Elam is packing his room to move into a new house. A small box can hold 8 books without breaking, while a large box can hold 12 books without breaking. He has at most 160 books to pack and less than 30 boxes total. Let s represent the number of small boxes and l represent the number of large boxes.

The inequalities s ≥ 0 and l ≥ 0 are part of the system that models this scenario.

Which inequalities complete the system?

a:s – l < 30
b:8s – 12l ≤ 160
c:s + l < 30
d:8s + 12l ≤ 160
s + l > 30
8s + 12l ≤ 160
s + l < 30
8s + 12l ≥ 160

   ( 0, 7 ) and ( 0,4 ) are  two points of the equation .

What Is an Equation, exactly?

An equation is a mathematical expression with two equal sides and an equal sign in between.

                                  An equation is, for instance, 4 + 6 = 10. 4 + 6 is visible on the equal sign's left side, and 4 + 6 is visible on the equal sign's right side.

    ( 4,0) & ( 0,7 )

Given constraint  is

        7x₁ + 4x₂ ≤ 28

  IF  x₁ = 0

         4x₂  =  28  

          x₂ = 7

        ( 0, 7 )

If x₂  = 0

    7x₁ = = 28

     x₁  = 4

       ( 4 ,0 )

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Working alone, Allen can build 1/8 of the fence in 1 hour and working together, Allen and Danny can build 1/X of the fence in 1 hour, where X is their combined rate.

Let's say the total time required to build the fence is T hours.

After 2 hours, Allen has completed 1/8 * 2 = 1/4 of the fence.

So, the remaining work to be done is T - 1/4.

When Allen and Danny work together, their combined rate is X = 1 / (1/8 + 1/16) = 4/7.

The total time taken by them to finish the remaining work is (T - 1/4) / (4/7) = (7/4) * (T - 1/4) = 7T/28 - 7/28.

So, the total time taken to build the fence is 2 + (7T/28 - 7/28) = 2 + 7T/28 = T.

Therefore, T = 2 + 7T/28 = 2 + 7 * (8 hours) / 28 = 2 + 4 hours = 6 hours.

So, Allen and Danny took 6 - 2 = 4 hours to build the fence after working together.

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The point that creates a right triangle with the points (3, 6) and (8, -2), which Christopher could place on the graph to create a right triangle is the point (8, 7.25)

A right triangle is a triangle with one ninety degrees (90°) interior angle.

The points on the right triangle Christopher already graphed (3, 6), and (8, -2)

The property of a right triangle is one of the interior angles is 90°, therefore, the legs or two of the sides of a right triangle are perpendicular.

The slope of the line joining the specified two points is found as follows;

Slope = (-2 - 6)/(8 - 3) = -8/5

The slope of the line perpendicular to the line segment Christopher used to join the points (3, 6), and (8, -6) is 5/8

The equation of the perpendicular line is therefore;

y - 6 = (5/8)·(x - 6)

y = (5/8)·(x - 6) + 6 = 5·x/8 + 18/8

y = 5·x/8 + 18/8

When x = 8, we get; y = 5 × 8/8 + 18/8 = 7.25

Therefore, the point (8, 7.25), forms a right triangle with the points (3, 6) and (8, -2)

A point Christopher can place on the graph to create a right triangle is (8, 7.25)

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If one side and two angles of a triangle are known, the triangle can be solved Law of Sines.

If A, B, and C are the measurements of the angles of a triangle, and a, b and c are the lengths of the sides opposite of the corresponding angles, then the ratio of side length to the sine of the opposite angle must all be the same.

                                      a/SinA = b/SinB = c/SinC

So, let's say that the value of 'a' is given and the value of angles A and B are also given. By using the law of sine, we can determine the value of 'b' as follows:

                                      a/SinA = b/SinB

                                      b = (a/SinA) SinB

Hence, if one side and two angles of a triangle are known, the triangle can be solved Law of Sines.

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y=3x-3, is the equation of a line with slope 3 passing through the mid-point of the line joining (1,2) and (3,4).

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

the mid-point of the line joining (1,2) and (3,4) is,

(1+3/2, 2+4/2)

=(2, 3)

slope= 3 =m

the equation => y =mx+c

so, 3 = 6+c

=> c= -3

now, the equation of a line => y=3x-3

Hence,  y=3x-3, is the equation of a line with slope 3 passing through the mid-point of the line joining (1,2) and (3,4).

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The experimental study design described is a 2x2 factorial design, where two independent variables (intervention and pretest) are crossed to create four groups for examining the main and interaction effects on the dependent variable.

Factorial designs allow researchers to examine the effects of multiple independent variables on a dependent variable. In this case, the two independent variables are the intervention (receiving vs. not receiving) and the pretest (receiving vs. not receiving). The two levels of each independent variable are crossed to create four different groups, two of which receive the intervention and two of which do not, two of which receive a pretest, and two of which do not.

This design allows the researcher to examine both the main effects of each independent variable and the interaction effects between the two independent variables on the dependent variable.

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Answer:

II and III only

Step-by-step explanation:

The right response is that 18 people covered 18 kilometers in total.

observe the instructions provided.

Try to form the following in light of the given circumstances: 6 + 7 + 5

Determine the difference or total for: 13 + 5.

Add up or subtract 18 and find the result.

Response: 18

How else do you determine the overall distance travelled?

As soon as a direction changes, note it. Determine the distance covered among each direction change in step two. Step 3: Total the distances from steps 2 and 3 to determine the total distance traveled.

To get the separation between any two points, use the Pythagorean theorem with the formula d=(((x 2-x 1)2+(y 2-y 1)2).

The length of the segment of the line connecting the two points is the distance between them. The shortest line segment between the point and the line will determine the distance between the two.

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                                      "complete question"

In training for a distance running event, Millicent runs 7 miles to a park. Then, she runs 5 miles to the beach before running 6 miles from the beach back to her house.

The journal for the completion of the two jobs and the sale of Job is given below:

A journal is a thorough account that captures all of a business's financial activities for use in account reconciliation in the future.

Preparation of the journal entries for the completion of the two jobs and the sale of Job 10

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The factors of the polynomial are (x + 1)(x - 3).

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

The upper side of the tiles shows the expression (x + 1), and the left side shows the expression (x - 3).

In both cases, you have to consider how many + x or - x is (one +x in one case and three -x in the other case).

If you multiply the factors, you get,

(x + 1)(x - 3) = x² - 3x + x - 3  

(x + 1)(x - 3) = x² - 2x - 3 .

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Answer:

I have graphed it and attached it to the explanation.

Step-by-step explanation:

If Logan has given out a total of 6.65 in nickels and dimes , then the number of dimes he has given out is  38 .

Let the number of nickels that Logan gave out be = n , and

the number of dimes that Logan gave out be =  d ;

From the information , we know that Logan gave out 50% more nickels than dimes,

that means ; n = d + 0.5d = 1.5d   ...equation(1) ;

We also know that the total amount given out in nickels and dimes is $6.65, and each nickel is worth of  $0.05 and each dime is worth of  $0.10,

So ,  n×0.05 + d×0.10 = 6.65 ;

Substituting the expression for n from the first equation into the second:

⇒ (1.5d)×0.05 + d×0.10 = 6.65 ;

Expanding and solving for d ;

we get ;

⇒ 0.075d + 0.10d = 6.65 ;

⇒ 0.175d = 6.65 ;

⇒ d = 6.65/0.175 = 38 ;

Therefore ,  Logan gave out 38 dimes.

The given question is incomplete , the complete question is

Logan works as a cashier. Today, he has given out 50% more nickels than dimes. if he has given out a total of 6.65 in nickels and dimes, How many dimes has he given out ?

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Answer:

I Don.t really know the answer

The volume of the round metal washer is  94.25 cm cube.

As inferred from the question, the shape of the round metal washer is that of a hollow cylinder with:

outer radius=  8 cm

inner radius =2 cm

thickness = 0.5 cm

we know that the formula for calculating the volume of a hollow  cylinder is as follows:

V = π ( [tex]R^{2}[/tex]-[tex]r^{2}[/tex])h cubic units

[ where R = outer radius, r= inner radius]

Putting the values in the above formula gives:

V=  π ( 8 - 2) X 0.5

-> V=  π (64-4) X 0.5 = 94.25 cm cube

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The total gallons of water made use of in the park after the new ride is installed is,

⇒ 21.0049 × 10⁶ gallons of water

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

A water park has pools, slides, and rides that, in total, make use of

2.1 × 10⁷ gallons of water.

And, They plan to add a ride that would make use of an additional 4.9 × 10³ gallons of water.

Hence, The total gallons of water made use of in the park after the new ride is installed is,

⇒ 2.1 × 10⁷ + 4.9 × 10³

⇒ 21000 × 10³ + 4.9 × 10³

⇒ (21,000 + 4.9) × 10³

⇒ 21,004.9 × 10³

⇒ 21.0049 × 10⁶ gallons of water

Thus, The total gallons of water made use of in the park after the new ride is installed is,

⇒ 21.0049 × 10⁶ gallons of water

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Based on the given angles, the missing answers of the sequences uploaded screenshots are:

The following answers are constructed based on the sequences of each problems not as the sequences of the uploaded screenshots.

3. Since ∠1 + ∠2 = 180°; then both are supplementary angles

4. Both ∠1 and ∠2 have equal size of angle and share no adjacent side; then both are vertical angles

5. 116° + 64° = 180°; then both are supplementary angle

8. Angles ∠3 and ∠4 are adjacent supplementary because it shares an adjacent side and its sum is 180°.

10. Angles ∠3 and ∠5 are vertical since they share no adjacent side but have equals size of angle.

12. Angles ∠1 and ∠5 are adjacent but neither complementary or supplementary because it sums are not 90° either 180°.

13. x and 107° are vertical angles; then:

x = 107°

15. x and 142° are supplementary angles; then:

x + 142° = 180°

x = 38°

17. ∠RST = 112°

∠RST = x + 87° = 112°

x = 35°

19. It is given that:

x + 127 = 180°

x = 53°

x = y = 53°

y + z = 90°

53° + z = 90°

z = 37°

21. ∠G + ∠H = 180°

51° + ∠H = 180°

∠H = 129°

22. ∠1 = ∠2

∠2 = 128°

23. ∠J + ∠K = 90°

∠J + 73° = 90°

∠J = 17°

2. Corresponding angles and congruent

4. Alternate interior angles and congruent

6. Consecutive interior angles and supplementary

8. Alternate exterior angles and congruent

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The required cost of the meal given as a hot dog is of $6 and the hamburger is of $8.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Let's call the cost of a hot dog meal "x" and the cost of a hamburger meal "y".

From Mrs. Hammond's purchase, we know that:

x + 3y = 30   -- - - - - -(1)

From Mr. Weber's purchase, we know that:

3x + 3y = 42 - - - - - -(2)

We can use substitution to solve for one of the variables in terms of the other. If we substitute the first equation into the second equation:

3x + 3y = 42

3x + 3(30 - x)/3 = 42

3x + 30 - x = 42

2x = 12
x = 6

now,
6 + 3y = 30
3y = 24
y = 8

Thus, the required cost of the meal given as a hot dog is of $6 and a hamburger is $8.

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Assume a stick of length 1 is randomly broken into two portions. The smaller piece's estimated length is 0.25.

The random variable L (the length for the shorter stick) has a uniform distribution.

Thus the probability density function for L is as follows:

This means 2 for all length in the range 0 - 0.5

Now, we calculate the expected value for random variable L as seen on the attachment. Based on the calculation, 0.25 is the smaller piece's estimated length for the randomly broken stick.

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The quantity of positive numbers smaller than or equal to [tex]$10,000$[/tex] is [tex]$\fbox{958}$[/tex].

We see that a number [tex]$n$[/tex] is [tex]$p$[/tex]-safe if and only if the leftovers from[tex]$n\mod p$[/tex] is greater than [tex]$2$[/tex] and less than [tex]$p-2$[/tex]; thus, there are [tex]$p-5$[/tex] residues [tex]$\mod p$[/tex] that a [tex]$p$[/tex]-safe number can have. Therefore, a number [tex]$n$[/tex] satisfying the circumstances of the issue may [tex]$2$[/tex] different residues [tex]$\mod 7$[/tex], [tex]$6$[/tex] different residues [tex]$\mod 11$[/tex], and [tex]$8$[/tex] different residues [tex]$\mod 13$[/tex]. According to the Chinese Remainder Theorem, for a number [tex]$x$[/tex] that is [tex]$a$[/tex] (mod b) [tex]$c$[/tex] (mod d) [tex]$e$[/tex] (mod f) has one solution if [tex]$gcd(b,d,f)=1$[/tex]. For instance, in this instance, the number [tex]$n$[/tex] can be: [tex]3 (mod 7) 3 (mod 11) 7 (mod 13)[/tex]so since [tex]$gcd(7,11,13)=1$[/tex], there is [tex]1[/tex] solution for [tex]n[/tex] for this case of residues of [tex]$n$[/tex]. As a result, according to the Chinese Remainder Theorem, [tex]$n$[/tex] can have [tex]$2\cdot 6 \cdot 8 = 96$[/tex] different residues mod [tex]$7 \cdot 11 \cdot 13 = 1001$[/tex]. Thus, there are [tex]$960$[/tex] values of [tex]$n$[/tex] satisfying the conditions in the range [tex]$0 < n \le 10010$[/tex]. Nevertheless, we now have to eliminate all values bigger than [tex]$10000$[/tex] that satisfy the conditions. We can simply see by looking at residues that the only suitable values are [tex]$10006$[/tex] and [tex]$10007$[/tex], so there remain [tex]$\fbox{958}$[/tex] values satisfying the conditions of the problem.

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Sigma notation for the sum is  ∑5ⁿ⁻⁴ (where n = 1 to 5)

Sigma notation is the most easiest way of writing a very large sum of elements of a sequence in a simple manner.

∑ is the symbol that is pronounced as "sigma".

"i" or "n" is called the index of summation

Given sum,

1/125 + 1/25 + 1/5 + 1 + 5

First term a is 1/125

Common ratio r = 1/25/1/125 = 5

Sequence can be written as

aⁿ = a.rⁿ⁻¹

aⁿ = 1/125 . 5ⁿ⁻¹

aⁿ = 5⁻³. 5ⁿ⁻¹

aⁿ = 5ⁿ⁻⁴

Sigma notation can be written as

∑5ⁿ⁻⁴ where n = 1 to 5.

Hence, Sum expressed as Sigma notation ∑5ⁿ⁻⁴ (where n = 1 to 5).

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The surface area of the rectangle prism is 52.05 in²

The total surface area of a prism is the sum of the areas of its lateral faces and its two bases.

The formula for the surface area of a prism is obtained by taking the sum of (twice the base area) and (the lateral surface area of the prism). The surface area of a prism is given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.

l = 7.2 in

b = 1 1/2 = 3/2

h = 1 3/4 = 7/4

SA = 2( 7.2×1.5+ 7.2 × 1.75 + 1.75×1.5)

SA = 2( 10.8 + 12.6 + 2.625)

SA = 2 ( 26.025)

SA = 52.05 in²

therefore the surface area of the rectangle prism is 52.05 in²

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The value of x considering the mean is two will be equivalent to 7.

The mean also known as the average is obtained by adding the data and then dividing it by the number of values. Here is an example: 3+6+4 = 13 / 3 = 4.3.

We know the mean is 2, based on this let's calculate the missing number:

The current number of cats: is 0+ 8 + 12 +3 =23 Based on this, the missing number would be 7, which would lead to a total of  8+12+24 = 44 cats divided by a total of 22, which means there are 2 cats per family.

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Answer: D

Step-by-step explanation:

45-4=41

45+4=49

Based on the given estimate that the candidate will receive 45% of the votes and the margin of error being 4%, the most appropriate conclusion would be option C:

The candidate will receive between 45% and 49% of the votes. To understand why this is the most appropriate conclusion, we need to consider the concept of margin of error. The margin of error is a measure of the uncertainty in the estimate and represents the range within which the true value is likely to fall. In this case, we have an estimated proportion of votes (45%) and a margin of error (4%).

To calculate the range within which the true value is likely to fall, we add and subtract the margin of error from the estimated proportion. Upper bound: [tex]45 + (4 of 45) = 45 + 1.8% = 46.8[/tex]  

Lower bound: [tex]45 - (4 of 45) = 45 - 1.8 = 43.2[/tex] %

Therefore, we can conclude that the candidate is likely to receive between 43.2% and 46.8% of the votes. Option C, which states that the candidate will receive between 45% and 49% of the votes, aligns with this conclusion. Option B (between 41% and 45%) is too conservative as it does not account for the upper bound of the margin of error,

Hence the correct option is C.

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Answer:

16 19/50

Step-by-step explanation:

first make improper fractions of both 3 9/10 and 4 1/5

mutltiply the denomiator (the number on the bottom) by the whole number, add the numerator (the number on the top) and put that number over the denomiator. 3 9/10 = 39/10 and 4 1/5 = 21/5. Multiply the improper fractions. numerator x numerator and write that on the top with a line under it. Multiply the denomiators and write that on the bottom. 39*21= 819. 10*5=50. your number would be 819/50. Then divide 819 by 50. You get 16 19/50

The correct justification of the equation from 2(y - 5) + 4 = 4 to 2y - 10 + 4 = 4 using distributive property of addition.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equation is given below.

2(y - 5) + 4 = 4

Apply distributive property of addition. Then the equation is written as,

2(y - 5) + 4 = 4

2y - 10 + 4 = 4

Simplify the equation further, then we have

2y - 10 + 4 = 4

2y - 6 = 4

2y = 10

y = 5

The correct justification of the equation from 2(y - 5) + 4 = 4 to 2y - 10 + 4 = 4 using distributive property of addition.

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Line segment is a a measurable part of a line that consists of two points, called endpoints.

a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Given that measurable part of a line that consists of two points, called endpoints is a line segment.

A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints.

Hence, line segment is a a measurable part of a line that consists of two points, called endpoints.

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Answer: I don't know

Step-by-step explanation:

Mark me as brainiest

Answer:

it's help me ttoo

Step-by-step explanation:

i need help with mathh please im going to fail

The volume of the solid is approximately 807.08 cubic units.

To determine the volume of the solid, we can use the method of cylindrical shells.

Imagine taking a slice of the solid parallel to the base, with the cross-sectional area being a square of side length x (where x is a function of the height). The volume of this slice is the product of the square area and the height. The height of the slice is equal to the difference in the radii of two consecutive circular cross sections.

The radius of the larger circular cross-section can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the radius) is equal to the sum of the squares of the other two sides (the height and half the side length of the square). Thus, we have:

r² = x² + (15-x)²

Solving for x, we get:

x = 15 * √(1 - (r/15)²)

The volume of the slice is then given by:

V = x² * (15 - x)

To find the total volume of the solid, we integrate this expression with respect to r from 0 to 15. The result is approximately 807.08 cubic units.

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