The perimeter of a square is 56. Express the length of a diagonal of the square in simplest radical form.?

The difference between the low temperature and the high temperature on Tuesday is -1.1°C.

From the information given, the temperature Monday evening was 16.4 c the temperature dropped an average of 1 1/4 degrees each hour for the next 14 hours until it reached its lowest temperature for the day on Tuesday.

Therefore, the temperature on Tuesday will be:

= 1 1/4(14)

= 17.5

The difference in the temperature will then be:

= 16.4°C - 17.5°C

= -1.1°C.

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Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

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Given:

The function is:

\(f(x)=\sqrt{7x-21}\)

To find:

The steps of finding the inverse function \(f^{-1}(x)\).

Solution:

We have,

\(f(x)=\sqrt{7x-21}\)

The steps of finding the inverse function are:

Step 1: Substitute \(f(x)=y\).

\(y=\sqrt{7x-21}\)

Step 2: Interchange x and y.

\(x=\sqrt{7y-21}\)

Step 3: Taking square on both sides, we get

\(x^2=7y-21\)

Step 4: Adding 21 on both sides, we get

\(x^2+21=7y\)

Step 5: Divide both sides by 7.

\(\dfrac{1}{7}x^2+3=y\)

Step 6: Substitute \(y=f^{-1}(x)\).

\(\dfrac{1}{7}x^2+3=f^{-1}(x)\), where \(x\geq 0\).

Therefore, the inverse of the given function is \(f^{-1}(x)=\dfrac{1}{7}x^2+3\) and the arrangement of steps is shown above.

Answer: \(9\pi\) meters; \(20.25\pi\) square meters

Step-by-step explanation:

The length of the string of lights is the circumference, which is \(2\pi(4.5)=9\pi\).

The amount of carpet is the area, which is \(\pi(4.5^2)=20.25\pi\)

The dοtted line is the line y=13x3, and the shaded area is abοve it.

As is well knοwn, the equatiοn fοr a straight line is y = mx + c. Where 'c' is the y-axis intercept and 'm' is the slοpe οn the y-axis. The fοrmula fοr a hοrizοntal line is y = 3.

In οrder tο graph the inequality y≥13x−3, we can first plοt the line y=13x3

(which has a slοpe οf 13 and a y-intercept οf -3) as a dοtted line.

Since the inequality is y≥13x−3, we must shade the area abοve the line.

The dοtted line is the line y=13x3, and the shaded area is abοve it.

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A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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Answer:

Answer:

x=4

Step-by-step explanation:6x+8x=2x

5+3=8 (when you move a number to the other side of an equals sign, it changes its value)

2x=8

2x/2 and 8/2

x=4

The related function for –6x + 8x – 5 = 3 is;

x = 4

We are given the equation;

–6x + 8x – 5 = 3

Let us simplify the numbers that have the variable x first. Thus;

–6x + 8x – 5 = 3 gives;

8x - 6x - 5 = 3

>> 2x - 5 = 3

Use addition property of equality to add 5 to both sides;

2x - 5 + 5 = 3 + 5

>> 2x = 8

Use division property of equality to divide both sides by 2 to get;

x = 8/2

Thus;

x = 4

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Answer:

See below

Step-by-step explanation:

Assuming the interest is compounded annually

x * (1 + .10)^5 = 1.61051  x

  your final amount will be  1.61051 times bigger than the initial deposit

The area of the circle is approximately 78.5 square meters.

To determine the area of a figure, we need to know what type of figure it is and what its dimensions are. The formulas for finding the areas of different types of figures are as follows:

Rectangles: Area = length x widthSquares: Area = side x sideTriangles: Area = 1/2(base x height)

Circles: Area = πr² (where π is pi and r is the radius)Problem 1:Let's say we have a rectangle with a length of 6 cm and a width of 4 cm.

To find its area, we use the formula Area = length x width. Substituting in our values,

we get:Area = 6 cm x 4 cm = 24 cm²Therefore, the area of the rectangle is 24 square centimeters.Problem 2:Next, let's look at a circle with a radius of 5 meters.

To find its area, we use the formula Area = πr². Substituting in our values, we get:Area = π(5 m)² = π(25 m²) ≈ 78.5 m²

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Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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Answer:

Die is not fair given that  Pvalue< 0.05, hence we reject Null hypothesis

a) H0: Die = fair

b) Ha : Die ≠ fair

c) df = 5

Step-by-step explanation:

The expected frequency of every face values = 20

a) state Null hypothesis

H0: Die = fair

b) Alternate Hypothesis

Ha : Die ≠ fair

c) degree of freedom

df = ( n - 1 )

   = ( 6 - 1 ) = 5

n = sample size ( number of faces a die has )

Note : After conducting hypothesis test

Pvalue ≈  0.0026

test statistic ≈ 18.30

Hence we can conclude that die is not fair given that  Pvalue < 0.05, hence we reject Null hypothesis

Answer:

D. 8.99

Step-by-step explanation:

You're welcome :)

Answer:

He saved $121

Step-by-step explanation:

All you have to do is divide $726/6 which gives you $121.

The total sunflowers and roses Lira has is 18 and 27 respectively

Let

Total flowers = x

Roses = 2/9 of x

= 2/9x

Remaining = x - 2/9x

= (9x-2x) / 9

= 7/9x

Sunflowers = 3/7 of 7/9x

= (3 × 7)/(7 ×9)x

= 21/63x

Tulips = 36

Total = roses + sunflowers + tulips

x = 2/9x + 21/63x + 36

x - 2/9x - 21/63x = 36

(63x -14x-21x) / 63 = 36

28/63x = 36

cross product

28x = 36 × 63

28x = 2268

x = 2268/28

x = 81

Therefore,

Total flowers = x

= 81 flowers

Roses = 2/9x

= 2/9 × 81

= 18 flowers

Sunflowers = 21/63x

= 21 / 63 × 81

= 27 flowers

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Answer:

Answer:

Option (A) and (E) are correct.

We can prove  ΔABC and ΔFGH  are similar by AA criterion or by showing that the  ratio of corresponding sides are equal.

Step-by-step explanation:

Given : two triangles, ΔABC and ΔFGH and we need to prove both are similar to each other.

We have to choose the correct options from the given choices.

Two triangles are said to be similar if their the corresponding sides are in proportion and the corresponding angles are congruent to each other.

that is

also measure ∠A and  ∠F  to show they are congruent as ∠H= ∠C = 90°

This can be observed by looking at the image . So when both triangle are congruent we an show by AA similarity criterion that  ΔABC and ΔFGH  are similar.

Thus, option (A) and (E) are correct.

We can prove  ΔABC and ΔFGH  are similar by AA criterion or by showing that the  ratio of corresponding sides are equal.Step-by-step explanation:

Recall that we can do the following picture

We want to find the height of this pyramid and are told the volume of the pyramid. Recall that the volume of a square pyramid of height h and base length b is given by the formula

In our case, we have V=12, and b=3. So we have the following equation

So, we should find the value of h from this equation. To do, we simply divide both sides by 3, so we get

so the height of the pyramid is 4 feet.

The given equation is y + 2 = 2(x + 3) and the x-intercept is -2.

To find the x-intercept of the equation y + 2 = 2(x + 3), we need to set y equal to zero and solve for x. The x-intercept occurs when the value of y is zero, meaning the graph crosses the x-axis.

Let's substitute y with 0 in the equation:

0 + 2 = 2(x + 3)

Simplifying the equation:

2 = 2(x + 3)

Dividing both sides by 2:

1 = x + 3

Subtracting 3 from both sides:

-2 = x

The x-intercept is -2. This means that the graph of the equation y + 2 = 2(x + 3) crosses the x-axis at the point (-2, 0).

The x-intercept represents the value of x where the graph intersects or crosses the x-axis. In this case, it occurs when x is equal to -2, and the y-value is zero.

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Answer:

\(l + w + d \leq 61\)

Step-by-step explanation:

Given

Sum of l, w and d be at most 61

Required

Write as inequality

First, we need to determine the sum of l, w and d

\(Sum = l + w + d\)

Next, we determine the type of inequality.

At most 61 means less than or equal to 61

So, the expression becomes:

\(Sum \leq 61\)

Substitute value for Sum

\(l + w + d \leq 61\)

Answer:

D

Step-by-step explanation: Ede 2021

Answer:

361-265＝96

96÷32＝3

3hours of labor was needed to complete the job

Answer:

705.81 and 705.810

Step-by-step explanation:

700 + 5 + 0.8 + 0.01 = 705.81

Answers:

705.810

705.81

Answer

Given the 2 equations

x = y + 4 → (1)

2x - 3y = - 2 → (2)

Substitute x = y + 4 into (2)

2(y + 4) - 3y = - 2 ← distribute and simplify left side

2y + 8 - 3y = - 2

- y + 8 = - 2 ( subtract 8 from both sides )

- y = - 10 ( multiply both sides by - 1 )

y = 10

Substitute y = 10 into (1) for corresponding value of x

x = 10 + 4 = 14

Solution is (14, 10 ) → D

Step-by-step explanation:

Answer:

x=3

x=3y=1

I hope this helps!

Step-by-step explanation:

x+y=4

2x-3y=3

y = 4-x

2x-3(4-x) = 3

2x-12+3x = 3

5x = 15

x = 3

y = 4-x

4-3 = 1

y = 1

The approximate perimeter of the right triangle is 57.89 cm.

To find the perimeter of the right triangle, we need to know the lengths of the other two sides.

Let's use the Pythagorean theorem, which asserts that the hypotenuse (the longest side) of a right triangle has a square whose sum is equal to the squares of the other two sides.

In this case, we know the length of the hypotenuse is 24 cm and the height (one of the other sides) is 16 cm. Let's call the third side x.

So we have:

\(24^2 = 16^2 + x^2\)

Simplifying, we get:

\(576 = 256 + x^2\)

Subtracting 256 from both sides, we get:

\(320 = x^2\)

Taking the square root of both sides, we get:

x ≈ 17.89

So the approximate perimeter of the triangle is:

P = 24 + 16 + 17.89 ≈ 57.89 cm

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The statement about the function is: "The function is decreasing for all real values of x where x < -4." D.

The given information tells us that the graph represents a downward-opening parabola.

The vertex of the parabola is located at (-4, 4) indicates that this point is the highest point on the graph.

As we move to the left of the vertex, the function values decrease, indicating a decreasing trend.

Moreover, the graph passes through the point (-6, 0), which lies to the left of the vertex.

This confirms that the function is decreasing for all real values of x less than -4, including x < -6.

On the other hand, the graph also passes through the point (-2, 0), which lies to the right of the vertex.

This does not impact the conclusion that the function is decreasing for x < -4, as the graph's behavior to the right of the vertex is not relevant to this particular statement.

Based on the given information and the properties of the downward-opening parabola, we can conclude that the function is decreasing for all real values of x where x < -4.

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Answer:

4.44444444444 or 40/9

Step-by-step explanation:

i searched it up

8 divided by 1 4/5 in fraction form will be 40 / 9. Then the faction number 40 / 9 in the decimal form will be 4.4444.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The mixed fraction number is converted into a faction number.

⇒ 1 4/5

⇒ 1 + 4/5

⇒ (5 + 4) / 5

⇒ 9/5

Then the quotient of the numbers 8 and 9/5 will be given as,

⇒ 8 / (9/5)

⇒ 8 x 5 / 9

⇒ 40 / 9

The faction number 40 / 9 in the decimal form will be 4.4444.

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Answer:

☆This is because ascending, not descending when looking on a graph.

☆The slope's number is a positive number.

Answer:

45 square ft^2

Step-by-step explanation: The formula of the area of the trapezoid is A=(a+b)/2 x h. A represents the top while b represents the bottom. 15+3=18 and 18/2=9. If multiply the result by 5, you get 45 as the answer.

Angle WZY is 50 degrees, angle WZX is also 50 degrees, and angle XZW is 160 degrees.

What is the inscribed angle theorem?

The inscribed angle theorem, also known as the central angle theorem, states that an angle formed by two chords in a circle is half the measure of the arc they intersect, or subtend, inside the circle.

To find all other angles in the circle with quadrilateral WXYZ inscribed in it and WY going through the center Q:

Since WY goes through the center, angle WYZ and angle WXY are both right angles (90 degrees)

By the inscribed angle theorem, angle WZY is equal to half the measure of the arc WX.

Since angle XYZ is given as 50 degrees, the measure of the arc WX is 2 times 50 degrees, which is 100 degrees.

Therefore, angle WZY is 50 degrees.

By the same logic, angle WZX is also 50 degrees.

Since angles WYZ and WXY are right angles, angles XZY and WZX are also right angles.

Finally, we can find angle WZY + angle XYZ + angle XZW + angle WZX = 360 degrees (sum of angles in a quadrilateral), and we can solve for angle XZW which is 160 degrees.

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Answer:

C

Step-by-step explanation:

Given

V = πr²h

Rounding to the nearest whole number gives

π ≈ 3

r ≈ 4

h ≈ 6

Then

V = 3 × 4² × 6 = 3 × 16 × 6 = 288 in³

Answer:

i feel like the answer is d srry if im wrong

Step-by-step explanation: