mass of a banana and can of cola

The length of the leg in the triangle is 11.6 units

From the question, we have the following parameters that can be used in our computation:

The length of the other leg using Pythagorean Theorem is

Other Leg = √(Hypotenuse² - One Leg²)

So, we have

Orher Leg = √(16² - 11²)

Evaluate

Other leg = 11.6

Hence, the other leg is 11.6 units

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The slope of a line can be determined by taking a ratio of the change in y-axis to the change in x-axis.

The y-intercept of any graph of a linear equation is at the point where the x-value is equal to zero (x = 0).

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

In Mathematics, the y-intercept is also referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Generally speaking, the slope-intercept form is modeled by this equation:

y = mx + c

Where:

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The equivalent expression in scientific notation is given as follows:

4.11 x 5.54/100.

A number in scientific notation is given as follows:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.

The numbers in this problem are given as follows:

The equivalent expression is obtained as follows:

4.11 x 5.54 x 10^(-2).

The negative exponent divides into the denominator, and 10² = 100, hence:

4.11 x 5.54 = 4.11 x 5.54/100.

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The total amount of time Rebecca's family spends at Mount Rushmore is 51 minutes.

Let's call the total amount of time Rebecca's family spends at Mount Rushmore "t".

According to the information given, 13 minutes of that time is spent watching a movie in the visitor center, which is 16% of the total time spent at Mount Rushmore.

This can be expressed as:

13 minutes / t = 16%

To find the total amount of time t, we need to isolate t in the equation. To do this, we can cross-multiply and solve for t:

13 minutes * 100% = 16% * t

13 minutes * 100% / 16% = t

So, the total amount of time t that Rebecca's family spends at Mount Rushmore is:

t = (13 minutes * 100%) / 16% = 812.5 minutes / 16 = 51 minutes

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You paid $16.05 with taxes for a meal.

The definition of the sales tax is given below.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

1) If you buy a meal from a restaurant that cost $15.00, and the tax is 7%,

then the amount of the tax is,

= 15 x 7 / 100

= $1.05

2) The sales tax:

The government levies a consumption tax known as a sales tax on the purchase of goods and services. At the point of sale, a traditional sales tax is imposed, collected by the shop, and forwarded to the government.

Therefore, the taxed amount is $1.05.

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The expressions on both sides of the equal sign are examples of the product of two polynomials, and the goal is to simplify these products into the standard form of a single polynomial. To do this, we use the distributive property of multiplication over addition.

Starting with the first expression (5x-3)(8x-4). We use the distributive property to expand the product of two polynomials into a single polynomial:

(5x-3)(8x-4) =

= (5x × 8x) + (5x × -4) + (8x × -3) + (- 4 × -3) =

= 40x² - 20x - 24x + 12 =

= 40x² - 44x + 12 =

= 10x² - 11x + 3.

In a similar manner, the second expression can be expanded and simplified. We use the distributive property to expand the product of two polynomials into a single polynomial:

(2x+8)(7x+6) =

= (2x × 7x) + (2x × 6) + (8 × 7x) + (8 × 6) =

= 14x² + 12x + 56x + 48 =

= 14x² + 68x + 48 =

= 7x² + 38x +24x.

So both expressions have been simplified into the standard form of a single polynomial, and both are equal to the expressions on the right side of the equal sign.

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Answer:

x = 3 and y = 1

Step-by-step explanation:

A) most efficient way is to multiply the first equation by 3 to eliminate the 'x' terms and get 9x - 15y = 12

if you add this to -9x + 3y = -24 you will get -12y = -12

y = 1

substitute 1 for 'y' to get 'x':  3x - 5 = 4

3x = 9

x = 3

Note that as labeled in the attached image:

1) Shapes D and F are similar

2) A and B are NOT similar because they have different ratios of side lengths

3) C and E are NOTE Similar. They are Different Shape.

1) To determine that both shapes are similar, all we need to divide the side lengths of D by two. This gives us:

Breath  - 6/2 = 3

Length - 14/ 7 = 7

Since the Breadth of F is 3ft and it's length 7ft, it means D and F are similar to the ratio of 2:1.

2) If the above logic is applied to A and B, we would see that the side lengths of both shapes have different ratios.

For both of them to be similar, since the breadths - 6/2 = 3 then the length of B ought to be 4ft since 12/4 = 3.

3) By mere observation and understanding of the definition of various shapes, we can tell that C and E are two different shapes.

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(A) The lack of any particular intervention or treatment is a distinguishing feature of a quasi-experiment.

Experimental and quasi-experimental studies are characterized by testing an intervention's effects.

If a human subject is included in an intervention, the researcher will randomly assign them to either receive the independent variable, such as a modified diet or nutritional supplement or to the control group.

Putting into practice an intervention without using randomization.

"In that, an independent variable is manipulated, quasi-experimental research is comparable to experimental research.

Because there is either no control group, no random selection, no random assignment, or no active manipulation, it varies from experimental research."

Therefore, (A) the lack of any particular intervention or treatment is a distinguishing feature of a quasi-experiment.

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Complete question:

What is the hallmark of a quasi-experiment?

A. the absence of any specific intervention or treatment.

B. high levels of control over treatment conditions.

C. random assignment of participants to conditions.

D. lack of random assignment of participants to conditions.

Answer:

14

Step-by-step explanation:

The probability that the committee contains at least one man is 16/21 or 0.7619 or 76.19%.

To find the probability, we divide the number of committees that contain at least one man by the total number of possible committees.

The total number of possible committees is the number of ways to choose 3 people from the 9 total people (6 women and 3 men). This can be calculated using the combination formula C(9,3) = 9! / (3!(9 - 3)!) = 84.

The number of committees that contain at least one man is the number of committees that contain exactly 1 man plus the number of committees that contain exactly 2 men plus the number of committees that contain exactly 3 men.

Exactly 1 man: C(3,1) x C(6,2) = 45

Exactly 2 men: C(3,2) x C(6,1) = 18

Exactly 3 men: C(3,3) = 1

Adding up the results of these three calculations, we find that the number of committees that contain at least one man is

45 + 18 + 1 = 64

probability of having at least one man = 64/84 = 16/21 = 0.7619 = 76.19%

So, the probability that the committee contains at least one man is 16/21 or 0.7619 or 76.19%.

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A mathematical description of hexagon is given above.

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

The bounded plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides.

Given is hexagon.

In geometry, a hexagon is a six-sided polygon creating the outline of a cube. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.

A regular hexagon is defined as a hexagon that is both equilateral and equiangular. It is bicentric, meaning that it is both cyclic (has a circumscribed circle) and tangential (has an inscribed circle).

Therefore, a mathematical description of hexagon is given above.

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Answer:

170.25

Step-by-step explanation:

The perimeter of the rectangle when the width is 15 inches, would therefore be 90 inches

The width of the rectangle is said to be half of the length which means that because the width is 15 inches, then the length would be:

= 2 x width

= 2 x 15

= 30 inches

As we now have the length as 30 inches and the width as 15 inches, the perimeter of the rectangle would therefore be :

= 30 + 30 + 15 + 15

= 60 + 30

= 90 inches

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The full question is:

The width of a rectangle is half of the length. What is the perimeter of the rectangle when the width is 15 inches?

Answer: Chronological order

Step-by-step explanation:

In composition and speech, chronological order is a method of organization in which actions or events are presented as they occur or occurred in time and can also be called time or linear order. Narratives and process analysis essays commonly rely on chronological order.

The 7th term in the expansion of [tex](a+b)^{9}[/tex] is [tex]36a^{7} b^{2}[/tex]

What is Binomial expansion?

An expression raised to any finite power can be expanded using the binomial theorem. The binomial theorem is a proper expansion technique with applications in probability, probability theory, and algebra. A binomial expression is an algebraic expression with two terms that are not the same.

The rth term in the expansion of [tex](a+b)^{n}[/tex] is [tex]^{n} C_{r}a^{r} b^{n-r}[/tex].

So, the 7th term in the expansion of [tex](a+b)^{9}[/tex] is [tex]^{n} C_{r}a^{r} b^{n-r}[/tex].

We know that [tex]^{n} C_{r}=\frac{n!}{(n-r)!r!}[/tex].

So,

[tex]^{9} C_{7}=\frac{9!}{(9-7)!7!} \\^{9} C_{7}=\frac{9*8}{2}\\ ^{9} C_{7}=36[/tex]

Therefore the 7th term in the expansion of [tex](a+b)^{9}[/tex] is equal to [tex]36a^{7} b^{2}[/tex].

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The value of x and y of the right triangle is x = y = 15.6

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ABC

Now , the measure of the hypotenuse of the triangle AC = 22

And , the triangle is a 45 - 45 - 90 triangle

So , the sides are in the ratio n : n : n/√2

And , if the measure of the two congruent sides of such a triangle is x each, then the three sides will be x, x and √2x

From the trigonometric relations ,

sin 45° = y/22

Multiply by 22 on both sides of the equation , we get

y = ( sin 45° ) 22

y = 22/√2

On simplifying the equation , we get

y = 15.6

And , the value of x = y = 15.6

Hence , the right triangle is solved

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The ratio will be Illustrated this:

1 minute or news = 20 minutes of music

2 minutes if news = 40 minutes for music

3 minutes of news = 60 minutes of music

4 minutes of news = 80 minutes of music

The ratio is 1:20.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

The ratio will be Illustrated this:

1 minute or news = 20 minutes of music

2 minutes if news = 40 minutes for music

3 minutes of news = 60 minutes of music

4 minutes of news = 80 minutes of music

In this case, one has to just multiply by 20.

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A histogram would be a better way to represent this data set, as it provides a clear visual representation of the frequency of different values.

A better way to represent the data set would be to use a histogram. A histogram is a graphical representation of a data set that is used to show how frequently certain values occur in the data set. A histogram can be created by first grouping the data into equal intervals, or bins, and then plotting the frequency of each bin on the y-axis of the graph. This allows for easy comparison of the frequency of different values. For example, in the case of the pharmaceutical company’s employee data, one could create a histogram with 5 bins that represent 6-10 months, 11-15 months, 16-20 months, 21-25 months, and 26-30 months. Then, one can plot the number of employees in each bin on the y-axis of the graph. This would provide a clear visual representation of the data set and make it easier to identify any patterns or trends in the data.

A histogram would be a better way to represent this data set, as it provides a clear visual representation of the frequency of different values.

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Answer:

a) 12b

b) 10h+5

Step-by-step explanation:

a) 12b means $12 x "b" unknown amount of books

b) 10h+5 means $10 x unknown amount of hours babysitting plus $5 gas which is a set cost no matter how many hours babysitting

I don't know if you need to put the $ in your answer or not, based on the directions i would say not.

The smallest integer that can possibly be the sum of an infinite geometric series whose first term is 9 is not possible.

An infinite geometric series is a series that continues indefinitely, where each term is found by multiplying the previous term by a constant ratio.

To determine the convergence limit, we must first determine if the series converges. The series converges if the absolute value of the common ratio is less than 1. If the series converges, the sum can be found using the formula:

S = a / (1 - r)

Where S is the sum, a is the first term of the series (9 in this case), and r is the common ratio. For the sum to be an integer, the denominator (1 - r) must equal 1, which means r must equal 0.

This is not possible, as the absolute value of the common ratio must be less than 1 for the series to converge.

Therefore, the sum of the series cannot be an integer.

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if ​Y=1​+X+u​, where X​, Y​, and ​u=v+X are random​ variables, v is independent of X​; ​E(v​)=0, ​Var(v​)=1​, ​E(X​)=1, and ​Var(X​)=2, then Var(Y|X​) = Var ( 1 + X + u | X)  = 0 + 4*2 + 1 = 8 + 1 = 9

if ​Y=1​+X+u​, where X​, Y​, and ​u=v+X are random​ variables, v is independent of X​; ​E(v​)=0, ​Var(v​)=1​, ​E(X​)=1, and ​Var(X​)=2, the variance of the following cases are calculated as:

Var(u|X​=1) = Var( v + X | X = 1) = Var( v + 1 )    

                = Var(v) + Var(1)                            

                 = 1 + 0 = 1

Var(Y|X​=1) = Var( 1 + X + u | X = 1 )

                = Var (1 + X + v + X|X=1)

                = Var(1 + 1 + v + 1)                      

                = Var(3) + Var(v)                      

                = 0 + 1 = 1

​Var(u|X​) = Var ( v + X | X)

            = Var ( v + X)

            = Var(v) + Var(X)

            =  1 + 2  = 3

Var(Y|X​) = Var ( 1 + X + u | X)

            = Var ( 1 + X + v + X | X)

            = Var ( 1 + 2X + v)

            = Var(1) + Var(2X) + Var(v)

              = 0 + 4*2 + 1 = 8 + 1 = 9

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In a lottery game where a player picks six numbers and repetition is not allowed, the player has a certain number of choices for each number. The number of choices for each number depends on the range of numbers from which the player can pick.

Let's say the range of numbers from which the player can pick is 1 to 49. For the first number, the player has 49 choices, because they can pick any number from 1 to 49. However, once the player has picked their first number, they have 48 choices for their second number, because they cannot pick the same number again. For the third number, the player has 47 choices, for the fourth number, 46 choices, for the fifth number, 45 choices, and for the sixth number, 44 choices.

The total number of different combinations of six numbers that the player can pick is calculated by multiplying the number of choices for each number. This can be written as 49 x 48 x 47 x 46 x 45 x 44. The total number of combinations is 10,068,347,520.

In other words, if a player picks six numbers from a range of 1 to 49, without repetition, the player has 10,068,347,520 different combinations of numbers to pick from.

It's important to understand that repetition is not allowed in this type of lottery game, as it would greatly increase the number of combinations. Allowing repetition would mean that the player could pick the same number multiple times, which would significantly increase the number of combinations and make the game much less challenging.

In conclusion, in a lottery game where a player picks six numbers from a range of 1 to 49, without repetition, the player has 10,068,347,520 different combinations of numbers to choose from. The number of choices decreases with each number picked, as repetition is not allowed, making the game more challenging.

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There will be total of 722 winning hands are in total.

Let's consider the two conditions for winning separately:

3 or more face cards:

There are 12 face cards in a standard deck of 52 cards, so there are [tex]${12 \choose k}$[/tex] ways to choose k face cards out of 5, where k = 3, 4, or 5.

The total number of winning hands in this case is [tex]{12 \choose 3} + {12 \choose 4} + {12 \choose 5} = 220[/tex]

All non-face cards with even numbers:

There are 16 even-numbered non-face cards in a standard deck,

So there are [tex]${16 \choose k}$[/tex] ways to choose k of these cards, where k = 0, 2, 4.

The total number of winning hands in this case will be:

[tex]{16 \choose 0} + {16 \choose 2} + {16 \choose 4} \\= 1 + 45 + 456 \\= 502[/tex]

The total number of winning hands is the sum of the number of hands that satisfy each condition,

So there are a total of 220 + 502 = 722 winning hands.

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The word problem "the difference of twice a number and one" is equal to 2n - 1.

In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used for showing the relationship which exist between two (2) or more variables, numerical quantities, as well as in conjunction with different mathematical operations.

In order to translate this word problem into algebraic expression, we would assign a variable to the unknown number and then translate the word problem into algebraic expression as follows:

Let the variable n represent the unknown number.

Translating the word problem into an algebraic expression, we have the following;

Algebraic expression = (2 × n) - 1

Algebraic expression = 2n - 1

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step 1 :

BODMAS

STANDS FOR:brackets, of, division, multiplication ,addition ,subtraction.

so now you have to open the brackets then add following bodmas formula.

NOTE;THE NUMBER OR SYMBOL BEFORE THE BRACKET IS PART OF THE BRACKET.

+(-11/29) is the same -11/29

33/58-11/29=11/58

the trick really is to use BODMAS

^^

Answer: The answer is 34 degrees.

Step-by-step explanation: Angle 1 and angle 5 are the same.

The system of equations that models the profit for each team is given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope and intercept for the functions in this problem are given as follows:

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