Find the dimensions of the cube

Answer:

[tex] \to \green{3\dfrac{3}{4}} \red\div \blue{ \dfrac{3}{8} }[/tex]

[tex] \to \rm \green{ \dfrac{15}{4} } \red \times \blue {\dfrac{8}{3} }[/tex]

[tex] \to \green{ \dfrac{ \cancel {15}^{5} }{ \cancel4}}\red\times\blue{\dfrac{ \cancel {8}^{2} }{ \cancel3} }[/tex]

[tex] \huge\boxed{\rm \color{cyan} \to10} [/tex]

[tex] \colorbox{gold}{Answer By} \: \: \: \\ \underbrace \colorbox{cyan}{ \color{purple}{SublimeRanter}}[/tex]

Answer:

10.

3 3/4 can be changed to 15/4.

Then you can use the, "Keep, Change, Flip" method:

15/4 * 8/3

Then multiply the numerators and denominators together:

15 * 8 = 120

4 * 3 = 12

Resulting with = 120/12

Now divide thew numerator by the denominator to get you final product:

120 / 12 = 10

The final answer is 10!

Step-by-step explanation:

Hope it helps! =D

The change in percentage of y when x increases by 5% will be 25%

Direct proportion is a mathematical comparison between two numbers where the ratio of the two numbers is equal to a constant value.

Given that, y is directly proportional to the square of x. we need to find the percentage increase when x is increased by 5%

Since, Y varies directly as the square of x.

Therefore, the general equation to show the direct variation :-

Y = kx²

Let the value of x be 25

25 will be x as 100%. therefore when x is 100%  the value of y will be

Y = 25²k

= 625k

Increasing the value of x by 5%,  

(105x25)/100 = 26.25

Therefore, 105% of 25 = 26.25.

Applying the variation equation, we obtain

Y = (26.25)²k

= 689.0625k

We will find the percentage change in y caused by an increase of x by 5%

(689.0625x100)/625 = 110.25%

Therefore, to find the percentage change in y when x increases by 5% will be,

(110.25-100)% =10.25%

Hence, the change in percentage of y when x increases by 5% will be 25%

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The answers to the equations y = -6x + 12 and y = -y + 3x = 6 are x = 2 and y = 0, respectively.

A location that satisfies every equation in a system of linear equations is the system's solution. You can graph a set of linear equations and find their points of intersection, or you can use algebra to figure out the variables.

Using substitution, we may solve by replacing y in the first equation with the second equation:

-(-6x + 12) + 3x = 6

Share the ominous symbol

6x - 12 + 3x = 6

combining similar terms

9x - 12 = 6

Separate the variable and add 12 to both sides to find the value of x:

9x = 18

x = 2

Substitute 2 with x in any equation to find the value of y:

-y + 3(2) = 6.

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We are given that the distribution of maximum oxygen uptake for elite athletes is approximately normal with mean 69 and standard deviation 7.6.

To find the probability that an elite athlete has a maximum oxygen uptake of at least 84.2 ml/kg, we need to standardize the value using the formula:

z = (x - μ) / σ

where,

x = the value of 84.2 ml/kg

μ = the mean of 69 ml/kg

σ = the standard deviation of 7.6 ml/kg.

Plugging in the values, we get:

z = (84.2 - 69) / 7.6

    = 2.03

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than or equal to 2.03 is 0.0217. Therefore, the probability that an elite athlete has a maximum oxygen uptake of at least 84.2 ml/kg is 0.0217.

z = (58.36 - 69) / 7.6

   = -1.36

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than or equal to -1.36 is 0.0869. Therefore, the probability that an elite athlete has a maximum oxygen uptake of at most 58.36 ml/kg is 0.0869.

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the reflection of the given function will be f(-x) = 0.5 4⁻ˣ and the graph of this function is attached below.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, a function as shown in the graph:

To reflect a function over the y-axis we use the rule:

f(-x) reflects the graph of f(x) over the y-axis. In other words,  to reflect f(x) over the y-axis, we just need to replace x with -x.

Let's find f(x) first using the standard exponential growth function:

f(x) = a( 1 + b )ˣ

From our graph, we can infer that f(x) = 1/2 when x =0, so let's replace those values in our function:

f(x) = a( 1 + b )ˣ

1/2 = a(1 +b)⁰

a = 1/2

We can also infer that f(x) = 8 when x =2. Since we already know that a = 1/2, let's replace the values to find and complete our function:

f(x) = a( 1 + b )ˣ

8 = 1/2(1 +b)²

4 = 1+b

b = 3

So putting it all together:

f(x) = 1/2( 1 + 3 )ˣ

Finally, we can apply the reflection rule to find the reflection over the y-axis:

f(-x) = 1/2(4)⁻ˣ

f(-x) = 0.5 4⁻ˣ

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The best fit line is a straight line that reflects the best feasible estimate of the connection between two variables in a dataset in statistics and data analysis. The line is deemed to have the "best fit" since it minimises the difference between the observed data points and the line's anticipated values.

The method of least squares is the most often used approach for identifying the best fit line, which entails finding the line that minimises the sum of the squared differences between the observed data points and the corresponding predicted values on the line. This approach yields a linear equation of the form y = mx + b, where "m" represents the line's slope and "b" represents the y-intercept.

The best fit line may be used to anticipate the relationship between the variables in the dataset, as well as to detect any outliers or atypical data points that may be influencing the overall relationship. It is often used to evaluate data and create predictions in domains including as economics, engineering, and social sciences.

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Bonjour !

Pour obtenir la deuxième ligne de l'équation que vous avez donnée, on peut tout simplement développer le terme Un+1 en utilisant la définition de Un+1 donnée par la relation de récurrence :

Un+1 = 2Un + 1/3(n+1)

En remplaçant Un+1 dans l'expression Un+1 - Un, on obtient :

Un+1 - Un = (2Un + 1/3(n+1)) - Un

On simplifie l'expression en combinant les termes similaires :

Un+1 - Un = 2Un - Un + 1/3(n+1)

Un+1 - Un = Un + 1/3(n+1)

Maintenant, pour obtenir la troisième ligne de l'équation, on peut factoriser Un - Un+1 en utilisant le signe moins :

Un - Un+1 = - (Un+1 - Un)

Un - Un+1 = - (Un+1 - 2Un - 1/3(n+1))

Un - Un+1 = - (-2Un - Un+1 - 1/3(n+1))

Un - Un+1 = 2/3Un + 1/3(n+1) - 1/3Un - 2/3Un - 1/3(n+1)

On simplifie à nouveau en combinant les termes similaires :

Un - Un+1 = -1/3Un + 1/3(n+1)

Enfin, pour obtenir la quatrième ligne de l'équation, on utilise l'associativité de l'addition pour regrouper les termes :

Un - Un+1 = -1/3Un + 1/3(n+1)

Un - Un+1 = 1/3(n+1) - 1/3Un

Un - Un+1 = 1/3(n+3 - Un)

J'espère que cela vous aide à comprendre la démonstration de cette relation de récurrence. N'hésitez pas à me poser d'autres questions si vous en avez besoin !

The value of x after the following code 'int x = 10; for (int y=5; y<20; y = 5) x = y' is executed will be 5.

The given for loop initializes the variable y to 5, then checks if y is less than 20, and then sets y to 5 again in each iteration. This means that the loop will execute only once with the value of y being 5, and after that, the loop condition will always be false because y is never incremented or changed in any way.

During the execution of the loop, the value of y is assigned to the variable x. Therefore, after the loop, the value of x will be 5.

So, the final value of x will be 5.

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From the given information provided, the probability of event F given that event E has occurred is 0.5.

Conditional probability is probability of an event A occurring with given that event B has occurred. It is denoted as P(A|B) and is calculated as follows:

P(A|B) = P(A and B) / P(B)

To find P(F/E), we use the conditional probability formula:

P(F/E) = P(E and F) / P(E)

We are given that P(E and F) = 0.1 and P(E) = 0.2. Substituting the given values in the formula, we get:

P(F/E) = 0.1 / 0.2

Simplifying this expression, we get:

P(F/E) = 0.5

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We know that the area of the given hexagon whose perimeter is 90ft is 584.56715 ft².

A hexagon, also known as a hexagon, is a six-sided polygon that forms the shape of a cube in geometry.

Any simple hexagon has 720° of internal angles in total.

No matter what kind of hexagon it is, they all have six sides.

This implies that all types of hexagons—regular, irregular, concave, and convex—have six sides apiece.

So, we know that the perimeter of the hexagon is 90ft.

Formula: 6a

Then, calculate the side as follows:

P = 6a

90 = 6a

a = 90/6

a = 15

Then, the area of the hexagon:

= 3√3/2a²

= 3√3/2*15²

= 584.56715

Therefore, we know that the area of the given hexagon whose perimeter is 90ft is 584.56715 ft².

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Answer: Here is the answers to your previous question that was deleted. As for this question, I believe the answer is the first one.

1) [tex]200\pi[/tex]
2) [tex]3\sqrt{3}[/tex]  
3) [tex]-1[/tex]  
4) 9  
5) 0.151

Step-by-step explanation:

#1

[tex]=\frac{dV}{dt} =\frac{4}{3} \pi .3r^3\frac{dr}{dt}[/tex]

[tex]=\frac{dV}{dt} =4\pi r^2\frac{dr}{dt}[/tex]

[tex]=\frac{dV}{dt} =4\pi r^2*2...[\frac{dr}{dt} =2][/tex]

[tex]=\frac{dV}{dt} = 8\pi r^2~~~ in^3/min[/tex]

         [tex]r=5[/tex]

[tex]=\frac{dV}{dt} =8\pi (5)^2[/tex]

[tex]=200\pi ~~~in^3/min[/tex]

#2

[tex]\frac{d}{dt} (x^2+y^2)=\frac{d}{dt} (16)[/tex]

[tex]2x(\frac{dx}{dt} )+2y(\frac{dy}{dt})=0[/tex]

[tex]2x(\frac{dx}{dt} )+-2y(\frac{dy}{dt})=0[/tex]
Divide both sides by 2.

[tex]x(\frac{dx}{dt})=-y(\frac{dy}{dt})[/tex]

[tex]\frac{dx}{dt}=\frac{-y(\frac{dy}{dt}) }{x}[/tex]

As the particle is passing through the point [tex](2,2\sqrt{3})[/tex] , So, the point will satisfy the equation. Substituting the value of [tex]x=2[/tex] , [tex]y=2\sqrt{3}[/tex] and [tex]\frac{dy}{dt} -3[/tex],

we get ,

[tex]\frac{dx}{dt} =\frac{((-2\sqrt{3})*(-3))}{2}[/tex]

[tex]=\frac{6\sqrt{3} }{2}[/tex]

[tex]=3\sqrt{3}[/tex]

#3

Go on to Desmos and put in [tex]x+3y=6[/tex] and look at x=0 and x=1 and use those two as your points.

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]=\frac{1-3}{2-0}[/tex]

[tex]=\frac{-2}{2}[/tex]

[tex]=-1[/tex]

#4

[tex]y=3x^2-4x-6[/tex]

[tex]\frac{dy}{dt} =5x-6[/tex]

[tex]\frac{dy}{dt}=5(3)-6[/tex]

[tex]\frac{dy}{dt} =9[/tex]

#5

[tex]V=s^3[/tex]

[tex]\frac{dV}{dt} =3*s^2(\frac{ds}{dt})[/tex]

[tex]-2=3*s^2(\frac{ds}{dt} )~~~~~~~~~~~~~Equation 1[/tex]

[tex]\frac{ds}{dt} =\frac{1.33}{s^2}[/tex]

[tex]V=s^3[/tex]

[tex](27)^0^.^3^3=(s^3)^0^.^3^3[/tex]

[tex]s[/tex] ≈ [tex]2.97 ~~~~~~~~~~~~~~~~~~~~~~Equation2[/tex]

Substitute equation2 to equation1, we get

[tex]\frac{ds}{dt} =\frac{1.33}{(2.97)^2} =0.151[/tex]

I hope this helps you! Cheers! ^^

All possible points should be equidistant from center.

so all the values here are possible.

(- 3, 2) ✓

(- 2, - 3) ✓

(2, - 3) ✓

(2, 3) ✓

(-2,3) ✓

(3, - 2) ✓

(- 3, - 2) ✓

Answer:

-10 - 4i

Step-by-step explanation:

We can rewrite the equation as (by getting rid of parentheses):

-8 + 3i - 2 - 7i

Now, we can add/subtract the values:

(-8-2) + (-7i+3i)

= -10 - 4i

Answer:

918

Step-by-step explanation:

The exponent is 81.m⁴.n²⁰

Here we have to determine the sign for exponential or radical expression

[tex](-3mn^5)^4[/tex]

Now using the exponent power rule (aˣ)ⁿ = aˣⁿ =. We get

= 81.m⁴.n²⁰

Therefore the exponent as a product of power is 81.

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the phrase "2 to the 3rd" (written as 23) means:

2 x 2 x 2 = 8.

23 and 2 x 3 = 6 are not equivalent.

Keep in mind that any number is itself when raised to the power of 1.

The outcome is always a fraction when the exponent is negative. A numerator and a denominator make up fractions. The numerator in this case is always 1. Assuming the negative exponent is positive, raise the number to that power to determine the denominator

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The second graph, first quadrant of coordinate plane titled Marie's round of golf could represent Marie's situation.

A coordinate plane is a two-dimensional plane made up of the x-axis and y-axis, two perpendicular number lines. Using the coordinates (x, y), which stand for the horizontal and vertical distances from the origin (the point where the x- and y-axes cross), it is possible to find locations in a two-dimensional space. The first quadrant, second quadrant, third quadrant, and fourth quadrant of the coordinate plane are designated in order anticlockwise.

Given that, she stayed at the first hole for the first 30 minutes. Then she drove away from the first hole for the next 2 hours.

The situation is best described by the graph 2, first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a line segment from 0 comma 0 to one half comma 0, a line segment from one half comma 0 to 2 and a half comma 5, and a line segment from 2 and a half comma 5 to 4 and a half comma 0.

Hence, the second graph could represent Marie's situation.

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Answer:

the answer is the graph shone below

i took the test and  IT WAS RIGHT  

Step-by-step explanation:

have a good day!

For converting fractions to decimals, we need to divide numerator with denominator,

So, the value of 51/16 as a decimal is equal to 3.1875.

In mathematics, the ratio of two integers is how a fraction is defined in mathematics.

The fraction indicates that it is the numerator value to denominator value ratio.

A decimal number is one in which the decimal point separates the whole number component from the decimal component.

From the question,

As we need to convert the given fractional value to decimal.

So, for determining the equivalent decimal value, we will simply divide the value given in the numerator to the value given in the denominator.

So, dividing 51 by 16

We will get it as:

51/16: 51 16 = 3.1875

As a result, 51/16 is equivalent to 3.1875 in decimal form.

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The correct way to measure the zone of inhibition is to place a known amount of an antimicrobial agent on a solid medium.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The zone of inhibition is then measured as the area surrounding the antimicrobial agent where microbial growth has been inhibited. This area is typically measured in millimeters. To accurately measure the zone of inhibition, it is important to ensure that the size of the inoculum and the amount of antimicrobial agent used remain constant. Additionally, it is important to consider the type of organism being studied, as different organisms can have different levels of susceptibility to the antimicrobial agent. Finally, the medium used should be appropriate for the organism being studied, as different media can produce different results.

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Answer:

Step-by-step explanation:

If 1in is equal to 47 feet irl, then that means that the actual width is 47ft and the actual length is 94ft.

Multiply those two together and you get 4,418 sq ft as your answer.

For the given trapezoid,

a) Length of AB is found by

   b² = 3² + 4²

b) Perimeter = 30 units.

What is a trapezoid?

A trapezoid is a quadrilateral with at least one pair of parallel sides. A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one.

The trapezoid is given in the figure below.

a) In this trapezoid, we can draw a perpendicular from B to the line AD. Let this point be E.

So the triangle ABE will be a right triangle.

Now the hypotensue will be AB.

Using Pythagoras' theorem, we can write the following relation.

AB² = AE² + BE²

From the graph of the trapezoid, we can get

AE= 4 -1 = 3 units

BE = 7 - 3 = 4 units

So if AB =b

The length of AB can be found using the,

b² = 3² + 4²

b = 5

Therefore the given statement is false.

b) The perimeter of trapezoid  = perimeter of triangle ABE + periemeter of rectangle BCDE

                                      = 5+4+3 +  2* (5+4)

                                      = 12 + 18 = 30 units.

Therefore for the given trapezoid, the perimeter is 30 units.

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To determine how many miles Theden needs to hike on the third day to finish the trail, we can subtract the distance he hiked on the first two days from the total trail distance:

Total trail distance = 40 miles

Distance hiked on first day = 12.8 miles

Distance hiked on second day = 16.9 miles

Total distance hiked on first two days = 12.8 + 16.9 = 29.7 miles

Distance left to hike on the third day = 40 - 29.7 = 10.3 miles

Therefore, Theden needs to hike 10.3 miles on the third day to finish the trail.

hello,

we already know that for 2 hours of babysitting, Mara earned $25.

to find how much she'd make for 5 hours of babysitting:

divide 25 by 2 which gets us 12.50.

if mara were to babysit for 5 hours, she'd make $62.50.

I hope this was helpful =]

The correct linear equation for the table is,

⇒ y = - 5x - 2

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table is shown in figure.

Now, Let two points from the table are (4, - 22) and (3, - 17).

Hence, Equation of linear function is,

⇒ y -  (- 22) = (- 17 - (-22)) / (3 - 4) (x - 4)

⇒ y + 22 = (5/- 1) (x - 4)

⇒ y + 22 = - 5 (x - 4)

⇒ y + 22 = - 5x + 20

⇒ y = - 5x + 20 - 22

⇒ y = - 5x - 2

Thus, The correct linear equation for the table is,

⇒ y = - 5x - 2

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Answer: 240 people

Step-by-step explanation:

If each class has 23 students and 1 teacher then there are a total of 24 people in each class. Multiply that by 10 classes, you should get 240 people.

18.42 years will it take to exhaust her annuity, i.e., run the account down to zero

Given the following information,

PV = $610,000

i = 6.5%

PMT = $40,000/year

The number of years for Ruth to exhaust all her funds from the account is 18.42

Using the financial calculator, we can easily find the value of n equals to 18.42 years in which the account finishes to zero.

n = 18.42 years

An annuity is a contract between you and an insurance company that requires the insurer to make payments to you, either incontinently or in the future. You buy an subvention by making either a single payment or a series of payments.

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Linda can choose any combination of three events that adds up to more than a kilometer but less than 1.5 kilometers

In order to find the best combination of events for Linda to sign up for to run a total of more than a kilometer but less than 1.5 kilometers, we must first determine the total distances of the individual events.

Depending on the events offered, Linda can choose three events that add up to more than a kilometer but less than 1.5 kilometers.

If Linda has the option of running the 100m, 200m, and 800m, she can satisfy her requirement of running more than a kilometer but less than 1.5 kilometers by choosing the 100m, 200m, and 800m.

This would add up to 1100m, which is slightly over a kilometer but below 1.5 kilometers.

Another option for Linda is to run the 100m, 400m, and 600m, which would add up to 1100m, once again satisfying her requirement.

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Answer:

A coefficient is a number that is multiplied by a variable or term in an algebraic expression.

Examples:

[tex]3x[/tex]

[tex]60x[/tex]

After reduced speed when race resumes the number of laps left are 6 2/3 laps.

What is the definition of speed?

The following is the definition of speed:

The rate with which the position of an item changes .

The ratio of distance travelled to time taken in travelling is known as speed. Speed is a scalar number because it has only one direction and no magnitude.

Formula for Speed

The speed formula is as follows:

s=d/t

Where,

s= speed in metres per second, d = distance travelled in metres, and t = time in seconds.

Now,

Total laps left for the lead car= 7 1/2

After race is paused or reduced speed for race until 5/6 of a lap

so only 1/6 of a lap had normal racing

so total lap left is 15/2-1+1/6

=45-6+1/6

=40/6

=20/3

=6 2/3

Hence,

          when race resumes the number of laps left are 6 2/3 laps.

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We need to add (t - 2πr) units of rope.

We have,

Let's call the radius of the hula hoop "r" and the distance from the center of the hula hoop to the rope "d".

We want to find the length of the rope we need to add in order to create a circle with radius "d" that is tangent to the hula hoop.

The distance between the center of the hula hoop and the center of the tangent circle is (r + d), so the diameter of the tangent circle is

2(r + d), and the length of the circle is 2π(r + d).

We want to find the value of d that will make the circle just touch the person's toes, so the radius of the tangent circle is equal to the length of the person's toes, which we'll call t.

So we have the equation:

2π(r + d) = t

Solving for d.

d = (t/2π) - r

The amount of rope we need to add is:

2πd = 2π((t/2π) - r) = t - 2πr

Thus,

We need to add (t - 2πr) units of rope.

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