Make sense of problems. Determine the number , and explain how you came up with he solution

The surface area of the sandbox assuming there is no lid is 21.3 feet

From the question, we are to determine the surface area of the sandbox

From the given information,

The dimension of the box is 3 feet by 4 feet

Thus,

Length = 4 feet

Width = 3 feet

and

The depth of the box is 8 inches

That is,

Height = 8 inches = 8/12 feet

Height = 2/3 feet

Now,

Using the formula for the surface area of a box

Surface area = (2lw + 2lh + 2wh)

If there is no lid,

The surface area becomes

Surface area = (lw + 2lh + 2wh)

Thus,

Surface area = (4×3 + 2×4×2/3 + 2×3×2/3)

Surface area = (12 + 16/3 + 4)

Surface area = (12 + 5.3 + 4)

Surface area = 21.3 feet

Hence, the surface area of the sandbox assuming there is no lid is 21.3 feet

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Answer:

bhe ganyan din

akin

Step-by-step explanation:

please help us

The inequalities that represent the problem is 5h + 2.50t ≤ 60

Each hamburger costs $5 and each taco costs $2.50.

He has a total of $60 to spend on hamburgers and tacos.

The inequalities that would be used to  represent the possible values for the number of hamburgers purchased, h, and the number of tacos purchased, t is as follows:

Therefore,

h = number of hamburgers purchased

t = the number of tacos purchased

Hence,

5h + 2.50t ≤ 60

Therefore, the inequalities that represent the problem is 5h + 2.50t ≤ 60

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Answer:

Step-by-step explanation:

6x - 32 = 4x + 16

2x - 32 = 16

2x = 48

x = 24

6(24) - 32 = 144 - 32 = 112

4(24) + 16 = 96 + 16 = 112

The value of x = 2.

Three points of collinear are A, B, and C. Here point B is between A and C.

The properties of collinear point are,

a>The slope of AB is equal to the slope of BC,

b>Line AB + BC = AC

c>The area is equal to 0.

As the three points are collinear, and from the second property we have

AB + BC= AC

Where, AB = 4x + 3

            BC = 3x + 2

So we have,

(4x + 3) + (3x + 2) =19

7x + 5=19

7x = 14

x=2

Therefore we get the value of x =2.

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The solution is an infinite solution.

An infinite solution can be defined as a solution with both sides equal to each other

Given the expression;

-15 - 3w = 4w - 2w

Let's simply the expression

Collect like terms

- 3w - 4w + 2w = 15

Add or subtract like terms

-5w = 15

Make 'w' the subject

w = 15/ -5

w = -3

Thus, the solution is an infinite solution.

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Answer: x = -1, 15

Step-by-step explanation:

15 = x²- 14x

⇒ x²- 14x-15 = 0

⇒  x²- 15x+x-15 = 0

⇒ x (x-15) + (x-15) = 0

⇒ (x-15) (x+1) = 0

Now,

x= -1, 15

The proof of the given algebra equation is; x = -40

We are given the algebra equation as;

(8 - 3x)/4 = 32

Using multiplication property of equality, multiply both sides by 4to get;

8 - 3x = 128

Using subtraction property of equality, subtract 8 from both sides to get;

-3x = 120

Using division property of equality, divide both sides by -3 to get;

x = -40

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Dimensions of new rectangle after getting scaled by factor of 5 are 10cm by 15cm. Option  (B) is correct.

What is scale factor?

In two similar geometric figures the ratio of their corresponding side is scale factor let the old dimension be x and scale  factor be a then new dimension will be a*x

If a>1 then their will be enlargement in the geometric figures

Given that rectangle that is 2 cm by 3 cm has been scaled by a factor of 5

It means scale factor be 5

New dimensions of given rectangle will be found by multiplying by 5

New length and breadth are 2*5=10

                                               3*5=15

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The average rate of change over the entire slide if the height of the slide is 2 feet is; -3.9

Average rate of change is defined as a measure of how much the function changed per unit, on average, over that interval.

First, we will calculate the average rate from x = 0 to x = 15:

We have:

R = ((80 - 10)/(0 - 15))

R = -4.667

Let us now calculate average rate of change for the entire interval supposing that the height of the slide is 2 feet,:

From x = 0 to x = 20, we have;

R = ((80 - 2)/(0 - 20))

R = -3.9

Thus, we can conclude that the average rate of change over the entire slide is; -3.9

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Answer:

slower than & -3.9

Step-by-step explanation:

The expression which represents the sales price of the bracelet in terms of the sticker price is; s = 0.65p and the evaluation for a sticker price of $60 is; $39.

It follows from the task content that the bracelet has been discounted 35% from its sticker price.

Hence, the sales price of the bracelet is therefore; (100 - 35)% of sticker price, p.

Therefore, we have;

s = (65/100) × p

s = 0.65p.

Ultimately, the evaluation for a sticker price of $60 is; s = 0.65(60).

s = $39.

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The complete sentence is 3 mi ≈ 4.827 km

The open sentence is given as:

3mi ≈ ____ km

In the standard unit of conversion, we have

1 mi ≈ 1.609 km

Multiply both sides by 3

3 * 1 mi ≈ 1.609 km * 3

Evaluate the product

3 mi ≈ 4.827 km

Hence, the complete sentence is 3 mi ≈ 4.827 km

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Answer:

choice 2,5,6

Step-by-step explanation:

Answer:

i took it like 2 years ago. i think its MNP, N, 1, and PNM?

The number of can collected by Carrie after one week if the pattern continued will be; 105 cans and hence, she met her goal.

It follows from the task content that Carrie's target for can collection was 100 units of can collected over 1 week.

Since, one week contains seven, 7 days, it follows that she has 7 days to meet her target.

Following from observation, she increased the number of cans collected each day following a pattern; 7, 8, 10, 13.... where the difference between two successive days increases by 1 each time.

Hence, the number of cans collected for the rest of the days are as follows;

Therefore, the total number of cans collected is; 7 + 8 + 10 +13 + 17 + 22 + 28 = 105 cans and hence, she meets her goal.

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The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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10 boxes will be required by the printing company

Company can fit 7000 calendars in 1 box

7000 calendars = 1 box

1 calendar = 1/7000

70000 calendar = 1/7000 * 70000

= 10 boxes

10 boxes will be required by the printing company

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According to the solving the distance between two points is:

= 14.77

In coordinate geometry, the distance formula is used to calculate the actual distance between two points. The formula for calculating the distance between two locations (x1,y1) (x 1, y 1) and (x2,y2) (x 2, y 2) is D=(x2x1)2+(y2y1)2 D = (x 2 x 1) 2 + (y 2 y 1) 2.

The length of a line segment seems to be the distance between two locations. Congruent segments are those with the same length. By drawing a line with a ruler, we may compute the approximate distance between two points.

Given points: (-4, 6) and (3, -7)

X₁ = -4
Y₁ = 6
X₂ = 3
Y₂ = -7

We know that the distance between two points:

distance = √((x₂ - x₁)²+(y₂ - y₁)²)

              = √((3 - (-4))²+((-7) - 6)²)

              = √((3 + 4)²+(-13)²)

              = √((7)²+(-13)²)

              = √((49)+(169))

              = √(218)

             = 14.77

According to the solving the distance between two points is:

= 14.77

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Answer:

C

Step-by-step explanation:

Taking a square root of a number that doesn't have a square root like [tex]\sqrt{17}[/tex] will result in an infinite number of random digits which is an irrational number. Hence, C is the answer.

D isn't the answer because even though [tex]\sqrt{5}[/tex] is irrational, you're adding [tex]\sqrt{5}[/tex] and then subtracting [tex]\sqrt{5}[/tex] from the total sum. Hence the total sum would be 5+14.

5+[tex]\sqrt{5}[/tex]+14-[tex]\sqrt{5}[/tex] =5+14+[tex]\sqrt{5}[/tex]-[tex]\sqrt{5}[/tex]= 5+14 ==> 19 is a rational number

Answer:

x = -54

Step-by-step explanation:

Let's solve your equation step-by-step.

[tex] \sf \: `-\frac{1}{3}x=18`[/tex]

Step 1: Multiply both sides by 3/(-1).

[tex] \sf( \frac{3}{ - 1} ) \times ( \frac{ - 1}{3} x) = ( \frac{3}{ - 1} ) \times (18)[/tex]

[tex] \sf \: x = - 54[/tex]

The equation is 6.5 (r-1) + 5.5  = 259 or 6.5 r - 1 = 259.

In this case, r stands for the overall number of rows.

The answer indicates that each row is 6.5 cm tall.

A formula known as an equation uses the equals sign (=) to express how two expressions are equal. The word "equation" and its cognates in other languages may have slightly different meanings. For instance, in French, an equation is defined as having one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. The task of solving an equation with variables entails figuring out which values of the variables cause the equality to hold true. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions. Identity equations and conditional equations are the two types of equations.

The height of the top row is 6.5 - 1 = 5.5 cm.

Except for this row, there are total rows of = (r-1)

So, 6.5 is the total length of these rows (r-1)

The overall length of the wall is therefore equal to the sum of the (r-1) row and the top row.

However, once more in line with the inquiry,

Exactly 259 centimeters must be on the wall.

⇒ 259 = 6.5(r-1) + 5.5

⇒ 6.5(r-1) + 5.5 = 259

⇒ 6.5 r - 6.5 + 5.5 = 259

⇒ 6.5 r - 1 = 259

Which is the required equation for finding the number of rows (r).

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Given that statements 1 and 2 are true statements, the conclusion agrees with the laws of syllogism.

In syllogism, we have a pattern of reasoning in which the flow is that the premise must lead to the conclusion. This implies that reasoning must be logically sound and unbiased.

Now let us look at the statements that we have here;

Statement 1 - .If the measure of an angle is between 90-180 , then it is obtuse

Statement 2 - If an angle is obtuse, then it is not acute.

We know that these are true syllogisms because mathematically, we define the obtuse angle as an angle that is greater than 90 degrees but less than 180 degrees.

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By using area formula, we get base is [tex]20 m[/tex]

What do you mean by area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. For instance, On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given that:

Area of a rhombus is [tex]400 m^{2}[/tex]

Height  of a rhombus is [tex]20 m[/tex]

We know that,

Area of rhombus = base × height

Substituting area and height in above formula

[tex]400[/tex] = base × [tex]20[/tex]

∴ Base = [tex]\frac{400}{20}[/tex]

           =[tex]20[/tex]

Therefore, by using area formula, we get base of a rhombus is [tex]20 m[/tex]

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Step-by-step explanation:

"complimentary" means together they have 90°.

"supplementary" means together they have 180°.

which can be easily and quickly found on any internet search.

7.

A = 70°

A + B = 90°

70 + B = 90

B = 90 - 70 = 20°

B + C = 180°

20 + C = 180

C = 180 - 20 = 160°

8.

A + B = 90°

B + C = 180°

C = 100°

B + 100 = 180°

B = 180 - 100 = 80°

A + 80 = 90

A = 90 - 80 = 10°

Answer:

Hi, here are the remaining values in order.

The following expression i.e.[tex]x^{\frac{10}{3} }[/tex] is rewritten as [tex](x^{3} )\sqrt[3]{x}[/tex]

Expression:

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

You can think of expression as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.

⇒ [tex]x^{\frac{10}{3} }[/tex] { given a exponential expression }

⇒ [tex]x^{\frac{9+1}{3} }[/tex] { spliting the power into parts }

⇒[tex]x^{3+\frac{1}{3} }[/tex]

⇒ [tex]x^{3}[/tex]×[tex]\sqrt[3]{x}[/tex]  { spliting the terms by using properties of exponent }

⇒  [tex](x^{3} )\sqrt[3]{x}[/tex]

Hence,   [tex](x^{3} )\sqrt[3]{x}[/tex] is rewritten form of the given expression  i.e.[tex]x^{\frac{10}{3} }[/tex]

Therefore,The following expression i.e.[tex]x^{\frac{10}{3} }[/tex] is rewritten as [tex](x^{3} )\sqrt[3]{x}[/tex]

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The image of ΔHOP with coordinates H(2,1), O(-3,4), and P(5,7).

(a) after 90° clockwise rotation is H'(1,-2,),O'(4,3),P'(7,-5) ,

(b) after 90° counterclockwise rotation is H''(-1,2),O''(-4,-3),P''(-7,5) ,

(c) after 180° rotation is H'''(-2,-1),O'''(3,-4),P'''(-5,-7) .

When a point (x,y) is rotated 90° in clockwise about the origin then the image after rotation becomes (y,-x) .

When a point (x,y) is rotated 90° in counterclockwise about the origin then the image after rotation becomes (-y,x) .

When a point (x,y) is rotated 180° about the origin then the image after rotation becomes (-x,-y) .

Part(a)

The ΔHOP with coordinates H(2, 1), O(-3, 4), and P(5, 7) is rotated 90° in clockwise direction ,

we know the points (x,y) becomes (y,-x),

So the image of ΔHOP after rotation becomes H' , O' , P'   .

H(2, 1) → H'(1,-2)

O(-3, 4) → O'(4,3)

P(5,7) →  P'(7,-5)

Part(b)

The ΔHOP with coordinates H(2, 1), O(-3, 4), and P(5, 7) is rotated 90° in counterclockwise direction ,

we know the points (x,y) becomes (-y,x),

So the image of ΔHOP after rotation becomes H'' , O'' , P''   .

H(2, 1) → H''(-1,2)

O(-3, 4) → O''(-4,-3)

P(5,7) →  P''(-7,5)

Part(c)

The ΔHOP with coordinates H(2, 1), O(-3, 4), and P(5, 7) is rotated 180°,

we know the points (x,y) becomes (-x,-y),

So the image of ΔHOP after rotation becomes H''' , O''' , P'''   .

H(2, 1) → H'''(-2,-1)

O(-3, 4) → O'''(3,-4)

P(5,7) →  P'''(-5,-7)

Therefore , The image of ΔHOP

(a) after 90° clockwise rotation is H'(1,-2,),O'(4,3),P'(7,-5) ,

(b) after 90° counterclockwise rotation is H''(-1,2),O''(-4,-3),P''(-7,5) ,

(c) after 180° rotation is H'''(-2,-1),O'''(3,-4),P'''(-5,-7) .

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Answer:

D

Step-by-step explanation:

the picture

Answer:

RS = 33

Step-by-step explanation:

from the number line

RT = RS + ST ( substitute values )

46 = RS + 13 ( subtract 13 from both sides )

33 = RS

Answer:

RS = 33

Step-by-step explanation:

Given that,

→ ST = 13

→ RT = 46

Then the value of RS will be,

→ RS + ST = RT

→ RS + 13 = 46

→ RS = 46 - 13

→ [ RS = 33 ]

Hence, the value is 33.

Answer: option c

Step-by-step explanation:

hope this helps

Basically, a sequence is a function whose domain is set of natural numbers and co-domain is set of real numbers.

Function:

A function relates each element of a set with exactly one element of another set (possibly the same set)

Real numbers:

Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”.

Domain

Domain is the set of all possible inputs of a function.

Co - Domain:

Co - domain is the set of its possible outcomes or results.

Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position.

That's why, every sequence must be the function itself.

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