Solve the question. Explain WHY

The weight of the 0.8-meter piece is 19.6 kilograms.

We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.

Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:

W₁/2.8m = 24.5kg/1m

Solving for W₁, we get:

W₁ = (24.5kg/1m) x 2.8m = 68.6kg

Now we can use the same ratio to find W₂:

W₂/0.8m = 24.5kg/1m

Solving for W₂, we get:

W₂ = (24.5kg/1m) x 0.8m = 19.6kg

Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.

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The following statement is true about the functions f(x) and g(x):

f(–2) = g(–2)

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of functions is given as

Functions f(x) and g(x)

From the attached graph, we can see that:

The values of the function f(x) at f(2), or f(4) do not have a match to the function g(x) at g(2) or g(4).

However, the functions intersect at x = -2

This means that f(-2) = g(-2)

Hence, the true statement about the functions is  f(–2) = g(–2)

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Complete question

Which statement is true regarding the graphed functions?

See attachment

f(4) = g(4) f(4) = g(–2) f(2) = g(–2) f(–2) = g(–2)

The answers are given below.

In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.

Given:

1) 2Sin(9θ).Cos(5θ)=1/2(Sin14θ+Sin4θ)

2) Sin(3θ)Sin(5θ)Cos(3θ)Cos(5θ)=1/2(Sin8θ+Sin2θ)

3)Cos6θ+Cos4θ=2Cos5θCosθ

4)Sin(13θ/2)+Sin9θ=2Sin(11θ/2)Sinθ

5)Cosθ=2√5/5

6)Cos2θ=23/2

7)Tan(π/12)=2-√3

8)Sin(165°)=√6-√2 /4

9)Cos(5π/18)Cos(2π/9)-Sin(5π/18)Sin(2π/9)=Cos(π/2)

                                                                      =0

Hence, these are the answers .

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Answer:

a = 18 ft is the answer.

Step-by-step explanation:

a = ?

b = 24 ft

c = 30 ft

According to the Pythagoras theorem,

a² + b² = c²

a² + 576 = 900

a² = 900 - 576

a² = 324

a = 18 ft

∴ a = 18 ft is the length of the missing leg.

Answer:

18 feet

Step-by-step explanation:

The Pythagorean theorem is a formula that can be used to find the unknown side length of a right triangle when given the length of the other two sides. The general formula for the Pythagorean theorem is the following,

\(a^2 + b^2 = c^2\)

Where (a) and (b) are the legs of the right triangle, or rather the sides adjacent to the right angle of the right triangle. Additionally, (c) is the hypotenuse or the side opposite the right angle of the right triangle.

Substitute in the given values and solve, let parameter (a) represent the unknown side of the triangle,

\(a^2 + b^2 = c^2\\\)

Substitute,

\((24)^2 + a^2 = (30)^2\\\)

Simplify,

\(576 + a^2 = 900\)

Inverse operations,

\(576 + a^2 = 900\\-576\\\\a^2 = 324\\\sqrt{}\\\\a = 18\)

The original price of the toy was $75.

The toy was discounted 20% and Jan saved $15. The discount is the savings which means that 20% of the original price is $15.

Assuming the original price is x, the expression to find it would be:

15 = 20% × x

15 = 0.2x

x = 15 / 0.2

x = $75

The original price of the toy was therefore $75

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The direct labor cost included in the Preble Company's flexible budget for March is $819,000.

To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.

Given:

Actual production and sales =n26,600 units

Actual direct labor rate = $13.00 per hour

Actual direct labor hours worked = 63,000 hours

Direct labor cost = Actual direct labor rate × Actual direct labor hours worked

Direct labor cost = $13.00/hour × 63,000 hours

Direct labor cost = $819,000

Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.

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Y-3 = -2(x+5)

Rewrite in slope intercept form:

y-3 = -2(x+5)

Simplify the right side:

y-3 = -2x -10

Add 3 to both sides:

y = -2x -7

The y intercept is -7

Answer:

sorry i don't know the answer

Answer:

so I know the first answer

Step-by-step explanation:

so total is 40 points but the total is divide by 2 points so we get 20 questions so if u get 6 wrong then you get 20-6=14... therefore the score with 6 wrong is 14

The length of one side of the equilateral triangle in terms of x is 6x.

To find the length of one side of the equilateral triangle in terms of x, we need to consider the perimeter of both the rectangle and the equilateral triangle.

The perimeter of a rectangle is given by the formula:

Perimeter of rectangle = 2(length + width)

In this case, the length of the rectangle is 7x cm, and the width is 2x cm. Substituting these values into the formula, we have:

Perimeter of rectangle = 2(7x + 2x) = 2(9x) = 18x

We are told that the equilateral triangle has the same perimeter as the rectangle.

Since an equilateral triangle has all sides equal, the perimeter can be calculated by multiplying the length of one side by 3.

Therefore, we have:

Perimeter of equilateral triangle = 3(side length)

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle (18x), we can set up the equation:

3(side length) = 18x

Dividing both sides of the equation by 3, we get:

side length = 6x

Hence, the length of one side of the equilateral triangle in terms of x is 6x.

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The complete question may be like: A rectangle measures 2x cm by 7x cm. An equilateral triangle has the same perimeter as the rectangle. What is the length of one side of the triangle in terms of x?

Note that as x gets larger, y gets smaller, but the product xy remains constant at 192.

In mathematics, a function is a relationship between two sets, called the domain and the range, such that each element of the domain corresponds to exactly one element of the range. A function takes an input value (or values) and produces an output value (or values) according to a specific rule or formula. The input values are the domain of the function, and the output values are the range of the function. Functions can be represented using equations, graphs, tables, or verbal descriptions. They are used to model relationships between variables in various fields of mathematics, science, engineering, economics, and many other areas.

Here,

If x and y vary inversely, this means that their product is a constant. We can use this fact to find the constant of proportionality k as follows:

k = xy

If we know that y is 24 when x is 8, we can substitute these values into the equation above to solve for k:

k = xy

= 8(24)

= 192

Now we can use this value of k to write the inverse variation function:

xy = 192

or

y = 192/x

To sketch a graph of this function for x > 0, we can plot a few points and connect them with a smooth curve. Here are some points we can use:

(x, y)

(1, 192)

(2, 96)

(4, 48)

(8, 24)

(16, 12)

(24, 8)

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Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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Given, equation of curve is

\(y = \frac{(x - 7)}{(x - 2)(x - 3)} .....(1)\\\)

To find the intersection of given curve with X-axis, Put y = 0 in equation 1, we get,

\(0 = \frac{(x - 7)}{(x - 2)(x - 3)} ......(2) \\ \)

x − 7 = 0 ⟹ x = 7

Thus, the curve cut the X-axis at (7,0).

Now, on differentiating equation of curve w.r.t. x, we get,

\( \frac{dy}{dx} \\ = \frac{(x - 2)(x - 3).1 - (x - 7)[(x - 2).1 + (x - 3).1]}{[(x-2)(x - 3) {}^{2}]} \)

Next answer is in pic.

Answer: a polygon is a shape with at least three straight sides and angles, and typically five or more

Step-by-step explanation:

Answer:

-3.33

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

x = 60, μ = 70, σ = 3

z = 60 - 70/3

z = -10/3

z = - 3.3333333333

Approximately, the students z score = -3.33

The number of each type of tickets sold are;

180 adults tickets

260 students tickets

60 children tickets

Let us solve to get the solution using 3 variables.

Let c be the number of children's tickets

Let s be the number of student tickets

Let a be the number of adult tickets

We are told that the total number of tickets was 500

Thus;

a + s + c = 500   ------(1)

The number of adult tickets was 3 times the number of children's tickets. Thus;

a = 3c   ------(2)

The total cost of the tickets was $8070. Thus;

18a + 15s + 12c = 7860  ----(3)

We conclude that solving these three equations simultaneously gives us;

a = 180 adults

s = 260 students

c = 60 children

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Answer:

There are 1645 seats in the theatre.

Step-by-step explanation:

The first row has 13 seats and each row has 2 seats more than the previous one which means

13,15,17...

As the terms are increasing with the same difference, d=2 this forms an arithmetic sequence.

where

\(d = 2\\a_1 = 13\\a_2 = 15\\a_3 = 17\)

The rule for an arithmetic sequence is given by:

\(a_n = a_1 + (n-1)d\)

Putting the value of a1 and d

\(a_n = 13+(n-1)(2)\\a_n = 13+2n-2\\a_n = 11+2n\)

We have to find total seats in the theatre for that the 35th term of sequence is required as their are 35 rows.

So,

Putting n=35

\(a_{35} = 11+2(35)\\= 11+70\\=81\)

Now we need to find the sum of the 35 terms

The formula for sum of arithmetic sequence is:

\(S_n = \frac{n}{2}(a_1+a_n)\\putting\ n=35\\S_{35} = \frac{35}{2}(a_1+a_{35})\\S_{35} = 17.5(13+81)\\S_{35} = 17.5(94)\\S_{35} = 1645\)

Hence,

There are 1645 seats in the theatre.

The mean absolute deviation is $106.6.

Given the table shows the amount Bill spent on 5 days last week.

DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.

Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,

the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:

Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406

The sum of all absolute deviations is:

10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.

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Answer:

m(∠y) = 64°

Step-by-step explanation:

From the figure attached,

m(∠e) = 90°

m(∠b) + 67° = 180° [Linear pair of angles]

m(∠b) = 180 - 67

          = 113°

m(∠c) + 75° = 180°  [Linear pair of angles]

m(∠c) = 105°

m(∠a) = m(∠d)

By the property of a polygon,

Sum of the interior angles of a polygon is given by,

Sum of interior angles = (n - 2) × 180°

Here, n = number of sides of the polygon

For n = 5,

Sum of interior angles = (5 - 2)×180°

                                     = 540°

m(∠a) + m(∠b) + m(∠c) + m(∠d) + m(e) = 540°

2m(∠d) + 113° + 105° + 90° = 540°

2m(∠d) + 308 = 540°

2m(∠d) = 540 - 308

m(∠d) = 116°

m(∠d) + m(∠y) = 180°

m(∠y) + 116° = 180° [Linear pair of angles]

m(∠y) = 64°

Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

Answer:

Hope it helps................

The function represented in the table is a linear function with equation

y = 0.2 x + 0.4 .

The coordinates of the points on the graph calculated from the table are :

(-1,0.2) , (0,0.4) , (2,0.8) and (5 , 1.4)

Taking a look at the y-coordinates we can see that they are increasing uniformly and linearly.

Plotting the points on the graph we get the line to be a straight line.

Hence the equation is linear.

So we can calculate the slope of the line as :

m = (1.4-0.8) / (5-2) = 0.6 / 3 = 0.2

Hence the graph is linear with slope 0.2 and y-intercept at 0.4

A linear function from the real numbers to the real numbers is one whose graph in Cartesian coordinates is a non-vertical line on the plane in calculus and related mathematical disciplines.

When the input variable is modified, the output often changes in a manner that is proportionate to the input variable's change.

Therefore the function is linear in nature.

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Answer:

5 extra cups.

Step-by-step explanation:

The values of x, y, and z of the parallelogram are -19°, -115° and 27°

A parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. The Sum of adjacent angles of a parallelogram is equal to 180 degrees.

for a parallelogram opposite angles are equal

-4x -1 = 75

-4x = 76

x = 76/-4

x = -19°

sum of adjacent angles are supplementary

(-y-10) + 75 = 180

-y + 65 = 180

-y = 180 - 65

-y = 115

y = -115°

Also

4z - 3 + 75 = 180

4z + 72 = 180

4z = 180 - 72

4z = 108

z = 108/4

z = 27°

In conclusion, the values of x = -19, y = -115, z = 27

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On solving the provided question, we can say that an explicit equation for the geometric sequence t(n) = \(t^2+ 6t - 8\) and a recursive equation for the geometric sequence; t(1) = -1

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

an explicit equation for the geometric sequence.

t(n) = \(t^2+ 6t - 8\)

a recursive equation for the geometric sequence.

t(1) = -1

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a) The number of bird feeders that the company must sell in a week to obtain the maximum profit = 100

b) Maximum profit = 3800

Maximum profit

Given that ,

f(x)=−0.40\(x^{2}\)+80x−200

f'(x) = -0.40 x \(2x\) + 80

      = - 0.80\(x + 80\)

f''(x) = - 0.80

a) For Maximum and minimum profit

f'(x) = 0

- 0.80\(x\) + 80 = 0

        0.80 \(x\)  = 80

                  \(x\) = 80 / 0.80

                     = 80 /80 x 100

                  \(x\) = 100

for x = 100 , f''(x) = -0.80

                   f''(x) < 0

Therefore, for x = 100 profit is maximum

Number of bird feeders = 100

b)Maximum profit

f(x) = -0.40 \(x^{2}\) + 80 \(x\) - 200

      = -0.40 x 100 x 100 + 8000 - 200

      = - 4000 + 8000 - 200

      = 4000 - 200

      = 3800

Therefore maximum profit = 3800

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it's neither

Step-by-step explanation:

It's not symmetrical

Answer:

C

Step-by-step explanation:

The function is neither

A graph of this sine wave function (y = sin(2x + π/2) + 1) is shown in the image attached below.

In Mathematics, a sine wave is also referred to as a sinusoidal wave, or just sinusoid and it can be defined as a fundamental waveform that is typically used for the representation of periodic oscillations, in which the amplitude of displacement at each interval is directly proportional to the sine of the displacement's phase angle.

Mathematically, a sine wave is represented or modelled by this mathematical expression:

y = asinbx

Where:

Next, we would solve the given sine wave function by taking the lowest common denominator (LCM) as follows:

y = sin(2x + π/2) + 1

y = sin((2(2x) + π)/2) + 1

y = sin((4x + π)/2) + 1

In conclusion, the amplitude (a) of this sine wave function is equal to 2.

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Answer:

72 inches

Step-by-step explanation: