The probability that a new machine will not need any repairs within t years from now is modeled by an exponential function of t. This probability is multiplied by 0.2 whenever the time period t is extended by 3 years as shown by the function belowf(t) = (0.2)^t/3 If the probability that the machine does not need repairs right now is 1, what is the probability that the machine will not need repairs within 12 years from now, according to the model? 0.8 0.05 0.008 0.0016

The constant of variation is 0.4.

What is constant of variation?

A direct variation's product of two variables or the product of two variables in an inverse variation The constant of variation is used in the direct variation equations = k and y = kx as well as the inverse variation equations xy = k and y = k.

We know that  y is directly proportional to the square of x.

Therefore we can use the formula,

y = kx^2

Putting the values of x and y,

10 = k (5)^2

=> 10 = k .25

=> 10/25 = k

=> k = 0.4

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The required expression equivalent to the given expression is 3²² .

An expression in mathematics is said to be algebraic if it was constructed using integer variables, constants, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

Given : the expression of the form ( 3 ⁴ ) ⁶ ÷ 3²

Simplifying we get:

= ( 3 ⁴ ) ⁶ ÷ 3²

= 3⁽²⁴⁻²⁾

=  3²²

Therefore the required expression equivalent to the given expression is

3²² .

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Answer: it should be 5

we can multiply 3x4 to get twelve so it must be the same for the other one

So 5x4=20

Step-by-step explanation:

have a great day!

Answer:

5

Step-by-step explanation:

12/4 = 3. 20/4 = 5

Side 12 divided by side 3 is four. You know four is now your key. Side 12 divided by 4 is Side 3. Side 20 divided by 4 is 5. So 5 is your answer.

Hope this helps! :)

Answer:

51 or above

Step-by-step explanation:

He already averages more then 78. But he at least needs a 51 in order for him to average 78. For him to get more than that he just needs a 52 or higher.

78 x 5 = 390

95 + 92 + 84 + 68 = 339

339/ 4 = 84.75 ( just to let you know the average before #5 )

390 - 339 = 51

51 is that last score needed

If the tangent of θ equals one (1), the true statement about the right-angled triangle side lengths is that: C. The sides opposite and adjacent to theta are the same length.

In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.

Mathematically, the tangent of an angle is given by this expression:

Tanθ = Opp/Adj

Where:

For this right-angled triangle, the tangent of the angle (θ) is given by:

Tanθ = Opp/Adj = 1

Opposite/Adjacent = 1

Cross-multiplying, we have:

Opposite = Adjacent

In conclusion, the opposite side length of this right-angled triangle is equal to its adjacent side length.

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Step 0 ---- 2

2+1

step 1 ------ 3

3+3

step 2 --------- 6

6+5

step 3 ----------11

11 + 7

step 4 ------------ 18

terms are 2, 3, 6,11, 18

There is an increment of odd numbers from a preceding term

2 increase to 3 by the first odd i.e 1

3 increase to 6 by the next odd i.e 3

6 increase to 11 by the next odd i.e 5

Therefore 11 will increase by the next odd, i.e 7

Thus, 11 + 7 = 18

You have to determine which of the given square roots can be expressed as a fraction:

1) The square root of one is 1

One can be expressed as a fracion:

So it is a rational number.

2) The square root of 2 is an irrational number and cannot be expressed as a fraction.

Its decimal expantion has no end, i.e. it has infinite decimal values.

3) Square root of three is an irrational number and cannot be expressed as a fraction.

4) The square root of 5 is an irrational number and cannot be expressed as a fraction.

In conclusion the only rational number in the given set is the square root of 1.

The correct answer is [B]

Binary and unary operations are the two most popular forms of operations. Trigonometric functions and negation are examples of unary operations that use only one value. Contrarily, binary operations, which include addition, subtraction, multiplication, division, and exponentiation, only accept two values. Here the same expression will be 5 ∑([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex]

Mathematical objects other than numbers can be used in operations. Logic operations like and, or, and not can be used to combine the logical values true and false. It is possible to add and subtract vectors. Utilizing the function composition operation, it is possible to combine rotations by first performing the first rotation and then the second. The binary operations union and intersection as well as the unary operation of complementation are operations on sets. Composition and convolution are two operations on functions.

Not all possible values of the domain may be covered by an operation's definition. For instance, it is impossible to square the roots of negative integers or divide by zero in real numbers. An operation's domain of definition, also known as the active domain, is the set of values for which the operation is specified. However, the set of real values obtained by the operation is its codomain of definition, active codomain, image, or range. The set that contains the values created is referred to as the codomain. [failed to verify] For instance, only non-negative numbers are produced by the squaring operation when applied to the real numbers; the set of real numbers is the codomain, but the non-negative numbers are the range.

4

∑(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex])

i=0

4

∑(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex])= (5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{0}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{1}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{2}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{3}[/tex])+(5[tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{4}[/tex])

0          

              = 5([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{0}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{1}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{2}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{3}[/tex])+([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{4}[/tex])

                    4

             = 5 ∑([tex]([/tex][tex]\frac{1}{3}[/tex][tex])^{i}[/tex])

                   i=0

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Compound interest formula:

A = P (1 + r/n )^nt

Where:

A = future vale

P= Principal investment = 9,000

r = interest rate in decimal form = 9/100 = 0.09

n = number of compounding periods = 4

t = years = 8

Replacing:

A = 9000 ( 1 + 0.09/4)^ (4*8)

A = 9000 (1.0225)^32

A= 18,342.93

The future value is $18,342.93

Given that

The figure is of a cone and we have to find the volume of the cone.

Explanation -

The diameter of the cone is 22km and the height is also 22 km.

So the radius will be

radius = r = d/2 = 22/2 km = 11 km

Hence, r = 11 km and h = 22 km

The formula for the volume of the cone will be

On substituting the values we have

So B is the correct option.

Final answer -

1. The statements that are true about the variables involved in this situation and the values for each variable are:

2. The number of rides Dina can go on using all of her tickets are

3. Yes, The number of rides equals the total number of tickets while maintaining going for a ride most once

The answer makes sense in the context of the situation because the numbers of rides are A. 7 and the number of tickets totals B. 24

given data

Dina has 24 tickets for carnival rides

She plans to go on a ride most once

Rides with no height requirement cost 3 tickets

Rides with a height requirement cost 4 tickets

1. The given statement includes: She plans to go on a ride most once. This means that Dina will not have a zero ride.

zero is a real number and a non negative integer hence option A is correct

2. Option C maintains she plans to go on a ride most once and the number of tickets used totals 24

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Given the information on the problem, we can write the following system of equations:

then, we can write the following augmented matrix:

now, if we multiply by 5 the first row and then substract it from the second row, we get:

notice that from the second equation, we can find the value of y:

now that we have that y = 4, we can use this value on the first equation to find x:

now, we have that the babysitter worked 1 hour before 11pm and 4 hours after 11 pm,then, the Burkes came home at 3 am

To determine the z-value so that the area to the right of z is 0.9429

7 * the smaller of two consecutive even integers is the same as -248 minus 6 * the larger integer. find the integers​

let

x ----> the smaller of two consecutive even integers

x+2 -----> the second integer

so

7x=-248-6(x+2)

solve for x

7x=-248-6x-12

7x+6x=-248-12

13x=-260

x=-20

the second number is

-20+2=-18

Looking at the series, we have a geometric sequence, where the first term is a1 = 5 and the common ratio is q = -3/5.

(This ratio can be calculated by dividing one term by the term before)

To find the sum of an infinite geometric sequence, we can use the formula below:

Since a1 = 5 and q = -3/5, we have:

Therefore the correct option is C.

The equations which show the total volume of the boxes Marcus shipped are as follows:

A. (20 × 10 × 7) + [2× (20 × 4 × 4)]

C. (20 × 10 × 7) + (20 × 4 × 4) + (20 × 4 × 4)

F. (200 × 7) + [2 × (80 × 4)]

Mathematically, the volume of a rectangular prism can be calculated by using this equation:

Volume = L × W × H

Where:

For rectangular prism 1, the volume is given by:

Volume 1 = L × W × H

Volume 1 = 20 × 7 × 10

Volume 1 = 200 × 7

Volume 1 = 1,400 cubic inches.

For rectangular prism 2, the volume is given by:

Volume 2 = L × W × H

Volume 2 = 20 × 4 × 4

Volume 2 = 80 × 4

Volume 2 = 320 cubic inches.

Since Marcus shipped 1 of the larger boxes and 2 of the smaller boxes, the total volume of the boxes Marcus shipped is given by these three (3) equations:

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y-axis

When a figure is reflected about any axis, the coordinate of that axis still remains the same, but the coordinate of the other axis is negated

For example:

If the point A(x, y) is reflected about the x-axis, the reflected image becomes A' (x, -y)

If the point A(x, y) is reflected about the y axis, the reflected image becomes A'(-x, y)

In this exercise, the point F(10, -5), after reflection, becomes F' (-10, -5)

Since the y-axis still remains -5 after reflection, this means that the point F was reflected across the y-axis.

After evaluating the limit we have came to find that the limit of [tex]\frac{x + 1}{x^2 -4x +4}[/tex] as x approaches 2 is ∞

A limit in mathematics is the value that a function, sequence, or index approaches as an input, or an index, approaches a certain value. The definitions of continuity, derivatives, and integrals depend on limits, which are fundamental to calculus and mathematical analysis.

The idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network, and it is closely related to the concepts of limit and direct limit in category theory.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

[tex]\lim_{x \to 2} \frac{1 + 0}{2x -4 +0}[/tex]

Evalúe 2 as x

⇒ [tex]\frac{1 + 0}{2x -4 +0}[/tex]

⇒ [tex]\frac{1}{2(2) -4 +0}[/tex]

⇒ [tex]\frac{1}{0}[/tex]

⇒ ∞

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The distance between the points E = (-4,5) and L = (1,-3) in the coordinate plane is  [tex]\sqrt{89}[/tex]

The points are E = (-4,5) and L = (1,-3)

We know the distance between the two points d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Where d is the distance between two points

[tex](x_{1},y_{1} )[/tex] and [tex](x_{2},y_{2} )[/tex] are the coordinates of the points

Here the given points are E = (-4,5) and L = (1,-3)

To find the distance between the given points, we have to substitute the values in the equation

d = [tex]\sqrt{1-(-4))^{2}+(-3-5)^{2} }[/tex]

d = [tex]\sqrt{5^{2}+(-8)^{2} }[/tex]

d = [tex]\sqrt{25+64}[/tex]

d = [tex]\sqrt{89}[/tex]

Hence, the distance between the points E = (-4,5) and L = (1,-3) in the coordinate plane is  [tex]\sqrt{89}[/tex]

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Answer:

B: 2.3 x 10^18

expination:

Substitute values into the formula.

F x L = 3.0 x 10*10

F x 1.3 x 10^−8 = 3.0 x 10^10

F = 3.0 x 10^10 1.3 x 10^−8 F = 2.3 x 10^18

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The function f is positive on the domain (-∞, 3)

The f(x) values corresponding to x-values are given. Also f(x) is a continuous linear function.

If we analyze the function values, the first 3 entries are positive, then from there the function values becomes negative.

Also it is clear from the function values that the function is decreasing from positive values to negative values.

The corresponding x-values for the positive values of the function are x = -3, x = 0 and x = 3.

Since f(x) is continuous linear function, the given x-values and f(x) values are not the only ones there. The domain and images are actually in the form of intervals, but here only certain values are given in the table.

Therefore, the function must be positive for x < -3 too.

Hence the domain where the function is positive becomes (-∞, 3).

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Answer:

4.5

Step-by-step explanation:

2/1 x 9/4 = 18/4 = 4.5

Answer:

4.5 is your answer

Step-by-step explanation:

hope it helps

The specific thing about this graph is it forms a straight line, and it extends to point of origin. The time x is on the x-axis and the distance y is on the y-axis. The coordinates on the graph are the same as the pairs in the table. (2, [tex]6\frac{2}{3}[/tex]) means Sam's mother ran  [tex]6\frac{2}{3}[/tex] km in 2 hours.

Relationships between two variables are called as proportional when you see that their ratios are equal. One variable in a proportional connection is always a constant value multiplied by the other. "Constant of proportionality" is the name that is given to this constant.

The graph of a proportionate connection is a straight line that passes through the origin and rises steadily. The graph's unit rate can be represented by the point on this graph.

The graph depicting this proportional relationship formed in the table can be seen in the image attached.

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The complete question is:

"Sam's mother has entered a 10K race. Sam and his family want to show their support of their mother, but they need to

figure out where they should go along the race course. They also need to determine how long it will take her to run the

race so that they will know when to meet her at the finish line. Previously, his mother ran a SK race with a time of

hours. Assume Sam's mother ran the same rate as the previous race in order to complete the chart.

Create a table that shows how far Sam's mother has run after each half hour from the start of the race, and graph it on

the coordinate plane to the right.

a) What are some specific things you notice about this graph?

b) What is the connection between the table and the graph?

c) What does the ordered pair (2,6 [tex]\frac{2}{3}[/tex]) Represent in the context of this problem?"

Answer:

.457

Step-by-step explanation:

The WHOLE area is = 1

so   1 - .543 = .457

Answer: A.

Step-by-step explanation:

Answer:

the perimeter of a triangle is 84 cm and its area is 336 cm? if one of its side is 30 cm find the length of reamining two side

Answer:

I can see that (0, 2) is the solution to this equation because that is the point where the lines intersect.

Step-by-step explanation:

[tex] - 3x + 2 = \frac{1}{2} x + 2[/tex]

[tex] - 3x = \frac{1}{2} x[/tex]

[tex]x = 0[/tex]

[tex]y = 2[/tex]

Answer:

12

Step-by-step explanation:

4xA+7=55

using PEMDAS multiplication comes first

A4+7=55

A4=55-7

A4=48

A=48/4

A=12

check:

4x12+7=12

Step-by-step explanation: