If x=3yz^2, what is y in terms of x and z?

4.372 × [tex]10^{13}[/tex] more kilograms the mass of the Antarctic iceberg than the mass of the Rock of Gibraltar.

Mass of the Antarctic iceberg = 4.55 × [tex]10^{13}[/tex]  

Mass of the rock of Gibraltar  = 1.78 × [tex]10^{12}[/tex]  

Excessive mass of Antarctic Icebergs than the rock of Gibraltar,

4.55 × [tex]10^{13}[/tex]  - 1.78 × [tex]10^{12}[/tex]  

Subtract easily both should be in the same power of ten,

= 4.55 × [tex]10^{13}[/tex]  - 1.78 × [tex]10^{12}[/tex]  

= 43.72  × [tex]10^{12}[/tex]  

= 4.372 × [tex]10^{13}[/tex]

Scientific notation is used to express quantities that are either too large or too little to be represented by decimals. Scientific format, standard index format, and standard format are other terms for the same thing.

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Step-by-step explanation:

a probability is always

desired cases / totally possible cases

28 students in total.

6 are female.

so, we have 28-6 = 22 male students.

7 of the 28 students have an A.

17 male students do not have an A.

that means 22-17 = 5 male students have an A.

and that means 7-5 = 2 of the female students have an A.

"given that they have an A".

that reduces our totally possible cases to 7.

the probability that an A-student is male is therefore

5/7 = 0.714285714...

and FYI

the probability that an A student is female is

2/7 = 0.285714286...

The probability that a student is male given that they have an A is approximately 0.538.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

We can use Bayes' theorem.

P(male | A) = P(A | male) x P(male) / P(A)

We are given:

P(A | male) = 7/17

(7 students are male and have an A, out of 17 male students)

P(male) = 17/28

(17 students are male, out of 28 total students)

P(A) = (6+7) / 28

(13 students have an A, out of 28 total students)

Plugging in these values.

P(male | A) = (7/17) x (17/28) / (13/28) = 0.538

Therefore,

The probability that a student is male given that they have an A is approximately 0.538.

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The hypotenuse of the given right angle triangle is: 50 cm

What is hypotenuse?

In mathematics, the hypotenuse is the longest side of a right angle triangle. It is defined as the standard formula, which states that the square of the hypotenuse is equal to the square of their adjacent sides.

According to the question, to calculate the hypotenuse with the given parameters. First name all the three vertices.

AB = 30 cm; BC = 40 cm; AC = ?

Using standard hypotenuse formula, which states:

AB² + BC² = AC²

⇒ 30² + 40² = AC²

⇒ AC² = 900 + 1600 = 2500

⇒ AC = 50 cm

Hence, the hypotenuse of the given right angle triangle is: 50 cm

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The test statistic for this hypothesis test is; t = 1.5

The formula for test statistic is;

t = (x' - μ)/(σ/√n)

where;

x' is sample mean

μ is population mean

σ is standard deviation

n is sample size

We are given;

Sample mean; x' = 8.12 hours

Population mean; μ = 8 hours

Standard deviation; σ = 0.72 hours

sample size ; n = 81 pilots

Thus;

t = (8.12 - 8)/(0.72/√81)

t = 0.12/0.08

t = 1.5

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Answer:

A,) 20

Step-by-step explanation:

First, I am assuming that the problem is 5k = 100, not "5k = 100k =" as it was written.

We need to end up with "k equals some number."  This is called solving for k.  In order to do this we need to have k by itself.  We look at the problem and ask, "what is preventing k from being by itself?"  In this case k has a "times 5" with it.  How can we get rid of that?  Well we can do the opposite of "times 5,"  and that is to divide the left side by 5.  That leaves k by itself which is exactly what we need.  But if do something to one side of an equation, we need to do it to the other side for the equation to still be true.  So in this case we also have to divide the right side by 5 also, which gives us 20 on the right side.  So in our original problem:

5k = 100

Divide both sides by 5 and we have the answer:

k = 20

Answer:

they're similar

Step-by-step explanation:

hello again ;)

Answer:

Step-by-step explanation:

15

The number of miles for which the cost of Uber and Lyft is the same is 30.

How to solve linear equations?
Given that the largest power of the variable (or pronumeral) in these equations is 1, linear equations are also known as first-degree equations. A line on the quadratic system is represented by a linear equation. This equation's general form is axe + b = 0, where a, b, and x are all integers and x is the variable. The y-axis is parallel to this form of equation's single solution, which it symbolizes.
The steps that should be followed while solving linear equations are listed below:
1) We must first determine which variable we need to isolate.
2) Next, make a distinction between variables and constants.
3) Arrange the constants on the right and the variables on the left.
4) Using established axioms, we carry out algebraic operations to determine the variable's value.

Let the number of miles covered be = x
Given, the cost of travel = Pickup Fee + Cost per mile
Given, the pickup fee for Uber = $ 0
The cost per mile for Uber = $ 0.25
Again, the pickup fee for Lyft = $ 3
The cost per mile for Lyft = $ 0.15
Thus, the cost of travel for Uber = 0 + 0.25x -- (i)
Also, the cost of travel for Lyft = 3 + 0.15x -- (ii)
As per question, (i) and (ii) are equal.
Thus, 0 + 0.25x = 3 + 0.15 x ⇒ (0.25 - 0.15)x = 3 ⇒ 0.10x = 3
⇒ x = 3/0.10 ⇒ x = 30
Thus, for 30 miles  the cost of Uber and Lyft is the same.

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Using inequality, we can conclude that maximum of 14 people can visit the amusement park.

So, (p) a maximum number of people who can visit the park:

Now, calculate as follows:

Therefore, using inequality, we can conclude that maximum of 14 people can visit the amusement park.

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No, Diego's estimation is not good because he overestimated the original value to nearly double the amount.

Overestimation is when we fix a value that is greater than the original value and underestimation when we fix a value that is less than the original value.

Given, Diego and his mom have been saving recycling items for months and today they traded them in they made 42 dollars on cans, 19 dollars on glass bottles, and 32 dollars on plastic bottles which are 83 dollars.

Diego estimates it to be 140 dollars which is nearly double the original amount and not a good estimate.

A good acceptable estimate can be of more or less than 5% of the original value.

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Answer: 333 Cookies

Step-by-step explanation:
Let E = Cookies by Esther
Let L = Cookies by Lee
The equation for amount of cookies: E+L

L=141
E=L+51
Substitute L
E=141+51=192
E+L=141+192=333

Answer:

[tex]10 \div x - 10 \div (x - 1) = 30[/tex]

The union of set A = {1, 5, 8, 12, 17} and B = {5, 17} is

AUB= {1, 5, 8, 12, 17}

This is further explained below.

Generally, The set that contains all of the elements that are part of both sets A and B, or all of the elements that are part of both sets combined, is referred to as the union of the two sets A and B. The symbol is used to represent the union of all the elements in the set.

In conclusion, The union of these sets sees the value of both sets represented

A = {1, 5, 8, 12, 17} and B = {5, 17}

AUB= {1, 5, 8, 12, 17}

Option A

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Answer:

Step-by-step explanation:

just like when you have 5+(17-8) you don't have to do all the work you can just do this 17-8 is 9 and that is  when you add 5+9 is 14

40

Explanation

Step 1

a)initially we have 8 dots

after that

in step 2, we have a new row and , now there are 8 dots per row, so

in step 3, we should have

and

as we can see, the rule works

Step 2

now, to find the patter in step 4, just apply

and

finally, to know the number of dots

Multiply the number of row, by the number of dots per row, so

therefore, the answer is 40

I hope this helps you

The functions whose graphs consist only of lines are-

A function is a relationship between a set of inputs (referred to as the domain) and a set of permissible outputs (referred to as the codomain), in which each input is connected to exactly one output. A function on one variable is frequently denoted by f.

Linear functions: A straight line just on coordinate plane is represented by a linear function. For instance, y = 3x - 2 symbolizes a straight line on the a coordinate plane and thus a linear function.

Constant functions: A constant function is employed to portray a quantity that remains constant over time and is considered the simplest type of real-valued function.

Linear absolute value functions: The Absolute Value Function is a two-linear function piecewise defined function.

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1) the equation is:

So we can rewrite the equation as a slope intercept so:

So the slope is -1/2

2) the equation is:

Now we evaluete the coordinates to see which one is not on the line so for (1,-1)

So is on the line

for (-1,-4)

So it is on the line

for (3,2)

So it is on the line

Finally for (1,2)

So (1,2) is not on the line

3) if the slope is -2 and goes to the point (3,-1) we can use the equation of a line to find the intercept so:

So the intercept is 5 so the equation is:

Answer:

Point Form:

(

−

13

4

,

−

7

4

,

1

)

Equation Form:

x

=

−

13

4

,

y

=

−

7

4

,

z

=

1

Step-by-step explanation:

The percentage of yield after cleaning and trimming the celery is 75%.

Given, a bunch of celery is bought which weighs 16 ounces.

After cleaning and trimming the celery, you are left with 12 ounces.

let the x be the percentage yield.

Based on the conditions, formulate:

16 × x = 12

⇒ 16x = 12

⇒ x = 12/16

minimize the terms.

⇒ x = 3/4

to convert it into percentage, multiply by 100

⇒ x = 3/4 × 100

⇒ x = 75%

Hence the percentage of yield is 75%.

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Answer:

probability is 1.

Step-by-step explanation:

In a lot of probability problems when asking for “at least two” is usually easier to see the opposite case, that is, the “none of them” case…

P(“at least one … X”) = 1 - P(“none of them … X”)

I will we exclude 29th of February, that is, considering none of the people was born on the leap day of a leap year.

First, let’s see what happens for 2 people. We can name one of those 2 people as “first” and the other as “second”. Whatever the birthday of the “first” one is, the other has 364 out of 365 days in the year to have a different birthday.

p(2) = 1–364/365 = 1/365

For 3 people, the “first” has a birthday, the “second” has a probability of 364/365 to have a different birthday and the third has a probability of 363/365.

p(3) = 1 - 364/365 * 363/365= (365^2 - 364*363)/365^2

For 4 people:

p(4) = 1 - 364/365 * 363/365 * 362/365

…

For n people, if n is less than 366:

p(n) = 1 - (364! / [365 - n]! )/365^(n-1)

p(n)=1−364!(365−n)!⋅365n−1

Obviously, if n is 366 or more, since we excluded the leap day there must be always 2 people with the same birthday (pigeonhole principle), and then in this cases the probability is 1.

The mean of all exam scores in the class is found = 71

Normally distribution

A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.

While data points are referred to as x in a normal distribution, they are called z or z-scores in the z-distribution. A z-score is a standard score that tells you how many standard deviations away from the mean an individual value (x) lies: A positive z-score means that your x-value is greater than the mean.

The z-score is found by;

z = (x - μ)/σ

x =  sample mean

μ =  mean score

σ =  standard deviation

Now, from this,

x = zσ + μ

For p = 80th percentile= 0.8, see z value from z score table.

z = 0.85

x = 85 points

85 = 0.85σ +  μ  .....eq 1

For p = 30% = 0.3, see the z value from the z score table.

z = -0.3802

x = 65

65 = -0.3802σ +  μ  .....eq 2

Solving eq 1 and 2.

σ = 16.25

Put in eq 1

μ = 71.19

μ = 71

Thus, the mean of all exam scores in the class is found = 71

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The volume of the cone has a value of 410.67 cubic meters

From the question. the height and the radius of the cone are given as

Height = 7 feet

Radius = 8 feet

The volume of the cone can be calculated using the following volume formula

Volume = 1/3πr^2h

Substitute the known values in the above equation

So, we have

Volume = 1/3 * 22/7 * 8 * 7^2

Evaluate the products

Volume = 410.67

Hence, the volume is 410.67 cubic meters

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There are 60 boys to make up the boys' teams and 40 girls to make up the girls' teams.

We are also told that the teams should be the same size.

This means that irrespective of the number of teams, each team should contain the same number of players.

Thus, the largest number of people that can be placed on a team is;

The highest common factor ;

The HCF is 10 x 2 = 20, therefore;

The largest number of people that can be placed on a team is 20.



The value of x for quadratic equation f(x) = 2x² + 3x when f(-5) is 35.

Given, f(x) = 2x² + 3x

To find: f(-5)

For the quadratic equation f(x) = 2x² + 3x substitute the value -5 in place of x as the f(-5) has been mentioned in the question.

So,

f(-5) = 2(-5)² + 3(-5)

A Square of -5 is 25 and 3 multiplied by -5 is 15,

f(-5) = 2(25) + (-15)

Multiple of 25 and 2 is 50 subtracted by 15,

f(-5) = 50 - 15

At last, subtract 50 by 15,

f(-5) = 35

∴ For equation f(x) = 2x² + 3x when f(-5), the value of x = 35.

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Answer:

AC=8

Step-by-step explanation:

2x=2(8)

2x=16

x=16÷2

x=8

Answer:

yes that is the correct answers

Using proportions, the coordinates of the point that divides directed line segment YX so that the ratio of YP to PX is 5 to 3 are given by:

[tex](x,y) = \left(\frac{3}{8}(x_y - x_x) + x_x, \frac{3}{8}(y_y - y_x) + y_x\right)[/tex]

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division from the given ratios.

Division of line segments is one application of proportions. The entire length of the line segment with endpoints XY is given by:

Y - X.

Now we have point P, dividing the line segment YX so that the ratio of YP to PX is 5 to 3, meaning that XP is 3/8 of XY, that is:

[tex]P - X = \frac{3}{8}(y - x)[/tex]

Then the x-coordinate of P is found as follows:

[tex]x - x_x = \frac{3}{8}(x_y - x_x)[/tex]

[tex]x = \frac{3}{8}(x_y - x_x) + x_x[/tex]

The y-coordinate is found applying the same rule with the y-coordinates of points X and Y, as follows:

[tex]y - y_x = \frac{3}{8}(y_y - y_x)[/tex]

[tex]y = \frac{3}{8}(y_y - y_x) + y_x[/tex]

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The equation which show the cost of windows:-

C = $75.75 * W

where W = no of windows

What is equation ?

A mathematical equation can be defined in a variety of ways.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Mathematical variables are used in even the most fundamental and straightforward algebraic equations.

$227.25 ÷ 3 =  $75.75

The equation which show the cost of windows:-

C = $75.75 * W

where W = no of windows

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The measure of the angles 2 and 3 are 70°

What is an angle?

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles also were generated when plane cross. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. In the case of a geometric angle, the arc is defined by the sides and is centered at the vertex.

Given, angle 1 = 40°

and, angle 2 = angle 3 = x

In a triangle, sum of angles = 180°

or, m∠1 + m∠2 + m∠3 = 180°

or, 2x = 180-40

or, 2x = 140

or, x = 140/2 = 70°

Hence, the measure of the angles 2 and 3 are 70°

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Answer:576 minutes

Step-by-step explanation:

The power as a product of powers can be rewritten  (2ax)³ as  (2ax )(2ax)(2ax )

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

The product can be defined as the multiplication operation of two or more terms so that another term can be gotten the same as the one that is been given that we were asked to rewrite.

Power is defined as the degree that is been found on the terms, the degree that can be on the term is 3, then it can be expressed in three terms

Therefore, the given expression is (2ax)³ can be rewritten as;

(2ax)³ =  (2ax )(2ax)(2ax )

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Answer:

Yes

Step-by-step explanation:

Parallel lines are 2 lines that go in the same direction that will never touch each other.

Hope that helps

Answer:

r=1

Step-by-step explanation:

1=2r-1

Add 1 on both sides

2=2r

Divide 2 on both sides

r=1