1/2(x+4)=1/2x+1 is there a solution

The surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

To find the increase in surface area, we first need to calculate the initial surface area of the box and then calculate the surface area after increasing the height.

The formula for the surface area of a rectangular prism is given by:

Surface Area = 2*(length width + length height + width*height)

Initial Surface Area:

Length (L) = 13 cm

Width (W) = 8.7 cm

Height (H) = 28 cm

Initial Surface Area = 2*(138.7 + 1328 + 8.7*28)

Next, we calculate the new surface area after increasing the height by 0.2 cm. The new height is:

New Height = Initial Height + Increase in Height = 28 cm + 0.2 cm

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2))

To find the increase in surface area, we subtract the initial surface area from the new surface area:

Increase in Surface Area = New Surface Area - Initial Surface Area

Let's calculate the values:

Initial Surface Area = 2*(138.7 + 1328 + 8.728) = 2(113.1 + 364 + 243.6) = 2*(720.7) = 1441.4 cm²

New Surface Area = 2*(138.7 + 13(28+0.2) + 8.7*(28+0.2)) = 2*(113.1 + 377.2 + 244.1) = 2*(734.4) = 1468.8 cm²

Increase in Surface Area = New Surface Area - Initial Surface Area = 1468.8 cm² - 1441.4 cm² = 27.4 cm²

Therefore, the surface area of the box increases by 27.4 cm² when the height is increased by 0.2 cm.

For such more questions on Increase in surface area

https://brainly.com/question/23851972

#SPJ11

Answer:

C(x) = 75x + 1908

Step-by-step explanation:

C(x) is the cost function.

The cost of making x bicycles is the sum of the fixed costs and the cost per bicycle.

The fixed cost is $1908.

The cost per bicycle is $75, so the per bicycle cost for x bicycles is 75x.

Add the two costs, and you get:

C(x) = 75x + 1908

we have a rate of 110 ml/hr so we can convert this rat to gtt/min so

and we simplify so:

The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Answer:

36

Step-by-step explanation:

48/8 = 6. 6*6 = 36.

In an expanded form, we are breaking up a number according to their place value.

For 504,969, we break-up each digit according to their place value except zero (0) because it has no significant value, hence, we get,

From the breakdown we made, B is the answer among the choices.

A view which Felix can use to construct the same figure include the following: A. a bottom row of 6 cubes, second row of 3 cubes, and top row of 1 cube.

In Mathematics and Geometry, an isometric sketch is sometimes referred to as an isometric drawing and it can be defined as a graphical (pictorial) representation of a physical object or geometric shape in technical and engineering drawings, especially by drawing all its three dimensions (3D) at full scale;

In this context, we can reasonably infer and logically deduce that the front view is a view which Felix can use to construct the same three-dimensional figure because its orientation influences the other views.

Read more on front view and dimensions here: https://brainly.com/question/29242295

#SPJ1

Answer:

the Dead Sea has the least elevation.

a.The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b.  the probability is 0.1399.

c. the quarterback can expect to throw about 2.27 passes before completing one.

d. the probability is 0.1865.

e. the probability is 0.7349.

The possibility or chance of an event occurring is measured by probability. The expression is given as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty. Compared to occurrences with a probability closer to 0, those with a probability closer to 1 are more likely to occur.

a. To construct a probability distribution table for the number of passes attempted before the quarterback has a completion, we can use the geometric probability distribution, which is given by:

P(X=k) = \((1-p)^{k-1}\)×p

where X is the number of attempts before the completion, p is the probability of completion on each attempt, and k is the number of attempts.

The probability distribution table for the first six attempts is shown below:

X P(X=k)

1 0.44

2 0.56 ×0.44

3 0.56²×0.44

4 0.56³ × 0.44

5 0.56⁴ ×0.44

6 0.56⁵×0.44

b. The probability that the quarterback throws 3 incomplete passes before he has a completion is given by:

P(X=3) = (1-0.44)³⁻¹× 0.44 × (1-0.44)⁰

= 0.56²×0.44

= 0.1399

Therefore, the probability is 0.1399.

c. The expected number of passes that the quarterback can throw before he completes a pass is given by the formula:

E(X) = 1/p

where p is the probability of completion on each attempt.

In this case, p = 0.44, so the expected number of passes is:

E(X) = 1/0.44

= 2.27

Therefore, the quarterback can expect to throw about 2.27 passes before completing one.

d. The probability that it takes more than 5 attempts before the quarterback completes a pass is given by:

P(X > 5) = 1 - P(X <= 5)

= 1 - [P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)]

= 1 - [0.44 + (0.56 × 0.44) + (0.56² ×0.44) + (0.56³ × 0.44) + (0.56⁴×0.44)]

= 0.1865

Therefore, the probability is 0.1865.

e. If the quarterback throws 8 passes on the opening drive, the probability that he completes at least half of them is given by the binomial probability distribution, which is given by:

P(X ≥ 4) = 1 - P(X < 4)

where X is the number of completed passes and the probability of completion on each attempt is p = 0.44.

Using the binomial probability distribution table or calculator, we can find:

P(X≥4) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

= 1 - [0.56⁸ + (8× 0.56⁷×0.44) + (28 × 0.56⁶ × 0.44²) + (56× 0.56⁵×0.44³)]

= 0.7349

Therefore, the probability is 0.7349.

To know more about distribution, visit:

https://brainly.com/question/31197941

#SPJ1

Answer:

what

Step-by-step explanation:

Answer:

2/5 or 0.4.

Step-by-step explanation:

6/15 = 2/5

According to the trigonometric function,  F(t) = 20 cos (2π/5)t where t represents time, in seconds. representing the pendulum ride of the sea dragon. It will take the pendulum 5 seconds to complete one full cycle.

A period on a graph function is the distance between two repeating points.

The graph repeats itself as it advances along the x-axis, as you can see.

Periods are the cycles of this predictable repetition. Every 6.28 units, or 2 pi radians, this graph repeats.

The equation is F(t) = 20 cos (2π/5)t

The amplitude of the equation is 20 and the graph makes 2π/5 oscillations at every t seconds

the period to complete an oscillation which is 2π

2π/5 * t = 2π

t = 2π * 5/2π  

t = 5 seconds

Learn more on trigonometry graphs at:

https://brainly.com/question/30023715

#SPJ1

The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.

The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.

To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.

Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.

Learn more about union of sets on:

brainly.com/question/2166579

#SPJ1

The integer n that satisfies the condition is n = 6.

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

(n +1)(7-n)(n-5)

To determine the smallest value of n, we make use of prime factorization and the rules of multiplication to simplify the expression

The prime factorization of (n +1)(7-n)(n-5) is n + 1, 7 - n and n - 5

Equate the expressions to 1

n + 1 = 1 gives n = 0

7 - n = 1 gives n = 6

n - 5 = 1 gives n = 6

n = 0 cannot be uses

When n = 6, we have

(n + 1)(7 - n)(n - 5) = (7)(1)(1) = 7, which is prime.

Hence, the integer is 6

Read more about prime at

https://brainly.com/question/1081523

#SPJ1

Answer:

Step-by-step explanation:

V = 108π in³

h = 4 in

r = √(3V/(πh)) = 9 in

Answer:

B

Step-by-step explanation:

If you have 108 pi and then you divided it to find the radius and all that stuffy stuff you will end up getting 9 and if you dont want to do it that way just substitute each one of the answer chooses as the radius until the volume gets you 108 pi cubic inches.

When a quadratic equation is given in the form y = a( x− ℎ )^2 + k the easily seen features are

Equation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation

The quadratic equation in the factored form is written as

y = a ( x − ℎ )^2 + k

This equation shows the coordinates of the vertex which is v(h, k)

The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis

"a" helps to determine if the curve opens upwards or downwards. when a is:

Learn more about factored form of quadratic equation here:

https://brainly.com/question/29339843

#SPJ1

Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

Answer:

<

>

<

Step-by-step explanation:

Lemme know if you need any in-depth help, 'kay?

The transformation of f(x) to g(x) is :

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

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

Read more about transformation at

brainly.com/question/27224272

#SPJ1

\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=16 \end{cases} \\\\\\ 16=\cfrac{k}{4}\implies 64 = k\hspace{9em}\boxed{y=\cfrac{64}{x}} \\\\\\ \textit{when x = 32, what's "y"?}\qquad y=\cfrac{64}{32}\implies y=2\)

Answer:

The table does not show the proportional relationship.

Step-by-step explanation:

When y varies directly with x, then the equation is

y ∝ x

y = kx

Where 'k' is called the proportionality constant.

Given the table

x         3        6      9      12

y         12      24    45    60

Let us check from the table whether the proportionality constant 'k' remains constant or not.

FOR (3, 12)

y = kx

k = y/x

   = 12 / 3 = 4

FOR (6, 24)

k = y/x

   = 24 / 6 = 4

FOR (9, 45)

k = y/x

   = 45 / 9 = 5

FOR (12, 60)

k = y/x

   = 60 / 12 = 5

From the above calculations, it is clear that the value of 'k' does not remain constant.

This means the value of 'k' for the points (6, 24) and (9, 45) is 4, while the value of 'k' for the points (9, 45) and (12, 60) is 5.

Hence, the table does not show the proportional relationship.

Part A :

Yes, the statement is true that  P( A and B ) = 0 .

Given,

Event A and Event B are mutually exclusive.

Thus P ( A and B ) = 0

Part B:

A and B are mutually exclusive events if they do not occur at the same time.

This means that A and B do not share any common outcomes and

P(A and B) = 0.

Part C:

Let,

The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.

A and B do not have any numbers in common so P(A and B) = 0.

Hence, A and B are mutually exclusive.

Learn more about Probability,

https://brainly.com/question/29492440

#SPJ1

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

A thus equals -89. The polynomial's equation can now be written as follows:

p(x) = -89(x-1) ² (x-3) ³

A mathematical equation is a statement that two quantities or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. An equation is used when two or more factors must be considered jointly in order to understand or define the overall situation.

The polynomials have variables of (x-1) squared if it has a dual zero at the value of x = 1. In a similar manner, if the polynomial contains a double zero at x = 3, we can infer that it has factors that are (x-3) cubed. Hence, the algebraic can be expressed as follows:

p(x) = A (x-1) ² (x-3) ³

We must figure out what the constant coefficient A is.

We can utilize the polynomial's passage through location (x, y) = to determine the value of A. (2, 89). Hence, we change x = 2 and y = 89 into the formula and find A:

89 = A (2-1) ² (2-3) ³

89 = A (-1) ² (-1) ³

89 = -A

To know more about Equation visit:

https://brainly.com/question/2228446

#SPJ1

A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

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

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

Read more about box plot at

https://brainly.com/question/3473797

#SPJ1