Speedometer readings for a motorcycle at 12-second intervals are given in the table.
t (s) 0 12 24 36 48 60
v (ft/s) 30 28 25 21 25 27
(a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals.
ft
(b) Give another estimate using the velocities at the end of the time periods.
ft
(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.
O (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.
O (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t.
O (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.

The solution for the given system of equations is (-1, 2).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

The given system of linear equations are y=-3x-1 ------(I) and 4x+3y=2 ------(II).

Substitute y=-3x-1 in equation (II), we get

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

4x-9x-3=2

-5x=5

x=-1

Substitute x=-1 in equation (I), we get

y=-3(-1)-1

y=2

Therefore, the solution for the given system of equations is (-1, 2).

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The probability that a car chosen at random will need no​ repairs = 72%; no more than one​ repair = 91%;  some​ repairs = 9%

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.

28% of all vehicles will require some sort of repair; of these, 19% will require one repair, 7% will require two repairs, and 2% will require more than two repairs.

The number of vehicles that would not require any form of repairs is equal to the entire number of vehicles less the proportion that requires repairs; for example, 100% - 28% = 72%. The total number of automobiles minus the percentage that require more than one repair equals the percentage of vehicles that will require no repairs or just one

; hence, 100% - (7% + 2%) = 91%. The total number of vehicles in need of repairs is equal to the product of those with two repairs and those with three or more.

the probability that a car chosen at random will need no​ repairs = 72%; no more than one​ repair = 91%;  some​ repairs = 9%

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A cylindrical can with volume 355 ml will use the least aluminum if its radius is about 3.84 cm and its height is about 7.67 cm.

The soda cans are advertised as having a volume of 12 ounces, or 355 milliliters. The remaining head space is just under 25 ml. The can weighs about 13 g by itself. 39 g, or about 11%, of sugar, make up 355 ml of Coke.

When canned at 4 °C and stored at 20 °C, 12 oz. soda cans typically have pressures of about 120 kPa and 250 kPa, respectively. A 7UP® can that has been refrigerated contains 210 kPa of pressure. Pepsi-Cola®, on the other hand, has 276 kPa at about 16 °C.

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On solving the provided question, we can say that - the slope of the following will be slope, m = [tex]4-6/4-2 = -2/2 = -1[/tex]

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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On solving the provided question, we can say that - the slope of the following will be slope, m = -1

what is slope?

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

here,

(x1,x2) = (6,4)

(y1,y2) = (2,4)

slope, m = 4-6/4-2 = -2/2 = -1

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Answer:

a. 1.6

b. 16

c. 0.16

d. 1.6

Answer:

9

Step-by-step explanation:

6 1/3 yards of material is 19/3 yards total. 6 yards broken into thirds is 18/3. 18 divided by 2 is 9. There are 9 total pieces to cut, and an extra 1/3 left over

On solving the provided question, we can say that - the value of the linear equation is 2y+8x = 140

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, we have 2y + 8x

and x = 10 ; y = 15

2y + 8x

20 + 120 = 140

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Answer:

|5-2x|<_11

=5+2x<11

=2x=11-5

2x=6

=X<-3

The distance from point A to point B is 781.5 ft.

Since the angle of elevation from point A to the lighthouse is 15 degrees, use the tangent function to find the height of the lighthouse. Let x be the height of the lighthouse,

tan(15°) = x / 862

Solve for x.

x = 862 (tan(15°))

Similarly, let y be the distance from point B to the lighthouse,

tan(8°) = x / y

Solve for y.

tan(8°) = 862 (tan(15°)) / y

y = 862 (tan(15°)) / tan(8°)

y = 1643.45 feet

Subtract 862 from 1643.45 to get the distance from point A to point B.

distance from point A to point B = 1643.45 - 862 = 781.45 ft = 781.5 ft

Therefore, the distance from point A to point B is 781.5 ft.

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Answer:

10 and 24units

Step-by-step explanation:

Pythagoras' Theorem applies to right angle triangles with the formula:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

where c is the longest side, with a and b the shorter ones (interchangable)

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

[tex] {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2[/tex]

Now we can find the side lengths.

[tex]5x = 5(2) = 10units \\ 12x = 12(2) = 24units[/tex]

Therefore the side lengths are 10 and 24 units.

Answer:

Using the cosines law

Step-by-step explanation:

So, we need to find the length of the other side, we will use the version of the Cosine Rule where a2 is the subject of the formula, which is given by, a2=b2+c2−2bccosA, Side a is the one we are trying to find. Sides band care the other two sides, and angle Ais the angle opposite side a. c2=a2+b2−2abcosC

Answer:

4

Step-by-step explanation:

Half means 1/2

Half of 8

= 1/2 x 8

= 8/2

= 4

Hence, half of 8 is 4.

Answer: 4

Step-by-step explanation:4 + 4 is 8 half of 4 is eight.

The coordinate points of the point P is (-3.5, 2.3).

What is a coordinate plane?

Two number lines combine to form a two-dimensional surface known as a coordinate plane. It is created when the origin, a point where the X- and Y-axes coincide, is crossed by a horizontal line.

The ratio in which the point 'P' divides the line segment RQ is -

a:b = 5:1

The coordinates of the end-points of line segment RQ are -

R(4, -1)  and  Q(-5, 3).

The coordinates of the point H are obtained when a point H divides a line segment with end points (p, q) and (s, t) in the ratio a:b -

H = [(as + bp)/(a + b)], [(at + bq)/(a + b)]

H = [(5*-5 + 1*4)/(5 + 1)], [(5*3 + 1*-1)/(5 + 1)]

H = (-21/6, 14/6)

H = (-3.5, 2.3)

Therefore, the coordinate points are obtained as H = (-3.5, 2.3).

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The line parallel to the given line 2x+3y=6 is 2x+3y=13.

The general equation of a line is y=mx+c where m is the slope of the line and c is the y-intercept.

The slope of the given line 2x+3y=6 is

3y=(-2x)+6

y=(-2/3)x+2

y=mx+c where m is the slope of the line

so the slope of the given line is (-2/3)

as the slope of two parallel lines is equal so the slope of the line parallel to the given line is also (-2/3)

(y-y1)=m(x-x1) where x1 is the x-coordinate and y1 is the y-coordinate.

Here x1=2 and y1=3

(y-3)=m(x-2)

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

3y-9=(-2x)+4

3y+2x=13

2x+3y=13

The line 2x+3y=13 is parallel to the given line 2x+3y=6.

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The x-intercept for the graph of y is found to be at x = 2.

The quadratic equation given is

y = x² - 4x + 4

Put y = 0

0 = x² - 4x + 4

It becomes perfect square for (x - 2).

It can be written as;

(x - 2)² = 0

Take square root on the both sides

x - 2 = 0

x = 2

Thus, the x-intercept for the graph of y is found to be at x = 2.

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The correct question is-

What is the x-intercept of the graph of y = x² - 4x + 4?

Answer:

139⁰

Step-by-step explanation:

since g and h are parallel

then n= 139⁰ (corresponding angles)

Volume of the triangle is 1420m³ given in the question.

There are various volumes for various geometric shapes. Cubes, cuboids, spheres, cylinders, cones, etc. are examples of common 3D shapes that we encounter on a daily basis.

Finding the volume is simple when dealing with shapes with a flat surface, like a cube or a cuboid. Cones, cylinders, and spheres are examples of curved shapes, and it is necessary to take into account both their curved surfaces' dimensions and their overall curvature. Possibly their diameters or radii

The term "irregular solids" refers to solids that lack precise measurements or shapes. A fixed formula that can be used to calculate the volumes of such solids is typically absent. It is possible to obtain these volumes in a variety of ways, one of which is the liquid displacement method, which is based on the Archimedes Principle.

Now volume triangle = area × height

⇒ 1/2 × 20 × 14.2 × 10

= 1420m³

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The standard form of the polynomial -n²(n² + 5n + 6) is  -n⁴ - 5n³ - 6n².

Polynomials are algebraic expressions that consist of variables and coefficients.

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on.

Hence, let's represent the polynomial in standard form as follows:

-n²(n² + 5n + 6)

Open the brackets

-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²

Hence,

-n²(n² + 5n + 6) = -n⁴ - 5n³ - 6n²

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The Two steps equation in mathematics are the equations that can be solved within exactly two steps.

What is a Two Step Equation ?

The Two Step Equation are the algebraic problems that  just take two steps to solve. It is a linear equation in one variable.

When solving the two step equation, we have to perform operation on both sides of the equation .

For Example : Solve [tex]2x+6=12[/tex] ;

Step1 : we Subtract -6 from both sides to isolate variable x.

⇒ [tex]2x + 6 - 6 = 12 - 6[/tex]

⇒ [tex]2x = 6[/tex]

Step2 : We Divide both the sides of equation by 2 and solve for x.

⇒ [tex]\frac{2x}{2} =\frac{6}{2}[/tex]

⇒ [tex]x = 3[/tex] ;

Therefore , the equation is solved in two steps .

The given question is incomplete , the complete question is

What is the two step equation in math ?

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The probability is 5/32.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

To roll exactly 4 odds out of 5 rolls is [tex](\frac{1}{2} )^{4}\frac{1}{2}[/tex]  where the odds are 1, 3, and 5 for 3/6=1/2 and the other 1/2 is the probability of rolling an even since we want exactly 4 odds.

Since there are 5 dice being rolled there are 5 ways to order them.

So the probability is 5/32.

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The graph C. represents the polynomial with zeros of -3, 0 and 2.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information about the graph's x-intercepts for the polynomial.

Alternately, we might state that the zeros of the polynomial are the x-intercept of its graph. Thus, the needed function is represented by the graph with the coordinates -3, 0, and 2.

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The complete question is as follows:

Select the correct answer.

Which graph best represents a function with zeros of -3, 0, and 2?

a: 235 92 U + 1 0 n → 90 36 Kr + 141 56 Ba + 3 1 0 n

b: 239 94 Pu + 1 0 n → 96 38 Sr + 143 55 Ba + 3 1 0 n

c: It is not possible to complete this nuclear fission reaction as it is not a valid input. There is no nuclide with the atomic number 94 and mass number 239.

Nuclear reactions are those that involve the nucleus of an atom. Nuclear fission involves the splitting of an atomic nucleus and the formation of two distinct atomic species.

Nuclear fission is a nuclear reaction in which the nucleus of an atom is split into two or more smaller nuclei, along with the release of a large amount of energy. In the first reaction, an atom of Uranium-235 (U-235) is hit by a neutron, which causes the nucleus to split into Krypton-90 (Kr-90) and Barium-141 (Ba-141) along with 3 neutrons. In the second reaction, an atom of Plutonium-239 (Pu-239) is hit by a neutron, which causes the nucleus to split into Strontium-96 (Sr-96) and Barium-143 (Ba-143) along with 3 neutrons.

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Answer:

5.5

Step-by-step explanation:

7*8=56

42-8=34

56-34=22

22/4=5.5

Answer:

6n-5

Step-by-step explanation:

let 'n' equal 'a number'

the equation above means you are multiplying 6 and that number, then reducing it by 5

Answer:

A, B, F

Step-by-step explanation:

Divide both sides of -4x<20 by 4, and we have A

Multiply both sides of -4x<20 by -1, since -1 is a negative number, we reverse the inequality, and we have B

Multiply both sides of -x<5 (A) by -1, since -1 is a negative number, we reverse the inequality, and we have F

54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.

A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.

given

To find P P, divide P

P by the total number of participants (students and chaperones), which is 81.

Seventh graders totaling 81 - 7 =

74 participated in the field trip.

54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.

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Answer:

C is the correct answer

From the graph we can see that at the given interval [-6,0] the graph decreases from left to right.

Initially the y-values is a little over 3 and then it decreases to about 0.5 at the end of the interval.

Thus, the graph of the function over the interval [-6,0] is decreasing.

Answer:

  $16,755

Step-by-step explanation:

You want the difference in interest earned on $66,000 after 19 years between an account earning 6 3/8% compounded annually, and one earning 5 3/4% compounded continuously.

The formula for the account value multiplier when interest is compounded annually is ...

  k = (1 +r)^t . . . . . . compounded annually at rate r for t years

When interest is compounded continuously, the multiplier is ...

  k = e^(rt)

The difference in account values between the two rates is ...

  ∆value = $66,000·(1 +0.06375)^19 -e^(0.0575·19))

  ∆value ≈ $16,754.70

Benjamin will have about $16,755 more than Christian after 19 years.

A triangle is a three-sided polygon with three vertices. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The correct answer Is option c) 6.

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

The diagram shows us a triangle [tex]$\mathrm{ABC}$[/tex], which

[tex]$$m \angle A=m \angle C=63^{\circ}, \quad A B=3 x$$[/tex]

units and [tex]$B C=(4 x-2)$[/tex] units.

The task Is to determine the length of the slde [tex]$\mathrm{AB}$[/tex].

[tex]$\mathrm{ABC}$[/tex] has the following

[tex]$$m \angle A=m \angle C$$[/tex]

In a triangle, we understand that

If the measurements of two angles are equal, then the lengths of the sides or each side are also equal.

so we must have

[tex]B C=A B \\\Rightarrow 4 x-2=3 x \Rightarrow 4 x-3 x=2 \Rightarrow x=2 .\end{aligned}$$[/tex]

As a result, [tex]$\mathrm{AB}$[/tex] will be of length

[tex]$$A B=3 x=3 \times 2=6$$[/tex]

As a result, the side [tex]$A B$[/tex] is 6 units long.

Therefore, the correct answer Is option c) 6.

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The coefficient of x² in 2 x² x³ is 2 n with number.

2 x² x³

= 2 x² (x³)

= 2 x² (x  x  x)

= 2 x² x  x  x

The coefficient of x² is 2.The expression 2 x² x³ can be written as 2 x² (x³). This can be further simplified to 2 x² (x  x  x). The coefficient of x² is 2, which means that the coefficient of x² in 2 x² x³ is 2. The coefficient of a term is the numerical factor of the term, or the number that is multiplied with the term. In this case, the coefficient of x² is 2, as it is the number multiplied with x².

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