Which expression is in simplest form

Answer:

The interest rate is 5.79% (to the nearest hundredth).

Step-by-step explanation:

To find the interest rate for the given deposit of $4000 accumulating to ​$5994.75, compounded monthly for 7 years, use the compound interest formula.

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given values:

Substitute the given values into the formula and solve for r.

[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{12 \times 7}[/tex]

[tex]\implies \sf 5994.75=4000\left(1+\dfrac{r}{12}\right)^{84}[/tex]

[tex]\implies \sf \dfrac{5994.75}{4000}=\left(1+\dfrac{r}{12}\right)^{84}[/tex]

[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}=1+\dfrac{r}{12}[/tex]

[tex]\implies \sf \sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1=\dfrac{r}{12}[/tex]

[tex]\implies \sf r=12\left(\sqrt[\sf 84]{\sf \dfrac{5994.75}{4000}}-1\right)[/tex]

[tex]\implies \sf r=0.057937950...[/tex]

[tex]\implies \sf r=5.7937950...\%[/tex]

Therefore, the interest rate is 5.79% (to the nearest hundredth).

In linear equation, 1161.8 lb is the total weight of the liquid in the tank, to the nearest full pound.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                         Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

d = 12 ft

r = 12 ft/2 = 6 ft

volume of sphere = (4/3)πr³

volume of hemisphere = (1/2)(4/3)πr³

volume = (2/3)π(6 ft³) =  12.56 ft³

weight = volume × density

weight = 12.56 ft³ × 92.5 lb/ft³

weight = 1161.8 lb

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Answer:

8^2

Step-by-step explanation:

The equations of the transformed graphs are f(x) = -√(x - 2) and f(x) = -(x + 3)² - 1, while the descriptions are added below

Graph 1

This function is a square root function

The parent function is the square root function, which is denoted as

f(x) = √x

The function is first reflected across the x-axis to give

f(x) = -√x

Next, the function is shifted to the right by 2 units

So, we have

f(x) = -√(x - 2)

This means that the function description is a reflection about the x-axis. followed by a horizontal shift to the right by 2 units

Graph 2

This function is a quadratic function

The parent function is the square root function, which is denoted as

f(x) = x²

The function is first reflected across the x-axis to give

f(x) = -x²

Next, the function is shifted down and left by 1 and 3 units respectively

This means that

f(x) = -(x + 3)² - 1

This means that the function description is a reflection about the x-axis. followed by a horizontal shift to the down and left by 1 and 3 units

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Answer:To calculate how much money Evie will owe after 12 years, we need to use the formula:A = P(1 + r)^nWhere:

A = the amount owed after n years

P = the initial amount borrowed

r = the annual interest rate as a decimal

n = the number of yearsIn this case, P = £600, r = 24% = 0.24, and n = 12. Plugging these values into the formula, we get:A = 600(1 + 0.24)^12

A = 600(1.24)^12

A = 600(7.8905)

A = £4,734.30 (rounded to the nearest penny)Therefore, after 12 years, Evie will owe approximately £4,734.30

Step-by-step explanation: I Helped you Can You help me

Answer:

Step-by-step explanation:

According to the question we are given with a right traingle Where base is 35 and the perpendicular is 12.

We need to find the unknown side that is the longest side (Hypotenuse) .

By using pythagoras theorem :

[tex]\longrightarrow \rm \: \: (H)^2 = (B)^2 + (P)^2 \\ [/tex]

here,

Putting the required values in the Pythagoras theorem we will get,,

[tex]\longrightarrow \rm \: \: (H)^2 = (35)^2 + (12)^2 \\ \\ \longrightarrow \rm \: \:(H)^2 =1225 + 144 \\ \\ \longrightarrow \rm \: \:(H)^2 = 1369 \\ \\ \longrightarrow \rm \: \:H = \sqrt{1369} \\ \\ \longrightarrow \rm \: \:H = 37 \\ [/tex]

Therefore, Unknown side of the right triangle i.e hypotenuse is 37 .

Answer:

f(x) = 3x-5

Step-by-step explanation:

Plug in the domain 0, in the other answer options

f(x) = -3x + 4 turns into f(x) = -3(0) + 4 and thats equal to 4, there is no value set to 4 in the range so that option is cancelled out

f(x) = x+2 turns into f(x) = 0+2 =2, there is no value set to 2 in the range so that option is cancelled out

f(x) = -5x + 3 turns into f(x) = -5(0) + 3, and thats equal to 3, there is no value set to 3 in the range so that option is cancelled out

f(x) = 3x-5 turns into f(x) = 3(0) - 5, and thats equal to -5, there is a value in the range that equals -5, you could also try any domain value into this equation and it would result into either -11, -5, 1, 7, or 13.

keep in mind f(x) is the range

The probability that at least 4 accounting majors are on the committee is E. 0.5874.

Probability operates on the principle of dividing the number of expected outcomes by the number of total outcomes. To find the probability that at least 4 accounting majors are on the committee, we can begin by determining the probability of having exactly 4, 5, 6, and 7 accounting majors on the committee. After finding these probabilities, we can then sum up the figures.

First, the total number of ways to choose 8 members from a group of 6+7=13 is:

13! / (8! * 5!) = 1287

Next, we will find the number of ways to choose exactly 4 accounting majors and 4 finance majors is:

6 choose 4 * 7 choose 4 = 15 * 35 = 525

Also, the number of ways to choose exactly 6 accounting majors and 2 finance majors is:

6 choose 6 * 7 choose 2 = 1 * 21 = 21

Finally, the number of ways to choose exactly 7 accounting majors and 1 finance major is:

6 choose 7 * 7 choose 1 = 0 * 7 = 0

Now, we will sum the total number of ways to choose a committee with at least 4 accounting majors as follows:

525 + 210 + 21 + 0 = 756

756 / 1287 = 0.587

Therefore, the probability of selecting a minimum of 4 accounting majors is thus 0.5874.

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Answer:

19% smaller

Step-by-step explanation:

A=πr^2

r=d/2

A=pi(d/2)^2

A=pi(.9d/2)^2=

81% of original

100%-81%=19%=Give this answer a like!

Equation in the standard slope-intercept form: y = 2X + 2

The slope intercept form of an equation is represented as follows:

y = mx + c

where, m = slope, c = y-intercept

We want to rewrite the equation X = (y - 2) ÷ 2 in slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept.

First, let's isolate y on one side of the equation by multiplying both sides by 2:

2X = y - 2

Next, let's add 2 to both sides:

2X + 2 = y

Finally, let's switch the sides to get the equation in the standard slope-intercept form:

y = 2X + 2

So the slope of the line is 2 and the y-intercept is 2.

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The angle ∠FNL in the given trapezium shows that ∠FNL is 122°

The opposite angles of a trapezium are not necessarily equal, unlike in a parallelogram.

However, the opposite angles of a trapezium are supplementary, which means that the sum of one pair of opposite angles equals 180 degrees.

In other words, if we label the angles of a trapezium as F, D, N, and L (with F and L being opposite angles, and D and N being opposite angles), then we have:

∠F + ∠L = 180 degrees

∠D + ∠L = 180 degrees

Thus, ∠FDL + ∠FNL = 180

4x - 14 + 9x - 40 = 180

13x - 54 = 180

13x = 234

x = 18

∠FNL = 9x - 40

∠FNL = 9(18) - 40

∠FNL = 122°

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Answer:

[tex]L_c=12.56 \ \text{feet}[/tex]

Step-by-step explanation:

From the question we are told that

Width of circular path [tex]w_c=2 \ \text{feet}[/tex]

Inner Diameter [tex]d_{in}=550 \ \text{feet}[/tex]

Outer diameter [tex]d_{out}=550+2\times2[/tex]  (inner diameter +  2 circular path width)

[tex]d_{out}=550+4[/tex]

[tex]d_{out}=554 \ \text{feet}[/tex]

Generally the equation for inner circumference of the circle  is mathematically given by

[tex]C_1=\pi d_{in}[/tex]

[tex]C_1=3.14\times550[/tex]

[tex]C_1=1727 \ \text{feet}[/tex]

Generally the equation for outer circumference of the circle  is mathematically given by

[tex]C_2=\pi d_{out}[/tex]

[tex]C_2=3.14\times554[/tex]

[tex]C_2=1739.56 \ \text{feet}[/tex]

Generally the difference in length of the two circumference  is mathematically given by

[tex]L_c=C_2-C_1[/tex]

[tex]L_c=1739.56-1727[/tex]

[tex]L_c=12.56 \ \text{feet}[/tex]

[tex]\cos(4x)=\cfrac{1}{2}\implies 4x=\cos^{-1}\left( \cfrac{1}{2} \right)\implies 4x= \begin{cases} \frac{\pi }{3}\\\\ \frac{5\pi }{3} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 4x=\cfrac{\pi }{3}\implies \boxed{x=\cfrac{\pi }{12}}~\hfill 4x=\cfrac{5\pi }{3}\implies \boxed{x=\cfrac{5\pi }{12}}[/tex]

The simplified expression for x+2x-8+3x+1-2x is 4x - 4.

Expression is a term used to describe a wide variety of communication methods such as verbal, nonverbal, written, and artistic. It is the way we communicate our thoughts, feelings, and ideas to others. It is an important part of our lives, from the simplest forms of communication like body language to more complex forms like written literature. Expression is a powerful tool for self-expression, communication, and connection.

The expression x+2x-8+3x+1-2x can be simplified by combining like terms.

First, the x-terms can be combined, resulting in 4x:
x + 2x + 3x - 2x = 4x

Next, the remaining constants can be combined, resulting in -4:
4x - 8 + 1 = -4

Finally, the resulting expression can be written as 4x - 4.

Therefore, the simplified expression for x+2x-8+3x+1-2x is 4x - 4.

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The value of simplification is 95.

What is simplification?

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easily with calculations and solving.

Here, we have

Given: (1000y) -1/2 * (3/x+1) when x = 1/3 and y = 1/10

we have to simplify the given expression.

= (1000y) -1/2 * (3/x+1)

When x = 1/3 and y = 1/10

Now we put the value of x and y in the given equation and we get

=  (1000/10) -1/2 × (3×3+1)

= 100 - 10/2

= 100 - 5

= 95

Hence, the value of simplification is 95.

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Answer: the first thing is your answer :)

thx for the points

Step-by-step explanation:

g

(

x

)

=

x

2

−

3

The parent function is the simplest form of the type of function given.

f

(

x

)

=

x

2

The transformation being described is from

f

(

x

)

=

x

2

to

g

(

x

)

=

x

2

−

3

.

f

(

x

)

=

x

2

→

g

(

x

)

=

x

2

−

3

The horizontal shift depends on the value of

h

. The horizontal shift is described as:

g

(

x

)

=

f

(

x

+

h

)

- The graph is shifted to the left

h

units.

g

(

x

)

=

f

(

x

−

h

)

- The graph is shifted to the right

h

units.

In this case,

h

=

0

which means that the graph is not shifted to the left or right.

Horizontal Shift: None

The vertical shift depends on the value of

k

. The vertical shift is described as:

g

(

x

)

=

f

(

x

)

+

k

- The graph is shifted up

k

units.

g

(

x

)

=

f

(

x

)

−

k

- The graph is shifted down

k

units.

Vertical Shift: Down

3

Units

The graph is reflected about the x-axis when

g

(

x

)

=

−

f

(

x

)

.

Reflection about the x-axis: None

The graph is reflected about the y-axis when

g

(

x

)

=

f

(

−

x

)

.

Reflection about the y-axis: None

Compressing and stretching depends on the value of

a

.

When

a

is greater than

1

: Vertically stretched

When

a

is between

0

and

1

: Vertically compressed

Vertical Compression or Stretch: None

Compare and list the transformations.

Parent Function:

f

(

x

)

=

x

2

Horizontal Shift: None

Vertical Shift: Down

3

Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

image of graph

The correct statement about diagram is m∠1 > m∠4. So correct option is D.

In mathematics, an angle is a measure of the amount of rotation between two rays or line segments that share a common endpoint, known as the vertex. The rays or line segments are typically referred to as the sides of the angle.

Angles are usually measured in degrees or radians, with a full rotation or circle being 360 degrees or 2π radians. Angles can be classified into different types based on their degree of rotation, such as acute angles, which are less than 90 degrees, right angles, which are exactly 90 degrees, obtuse angles, which are greater than 90 degrees but less than 180 degrees, and straight angles, which are exactly 180 degrees.

Angles can be added, subtracted, multiplied, and divided, and they can be used to solve a wide range of problems in geometry and trigonometry. For example, angles are used to calculate the measurements of geometric shapes, such as triangles, circles, and polygons, and they are also used to calculate distances and heights using trigonometric functions such as sine, cosine, and tangent.

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22π  m²  is the exact surface area of a cylindrical propane tank.

What are volume and surface area?

The entire area of all the faces makes up the surface area of a three-dimensional form. We measure the areas of each face and put them together to determine the surface area of a shape.

                    The surface-area-to-volume ratio, also known as the surface-to-volume ratio or abbreviated as SA:V, refers to how much surface area there is in each unit volume of an object or collection of objects.

A=2πrh+2πr²

 =2π * 1* 10 +2π* 1²

  = 2π( 10 + 1)

  = 2π * 11

  = 22π  m²

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The first three terms in decreasing powers of X are as follows.

x5−10x4X−1+40x3X−2+…

A relation is any subset of a Cartesian product.

As an illustration, a subset of is referred to as a "binary connection from

A to B," and more specifically, a "relation on A."

A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.

Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).

A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).

Every function, as you can see from these definitions, is a relation from X.

Hence, The first three terms in decreasing powers of X are as follows.

x5−10x4X−1+40x3X−2+…

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Answer:

101 = k + 33

101 - 33 = k + 33 - 33

68 = k

this is your required answer

Step-by-step explanation:

Rate A = 1 pool / 4 hrs = 1/4 pool/hr

Rate B = 1 pool / 5 hrs = 1/5 pool / hr

Now combine the rates to fill 1 pool

1 pool / ( 1/4 pool/hr + 1/5 pool / hr) = 1 / ( 1/4 + 1/5)  hr = 2.22 hrs

  ( or  2 hrs 13.3 min)

Yes, the length and width can be decimal numbers each one with decimal place, but not in every case.

The size of a two-dimensional surface or region is expressed in terms of area. Square units like square inches, square feet, or square metres are frequently used to measure it. The area of a shape or region is determined by counting the number of unit squares that can fit inside it without overlap.  

for example, lets take length =2.5 feet

and width=3.2 feet

area of table top=8 feet²

Taking another case:

length =1.2 feet

and width=3.5 feet

area of table top=4.2 feet²

if the length and width are decimal numbers, then the area would also be a decimal number or whole number, But, this is not possible in every cases.

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The complete question is:

The area of Kamar’s tabletop is a whole number of square feet. Could the length and width be decimal numbers each with one decimal place? Explain your answer.

Answer:

the definition of adjacent mathematically means two angles if they have a common side and a common vertex.

Step-by-step explanation:

a would b adjacent to d. c would be adjacent to d.

Answer:

D

[tex]3. \frac{11\pi}{6} [/tex]

Step-by-step explanation:

When we determine the point's coordinates, first we have to write the polar ones (they are on the horizontal line) and then the south ones (they are around the circle)

I think this is the right answer

Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test​ scores.

A percentile in statistics refers to a score's position in relation to other scores in a given set. Although percentile has no one fixed meaning, it is frequently described as the proportion of numbers within a collection of data scores that are lower than a particular value.

Percentile shows the proportion of persons who fall below a given value. When we declare that a score of 365 out of 400 represents the 90% percentile on an exam, it means that 90% of test-takers received scores that were lower than or equal to 365.

Give: Seven of the ten test results are inside the 85th percentile.

The percentage of those who received less than or equal to 85 is just as follows: 7/10 = 0.7.

percentile rank:

0.7*100 = 70

Thus, the percentile rank of just an 85 on a test is: 70 percentile for the given test​ scores.

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Answer:

4 and the second one -8

Step-by-step explanation:

in the first one you have to 2 and take away 4 so you get a negative number and the you take one more number and then add 7

in the second one you have -5 and then take away 6 and then add 3