100 POINTS!!
Select the correct answer.
The function g(x)=x² is transformed to obtain function :

h(x) = g(x) + 1.

Which statement describes how the graph of his different from the graph of g?

A. The graph of h is the graph of g horizontally shifted left 1 unit.

B. The graph of h is the graph of g vertically shifted down 1 unit.

C. The graph of h is the graph of g horizontally shifted right 1 unit.

D. The graph of h is the graph of g vertically shifted up 1 unit.

(C) Investment A is an ordinary annuity with 3,906.64 in the account after 1 year is correct option.

Both Investment A and Investment B are annuities, but we need to determine which one is an ordinary annuity. An ordinary annuity is one in which payments are made at the end of each period, while in an annuity due, payments are made at the beginning of each period.

Looking at the table, we can see that Investment A and Investment B both have payments made at the end of each month, so they are both examples of ordinary annuities.

To calculate the future value of each annuity after one year, we can use the formula:

[tex]FV = P \times [(1 + r)^n - 1] / r[/tex]

where:

FV is the future value of the annuity

P is the payment amount

r is the interest rate per period (in this case, 3.5% per month)

n is the number of periods (12 in this case, since we're looking at one year)

For Investment A, we have P = 350, r = 0.035, and n = 12. Plugging these values into the formula, we get:

FV = 350 × [(1 + 0.035[tex])^12[/tex] - 1] / 0.035

= 3,906.64

Therefore, the answer is (C) Investment A is an ordinary annuity with 3,906.64 in the account after 1 year.

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In the figure, AB is a diameter, and AB⊥CD, If m AC = 54°, BD is 36°. Option A

In a circle, a diameter divides it into two equal parts and forms a straight line that measures 180°.

Given that AB is a diameter = 180°.

AB is perpendicular to CD, therefore m∠AC + m∠BD = 90°.

Substituting m∠AC =54°, we get m∠BD + 54°  = 90°.

Solving for m∠BD, we get 90° - 54° = 36°.

There BD is 36°.

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Diagonals that bisect each other: Rhombus, Rectangle, Square.

Diagonals that bisect each other and are congruent: Rectangle, Square.

Diagonals that bisect each other and are perpendicular to each other: Square.

A parallelogram does not necessarily have diagonals that bisect each other.

A rhombus has diagonals that bisect each other.

This means that the diagonals intersect at their midpoints.

A rectangle has diagonals that bisect each other.

Additionally, the diagonals of a rectangle are congruent, meaning they have the same length.

A square has diagonals that bisect each other.

The diagonals of a square are congruent and perpendicular to each other.

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The Triangle is Equilateral and Equiangular.

We will use theses property of Equilateral Triangle as

We have a Triangle.

The Triangle all three angles measured 60 degree each.

and, We know the equilateral Triangle all angles measures 60 degree.

Now, from the figure all the three sides of triangle are equal.

and, we know Equilateral triangle have the three sides equal

Thus, the Triangle is Equilateral and Equiangular.

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The amount of walking space between two tables at the point where they are the closest is 0.9 m.

We are given that;

The space allowed per chair = 45 cm.

Number of tables=30

Now,

we find the length of a side of a square that contains a table by adding twice the radius of a table to twice the space allowed per chair. The formula is: side length=2×radius+2×space per chair

Plug in the given values and simplify. The calculation is: side length=2×0.9+2×0.45=2.7

Now subtract the diameter of a table from the side length to get the walking space between two tables. The formula is: walking space=side length−diameter

Plug in the given values and simplify. The calculation is: walking space=2.7−1.8=0.9

To express our answer in meters. walking space=0.9 m

Therefore, by the algebra the answer will be 0.9 m.

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Hannah needs to invest approximately $3173.79 now to have $6500 in 10 years at an interest rate of 7% compounded continuously.

Use the formula for continuous compounding to solve this problem:

[tex]A = Pe^{(rt)[/tex]

where A is the future value, P is the present value (the amount Hannah needs to invest), r is the annual interest rate (as a decimal), and t is the time in years.

We want to find P, so we can rearrange the formula as:

[tex]P = \dfrac{A}{e^{(rt)}}[/tex]

Substituting the given values, we get:

[tex]P = \dfrac{6500}{e^{(0.07\times10)}}[/tex]

P≈ $3173.79

Therefore, Hannah needs to invest approximately $3173.79 now to have $6500 in 10 years at an interest rate of 7% compounded continuously.

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The simplified expression of [tex]\sqrt[4]{567(x^9)(y^{11})}[/tex] is [tex]3x^2y^2\sqrt[4]{7xy^3}[/tex].

Given expression:

[tex]\sqrt[4]{567(x^9)(y^{11})}[/tex].

We can simplify the expression using the property that says for any non-negative numbers a and b, and any integer n ≠ 0,

[tex](a\times b)^{n} = a^n \times {b^n}[/tex]

Using this property, we can simplify the expression as follows:

[tex](567x^9y^{11})^{1/4} = (567)^{1/4} \times (x^9)^{1/4} \times (y^{11})^{1/4}[/tex]

Now we need to simplify,

[tex](81\times 7)^{1/4}x^{9/4}y^{11/4}\\=(81)^{1/4}(7)^{1/4}(x^{\frac{8}{4}+\frac{1}{4})(y^{\frac{8}{4}+\frac{3}{4})[/tex]

Also,

[tex]{3^4}^{1/4}(7)^{1/4}(x^{2+\frac{1}{4}})(y^{2+\frac{3}{4}})\\=3^1 7^{1/4}x^2x^{1/4}y^2y^{1/4}\\=3x^2y^2(7^{1/4}x^{1/4}y^{3/4})\\=3x^2y^2(7xy^3)^{1/4}\\=3x^2y^2\sqrt[4]{7xy^3}[/tex]

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The solutions are x = 0, 0, -2 and 5.

Given is a polynomial we need to solve it,

3x⁴-9x³-30x².

We know that a polynomial will have the number of solutions equal to its highest degree,

Here the highest degree of the polynomial is 4 so there will be 4 solutions.

3x⁴-9x³-30x²

[tex]= 3x^2\left(x^2-3x-10\right)[/tex]

[tex]= x^2-3x-10 =\quad \left(x+2\right)\left(x-5\right)[/tex]

[tex]= 3x^2\left(x+2\right)\left(x-5\right)[/tex]

Therefore, the solutions are x = 0, 0, -2 and 5.

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Answer:

  8

Step-by-step explanation:

You want to know the measure of segment XY if ∆XYZ ≅ ∆MNL and MN = 8.

Segment XY is named using the first two vertices listed in the name of ∆XYZ. That means the segment is the same length as the one named by the first two vertices listed in the name of congruent ∆MNL, segment MN.

Segment MN is given as 8 units long. Segment XY is congruent, so is also 8 units long.

  XY = 8 units

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The height of the triangle must increase by 4.29 feet so that the area would increase by 1.2 square feet.

To calculate the area of a triangle, you can use the formula presented as follows:

[tex]\sf Area = \huge \text(\dfrac{1}{2}\huge \text) \times base \times height[/tex]

In which the parameters are given as follows:

Considering the triangle that has a base of 14 feet and a height of 6 feet, the area of the triangle is given as follows:

[tex]\sf A = 0.5 \times 14 \times 6[/tex]

[tex]\sf A = 42 \ square \ feet.[/tex]

An increase of 1.2 square feet would lead to an area of 43.2 square feet, hence the height would be of:

[tex]\sf 4.2h = 43.2[/tex]

[tex]\sf h = \dfrac{43.2}{4.2}[/tex]

[tex]\sf h = 10.29 \ feet[/tex].

Then the increase in the height would be of:

[tex]\sf 10.29 - 6 = 4.29 \ feet[/tex].

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Answer:

40 is the surface area.

Explanation on hiw to get the answer:

The cosine value is given as follows:

[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]

The tangent value is given as follows:

[tex]\tan{\theta} = -\frac{\sqrt{7}}{4}[/tex]

First we must obtain the secant value, according to the identity presented as follows:

[tex]\sec^2{\theta} = 1 + \tan^{2}{\theta}[/tex]

Replacing the tangent into the expression, we have that:

[tex]\sec^2{\theta} = 1 + \frac{7}{16}[/tex]

[tex]\sec^2{\theta} = \frac{23}{16}[/tex]

[tex]\sec{\theta} = \frac{\sqrt{23}}{4}[/tex]

The secant is positive, as the angle is in the fourth quadrant, where the cosine is positive.

The cosine is then given as follows:

[tex]\cos{\theta} = \frac{1}{\sec{\theta}}[/tex]

[tex]\cos{\theta} = \frac{4}{\sqrt{23}} \times \frac{\sqrt{23}}{\sqrt{23}}[/tex]

[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]

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Answer:

im pretty sure the slope would be 3 over 7 (3/7)

Step-by-step explanation:

The value of s in the circle is 11.

We have,

When two chords in a circle have the same arc length intercepted by the chords, it means that the distances from each endpoint of the chords to the center of the circle are equal.

Now,

The arc length XY and WZ are the same.

This means,

Chord XY and Chord WZ are equal.

Now,

2s = s + 11

Solve for s.

2s - s = 11

s = 11

Thus,

The value of s in the circle is 11.

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Answer:

The estimated probability that exactly two of the three guests randomly picked were not there for personal reasons is 0.25.

The estimated probability that it takes at least four guests to find one who is staying for personal reasons is 0.125.

A point that best represent the location for them to put the science project is: A. (6.5, 6).

In order to determine the midpoint of a line segment with two (2) end points, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

By substituting the given end points into the formula for the midpoint of a line segment, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(5 + 8)/2, (8 + 4)/2]

Midpoint = [(13)/2, 12/2]

Midpoint = (6.5, 6).

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Solving a linear equation we can see that the smallest number is 5.

A set of 3 consecutive odd numbers can be written as:

x, x + 2, and x + 4

the middle one is x + 2, and we know that 4 times the second must be equal to the sum of the other two plus 14, then we can write the linear equation:

4*(x + 2) = x + x + 4 + 14

Solving this linear equation we will get:

4x + 8 = 2x + 18

4x -2 x=  18 - 8

2x = 10

dividing both sides by 2, we will get:

x = 10/2

x = 5

That is the smalles odd number.

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The minimum number of extra squares that need to be shaded so that the pattern has rotational symmetry of order is 3

From the question, we have the following parameters that can be used in our computation:

The composite figure

On the extension at the left-hand side of the figure, we can see that

The shaded shape is a rectangle while other shaded shapes are squares

This means that the other shaded squares must be extended to form a rectangle

There are three of the squares that can be extended to rectangles

Hence, the minimum number of squares is 3

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The total area that needs to be covered which is indicated by the shaded area would be =220ft²

To calculate the area that needs to be covered, the formula that should be used is the formula for the area of a rectangle which is given below as follows;

Area of rectangule =2( length×width)

where ;

length = 22ft

width = 5ft

area = 2× 22×5

= 220ft²

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The required, distance that Zeek traveled in scientific notation with units is 3.3696 × 10¹³ miles.

The distance traveled by Zeek is:

84,240,000,000,000 miles away / 2.5 = 33,696,000,000,000 miles away

We can write this in scientific notation as:

3.3696 × 10¹³ miles

Thus, the required, distance that Zeek traveled in scientific notation with units is 3.3696 × 10¹³ miles.

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Answer:

301.593 mm²

Step-by-step explanation:

surface area of cylinder = 2π r² + 2π r h

where r = radius and h = height

so we have surface area = 2π (4)² + 2π (4) (8)

= 32π + 64π

= 96π mm² (in exact form)

= 301.593 mm² (to one-thousandth of mm)

The interquartile range for the average of 15 cities is 1.8.

a) X ~ N(9.6, 1.3)

b) X bar ~ N(9.6, 0.13)

c) The probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants can be calculated using the z-score formula: P(X < 9.3) = P(Z < (9.3 - 9.6) / 1.3) = 0.338.

d) The probability that the average amount of pollutants is less than 9.3 can be calculated using the z-score formula: P(Xbar < 9.3) = P(Z < (9.3 - 9.6) / 0.13) = 0.819.

e) The assumption that the distribution is normal is indeed necessary for part d.

f) The IQR for the average of 15 cities can be calculated as follows: Q1 = 8.7 and Q3 = 10.5. IQR = 10.5 - 8.7 = 1.8.

Therefore, the interquartile range for the average of 15 cities is 1.8.

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If a subset A of natural numbers (N) satisfies the conditions 0 ∈ A and if n ∈ A, then n+1 ∈ A, then A must be equal to the set of all natural numbers (N).

We will use a proof by contradiction to demonstrate this.

Assume that there exists a subset A of natural numbers that satisfies the given conditions, but A is not equal to N.

This means there exists a natural number k that is not in A.

Let B = N - A be the set of natural numbers that are not in A.

B is non-empty because it contains at least k.

Since 0 ∈ A, but k ∉ A, there must be a smallest natural number in B. Let's denote it as b.

Now, according to the given conditions, if n ∈ A, then n+1 ∈ A.

We can apply this repeatedly to obtain n+1, (n+1)+1, (n+1)+1+1, and so on.

Considering b-1, it is a natural number that is not in B because b is the smallest natural number in B. So, b-1 ∈ A.

Using the condition that if n ∈ A, then n+1 ∈ A, we can apply it repeatedly to b-1 to get (b-1)+1, (b-1)+1+1, and so on.

This implies that b, b+1, b+2, and so on, all belong to A.

However, this contradicts the fact that b is the smallest natural number in B, and A is defined such that it includes all natural numbers greater than or equal to 0.

Therefore, our assumption that A is not equal to N is false, and we can conclude that A = N.

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The composition (f o g)(x) = 10/(x+10) and its domain is all real numbers except x = -10.

a) To find (f o g) (x), we need to substitute g(x) into f(x) wherever we see x. That is,

(f o g) (x) = f(g(x)) = f(10/x) = (10/x) / (10/x + 1)

b) To find the domain of (f o g) (x), we need to look for any values of x that make the denominator of the expression equal to zero, since division by zero is undefined. Thus, we solve the equation:

10/x + 1 = 0

10/x = -1

x = -10

Therefore, the domain of (f o g) (x) is all real numbers except x = -10, since that value makes the denominator equal to zero. In interval notation, the domain is:

(-∞, -10) U (-10, ∞)

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Answer:

7.638m

Step-by-step explanation:

part 1. The job offers into a salary are:

The Adjusted Salary for Minneapolis, MN is  $220.38

The Adjusted Salary for Omaha, NE is  $322.15

part 2.

We could conclude that the job offer in Omaha, NE is better because of its the adjusted salary as it offers  a higher salary in an average USA city.

For Minneapolis, MN:

Adjusted Salary = (Offered Salary + Benefits) / Cost of Living Index

Adjusted Salary = ($21,000 + $2,400) / 106.1

Adjusted Salary = $23,400 / 106.1

Adjusted Salary =  $220.38

For Omaha, NE:

Adjusted Salary = (Offered Salary + Benefits) / Cost of Living Index

Adjusted Salary = ($27,500 + $1,200) / 89.2

Adjusted Salary = $28,700 / 89.2

Adjusted Salary = $322.15

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Answer:

Step-by-step explanation:

17

5 divided by 135

The values of the probabilities are P(5) = 1/8 and P(Number > 2) = 75%

From the question, we have the following parameters that can be used in our computation:

The spinner

There are 8 sections on the spinner

So, we have

Section = 8

One of the sections is 5

So, we have

P(5) = 1/8

There are 6 sections greater than 2

So, we have

P(Number > 2) = 6/8

Evaluate

P(Number > 2) = 75%

Hence, the probabilities are 1/8 and 75%

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