The table and corresponding frequency polygon show information about the heights of members of a swimming club. What fraction of members were between 150 and 160 cm tall? Frequency < Back to task น 151 10- 5- 0+ 120 130 140 150 Height (cm) Search 160 Watch video 170 Height (cm) Midpoint 120< x≤130 125 130< x≤140 135 140< x≤150 145 150 160 155 160 < x≤160 165 Answer >​

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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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 statement that is NOT one of the axioms of Euclidean geometry is D. If two planes intersect, their intersection is a point.

Euclidean geometry is a branch of mathematics that deals with the study of two-dimensional and three-dimensional figures using a set of axioms or postulates.

The axioms of Euclidean geometry are a set of five statements that are used as the foundation for all of the theorems and proofs in Euclidean geometry.

The first two axioms are relatively straightforward and intuitive, while the third axiom involves the use of circles to construct geometric figures. The fourth axiom establishes the concept of a right angle, which is a 90-degree angle, while the fifth axiom deals with the concept of parallel lines and their relationship to intersecting lines.

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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:

Step-by-step explanation:

make them all the same denominator so

the least common denominator for all of them is  24:

1/3 x 8/8=8/24

5/6x4/4=20/24

3/8x3/3=9/24

so from least to greatest it is:

1/3, 3/8, 5/6

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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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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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)

[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]

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]

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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Answer: >

Step-by-step explanation:

Answer:

8^2

Step-by-step explanation:

The function m(t) shifts the time frame by 1hr later the original function d(t).

The function s can be written in terms of d as follows:

s (r) = d ×  [tex](r+7)^{-1}[/tex]

The core concept of calculus in mathematics is a function. The relations are certain kinds of the functions. In mathematics, a function is a rule that produces a different result for every input x. In mathematics, a function is represented by a mapping or transformation. Letters like f, g, and h are widely used to indicate these operations.

In this situation, d (5) = 0.25 means that Tyler is 0.25 minutes away from his home at 7:05am. This is because Tyler's distance from his house at time t after 7am is provided by the function d (t).

Tyler's school starts at 9 a.m. with a 120-minute delay. As a result, if d (5) = 0.25, Tyler has walked for 5 minutes, and his distance function s (r) calculates his distance starting at 7 minutes after 7 a.m. with a 120-minute start delay. The matching point, then, indicates Tyler's separation from his home at 7 minutes after 9 a.m. If he started walking at 7 am and took 5 minutes.

The function s can be written in terms of d as follows:

s (r) = d ×  [tex](r+7)^{-1}[/tex]

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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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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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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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The 18th term of the sequence is -140

It is important to note that the formula for the nth term of an arithmetic sequence is expressed with the equation;

an = a + (n - 1) d

Such that the parameters are enumerated as;

From the information given, we have;

The sequence is;

-21, -14, -7, 0, 7, ...

Then, the common difference = -14 - (-21) = -14 + 21 = -7

Substitute the value

a18 = -21 + (18 - 1) -7

expand the bracket

a18 =-21 + (17)-7

a18 = - 21 - 119

a18 = - 140

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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:

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

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.

The inverse of the linear function, f(x), f(x) = (2x - 3)/5 is f⁻¹(x) = (5·x + 3)/2. The correct option is option A

A. f⁻¹(x) = (5·x + 3)/2

The inverse of a function is a function that reverses the effect the original function.

The original function is; f(x) = (2·x - 3)/5

The inverse of f(x) can therefore be found by making x the subject of the equation as follows;

f(x) = (2·x - 3)/5

5 × f(x) = (2·x - 3)

5 × f(x) + 3 = 2·x

2·x = 5 × f(x) + 3

x = (5 × f(x) + 3)/2

Plugging in x = f⁻¹(x) and f(x) = x, in the above equation, we get;

f⁻¹(x) = (5 × x + 3)/2

The correct option that is an inverse of f(x) is therefore, option A

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Answer:

101 = k + 33

101 - 33 = k + 33 - 33

68 = k

this is your required answer

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

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

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).