Use the drop-down menus to answer the questions. What do the numbers on the left, or y-axis, represent? how many students spent 2 or more hours studying? how many students spent fewer than 2 hours a night studying?.

(m,n) are chosen uniformly among all relatively prime pairs of integers up to N and then  N→∞

One thing is certain in this case: if m and n are prime numbers other than 2, we can be sure that they are relatively prime since (m, n) = 1. Additionally, since m + n is even, it is impossible for it to be a prime, and the probability in this situation is 0.

We require a sample space before we can discuss the probability of anything. To put it simply, we must comprehend how the relatively prime integers m and n came to be chosen. Questions concerning the likelihood that something will occur have no meaning if not.

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The question is wrong and stands no meaning, the possible question might be

Suppose positive integers m and n are relatively prime. What is the probability that (m + n) is a prime number?

Answer:

There were 528 students in Greenville school

The length s of the circular arc is 6.75π units

What is an angle?

Two lines intersect at a location, creating an angle. An "angle" is the term used to describe the width of the "opening" between these two rays. Angles are used in the design of buildings, roadways, and sports venues by engineers and architects.

A figure made by two intersecting lines or two rays extending from the same point is called an angle.The character ∠ is used to represent it. Angles are frequently expressed in degrees and radians, a unit of circularity or rotation. We encounter angles frequently in life.

Formula for the length s of the circular arc when angle θ is in radians:

s=r θ

=> s= 9(3π/4)  = (9*3*π)/4 = 6.75π units

Thus, the  length s of the circular arc is 6.75π units

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Answer: The sequence is defined by the rule f(n) = 2n^2 + 4.

To find the first 4 terms of the sequence, we need to plug in the values of n into the rule and calculate f(n) for each value of n.

n = 1: f(1) = 2(1)^2 + 4 = 2 + 4 = 6

n = 2: f(2) = 2(2)^2 + 4 = 8 + 4 = 12

n = 3: f(3) = 2(3)^2 + 4 = 18 + 4 = 22

n = 4: f(4) = 2(4)^2 + 4 = 32 + 4 = 36

So, the first 4 terms of the sequence are 6, 12, 22, 36

Step-by-step explanation:

Answer:

72 cm

Step-by-step explanation:

you said that the width is is 36 and the length is 2x as long making it 36*2 which is 72

Choose three values for x and list them in a table.

Choose three x values and list them in a table to graph the equation. (Hint: choose values that are simple to calculate, such as 1, 0, and 1.) To determine the matching y-coordinate, substitute each value in the equation and simplify. Draw a straight line between the points of the ordered pairs.

Find two points on the line with integer coordinates.

Starting with the point on the left, draw a right triangle connecting the first and second points.

Count the rise and run on the triangle’s legs.

To calculate the slope, divide the increase by the run. M=riserun.

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An expression (5 - 22x) must be added to polynomial 4x⁴ - 2x³ - 6x² + x - 5 so that the result is exactly divisible by a polynomial 2x² + 3x - 2.

Here we have been given two polynomials.

Let us assume that f(x) = 4x⁴ - 2x³ - 6x² + x - 5 and g(x) = 2x² + 3x - 2

​we need to find an expression (polynomial) that should be added to 4x⁴ - 2x³ - 6x² + x - 5 so that the result is exactly divisible by 2x² + 3x - 2

If we divide a polynomial  f(x) = 4x⁴ - 2x³ - 6x² + x - 5 by g(x) = 2x² + 3x - 2 using polynomial long division method, the result is:

f(x) / g(x)

= ( 4x⁴ - 2x³ - 6x² + x - 5) ÷ (2x² + 3x - 2)

= [(2x² + 3x - 2) × ( 2x² - 4x + 5)] + (5 - 22x)

This means, the quotient is  ( 2x² - 4x + 5) and the remainder is (5 - 22x)

(see in attachment)

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The complete question is:

What must be subtracted from 4x⁴-2x³-6x²+x-5 so that the result is exactly divisible by by 2x²+3x-2​?

Answer:

If for every 5 calendars that Josh sold, Laure sold 4, and Josh sold 45 calendars last month.

Lauren sold 4/5 * 45 calendars = 36 calendars last month.

Step-by-step explanation:

Answer:

We know that for every 5 calendars Josh sold, Lauren sold 4. This is a ratio of 5:4, which means that for every 5 calendars Josh sells, Lauren sells 4.

We also know that Josh sold 45 calendars last month. We can use this information to find out how many calendars Lauren sold by using the ratio of 5:4.

We can set up the equation:

5/4 = 45/x

Where x represents the number of calendars that Lauren sold.

We can solve for x by multiplying both sides of the equation by x:

5x = 4*45

x= 4*45/5

x= 36

So Lauren sold 36 calendars last month.

Answer: D and B

Step-by-step explanation:

17. Trying out all of the answers, you can find that D works

18. Also trying out all four answers, you can find that B works

Answer:

x=-2, y=-4

Step-by-step explanation:

Substitute x=y+2

Simplify [ 7y +10 = -18 ]

Substitute y = -4

Simplify x = -2

The factored form and the vertex form of the given quadratic equation is given by :

Standard quadratic equation is  : ay²+ by + c

Factored form of the quadratic equation is : A ( y - p )( y - q ).

Vertex form of the quadratic equation is : A ( y - h )² + k .

As given in the question,

Let us consider the standard quadratic equation be :

ay²+ by + c

Example : 3x² + 15x  + 18

Factored form is :

= 3 (x² + 5x + 6 )

= 3 ( x² + 2x + 3x + 6 )

= 3 ( x + 2 )( x + 3 )

Standard factored form is :  A ( y - p )( y - q )

Let ( h ,k ) be the vertex of the quadratic equation ,

Vertex form is given by : A ( y - h )² + k

Therefore, the factored and the vertex form of the given quadratic equation is equal to

Standard quadratic equation is  : ay²+ by + c

Factored form of the quadratic equation is : A ( y - p )( y - q ).

Vertex form of the quadratic equation is : A ( y - h )² + k .

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The expression to represent the given phrase is 21/b.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, 21 divided by a number b.

The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

So, the expression is 21/b

Therefore, the expression to represent the given phrase is 21/b.

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In option D the location of point P represents the probability of an event that is likely but not certain.

The likelihood that an event will occur is measured by its probability. In our example, the point P on the number line is exactly equally distant from both 0 and 1 in option A, demonstrating that this event is equally likely. The fact that the point P is close to 0 in option B indicates that it is extremely unlikely. Option C has the point P after the point 1, which makes it certain because any probability cannot be larger than 1, which demonstrates that the event is unavoidable. In Option D point P's proximity to 1 demonstrates that it is extremely likely but not certain.

The complete question is:

On which number line the location of point P represent the probability of an event that is likely, but not certain?

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Answer:

Step-by-step explanation:

You too mate. Cheers!

The value of x in the given ΔCSU is 17.7.

Given data :

m∠CSU = 10x + 3

m∠CUS = 30x - 13 x

The three angles form the triangle ΔCSU then the addition of them makes 180°.

ΔCSU = 180

m∠CSU = 10x + 3

10x + 3  = 180

10x  = 180 - 3

x = 177 / 10 = 17.7

So,

m∠CSU = 10x + 3

Applying the value of x

= 10 x 17.7 + 3

= 180

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We are using ln more than log because, we compare all log with different base value with ln.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

As mentioned above, we use natural logs (i.e., logarithms in base e) because coefficients on the natural-log scale may be directly interpreted as roughly proportionate differences: for example, with a coefficient of 0.06, a change of 1 in x corresponds to a roughly 6% change in y, and so on.

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The point at which the perpendicular bisectors intersect in a triangle is called the circumcenter. The circumcenter is the center of the circumcircle, which is a circle that passes through all three vertices of the triangle.

It is the center of the circle that is tangent to each side of the triangle. The circumcenter is equidistant from each vertex of the triangle and can be calculated by finding the intersection of the perpendicular bisectors of the triangle. The perpendicular bisectors of a triangle are lines that pass through the midpoints of the sides of the triangle and are perpendicular to the sides.

The circumcenter is important in triangle geometry because it helps to define the triangle and its properties. Knowing the circumcenter of a triangle can be useful in finding the triangle's area, medians, altitudes, and angle bisectors.

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The right expression for determining the number of sit ups Jean did in this week is , x = 2× 3 + 3×3 and in count it is equals to 15.

We have, Last week the number of sit ups done by Jean on Monday = 2 sit ups

the number of sit ups done by Jean on Wednesday = 3 sit ups .

But this week, her sit ups are three times as many sit ups as last week. Let us assume the number of sit ups she did in this week be "x".

Total sit ups done by her in last week = 2 + 3

= 5

The expression, used by her to calculate the number of sit ups she did this week = 2+3×3 --(*)

According to problem, In this week the number of sits ups that she did, x = 3× 5 or 2× 3 + 3×3 = 15 .

So, the right expression can be written as x =

2× 3 + 3×3 . Now, comparing the both expression to determine the error in her expression. The error in her expression is that she skip the 3 times in case of Monday sit ups.

Hence, the the number sit ups she did this week is 15 or 2× 3 + 3×3 .

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Complete question:

Last week, Jean did two sit-ups on Monday and three sit-ups on Wednesday. This week, Jean did three times as many sit-ups as last week. Jean used the expression to find the number of sit-ups she did this week. Explain and correct her error.

The type of sampeling performed by the truck manufacture is known as Simple random sampling .

The sampling probability of an element or member of the population is its likelihood of being included in the sample during the drawing of a single sample in the theory pertaining to sampling from limited populations.

Probability sampling methods include simple random sampling, systematic sampling, stratified sampling, and cluster sampling.

A selection of participants from a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling. Every person in the population has the same probability of getting chosen.

A probability sampling technique called systematic sampling involves picking people from the population at regular intervals, such as every 15th person on a list of the population. This can mimic the advantages of straightforward random sampling if the population is arranged in a random order.

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Answer:

x=6

y= 18

Step-by-step explanation:

[tex]\frac{a^{18}b^{24} }{a^{12} b^{6} } = a^{6} b^{18}[/tex]

18-12=6

24-6=18

Answer:

Step-by-step explanation:

(9)^-5/2 = (1/9)^5/2 = (1/59049)^(5/2) = 1/(59049)^(5/2) = 1/243^(5/2) = 1/243^(5/2) = 1/(3^5)^(5/2) = 1/3^(5*5/2) = 1/3^25/2 =1/3^(25/2) = 1/3^12.5 = 1/(3^12.5) =1/3^12.5 =1/43046721 = 1/43046721

The equation of the line can be calculated using the formula y = mx + c where 'm' represents the slope and 'c' represents the y-intercept of the line.

As given in the question,

Standard equation of the line for grade 9 is given by :

y = mx + c

Here 'm' represents the slope of the line.

Slope of the line = ( y₂ - y₁ ) / ( x₂ - x₁ )

( x₁ , y₁ ) and ( x₂ , y₂ ) are any two coordinates on the line.

And 'c' is known as the y - intercept of the line which is calculated where line cuts the y-axis.

Therefore, the required equation of the line can be calculated using the standard formula y = mx + c.

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Answer:

9 x 5 = 45

Step-by-step explanation:

An example: Tom worked for 5 hours today, for each hour, he earned $9, how much money did he earn in total?

$9 x 5 hours of work = $45 for 5 hours

The vector coordinate's separation from the vector space's origin is determined by the L2 norm. As a result of its calculation as the Euclidean distance from the origin, it is sometimes referred to as the Euclidean norm.

In mathematics, the length of a line segment connecting two points in Euclidean space is known as the Euclidean distance.

It is sometimes referred to as the Pythagorean distance since it can be determined from the points' Cartesian coordinates using the Pythagorean theorem.

The vector coordinate's separation from the vector space's origin is determined by the L2 norm.

As a result of its calculation as the Euclidean distance from the origin, it is sometimes referred to as the Euclidean norm.

Therefore, the vector coordinate's separation from the vector space's origin is determined by the L2 norm. As a result of its calculation as the Euclidean distance from the origin, it is sometimes referred to as the Euclidean norm.

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The degree of polynomial 3x^4-0x^3+0x^5 is 4

Degree of a polynomial is the highest power that its terms pertain (for multi-variables, the power of term is addition of power of variables in that term).

Thus, in

x^3+3x+5

, the degree of the polynomial is 3 as the highest power in its terms is 3.

(power and exponent are same thing)

Given;

Polynomial= 3x^4-0x^3+0x^5

The highest degree from first observation seems to be 4 but the term with exponent 4 is being multiplied with zero so the degree is then 4;

Therefore, the correct degree will be 34

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For k = 2, the given system of equation contains no solution, hence represent parallel lines.

There are no solutions to a system with parallel lines. Observe that the slope of parallel lines is the same. The lines will have the same steepness with distinct intercepts when graphed. Since parallel lines will never connect, there is no solution to the problem.

When the graphs are parallel, a system of linear equations cannot have a solution.

For a system of equations representing parallel lines means they do not intersect, hence, have no solutions.

For a system of equations [tex]$a_1 x+b_1 y+c_1=0 ; a_2 x+b_2 y+c_2=0$[/tex] to have no solution, the condition to be satisfied is

[tex]$\frac{a_1}{a_2}=\frac{b_1}{b_2} \equiv \frac{c_1}{c_2}$$[/tex]

[tex]$\Rightarrow \frac{\mathrm{k}}{4}=\frac{-3}{-6} \equiv \frac{6}{150}$$[/tex]

For k = 2, the given system of equation contains no solution, hence represent parallel lines.

The complete question is:

The value of k, for which the system of equations k x-3 y+6=0,4 x-6 y+150 represent parallel lines is

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If Mrs. Haley washed [tex]\frac{2}{5}[/tex] of her laundry and her son washed [tex]\frac{1}{3}[/tex] of it , then most laundry was washed by Mrs. Haley and the amount of laundry that is still needs to be washed is [tex]\frac{4}{15}[/tex]  .

The fraction of laundry that Mrs. Haley washed is = [tex]\frac{2}{5}[/tex] ;

the fraction of laundry that her son washed is = [tex]\frac{1}{3}[/tex] ;

On comparing both the fraction we get that [tex]\frac{2}{5} > \frac{1}{3}[/tex] ;

So , Mrs. Haley washed more clothes than her son .

In total they both washed ⇒ [tex]\frac{2}{5} +\frac{1}{3}[/tex] = [tex]\frac{11}{15}[/tex] of clothes ;

The amount of laundry that is left to be washed is = [tex]1-\frac{11}{15}[/tex]

On simplifying,

we get ,

= [tex]\frac{4}{15}[/tex] ;

Therefore , there is still [tex]\frac{4}{15}[/tex] of laundry that needs to be washed by them .

The given question is incomplete , the complete question is

Mrs. Haley washed 2/5 of her laundry. Her son washed 1/3 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?

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Answer:

g(6) = 150

Step-by-step explanation:

g(x) = 4[tex]x^{2}[/tex] - x + 12

x = 6

g(6) = 4[tex](6)^{2}[/tex] - (6) + 12

       = 4 (36) - 6 +12

       = 144 - 6 + 12

       =  150

The  constant of proportionality is  10  

What are direct and indirect variations ?

One quantity directly changes in response to a change in another quantity, which is referred to as direct variation. This suggests that if one quantity increases, the other will follow suit and rise in proportion. In a similar manner, if one quantity declines, the other amount also declines.

When one parameter declines while the other rises or vice versa, this is known as inverse variation. This means that the magnitude or absolute value of one item decreases as the other quantity rises, resulting in a constant value for their product. This item is also referred to as the proportionality constant.

From the table, y values increase as the x values increase.

This is a direct variation and is given by y=kx.

k is the constant of proportionality

k= y/x

Substitute any pair of x and y values

k= 2/(1/5)  = 2*5 = 10

Thus, the  constant of proportionality is  10  

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In order for (x - k) to be a factor of f(x), it must also be a zero of f(x). An integer-coefficient polynomial function's rational zeros are equal to the constant term's factor divided by the leading coefficient's factor.

When exponents, constants, and variables are joined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).

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