help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!

The number of runs up and runs down for the preceding data is 5.

Runs up refers to the number of observations that are higher than the number of observations before them.

Runs down refers to the number of observations that are lower than the number of observations before them.

As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.

Therefore,

Runs up = 2nd + 4th + 6th observations

             = 3

As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down

Therefore,

Runs down= 3rd +5th observations

                 =2

Therefore,

Runs up + Runs down  =3+2

                                        =5

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The minimum monthly payment for Brian is $25.

The minimum payment is the smallest amount of money you must pay each month to maintain the status of your account. The statement balance is your total account balance for that billing cycle. The current balance is the sum of your most recent bill plus any charges.

From the information, the minimum monthly payment for Brian's credit card is 3.5% of his balance or $25

Since the balance was $722, the amount will be:

= 3.5% × $722

= 0.035 × $722

= $25.27

Since $25.27 is more than $25, the minimum monthly payment is $25.

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South direction was she facing.

What does the word "direction" mean?

Direction can refer to the way something moves, the way you must go to get somewhere, the way something is beginning to take shape, or the direction you are facing.

                                  When you turn right rather than left, that is an illustration of direction.

Which forms of direction are there?

There are only four genuine directions north, south, east, and west. Northeast, Southeast, Southwest, and Northwest are the directions on the compass that are located midway between these cardinal points.            

                                                 These transitional locations are referred to as intermediate directions. Maps and globes only display east-west and north-south lines.

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The ratio of Revani's nickels to dimes to quarters is 40nickels:40dimes:40quarters.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other numbers.

The total coin = 120

2/6 of 120coins that are nickels = (2 × 120)/6

2/6 of 120coins that are nickels = 40 nickels

2/6 of 120coins that are dimes = (2 × 120)/6

2/6 of 120coins that are dimes = 40 dimes

since the rest coins are quarters;

the numbers of quarters = 120 - (40nickels +40dimes)

numbers of quarters = (120 - 80)coins

numbers of quarters = 40coins

Therefore, the ratio of nickels to dimes to quarters is 40:40:40 respectively.

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Answer:

272 bison

Step-by-step explanation:

y(5)=240[tex](1+0.025)^{5}[/tex]

y(5) = 271. 5 bison ≈272 bison

[tex]tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the opposite} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\pm\sqrt{5^2 - 3^2}=b\implies \pm 4=b\implies \stackrel{IV~Quadrant}{-4=b}~\hfill tan(\alpha)=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]tan(\alpha - \beta) \implies \cfrac{\stackrel{tan(\alpha)}{-\frac{4}{3}}- \stackrel{tan(\beta)}{\frac{4}{3}}}{1+ \stackrel{tan(\alpha)}{\left( -\frac{4}{3} \right)}\stackrel{tan(\beta)}{\left( \frac{4}{3}\right)}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{1-\frac{16}{9}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{\frac{-7}{9}} \\\\\\ \cfrac{-8}{3}\cdot \cfrac{9}{-7}\implies \cfrac{24}{7}\implies {\Large \begin{array}{llll} 3\frac{3}{7} \end{array}}[/tex]

MAIN ANSWER: using strong induction that every positive integer can be written as sum of distinct powers of two is 20=2²+2⁴

supporting answer The statement is true for all positive integers by mathematical induction. Strong induction can be used to demonstrate that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the

2²=4

2⁴=16

4+16=20

final answer is 20=2²+2⁴

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Using strong induction that every positive integer can be written as sum of distinct powers of two is 20=2²+2⁴

What is positive integer?

Natural numbers are those in mathematics that are utilised for counting and ordering. Cardinal numbers are those used for counting, and ordinal numbers are those used for ordering.

The statement is true for all positive integers by mathematical induction. Strong induction can be used to demonstrate that every positive integer  can be written as a sum of distinct powers of two, that is, as a sum of a subset of the

2²=4

2⁴=16

4+16=20

Final answer is 20=2²+2⁴

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A possible first step Vivi could take is multiply each term in the second equation by 2 and she can also multiply each term in the second equation by 4. The correct option is d. Both a and c could work.

From the question, we are to determine the statement that correctly describes a possible first step Vivi could take

From the given information,

The given system of equations is

4x + 6y = -14

-x + 3y = -10

To eliminate y, we can multiply each term in the second equation by 2 and then subtract

2 × [-x + 3y = -10

-2x + 6y = -20

Then, subtract

4x + 6y = -14

-{ -2x + 6y = -20

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

6x = 6

To eliminate x, we can multiply each term in the second equation by 4 and add the equations,

4 × [-x + 3y = -10

-4x + 12y = -40

Then, add

4x + 6y = -14

+{ -4x + 12y = -40

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

18y = -54

Hence, we can multiply each term in the second equation by 2 and we can also multiply each term in the second equation by 4.

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Answer:

p=8

Step-by-step explanation:

[tex]2(p+1)=18\\\frac{2(p+1)}{2}=\frac{18}{2}\\p+1=9\\p+1-1=9-1\\p=8[/tex]

Answer:P=8

Step-by-step explanation:

I TOOK THE TEST

The average angular velocity during the dive is 10.78 rad/sec.

Given,

displacement of the diver = 10.4m

as the diver falls freely then the acceleration will be g=9.8 [tex]m/s^2[/tex]

To find average angular velocity during dive use formula,

[tex]\omega=\frac{\theta}{t}[/tex]

where, θ=angular displacement and t= time taken to reach water

the diver makes 2.5 revolutions, here 1 revolution is 2π radians then total angular displacement is

θ=2.5* 2π=15.7 radian

To find time taken, use formula [tex]s=ut+\frac{1}{2}gt^2[/tex]

here u=initial velocity=0

s=displacement of diver=10.4m

[tex]10.4=0+\frac{1}{2}9.8t^2\\\\10.4=4.9t^2\\\\2.122=t^2\\\\t=1.456 s[/tex]

angular velocity, [tex]\omega=\frac{15.7}{1.456}=10.78\ rad/sec[/tex]

Thus, the average angular velocity during the dive is 10.78 rad/sec.

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The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)

From the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.

The given expression is

18 + 24

First, we will determine the greatest common factor of 18 and 24

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

Thus,

The greatest common factor is 2 × 3 = 6

Now, we will write the expression using the greatest common factor and the distributive property

18 + 24

6(3 + 4)

Hence, the expression is 6(3 + 4)

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The perimeter of the quadrilateral is 46 units, so the correct option is d.

The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.

Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:

L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)

The length between the first two vertices: (−6, −2), (0, −10)

L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10

The length between the second two vertices:  (0, −10), (5, 2)

L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13

The length between the third two vertices:  (5, 2), (−1, 10)

L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10

The length between the fourth two vertices:  (−1, 10), (−6, −2)

L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13

Then the perimeter is:

P = 10 + 13 + 10 + 13 = 46

The correct option is D.

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Answer:

Step-by-step explanation:

[tex]\tt 6(x-2)(x-3) + 4(x-2)(x - 5)[/tex]

When, x = -3

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

To find the value of 6(x-2)(x-3) + 4(x-2)(x - 5), we need to substitute x with -3.

[tex]\tt 6\left(-3-2\right)\left(-3-3\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]

[tex]\tt (6)(-5)(-3-3)+4(-3-2)(-3-5)[/tex]

[tex]\tt -30\left(-6\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]

[tex]\tt -30\left(-6\right)+4\left(-5\right)\left(-3-5\right)[/tex]

[tex]\sf -30\left(-6\right)+4\left(-5\right)\left(-8\right)[/tex]

[tex]\tt 180+4\left(-5\right)\left(-8\right)[/tex]

[tex]\tt 180-\left(-160\right)[/tex]

[tex]\tt 180-\left(-160\right)[/tex]

[tex]\tt =340[/tex]

Therefore, the value of 6(x-2)(x-3) + 4(x-2)(x - 5) is 340!

____________________

Hope this helps!

Have a great day!

Set I is the set of ordered pairs which is a function. Choose A.

A function is a relationship between inputs where each input is related to exactly one output.

Based on the definition of function as seen above. Let's check the set of ordered pairs:

Given:

I. { (3, 7), (-1, 9), (-5, 11)}

II. { (9, -5) , (4, -5) , (-1, 7)}

III. { (-2, 1) , (3, -4) , (-2, -6)}

In set I, each input (i.e. 3, -1 and -5 ) has different output (i.e. 7, 9 and 11 ). Thus, set I is a function

In set II, two inputs (9 and 4) have the same output (i.e. -5). Thus, set II is not a function

In set III, the same input (i.e. -2 ) has different outputs (i.e. 1 and -6). Thus, set III is not a function

Therefore, the set of ordered pairs which is a function is I. So option A. is the answer

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The fifth term of the given nonlinear sequence, where each term is split by three, is nine, while the second term will be 243.

A non- linear sequence is a pattern of numbers that always rises (or lowers) by the same amount. The common difference is the amount that it rises or falls by. They consist of Fibonacci-type sequences, geometric progressions, and quadratic sequences. Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope. Every pair of points on the graph do not have the same slope.

Here,

a5=9

rule= divide by 3

a4=9*3

=27

a3=27*3

=81

a2=81*3

=243

The second term of the given non-linear sequence where fifth term is 9 and each term is divided by 3 will be 243.

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The perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

Given that, the breadth of a rectangle =5 units and the length of a rectangle =(x-2) units.

The perimeter of a rectangle is the total distance of its outer boundary. It is twice the sum of its length and width and it is calculated with the help of the formula: Perimeter = 2(length + width).

Here, perimeter =2(x-2+5)

= 2(x+3)

= 2x+6 units

Area of a rectangle =length × width

= (x-2) × 5

= 5x-10 square units

Therefore, the perimeter of a rectangle is 2x+6 units and the area of a rectangle is 5x-10 square units.

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The perimeter of the new enlarged garden whose side length lengthened by factor of 8 is equal to 576ft.

As given in the question,

Shape of the garden is right triangle

Let 'x' , 'y' , and 'z' represents the three sides of the triangle shape garden.

Perimeter of the garden = 72 ft

⇒ x + y + z = 72 ft  __(1)

Now, length of the each sides of the new garden is lengthened by factor of 8.

Sides of the new garden are '8x' , '8y' , and '8z'

Perimeter of the new garden = 8x + 8y + 8z

⇒ Perimeter of the new garden = 8 ( x + y + z )

⇒ Perimeter of the new garden = 8 (72)

⇒ Perimeter of the new garden =  576 ft

Therefore, perimeter of the new garden is equal to 576ft.

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Answer:

p=45-2.5f

Step-by-step explanation:

5f+2p=90

We have to isolate p in one side

5f+2p=90

-5f. -5f

2p=90-5f

/2. /2. /2

p=45-2.5f

Hopes this helps please mark brainliest

According to the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.

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The football field is longer than soccer field.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

We have a soccer field that is 105 meters long and a football field is 120 yards long.

In one yard, we have -

1 yard = 0.9144 meters

Then, in 120 yards, we will have -

120 x 0.9144 = 109.728 meters

Now, 109.728 meters > 105 meters.

Therefore, the football field is longer than soccer field.

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The expression, 2·√(10) × 5·√(12), that has the symbol of the square root radical, can be simplified using the laws of indices, as follows:

2·√(10) × 5·√(12) = 20·√(30)

The laws of indices are the set of rules for the simplification of the multiplication, division, and other combination of mathematical operations that involve expressions that have powers of variables or constants.

The specified radical expression is; 2·√(10) × 5·√(12)

The radical expression indicates the square root of the number under the expression, which is the value within the expression raised to the power (1/2)

The terms under the radical expression, that have the same index of (1/2) can therefore be multiplied together as follows;

2·√(10) × 5·√(12) = 2 × 5 ×√(10) × √(12)

2 × 5 ×√(10) × √(12) = 10 ×√(10) × √(12)

10 ×√(10 × 12) = 10 ×√(120)

10 ×√(120) = 10 ×√(4 × 30)

10 ×√(4 × 30) = 10 × 2 × √(30)

10 × 2 × √(30) = 20 × √(30)

Therefore; 2·√(10) × 5·√(12) = 20 × √(30) = 20·√(30)

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Solution to the inequality on the number line is y < 4 and y > −4.

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

When resolving an inequality, you can do one of the following:

• Add the same amount to each side;

• Subtract the same amount from each side;

• Multiply or divide each side by the same positive amount.

You must flip the inequality symbol if you multiply or divide each side by a negative number.

Let's solve your inequality step-by-step.

|y| < 4

Solve Absolute Value.

|y| < 4

We know y < 4 and y > −4

y < 4  (Condition 1)

y > −4  (Condition 2)

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The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)

In this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:

cos 3x / (sin x · cos x)

Second, use trigonometric formulas:

cos (x + 2x) / (sin x · cos x)

(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)

cos 2x / sin x - sin 2x / cos x

csc x · cos 2x - sec x · sin 2x

The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.

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The probability that exactly one of the next four calls results in a reservation being made is 40.75%

What is probability?

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.

Here, we have

A random call to their reservation phone line results in a reservation being made is 0.31

Now, we find

Exactly one call gets resevervation = 4 * (1-0.31)3(0.31)

= 0.4075 = 40.75%

Now we can simulate an experiment by using random numbers from 0 to 100,000 as probability values between 0 and 31,000 are p to reservation otherwise they don't.

Hence, the probability that exactly one of the next four calls results in a reservation being made is 40.75%

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Answer:

y^2

Step-by-step explanation:

a^m/a^n = a^(m - n)

y^5/y^3 = y^2

The function rule for g(x) is g(x) = (x - 3)² - 3

From the question, we have the following function

f(x) = x²

Also, we have the following transformation statements:

First, we have: f(x) is translated to the right 3 units

This means that

g(x) = f(x - 3)

So, we have

g(x) = (x - 3)²

Next, we have: f(x) is translated down 3 units

This means that

g(x) = f(x - 3) - 3

So, we have

g(x) = (x - 3)² - 3

Hence, the transformation is g(x) = (x - 3)² - 3

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The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).

When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, f(x) = 4x² - 1. and g(x) = 2x - 1.

Now, g(f(2)) is the output of f(2) is the input of g(x).

∴ f(2) = 4(2)² - 1.

f(2) = 15.

Now, g(f(2)) = 2(15) - 1.

g(f(2)) = 29.

Also given,

f(x) = x² and g(x) = x - 1.

Now, 2.f(g(x)).

2.f(g(x)) = 2.f(x- 1).

2.f(g(x)) = 2(x - 1)².

2.f(g(x)) = 2(x² - 2x + 1).

2.f(g(x)) = 2x² - 4x + 2.

2.f(g(x)) = 2x² - 2x - 2x + 2.

2.f(g(x)) = 2x(x - 1) - 2(x - 1).

2.f(g(x)) = (x - 1)(2x - 2).

There is no restriction to the domain of this quadratic function.

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The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.

A geometry translation is an isometric transformation, meaning that the original figure and the image are congruent.

Given that, WXY is the image of RST after a translation 3 units up.

As we know in translation, both figures are congruent so, we have,

WX = RS

XY = ST

WY = RT

And

∠ R = ∠ W

∠ S = ∠ X

∠ T = ∠ Y

Hence, The correct options are: The length of side RS equals the length of side WX and The measure of angle R equals the measure of angle W.

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The number of stores in each level of the shopping mall are 56 stores.

An equation is an expression that can be used to show the relationship between variables and numbers. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let x represent the number of stores on each level.

A shopping mall has 226 stores on 4 levels. If there are same number of stores in each level:

(4 × x) = 226

4x = 226

Divide

x = 226 / 4

x = 56.5

There are about 56 stores per level.

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The function in the context of this problem is modeled as follows:

t(r) = 12/(6 + r)

In which the input and output of the function are given, respectively, by:

Then the numeric value at t = 3 represents the time in hours it takes for the boat to cross the river when the velocity of the river is of 3 kilometers per hour.

The vertical asymptote of a function are the values of the input for which the function is not defined.

A fraction is not defined at the zeros of the denominator, hence:

t + 6 = 0

t = -6 is the vertical asymptote of the function.

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