Y varies directly as X and Y=39 when X = 52 find Y when X = 22

Answer: 540°.

Step-by-step explanation:

by

The value of x is given as follows:

x = 24.

The measure of angle DFE is given as follows:

<DFE = 62º.

To obtain the measures, we consider that the sum of the measures of the internal angles of a triangle is of 180º.

The internal angle measures for this problem are given as follows:

Hence the value of x is obtained as follows:

180 - 5x + 14 + 44 + 3x - 10 = 180

228 - 2x = 180

2x = 48

x = 24.

The measure of angle DFE is obtained as follows:

<DFE = 3(24) - 10

<DFE = 72 - 10

<DFE = 62º.

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The series 1/2 + 1/5 + 1/10 + 1/17 + 1/26 + ... converges

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

1/2 + 1/5 + 1/10 + 1/17 + 1/26.....

To apply the Integral test to given series, we can compare it to the area under the function 1/x.

As a general rule, the function 1/x is a decreasing function on the interval (1, ∞),

This means that the series converges.

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Answer: 4.2

Multiply both sides by 10

0.42 (10) = 0.1 (10)

4.2 = 1

Answer:

4.2

Step-by-step explanation:

Answer: x/2

Step-by-step explanation: Good morning. I am not sure what you mean by "A number x", so I suppose that is a typo.

Answer: x/2 IS CORRECT

Step-by-step explanation:

I TRIED IT :)

Answer:

0.955

Step-by-step explanation:

Height= volume x pi x radius squared (h = V x pi x r^2)

Volume (V) = 243

Height (h) = ?

Pi = 3.14

Radius (r) = 9

Diameter to radius = 18/2 = 9

h = 243 x 3.14 x 9^2

=0.955

The truth about the pattern that we have here is that all of the numbers are:    odd.

In the number pattern given, each term is 2 less than the previous term. Starting from 13, we have 11 (13 - 2), 9 (11 - 2), and 7 (9 - 2). All of these numbers are odd, making answer D the correct choice.

A. All the numbers are multiples of 3: This is not true, as 9 is the only number that is a multiple of 3.

B. All the numbers are even: This is not true, as all of the numbers are odd.

C. All of the numbers are prime: This is not true, as 9 is not a prime number.

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The interest rate required to pay a simple interest of $600 from an investment of $5000 in 2 years is 6%.

Simple interest is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for r.

I = P × r × t

r = I / Pt

r = 600 / ( 5,000 × 2 )

r = 600 / ( 10,000 )

r = 0.06

Interest rate = r × 100%

Interest rate = 0.06 × 100%

Interest rate = 6%

Therefore, the interest rate is 6%.

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The graph of the function y = f(x + 16) is a transformation of the original function f. This transformation has shifted the graph of f to the right by 16 units on the x-axis. This means that the value of x in the original function has been increased by 16, which has an effect on the corresponding value of y in the transformed function.

For example, if the point (a, b) is on the graph of f, then the point (a + 16, b) will be on the graph of y = f(x + 16). The x-coordinate of the point has been increased by 16, and since the transformation is a horizontal shift, the y-coordinate remains unchanged.

In summary, the graph of y = f(x + 16) is a reflection of the graph of f about the vertical axis. The transformation has the effect of shifting the graph to the right, but preserving the shape and overall form of the original function.

x = 15/2

do u need an explanation?

The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, ria is buying plates and cubs for a party. she wants the same numbers of each. Plates are sold in packs of 8. cups are sold in packs of 12.

Plates = 8 per pack

Cups = 12 per pack

the Lowest common multiple of 8 and 12

8 = 16, 24, 32, 40, 48, 56, 64, 72, 80

12 = 24, 36, 48, 60, 72

The Lowest common multiple of 8 and 12 is 24

The least number of plates and cups she can buy is 24

Packs of plates = 24 plates / 8 per pack

= 3 packs

She will buy 3 packs of plates

Packs of cups = 24 / 12 per pack

= 2 packs

She will buy 2 packs of cup

Therefore, The least number of plates and cups she can buy is 24. She will buy 3 packs of plates and 2 packs of cup

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Based on the manufacturing overhead applied to production during the period of $432,000, the fixed manufacturing overhead cost is $286,200.

The manufacturing overhead applied is determined as the product of the predetermined overhead rate and the actual machine hours consumed during the period.

Estimated machine hours to be worked = 55,000 hours

Actual machine hours during the period = 54,000 hours

Total manufacturing overhead applied to production = $432,000

Estimated variable manufacturing overhead per machine hour = $2.70

Total variable manufacturing overhead = $145,800 ($2.70 x 54,000)

Fixed manufacturing overhead (MOH) cost = $286,200 ($432,000 - $145,800)

Thus, the fixed manufacturing overhead cost is the difference ($286,200) between the total overhead cost applied and the variable manufacturing overhead cost.

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The mathematical expression, for the given phrase is n / 8

A mathematical statement, containing variables and numbers related by a mathematical operator, is called an expression.

Given that, a mathematical phrase: The quotient of a number by eight, we are asked to convert it into a mathematical expression,

Let n be the unknown number,

The quotient shows a result of division of two numbers,

Therefore,

The quotient of a number, n by eight, can be written as,

n / 8

Hence, the mathematical expression, for the given phrase is n / 8

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The expression to represent the given statement is:33 - (2 * 22 * ½x)

The expression "33 - (2 * 22 * ½x)" represents a mathematical calculation. Breaking it down, we start with the product of 2 multiplied by 22, which equals 44. Then, we multiply the result by ½x, where ½ represents one-half and x is a variable. This gives us the term 44 * ½x. Finally, we subtract this term from 33. In simpler terms, we have 33 minus half of 44 times x. The expression allows us to compute the value of the expression based on the input for the variable x, providing a way to evaluate the equation numerically.Let's dive deeper into the explanation.

The given expression is "33 - (2 * 22 * ½x)".

To simplify it, let's break it down step by step:

The term "2 * 22" is a multiplication operation that calculates the product of 2 and 22, resulting in 44.

Next, we have "½x". Here, ½ represents one-half, or 0.5. Multiplying 0.5 by x gives us 0.5x.

Putting it together, we have the term "44 * ½x". This means multiplying 44 by 0.5x, resulting in 22x.

Finally, we subtract the term "22x" from 33, giving us the expression "33 - 22x".

In summary, the expression represents the number 33 minus the product of 22 and the value of x, denoted as 22x. This expression allows us to calculate the result by substituting a specific value for x. It provides a way to compute the numerical outcome based on the given mathematical relationship.

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Answer:The length of AC to one decimal place in the trapezium is 18.1 cm

Step-by-step explanation: Using Pythagoras theorem, we can find the length AC

Pythagoras theorem

c² = a² + b²

Therefore, draw a line from the point B to the line AD and call it line BX.

BX ║ CD

Therefore,

16² - 7² = BX²

256  - 49 = BX²

BX² = 207

BX = √207

BX = 14.3874945699

BX = 14.4 cm

Therefore,

11² + 14.4² = AC²

121 + 207.36 = AC²

AC = √328.36

AC = 18.120706388

AC = 18.1 cm

The sum of the measures of the exterior angles of the polygon is,  360°

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

A polygon,

Having 9 equal sides,

The sum of the measures of the exterior angles of the polygon = ?

The sum of each interior & exterior angles are 180°

Suppose, interior angles  are respectively

a, b, c, d, e, f, g, h, i,

Now, exterior angles are respectively

180°-a, 180°-b, 180°-c, 180°-d, 180°-e, 180°-f, 180°-g, 180°-h, 180°-i,

The sum of the measures of the exterior angles of the polygon =

180°-a  + 180°-b +180°-c +180°-d + 180°-e + 180°-f  + 180°-g +180°-h + 180°-i,

1620 - (a + b + c + d + e + f + g + h + i)

Sum of all the interior angles  = (9-2)x180°

                                                  =  1260°

The sum of  the exterior angles of the polygon =  1620 - 1260°

                                                                               =   360°

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Answer:

30mg

Step-by-step explanation:

10 mg/mL x 3 mL

The amount invensted at 5% and 7% are 3500 and 4500 respectively.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, an amount $8000, is invested at 5% and 7%, with annual interest is $490,

For this we will establish the a system of equations,

x + y = 8000......(i)

0.05x + 0.07y = 490

Multiplying by 100,

5x + 7y = 49000.....(ii)

Multiplying eq(i) by 5,

5x + 5y = 40000

Subtract eq(i) from eq(ii)

2y = 9000

y = 4500

Put y = 4500 in eq(i)

x = 8000 - 4500

x = 3500

Hence, the amount invensted at 5% and 7% are 3500 and 4500 respectively.

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Answer:

[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\[/tex]

[tex]a=38.5[/tex] ft

[tex]b=51[/tex] ft

[tex]c=76[/tex] ft

Step-by-step explanation:

Here is the formula for the Law of Sines.

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]`

In this example we are given

[tex]\angle A =27.2 \textdegree\\\angle C=115.5 \textdegree\\c=76.0[/tex]

Angle B

The sum of the interior angles in a triangle add up to 180º. Given 2 angles, we can evaluate the 3rd.

[tex]180\textdegree-115.5\textdegree-27.2\textdegree=37.3 \textdegree[/tex]

[tex]\angle B=37.3 \textdegree[/tex]

Side a

We can use the Law of Sines formula  [tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]  to evaluate side a.

Inserting our values into the equation gives us

[tex]\frac{a}{\sin 27.2}=\frac{76}{\sin 115.5}[/tex]

Cross multiply to evaluate side a.

[tex]76*\sin 27.2=a*\sin 115.5[/tex]

Divide both sides by [tex]\sin 115.5[/tex].

[tex]\frac{76*\sin 27.2}{\sin 115.5} =a[/tex]

[tex]38.49=a[/tex]

Side b

We can use the Law of Sines formula  [tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]  to evaluate side b.

Inserting our values into the equation gives us

[tex]\frac{b}{\sin 37.3}=\frac{76}{\sin 115.5}[/tex]

Cross multiply to evaluate side b.

[tex]76*\sin 37.3=b*\sin 115.5[/tex]

Divide both sides by [tex]\sin 115.5[/tex].

[tex]\frac{76*\sin 37.3}{\sin 115.5} =b[/tex]

[tex]51.03=b[/tex]

[tex]\angle A= 27.2 \textdegree\\\angle B=37.3 \textdegree\\\angle C=115.5 \textdegree\\a=38.5\\b=51\\c=76[/tex]

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sin(A) / a = sin(B) / b = sin(C) / c

where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the sides opposite those angles.

The correct statements regarding the translation from function f(x) to function g(x) are given as follows:

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The translations for this problem are defined as follows:

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Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

Since the depth of the water 'd' (in feet) and the velocity of the wave 'v' (in feet per second) are related by the equation

v = √(16d)

a wave forms in water with a depth of 300 feet,

therefore d = 300 ft

so, we get,

velocity = √(16*300)

             = 4√300

             =4*17.32

             =69.28

Hence, Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.

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The standard form of the equation (x + 2)² = 4 (x + 5) + y is:

x² + y - 16 = 0

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The standard form of an equation is Ax + By = c.

Now,

(x + 2)² = 4 (x + 5) + y

x² + 4x + 4 = 4x + 20 + y

x² + 4 = 20 + y

x² + y = 20 - 4

x² + y = 16

x² + y - 16 = 0

Thus,

x² + y - 16 = 0 is the standard form of an equation.

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The probability that neither of them is chosen for inspection is given as follows:

a) 81 %

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

n = 2, p = 0.1.

The probability of neither is P(X = 0), hence:

P(X = 0) = (1 - 0.1)² = 0.81.

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The value of function relating the number of people, n, to the cost, C is,

⇒ C (n) = 7n ; if 0 < n < 15

           = 105n ; if n ≥ 15

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A museum charges $7 per person for a guided tour with a group of 1 to 14 people or a fixed $105 fee for a group of 15 or more people.

Hence, he value of function relating the number of people, n, to the cost, C is,

⇒ C (n) = 7n ; if 0 < n < 15

           = 105n ; if n ≥ 15

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Answer:

sec 30° = 1/cos 30° = 2.

Step-by-step explanation:

The secant function (sec) is the reciprocal of the cosine function. So, sec(x) = 1/cos(x). The value of cosine at 30 degrees is sqrt(3)/2, and its reciprocal is 2/sqrt(3), which can be simplified to 2. Hence, sec(30°) = 2.

Answer: equal to the sum of the area of all of its faces

Step-by-step explanation:

Answer:

$ 4.86

Step-by-step explanation:

Subtract 7.19 and 2.33

7.19-2.33=4.86

The general solution of the ODE is:

y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1

y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1

This is a first-order linear ordinary differential equation (ODE) with constant coefficients. It can be solved using the method of integrating factors.

Let's multiply both sides by the integrating factor e^(∫p(x)dx), where p(x) = 1.

e^(∫p(x)dx) * Dy/dx + e^(∫p(x)dx) * y = e^(∫p(x)dx) * f(x)

D/dx (e^(∫p(x)dx) * y) = e^(∫p(x)dx) * f(x)

Integrating both sides, we get:

e^(∫p(x)dx) * y = ∫ e^(∫p(x)dx) * f(x) dx + C

where C is an arbitrary constant of integration.

Using the initial condition y(0) = 1, we can find the value of the constant C.

y(0) = 1 = e^(∫p(x)dx) * y(0) = e^(∫p(x)dx) * 1 = ∫ e^(∫p(x)dx) * f(x) dx + C

So, C = 1 - ∫ e^(∫p(x)dx) * f(x) dx

For 0 ≤ x ≤ 1, we have f(x) = 1 and:

∫ e^(∫p(x)dx) * f(x) dx = ∫ e^x dx = (e^x - 1) / 1

For x ≥ 1, we have f(x) = -1 and:

∫ e^(∫p(x)dx) * f(x) dx = ∫ -e^x dx = -(e^x - 1) / 1

Therefore, the general solution of the ODE is:

y(x) = e^-x * (1 - (e^x - 1) / 1) + (e^x - 1) / 1 * (e^x + 1) / 1, 0 ≤ x ≤ 1

y(x) = e^-x * (1 + (e^x - 1) / 1) - (e^x - 1) / 1 * (e^x + 1) / 1, x ≥ 1

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the equation of  line passes through points (0, -3) and (4, -1) is 4y  = 3x -12.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, an equation of a line in the graph.

Since the graph shows that the line passes through points (0, -3) and (4, -1).

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept (value of y at x =0)

since

slope = (y - y')/(x -x')

In our case,

slope (m) = (-1 - (-3))/(4 -0)

m = 3/4

b = -3

Thus, the equation of the line:

y = 3/4x - 3

or, 4y  = 3x -12

therefore, the equation of the line will be 4y  = 3x -12.

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