Select All The Numbers That Are Equivalent.4.836 106 And 4,836,000,0005.812 10-7 And 0.00000058125.46 (2024)

Given the following question:

[tex]-1,5,\frac{1}{2},\frac{5}{7},0,\sqrt[]{2},\sqrt[]{8},-1.27,\frac{76}{77}[/tex]

Natural numbers are positive integers.

5 is a natural number

Whole numbers are integers, neither fraction or decimals just integers.

5, and 0 are whole numbers

Integers are a set of numbers that can be expressed without being a fraction/decimal.

-1, 5, and 0 are integers.

Rational numbers are a set of numbers that can be written as fractions.

-1, 5, 1/2, 5/7, 0, 76/77, 1.27 are all rational numbers they can all be expressed as a fraction.

(zero is also rational)

Irrational numbers cannot be expressed as a fraction

√2, √8,

Real numbers are numbers that include rational and irrational numbers.

-1, 5, 1/2, 5/7, 0, 76/77, -1.27, √2, √8

The total cost of all the items mentioned can be expressed as

12.99 + 1.19 P = C

Given : Sara needs to purchase one notebook

Also it is given that pack of pencils is represented by P

Since a notebook costs = $ 12.99

And pack of pencils cost = $ 1.19

Thus the total cost can simply be represented by adding all the above mentioned items

this means it can be written as

12.99 + 1.19 P = C where C represents the total cost { given }

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The given expression:

[tex]-7\times7+9\times\frac{-1}{-1}[/tex]

Apply BODMAS Rule : Brackets, Of, Division, Multiplication, Addition, Subtraction

According to BODMAS rule, we first simplify division:

[tex]-7\times7+9\times\frac{-1}{-1}=-7\times7+9\times1[/tex]

Simplify multiplication:

[tex]-7\times7+9\times1=-49+9[/tex]

Simplify addition:

[tex]-7\times7+9\times\frac{-1}{-1}=-40[/tex]

Answer: -40

The probability that any given person is a universal donor is 7.2%. This means that the probability that a person is not a universal donor is 92.8%.This indicates that there is a 0.65 percent chance that at least 1 out of every 10 randomly selected individuals is a universal donor.

Now, if we choose 10 people at random, we can use the binomial distribution to calculate the probability that at least 1 of them is a universal donor. The binomial distribution tells us that the probability of getting exactly k successes in n trials is:

P(k; n, p) = (n choose k) p^k (1-p)^(n-k)

where n is the number of trials, p is the probability of success on a single trial, and k is the number of successes.

plugging in our values, we get:

P(1; 10, 0.072) = (10 choose 1) (0.072)^1 (1-0.072)^9

P(1; 10, 0.072) = 10(0.072) (0.928)^9

P(1; 10, 0.072) = 0.65

This means that the probability that at least 1 out of 10 people chosen at random is a universal donor is 0.65.

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The graph of y = 1/2x is as shown below.

In this question, we need to graph an equation y = 1/2 x on the coordinate plane.

First we find the the coordinates of points passing through y = 1/2 x

The function is undefined at x =0 .

For x = 1,

y = 1/2

For x = -1

y = -1/2

For x = 2,

y = 1/4

So, we get coordinates (1, 1/2), (-1, -1/2), (2, 1/4)

We plot these points on the coordinate plane.

Therefore, the graph of y = 1/2x is as shown below.

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On solving the given equation the value of y=7/10 so this value the given equation will be true as the definition of solution of equation says ,"A solution to an equation is a number that can be plugged in for the variable to make a true number statement. "

What is solution to equation?

A number that can be entered for the variable to produce a true number statement is the solution to an equation. One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side. Systems of equations can be solved using one of three techniques: graphing, substitution, or elimination. Simply plot the given equations on a graph and locate the point(s) where they all intersect to solve a system by graphing. You can find the values of the variables you are solving for by finding the coordinate of this point.

Here,

12y - 1/2 = 9y +8/5

3y=8/5+1/2

3y=(16+5)/10

3y=21/10

y=7/10

According to the definition of an equation's solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," the value of y will be 7/10 when the given equation is solved.

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We have to use the equation

[tex]d=rt[/tex]

Where r = 12 mph, d = 20 miles, let's find t.

[tex]\begin{gathered} 20=12t \\ t=\frac{20}{12}=\frac{10}{6}=\frac{5}{3} \end{gathered}[/tex]

She'll take 5/3 hours to get there which is equivalent to 1 2/3 hours.

Let's transform 2/3 hours to minutes to find the exact time she has to leave.

We know that 1 hour is 60 minutes.

[tex]\frac{2}{3}hr\cdot\frac{60\min}{1hr}=\frac{120}{3}\min =40\min [/tex]

So, she will take exactly 1 hour and 40 minutes.

If you have to get there at 10:00 A.M., then she has to leave at 8:20 A.M.

Given:

Weekly wage = $2456

A career starts 24 years and ends in 65 years.

Find-: Lifetime earring.

Sol:

Total years of working is:

[tex]\begin{gathered} =65-24 \\ =41 \end{gathered}[/tex]

In one year 52 weeks

For 41 years total week is:

[tex]=41\times52[/tex]

Lifetime earnings.

[tex]\begin{gathered} =41\times52\times2456 \\ =5236192.00 \end{gathered}[/tex]

So lifetime earning is 5236192.00

Answer:

x=14

Step-by-step explanation:

x/7=2

7 x x/7 = 7x2

The width of the rectangle is equal to 3.42 meters

Let the width of the rectangle be represented by the variable x

thus from the question we can say that the length of the rectangle is 3 + x

Given is the area of the rectangle

we know that the area of the rectangle is Length × Breadth

Given area of the rectangle = 22 square meters

thus Area = Length × Breadth

On substituting the value we get

22 = ( 3 + x ) ( x )

x² + 3x = 22

x² + 3x - 22 = 0

b² - 4ac = 9 + 88 = 97

thus - b ± [tex]\sqrt{b^{2} -4ac}[/tex] / 2a

= - 3 ± 9.84 / 2

Thus the two values of x we will get are :

x= -12.84 / 2 = -6.42 which is rejected because width cant be negative

thus the value of x = 6.84 / 2 =3.42 meters

Thus we get values of x as

x = 3.42 meters

Thus the required width of the rectangle = 3.42 meters

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The distance travelled by the plane is 1365 miles.

Given,

Speed of the pane =455 miles per hour

Time taken =3 hours

To find distance covered by the plane use formula,

[tex]speed =\frac{Distance}{Time taken}\\ \\Distance=Speed * time taken\\\\Distance=455*3\\\\Distance=1365 miles[/tex]

Thus, the distance travelled by the plane is 1365 miles.

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Answer:

≈ 466 cm

Step-by-step explanation:

the total length of wire required is

outside sides of square + 4 straight pieces + circumference of circle

= (4 × 70) + (4 × 15) + (π d ← d is the diameter )

= 280 + 60 + 40π

= 340 + 125.66

= 465.66

≈ 466 cm ( to the nearest cm )

We need to find out the total length of wire needed to make this design. We can do this by finding out the perimeter of square and Circle and finally adding the lengths of the four 15cm wire used .

Given data:-

length of side of square= 70cmdiameter of Circle= 40cm , r = 20cm 15cm four wires

Perimeter of the square:-

[tex]\longrightarrow p_s = 4(side) \\ [/tex]

[tex]\longrightarrow p_s = 4(70cm) \\ [/tex]

[tex]\longrightarrow p_s = 280cm \\ [/tex]

Perimeter/circumference of the circle:-

[tex]\longrightarrow p_c = 2\pi r \\ [/tex]

[tex]\longrightarrow p_c = 2(3.14)(20cm) \\ [/tex]

[tex]\longrightarrow p_c = 125.71 cm \\ [/tex]

Additionally length of four wires would be 15cm*4 = 60cm .

So , total length of the wire required,

[tex]\longrightarrow l =( 125.71 + 280+60)cm \approx \boxed{466\ cm}\\ [/tex]

and we are done!

Range of the function f(x) = 3x² +18x is [-27,∞).

What is the range of a function?

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

Here, we have f(x) = 3x² +18x.

Let f(x) = y

⇒ y = 3x² +18x

⇒ y = 3(x²+6x)

⇒ y/3 = x²+6x

⇒ y/3 = x²+ 6x + 9 - 9

⇒ y/3 = (x+3)² - 9

⇒ y/3 + 9 = (x+3)²

⇒ (y+27)/3 = (x+3)²

Taking square root on both sides, we get

⇒ [tex]\sqrt{(y+27)/3}[/tex] = x+ 3

⇒ [tex]\sqrt{(y+27)/3} - 3[/tex] = x

Now since f(x) = y ⇒ x = f⁻¹(y)

⇒ f⁻¹(y) = [tex]\sqrt{(y+27)/3} - 3[/tex]

⇒ range = [-27,∞).

Therefore, range of the function f(x) = 3x² +18x was found to be [-27,∞).

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Answer:

9

Explanation:

Given the expression:

[tex]4a+7[/tex]

When the value of a =1/2

[tex]\begin{gathered} 4a+7=4(\frac{1}{2})+7 \\ =2+7 \\ =9 \end{gathered}[/tex]

The value of the expression when a=1/2 is 9.

[tex]\begin{gathered} \text{ principal=?} \\ A=1000 \\ \text{rate}=8\text{ \%=}\frac{8}{100}=0.08 \\ t=7 \\ P=\frac{A}{(1+\frac{r}{n})^{nt}} \\ P=\frac{1000}{(1+\frac{0.08}{12})^{12\times7}} \\ P=\frac{1000}{1.74742205143} \\ P=572.271592419 \\ P=\text{ \$}572.27 \end{gathered}[/tex]

The addition of the given two functions f(x) = –4x – 2 and g(x) = 2x ^2 + 4x-5 will be (f · g)(x) = 2x²-9

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

Given f(x)= -4x-2

g(x)=2x²+4x-5

For (f-g)(x) = -4x-2+2x²+4x-5

=2x²-9

(f-g)(x) = 2x²-9

Hence, The addition of the given two functions will be (f · g)(x) = 2x²-9

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The point of maxima of any function can be known by equating its derivative to zero. The rocket will take 1.5 sec to reach the maximum height and the maximum height is 27 feet.

What is differentiation?

The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).

Its geometric aspect is the slope of the function at a given point.

Given that,

Initial height of the launching pad is 4 feet,

Initial velocity of rocket is 48 feet/sec,

Height of the rocket as a function of time, h(t) = -16t² + 48t + 3

In order to find the time for maximum height equate h'(t) = 0 as follows,

-32t + 48 = 0

⇒ t = 48 / 32

⇒ t = 3 / 2

⇒ t = 1.5

To find the maximum height find h(t) for t = 1.5 as follows,

h(1.5) = -16 × 1.5² + 48 × 1.5 + 3

= -36 + 60 + 3

= -36 + 63

= 27

Hence, the time taken by the rocket to reach the maximum height is 1.5 sec and the maximum height reached is 27 feet.

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Answer:

it's 4

Step-by-step explanation:

#4 because we can see how x repeats its self 2 times such as (-3,0) and (-3,8)

Answer: The dress was $66

Step-by-step explanation:

55(120) divided by 100 and you'll get the price of the dress :)

Point = (3,-4)

After a translation left 2 units(-2) and 2 units up

(3-2,-4+2) = (1,-2)

Using trigonometric functions, the value of cos O in simplest terms is 5/17.

What are trigonometric functions?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (CSC).

So, we know that: cos α = Adjacent Side/Hypotenuse

We have,

adjacent side = 5hypotenuse = 17OM = 17 and ON =5

As we know,

cos O = Adjacent Side/Hypotenuse

We obtain:

cos O = ON/OMcos O = 5/17

Therefore, using trigonometric functions, the value of cos O in simplest terms is 5/17.

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Answer:

6 Seconds

Step-by-step explanation:

The car come to a complete stop after the time of 6 seconds.

What is defined as the velocity?Velocity is a vector assertion of an object's or particle's displacement with respect to time. The meter per second (m/s) is the standard unit of velocity magnitude (also recognized as speed). Alternatively, velocity magnitude can be expressed in centimeters per second (cm/s).

For the given question;

A car's velocity is modeled by v(t) = 0.5t² – 10.5t + 45.

The time inequality is given as; 0 ≤ t ≤ 10.5.

To calculate the time for which velocity becomes zero.

Put v(t) = 0.

v(t) = 0.5t² – 10.5t + 45 = 0

0.5t² – 10.5t + 45 = 0

Divide equation by 0.5.

t² – 21t + 90 = 0

factorize the values.

(t - 15)(t - 6) = 0

t = 15 and t = 6 seconds

As, 0 ≤ t ≤ 10.5.

Thus, t = 6 seconds.

Therefore, the car come to a complete stop after the time of 6 seconds.

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Answer:

Here is the equation in quadratic form:

x= 3±i√47/4

The component form of vector v with initial point (-6,2) and terminal point (7,-3) is (13,-5).

What is component form of vector?

The component form of a vector is represented as x, y >, where x denotes the direction of travel (right or left) and y denotes the direction of travel (up or down) of the vector. Any two-dimensional vector may be conceived of as exerting influence in two separate directions. In other words, it can be considered to have two pieces. Components are the individual pieces that make up a two-dimensional vector. A vector's elements show how that vector will act in a specific direction.

Here,

initial point A=(-6,2)

terminal point B=(7,-3).

AB=(Bx-Ax, By-Ay)

=(7-(-6), -3-2)

= (13, -5)

The component form of the vector v with the starting points (-6, 2) and terminal points(7, -3) is (13,-5).

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The expression to represent the change in elevation would be 13 - 150.

The change in elevation would be - 137 feet.

How to find the change in elevation?

The change in elevation refers to the difference between the elevation that a person ends up in, from the elevation that they started out at.

The change in elevation for the goat would therefore be:

= Ending elevation - Starting elevation

= 13 - 150

= - 137 feet

In conclusion, the change in elevation of the goat in its travels was - 137 feet.

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48.233 milliliters of acid are there.

Given:

A chemist is using 347 milliliters of a solution of acid and water.

13.9% of the solution is acid.

converting 13.9% to decimal:
13.9% = 13.9/100

13.9% = 0.139

milliliters of acid = total milliliters*0.139

= 347*0.139

= 48.233 milliliters.

Therefore 48.233 milliliters of acid are there.

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For 2 Volunteers hours= 12 days

For 3 = X days = 10 days

For 4= 8 days

For 5 = 6 days

from 12 to 4 there are 8

And from 6 to 2, there are 4

Then divide 8/4= 2

Part B) Is an INVERSE relationship, because more volunteers, means less time

Part C) Independent variable is , number of volunteers

Dependent variable is time to clear soccer field

Part D) How many volunteers in 1 day ?

= 12+2= 14 volunteers

Answer: The property being demonstrated for each expression is the commutative property of addition.

Step-by-step explanation:

Answer:

1.associative property, 2.commutative property, 3.identity property.

Step-by-step explanation: i got it right on edge

Answer:

3x+y=-17

Step-by-step explanation:

Standard form is written as: Ax+By=C where the slope is always -A/B

-A/B = -3/1

A= 3 and B=1

3x+y=C

Plug in point to solve for C

3(-8)+7=C

-24+7=C

-17=C

3x+y=-17

The slope is [tex]\frac{3}{4}[/tex]

What is slope ?

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not. Any two clearly separated points on a line can be used to calculate the slope of any line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.

here the given two pints are

[tex](x_1,y_1)=(-2,4)\\(x_2,y_2)=(6,10)[/tex]

Now using slope formula,

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

=> slope m = [tex]\frac{10-4}{6+2}[/tex]

=> slope m = [tex]\frac{6}{8}[/tex]

=> slope m = [tex]\frac{3}{4}[/tex]

Therefore the slope is [tex]\frac{3}{4}[/tex].

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