On July 27, 2018, Mars will be about 57.6 million km from the earth. It will not be that close again until 2035. If a manned spacecraft could travel 40,000 km/hr, approximately how long would it take the spacecraft to reach Mars from Earth?

The base of an exponent is a number that is increased to a definite power. So, the base of an exponent defines the number that is multiplied by itself.

An exponent is a number or letter written above and to the right of a mathematical expression said the base. It indicates that the base is to be increased to a certain power.

In 2³ = 2 × 2× 2, 2 is the base number which is to be multiplied by itself thrice and could be also called “two to the power of three” or “two to the third power” In 2³= 2 × 2× 2, 3 is the exponent which represents the number of times 2 is to be multiplied by itself.

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The triangle is a perfect right angle triangle  since it satisfies the Pythagoras theorem .

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of the angles is a right angle (90°). Triangle ABC is a right triangle in the illustration, consisting of the base, altitude, and hypotenuse. Here, the hypotenuse is BC, the height is AC, and the base is AB. The significant side of a right triangle is the hypotenuse, which is the longest side and sits in opposition to the triangle's right angle.

By using pythagoras theorem

[tex]\sqrt{24\x^{2} + 7\x^{2} } = 25[/tex]

The triangle si a perfect right angle triangle  since it satisfies the Pythagoras theorem .

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To use substitution to determine which value of x makes the equation true, we must first have an equation to substitute the values from the set {4, 8, 10} into.

If we don't have an equation, we can't use substitution.

It would be helpful if you could provide an equation to solve with the set {4, 8, 10}

The expected value of Isabel's game is given as follows:

E(X) = 0.

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

The game is composed by choosing eight balls, which are equally as likely to be chosen.

Then the probability distribution of earnings is given as follows:

Hence the expected value of the price is given as follows:

E(X) = 1/8 x (1 + 2 + 5 + 6 + 8 + 10) - 16 x 2/8.

E(X) = 0.

The problem asks for the expected earnings.

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Therefore , the solution to the given problem of circle comes out to be  

572 yard^2.

Each point in the plane that is a certain distance from some other point forms a circle (center). Thus, it is an curve composed of spots that are spaced apart from one another in the plane. Additionally, at every angle, it is axis of rotation symmetric about the center. The closed, two-dimensional plane of a circle has every pair of points uniformly separated from the "center." With tracing a path through the circle, one can create a line of circular symmetry. Additionally, at every angle, it is radially symmetric about the center.

Here,

area=pi times

radius2 area=3.14 times 13.52

=>3.14 times diameter=2radius dameter/2

=>radius d=27 27/2=radius.

The answer, 182.25=572.265,

Area is 572 yards.

Therefore , the solution to the given problem of circle comes out to be  

572 yard^2.

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The decision rule for is to reject null if critical value is higher than the test statistic, since there is insufficient evidence to show that the machines are underfilling the bag.

First we have to solve for the test statistic

t = x - u / s /√n

the variables are stated as:

where x = 444

u = 447

n = 24

s = 10

we would have the test statistic solved as :

444 - 447 / 10 / √24

-3 / 2.0412

= -1.4697

at 0.1 significance level, we would have:

degree of freedom

n - 1

= 24 - 1 = 23

the critical value is -1.3194.

Because the critical value is  greater than the test statistic, we are going  to  reject the null.

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Integers are a type of real number that just includes positive and negative whole numbers and natural numbers. Real numbers can include fractions due to rational and irrational numbers, but integers cannot include fractions.

$75.50 and 18 cents - $35.50 and 8 cents = $40.00 and 10 cents per mile. For x miles, we multiply $40.00 and 10 cents by x miles.

Also, we could convert dollars to cents by multiply it by 100 Since $1 =100 cents.

7568 - 3558 cents = 4010 cents. For x miles, 4010X cents.

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Answer:

Step-by-step explanation:

V=(1/3)hπr^2

<=> 4487 = 1/3x21πxr^2

<=> r^2 = 641/π

<=> r = squrt( 641/π)

The statement that must be true since the average rate of change T(d) for the interval d = 4 and d = 10 is 0 is this:

C: The same number of tickets was sold on the fourth day and tenth day.

The average rate of change is a measurement that shows how much the function of a unit changes over a given interval. In the above question, we can see that the average rate of change given the two intervals is zero and this means that there was no change among the variables.

Thus, we can conclude that the number of tickets that were sold on day 4 was also the number of tickets sold on day 10.

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Answer:

x=138

Step-by-step explanation:

A triangle's angles equal to 180

104+34=138

180-138=42

X and 42 are a liner pair so they equal 180

138+42=180

x=138

The vertex of the parabola is at (0, 0), the focus of parabola is at (2, 0) and axis of symmetry of parabola is x-axis.

A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

One definition of a parabola includes a line and a point (the focus) (the directrix). The directrix is not the main focus. The locus of points in that plane that are equally spaced apart from the directrix and the focus is known as the parabola.

Given a horizontal parabola centered on the origin opens to the left,

the equation for a horizontal parabola,

(y − b)² = 4p(x − a), p≠0

a and b are the vertex of parabola,

since the parabola is centered on the origin, a and  b are (0, 0)

vertex of parabola is at (0, 0),

and for horizontal parabola axis of symmetry is the x-axis.

focus of parabola is at (a + p, b)

given p = 2

focus of parabola is at (0 + 2, 0) = (2, 0)

Hence vertex at (0, 0), focus at (2, 0), and symmetry with the x-axis.

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The circumference of circle B is 14 m

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: The circumference of circle A as 2²/₃ m and circumference of circle B as 1¹/2 times the diameter of circle A

let the radius of the circle A be r then we have

2πr=8/3

r=4/3×7/22

r=14/33 m

or diameter of the circle A= 28/33

Again let the circumference of the circle be x then we have

x=28/3 ×3/2

x=14

Hence, The circumference of circle B is 14 m

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Step-by-step explanation:

82=−3(−4a+3)−5

Step 1: Simplify both sides of the equation.

82=−3(−4a+3)−5

82=(−3)(−4a)+(−3)(3)+−5 (Distribute)

82=12a+−9+−5

82=(12a)+(−9+−5) (Combine Like Terms)

82=12a+−14

82=12a−14

Step 2: Flip the equation.

12a−14=82

Step 3: Add 14 to both sides.

12a−14+14=82+14

12a=96

Step 4: Divide both sides by 12.

[tex]\frac{12a}{12} = \frac{96}{12}[/tex]

a=8

The horizontal line test is a procedure that can be used to determine if a function is a one-to-one function. This means that, for every y-value in the function, there is only one distinctive x-value.

The purpose of the horizontal line test is to decide whether or not a given function is one-to-one considering its graph. A function from one set to another is a relation between the two sets in which each element of the first set is assigned to a single element in the second.  In other words, a function f is one-to-one

                           [tex]f(x_{1}) = f(x_{2})[/tex]  ⇒ [tex]x_{1} = x_{2}[/tex]

for every [tex]x_{1} , x_{2}[/tex] n the domain of f.

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Susie AnnaMarie spent 6 hours cutting grass

Let a represent the number of hours Susie AnnaMarie spent cutting grass

Let b represent the number of hours Susie AnnaMarie spent tutoring

a + b = 14..........equation 1

12a + 14b= 184.........equation 2

From equation 1

a + b= 14

a= 14-b

Substitute 14-b for a in equation 2

12(14-b) + 14b= 184

168 - 12b + 14b= 184

168 + 2b= 184

2b=  184-168

2b= 16

b= 16/2

b= 8

Substitute 8 for b in equation 1

a + b= 14

a + 8= 14

a= 14-8

a= 6

Hence Susie AnnaMarie spent 6 hours cutting the grass

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Mia spend 1/4 of her money on a ticket, he has 30 pound left. Therefore the ticket was 120 pound.

Pound:

The sterling  is the currency of the United Kingdom and nine associated territories. The pound (symbol: £) is the primary unit of sterling, and the word "pound" is also commonly used to refer to British currency, and in international contexts is often British It is called pound or pound sterling.

The sterling is the world's oldest currency still in use and has been in continuous use since its creation. It is currently the fourth most traded currency in the foreign exchange market, after the US dollar, the euro and the Japanese yen. Together, these three currencies and the renminbi form a basket of currencies for calculating the value of the IMF's Special Drawing Rights. As of late 2022, the pound is the world's reserve currency and he is also the fourth most held reserve currency.

According to the question:

Since, 1/4 of her money is spent on the tickets.

Then , there left 3/4 part of money.

Therefore,

So she spent a total of 1/4 of her money in the tickets, and therefore had 3/4 of her money left at the end. So 3/4 of the money she started with is 30 pound.

Therefore she started with 30 * 4 = 120 pound.

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The probability that they share the same color is 7/15.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability.

A straightforward illustration is tossing a fair (impartial) coin.

The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half (which may also be.

According to our question-

Then n(S)= number of ways of drawing 2 balls out of (6+4)=10

Let E= event of getting both balls of same color

Then, n(E)= no of ways (2 balls out of six) or (2 balls out of 4)

= 6C 2​+ 4c2

∴P(E)= n(S)/n(E)= 45/21= 15/7

7/15

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The change in profit for each owner is -$22.00c

You should be aware that change in profit in this regard talks about how much money each partner is going to loose over what he or she gains initially

The given parameters that will help us to understand the question are

This implies that the 100 dollars will be shared among the five partners in this way

110/5 = 22.00

In conclusion each partner gets a change in profit of $22.00

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So, on solving the provided question, we can say that the equations will be y=2x; y=2x +2; y=2x+4; y=2x+6

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equations will be

y=2x

y=2x +2

y=2x+4

y=2x+6

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The correct question is

Review the scatter plot.

Select the equation which best represents the linear model, the line of best fit. Responses

y=2x

y=2x +2

y=2x+4

y=2x+6

Answer:

As it is a right angle triangle, you can find a by Pythagoras Theorem.

[tex] {a}^{2} + {51}^{2} = {60}^{2} \\ a = \sqrt{( {60}^{2} - {51}^{2} )} \\ a = 31.63 \: yd[/tex]

The dimensions of the paint, obtained by factoring the polynomial function for the area of the tray, 42·x + 135·x + 108 are as follows;

(a) The width of the tray = 6·x + 9

(b) Area of the square paint compartment is 9 in²

(c) The width of the edges is 12 inches

The factors of a polynomial are other polynomials of lesser degree, that when multiplied together, produces the polynomial which is factored.

The area of the paint tray = 42·x² + 135·x + 108 in²

The dimensions of the square paint compartment are the same

Space along the edge of the tray = 2 × space between the squares

(a) The length of the tray obtained from the diagram in the question = 7·x + 12 inches

Using an online tool, we get;

42·x² + 135·x + 108 = 3·(2·x + 3)·(7·x + 12)

The area of a rectangle = Length × Width

Therefore, the width of the tray = The area ÷ The length

Width = (42·x² + 135·x + 108)/(7·x + 12) = 3·(2·x + 3)

(b) Let s represent the side length of each square paint compartment, we get;

Width of four compartments + 3 spaces between compartments = (7·x + 12) - 2 × 2·x

Width of four compartments + 3 spaces between compartments = 4·s + 3·x

4·s + 3·x = (7·x + 12) - 2 × 2·x = 3·x + 12

4·s = 3·x + 12 - 3·x = 12

s = 12/4 = 3

s = 3

The side length of each square = 3 inches

The area of each square paint compartment = s²

s² = 3² = 9

(c) Where the width = 45 inches, we get;

3·(2·x + 3) = 45

2·x + 3 = 45/3 = 15

2·x + 3 = 15

2·x = 15 - 3 = 12

x = 12/2 = 6

x = 6

The width of the edges of the tray = 2·x

2·x = 2 × 6 = 12

The width of the edges of the tray = 12 inches

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The probability of all 6 locations being in water is 0.9994.

The probability of a single location being in water is 0.71. When finding the probability of 6 locations all being in water, we can use the binomial probability formula:

P(x=6) = (n!/(x!(n-x)!)(p^x)(q^(n-x))

where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.

Plugging in the values, we get:

P(x=6) = (6!/(6!(6-6)!)(0.71^6)(0.29^(6-6))

P(x=6) = 0.9994

Therefore, the probability of all 6 locations being in water is 0.9994.

The probability of all 6 locations being in water is 0.9994.

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A division is to separate into two or more equal parts, areas, classes, categories, groups, or divisions.

In another word, the meaning of divide is to distribute the whole thing to a group in equal parts or make equal parts. The symbol used to represent divide or division is ÷, slash (/), or a horizontal line ( _ ).

There are four important terms used in the division operation:

dividend, divisor, quotient, and remainder.

The formula to calculate the division of two numbers is:

Dividend ÷ Divisor = Quotient + Remainder.

Here,

The dividend is the number, which is divided

The divisor is the number, which divides the number into equal parts

The quotient is the result of the division operation

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The Wien Apetrol UC 20142000 was a unique and innovative venture that aimed to provide clean energy solutions to the people of Austria.

x = -7

ma = 54

m23 = 54

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Answer:

35

Step-by-step explanation:

When Alonzo splits 3/4 pounds of candy among 4 people the unit rate in pounds per person is 3/16 pounds per person

The ratio of two measures, with one as the second of the item, is known as unit rate.

For the problem where Alonzo have to split 3/4 pounds of candy, the  unit rate is solved by division.

In this case, Alonzo will divide each the 3/4 pounds by 4 to get a value of which is the unit rate

The unit rate of candy in pounds per person

= 3/4 pounds / 4 persons

= 3/16 pounds per person

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Answer:

3/10

Step-by-step explanation:

If homeroom 101 has 1/2 of the bulletin board, and 3/5 of their side is used.

To calculate the area that is using we multiply both values,

1/2 x 3/5 = 3/10

Which is our answer!

The first equation is based on the fact that Devon is 34 years older than his son Milan:

d = m + 34 (1)

The second equation is based on the fact that the sum of their ages is 44:

d + m = 44 (2)

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts, separated by an equals sign (=). For example, the equation 2x + 3 = 7 is a statement that the expression 2x + 3 is equal to the expression 7. The expressions on either side of the equals sign are often referred to as the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations can be used to model and describe a wide range of real-world situations, including physical phenomena, financial models, and scientific relationships. Equations can be simple or complex, involving one or more variables and a variety of mathematical operations. Equations can be solved to find the value of the variable(s) that make the equation true.

We can use the information provided to write a system of equations to describe the situation.

The first equation is based on the fact that Devon is 34 years older than his son Milan:

d = m + 34 (1)

The second equation is based on the fact that the sum of their ages is 44:

d + m = 44 (2)

To find how old is Devon we can use either of the equation. Let's use equation (1)

d = m + 34

We know that Milan is x years old, We can substitute that in equation (1)

d = x + 34

So, Devon is 34 years older than Milan.

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A
____
M = 10
5x10 = 50