,

ASA also known as Angle-side-angle is a rule used to prove whether a given set of triangles are congruent.

In geometry, ASA rule states that "If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent."

When we compare the given triangle to this rule then we clearly identify whether the triangle is congruent or not.

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Answer:

add up the exponents of each term and select the highest sum.