An element with a mass of 240 grams decays by 17.4% per minute. To the nearest
tenth of a minute, how long will it be until there are 20 grams of the element remaining?

The value of variable x in the equation is -1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

To solve the equation , we have to find the variable x.

A variable is a number represented with letter in an equation.

Hence,

2³ˣ⁺¹ = 1 / 4

Using law of indices, we have to make the base equal.

Hence,

1 / 4 = 2⁻²

Therefore,

2³ˣ⁺¹ = 2⁻²

The base will cancel each other

3x + 1 = -2

subtract -1 from both sides of the equation

3x + 1 - 1 = -2 - 1

3x = -3

divide both sides by 3

x = -3 / 3

x = -1

Therefore,

x = -1

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The exponent [tex]3^{21}[/tex] is 9 times greater than the exponent [tex]3^{19}[/tex]

What are Exponents?

Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself.

Solution:

To solve this type of question all we need to know are the Rules of Exponents with their help any question of this type can be solved

Since we are required to find the number of times the value os greater so we will divide the numbers

3^21 / 3^19

By rule of exponents if a^b/a^c then we can write it as a^(b-c)

Similarly 3^21 / 3^19 = 3^(21 - 19) = 3^2 = 9

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Answer:

Step-by-step explanation:

Answer:

-3.5(x-14)+9x=5.5x + 49 is a TRUE statement that equals 0. It has infinite solutions.

Step-by-step explanation:

Answer:

22 divided by 2 is 11

Step-by-step explanation:

The angle of the elevation comes to be 41.94 degrees.

The angle of elevation is the angle that is to be formed between the horizontal line and the given line of sight. If the line of sight is upward from the given horizontal line, then the angle formed is an angle of the elevation.

The most crucial area of mathematics is trigonometry. Combining the Greek "Trigonon" and "Metron," which respectively mean "triangle" and "measure," creates the word "trigonometry." It is the examination of the relationship between a right-angled triangle's sides and angles. By employing formulas and identities based on this relationship, it is thus possible to determine the measure of a right-angled triangle's unknown dimensions.

As in the case of right angled Triangle

From Trigonometry,

tan (α) =  [tex]\frac{124}{138}[/tex]

α = arctan(  [tex]\frac{124}{138}[/tex] )

α = 41.94 degrees

and in radians = 0.732

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Answer:

The area of the square is 225 square kilometres.

Step-by-step explanation:

So,

A = (15)² km

A = 225 km²

Thus, The area of the square is 225 square kilometres.

The expression in terms of xx that represents the total amount that Hailey paid is (2912/625)xx .

What is business Mathematics?  

Business mathematics is the branch of mathematics utilized by businesses to track and coordinate their operations. Accounting, inventory management, marketing, sales forecasting, and financial analysis are all areas where commercial businesses apply mathematics.

According to Question:

let the the subtotal on the bill was xx dollars

A tax of 8% is added on bill then Bill becomes xx + 8% of xx

The of 8% on bill = (108/100)xx

Now the Final bill = xx + (108/100)xx

                    = (208/100)xx

Hailey decides to leave a tip of 24% on the entire bill (including the tax)

So the Total Amount = (208/100)xx + 24% of Final bills

⇒

24% of (208/100)xx = (208/100)(124/100)xx

The Total amount = (208/100)xx +(208/100)(124/100)xx

Let the Amount be A

hence, expression in terms of xx that represents the total amount that Hailey paid is A = (208/100)xx +(208/100)(124/100)xx

⇒ A = (52/25)xx +(52/25)(31/25)xx

⇒ 625A = 625((52/25)xx +(52/25)(31/25)xx)

⇒ 625A = 1300xx + 1612xx

⇒ 625A = 2912xx

⇒ A = (2912/625)xx

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The quotient of x⁴ – 3x³ – 7x + 1 ÷ x + 2 is x³ - 5x² + 3x and the remainder is 5

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

x^4 – 3x^3 – 7x + 1 ÷ x + 2

Rewrite as

x⁴ – 3x³ – 7x + 1 ÷ x + 2

This means that

Divisor = x + 2

Dividend = x⁴ – 3x³ – 7x + 1

Using the synthetic division, we have the following setup

-2 |    1     -3    -7     1

Bring down the first factor

-2 |    1     -3    -7     1

        1

Multiply by -2

-2 |    1     -3    -7     1

              -2

        1

Repeat the above steps as follows

So, we have

-2 |    1     -3    -7     1

              -2    10    -6

        1      -5    3    5

The last number represents the remainder of the division

This means that

Remainder = 5

Quotient = x³ - 5x² + 3x

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A 12-foot ladder is resting against a wall and makes an angle of 52 degrees with the ground, the height to which the ladder will reach the wall is 9.456 foot.

Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is a term used to describe everything that may be measured vertically, high or low.

From the lowest to the highest point to the lowest point, it calculates the vertical distance. In general, it refers to a coordinate geometry object's measurement along the y-axis.

let, h = height of ladder

Given that,

length of ladder = 12 ft

angle with the ground = 52°

As we know,

sinθ = h/12

or, sin (52°) = h/12

or, 0.7880 = h/12

or, h = 9.456 foot.

the height to which the ladder will reach the wall 9.456 foot.

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Answer:

its d I did the test hope its helps

Answer:

To graph the relationship between the pool's water level and time, we can start by creating a table of values for the water level at different times. Here is an example of such a table:

Time (minutes) Water Level (centimeters)

0 0

1 6

2 12

3 18

4 24

5 30

6 36

7 42

8 48

9 54

10 60

11 66

12 72

13 78

14 84

15 90

16 96

17 102

18 108

19 114

20 120

We can then plot these values on a graph, with the time on the x-axis and the water level on the y-axis. The resulting graph would be a straight line that slopes upwards, starting at the origin (0, 0) and ending at (20, 120).

The graph shows that the water level in the pool increases linearly with time. The slope of the line represents the rate at which the water level is increasing, which in this case is 6 centimeters per minute.

Step-by-step explanation:

The equation of the parabola that has a vertex  (-3,4) and passes through  (2,8) is 25y = 4x² + 24x + 13.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the DirectX and focus, respectively.

Given:

The vertex = (-3, 4) and the point = (2, 8)

Write the equation using the standard form given below,

[tex]y = a (x - h)^2 + k[/tex]

y = a[x - (-3)]² + 4

y = a(x + 3)² + 4

Now put the coordinates,

8 = a (2 + 3)² + 4

8 = 25a + 4

a = 4 / 25

Put the value of a in the above equation,

y = 4/25 × (x + 3)² + 4

25y = 4 (x² + 9 +6x) + 100

25y = 4x² + 36 +24x + 100

25y = 4x² + 24x + 13

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△KML is congruent to △QNP (△KML ≅  △QNP) under SSA conditions.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Slide, twist, flip, and turn these triangles to create an identical appearance.

They are in alignment with one another when moved.

If two triangles meet all 5 requirements for congruence, then they are congruent.

They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS) (RHS).

So, in the given triangle:

Prove that: △KML ≅  △QNP

∠L = ∠P = 90° (Equal: Given)

ML = QP = 12 units (Equal: Given)

Mk = QN = 15 units (Equal: Given)

So, △KML ≅  △QNP is under SSA condition.

Therefore, △KML is congruent to △QNP (△KML ≅  △QNP) under SSA conditions.

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The speed of car is 50 miles per hour and the speed of the motorcycle is 40 miles per hour.

Let M = speed of the motorcycle.

Hence, speed of the car = 2M - 30.

Distance covered = Time taken x Speed.

Hence in 2 hours,

Distance covered by motorcycle = 2M

Distance covered by car = 2(2M-30).

Given, the car is 20 miles ahead of the motorcycle.

Hence,

2(2M-30) = 2M + 20

4M-60 = 2M + 20

2M = 80

M = 40

2M-30 = 2(40)-30 = 80-30 = 50

Therefore, speed of motorcycle is 40 miles per hour and speed of car is 50 miles per hour.

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The solutions to the equation word problems are as follows;

1) Amount jane will have is 50 + 2d

2) Amount Elis will have = 24 + 6d

3) The equation is; 50 + 2d = 24 + 6d

4) Amount each has saved = $63

We are given that;

Amount Jane has = $50

Amount Elis has = $24

Amount saved by Jane each day = $2

Amount saved by Elis each day = $6

1) After d days of saving, amount jane will have is;

A = 50 + 2d

2) After d days of saving, amount Elis will have is;

A = 24 + 6d

3) The equation that will be used to show when Joan and Elis would have saved same amount is;

50 + 2d = 24 + 6d

4) 50 + 2d = 24 + 6d

26 = 4d

d = 26/4

d = 6.5 days

Amount each has saved = 50 + 2(6.5) = $63

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The measure of the angle x would be 30.26°.

What are inverse trigonometric functions?

Inverse trigonometric functions are functions that "undo" the action of the trigonometric functions. They allow us to find the angles of a right triangle given the values of the sides, or to find the values of the sides given the angles.

In the given triangle, by using sine ratio we can write

        sin(x°) = BC/AC

       [tex]sin(x^o)=39/74\\\\x^o=sin^{-1} \frac{39}{74}\\\\x^o=sin^{-1}{0.5270}\\\\x^o=30.26^o[/tex]

Hence, the measure of the angle x would be 30.26°.

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The word problem 4 and one tenth times negative 4 times 5 over 12 have a product of negative 8 and one fifth

Multiplication is one of the basic mathematical operator which is used to solve the given problem. It is the inverse of division. the result of multiplication is called the product

Rewriting the word problem 4 and one tenth times negative 4 times 5 over 12 to figures

4 1/10 * -4 * 5/10

solving the equation

= 4 1/10 * -4 * 5/10

= 41/10 * -4 * 5/10

= -41/5

= -8 1/5

The product of the multiplication is negative 8 and one fifth

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Answer: In order to describe a translation using arrow notation, we need to specify the direction and distance of the translation. In the case of the given translation, point P is translated to point P' by moving 6 units to the left and 2 units down. This can be represented using arrow notation as follows:

P' = P ← 6 ↓ 2

Here, the symbol ← represents a leftward movement, and the symbol ↓ represents a downward movement. The numbers 6 and 2 indicate the distance of the movement in the respective directions. This means that point P is translated to point P' by moving 6 units to the left and 2 units down from its original position.

The force on the object is 40N

Force can be described as the influence that can change the motion of an object.

It is seen as an external agent having the capability of changing a body's state of motion or rest.

It causes b in velocity of an object with mass , that is,  to accelerate. Force can also be described as either a push or a pull.

It is described as a vector quantity, that is, it has both magnitude and direction.

The formula for determining force is given as;

F = ma

Where;

Substitute the values

F = 10(4)

F = 40N

Hence, the value is 40N

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On solving the provided question, we can say that - by equation, total amount of water removed was  = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters

An equation is a mathematical formula that expresses equality by joining two expressions together with the equal symbol =. A formula that claims two formulae are equal is the definition of an equation in algebra in its most basic form. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. An equal sign is a part of all mathematical formulas, including equations. Often, algebra is used in equations. In mathematics, algebra is employed when we don't know the precise quantity to calculate.

R'(2) = R(3) - R(1) /3-1 = 950-1190/2 = /120L/hr

total amount of water removed was  = 1.R(0) + 2.R(1) + 3.R(3) = 1(1340) + 2(1190) + 3(950) + 2(740) = 8050 liters

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Answer:
You sold 15 vegetarian sandwiches and 10 turkey sandwiches.

Step-by-step explanation:

First, let's call the number of vegetarian sandwiches sold "V" and the number of turkey sandwiches sold "T".

We can set up the following equation: 3V + 4T = 85

Next, we need to find the values of V and T that satisfy this equation. To do this, we can use the fact that V and T must be whole numbers since we cannot sell a fraction of a sandwich.

We can start by trying V = 1 and T = 6. Plugging these values into the equation, we get: 3(1) + 4(6) = 18 + 24 = 42

Since 42 is not equal to 85, this means that V and T cannot both be 1 and 6.

We can try other values of V and T that are whole numbers until we find a combination that satisfies the equation. One way to do this is to use trial and error.

For example, we can try V = 2 and T = 5, which gives us: 3(2) + 4(5) = 6 + 20 = 26 This is still not equal to 85, so we can try other values. We can also use the fact that V + T = 25 (since we sold a total of 25 sandwiches) to help us solve the equation.

If we set V + T = 25, then we can rewrite the original equation as: 3V + 4(25 - V) = 85 Solving for V, we get: 3V + 100 - 4V = 85 Combining like terms, we get: -V = 15 Dividing both sides by -1, we get: V = 15

Since V + T = 25, this means that T = 25 - 15 = 10

Therefore, we sold 15 vegetarian sandwiches and 10 turkey sandwiches.

The probability that the committee includes all 3 women is 0.00018

In this question, we have been given there are 97 men and 3 women in an organization.

A simple random sample of 5 people is taken to form a committee.

We need to find  the probability that the committee includes all 3 women.

Total number of people in the organization: 97 + 3 = 100

Usinng combination formula the possible number of 5 people committee:

100C5

= 100! / 5!(100 - 5)!

= 75287520

The number of outcomes for the committee includes all 3 women would be:

5C3 = (97C2)*3

       = 13968

So, the probability that the committee includes all 3 women would be,

P = 13968 / 75287520

P = 0.00018

Therefore, the required probability is 0.00018

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The equation of the line is (b) y = 2.25x - 6.25

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

Points = (3, 1/2) and (5, 5)

A linear equation can be represented as

y = mx + c

Substitute the known values in the above equation, so, we have the following representation

1/2 = 3m + c

5 = 5m + c

Subtract the equations

2m = 4.5

Divide by 2

m = 2.25

Substitute m = 2.25 in 5 = 5m + c

5 = 5 * 2.25 + c

So, we have

c = 5 - 5 * 2.25

Evaluate

c = -6.25

Recall that

y = mx + c

So, we have

y = 2.25x - 6.25

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Complete question

Select the equation for the line crossing the points (3,1/2) and (5,5).​

(a) y = 5x + 2

(b) y = 2.25x - 6.25

(c) y = 2.25x + 6.25

(d) y = -5x - 2

The approximate mean and standard deviation of the number of chips meeting specifications are: μ = 16.2; σ = 1.273

In this question, we have been given a factory makes silicon chips for use in computers. it is known that about 90% of the chips meet specifications. every hour a sample of 18 chips is selected at random for testing and the number of chips that meet specifications is recorded.

we need to find  the approximate mean and standard deviation of the number of chips meeting specifications

Since 90% meet specifications we can say p = 0.9

So, q = 1 - p

q = 1 - 0.9

q = 0.1

here,  a sample size is n = 18

So, the mean would be,

μ = np

μ = 18 * 0.9

μ = 16.2

And the standard deviation would be,

σ = √npq

σ = √(18 * 0.9 * 0.1)

σ = 1.273

Therefore, the mean (μ) = 16.2 and the standard deviation (σ) = 1.273

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The simplest form of  [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is found to be  8.66025403784 .

A fraction is  in  its  simplest form   when   the    numerator   and   the denominator have  no common factors besides one.

Reducing equation is a method of rewriting the equation in a simpler form. Certain equations in mathematics are not in the form of linear equations but they can be put in the form of linear equations by performing some mathematical operations on them. After reduction of these equations in linear form they can be solved and the value of unknown can be calculated easily.

Given the equation is;

[tex]2\sqrt{3} + 3\sqrt{3}[/tex]

Now solving it ,

[tex]2\sqrt{3} + 3\sqrt{3}[/tex]

By adding this we get,

[tex]5\sqrt{3}[/tex]  (∵ [tex]\sqrt{3}[/tex] is common in both )

= 8.66025403784

The decimal (or) simplified value of [tex]2\sqrt{3} + 3\sqrt{3}[/tex] is  8.66025403784.

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The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.

Hence, The vertex domain of g(x)=|X-7| is (7,0) (-∞,∞) and (0,∞) and the function f(x)=|x| is vertically shifted.

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Answer:

Step-by-step explanation:

Let's call the two numbers x and y. We can set up the following equation to represent the problem:x + y = 679y = x + 431Substituting the second equation into the first equation, we get:x + (x + 431) = 679Combining like terms, we get:2x + 431 = 679Subtracting 431 from both sides, we get:2x = 248Dividing both sides by 2, we get:x = 124Substituting this value back into the equation y = x + 431, we get:y = 124 + 431 = 555Therefore, the two numbers are 124 and 555.

An isosceles triangular prism, its surface area becomes: 568 feet²

The faces of a polyhedron called an isosceles triangular prism are made up of polygons. It has six edges, five faces, and five vertices. Isosceles triangles make up the two portions at the base that face each other and rectangles make up the vertical faces of the five faces.

where the isosceles triangle's base has equal sides measured in "a" units, each triangle's base measured in "b" units, the triangle's height measured in "h" units, and the length of the congruent rectangles measured in "l" units.

The surface area of an isosceles triangular prism is:

Surface area = (b × h) + (2× l × a) + (l × b)

here, b = the base of each of the triangle = 16 feet

h = the height of the triangle = 18 feet

l = length of the congruent rectangles = 10 feet

a = isosceles triangle in the base have the equal sides be "a" units = 6 feet

Now, Surface area = (16 × 18) + (2 × 10 × 6) + (10 × 16)

or, Surface area = 568 feet²

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Answer:

The surface area of a sphere is 2461.76 units.

Step-by-step explanation:

where,

π = 3.14 or 22/7

r = radius of sphere

Here, we know that

radius = diameter ÷ 2 = 28/2 = 14 units

So,

A = 4 π r²

A = 4 × 3.14 × (14)² units

A = 12.56 × 196 units

A = 2461.76 units

Thus, The surface area of a sphere is 2461.76 units.

Answer:  the surface area of the sphere of diameter 28cm is 2464 cm²

Step-by-step explanation:

     Given, diameter = 28 cm

      hence, radius of the sphere = d/2 = 28/2 =14 cm

 Therefore, the surface area of a sphere of radius (r) = 4пr²

                 where п= 22/7= 3.14

                                            = 4×3.14×14×14

                                            = 2464 cm²