A regular-size box of cereal measures 3 1/2 inches by 8 1/2 inches by 15 inches. The manufacturer also sells an individual-size box that has a volume that is 1 1/0 of the volume of the regular-size box.

What is the volume of the individual-size box of cereal?

Enter your answer as a mixed number in simplest form by filling in the boxes.

Equations now take the shape:

  [1]    3x - 4y = 24

  [2]    3x + 4y = 6

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Answer:

C. 21.35 inches

Step-by-step explanation:

circumference = πd

circumference = 3.14 × 6.8 inches

circumference = 21.35 inches

Question 23

Using the alternate interior angles theorem, [tex]m\angle BCA=20^{\circ}[/tex].

Question 24

[tex]\overline{AD} \cong \overline{DC}[/tex] by the definition of a rhombus. This means that [tex]\triangle ADC[/tex] is isosceles. It follows that [tex]m\angle ACD=20^{\circ}[/tex]. Using the angle sum of a triangle, [tex]m\angle CDA=140^{\circ}[/tex].

Question 25

All rhombi are parallelograms, and diagonals of parallelograms bisect each other. This means that [tex]AC=2(4)=8[/tex].

The tortoise travelled the maximum distance of 9 m estimated from the time graph journey of a tortoise.

Distance-time graphs demonstrate how a moving object's distance travelled varies over time.

For the stated time graph of the journey of tortoise.

On x axis - time taken.

On y axis - distance covered by the tortoise.

Thus, the maximum distance is covered by the tortoise is 9 m at the time of 3 minutes.

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The zeroes of the equation x² + 3x - 40 is -8 or 5.

A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

Given:

F(x) = x² + 3x - 40

Now, solving the quadratic Equation

x² + 3x - 40 = 0

x² + 8x - 5x - 40 = 0

x(x + 8) - 5(x + 8)=0

(x+8) (x-5)= 0

So, x+8 = 0 or x-5=0

x=-8 or x= 5

Hence, the zeroes are -8 and 5.

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Answer:

x = 2

Step-by-step explanation:

The triangle shown in the image is a right triangle.

a√2 = √8

a = √4

Remember we said a represents legs, in the image x represents the legs so the answer is:

x = √4 and √4 = 2, therefore the answer is 2.

A system of linear inequalities represented by the graph are;

Inequality 1: y ≤ 3x - 3

Inequality 2: y ≥ ¹/₂x - 3

Inequalities that use < or > symbols are usually plotted with a dashed line that shows us that the line is not included in the region. Meanwhile, Inequalities that use ≤ or ≥ symbols are normally plotted with a solid line that shows us that the line is included in the region.

The general formula of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, the graph that rises to the right side in the first quadrant has;

Slope = (3 - 1)/(3 - 2)

Slope = 3

the y-intercept is at y = -3

Thus, equation is;

y ≤ 3x - 3

Thus, the graph that rises to the left side in the second quadrant has;

Slope = (1 - 0)/(2 - 0)

Slope = 1/2

the y-intercept is at y = 1

Thus, equation is;

y ≥ ¹/₂x - 3

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Answer: C

Step-by-step explanation:

The probability of selecting a student from the class who is a pet owner or prefers cats to dogs is; 0.4

In probability, If events A and B are not mutually exclusive, then the probability of A or B is expressed as;

p(A or B) = p(A) * p(B).

Total number of students = 26

Total number of students that are pet owners = 18

Total number of students that prefers cats to dogs = 26 - (8 + 3) = 15

Thus;

P(pet owner) = 18/26

P(prefers cats to dogs) = 15/26

P(Pet owner or prefers cats to dogs) = (18/26) * (15/26)

= 0.4

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1.125 cups of frozen mango is needed to serve one

A smoothie recipe contains 2 1/4 cups of frozen mango

This recipe can serve a total number of two people

The first step is to change the mixed fraction to an improper fraction

2 1/4

9/4

The number of cups of frozen mango needed to serve one person is

9/4 ÷ 2

9/4 × 1/2

= 9/8

= 1.125

Hence the number of cups of frozen mango required to serve one person is 1.125

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Answer:

TQN

Step-by-step explanation:

The slope of the line that goes through the points (0, 2) and (1, -1) is -3.

What is the slope of the line?

The slope of a line is a number that describes the steepness of a line and the direction it is heading. It is also known as the "rise over run" or the "rate of change" of a line. The slope of a line is typically represented by the letter "m" and is found using the formula:

slope = (y2 - y1) / (x2 - x1)

To find the slope of a line, you need two points on the line (x1, y1) and (x2, y2) and substitute their coordinates into the slope formula.

To find the slope of a line, we use the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, we have two points: (0, 2) and (1, -1). To find the slope between these two points, we can substitute their coordinates into the slope formula:

slope = (-1 - 2) / (1 - 0)

slope = -3

Hence, the slope of the line that goes through the points (0, 2) and (1, -1) is -3.

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Answer:

Height = 557.1 to 1dp.

Step-by-step explanation:

Surface area of the given prism

= 2(12*3 + 12*10 + 10*3)

= 7272

The new prism must have surface are 2*7272 = 14544.

Let the new height be h, then:

2(3h + 10h + 30) = 14544

6h + 20h = 14544 - 60

26h = 14484

h = 14484/26

  = 557.1 cm.

Point A has coordinates (x1, y1). The x-coordinate, x1, is the horizontal distance from the origin, while the y-coordinate, y1, is the vertical distance from the origin.

Coordinates in math refer to a pair of numbers that indicate the position of a point on a two-dimensional graph or in a three-dimensional space. The two numbers are usually referred to as the x-coordinate (or abscissa) and the y-coordinate (or ordinate). In three-dimensional space, the third number is referred to as the z-coordinate (or applicate). A point located at (3, 4) on a two-dimensional graph would be located 3 units along the x-axis and 4 units along the y-axis. Similarly, a point located at (3, 4, 5) in three-dimensional space would be located 3 units along the x-axis, 4 units along the y-axis, and 5 units along the z-axis.

Both coordinates indicate the exact location of Point A in a coordinate system. For example, if Point A is located at (2, 4), it means that the x-coordinate of Point A is 2, which is 2 units away from the origin in a horizontal direction, and the y-coordinate of Point A is 4, which is 4 units away from the origin in a vertical direction. The origin is usually located at (0, 0) in a coordinate system.

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Using substitution method to solve the system of linear equation, the number of children is 90 and adults is 93.

In mathematics, a system of linear equations is the collection of two or more linear equations that share the same variables. The maximum power of the variable in the linear equations in this situation is 1, making them first-order equations. A linear equation may have one, two, or three variables. We can therefore create linear equations with n variables.

To solve this problem, we have to define our variables and then write the equations.

Let;

x + y = 183 ...eq(i)

1.75x + 2.5y = 390 ...eq(ii)

solving both equations

From equation (i)

x + y = 183

x = 183 - y ...eq(iii)

Put equation (iii) into equation (ii)

1.75(183 - y) + 2.5y = 390

y = 93

Put y = 93 into equation (i)

x + 93 = 183

x = 90

The number of child is 90 and adult is 93

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Since the midsegment of each trapezoid is parallel to each base and is half, it has a GH value of 0.85.

Having at least one pair of parallel sides, a trapezoid is a quadrilateral in American and Canadian English. In the UK and other nations that speak English, it is referred as as the Trapezium. A trapezoid is a convex quadrilateral according to Euclidean geometry. Its parallel sides make up the trapezoid's base. The trapezoid, a convex quadrilateral, is defined by an identical pair of opposite sides that are parallel to one another. On paper, the two-dimensional trapezoid shape seems like a table. The term "quadrilateral" in Euclidean geometry refers to a polygon with four sides and four vertices.

given

A trapezoid's midsegment runs parallel to each base and is half as long as all of the bases combined.

1/2 * 3x - 6 = 2x

3x - 6 = 4x

= -6 = 7x

x = 0.85

Since the midsegment of each trapezoid is parallel to each base and is half, it has a GH value of 0.85.

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The equation of the line with a slope of 2/3 passing through (-4, 1) is y = (2/3)x + 11/3

An equation is an expression relating two or more numbers and variables.

The slope - intercept form of a linear equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The equation of a line passing through (x₁, y₁) with a slope of m is given by:

y - y₁ = m(x - x₁)

The line has a slope of 2/3 and pass through point (-4, 1). Hence:

y - 1 = (2/3)(x - (-4))

y - 1 = (2/3)(x + 4)

y = (2/3)x + 11/3

The equation of the line is y = (2/3)x + 11/3

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Answer:

x-intercept = -2; y-intercept = -7

Step-by-step explanation:

Answer: (0,10) and (3,1)

Step-by-step explanation:

Before I solve the system, I am going to rewrite it to make it easier for me to understand it.

[tex]y=(x-3)^2+1\\y=-3x+10[/tex]

Notice that f(x) and g(x) have been changed into y. The reason is because f(x) and g(x) are the same and stand for y, but we only use f and g to distinguish between the 2 equations. We can use equal values to solve.

[tex](x-3)^2+1=-3x+10[/tex]              [exponent]

[tex]x^2-6x+9+1=-3x+10[/tex]        [add both sides by 3x]

[tex]x^2-3x+10=10[/tex]                        [subtract both sides by 10]

[tex]x^2-3x=0[/tex]                                  [factor]

[tex]x(x-3)=0[/tex]

Notice that x=0 and x-3=0. This means the solutions are x=0 and x=3.

To find the actual full solution, we have to plug those points back into the original equations.

[tex]-3(0)+10=0+10=10\\-3(3)+10=-9+10=1[/tex]

Therefore, the solutions to this system are (0,10) and (3,1).

The given linear relationship slope of the line is D) 6.

What is slope?

An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). The ratio of how much y grows as x grows by a certain amount is known as the slope of a line. A line's slope, or the amount by which y rises as x rises, indicates how steep a line is. The slope is constant (the same) along the line.

Here from given tables lets take any two points to find slope, then

[tex](x_1,y_1)=(0,-6) and (x_2,y_2)=(1,0)[/tex]

Now using slope formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] then

=> m = [tex]\frac{0-(-6)}{1-0}[/tex]

=> m =[tex]\frac{6}{1}[/tex]

=> m = 6.

Hence the slope of the given table is D)6.

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Answer:113.1 square feet

Step-by-step explanation:

Answer:A

Step-by-step explanation:

Answer:

22,256

Step-by-step explanation:

If the speedometer reading is 60, your actual speed is miles. miles per hour. Since the value of k = 1.1128 for the two tires in comparison, 1.1128 (20,000) = 22,256 miles (actual) and 1.1128 (60) = 66.768 miles per hour (actual). The percent error is 11.28% for both readings.

Therefore , the solution of the given problem of expression comes out to be as a result, we can minimize the radical statement by doing the actions listed below.

the value of an object  variable is represented by collections of numbers, signs, and procedures (like + and).Examples: The equation is 5+7. 3 x/2 is an alternative formula. An expression lacks the equals symbol.

Here,

To simplify a radical expression, use the Product Property.

1) Determine the radical's largest factor, which is also the index's precise power. Use that factor to rewrite the radicand as the intersection of two factors.

2) Apply the product rule to the radicals to rewrite them as the outcomes of two additional radicals.

3. Decompose the root of the ideal power.

Therefore, by taking the methods outlined above, we may simplify the radical expression.

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The answer is 10 minutes

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Abrams family had a 30-gallon baby pool that they could fill in just 2 minutes. Thus speed = 30/2

                                              =15 gallons per day

Thus to fill 150 gallons the time required is 150/15=10 mins

Hence, The answer is 10 minutes

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Answer: B

Step-by-step explanation:

2/3 = 1/3 and 1/4 is already there

Hope this helps !

Answer:

Step-by-step explanati

Your answer would be A.

Answer:

10:15

Step-by-step explanation:

fsd