Change Decimals To Fractions And Reduce To Lowest Terms 0.025 (2024)

SOLUTION

[tex]\begin{gathered} \text{If x}^2\text{ = 34} \\ We\text{ take the roots of both sides } \\ \text{x}^2\text{ = 34} \\ \sqrt[]{x^2}=\sqrt[]{34} \\ x=5.83 \end{gathered}[/tex]

Since x = 5.83, this means that x is between 5 and 6.

So the first option is correct.

Answer:

Its an function

Step-by-step explanation:

Since there is one value of y for every value of x

x

SOLUTION FOR NUMBER 18

Explanation:

To convert from Cartesian coordinates to polar coordinates to, you can use:

[tex]\begin{gathered} (x,y)\rightarrow(r,\theta) \\ where; \\ r=\sqrt{x^2+y^2} \\ \theta=tan^{-1}(\frac{y}{x}) \end{gathered}[/tex][tex]\begin{gathered} r=\sqrt{2^2+4^2}=\sqrt{20}=2\sqrt{5} \\ \theta=tan^{-1}(\frac{4}{2})=63.43\degree \end{gathered}[/tex][tex]\begin{gathered} The\text{ polar coordinates is;} \\ (r,\theta)=(2\sqrt{5},\text{ 63.43}\degree) \end{gathered}[/tex]

A cylindrical soup can has a radius of 1.5 in. and is 6 in tall. Find the volume of the can. 4 x in.3 Round your answer to the nearest tenth if necessary.​

Given:

r = 1.5 in.

h = 6 in.

Required:

Volume of the cylinder in the nearest tenths

Solution:

Volume = Area of the base x height

Volume of the cylinder = Area of a circle x height of the cylinder.

[tex]\begin{gathered} V=\pi r^2h^{} \\ V=\pi(1.5)^2(6) \\ V=42.41in^3=42.4in^3 \end{gathered}[/tex]

Answer:

[tex]V=42.4in^3[/tex]

(rounded off to the nearest tenths)

I'm done with the solution. Do you have question so far?

Our prism has 6 faces. 2 equal basis and 4 equal sides. To calculate the area of the base, we just have to use the area formula since we already know the value for the diagonals. To calculate the area of the sides of our prism we have to calculate the side length of the rhombus.

A rhombus has the following properties:

Opposite angles are equal. All sides are equal and, opposite sides are parallel to each other. Diagonals bisect each other perpendicularly.

Since the diagonals bisect each other perpendicularly, half the diagonals and the side of the rhombus form a right triangle.

Using the pythagorean theorem, we can determinate the side length our rhombus.

[tex]\begin{gathered} (\frac{6}{2})^2+(\frac{8}{2})^2=s^2 \\ 3^2+4^2=s^2 \\ s=\sqrt{9+16} \\ s=5 \end{gathered}[/tex]

The side length of our rhombus is equal to 5 units. Now that we have all the measures, we can calculate the total surface area. The area of a rhombus is equal to half the product of the diagonals.

[tex]A_b=\frac{6\times8}{2}=\frac{48}{2}=24[/tex]

The sides of our prism are rectangles, therefore, the area is given by the product between its distinct sides.

[tex]A_s=12\times5=60[/tex]

Since we have 4 sides and 2 basis, the total surface area is:

[tex]S=2A_b+4A_s=2(24)+4(60)=48+240=288[/tex]

The surface area of our prism is equal to 288 units². The answer is option B.

Answer:

3.2 gallons

Explanation:

The dimension of the room

• Length= 20 feet

,

• Wide = 15 feet

,

• Height = 8 feet

First, we determine the Surface Area of the wall in the room.

[tex]TS.A.=2(LH+WH)[/tex]

Substituting the given values, we have:

[tex]\begin{gathered} TSA=2(20\times8+15\times8) \\ =2(160+120) \\ =2(280) \\ =560\text{ square f}eet \end{gathered}[/tex]

Since the room needs 2 coats of paint, the total surface area to be covered will be:

[tex]\begin{gathered} =2\times560 \\ =1120\text{ square f}eet \end{gathered}[/tex]

Since 1 gallon of paint covers 350 square feet, the number of gallons needed will be:

[tex]\begin{gathered} =\frac{1120}{350}\text{ gallons} \\ =3.2\text{ gallons} \end{gathered}[/tex]

You have the following expression:

64 ÷ 42·16​

In order to simplify the previous expression, first multiply the factors 42 and 16:

42·16​ = 672

next, simplify the fraction 64/672:

64/672 divide by 2 both numerator and denominator

32/336 divide by 2

16/168 divide by 2

8/84 divide by 2

4/42 divide by 2

2/21

Hence, the simplied expression is 2/21

4 hours is a whole number, to express a whole into a fraction you have to put the number in the numerator and 1 in the denominator:

[tex]4=\frac{4}{1}[/tex]

2 acres is also a whole, using the same method you can express it as an impropper fraction:

[tex]2=\frac{2}{1}[/tex]

Problem given

Tonia is saving $15.00 each week to buy a bicycle. The bicycle costs $129.99. Which inequality can be used to determine the number of weeks, w, in which Tonia must save money so that she has more than enough money to buy the bicycle?

Solution

For this problem we know that w represent the number of weeks. The bycle cosys $129.99 and taking in count the info given the best answer would be:

15w > 129.99

Becuase after 129.99/15 weeks Tonia will ahve enough money to buy the bicycle

Ohh

To find the opposite of a number we can draw a number line.

If we go to the right of zero, we have positive numbers.

TO the left, we have negative numbers.

The opposite of a number is the number that is the same distance from zero but on the other side.

So, the opposite of 10 is -10.

After a sequence of reflections, translations and rotations, segment AB would be located in a different place and a different way, but its length would not change. It means, after these transformations, the segment will always be 4 units long, then, an image of segment AB could be each segment that measures 4 units. Those are:

line segment CD

line segment GH

line segment NP

Given a table represents a linear relation between x and y

We will use two points from the table to write the equation of the line in the slope-intercept form: y = mx + b

As shown in the table:

When x = -1, y = 0

When x = 0, y = -4

we will find the slope (m) as follows:

[tex]slope=m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4-0}{0-(-1)}=\frac{-4}{1}=-4[/tex]

The value of b = the value of y when x = 0

So, b = -4

So, the answer will be option D. y = -4x - 4

Answer:

Explanation:

Given:

Final Amount = $1000

Time in years = 3

interest rate = 3.25% = 0.0325

To find the principal amount for the given investment, we use the formula:

[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]

Where:

P= Principal Amount

A=Final Amount

r= interest rate in decimal

t=time in years

n= the number of times interest is compounded per unit t

It is mentioned that it is compounded annually, so the value of n=1.

P=1000(1.0325) -³ is from the formula:

We plug in what we know:

[tex]\begin{gathered} P=\frac{A}{(1+\frac{r}{n})^{nt}} \\ =\frac{1000}{(1+\frac{0.0325}{1})^{(1)(3)}} \\ \text{Simplify} \\ =\frac{1000}{(1+0.0325)^3} \\ P=\frac{1000}{(1.0325)^3}=908.51 \\ or \\ P=1000(1.0325)^{-3} \\ \text{Calculate} \\ P=908.51 \end{gathered}[/tex]

Therefore, Kyle should invest $908.51

Since 2/3 of 24 had regular coffe, then:

[tex]24\cdot\frac{2}{3}=\frac{24\cdot2}{3}=\frac{48}{3}=16[/tex]

We have that 16 people had regular coffe. Now for the people that had decaf:

[tex]24\cdot\frac{1}{8}=\frac{24}{8}=3[/tex]

There were 3 people that drank decaf. The remaining had the specialty coffe, then:

[tex]24-16-3=24-19=5[/tex]

Therefore, 5 people asked for the specialty coffee

The hierarchy says that the first operation is the one in the parenthesis

[tex](5+9\times4)[/tex]

The next step is the multiplication

[tex](5+9\times4)=(5+36)=41[/tex]

The next step is to multiply the previous result by 5

[tex]41\times5=205[/tex]

And finally, divide by 5

[tex]\frac{205}{5}=41[/tex]

The answer is 41.

Answer:

Explanation:

Given:

The volume of the quarter sphere sized tank = 226,195

The volume of tank 1 and 2 volume = 81640

Maximum density of killer whales = 0.000011142 whales per cubic ft

To find:

the maximum number of killer waves allowed in the main show tank

The formula for density:

[tex]density\text{ = }\frac{mass}{volume}[/tex][tex]undefined[/tex]

ANSWER:

5

STEP-BY-STEP EXPLANATION:

We can determine the value of a by means of the table shown in the statement.

According to the table when x is equal to 21, the value of a is equal to 5.

Input data

f(x) in graph

g(x) is defined

[tex]g(x)=-(x-1)(x-7)[/tex]

Procedure

[tex]\begin{gathered} g(x)=-(x^2-7x-x+7) \\ g(x)=-(x^2-8x+7) \\ g(x)=-x^2+8x-7 \end{gathered}[/tex]

The maximum values of f(x) and g(x) are the same (True)

g(0) is greater than f(0) (False)

The y-intercept of f(x) is greater than the y-intercept of function g(x) (True)

Both have zeros that are negative (False)

The axis symmetry for g(x) is greater than the axis of symmetry for f(x) (True)

Answer:

Trinomial

Explanation:

Given the below polynomial;

[tex]x^2+5x-6[/tex]

To be able to classify the above polynomial, we need to ascertain the number of terms it has;

[tex]\begin{gathered} x^2\colon1st\text{ term} \\ 5x\colon2nd\text{ term} \\ -6\colon\text{ 3rd term} \end{gathered}[/tex]

We can see that the polynomial has 3 terms, so it can be classified as a trinomial.

The slope of the equation is -9/2

Here, we want to identify the slope of the equation.

Firstly, what we need to do is to express the equation in the standard form

The standard form of the equation of a line is;

y = mx + c

where m represents the slope of the linear equation and c represents the y-intercept of the linear equation

So making y the subject of the equation, we have;

2y = -9x - 7

divide through by 2;

y = -9x/2 - 7/2

The slope of the equation is the coefficient of x which is -9/2

Given:

Find-:

a) Sum of the measure of the interior angle

b) Sum of the measure of the exterior angle.

Sol:

Given figure is a hexagon and each Interior angle of the hexagon is 120

So the Sum of interior angles is:

[tex]\begin{gathered} =120+120+120+120+120+120 \\ \\ =720 \end{gathered}[/tex]

An exterior angle of the hexagon is:

[tex]\begin{gathered} =180-120 \\ \\ =60 \end{gathered}[/tex]

Sum of an exterior angle is:

[tex]\begin{gathered} =60+60+60+60+60+60 \\ \\ =360 \end{gathered}[/tex]

We are given the function f(x) = x^3 - 6x^2 + 10x - 3, where x is a real number. We are supposed to translate it by (-2, 3) which means that we are moving the entore graph 2 units to the right and 3 units up.

The first thing to do is write the cubic function in the form f(x) = a(x - h)^3 + k where h is the horizontal translation and k is the vertical translation.

So, f(x) = x^3 - 6x^2 + 10x - 3 moved 2 units to the right and 3 units up would be written as:

[tex]C=(x+2)^3-6(x+2)^2+10(x+2)-3+3[/tex]

We can simplify this as:

[tex]\begin{gathered} C=(x+2)^{3}-6(x+2)^{2}+10(x+2)-3+3 \\ C=(x^3+6x^2+12x+8)-6(x^2+4x+4)+(10x+20) \\ C=x^3+6x^2+12x+8-6x^2-24x-24+10x+20 \\ C=x^3-2x+4 \end{gathered}[/tex]

The graph crosses the y-axis when x = 0.

[tex]\begin{gathered} C=x^{3}-2x+4 \\ y=0^3-2(0)+4 \\ y=4 \end{gathered}[/tex]

The point where the graph crosses the y-axis is (0, 4).

Arithmetic Sequence

To answer this question, we need to find the value of the 10th term of the arithmetic sequence. An arithmetic sequence is given by:

[tex]a_n=a_1+(n-1)d[/tex]

In this case, we have that:

a1 = 0

n = 10

d = 100 - 0 ---> d = 100

Then, applying the previous formula, we have:

[tex]a_{10}=0+(10-1)\cdot100\Rightarrow a_{10}=9\cdot100\Rightarrow a_{10}=900[/tex]

Then, the 10th term in this arithmetic sequence is equal to 900.

Geometric Sequence

We need to apply the formula to find a term in a geometric sequence:

[tex]a_n=a_1\cdot r^{n-1}[/tex]

We have that the first two terms are 5 and 10. The common ratio, r, is given by dividing the second term by the first term:

[tex]r=\frac{10}{5}\Rightarrow r=2[/tex]

Then, we have:

a1 = 5

r = 2

n = 10

Therefore:

[tex]a_{10}=5\cdot2^{10-1}\Rightarrow a_{10}=5\cdot2^9\Rightarrow a_{10}=5\cdot512\Rightarrow a_{10}=2560[/tex]

The 10th term in this geometric sequence is equal to 2560.

Hence, the 10th term of the geometric sequence here is greater than the one in the arithmetic sequence, that is:

• 10th term geometric sequence = 2560

,

• 10th term arithmetic sequence = 900

Given:

Point is:

[tex](3.2,-4.8)[/tex]

Find-: Polar coordinates.

Sol:

In general polar coordinates is:

[tex]\text{ Polar coordinates }=(r,\theta)[/tex]

Where,

[tex]\begin{gathered} r^2=x^2+y^2 \\ \\ \tan\theta=\frac{y}{x} \end{gathered}[/tex]

(x,y) represent the point.

So, the polar coordinates is:

[tex]\begin{gathered} r^2=x^2+y^2 \\ \\ r^2=(3.2)^2+(-4.8)^2 \\ \\ r^2=10.24+23.04 \\ \\ r^2=33.28 \\ \\ r=\sqrt{33.28} \\ \\ r=5.769 \end{gathered}[/tex]

Value of tan of angle is:

[tex]\begin{gathered} \tan\theta=\frac{y}{x} \\ \\ \tan\theta=\frac{-4.8}{3.2} \\ \\ \tan\theta=-1.5 \\ \\ \theta=-56.31 \end{gathered}[/tex]

In radian form angle is:

[tex]\begin{gathered} \theta=-56.31\times\frac{\pi}{180} \\ \\ \theta=-0.313\pi \end{gathered}[/tex]

So polar form is:

[tex](5.769,-0.313\pi)[/tex]

The probability of obtaining (a) at most four "ones" will be; 91.31%.

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The first step is using the binomial distribution which is = np or n (1-p)

The binomial distribution will be n = 10 and p = 3/7;

np = 10 x 3/7 = 4.2

n(1-p) = 200 x (4/7)

= 166.67

We can see that Both n(1-p) and np are much higher than 5,

Therefore,

P(Y ≤ 40.5) = P(z ≤ (40.5-μ)/σ)

= P(z≤1.36)

= 0.9131

= 91.31%

Thus, the probability of obtaining (a) at most four "ones" will be; 91.31%.

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ1

Linear

Explanation

A linear funciton is a statistical term used to describe a straight-line relationship between two variables,it is defined by

[tex]y=mx+b[/tex]

so, if we hve have

EACH INK CARTRIDGE PURCHASED FOR A PRINTER COST $12

it means the total cost depends on the number of printers and the rate,so

[tex]total\text{ cost =}rate*number\text{ of printers}[/tex]

let

total cost = y

rate= $12

number of printers = 1, so

[tex]y=12x[/tex]

therefore,the answer is

Linear

I hope this helps you

Given data:

The given fixed cost is $75.

The labor charges per hour is $50.

The expression for the total call is,

[tex]\begin{gathered} 325=75+(50)x \\ x=5 \end{gathered}[/tex]

Thus, the value of time is 5 hours, so option (B) is correct.

Answer:

a. The equation is y = 44x

b. The slope is 44, which means savings for a particular week x is 44 times the said week.

Explanation:

To write an equation that represents the given graph, we need to find the slope. Let us select two points (2, 88), (4, 176)

The slope is:

[tex]\frac{176-88}{4-2}=\frac{88}{2}=44[/tex]

The equation is:

[tex]y=44x[/tex]

This is with y-intercept being 0.

The slope of the graph is 44, it means the savings for a particular week x is 44 times the said week.

Given:

Rob's measurements were 2.4 lbs, 2.2 lbs, 1.6 lbs, 1.4 lbs, and 2.3 lbs.

To find:

The range and mode of the given data.

Explanation:

Using the range formula is,

[tex]\begin{gathered} R=Largest\text{ value - Smallest value} \\ =2.4-1.4 \\ =1 \end{gathered}[/tex]

Therefore, the range is 1.

As we know, the mode is the number that occurs the maximum number of times.

So, the date has no mode value.

Final answer:

• The range is 1.

,

• There is no mode.