Every day your heart creates enough energy to drive a truck for 32 kilometers. If you combined the energy created all the students in your math class for a week, how many meters could the truck drive?
PLEASE SHOW FULL WORK:>

The position of the sprinter is equal to the value of definite integral of the given velocity function v(t). The position at t = 4, 7, and 9 is 8, 8, 0.

The velocity is the first derivative of the position function. The position function is given in the attached picture.

s'(t) = v(t)

The position at time t is therefore equal to the definite integral from t = 0 to time t.

Since the graph is linear, the evaluation of each definite integral is equal to the area of triangles underneath the lines.

∫₀⁴ v(t) dt = (1/2) x 2 x 6 = 6

∫₄⁷  v(t) dt = (1/2) x 1 x 8 - (1/2) x 2 x 4  = 0.

∫₇⁹  v(t) dt = 2 x (-4) = -8

The position at t = 0 is s(0) = 2

Hence,

s(4) = s(0) + ∫₀⁴ v(t) dt  = 2 + 6 = 8

s(7) = s(0) +  ∫₀⁴ v(t) dt + ∫₄⁷  v(t) dt = 2 + 6 + 0 = 8

s(9) = s(0) +  ∫₀⁴ v(t) dt + ∫₄⁷  v(t) dt  + ∫₇⁹  v(t) dt = 2 + 6 + 0 - 8 = 0

The graph in your question was missing. Most likely it was like on the attached picture.

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Answer: the third one

y=2^x-1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Answer is 12.5 because...

200/5=40

40x12.5=500

So that means 12.5x40=500

The number of toys based on the information will be 5.

From the information, Edgar works in the shipping department of a toy manufacturer. Toy cars weigh 6 pounds apiece and are shipped in a container that weighs 5 pounds when empty. Toy trucks, which weigh 3 pounds apiece, are shipped in a container weighing 20 pounds.

This will be Illustrated as:

5 + 6t = 20 + 3t

Collect the like terms

6t - 3t = 20 - 5

3t = 15

Divide.

t = 15 / 3

t = 5

The number of toys is 5.

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The probability that Jay fails the final exam and passed the remedial exam is P(fail the final and passed the remedial) = 0.32.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

After giving the final exam, the professor found that many of his students failed the test, so he decided to give a remedial exam.

The probability that a student passes the final exam is 0.6. Given that a student fails the final exam, the probability that the student passes the remedial exam is 0.8.

We are given the following probabilities:

P(passes the final exam) = 0.6

P(fail the final exam = (1 - 0.6) = 0.4

P(passes through the remedial | failed the final) = 0.8

We have to find P(fail the final and passed the remedial).

P(fail the final and passed the remedial) = P(passes the remedial | failed the final)*P(failed the final)

P(fail the final and passed the remedial) = 0.8 x 0.4

P(fail the final and passed the remedial) = 0.32

Hence, the probability that Jay fails the final exam and passed the remedial exam is P(fail the final and passed the remedial) = 0.32.

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On solving the provide question, we got to know that volume of cube is  and volume of cuboid is , so volume cube is greater.

We are aware that a rectangle has four corners and is a two-dimensional form. Think of the form as a collection of parallel rectangles. The resultant form is known as a cube. Take a look at the following three-dimensional cube. Height, Width, and Length

The volume of the cube = [tex]a^3[/tex]

Where a is the length of the side = 7cm

volume of cube =                  

[tex]7*7*7[/tex]We are aware that a rectangle is a two-dimensional shape with four corners. Consider the shape to be a set of parallel rectangles. The resulting shape is referred to as a cube. Look at the following cubic object in three dimensions. Length, Width, and Height

volume of the cuboid = l*b*h =

[tex]7*8*4 = 224 cm^2[/tex]

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Answer:

20) Rhombus | 21) Rhombus | 22) Square

Step-by-step explanation:

20) All sides are congruent, but there is no right <'s, and therefore it is just a Rhombus.

21) A Rhombus has diagonals that bisect each other and are congruent, which is shown in 21.

22) A square is a shape with all sides congruent and at least 1 right angle, which the diagram meets.

Hopefully this helps!

For the given expression, the correct answer is C, 7x².√2x⁴.6√2x¹² = 84x¹⁰.

Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.

A variable is a letter, like x, y, or z, that stands in for an arbitrary number. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6.

Given,

the expression is 7x².√2x⁴.6√2x¹²,

Solving the under root,

⇒ 7x².√2x².6√2x⁶

⇒ 7x² . √2 x². 6. √2 . x⁶     [√2 × √2 = 2]

⇒ 7 × 6 × 2 × x¹⁰ = 84 x¹⁰

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Answer:

look back through your lessons.

Step-by-step explanation:

what do you know about this question? if you go back through your lessons, you might be able to find a way to do this equation.

Answer:Therefore the surface area of the solid formed is about 598.33 in²

Step-by-step explanation:If the height of a right triangular prism is 1 5/6 inches. The surface area of the solid formed is: 598.33 in².

Surface area

First step

Right triangular prism=1 5/6 inches= 11/6 inches

Height of the base=8 2/3 inches = 26/3 inches

Second step

Surface area = 5(10× 10) + (0.5÷ 10 × 26/3) + 3(10× 11/6)

Surface area = 5(100) +43.33+ 3(18.33)

Surface area = 500) +43.33 + 55

Surface area = 598.33 in²

The table with values in the equivalent ratio is completed as

1 : 1/2

4 : 2

6 : 3

1/2 : 1/4

When we compare ratios, equivalent ratios are the ones that don't change. In order to determine whether or not different ratios are equivalent, we compare them side by side. An example makes it clear that the ratios 1:2 and 2:4 are equivalent. With the aid of division and multiplication, we can determine the two equivalent ratios.

In order to create a ratio that is equal to one that is already given, we must multiply or divide the given ratio's two terms by a non-zero number.

1 cup of flour = 1/2 cup of water

4 cups of flour = 1/2 × 4

                       = 2 cups of water

1/2 cup of flour = 1/2 × 1/2

                          = 1/4 cups of water

2 cups of water = 4 cups of flour

1 cup of water = 4/2

                          = 2  cups of flour

3 cups of water = 2 × 3

                           = 6 cups of flour

Thus, the table with values in the equivalent ratio is completed as 1 : 1/2, 4 : 2, 6 : 3 and 1/2 : 1/4.

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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:

581.3

Step-by-step explanation:

Option (D) A: -2/5, B: -1/5, C: -4/5, and D: -2/5 given the correct value of the number line.

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics.

It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

The set R of all real numbers, considered as a geometric space, namely the Euclidean space of dimension one, is the formal definition of the number line in advanced mathematics, also known as a real line or real number line.

So, according to the given number line:

A: -2/5
B: -1/5
C: -4/5
D: -2/5

Therefore, option (D) A: -2/5, B: -1/5, C: -4/5, and D: -2/5 given the correct value of the number line.

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The polynomial is x^4 - 8x^3 - 30x^2 + 144x + 405 = 0. The solution is obtained using the concept of bi-quadratic equation.

A 4-degree equation is a bi-quadratic equation.

Sometimes the phrase "bi-quadratic equation" is used as a substitute for the phrase "quartic equation." Such problems variable are straightforward to resolve because they can be reduced to quadratic equations in the variable x=z^2, which can then be solved for x using the quadratic formula and then in terms of the original variables by calculating the square roots.

Here,

We are given two roots of the bi-quadratic equation which are -3 and 7 - 2i.

Now, we will find the other two roots of the bi-quadratic equation by using the conjugates of the given roots.

In order to find the conjugate of complex numbers, we have to change the sign of the imaginary part.

So, we will get the conjugate of 7 - 2i = 7+2i

Thus, all the four roots of the bi-quadratic equation are -3, 7+2i, 7 - 2i and -3.

If two roots of an equation are given as a and b, then we can express the equation as (x-a) (x-b) = 0.

So, using this, we will form the equation with two imaginary roots 7+2i and 7−2i, which is given as:

[x-(7−2i)][x-(7+2i)]=0

⇒[x-7+2i][x-7-2i]=0

⇒[(x-7)+2i][(x-7)−2i]=0

Using the identity (a+b)(a-b)=a^2-b^2 , we get

(x-7)^2-(2i)^2=0

∵i=√-1

⇒(x-7)^2+(√-4)^2=0

⇒(x-7)^2+(-4)=0

⇒(x-7)^2 - 4=0

Now we will form the equation with roots -3 and -3, which is

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

⇒(x+3)^2=0

Finally, we will now find the product of these two quadratic equations to get the required bi-quadratic equation

⇒[(x-7)^2 - 4] [(x+3)^2]=0

⇒[x^2 + 49 - 14x -4] [x^2 + 9 + 6x]=0

⇒[x^2 + 45 - 14x] [x^2 + 9 + 6x]=0

⇒x^4 + 9x^2 + 6x^3 + 45x^2 + 405 + 270x - 14x^3 - 126x - 84x^2 = 0

⇒x^4 - 8x^3 - 30x^2 + 144x + 405 = 0

Hence, the required polynomial is x^4 - 8x^3 - 30x^2 + 144x + 405 = 0

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Answer:

----------------------------

Total number of frequencies:

Number of frequencies with the outcome of less than 2:

Probability of a number less than 2:

The matching choice is D.

Answer:

[tex]\sf D. \quad \dfrac{12}{60}[/tex]

Step-by-step explanation:

Experimental probability is based on the actual results of an experiment.

Theoretical probability is based on possible outcomes based on assumptions.

Experimental probability

Calculated by dividing the number of times an event happens by the total number of trials in an actual experiment.

[tex]\boxed{\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}}[/tex]

From inspection of the given table, the actual results (frequency) of landing on a number less than 2 is 12.

The total number of trials is 60.

Therefore:

[tex]\sf \implies P(x < 2)=\dfrac{12}{60}[/tex]

Noah's ambition was $90, and he raised $54 toward that total, or 60% of his fundraising target, in order to benefit the animal sanctuary.

A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter. There is frequently just one variable, which is also the symbol. example: 2x - 4 = 2.

given

60% x what= $54

Then, by converting 60% to a decimal, we can turn it into a useful number: 0.6. We will substitute x for what because we also need to make "what" simpler to use:

0.6x=54

Get x by itself next, which is referred to as isolating the variable. To accomplish this, divide both sides by 0.6, which is referred to as employing inverse operations.

You must obtain x=90.

Noah's ambition was $90, and he raised $54 toward that total, or 60% of his fundraising target, in order to benefit the animal sanctuary.

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If almost a billion people on the planet don't have access to clean drinking water. The percent of them that  lived without clean drinking water is 12.82%.

Given data:

Total number of people =  7.8×10^9

Number of people that lived without clean water = 1 billion

Number of people that lived without clean water = 1,000,000,000 = 1 × 10^9

So,

Percentage of people without clean water=  Number of people that lived without clean water  / Total number of people

Percentage of people without clean  water = 1 × 10^9 / 7.8×10^9 × 100

Percentage of people without clean water = 1/ 7.8 × 100

Percentage of people without clean water= 12.82%

Therefore 12.82% people lived without clean water.

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On solving the provided question, we can say that vertices D(1, 4), E(5, 5), F(4, 1) and G(0, 0),  area of rhombus = S*S = 5*5 = 25 cm sq.

A rhombus is an equal-sided quadrilateral in Euclidean plane geometry. The term "equilateral triangle" also refers to a quadrilateral whose sides are of the same length. A parallelogram has a unique variation known as a rhombus. In a rhombus, the opposite sides and angles are parallel and equal. A rhombus's diagonal is split in half by a right angle, and each of its sides is the same length. Rhombic diamonds and diamonds are other names for rhombuses. The length of every side is the same. Diagonals are equal in a rhombus. At a 90° angle, parallel lines split in half. 180 degrees is the sum of adjacent angles.

here,

vertices D(1, 4), E(5, 5), F(4, 1) and G(0, 0)

so area of rhombus = S*S = 5*5 = 25 cm sq.

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Answer:

a)  See below.

[tex]\textsf{b)} \quad y=940\left(1.0257\right)^{2x}[/tex]

c)  x is the number of years.

d)  y is the account balance in dollars.

e)  $1728.29

Step-by-step explanation:

Interest is compounded semi-annually, so:

Therefore, calculate 1.0257% of the balance every 6 months:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} \rm Years& \rm Account\;balance\;(\$) \\\cline{1-2} \vphantom{\dfrac12} 0& 940.00\\\cline{1-2} \vphantom{\dfrac12} 0.5& 964.16\\\cline{1-2} \vphantom{\dfrac12} 1& 988.94\\\cline{1-2} \vphantom{\dfrac12} 1.5&1014.35\\\cline{1-2} \vphantom{\dfrac12} 2&1040.42\\\cline{1-2} \vphantom{\dfrac12} 2.5&1067.16\\\cline{1-2} \vphantom{\dfrac12} 3&1094.59\\\cline{1-2} \end{array}[/tex]

An equation that models this situation is:

[tex]\implies y=940\left(1+\dfrac{0.0514}{2}\right)^{2x}[/tex]

[tex]\implies y=940\left(1.0257\right)^{2x}[/tex]

x is the number of years.

y is the account balance in dollars.

To calculate how much will be in the account after 12 years, substitute x = 12 into the equation from part (b):

[tex]\implies y=940\left(1.0257\right)^{2 \times 12}[/tex]

[tex]\implies y=940\left(1.0257\right)^{24}[/tex]

[tex]\implies y=940\left(1.8386054...\right)[/tex]

[tex]\implies y=1728.2890...[/tex]

Therefore, $1728.29 will be in the account after 12 years.

The value of y in the table would be greater than the value on the graph, when x = 11 by: B. 110.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

For the table, an equation which represent its data points is given by:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 270 = (360 - 270)/(4 - 3)(x - 3)

y = 90(x - 3) + 270

y = 90x - 270 + 270

y = 90x.

When x = 11, the value of y is given by:

y = 90(11)

y = 990.

For the graph, an equation which represent its data points is given by:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 160 = (320 - 160)/(4 - 2)(x - 2)

y = 80(x - 2) + 160

y = 80x - 160 + 160

y = 80x.

When x = 11, the value of y is given by:

y = 80(11)

y = 880

Next, we would determine the difference:

Difference = 990 - 880

Difference = 110.

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On solving the provided question, we can say that we have two quadratic equations; t² +9t + 36 > t² + 11t + 12 => t>12

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here,

we have two quadratic equations

Mall A is modeled by -t² +9t + 36,

Mall B is modeled by - t² + 11t + 12,

t² +9t + 36 > t² + 11t + 12

-2t > -24

t>12

Mall A when t = 3 hours = [tex]3^2 +9*3 + 36 = 9+27+36 = 72[/tex]

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What the area of the pre-image should be multiplied by to obtain the area of the image rectangle is; 4

The scale factor in the dilation of a mathematical object is one that determines how much larger or smaller the image will be when compared to the original image.

Now, the formula for area of a rectangle is;

A = LW

Where;

L is length

W is width

If the rectangle is dilated by a scale factor of 1/2, then it means that;

New length = ¹/₂L

New Width = ¹/₂W

New Area = ¹/₂L * ¹/₂W

= ¹/₄LW

Thus, to get the pre image are, we have;

Area of pre-image = 4 * Area of new image

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Therefore , the solution to the given problem of triangle comes out to be the length MP is measured at 6 units.

Due to its three vertices and three sections, a component is a polygon. It has a simple geometric form. Triangle ABC refers to a triangle only with points A, B, and C. When components are not collinear, a singular plane and triangle are found. Triangles are regarded as polygons since they have three corners and a right side. The points where a triangle's three sides intersect are known as the triangle's corners. By compounding three triangle angles, one gets 180 degrees.

Here,

Triangle OMN is provided.

Now, OMN and OPQ are comparable. It follows that the side lengths are in proportion to one another. We can write:

=>OP = OM = PQ = MN

=>OM = PQ/MN in 12

=>(OP + PM)/12 = PQ/MN

Considering that -

=>PQ = MP + 2

=>12/(OP plus PM) = (MP plus 2)/MN

=>12MN equals (MP + 2)(OP + PM).

=>12 × 12 = (MP + 2)(MP + 12)

=>2 MP plus 12 MP plus 2 MP plus 24 = 144

=>(MP)² + 14(MP) - 120 = 0

We can write - if MP = x.

=>x² + 14x - 120 = 0

=>(x + 20)(x - 6) = 0

=>(x + 20) = 0 and (x - 6) = 0

x = - 20 and x = 6

There can be no negative lengths, hence x = 6

Consequently, the length MP is measured at 6 units.

Therefore , the solution to the given problem of triangle comes out to be the length MP is measured at 6 units.

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Answer:

$203

Step-by-step explanation:

Please mark brainliest

The value of expression 254 ÷ 6 is, 42.33.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ 254 ÷ 6

Divide the numbers as;

⇒ 254 ÷ 6

⇒ 254 / 6

⇒ 42.33

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Answer:

4.85

Step-by-step explanation:

8.09-3.24+4.85

The correct answer is 75001+9< 75100.The 75010 is less than 75100.Because we can count to prove it.

The greater than and less than symbols are generally used to represent the inequality expressions. The symbol used to represent greater than is “>” and less than is “<”. If one value is larger than the other value we use greater than. Similarly,if we want to represent one value that is less than the other value we use less than.

Many teachers use the Alligator Method analogy to teach greater than and less than. They will draw an Alligator mouth on the greater than and less than signs.We can say the alligator is going to want to eat more.

Now

75001+9= 75010

This will seventy five thousand and ten

75100 = seventy five thousand and one hundred

So,  75001+9 <75100

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The method that will be used in solving for x in the expression 5x + 6x = 22 is simplifying using addition and division operation

solving the equation gives x to be equal to 2

The expression given 5x + 6x = 22 is a linear function having one unknown variable and the solution is sought by using the relevant mathematical operations

Applying addition operation in solving for x

5x + 6x = 22

11x = 22

Applying division operation in solving for x

11x = 22

x = 2

hence, the solution of the the expression is x = 2

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