solve the inequality

x/4 + 1 <6

Answer:

22.5 minutes

Step-by-step explanation:

Initially, there were 9 students with 30 minutes to clean up the mess. This means they had a total of 9 · 30 = 270 student minutes to clean up the mess.

After the 3 additional students were added, there were a total of 9 + 3 = 12 students on the clean-up crew.

Now, let's assume the time they need to clean up the mess is "t" minutes. Since the number of students and the time are inversely proportional to the amount of work done, we can set up the following equation based on the idea that the amount of work done is the same before and after the addition of the 3 students:

9 · 30 = 12 · t

Solving for "t":

270 = 12t

t = 270 / 12

t = 22.5

So, the principal should give them approximately 22.5 minutes to complete the job with the new crew of 12 students.

Answer:

Step-by-step explanation:

where is the equation?

Answer:

Step-by-step explanation:

Multiply 4.75 by 2 to find out how much money Maurice gets when finishing 2 chores. $4.75 x 2 = $9.50. So, write $9.50 under 2. For three chores, multiply $4.75 by 3. $4.75 x 3 = $14.25. Write $14.25 under 3.

Answer:

  $2.21

Step-by-step explanation:

You want to know the savings between using a $10 off coupon and taking a 15% discount, if the tax rate is 10.3%.

The price with the coupon is ...

  $79.99 -10.00 = $69.99

When tax is added, the total becomes ...

  $69.99 × 1.103 ≈ $77.20

The price with the discount is ...

  $79.99 × (1 -0.15) ≈ $67.99

When tax is added, the total becomes ...

  $67.99 × 1.103 ≈ $74.99

The savings by making use of the discount is ...

  $77.20 -74.99 = $2.21

The total savings between the coupon and the discount is $2.21. That is, you save $2.21 more by using the discount instead of the coupon.

__

Additional comment

The question seems a bit ambiguous. The word "or" suggests you cannot use both discounts. If you do, the total amount saved will depend on the order in which they are applied.

You get the best result by taking the $10 off the sale price. Doing that gives you a total savings of about $24.27 off the normal price with tax.

Answer:

2

Step-by-step explanation:

20% = 0.2

What is 20% of 10?

We take

10 times 0.2 = 2

So, 20% of 10 is 2.

the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.

In structural mechanics and engineering, the stiffness matrix is a mathematical representation of the stiffness of a structure, which relates the forces and displacements of the structure. The size of the stiffness matrix depends on several factors, including the number of degrees of freedom and the type of elements used in the analysis. The number of degrees of freedom (DOF) in the system determines the size of the stiffness matrix. DOF refers to the number of independent displacements or rotations that a structure can undergo in response to external forces. For example, a simple beam structure might have two DOF (vertical displacement and rotation), while a more complex structure such as a truss or frame might have many more DOF. The size of the stiffness matrix also depends on the type of elements used in the analysis. Different types of elements have different degrees of freedom and stiffness properties, which affect the size and shape of the stiffness matrix. For example, a truss element has two DOF and a constant axial stiffness, while a beam element has four or six DOF and variable stiffness properties that depend on its geometry and material properties.

In summary, the size of the stiffness matrix depends on the number of degrees of freedom and the type of elements used in the analysis. It is an important tool in structural mechanics and engineering for analyzing the behavior and performance of structures under different loading conditions.

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The answer is: 1 part sample, 9 parts diluent, 1 part of the first dilution, 9 parts diluent, 1 part of the second dilution, 9 parts diluent

When creating a serial dilution, the starting concentration is typically given as a ratio of sample to diluent. For example, a 1/10 dilution would mean that there is one part of sample and nine parts of diluent.

Now when we create a serial dilution from 1/10 to 1/1000, the first dilution will be 1 part sample and 9 parts diluent. The second dilution will be one part of the first dilution and nine parts diluent. The final dilution will be one part of the second dilution and nine parts diluent.

Thus, the answer is:

1 part sample

9 parts diluent

1 part of the first dilution

9 parts diluent

1 part of the second dilution

9 parts diluent

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____ The given question is incorrect, the correct question is given below:

When creating a serial dilution from 1/10 to 1/1000, the first dilution will be _______ part sample and ______ parts diluent. The second dilution will be one part ____ and nine parts _____. The final dilution will be one part _____ and nine parts diluent.

Choices:

1(one)

9(nine)

1/10 dilution

1/100 dilution

1/1000 dilution

diluent

We can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.

A relation between a collection of inputs and outputs is known as a function.

A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Each function has a range, codomain, and domain.

The usual way to refer to a function is as f(x), where x is the input.

One function, many. function onto (Surjective Function) into perform.

The function of a polynomial.

So, by observation we can find out the function:

y = 128(0.5)ˣ

Assume the teams after 1st round:

y = 128(0.5)ˣ

y = 128(0.5)¹

y = 128*0.5

y = 64 (Half od 128)

Therefore, we can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.

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There are approximately 1 teaspoon in 5 milliliters. Therefore, in 10 milliliters we have 2 teaspoons approximately.

When converting between milliliters and teaspoons, it's important to know that 1 teaspoon is equal to approximately 5 milliliters. Therefore, to convert 10 milliliters to teaspoons, you would divide 10 by 5, which gives you 2. This means that there are approximately 2 teaspoons in 10 milliliters. It's worth noting that while teaspoons are commonly used in the United States and other countries that use the imperial system of measurement, most countries use the metric system, which uses milliliters as the standard unit of volume. Therefore, it can be helpful to know how to convert between these units of measurement, particularly if you're following a recipe or taking medication that uses a different system than what you're used to.

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The inequality form is 4/3<x<11.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given inequality is log₂(3x-4)<log₂(2x+7)

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form: 4/3<x<11

Interval Notation:(4/3,11)

Therefore, the inequality form is 4/3<x<11.

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Answer: 1/2

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

10% * 60 = 6

20% * 60 = 12

Answer:

5, 18 and 7 respectively

Step-by-step explanation:

4+9+5=18

18+7=35

Answer:The top box is 11 making the middle boxes 15 20

Step-by-step explanation:

4 11 9

4+11  11+9

15 20

15+20

35

Answer: 6 square inches

Step-by-step explanation:

Since the pizza is 16 inches and there is 8 slices divide.

16 inches ÷ 8 slices = 2 inches per slice

Each slice is 2 inches.

Since each slice is 2 inches multiply by 3 slices to get how many square inches she ate.

2 inches per slice x 3 slices = 6 square inches

Therefore she ate 6 square inches of pizza.

The sample size for the given data is 17

The sample size is a term used in market research for defining the number of subjects included in a sample size.

Given that, a sample size has an 80% confidence interval, the population standard deviation is s = 120, the margin of error to be approximately 10, We need to find the sample size,

Sample size = (z-score)²×SD×(1-SD) / (confidence interval)²

z-score of 80% confidence interval = 1.28

Sample size = (1.28)²×0.12(1-0.12)/0.10²

= 1.6384×0.12×0.88/0.01

= 17.30

Hence, the sample size for the given data is 17

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The total square centimeters of mirrors covering the lateral surfaces is

171.5 cm².

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.

Given:

Perpendicular height = 14.3

So, the Surface area of Prism is

= 5 x 10 x 3 + 1/2 x 5 x 4.3 x 2

= 150 + 21.5

= 171.5

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One possible solution is to tutor for 11 hours and clear tables for 5 hours

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

25x + 9y ≥ 270

x + y ≤ 18

Where

x = hours tutoring

y = hours cleaning tables

Next, we plot the graph (see attachment)

One solution from the graph is (11, 5)

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None of the given polygons appears to be regular.

A regular polygon is a polygon with all sides and angles of equal measure. In other words, a regular polygon is a shape with straight sides that has all angles and sides of equal length.

The simplest example of a regular polygon is a equilateral triangle, which has three sides of equal length and three angles of equal measure. Another example is a square, which has four sides of equal length and four right angles of equal measure.

Figure A is a rhombus, which has opposite sides parallel and all sides equal, but it has two acute angles and two obtuse angles, so it is not regular.

Figure B is a parallelogram, which has opposite sides parallel, but not all sides and angles equal, so it is not regular.

Figure C is a right-angled triangle, which has one right angle, but not all sides and angles equal, so it is not regular.

Figure D is a trapezoid, which has at least one pair of parallel sides, but not all sides and angles equal, so it is not regular.

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5/3 :8/3= 5/3 X3/8 =5/8

The count of the ways in which to chose 4 candies from a store that sells 30 candy bars, obtained by the combination formula, are 27405 ways

A mathematical combination, is the ways in which a number of items can be chosen from a set of items, excluding a reference to the order in which the items are selected.

The number of ways k items can be chosen from n items, can be found by using the following combinations formula;

[tex]\binom{n}{k} = \frac{n!}{k!\cdot (n-k)!}[/tex]

Therefore, the number of ways 4 candies can be chosen from a store that sells 30 candy bars can be found by plugging in k = 4, and n = 30 as follows;

[tex]\binom{30}{4} = \frac{30!}{4!\cdot (30-4)!} = 27405[/tex]

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Answer:

zero

Step-by-step explanation:

If a system of equations is graphed as 2 lines, then if the lines intersect, they intersect at one single point, and that point is the solution. There is one solution.

If the lines are parallel and do not intersect, then there is no solution. The number of solutions is zero.

Answer: zero

Answer:

See explanation

Step-by-step explanation:

40% of the original $54 is $21.60, therefore the pants are $21.60 off of their original price. This makes the pants $32.40.

20% of the new $32.40 is $6.48, therefore the pants are $6.48 off of the 40%-off price. This makes the pants $25.92 for their final price.

On dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -

h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is to divide (3x³ - 2x² +4x - 3) by (x² + 3x + 3).

Let us assume that -

f(x) = (3x³ - 2x² + 4x - 3)

g(x) = (x² + 3x + 3)

We can write -

h(x) = f(x)/g(x)

h(x) = (3x³ - 2x² + 4x - 3)/(x² + 3x + 3)

h(x) = 3x + {(- 11x² - 5x - 3)/(x² + 3x + 3)}

h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}

Therefore, on dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -

h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.

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Answer:

AS a fraction: 1[tex]\frac{11}{20}[/tex]

AS a decimal: 1.55

Step-by-step explanation:

4/5 + 3/4

least common multiple of 5 and 4 is 20. Conver [tex]\frac{4}{5}[/tex] and [tex]\frac{3}{4}[/tex] to fractions with denominator 20.

16/20 + 15/20

since [tex]\frac{16}{20} and \frac{15}{20}[/tex]  have the same denominator, add them by adding their numerators.

[tex]\frac{16 + 15}{20}[/tex]

Add 16 and 15 to get 31.

[tex]\frac{31}{20}[/tex]

[tex]\frac{31}{2^{2}x5 } = 1\frac{11}{20}[/tex]

Hope that helps and have a great day! =) ~sunshine~

The inverse function of f (x) = 1/3x - 2 is f⁻¹(x) = 3(x + 2), the value of a is 3, and the value of x-intercept is x = -2.

The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.

Each element of X receives exactly one element of Y when a function from one set to the other is used.

According to the question,

f (x) = 1/3x - 2

now to find inverse ,

Add 2 to x term  and then divide by 1/3 so, we get,

f⁻¹(x) = (x + 2) / 1/3

f⁻¹(x) = 3(x + 2)

now, compare with f⁻¹(x) = a (x + 2)

a = 3

Calculate the x-intercept by putting f(x) = 0

0 = x + 2

x = -2

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We can write the inequality as -

{x} < (1/4){8x + 4}

Given is the statement as -

"A number is less than one-fourth the sum of eight times the number and four"

We can write the statement as follows.

Let the number be {x}. Then, we can write the inequality as -

{x} < (1/4){8x + 4}

Therefore, we can write the inequality as -

{x} < (1/4){8x + 4}

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Answer:  The formula for finding the area of a triangle is A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).

Plugging in the given coordinates, the area of the triangle is:

A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1))

A = 1/2(-3)(-2)+(-2)(3)+1(-3)

A = -9+6-3

A = 4

Step-by-step explanation:  Step 1: Identify the formula for finding the area of a triangle: A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).

Step 2: Plug the given coordinates into the formula: A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1)).

Step 3: Simplify the equation: A = 1/2(-3)(-2)+(-2)(3)+1(-3).

Step 4: Solve the equation: A = -9+6-3.

Step 5: Find the area of the triangle: A = 4.

A two-dimensional form having four sides, four vertices, and four angles is referred to as a quadrilateral. Examples are: Trapezium, Parallelogram, Rectangle, Rhombus, Square and Kite.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we might have several sorts of quadrilaterals. Hence a Quadrilateral is of 4 sides, vertices and angles. It consists of 360 degrees.

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