The product of two consecutive natural numbers is 1. 5 times the square of the lesser number.

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 .

To learn more about Expression, refer:

https://brainly.com/question/1859113

#SPJ4

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.

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).

To learn more about polynomials here:-

brainly.com/question/2833285

#SPJ4

Answer:

Step-by-step explanation:

You too mate. Cheers!

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 value of x is √589. The ladder will reach √589 feet up of the wall.

What is the right triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

Given that a ladder is placed against a wall. The length of the ladder is 25 feet. The distance of the ladder from the wall is 6 inches. Thus it forms a right triangle.

Assume that by using the ladder a man reaches x feet up the wall.

Then the base of the right triangle is 6 inches.

The hypotenuse is 25 inches. The height of the right triangle is x inches.

Applying Pythagorean theorem:

6² +x² = 25²

36 + x² = 625

x² = 625 -36

x² = 589

Taking square root on both sides:

x = √589 feet

To learn more about Pythagorean theorem, click on the below link:

https://brainly.com/question/10522165

#SPJ1

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.

To learn more about an expression visit;

https://brainly.com/question/28170201.

#SPJ1

On the basic of empirical rule, the estimate value of proper Millatti of a zebra living between 16. 6 and 24. 4 years is 0.6826.

We have, the lifespans of zebras in a particular zoo or normally distributed.

Average zebra lives,µ = 20.5 years

Standard deviations,σ = 3.9 years

We have to estimate the proper Millatti of a zebra living between 16. 6 and 24. 4 years.

In line accordance with the empirical rule : is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).The rule states that (approximately):

We have to determine value of

P(16.6 < x< 24.4 ). The Z-Score formula, Z is defined as (x - µ)/σ . Now,

Z = (24.4 - 20.5)/3.9

=> Z = 3.9/3.9

=> Z = 1

This value of Z = 1 tells us that row score for 24.4 years is one standard deviations from mean. In other words, 68% of the values between Z = -1 and Z = 1 , i.e., -1 < z < 1. Normal distribution is symmetric, so half area above the Z = 1 and half below Z = -1. So, P( -1 < z < 1) = P(16.6< x<24.4 ).

so the probability of a zebra living between 16. 6 and 24. 4 years is P(16.6 < x< 24.4 ),

= P( -1 < z < 1)

= P( z> 1 ) - P( z< -1)

= 0.68269

Hence, the required probability is 0.6826.

To learn more about empirical rule, refer:

https://brainly.com/question/30396053

#SPJ4

Answer:

x=-2, y=-4

Step-by-step explanation:

Substitute x=y+2

Simplify [ 7y +10 = -18 ]

Substitute y = -4

Simplify x = -2

12 makes up the larger triangle's missing side.

Similar triangles are triangles that have an equal shape, however, their sizes might also additionally vary. All equilateral triangles, squares of any facet lengths are examples of comparable objects. In different words, if triangles are similar, then their corresponding angles are congruent and corresponding facets are in the same proportion 

Given, the two triangles are similar

From the condition of the similar triangle:

There are three sets of matching sides that are proportionate. In addition to being proportional and having equal corresponding angles, two pairs of corresponding sides are also identical.

thus the ratio of the two sides will be the same

? / 15 = 4/5

? = 12

therefore, the Missing side of the bigger triangle is 12.

Learn more about similar triangles here:

https://brainly.com/question/14926756

#SPJ1

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.

To learn more about  graph to refer:

https://brainly.com/question/17267403

#SPJ1

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

Read more about Degree of Polynomials at; brainly.com/question/12700460

#SPJ1

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.

To learn more about probability refer to  :

https://brainly.com/question/16928409

#SPJ1

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?

Learn more about Fraction here

https://brainly.com/question/22731479

#SPJ4

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.

To know more about logarithmic function visit:

brainly.com/question/30284289

#SPJ4

As per the given measurement the centigrams of protein are in 3d fluid ounces of milk is 8504.86

The term measurement id known as the process of associating numbers with physical quantities and phenomena.

Here we know that one cup of skim milk contains 8 grams of protein.

Now, we have to find the amount of centigrams of protein are in 3d fluid ounces of milk.

As we all know that one ounce is equal to 2834.9553.

Then if we want the centigram value, then we have to multiply the number with 2834.9553, then we get the result as,

=> 3 x 2834.95

=> 8504.86

To know more about measurement here.

https://brainly.com/question/18827844

#SPJ4

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.

Know more about L2 distance here:

https://brainly.com/question/28217907

#SPJ4

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: 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: expression A and D have the same answer so option C

Step-by-step explanation:

they both get the answer of -0.86

Answer: there are two anwers to this question.

A and D give the same value, B and C also give the same value.

Answer:

We can use trigonometry to solve this problem.

Let's call the angle of elevation of the zip-line as "x"

We can use the tangent function to find the angle of elevation:

tan(x) = Opposite/Adjacent

Where opposite is the height of the pole (70 feet) and adjacent is the horizontal distance between the base of the pole and the stake (70 feet).

So we can write:

tan(x) = 70/70

As the adjacent and opposite sides are the same, the tangent of the angle is 1.

The angle of elevation of the zip-line is x = arctan(1) = 45 degrees

To find the amount of cable needed we can use the Pythagorean theorem, as we have a right triangle with the zip-line as the hypotenuse, the height of the pole as one leg, and the horizontal distance between the base of the pole and the stake as the other leg

The cable length is equal to the hypotenuse of the right triangle, which can be calculated as the square root of the sum of the squares of the other two sides:

cable length = √(70² + 70²) = √(4900 + 4900) = √(9800) = 99 feet

So the amount of cable needed to make the zip-line is 99 feet.

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)

Learn more about a polynomial here:

https://brainly.com/question/28936357

#SPJ4

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​?

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  

To learn more about the variations from the given link

https://brainly.com/question/5247042

#SPJ1

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

Answer:

also Y=mx+b

Step-by-step explanation:

for stater X1=3 X2=1 and Y1=8 Y2=4

              m=rise run=ΔyΔx

               m=y2−y1x2−x1

                     m=4-1/8-3

                       m=3/5

(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.

Know more about prime numbers

https://brainly.com/question/145452

#SPJ4

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 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.

Learn more about equation here

brainly.com/question/29538993

#SPJ4

Answer:

$12.99

Step-by-step explanation:

initial cost of the shirt = $12

sales tax on the shirt = 8.25%

So the final price of the shirt would be ,

initial cost + 8.25% of initial cost

That would be,

$12 + 8.25% of $12

$12 + $0.99

$12.99

And we are done!

-Rishabh

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.

The quarterly decay rate is given by \rm P = 200(0.9875)^n  and this can be determined by using the exponential decay function.

In mathematics, exponential decay refers to the process of decreasing an amount at a constant percentage rate over time. It may be stated as y=a(1-b)x, where y is the final amount, an is the original amount, b is the decay factor, and x is the time elapsed.

A school of fish has a population of 200.

The population is decreasing at a rate of 5% a year.

The formula of exponential decay is given by the equation:

[tex]\rm P = P_0\left(1- \dfrac{r}{100}\right)^n ----- (1)[/tex]

where n is the number of quarters for total decay, r is the rate of decay per quarter,P_0 is the initial population and P is the final population.

Now, put the values of known terms in the equation (1).

[tex]\rm P = 200\left(1-\dfrac{1.25}{100}\right )^n\\\rm P = 200(1-0.0125)^n\\\rm P = 200(0.9875)^n[/tex]

The quarterly decay rate is given by [tex]\rm P = 200(0.9875)^n .[/tex]

For more questions on Decay Rate

https://brainly.com/question/25537936

#SPJ4