3x−3≥9​ Responses x = 1 x, = 1 x = 2 x, = 2 x = 3 x, = 3 x = 4 x, = 4

Answer

The area of the platform :

56 = (3x+2) × x

Explanation (+ solving for x)

Let the width of Rectangular Platform is x feet.

Then,

Length of Rectangular Platform is (3x+2) feet

Area of Rectangular Platform = Length × width

[tex]56=(3x+2) × x \\ 56 = 3x² + 2x \\ 3x² +2x-56= 0 \\ x = \frac{ -2±\sqrt{ {2}^{2} - 4 \times 3 \times ( - 56)} }{2 \times 3} \\ = \frac{-2± \sqrt{4 + 672} }{6} \\ = \frac{ - 2±26}{6} \\ = - \frac{28}{6} or \: 4 [/tex]

Since x can't be negative,

Value of x is 4 feet.

So, width of Platform= 4

feet Length of Platform = 14 feet

Answer:

0.5

Step-by-step explanation:

If you flip a coin, the probability of getting a head is 0.5 or 0.5 on the probability scale.

It is worth noting that when a coin is fair, the probability of getting a head or a tail is always 0.5 or 50%.

So in the probability scale you should place a cross on the point 0.5 which indicates the probability of getting a head.

Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models.

Interval                      Relative Frequency

−0.34≤x<−0.31                     0.02

−0.31≤x<−0.28                     0.15

−0.28≤x<−0.25                    0.33

−0.25≤x<−0.22                    0.36

−0.22≤x<−0.19                     0.11

−0.19≤x<−0.16                      0.03

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

According to the question,

The values that are one standard deviation away are:

0.33 + 0.36 = 0.69

As per the empirical rule, the value will be: 0.68

Consequently, with two standard deviations, the quantities have always been 0.95, and according to the empirical rule. So the empirical rule followed by the data.

Therefore the correct option is (B).

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The complete question includes :

The mean and standard deviation of the sample data collected on continuous variable x, x are −0.25 and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals.

Answer:

Lana: 4 / 14 = 3.5
Markus: 4 / 20 = 5

I'm not completely sure how they can have the same amount of marbles for both of them but... Markus does have 2.5 more than Lana in each bag.

Hope this helps <3

Step-by-step explanation:

Let's call the number of marbles in each bag "x". We can set up two equations based on the given information:

4x = 14 (for Lana)

4x = 20 (for Markus)

Solving for x in each equation, we get:

x = 14/4 = 3.5 (for Lana)

x = 20/4 = 5 (for Markus)

So Markus has 5 marbles in each bag, which is 1.5 more marbles per bag than Lana.

Answer:

hi

Step-by-step explanation:

The amount of interest Sai will pay is $312.50.

Interest is the cost associated with borrowing money, or the return earned for lending money. It is typically expressed as a percentage of the principal amount borrowed or lent, and is usually paid periodically over the life of the loan. Interest can also be earned from investments, such as savings accounts, bonds, and other financial instruments. The rate of interest charged or earned varies depending on the nature of the loan or investment, the risk associated with the transaction, and the creditworthiness of the borrower or investor.

This is calculated by multiplying the principal amount of $12,500 by the interest rate of 2.5%, which equals 0.025. Then, the 0.025 is multiplied by the loan period of 24 months to come up with the total interest. Therefore, $12,500 x 0.025 x 24 = $312.50.

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Similarly, 27 out of the 32 ages are equal to or less than 71, so the percentile of 71 is 27/32, which is equal to 84.375%. This means that 84.375% of the Academy. Award winning best actors are 71 years old or younger.

The percentile of a number is the percentage of numbers that are equal to or less than that number. In this case, 27 out of the 32 ages are equal to or less than 71, so the percentile of 71 is 27/32, which is equal to 84.375%. This means that 84.375% of the Academy Award winning best actors are 71 years old or younger.

The percentile of a number is the percentage of numbers that are equal to or less than that number. For example, among the 32 Academy Award winning best actors, 37 is the 14th smallest number, so the percentile of 37 is 14/32, which is equal to 43.75%. This means that 43.75% of the Academy Award winning best actors are 37 years old or younger. Similarly, 27 out of the 32 ages are equal to or less than 71, so the percentile of 71 is 27/32, which is equal to 84.375%. This means that 84.375% of the Academy Award winning best actors are 71 years old or younger.

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The sample for this situation is People who responded to the survey.

What is the sample?

A sample is a group of elements chosen from the population. The features that describe the population are called the parameters and the properties of the sample data are known as statistics. Population and sample both are important parts of statistics.

A sample is a subset of the population that is selected for a study.

In this case, the population is the group of people who might be interested in visiting the theme park in Florida.

The park wants to attract more visitors, so they post a survey on a travel website asking viewers which attractions they would like to see at the park.

The sample is the group of people who responded to the survey, as it represents the subset of the population that the park is trying to gather information from.

Hence, The sample for this situation is People who responded to the survey.

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A regular singular point is a point at which the differential equation has a non-removable singularity. The point x=0 is a regular singular point for problems 1-4. Two solutions for x>0 can be found by solving the differential equation around x=0.

A regular singular point is a point at which the differential equation has a non-removable singularity. In order to identify a regular singular point, we must first identify the point at which the equation has a non-removable singularity. For problems 1-4, the point x=0 is a regular singular point. To find two solutions for x>0, we can solve the differential equation around x=0. First, we must identify the coefficients of the equation, which will allow us to determine the order of the equation. Once we have determined the order, we can use the properties of regular singular points to find two solutions for x>0. For example, the equation may be of the form y' + P(x)y = Q(x), where P(x) and Q(x) are functions of x. Using the properties of regular singular points, we can solve for two solutions of the form y = x^r*F(x), where F(x) is a function of x and r is the order of the equation.

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Yes, the lines represented by the equations at right are parallel. This can be seen by examining the slopes of the equations. The slope of the first equation is -3/5 and the slope of the second equation is -3/5. Since the slopes are equal, the lines are parallel.

To determine if two lines are parallel, we need to compare their slopes. The equation of the first line is y = -3x/5 and the equation of the second line is y = 5x/3. To calculate the slope of the first line, we need to take the coefficient of x (-3/5) and divide it by the coefficient of y (1).

The resulting slope is -3/5. To calculate the slope of the second line, we need to take the coefficient of x (5/3) and divide it by the coefficient of y (1). The resulting slope is also -3/5. Since the slopes of both lines are equal, the lines are parallel.

The equation of the first line is y = -3x/5 and the equation of the second line is y = 5x/3. To calculate the slope of the first line, we need to take the coefficient of x (-3/5) and divide it by the coefficient of y (1).

The resulting slope is -3/5. To calculate the slope of the second line, we need to take the coefficient of x (5/3) and divide it by the coefficient of y (1). The resulting slope is also -3/5. Since the slopes of both lines are equal, the lines are parallel.

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The values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.

The given number is 123,000 which is the mth number in the nth row.

The rows contain two more numbers than the previous row.

Let us assume that the first row has m1 numbers.

Therefore, the second row has m1 + 2 numbers, the third row has m1 + 4 numbers, and so on.

We can represent the above information in a general formula as;

m1 + 2 (n - 1) = m

where m1 is the number of elements in the first row and n is the row number in which 123,000 is present.

By solving the above equation, we get

m1 = m - 2 (n - 1)

Now, we can calculate the value of n as;

n = (m - m1) / 2 + 1

Substituting the values of m and m1, we get

n = (123,000 - m1) / 2 + 1

Therefore, the values of m and n are m = 123,000 and n = (123,000 - m1) / 2 + 1.

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Answer:

x+50

Step-by-step explanation:

I hope it helps

thanks

The unit circle has a radius of 1, so it is the shortest distance from the origin to (x1,x2).

The vector of minimal length in Rn whose components add up to 1 is called the unit vector. The unit vector is calculated by dividing each component of the vector by the sum of all components. Thus, in Rn, the unit vector is given by (x1/s, x2/s, ..., xn/s), where s is the sum of all components.

In the case n=2, the unit vector is given by (x1/s,x2/s). Geometrically, this vector is the vector from the origin to the point (x1,x2) on the unit circle. This vector has minimal length because the unit circle has a radius of 1, so it is the shortest distance from the origin to (x1,x2).

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The rate of customer entry into the store at 5:00 p.m. (t = 9) is -3 customers/hour.

In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

A fraction is a part of a whole number, and a way to split up a number into equal parts. It is written as the number of equal parts being counted, called the numerator, over the number of parts in the whole, called the denominator.

Given the number of patrons entering the restaurant every two hours beginning at 8:00 am.

To find the rate of customer entry into the store at 5:00 p.m. (t = 9).

[tex]$\frac{36-42}{6-4}=\frac{-6}{2}=-3$[/tex]

Therefore, the rate of customer entry into the store at 5:00 p.m. (t = 9) is -3 customers/hour.

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Answer:

  17

Step-by-step explanation:

You want the determinant of the coefficient matrix for the equations ...

The matrix of coefficients is formed by listing the coefficients of the equation variables on rows of the matrix, in the same order for each row.

Here it is:

  [tex]\left[\begin{array}{cc}3&4\\-2&3\end{array}\right][/tex]

The determinant of a 2×2 matrix is the difference between the product of terms on the down diagonal and that on the up diagonal.

  det = (3)(3) -(-2)(4) = 9 + 8 = 17

The determinant of the coefficient matrix is 17.

__

Additional comment

Many scientific and graphing calculators can find this for you. A spreadsheet can be useful for this purpose, too.

The determinant is only defined for a square matrix. For sizes larger than 2×2, the arithmetic is a little different.

Answer:

A tangible asset is an asset that has physical substance. Examples include inventory, a building, rolling stock, manufacturing equipment or machinery, and office furniture. There are two types of tangible assets: inventory and fixed assets.

Step-by-step explanation:

Polynomial equations are those created by combining variables, exponents, and coefficients.The cost of coffee is 8 and the cost of tea is 4.

The higher exponent, known as the degree of the equation, might have several exponents.

When there is at least one algebraic term with at least one variable and all of the exponents are integers that are equal to or larger than zero, the equation is said to be a polynomial equation.

Coffee cost = Rs 8

Tea cost = Rs 4

Let the price of coffee be X

and the price of Tea be y , then

45 x + 41 y = 524

20 x + 11y = 204

y = 524 - 45 x /41=

= 20 x + 11( 524 -45 x)/41)

= 204

820 x + 5764- 495 x = 204* 41

325x = 2600

x = 8 y = 524 - 8* 45/45

y = 4

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Polynomial equations are those created by combining variables, exponents, and coefficients. The cost of coffee is 8 and the cost of tea is 4.

The higher exponent, known as the degree of the equation, might have several exponents.

When there is at least one algebraic term with at least one variable and all of the exponents are integers that are equal to or larger than zero, the equation is said to be a polynomial equation.

Coffee cost = Rs 8

Tea cost = Rs 4

Let the price of coffee be X

and the price of Tea be y , then

45 x + 41 y = 524

20 x + 11y = 204

y = 524 - 45 x /41=

= 20 x + 11( 524 -45 x)/41)

= 204

820 x + 5764- 495 x = 204* 41

325x = 2600

x = 8 y = 524 - 8* 45/45

y = 4

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Answer:

You can add 45 grams of water to 15 grams of sugar to make a 25% sugar solution.

Step-by-step explanation:

To make a 25% sugar solution, you need to add a certain amount of water to 15 grams of sugar. To determine this amount, you can use the following formula:

(desired concentration / 100) x total volume = amount of solute (in this case sugar)

We know that the desired concentration is 25%, and the amount of solute is 15 grams. To find the total volume, we can use the following formula:

amount of solute / desired concentration = total volume

15 grams / 0.25 = 60 grams

So the total volume of the solution is 60 grams, and the amount of water you need to add to make a 25% sugar solution using 15 grams of sugar is 45 grams.

You can add 45 grams of water to 15 grams of sugar to make a 25% sugar solution.

Another way to think of it is to add 3 times the amount of water as the amount of sugar, since 25% of 60g is 15g

A solid whose cross-section is defined by a(x), the volume of the solid given by      [tex]\int\limits^a_b {A(x)} \, dx[/tex]

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On solving the provided question, we can say that since it is a cuboid books could you fit on your bookshelf  = 24*12*36/8.5*11*1.5 = 10368/140.25 = 73.9251336898 = 73 books

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

since it is a cuboid

books could you fit on your bookshelf  = 24*12*36/8.5*11*1.5 = 10368/140.25 = 73.9251336898 = 73 books

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Answer:

The price: 16.5

The total payment: 18.82

The amount of tax: 18.82-16.5 = 2.32

Tax rate = The amount of tax / The price = 2.32/16.5 = 0.14 = 14%

The slope of the equation of the line is 0 and the y-intercept is 6. To find the slope and y-intercept of the equation of the line, we need to first rewrite the equation in the standard form of y = mx + b.

The slope of the equation of the line is 0 and the y-intercept is 6.

Slope: 0

y-intercept: 6

To find the slope and y-intercept of the equation of the line, we need to first rewrite the equation in the standard form of y = mx + b.

In this equation, m is the slope and b is the y-intercept.

The equation is given as y − 6 = 0.

We can rewrite this equation as y = 0 + 6.

This can be rewritten as y = 0x + 6, where 0 is the slope and 6 is the y-intercept.

Therefore, the slope is 0 and the y-intercept is 6.

The slope of the equation of the line is 0 and the y-intercept is 6.

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Step-by-step explanation:

I think the actual equation you meant to write was 5x⁴ + 7x³ - 2x² - 3x + c.

You're going to equate the whole equation to 0 and replace x for -1( because x + 1 is a factor)

= 5(-1)⁴ + 7(-1)³ - 2(-1)² - 3(-1) + c = 0

= 5 - 7 - 2 + 3 + c = 0

= - 1 + c = 0

Therefore c = 1

Answer:

5 hardcover and 3 paperback books

Step-by-step explanation:

h=hardcover books

p=paperback books

h + p = 8  ==> since the number of hardcover and paperback books add up

                     to 8 total books

4h + 2p = 26  ==> since the cost of each hardcover book is $4 and

                           the cost of each paperback book is $2, and the

                           total cost of all 8 books bought is $26

(h + p = 8) * 2  ==> multiply the equation by 2 to get 2p from p.

2h + 2p = 16  ==> simplify

  4h + 2p = 26

- (2h + 2p = 16)

4h-2h + 2p-2p = 26-16  ==> subtract the two equations to isolate h

2h + 0 = 10  ==> simplify

2h = 10

h = 5  ==> divide both sides by 2

5 + p = 8  ==> substitute h=5 into the equation h + p = 8

p = 3  ==> subtract 5 on both sides to isolate p

Hence, 5 hardcover and 3 paperback books were sold.

Using multiplication operation, the total number of packages of shredded cheese is 56.

Multiplication operation is one of the four basic mathematical operations, including subtraction, division, and addition.

Multiplication operation has the following parts: multiplicand (the number being multiplied), the multiplier (the number doing the multiplication), the equal symbol, and the product (the result of the multiplication operation)

The number of rows = 7

The number of packages of shredded cheese per row = 8

The total number of packages = 56 (7 x 8)

Thus, the number of packages in the refrigerator is 56 shredded cheese.

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In general, there were more people per table on Tuesday with 8 number of people per table.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

By critically observing the given dot plots which is used to illustrate the numbers of people per table at a bingo hall on two nights, we can reasonably infer and logically deduce that there were more people per table on Tuesday than on Wednesday.

In conclusion, there were 8 number of people per table on Tuesday while there were 5 number of people per table on Wednesday.

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Using the substitution method the equation 4x - y = 3 and 6y = 4 + 2x is solved to be

In this method, the equation 4x - y = 3 will first be written in terms of y

4x - y = 3

y = 4x - 3

substituting y = 4x - 3 into 6y = 4 + 2x

6y = 4 + 2x

6(4x - 3) = 4 + 2x

24x - 18 = 4 + 2x

collecting like terms

24x - 2x = 18 + 4

22x = 22

x = 1

substituting x = 1 into y = 4x - 3

y = 4x - 3

y = 4(1) - 3

y = 4 - 3

y = 1

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Answer:

6.5

Step-by-step explanation:

Proportional relationship:

[tex]y \propto x \implies y=kx[/tex]

where k is the (non-zero) constant of proportionality.

To determine the constant of proportionality, substitute the given values into the equation and solve for k:

[tex]\implies 19.50=3k[/tex]

[tex]\implies k=6.5[/tex]

Therefore, the constant of proportionality is 6.5.

The three right triangles are all similar. The ratios of the sides of the triangles are AB/BC = 3/4, BC/CD = 2/3, and AD/DC = 5/6.

a) All three of the right triangles are similar.

b) Triangle ABC:   AB/BC = 3/4

Triangle BCD:   BC/CD = 2/3

Triangle ADC:   AD/DC = 5/6

a) All three of the right triangles are similar because they all have three sides and two angles that are equal.

b) To find the ratios of the sides of the triangles, we use the Pythagorean Theorem.

Triangle ABC: AB^2 + BC^2 = AC^2. Therefore, AB/BC = (3/4)^2/(5/4)^2 = 3/4.

Triangle BCD: BC^2 + CD^2 = BD^2. Therefore, BC/CD = (2/3)^2/(4/3)^2 =2/3.

Triangle ADC: AD^2 + DC^2 = AC^2. Therefore, AD/DC = (5/6)^2/(7/6)^2 = 5/6.

The three right triangles are all similar. The ratios of the sides of the triangles are AB/BC = 3/4, BC/CD = 2/3, and AD/DC = 5/6.

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Answer:

20 or +-20

Step-by-step explanation:

They are asking for an nth root. This is generic-speak for square root, third root, fourth root, etc.

Since n is 2, they are talking about 2th root...really 2nd root. But we commonly call that square root.

Square root of 400 is 20. (That's the principal square root because its positive) They asked for real roots, so, technically -20 is also a square root of 400.

20^2 = 400 and

(-20)^2 = 400

So square root of 400 is +- 20.

Or if this is an intro class, then just 20 is probably a good enough answer.