Solve part A on the picture

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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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 pattern with matches is formed by systematically manipulating the arrangement of matches, adding or removing them in each step according to a defined rule.

The pattern with matches can be formed by following a specific arrangement or sequence. Each step in the formation of the pattern involves adding or removing matches in a deliberate manner. Let's examine the steps involved in creating the pattern:

Start with a base shape: The pattern typically begins with a basic shape or arrangement of matches. This could be a square, triangle, or any other simple form. For example, let's consider a square shape.

Manipulate the arrangement: To create the pattern, matches are added or removed from the base shape in each step. The exact manipulation depends on the desired pattern. For instance, let's say we want to create a pattern where each subsequent shape has one less match along one side.

Repeat the process: The manipulation is repeated in a systematic way to create a sequence of shapes. Each new shape is derived from the previous one by adding or removing matches according to the defined pattern rule. This repetition generates a series of shapes that form the complete pattern.

Observe the resulting pattern: By following the defined rules for adding or removing matches, a visually appealing and consistent pattern emerges. The pattern can exhibit various characteristics such as symmetry, repetition, or gradual change.

The specific details of the pattern formation may vary depending on the desired design. Different patterns can be created by altering the rules for adding or removing matches, changing the starting shape, or modifying the manipulation process.

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Answer:

The option that the margin of error accounts for in the given interval is sampling variation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

17

5 divided by 135

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 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 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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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:

720 m^2

Step-by-step explanation:

Solution:

The formula for the surface area of a triangular prism is:

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

= (S1 +S2 + S3)L + bh

where,

Given:

side 1 (S1) : 5 m

side 2(S2): x m

side 3(S3): 12 m

length (l)=22m

Here we need to find side 2, we can easily find it using Pythagoras' theorem.

a^2+b^2=c^2

5^2+12^2=x^2

x^2=169

x=[tex]\sqrt{169}=13 m[/tex]

therefore, side 2 is 13 m.

Substituting value in the formula

Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area)

= (S1 +S2 + S3)L + bh

Surface Area=(5+13+12)*22+5*12= 720 m^2

Answer:

720 m²

Step-by-step explanation:

The given diagram shows a triangular prism.

A triangular prism consists of two congruent triangular bases and three rectangular faces connecting these bases.

To calculate the surface area of the triangular prism, we first need to calculate the length of the hypotenuse of the right triangular base. To do this, we can use Pythagoras Theorem:

[tex]\begin{aligned}\sf Hypotenuse\;of\;triangular\;base&=\sqrt{5^2+12^2}\\&=\sqrt{25+144}\\&=\sqrt{169}\\&=13\; \sf m\end{aligned}[/tex]

The surface area of a triangular prism is the sum of the areas of all its faces. Therefore:

[tex]\begin{aligned}\sf Total\;surface\;area&=2\left(\dfrac{1}{2} \cdot 5 \cdot 12\right)+12\cdot 22+5 \cdot 22+13 \cdot 22\\\\&=60+264+110+286\\\\&=720\; \sf m^2\end{aligned}[/tex]

Therefore, the total surface area of the given triangular prism is 720 m².

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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Three types of financial institutions that would offer various financial services are Banks, Credit Unions and Investment Firms.

Three types of financial institutions that would offer various financial services are:

Banks: Banks are traditional financial institutions that provide a wide range of financial services, including savings and checking accounts, loans, mortgages, credit cards, investment services, and more. They also offer services like ATM access, online banking, and mobile banking.

Credit Unions: Credit unions are member-owned financial cooperatives that offer similar services to banks, such as savings and checking accounts, loans, and mortgages. Credit unions often provide competitive interest rates and lower fees compared to banks. They are typically organized around a specific community, occupation, or group of individuals.

Investment Firms: Investment firms, also known as brokerage firms or investment banks, specialize in providing investment-related services. They assist clients in buying and selling stocks, bonds, mutual funds, and other investment products. Investment firms may also offer financial advisory services, wealth management, retirement planning, and access to research and market analysis.

These financial institutions play a crucial role in managing and facilitating various financial services to individuals, businesses, and organizations.

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Step-by-step explanation:

To find the expected value of the number of bids won, E(X), we need to multiply each value of X with its corresponding probability and then sum these products.

E(X) = (X1 * P1) + (X2 * P2) + (X3 * P3)

Here, X1 = 0, X2 = 1, X3 = 2, and their corresponding probabilities are P1 = 0.81, P2 = 0.18, and P3 = 0.01.

E(X) = (0 * 0.81) + (1 * 0.18) + (2 * 0.01)

E(X) = (0) + (0.18) + (0.02)

E(X) = 0.20

The expected value of the number of bids won is 0.20.

After considering the given data we conclude that the system of equations are x=-3 and y=2², under the condition that the given system of equations are x+2y=1 -3x-2y=5

considering the system of equations x+2y=1 and -3x-2y=5. The coefficient matrix is

| 1  2 |
| -3 -2 |

and its determinant is 1×(-2)-(-3)×2 = 4. The matrix obtained by replacing the first column by the right-hand sides of the equations is

| 1  2 |
| 5 -2 |

and its determinant is 1×(-2)-5×2 = -12. The matrix obtained by replacing the second column by the right-hand sides of the equations is

| 1  1 |
| -3 5 |

and its determinant is 1×5-(-3)×1 = 8. Therefore, x=-3 and y=2².
Cramer's rule consist of a  formula which is required for  solving a system of linear equations with as many equations as unknown variables, applying determinants. It expands the solution in terms of the determinant of the coefficient matrix and the matrices taken from it by replacing one column by the right-hand sides of the equations.
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Answer:

40 is the surface area.

Explanation on hiw to get the answer:

The given system of equations has no solution.

Given that a system of equations, 12x + 36y = −3 and −12x − 36y = 0, we need to solve it,

We know for a system of equations =

a₁x + b₁y = c₁ and a₂x + b₂y = c₂

If a₁ / a₂ = b₁ / b₂ = c₁ / c₂ then the system has infinite solutions.

If a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂ then the system has no solutions.

If a₁ / a₂ ≠ b₁ / b₂ then the system has a unique solution.

comparing the coefficients given,

-12/12 = -1

-36/36 = -1

-3/0 = -3

We get here the condition of a₁ / a₂ ≠ b₁ / b₂, which means that the system has no solution.

Hence the given system of equations has no solution.

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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 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:

  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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If the workers' union at a particular university is quite strong.  the probability that exactly 4 of the workers interviewed are union members is 0.1699.

You must count all conceivable outcomes as well as favourable outcomes in order to compute probability. The number of favourable outcomes divided by the total number of possible outcomes yields the chance that an event will occur.

Using this formula to the probability

P(X = k) = (n choose k) * [tex]p^{k}[/tex] * [tex](1-p)^{n-k}[/tex]

Where:

X = random variable

n = 5

p = 0.96

k = 4

Let plug in the formula

P(X = 4) = (5 choose 4) *[tex]0.96^{4}[/tex] *[tex](1-0.96)^{5-4}[/tex]

= 5 *[tex]0.96^{4}[/tex] * 0.04

= 0.1699

Therefore the probability is 0.1699.

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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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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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The student would spend $18 on books and lab manuals.

An expenditure refers to the spending of money on something or the money that is spent on something.

Total Expenditure = Lab fee + Materials fee + Tuition + Books and lab manuals + Tools

Total Expenditure = 8% + 10% + 38% + 18% + 26%

Total Expenditure = 100%

We will calculate the amount spent on books and lab manuals. The amount spent on books and lab manuals is:

= (Books and lab manuals percentage / Total Expenditure percentage) * $100

= (18% / 100%) * $100

= 0.18 * $100

= $18.

Missing details:

On pie chart  for School Expenditures; Lab fee = 8% Materials fee =10% Tuition = 38% Books and lab manuals = 18% Tools = 26%

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Step-by-step explanation:

The formula for the nth term of an arithmetic sequence is:

a_n = a + (n - 1)d

where a is the first term, d is the common difference, and n is the term number.

Substituting a=1 and d=5, we get:

a_n = 1 + (n - 1)5

Simplifying this expression, we get:

a_n = 5n - 4

Therefore, the formula for the nth term of the arithmetic sequence with first term a=1 and common difference d=5 is a_n = 5n - 4.

Answer:

nth=3n+1. (B) nth=5n−13. Explanation: the nth term of an Ap is given by. nth=a+(n−1)d. (A). nth=4+(n−1)3. nth=4+3n−3.

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 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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Answer:

Step-by-step explanation:

20=17+12+9 so the answer is 4982

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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