3x-1>-4 and -2x-3<1 in interval notation

Answer:

Malleability and ductility refer to a material's ability to be shaped, bent, or stretched without breaking. Malleability is a measure of how easily a material can be hammered, pressed, or rolled into different shapes, while ductility is a measure of how much a material can be stretched before it breaks. Metals and alloys are generally highly malleable and ductile, while concrete and glass are less so

Step-by-step explanation:

The number of apples after the increase will be 18.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentage is %.  In order to change a number to a percentage, multiply by 100.

After the apples are increased, the new number of apples would be half more than the initial number of apples.

The formula that can be used to determine the new number of apples is: New number of apples = original number of apples x (1 + increase/100)

= 12 x (1 + 50/100)

= 12 x (1 + 0.5)

= 12 x 1.5 = 18

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Answer:

11%

Step-by-step explanation:

110 divided by 10 is 11% or 11 times 10 is 110

Answer:

10% of 110 is 11

Step-by-step explanation:

Finding the fraction of a number is the same as multiplying a fraction with the number

10/100 of 110 = 10/100 x 110

so the answer is 11

In response to the supplied query, we may state that there is a proportionality  statistically significant difference between the two population proportions because the interval comprises 0.

Relationships are regarded to as proportional when they continuously have the same ratio. For instance, the number of trees in an orchard and the number of apples in a harvest of apples depend on the average number of apples produced by each tree. A linear relationship between two numbers or variables is referred to as being proportional in mathematics.

The following is the point estimate for the variance between the two sample proportions:

ME is equal to z/2 * [p1(1 - p1) / n1 + p2(1 - p2) / n2]

where:

The z-score that corresponds to the required degree of confidence, in this case 90%, is z/2, or 1.645.

The proportions of the sample are p1 and p2.

These are the sample sizes, n1 and n2.

When we enter the values, we obtain:

ME = 1.645 * √[(0.9512)(1 - 0.9512) / 820 + (0.9891)(1 - 0.9891) / 804]

ME = 0.0528

-0.0379 ± 0.0528

or

-0.0907 to 0.0149

As a result, we have 90% confidence that the actual change in population proportions is between -0.0907 and 0.0149. We cannot infer that there is a statistically significant difference between the two population proportions because the interval comprises 0.

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The sections of each course it should offer are 3 finite maths, 2 applied calculus and 2 computer methods

Let's use the following variables to represent the unknowns:

From the problem, we can write the following system of equations:

x + y + z = 7 (total number of sections)

40x + 40y + 10z = 220 (total number of students)

40000x + 60000y + 29000z = 298000 (total revenue)

Simplify

x + y + z = 7

4x + 4y + z = 220

40x + 60y + 29z = 298

We can solve this system of equations using substitution

So, we have

x = 7 - y - z

By substitution, we have

4(7 - y - z) + 4y + z = 22

This gives

28 - 4y - 4z + 4y + z = 22

So, we have

28 - 3z = 22

This gives

3z = 6

Divide

z = 2

Recall that

40x + 60y + 29z = 298

So, we have

40x + 60y + 29*2 = 298

40x + 60y + 58 = 298

This gives

40x + 60y = 240

Divide by 20

2x + 3y = 12

Also, recall that x = 7 - y - z

So, we have

2(7 - y - z) + 3y = 12

This gives

2(7 - y - 2) + 3y = 12

2(5 - y) + 3y = 12

Open brackets

10 - 2y + 3y = 12

Evaluating the like terms, we have

y = 2

Lastly. we have

x = 7 - y - z

x = 7 - 2 - 2

x = 3

Hence, the number of sections of Finite Math is 3

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Based on the 2009 season, the Texas Rangers have a winning percentage of .533. The probability that the Rangers win 4 of their next 5 games is 18.8%.

We can use the binomial distribution formula to find the probability that the Texas Rangers win exactly 4 of their next 5 games:

P(4 wins) = (5 choose 4) * (.533)^4 * (1-.533)^1

= (5! / (4! * 1!)) * (.533)^4 * (.467)^1

= 5 * 0.533^4 * 0.467^1

= 18.8%

where "choose" is the binomial coefficient, which represents the number of ways to choose a subset of size k from a set of size n, and is given by:

(n choose k) = n! / (k! * (n-k)!)

So the probability that the Rangers win 4 of their next 5 games is 18.8%,.

Therefore, the answer is B.

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Answer: PP(Percentage) + PP or PP(1.%)

Step-by-step explanation:

Answer:

19,306 = 10 + 90 + 30 + 60

Step-by-step explanation:

The formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.

The geometric sequence equations has the general form an=a1rⁿ⁻¹, where r denotes the common ratio, a1 denotes the first term, and n denotes the term's position in the sequence.

sequence: 2, 4, 8, 16, 32, …

a1 = 2

r = 4/2 = 2

So,

an = 2(2)ⁿ⁻¹

Thus, the formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.

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The type of triangle AABC is an equilateral triangle, as it is formed by the midsegments of the equilateral triangle ADEF.

Since the midsegments of a triangle are parallel to its opposite sides and half the length of the opposite sides, the midsegments of an equilateral triangle are congruent to each other, and their length is half the length of the sides of the equilateral triangle.

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

[tex]x = \dfrac{p+m}{2} and y = \dfrac{q+n}{2}[/tex]

We are given that;

An equilateral triangle DEF

AAB is formed by the midsegments of triangle ADEF, which means that AAB is also an equilateral triangle. To see why this is true, we can use the following argument:

The midsegment of DE is parallel to AB and has half the length of AB.

The midsegment of EF is parallel to AA' and has half the length of AA'.

The midsegment of FD is parallel to BB' and has half the length of BB'.

Therefore, AB = AA' = BB', and the angles at A and B are both 60 degrees (since DEF is equilateral).

Thus, AAB is an equilateral triangle, because all its sides are equal in length and all its angles are equal to 60 degrees.

Therefore, by midpoint the answer will be equilateral triangle.

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The remaining feet long is A. 3 7/12 feet long

How to determine this

Kelsey has a board of 6 1/3 feet long

When he uses 2.75 feet

To calculate the remaining feet

= 6 1/3 - 2.75 feet long

By converting 2.75 to fraction

2.75 = 2 3/4

= 11/4

6 1/3 = 19/3

So, 19/3 - 11/4

= 43/12

= 3 7/12

Therefore, the remaining piece is 3 7/12 feet long

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The expression for the quadratic function can be written as:

g(x + a) - g(x) = 4ax + 2a² - 4a

Here we want to find the expression:

g(x + a) - g(x)

For the quadratic function:

g(x) = 2x² - 4x

So just let's evaluate the function in these values, we will get:

g(x + a) =2*(x + a)² - 4*(x + a)

Expanding that we will get:

            = 2(x² + 2ax + a²) - 4x - 4a

            = 2x² + 4ax + 2a² - 4x - 4a

Subtracting the original equation we will get:

g(x + a) - g(x) = 2x² + 4ax + 2a² - 4x - 4a - 2x² - 4x

                     = 4ax + 2a² - 4a

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In response to the aforementioned query, we may say that Point M's slope coordinates are therefore (39/25, 69/25).

A line's slope determines how steep it is. The gradient is mathematically expressed as gradient overflow. By dividing the vertical change (run) between two spots by the height change (rise) between the same two locations, the slope is determined. The equation for a straight line, y = mx + b, is written as a curve form of an expression. When the slope is m, b is b, and the line's y-intercept is located (0, b). For instance, the y-intercept and slope of the equation y = 3x - 7 (0, 7). The location of the y-intercept is where the slope of the path is m, b is b, and (0, b).

A and B's respective y-coordinates are at the midpoint of the triangle AB.

[tex]((x A + x B)/2, (y A + y B)/2)[/tex]is the midpoint.

[tex]((-4 + 2)/2, (2 + 10)/2)[/tex] is the midpoint.

Midway = [tex]( -1, 6 )\\[/tex]

Slope of AB: The slope of AB is equal to the product of the y-value and the x-value, or:

slope is equal to [tex](y B-y A) / (x B-x A).\\[/tex]

slope = [tex](10 - 2) / (2 - (-4))\\[/tex]

slope = 8/6 = 4/3

[tex]y - y 1 = m * (x - x 1)\\y - 6 = (-3/4) * (x + 1)\\y - 6 = (-3/4)\\x - (3/4)\sy = (-3/4)x + (21/4)[/tex]

Point M's coordinates are:

[tex]y = (-3/4)x + (21/4)\\4x/3 + 2 = (-3/4)x + (21/4)\\16x + 24 = -9x + 63\s25x = 39\ = 39/25\\y = (-3/4)(39/25) + (21/4) = 69/25\\[/tex]

Point M's coordinates are therefore (39/25, 69/25).

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The scale factor for the given transformation is -

{k} = 2/3.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Given is a figure {Q} that is a transformation of figure {P}.

The base length of the figure {P} is 15 cm. The base length for figure {Q} is 10 cm. So, we can write the scale factor as -

{K} = 10/15

{K} = 2/3

Therefore, the scale factor for the given transformation is -

{k} = 2/3.

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We can write the addition matrix as -

(I + 2A) →

[- 1  4]

[8  11]  

The identity matrix is the only idempotent matrix with non-zero determinant.

Given is the matrix relation as -

(I + 2A)

We can write the addition of matrix as -

(I + 2A) →

[1  0]

[0  1]  

+

2[-1  2]

2[4  5]

(I + 2A) →

[1  0]

[0  1]  

+

[-2  4]

[8  10]

(I + 2A) →

[- 1  4]

[8  11]  

Therefore, we can write the addition matrix as -

(I + 2A) →

[- 1  4]

[8  11]  

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Answer:

Step-by-step explanation how do I use this appp :

Answer:

Your blank answer is 4.68

Step-by-step explanation:

Well lets make the missing blank into a variable.

12 - x = 7.32

This way we can solve for x. Simplify.

Add x to both side.

12 = 7.32 + x

Subtract 7.32 to both side leaving you x.

12 - 7.32 = x

x = 4.68

Answer:

12 - 4.68 = 7.32

Step-by-step explanation:

Now we have to,

→ Find the missing number in the equation.

Let us assume that,

→ Missing number = m

Forming the equation,

→ 12 - m = 7.32

Then the value of m will be,

→ 12 - m = 7.32

→ -m = 7.32 - 12

→ -m = -4.68

→ [ m = 4.68 ]

Hence, the answer is 4.68.

π - This is an irrational number. 22/7 - The number is rational but not an integer. 3.3 - The number is an integer but not a whole number.

The term "rational number" refers to any number that can be stated as a fraction, as well as a positive, negative, or zero. If q is not equal to zero, it may be expressed as p/q.

Irrational numbers are those that are not logical in nature. Let's explain; irrational numbers may be expressed as decimals but not as fractions, hence they cannot be expressed as the ratio of two integers.

π - This is an irrational number.

22/7 - The number is rational but not an integer.

3.3 - The number is an integer but not a whole number.

The number is a whole number but not a natural number.

9 -This number can be written as a natural number.

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Therefore , the solution of the given problem of function comes out to be  height is 64 feet .

What is meant by the word function?

The study of mathematics includes histology, architecture, and both actual and fictitious geographic locations, as well as arithmetic, numerals, and their divisions. A function explains the relationships between different components, each of which has a corresponding result. A function is made up of a variety of components that, when put together, produce specific outputs for each input.

Here,

The highest spot on the ball's trajectory, which is at the vertex of the parabolic path, must be identified in order to calculate the maximum height the ball has ever attained.

The following equation describes the height of the projectile as a function of time:

s = -16t² + 64t

We can apply the following method to determine the parabola's vertex:

t = -b/2a

where b = 64 and a = -16.

By replacing these numbers, we obtain:

t = -64/(2*(-16)) = 2

Thus, after two seconds, the utmost height is reached.

We can enter t = 2 into the calculation to get the height at this point:

s = -16(2)² + 64(2) = 64 feet

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The scale factor of the dilation is 1/2.

Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Here given that blue figure is the dilated image of the black figure.

Dilation is the reduction.

The bottom left point is (2, 2) and top let point is (2, 4) of blue figure.

Length of the left segment of blue figure = [tex]\sqrt{(2-2)^2+(4-2)^2}[/tex]

                                                                    = 2

The bottom left point is (4, 4) and top let point is (4, 8) of black figure.

Length of the left segment of black figure = [tex]\sqrt{(4-4)^2+(8-4)^2}[/tex]

                                                                      = 4

Scale factor = Ratio of corresponding sides

                    = 2/4

                    = 1/2

This will be the same if we take another corresponding sides.

Hence the scale factor is 1/2.

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The two fractions' sum is therefore (a + b) / (a² × b²).

A sum, usually referred to as a summation, is the product of combining two or more quantities or numbers. A summation always has an even term count. It could be two terms simply, or it might total 100,000 or a million. Many terms can be included in some summations.

We require a common denominator in order to add these two fractions.

The first fraction's denominator is a² × b, and the second fraction's denominator is a × b².

Get the supreme strength of each component that exists in either denominator, then utilize the result of these factors to determine the least frequent multi of these two denominators:

LCM (a² × b, a × b²) = a² × b²

The two fractions can now be rewritten using the following common denominator:

1/(a² × b) + 1/(a × b²) = (1 × b + 1 × a) / (a² × b²)

If we condense this phrase, we get:

1/(a² × b) + 1/(a × b²) = (a + b) / (a² × b²)

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A triangular pyramid is a solid figure made of only triangular faces.

A triangular pyramid is a type of pyramid that has a triangular base and three triangular faces that meet at a common point or apex. The triangular base is usually referred to as the base face of the pyramid, while the remaining three triangular faces are called lateral faces.

The properties of a triangular pyramid include:

It has one base face and three lateral faces.

All four faces are triangles.

It has four vertices or points.

It has six edges or line segments.

To find the volume of a triangular pyramid, the area of the base face and the height of the pyramid must be known.

Triangular pyramids can be found in many real-world applications, such as in the design of buildings and structures, in geometry and mathematics, and in the study of crystals and minerals. They are also used in computer graphics to create 3D models of objects and environments.

A triangular pyramid is a solid figure made of only triangular faces.

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Answer:

Where's the question...

Answer: C

Step-by-step explanation:

We can state this by responding to the provided question December 31: equation Interest Paid 184 Interest Expensed 184 (To charge interest for one month on the Paola Bank note)

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The journal entries for the mentioned transactions are as follows:

Jan. 2: 40,000 in product inventory and 40,000 in accounts payable (To record the purchase of merchandise on account)

April 1: Cash 40,600 Accounts Payable 40,000 Interest Payable 600 (To record the payment of the Nunez note and interest)

Oct. 1: Cash 70,110 Notes Payable 68,400 Interest Payable 1,710 (To record the payment of the Marson note and interest)

Cash 27,600 Notes Payable 27,600 as of December 1

(In order to document the note's issuance to Paola Bank)

December 31: Interest Paid 184 Interest Expensed 184

(To charge interest for one month on the Paola Bank note)

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Answer:

less than

Step-by-step explanation:

just multiply top and bottom untill the denominator is the same

a. The mean of the sampling distribution is 0.2 and the standard deviation is 0.027. b. The probability that Cindy will get at least 48 orange Stattle is approximately 0.0901.

A method for estimating the probability of a binomial distribution using a normal distribution is known as the normal approximation to the binomial distribution. When the sample size is sizable and the success probability is not too close to 0 or 1, it can be employed. To utilise this approximation, we must first get the binomial distribution's mean and standard deviation, then normalise the distribution using the z-score calculation.

As 20% of the candies are orange, the mean of the sampling distribution of p is equal to the population percentage, which is 0.2.

The standard deviation of the sampling distribution of p can be found using the formula:

σp = sqrt((p * (1 - p)) / n)

Substituting the values:

σp = sqrt((0.2 * 0.8) / 220) = 0.027

So the mean of the sampling distribution is 0.2 and the standard deviation is 0.027.

b. Let X be the number of orange Stattles in the bag.

The z-score is given as:

z = (X - μ) / σ

z = (48 - 44) / 2.974 = 1.34

So the probability that Cindy will get at least 48 orange Stattles in her next 14 ounce bag is approximately 0.0901.

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The solution to the inequalities, y < 6 and y > x + 3 is the common intersecting region.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, y < 6.

Now, To determine wether it inclues the origin or not we'll set, y = 0.

So, 0 < 6 is true so y < 6 includes the origin.

Now, y > x + 3.

0 > 0 + 4 is not true therefore, y > x + 3 doest not inclue the origin.

The solution to these now can be determine by the common intersecting region.

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Answer:

The polynomials are:

-7x²+ 5/3x

6x² + 5x

-x^2+5x

The expression x^2+ 5x1/5 is not a polynomial because it contains a fraction with x in the denominator.

If 4 men, each working an 8-hour day, have to complete 224 hours of work, then the number of days required to complete the work is:

Total number of hours of work / Number of hours of work done by 4 men in a day

= 224 / (4 x 8)

= 7

So, it will take 4 men, each working an 8-hour day, 7 days to complete the project.

II. Each of the 4 men will work for 7 days, and each man works 8 hours a day. So, the total number of hours worked by all the men is:

Total number of men x Total number of days x Number of hours worked by each man per day

= 4 x 7 x 8

= 224 hours

Therefore, the total cost of employing all 4 men is:

Total number of hours x Rate per hour

= 224 x $57.50

= $12,880

III. If the 4 men have to complete the project in 4 days, then the number of hours of work they have to do each day is:

Total number of hours of work / Total number of days to complete the project

= 224 / 4

= 56 hours

Each man works 8 hours a day, so the total number of hours of overtime they have to put in per day is:

Number of hours of work per day - Number of hours worked by each man per day

= 56 - 8

= 48 hours

Therefore, each man must put in 6 hours of overtime per day to complete the project in 4 days.

IV. If the overtime rate of payment is l times as much as the regular hourly rate, then the overtime rate of payment is:

l x $57.50

= $57.50l

Let the overtime rate of payment be $r per hour. Then:

r = $57.50l

The cost of the project is the sum of the cost of regular hours and the cost of overtime hours. The cost of regular hours is:

Number of regular hours x Regular hourly rate

= 4 x 8 x 7 x $57.50

= $16,240

The cost of overtime hours is:

Number of overtime hours x Overtime hourly rate

= 4 x 6 x 7 x $57.50l

= $12,180l

So, the total cost of the project is:

Total cost = Cost of regular hours + Cost of overtime hours

= $16,240 + $12,180l

Answer:

Step-by-step explanation:

(i) To complete the project, 4 men will need to work a total of 224 hours. Each man works for 8 hours per day. Therefore, the number of days it will take to complete the project is:

Number of days = 224 total hours / (4 men x 8 hours/day) = 7 days

So it will take 4 men, each working 8 hours per day, 7 days to complete the project.

(ii) Each man is paid $57.50 per hour, and they will work for a total of 7 x 8 = 56 hours altogether. Therefore, the total cost of employing them all is:

Total cost = 4 men x $57.50/hour x 56 hours = $12,320

(iii) If the project is to be completed in 4 days, each man will need to work for a total of:

224 total hours / (4 men x 4 days) = 14 hours per day

Since each man already works for 8 hours per day, they will need to put in an additional 6 hours of overtime per day to complete the project in 4 days.

(iv) The regular hourly rate is $57.50 per hour, and the overtime rate is 1.5 times the regular hourly rate (150% of the regular hourly rate). Therefore, the overtime rate is:

Overtime rate = $57.50 x 1.5 = $86.25/hour

To find the total cost of the project, we need to add the cost of the regular hours and the cost of the overtime hours. The cost of the regular hours is:

Regular hours cost = 224 regular hours x $57.50/hour = $12,880

The cost of the overtime hours is:

Overtime cost = (4 men x 6 overtime hours/man/day x 4 days) x $86.25/hour

= 96 x $86.25

Therefore, the total cost of the project is:

Total cost = Regular hours cost + Overtime cost

= $12,880 + $8,280

= $21,160

where the overtime rate is 1.5 times the regular hourly rate.